Encyclopedia of Nanoscience and Nanotechnology 9781588830623, 1588830624

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Encyclopedia of Nanoscience and Nanotechnology Volume 6 Number 1 2004 Nanoanalysis of Biomaterials

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Matthias Mondon; Steffen Berger; Hartmut Stadler; Christiane Ziegler Nanoassembly for Polymer Electronics

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Tianhong Cui; Yuri Lvov; Jingshi Shi; Feng Hua Nanobiosensors

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Tuan Vo-Dinh Nanocables and Nanojunctions

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Yuegang Zhang; Weiqiang Han; Gang Gu Nanocapsules

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Zhi-dong Zhang Nanocatalysis

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S. Abbet; U. Heiz Nanochemistry

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Sebastian Polarz Nanocluster Characterization by EXAFS Spectroscopy

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Giuseppe Faraci Nanoclusters and Nanofilaments in Porous Media

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Parasuraman Selvam Nanocomposites of Polymers and Inorganic Particles

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Walter Caseri Nanocomputers: Theoretical Models

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Michael P. Frank Nanocontainers

301

Samantha M. Benito; Marc Sauer; Wolfgang Meier Nanocrystal Memories

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E. Kapetanakis; P. Normand; K. Beltsios; D. Tsoukalas Nanocrystalline Aluminum Alloys

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Livio Battezzati; Simone Pozzovivo; Paola Rizzi Nanocrystalline and Amorphous Magnetic Microwires

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A. Zhukov; J. González; M. Vázquez; V. Larin; A. Torcunov

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Nanocrystalline Barium Titanate

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Jian Yu; Junhao Chu Nanocrystalline Ceramics by Mechanical Activation

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J. M. Xue; Z. H. Zhou; J. Wang Nanocrystalline Diamond

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Narendra B. Dahotre; Padmakar D. Kichambare Nanocrystalline Phosphors

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Guangshun Yi; Baoquan Sun; Depu Chen Nanocrystalline Silicon Superlattices

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David J. Lockwood; Leonid Tsybeskov Nanocrystalline Silicon: Electron Spin Resonance

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Takashi Ehara Nanocrystalline TiO2 for Photocatalysis

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Hubert Gnaser; Bernd Huber; Christiane Ziegler Nanocrystals Assembled from the Bottom Up

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Edson Roberto Leite Nanocrystals from Solutions and Gels

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Marc Henry Nanocrystals in Organic/Inorganic Materials

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Peter Reiss; Adam Pron Nanodeposition of Soft Materials

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Seunghun Hong; Ling Huang Nanodielectrophoresis: Electronic Nanotweezers

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P. J. Burke Nanoelectromechanical Systems

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Josep Samitier; Abdelhamid Errachid; Gabriel Gomila Nanoelectronics with Single Molecules

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Karl Sohlberg; Nikita Matsunaga Nanoembossing Techniques

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Yong Chen Nanofabrication by Glancing Angle Deposition

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Brian Dick; Michael J. Brett Nanofibers

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Jason Lyons; Frank K. Ko

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Nanofluidics

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P. Mela; N. R. Tas; A. van den Berg; J. E. ten Elshof Nanofluids

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Stephen U. S. Choi; Z. George Zhang; Pawel Keblinski Nanohelical/Spiral Materials

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S. Motojima; X. Chen Nanoicosahedral Quasicrystal

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J. Saida; A. Inoue Nanomagnetics for Biomedical Applications

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Chong H. Ahn; Jin-Woo Choi; Hyoung J. Cho Nanomagnets for Biomedical Applications

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Pedro Tartaj Nanomaterials by Severe Plastic Deformation

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Yuntian T. Zhu; Darryl P. Butt Nanomaterials for Cell Engineering

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Xiaoyue Zhu; Tommaso F. Bersano-Begey; Shuichi Takayama Nanomaterials from Discotic Liquid Crystals

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Gregory P. Crawford; Robert H. Hurt Copyright © 2004 American Scientific Publishers

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Encyclopedia of Nanoscience and Nanotechnology

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Nanoanalysis of Biomaterials Matthias Mondon, Steffen Berger, Hartmut Stadler, Christiane Ziegler University of Kaiserslautern, Kaiserslautern, Germany

CONTENTS 1. Introduction 2. Biomaterials 3. Nanoanalytical Tools 4. Nanoanalysis of Biomaterials 5. Conclusions Glossary References

1. INTRODUCTION Nanotechnology has been a fast-developing field over the last decade. Features of dimensions below 100 nm are an interesting and important field of studies in a world of miniaturization in engineering but as well in the already small world of biology. New methods of analysis have to be developed along the way, as conventional light microscopy techniques are unable to resolve features of these dimensions. In this chapter recent progress in nanoanalytics in biomaterial respectively biointerface research is reviewed, focusing on publications that are relevant for the characterization of the surfaces of biomaterials rather than the characterization of biofilms on biomaterials. Scanning probe microscopy (SPM) methods, that is, scanning force microscopy (SFM), scanning tunneling microscopy (STM), and related techniques are unique to investigate on a molecular and even on an atomic level surfaces and molecules interacting with them. Morphology and roughness are important parameters that can be characterized with them. Further fields are the spatial arrangement of chemical functional groups and their interaction with the surrounding medium. The techniques based on the electron-sample interaction like scanning electron microscopy (SEM) and transmission electron microscopy (TEM) are also able to achieve material- or morphology-dependent information with nanometer resolution and are therefore important tools in biological and materials science. ISBN: 1-58883-062-4/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

The issue of nanotechnology has become also part of the world of biomaterials for production as well as for analysis to investigate phenomena occurring on this scale. Biomaterials include a wide range of metals and alloys, glasses and ceramics, natural and synthetic polymers, biomimetics, composites, and natural materials, including combinations of synthetic and living tissue components. Materials in contact with biological systems are of great relevance not only in medicine but for many applications in engineering, food processing [1], marine environments [2], and biosensing [3]. The use of biomaterials is therefore part of the larger area of biological surface science (BioSS) that stretches as well into areas like tissue engineering, biosensors and biochips for diagnostics, artificial photosynthesis, bioelectronics, and biomimetic materials [4]. The market volume for medical biomaterials exceeds a billion Euro per year. In the United States alone the current value is over 700 million Euro [5]. More than 500,000 arthroplastic procedures and total joint replacements are performed annually in the United States [6]. Clinical implants like artificial tooth replica, knee and hip joints, blood vessels, heart valves, and intraocular lenses are in use for many years now and applied with hundreds of thousands of patients improving their quality of life. A lot of materials consist of metals and ceramics but the use of polymers for new medical products and materials has increased strongly over the last decades to keep improving current health care procedures. These biomaterials must meet the demands of materials science on various length scales as well as clinical requirement. The mechanical specifications range from high loads in implantology for hip and knee replacements to high elasticity of artificial blood vessels. They have to be accompanied by others, for example, high transmittance in intraocular or contact lenses. In many cases blood compatibility with suppression of blood coagulation between the physiological environment and the biomaterial surface is necessary. A good understanding of the interaction with the biological environment, namely with biomolecules like proteins, cells and tissue, is crucial in order to be able to improve the functionality of biointerfaces. This interaction is essential for many applications like lubrication, adhesion, and recognition Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 6: Pages (1–22)

Nanoanalysis of Biomaterials

2 in biological systems and for biocompatibility of the implant interface [7]. The interface is important for biomaterials, as it defines the interaction with the environment. The knowledge of the surface structure, the surrounding medium in direct contact (e.g., water structure [8]), and the chemical composition is essential to understand further reactions taking place at the biomaterial’s surface. The interface structures are in dimensions of a few nanometers for proteins up to the micrometer range for cells in the field of biomaterials. In Figure 1 an overview of the interfaces on different scales is presented to show the parameters that can be of interest. Macroscopically, the shape of an implant, the structure, and its mechanical stability are important. The microscopic level is determined by the morphology (i.e., the domain structure, the presence of ionic groups, and the chemical composition respectively modification), the topography (i.e., the surface roughness, planarity, and feature dimensions), and the hardness respectively elasticity (Young’s modulus). These characteristics determine other features like wetting behavior and interaction forces (inter- and intramolecular) including cell-surface or cell-cell interactions. Various degrees of information about these properties can be

obtained using different analysis methods including microscopic and spectroscopic methods. The field of investigation is extending further as the material properties have to be characterized after manufacturing, sterilization, before and after clinical insertion, and before, after, and especially during the immersion in simulated natural environments. The resulting changes of the interaction, namely corrosion and the buildup of a biofilm, have to be characterized. The surface properties as well should be characterized thoroughly as it is essential for correlating any surface modifications with changes in biological performance. In the following, techniques that are able to resolve features of materials on the nanometer scale (Section 3) as well as applications for biomaterial research (Section 4) are presented. The whole topic is introduced by a more general discussion of functionality, properties, and types of biomaterials (see Section 2). The focus in experimental work will be put on methods investigating materials on the nanometer scale, that apply to nanometer resolution in x-, y-, and z-direction. Methods leading to a resolution in the nanometer regime in only one or two dimensions will be described only shortly. Investigations of the above introduced groups of biomaterials including metals, ceramics, polymers as well as biological specimens are presented. In the context of this review biomaterials are defined as materials used in medicine which are in contact with the tissue of the patient. Therefore special emphasis will be put on medical implant materials and the characterization with scanning probe techniques. Experiments dealing with hard tissues like teeth and bone and the influences of substrates on biofilm formation will be briefly mentioned.

2. BIOMATERIALS Biomaterials can be classified with respect to their chemical composition and their use. Generally, the following criteria have to be fulfilled by biomaterials: • Functionality: The biomaterial must replace at least in the important parts natural body functions. This means that, for example, for bone substitution a suitable mechanical stability has to be achieved. • Biocompatibility: The biomaterial must not cause negative body reactions resulting, for example, in inflammation. Furthermore, a good integration into the body environment is favorable. • Aesthetical aspects: Biomaterials used for external implants should not deface the patient. Preferably, they should look like the replaced tissue.

Figure 1. Different relevant length scales in biomaterials research demonstrated at hand of a bone implant. The biomaterial-tissue interaction is based on molecular events, which affect meso- and macroscopic material properties. On larger scales additional (e.g., cellular, mechanical) effects resulting from combining individual units (molecules, cells, crystallites) to a more extended ensemble arise.

Surface properties influence strongly the mechanical function, the biochemical interaction, and the optical appearance of the biomaterial. Therefore the interface of the materials deserves special interest in investigation, control, and modification of properties to reach the criteria mentioned above. Mechanical aspects are relevant for applications which require force transfer (e.g., bone substitution), which impose dynamic loads on, for example, artificial joints, and which, for example, in the case of substitutes for blood vessels, meet certain hydrodynamic respectively fluid-mechanical properties. The interaction of the biomaterial with the body

Nanoanalysis of Biomaterials

environment concerns the tissue contact (cell adhesion and fixation), the tissue organization (cell-to-cell linkage and communication), and the exchange of substances across the interface. Optical appearance is determined by light transmission (e.g., of contact lenses) or light reflection (e.g., of natural looking tooth replacements). Mechanical, biochemical, and optical properties depend mainly on the topography and the chemistry of the surface. Topography may be defined as size, shape, distribution, and hierarchy of surface features. These features are either discrete (holes and peaks) or continuous (furrows and ridges) in random (statistical), fractal (self-similar on different length scales), or periodic distribution across the surface. Rough surfaces exhibit a larger surface area and more contact points for biological molecules and cells. The reason for larger entities like cells to adhere to the surface and how they arrange their layer growth is dependent on the size and distribution of the surface features: Cavities which are smaller than single cells cannot be colonized, while larger structures regulate the direction, connectivity, and differentiation of the growing cell layer. A hierarchical surface consists of structure elements with increasing complexity, for example, two-dimensional planes scrolled up to threedimensional fibers which are organized in three-dimensional fiber composites. Examples of those materials were synthesized with carbon nanotubes with increased mechanical stability and electrical conductivity and decreased thickness compared to common wires [9–11]. In principle such materials are also interesting for biomaterials as on one hand they show a very large surface area and on the other hand they enable combinations of surface sections with different properties and therefore different cell types within a single superstructure. The chemical properties of the interface between biomaterial and body environment determine the interaction of the surface with water molecules, ions, biological macromolecules, and cells. The surface reactivity depends on the chemical composition, the production process, and the pretreatment before use of the materials and is essential for fixation, growth, and proliferation of tissue and bone cells. Cell adherence via membrane receptors and adhesion proteins is influenced by active surface groups (generated, e.g., by oxidation of metals or coating of materials with specially designed polymer layers) which regulate the adsorption of the anchoring protein layer. The functionalization of the substrate additionally controls the wetting behavior where particularly hydrophilic surfaces show enhanced cell adhesion. The latter is due to the fact that systems like cells and hydrophilic surfaces reach a thermodynamically favorable state by combining their high-energy surfaces. In addition, even hydrophobic interfaces like gold can get more hydrophilic by protein adsorption [12] which may help to increase biocompatibility. Polarizability and charging of the interface affect electrostatic interactions between charged species and the surface. Charge screening and complexation by multivalent ions present in all types of body fluids allow attraction between molecular and surface groups of like charges and stabilize the biological layers. At conductive interfaces electrochemical reactions with charge transfer between the electrolyte solution and the substrate may occur, which interfere with the cellular metabolism and the

3 conformation of adsorbed adhesion proteins. This can set free toxic substances and cause allergic and inflammatory body reactions. Topographical as well as chemical effects play a role for tribological properties of biomaterials. Tribology describes the behavior of interfaces in motion and gets important when implants are designed to support body movements. In this case friction, wear, and lubrication of implant and body respectively different moving implant elements influence function and longevity of the applied biomaterial. Interfacial friction depends on kind and strength of interaction forces, the clasping of surface uprisings and troughs, and force transfer properties of intermediate fluids. Hardness, cohesion, and adhesion of the individual surfaces in contact determine to what extent the materials are worn off by abrasion (e.g., scratch and particle formation), adhesion (e.g., welding processes), and surface fatigue (e.g., crack formation). Liquid films in the crevice between two hard surfaces can reduce friction and wear. The effect of such lubricants is influenced by surface chemistry and separation as well as by the viscoelastic and hence force transferring properties of the fluids themselves. This comprehensive discussion of biomaterials in view of surface properties shows that the interplay between implant and body environment can be very complex and includes a large variety of parameters from materials science, biology, and medicine explained in more detail in [7]. The need of surface analysis with nanometer resolution arises on one hand from the importance of the interface between natural and artificial material and on the other hand from the high dependence of the macroscopic behavior on the microscopic appearance of the biomaterial. In the following the main different chemical substance classes for biomaterials will be described shortly. Biomaterials can be divided into native materials like teeth and bone, and artificial biomaterials which are in contact with biological systems like implants in medicine. Within these fields the materials in their actual state of occurrence and model surfaces like thin layers on supports are under investigation. The three metal systems mainly utilized in implantology are stainless steel, cobalt-chromium alloys, and titanium. Such metals are mainly used in bone replacement and here titanium is the most important metal because of its good biocompatibility and nearly bonelike mechanical properties. That is why titanium and its alloys TiAl6V4 and TiAl6Nb7 are frequently applied as biomaterials for hard tissue replacement such as dental and orthopedic (e.g., hip and knee joint prosthesis) implants, in the audiological field, and for cardiovascular applications such as mechanical heart valves and as material for surgical instruments such as vascular clamps, needle holders, and forceps [13]. Titanium surfaces are covered by a 2- to 6-nm-thick oxide layer that is formed spontaneously in the presence of oxygen. This layer contributes to the biocompatibility of titanium by preventing corrosion and the release of ions from the metal surface [7]. The oxide layer thickness and surface morphology can be altered by according treatment or coatings applied to change the physicochemical properties and the biological response [13].

4 Stainless steel is also used for orthopedic implants. Its lower biocompatibility and its mechanical properties, which are less bonelike than titanium, reduce the use as human implant material, but it is cheaper than other metals and therefore is still used in animal medicine and for surgical instruments. Other applications of steel are cardiovascular stents. Cobalt-chromium-molybdenum alloys are very hard and in combination with other smooth surfaces very abrasionproof. They are therefore an ideal material for joint implants. In many patients Co-Cr-Mo, that is sintered from Co-Cr-Mo beads, is used as a femoral hip implant. Gold as one of the oldest implant materials is used not only as dental restorative material but also as electrode material for implantable biosensors or to increase the contrast in electron microscopy. An overview on studies concerning metals as biomaterials is given in Section 4.1. Bone, tooth enamel, and dentin have a composition which is very similar to that of special ceramic materials like hydroxyapatite, calcium phosphate, and calcium carbonate. These materials in their natural or manmade origin are used as coatings to increase the biocompatibility of implant materials. On the other hand they can replace parts of bones; for example, porous hydroxyapatite is a good basis for new bone growth. Biologically active glass or bioglass is similar to ceramics and assists actively new bone formation. It is therefore used in every place where bone has to be built up. This is necessary after tumor surgery or if natural bone is destroyed by an inflammation. Ceramic and glassy materials are further considered in Section 4.2. Another kind of biomaterials are the polymers. They can be tailor-made for many different applications as their properties and their composition are variable in a large range. Polymers can be used as manufactured or treated with different techniques to yield special functional groups at the surface for specific interaction, increased surface energy, hydrophilicity respectively hydrophobicity, or chemical inertness. Furthermore, such surface layers may induce crosslinking to increase hardness, remove weak boundary layers or contaminants, modify the surface morphology (increase or decrease of surface crystallinity and roughness), or increase surface electrical conductivity or lubricity. A review of these modifications, examples, and characterization is given in [14]. Polymers like high molecular weight polyethylene (HMWPE) are used as counterpart for the titanium ball head in artificial hip joints. Poly(tetrafluoro ethylene) (PTFE) and other fluorinated polymers are used for blood vessel replacements and catheters, poly(methyl methacrylate) (PMMA) for intraocular lenses, silicone acrylate for contact lenses, polyurethane for pacemakers and left ventricular assist devices, cellulose for renal dialyzers, and silicone for catheters and breast implants [15]. Biodegradable polymers like poly(sebacic anhydride) (PSA) and poly(DLlactic acid) (PLA) are naturally removed from the body after a definitive time span and can be used for controlled drug delivery [16]. Generally, carbon in different forms (e.g., diamond, graphite, or activated carbon) is an important biomaterial particularly because of its high blood compatibility. Glassy polymeric carbon (GPC) made from phenolic resins by pyrolization, is mostly used as coating, for example, in prosthetic heart valves and other prosthetic devices [17, 18]. Some selected studies on polymers are discussed in Section 4.3.

Nanoanalysis of Biomaterials

A newer group of materials used in implantology are composites, especially composites of inorganic material and polymers which combine the advantages of both. Examples can be found in Section 4.4.

3. NANOANALYTICAL TOOLS A wide range of applications use the methods described in this section as nanoanalytical tools. This field is extending rapidly and new applications and methods are developed constantly. A short description will be given of the methods and the parameters investigated with them. The possible areas of application and examples are given in Section 4. Particularly, scanning force microscopy (SFM) is stressed which has proven to be a valuable and easy to handle method for studies on biomaterials. Additional advantages can be found in the nondestroying operation which is applicable under ambient conditions. Experimental setups revealing nanometer resolution in only one dimension are discussed at the end of this section.

3.1. Scanning Probe Techniques Scanning probe techniques have been a valuable tool since their invention in the 1980s [19, 20]. In these experimental methods distance-dependent interactions like tunneling current, force, or light transmission between a sharp needle (“tip” or “probe”) in close proximity to a surface (“sample”) are utilized to produce an image of the sample. Two principal measurement modes were implemented: (i) to maintain a constant vertical probe position while measuring the interaction change often due to surface topography (“constant distance mode”), and (ii) to maintain constant interaction while adjusting the distance with the feedback signal reflecting surface topography (“constant interaction mode”). Both modes offer the possibility to characterize surfaces down to the atomic scale in a great variety of environments from ultrahigh vacuum to aqueous solutions. It is as well possible to characterize time-dependent reactions like crystallization or corrosion processes, as it can be done continuously and hence on-line. To scan a probe over a surface in the desired way while reacting to the topography of the sample, positioning tools with spatial resolution in the 0.1-nm regime are necessary. The latter is fulfilled by piezoelectric actuators made of ceramics like PZT (lead zirconate titanate) or PMN (lead magnesium niobate), which in different directions can be extended by less than the size of one crystal unit cell. With a suitable detection unit to measure small interaction changes connected to a distance feedback circuit and digital data representation, an image of the surface can be portrayed. Experimental adaptations and extensions based on the interaction mechanisms originally used for imaging purposes lead the way to monitor more complex features than the topography as described below. In scanning tunneling microscopy (STM) the current of electrons tunneling between a conductive wire (preferentially heavy metals like tungsten, platinum, or iridium) with an atomically sharp tip and a (semi-) conductive surface across vacuum is measured (Fig. 2). The tunneling current decays exponentially with increasing distance between tip

Nanoanalysis of Biomaterials

5

controller piezo-crystal current amplifier tunneling-current

Figure 2. Schematic drawing of the STM principle.

and surface and additionally depends on the local densities of electronic states of the tunneling partners and the work function of the sample. Because of its strong distance behavior only the atom at the very end of the tip and the nearest surface atom are involved within the tunneling event. A slight change in distance according to progression along rows of surface atoms alters the tunneling current in a measurable manner so that true atomic resolution can be achieved. Experimentally the onset of a tunneling current is obtained by approaching tip and surface to less than a few tenths of a nanometer under a constant bias voltage. The sign of the bias determines the direction of the tunneling current; this means unoccupied electronic surface states are probed with occupied electronic tip states or vice versa. Scanning the surface row by row either at constant height or constant current (see above) reveals the surface topography. Additionally, STM can be applied to probe electronic structures. Modulating the tip-surface distance and measuring the change of the tunneling current at constant bias allows to extract the local work function of the sample. Modulating the bias and measuring the corresponding current changes at a constant tip-surface distance allows to extract the electronic states around the Fermi level of the sample (STS, scanning tunneling spectroscopy). This can lead to some chemical information about the surface, but for more detailed information electronic core levels have to be sensed, which is not possible with the STM (see [21] and especially references therein). Scanning electrochemical microscopy (SECM) measures highly localized electrochemical currents associated with charge transfer reactions on metallic sample surfaces under liquid environment [22, 23]. In macroscopic measurements it can be compared with cyclovoltammetry. The reactions occur in a four-electrode electrochemical cell under bipotentiostatic control. There are two mechanisms respectively pathways of image production. Electron tunneling and electrochemical reactions via a water bridge occur according to the applied voltage. It can be used for the detection of localized electrochemical reactions at surfaces. It can also be used for microstructuring biomaterials like titanium [24]. In addition SECM is also capable of probing the kinetics of solution reactions and adsorption phenomena and monitoring heterogeneous electron transfer kinetics associated with processes on conducting surfaces [25].

The invention of the scanning force microscopy (SFM) was a breakthrough for these techniques as it is possible to image nonconducting substrates with a resolution of 0.2 nm laterally and 0.001 nm vertically. It does not require specimens to be metal coated or stained. Noninvasive imaging can be performed on surfaces in their native states and under near physiological conditions. It has been proven to be particularly successful for imaging biological samples, such as proteins, nucleic acids, and whole cells. By scanning, dynamic processes can be imaged, such as erosion, hydration, physicochemical changes, and adsorption at interfaces. Therefore the SFM is currently the SPM technique with the widest applicability for biomaterial research. In SFM a small tip attached to a micro beam (cantilever) is scanned across the surface of the specimen and deflected by topographic features. The force of interaction may be repulsive or attractive, giving rise to different modes of operation. Moving the cantilever from the interaction free zone far above the surface, it snaps into contact (Fig. 3) due to the attractive force between the tip and the sample, which can be described in a simple way by the Lennard Jones potential. The piezo pushes the tip further towards the sample and the positive repulsive force reaches a maximum. As the piezo is retracted the repulsive force is reduced and the force changes sign. If the bending force of the cantilever gets larger than the attractive force towards the surface, the tip loses contact. The tip can be held in the repulsive regime of the Lennard Jones potential or oscillated in the attractive or repulsive regime, resulting in different interactions [26, 27]. These differences are important as biomolecules are deformed by applying a load of some nanonewtons as present in contact mode [28]. The deflection is usually monitored by a laser beam that is reflected and detected with a four split photodiode. This signal is used to maintain a constant force via a feedback loop and to monitor the height data. The SFM can be operated in a variety of modes that can provide different information about the sample. Usually the z-deflection is monitored and interpreted according to the parameters under investigation. An easy to read overview covering many scanning probe

return from surface towards surface

Cantilever deflection [nm]

monitor

linear deflection on stiff surfaces 0

interaction free region -90

point of contact to sample "jump in" adhesion 0

200

400

Piezo-z-position [nm] Figure 3. Cantilever deflection versus sample-z-position curve on a stiff surface monitored via SFM.

Nanoanalysis of Biomaterials

6 techniques is given in [29] while in [30] results obtained by SFM in the field of nanotribology are reviewed. Sensing of the z-position is usually done via the monitoring of the z-piezo voltage. This can cause ambiguities as piezo crystals exhibit hysteresis. This is overcome by monitoring the distance separately via inductive or fiber-optical sensors [31]. For dynamic modes [32] the application of an additional oscillation to the cantilever by a piezo crystal has to be performed. Magnetically driven cantilevers are used as well for actuation [33]. The quality of SFM data is essentially determined by the cantilever and the tip, influencing the resolution of topography and force measurements. Micromechanical properties of the cantilever and the shape and chemical composition of the tip, which comes into direct contact with the sample, are essential. High aspect ratios and small tip radii are desirable for imaging steep slopes and deep crevices. Depending on the mode of operation, different parameters have to be optimized, which can be realized according to the methods described in the following. Silicon and silicon nitride cantilever fabrication based on photolithographic techniques is well established. Metalbased (Ni) cantilevers [34] and cantilevers made of piezoelectric material (lead zirconate titanate) are produced as well for independent actuation and sensing [35]. Cantilevers of various shapes (e.g., rectangular or V-shaped) and dimensions (usually 100 to 200
m in length) are available. New approaches to a further miniaturization of the system have been made on microfabricated aluminum probes with length scales of 9
m [36–39]. Coatings (Cr-Au, Pt, Al, TiN, W2 C, TiO2 , Co, Ni, Fe, Au with biological coating) can be applied to the cantilever to modify it against corrosion in the liquid phase or for different applications when conductive, magnetic, or biological properties are necessary. The resonance frequency of the cantilever ranges between several kHz to several hundred kHz. Cantilevers with high resonance frequencies are used in dynamic modes as the tip oscillates with several hundred kHz above the surface. The stiffness of the cantilever is defined by the force constant k and ranges between 0.01 and 100 N/m for the vertical deflection. The soft (k < 01 N/m) cantilevers are used in contact modes to minimize the disturbance of the sample. Rigid cantilevers with a force constant larger than 1 N/m are used in noncontact or dynamic modes since they exhibit high resonant frequencies and small oscillation amplitudes of about several nanometers. The force constant for the lateral twisting can be determined for friction measurements [40] and the movement of the cantilever has been modeled accordingly with finite element analysis [41]. The mechanical behavior and the determination of the spring constant are well described in literature [42–49]. The tip itself can consist of different materials or is coated according to the application. For some applications a hard surface is necessary and a diamond-like coating (DLC) is applied [34]. The production of DLC coatings is described in [50]. Different functionalities [51–53] can be applied. Cantilever tips can be modified by chemical [54] and biochemical [55] functionalization. Via silanization [56, 57] or via thiols, self-assembled monolayers (SAMs) are produced for

further modification [53]. Proteins and bacteria [58] can be attached to the tip. Additional materials which vary the shape of the tip can be deposited, such as polystyrene, borosilicate and silica spheres, C60 molecules [59], carbon-nanotubes in general [60–63], or single-wall nanotubes with diameters of 3 Pas had the best properties, especially when they were heat treated at 175
C. Controlled release glass (CRG) based on calcium and sodium phosphates differs substantially from commercial glass in that it dissolves completely in aqueous environment. The solution rate can be predetermined and adjusted by altering the chemical composition. A SEM study of the hemocompatibility [189] of such glass indicated that selected and controlled compositions of these materials might provide good blood-contacting surfaces.

4.3. Polymers Many different ways to use polymers as biomaterial are reported. This field spreads from vascular implants [193– 196] and bone replacement [197–200] to intraocular lenses [201].

4.3.1. Structure and Mechanical Properties High- and low-density polyethylene (HDPE and LDPE), isotactic and atactic polypropylene (iPP and aPP), and polymer blends were investigated regarding the friction coefficient and the elastic modulus via SFM. Structural changes and the mechanical property changes around the glass transition temperature have been monitored during temperature runs. The enhanced ordering of the backbone correlates to the increased surface modulus. Additionally, the elastic modulus, the time-dependent relaxation process, and the friction properties were measured as a function of pressure. Loads between 1 and 1000 nN were applied. At low pressure the deformation of the polymer is elastic. With increasing pressure there is a phase transition to a plastic behavior attributed to a polymer alignment effect. Friction properties were investigated concerning the contact pressure and contact area, revealing an increased elastic modulus with increased density and crystallinity and a linear increase with contact pressure. Stretching of LDPE was shown to lead to surface roughening and alteration of surface mechanical properties. These experiments show that a material subject

Nanoanalysis of Biomaterials

16 to complex mechanical stresses will change continuously its surface mechanical properties as the nature of the stress changes [102]. Polyethylene and the influence of low molecular weight additives that are added to prevent oxidation were investigated via friction versus load curves. For loads of 1000 nm, the lower friction of the polymer with additives gives way to friction properties of the different samples that are identical [102]. Polyurethane copolymers with hydrophobic and hydrophilic side chains were investigated regarding the mechanical properties changing with the hydrogen bonding between soft (SS) and hard segments (HS). The adhesion force showed a maximum at 57% HS correlated with the highest number of nonassociated urethane groups. The friction mechanisms were investigated as well, showing different mechanisms for the different compositions [102]. The surface structure of six different polycarbonate polyurethane copolymers was investigated with SFM in topography and phase modes. The stoichiometry of the reagents and the chemistry of the hard segment were changed, varying the contribution of diisocyanate, poly(hexyl, ethyl) carbonate, and butane diol. The 1,6-hexane diisocyanate showed a stronger phase separation and the highest values of mean square roughness (RMS) with 3.3 to 10.0 nm with regard to methylene bis(p-phenyl isocyanate) and methylene bis(p-cyclohexyl isocyanate) that have RMS values of 0.8 respectively 0.25 nm. These values have to be viewed with respect to the image processing of a third-order flatten. This is only obvious in this article as the image processing is usually not mentioned, and therefore the values of the other investigations must be examined closely as well. The polymers presented relatively stiff rodlike structures with dimensions of 12 nm in width and 170 nm in length [202]. Investigations on polyurethane and rubber were done with force indentation curves [28]. Differences between polystyrene (PS) and poly(methylmethacrylate) (PMMA) could be determined by measuring the adhesion differences of the different polymers by PFM [95]. Polymer blends of poly(styrene)-blockpoly(ethene-co-but-1-ene)-block-poly(styrene) with isotactic and atactic polypropylenes were characterized observing the morphology according to different thermal treatments. It was possible to monitor microphase separations with tapping mode in the phase image [203]. Interfaces between PMMA and polystyrene (PS) could be identified with HM-LFM [84] as well as interfaces between poly(acrylonitrile-co-styrene) and polybutadiene respectively between polypropylene and poly(propylene-co-ethylene) [85]. Fractographic investigations looking at the surfaces after a fracture of dental composites consisting of silicon dioxide fillers in a matrix of dimethacrylate resins are presented in [107]. The pristine surfaces and the results of different preparation methods for poly(ethylene glycol) (PEGMA) grafted poly(tetrafluoro ethylene) (PTFE) surfaces were investigated with SFM. The PEGMA treated surfaces exhibited a larger RMS of 144 nm with regard to 129 nm RMS of the pristine PTFE [204]. Hexafluoroethane and tetrafluoroethylene films produced by glow discharge plasma deposition show with SFM a pinhole free and smooth surface

with a RMS roughness of 0.4 to 2 nm. Scanning in contact mode with moderate applied loads yields rippled films. At small scan sizes, and high velocities and load, the film disrupts. The surface modulus was estimated between 1.2 and 5.5 GPa [205]. Poly(vinylidene difluoride) (PVDF) and poly(vinylidene fluoride/hexafluoropropylene) [P(VDFHFP)] polymers were radiation grafted with polystyrene (PS) yielding an increase in surface roughness upon irradiation and a smoothing of the valleys by further functionalization by chlorosulfonation and sulfonamidation [206].

4.3.2. Response to Proteins In the field of ultrafiltration of biological fluids such as blood, biofouling respectively membrane fouling is an important issue resulting in pore plugging, pore narrowing, and cake deposition. Hydrophobic polysulfone membrane interactions with hen egg lysozyme were investigated with the surface force apparatus and the topography with SFM [207]. Forces between cellulose acetate films and human serum albumin, HSA, respectively ribonuclease A, RNase, were investigated in the same way [208]. The comparison of forces between the proteins fibronectin, fibrinogen, and albumin and a hydrophilic cellulosic membrane, a hydrophilic glass surface, and a hydrophobic polystyrene surface showed that the forces on hydrophobic surfaces are an order of magnitude larger than the ones on hydrophilic surfaces. Additionally, the influence of surface structure on hydrophilic surfaces was described [209]. Collagen on native and oxidized poly (ethylene terephthalate) (PET) was investigated with the aid of X-ray photoelectron spectroscopy (XPS). Time-dependent differences were observed in stability at times between 5 s and 5 min with an easy-to-disturb surface structure (scan ranges from 2 to 5
m) as monitored via SFM. The investigations were done in air, leaving the results ambiguous, as the topographical information can be altered by drying leading to different structures and orientations on the surface [210].

4.3.3. Tissue Response The tissue response to polymers is investigated in a variety of studies [200, 211–214]. There are different attributes, which complicate the use of polymer vascular implants. Especially for small-diameter vascular grafts the blocking is an important problem. For example, calcification decreases the vascular diameter. So calcification of subdermally implanted polyurethane is enhanced by calciphylaxis as shown by SEM [194]. Another aim is to decrease the thrombogenicity [195] of polymeric biomaterials. These “heparin-like” polymers have a specific affinity for antithrombin III and thus are able to catalyze the inhibition of thrombin. In this study sulfur, sodium, fluorine, and carbon are determined by SEM combined with energy dispersive X-ray analysis. The objective of another project [196] was to define a series of assays for the evaluation of hemocompatibility of cardiovascular devices. In [193] a polyamino-acid urethane copolymer coated vascular prosthesis (1.5 mm diameter) was developed to enhance endothelialization. SEM showed the homogeneous coating of clinically available synthetic PTFE grafts. Prosthetic heart valves made of isotropic pyrolytic carbon (LTIC) are

Nanoanalysis of Biomaterials

a successful biomaterial application which is investigated together with other difficult-to-image biomaterials in [17]. Low-voltage, high-resolution scanning electron microscopy shows that LTIC valve leaflets are significantly rougher than previously described, and that LTIC induces extensive platelet spreading in vitro, even in the presence of considerable albumin. Calcification is also crucial in the use of intraocular lenses [201]. To assess this, intraocular lens optic materials were implanted intramuscularly and/or subcutaneously in rabbits for up to 90 days. SEM and energy dispersive X-ray spectroscopy (EDX) were used to detect discrete nodules containing both calcium and phosphate. Calcification only was noted on intramuscularly, subcutaneously, and intraocularly implanted experimental acrylic and intramuscularly implanted hydrogel material. In contrast, the intramuscularly or subcutaneously implanted silicon, PMMA, and acrylic optic materials showed no calcification. Glassy polymeric carbon was treated by bombardment with energetic ions in different curing states. The roughness that leads to a better thromboresistance was monitored with SFM [18]. An approach to manage chronic osteomyelitis (inflammation of the periosteum) utilizes the implementation of antibiotic-impregnated PMMA beads for local delivery of antibiotics. The study of the getamicin sulphate release from a commercial acrylic bone cement was presented in [197]. A very interesting feature is the biodegradability of some polymers either natural or synthetic. The surface structure of blends with different composition of poly lactic acid (PLA) and poly sebaic acid (PSA) and their degradation properties were investigated. Single component PLA exhibits a smooth surface whereas PSA films possess spherulites at the surface. Blends of 70%, 50%, and 30% PLA exhibited granular respectively pitted surface structures but no fibrous structures visible in SFM. The monitoring of the erosion within 10 minutes showed that PLA is present in granules [16]. Phase imaging with the SFM yields phase shifts at different compositions ranging between 45
and 52
. The presence of PSA microdomains in blend of 50% PSA could be confirmed [215]. Screws, made of poly-L-lactic acid, were inserted axially into the right distal femur in 18 rabbits. The degradation and phagocytosis were assessed histologically and by TEM [198]. In the TEM specimens, polymeric particles of an average area of 2
m2 were seen to be located intercellularly with phagocytic cells. In 4.5-year specimens, the size of the polymeric particles, measured as area and perimeter, was significantly smaller than that of the 3-year specimens. The findings indicate that the ultimate degradation process of PLA is much longer than it was previously thought. Porous structured polymers to mimic natural extracellular matrix were investigated in [216] and in [217]. A biodegradable blend of starch with ethylene-vinyl alcohol copolymer (SEVA-C) with hydroxyapatite as filler was investigated, monitoring the degradation and the buildup of calcium phosphate crystals over a time span of up to 30 days in simulated body fluid. Only with the filler the buildup of the calcium phosphate layer could be observed. Within 8 hours

17 the roughness increased, after 24 hours calcium phosphate nuclei covered the surface, and after 126 hours a dense and uniform layer was present [218].

4.4. Composites Composites of different material systems can combine the advantages of both. Therefore a variety of composite materials have been developed. One distinguishes composites which work as bone cements [172, 219, 220] and those that include living cells and were used for tissue engineering [176, 221]. To quantify the bone-implant interface of high-strength HA/poly(L-lactide) (PLA) composite rods an affinity index was calculated, which was the length of bone directly joined to the rods, expressed as a percentage of the total length of the rod’s surface [219]. Calcined and uncalcined HA particles which amount to 30 or 40% by weight of the composite were implanted in the distal femora of 50 rabbits and after 2, 4, 8, and 25 weeks they were examined by SEM, TEM, and light microscopy. In all composites new bone formation could be examined after 2 weeks. SEM showed direct bone contact with the composites without intervening fibrous tissue. The affinity indices of all the composite rods were significantly higher than those of unfilled control PLA rods. The maximum affinity index (41%) was attained at 4 weeks in 40% calcinated HA-containing rods. Another approach to use composites is to increase the compressive strength of calcium phosphate cement (CPC) [220], which limits their use to non-load-bearing applications, by the means of water-soluble polymers. Composites formulated with the polycations poly(ethylenimine) and poly(allylamine hydrochloride) exhibited compressive strengths up to six times greater than that of pure CPC material. SEM results indicate a denser, more interdigitated microstructure. The increased strength was attributed to the polymer’s capacity to bridge between multiple crystallites and to absorb energy through plastic flow. Glass-ceramic, as mentioned previously, is also used in composites with bisphenol-a-glycidyl dimethacrylate (Bis-GMA)-based resin. These were compared with composites containing HA or -tricalcium phosphate (TCP) as the inorganic filler [172]. After 10 weeks of implantation into tibial metaphyses of rabbits, the ceramic-containing sample was in direct contact with bone and ceramic particles were partially adsorbed at the surface. The HA-containing cement was in contact with partially mineralized extracellular matrix. In 25-week specimens, ceramic particles were completely absorbed and replaced by new bone, and there was no intervening soft tissue. The tissue response of nano-hydroxyapatite/collagen composite was investigated in [176]. At the interface of the implant and marrow tissue, solution-mediated dissolution and giant-cell-mediated resorption led to the degradation of the composite. Interfacial bone formation by osteoblasts was also evident. The composite can be incorporated into bone metabolism instead of being a permanent implant. Nano-HA was also used in a porous collagen composite, to build up a three-dimensional osteogenic cell/nano-HA-collagen construct [221]. SEM and histological examination have demonstrated the development of the cell/material complex. Other biodegradable composites are

Nanoanalysis of Biomaterials

18 based on polyhydroxybutyrate-polyhydroxyvalerate (PHBPHV) [222]. SEM showed that the intended compositions of composites were achieved and bioceramic particles were well distributed in the polymer.

4.5. Biological Samples In the dental field enamel and dentin are materials under investigation. Effects of demineralization, for example, by soft drinks on the natural tooth structure, and improvements of resin adhesion important in dental therapy were studied. Topographical changes of human teeth in various liquids were characterized in [223]. The initially smooth and finely grained surfaces were changed to a rougher and more coarsely grained surface. Dissolution rates for soda pops with pH values between 4 and 5 were calculated to be 3 mm/year in contrast to water with a rate of 0.4 mm/year. The change in mechanical properties of tooth enamel induced by demineralization via soft drinks was investigated in [224]. The changes in hardness are the first step in the dissolution process. The influence of different drinks (orange juice, a black currant drink, and water) could be determined in hardness and topography, where orange juice showed the strongest demineralization. A small critical discussion about the applicability of the model of enamel erosion characterized via SFM topography measurements is given in [225]. The influence of sodium hypochloride on dentin and dentin collagen was characterized by checking on the topography and the hardness respectively the reduced elastic modulus via an SFM in contact mode respectively a nanoindenter [226]. Dentin was removed, leaving a remnant collagen matrix and resulting in a hardness of 75% of its original value. The enhanced roughness could provide a better bonding substrate because of the enhanced surface area. The mechanism of the bonding via the adhesive Gluma consisting of glutardialdehyde and hydroxyethylmethacrylate (HEMA) could be elucidated with SFM imaging of the interaction taking place upon introduction of the adhesive to the tooth hard tissue. It forms a solid layer covering the dentin tubules. The mechanism of the amide-induced polymerization of aqueous HEMA glutardialdehyde mixtures could be confirmed by SFM [227]. Other similar SFM investigations on dentin are published in [107] and a detailed review of characterization of dentin, enamel, and collagen covering as well macroscopical features is given in [120]. The ultrastructure and nanoleakage of dentin bonding by the use of a two-step, polyalkenoic acid-containing, self-priming dentin adhesive in human molars was observed by TEM [228] to also check the effect of a 5% sodium hypochlorite solution (NaOCl) treatment. The NaOCl should remove the collagen fibrils at demineralized dentin and so may facilitate the infiltration of adhesive resins into a dentin substrate. To get a comparison, dentin was also acid-etched by 35% H3 PO4 ; the leakage manifestations were similar for both treatments. So no additional advantage in using NaOCl with the used adhesives was found. Some final features of surface investigations by nanoanalytical tools discussed in the remainder of this section show in which broad range of biologically modified surfaces scanning probe techniques can be used. These studies include molecular layers like lipids or proteins and extend to cellular

arrangements. They are only a small selection showing the principal ability of the technique. The activity of a liposome layer with ganglioside G(M1) was tested with SFM [229]. Supported phospholipid bilayers (SPBs) as model substrates for cell membranes are imaged with SFM in [230]. The height, adhesion, and friction of mixed phospholipid layers is monitored in [231]. Microelastic mapping of living cells was done by SFM [28, 232]. A recent overview of the characterization of bacterial biofilms is given in [163]. Still a lot of experiments were done in ambient conditions and biological materials such as hexagonal packed intermediate (HPI) layers, DNA, tobacco mosaic virus, and collagen deposited on various substrates were imaged with noncontact dynamic force modes with little destruction but not in native states [233]. STM as well is usually used for investigations of biological films in air, leaving a change in structure. Pictures could be taken from C-phycocyanin (C-PC) which was isolated from the blue-green alga Spirulina platensis [234], and tobacco mosaic virus [235]. Nonhuman hard tissue like abalone nacre [236] was imaged and mineralization pathways revealed to form single crystals [237], and the elasticity of cow cartilage was tested [28]. The magnetic force from a magnetotactic bacterium [238] could be imaged with the magnetic force mode with SFM. Membrane deformation of living glial cells [239] or fibroblasts [240] were done via SFM. Other measurements are mentioned in [241] where local elastic properties respectively Young’s modulus were mapped via force mapping. The viscous properties of cells have been investigated on kidney epithelial cells with laser tracking microrheology. Comparisons with other authors are given, revealing cytoplasmic viscosities that range for different experiments within five orders of magnitude around 2 ·103 Pa·s [110]. Also viscous properties of fibroblasts were measured with magnetic bead microrheometry [109]. An overview of renal cell characterization with the SFM is given in [242]. Immobilized antibodies have been characterized by SECM to monitor the active binding sites [243]. Microelastic properties of bone marrow (cow tibia) were measured via SFM in [244]. This demonstrates that nanoanalytical tools not only are useful for characterizing the pure biomaterial surface alone but are also helpful for investigating surfaces in contact with biological materials of all kinds.

5. CONCLUSIONS This chapter illustrates the impact of new imaging techniques such as SPMs on biointerface analysis of biomaterials. SFM and STM investigations provide structural, rheological, and functional information about surfaces. Force distance curves contain complex information about interactions of biofilms with the substrate. Electron microscopy as a “classical” tool complements the techniques, in particular because imaging artifacts are much better known than in SPM.

Nanoanalysis of Biomaterials

There are two trends to be seen. First, new methods are being developed, such as scanning near-field optical microscopy, another member of the SPM family. This method will combine all possibilities of optical microscopies, in particular all labelling techniques, but without the diffraction limit of resolution. However, there are still technological hurdles, in particular to produce bright and narrow light sources routinely. As soon as these problems are overcome, this method will play an increasing role in biomaterial research. The second trend goes to multifunctional analysis on the nanometer scale, which will allow the understanding of the basic mechanisms of interaction between biological and synthetic materials. This will further help to improve biointerfaces used for biomaterials. The challenge is now to develop multifunctional tools that are easily accessible and suitable for the analysis of biomaterials based on SPM techniques, as well as in combinations with methods characterizing macroscopic properties to bridge the gap between these two worlds. Still, all these new methods are in their infancies in their use on biomaterials. However, in the near future they will become much more common and effective and will influence the field substantially.

GLOSSARY Arene cavity The cavity formed by the enclosure of the aromatic rings in a calixarene. Calix[n]arenes A group of phenolic macrocyclic molecules resulted from the condensation of para-substituted phenol and formaldehyde. (‘n’ refers to the number of phenolic units.) Crystal structure Three-dimensional arrangement of atoms derived from single crystal X-ray diffraction that provides information about the structure, conformation, and geometry of the molecule. Functionalization Chemical modification on the lower or upper rim leading to the formation of derivatives containing appropriate functional groups. Lower rim The rim containing the phenolic -OH groups in a para-substituted calixarene. Metalloenzymes Those enzymes that exhibit their function as a result of the presence of a specific metal ion. Receptor A molecule that possesses the ability to bind to neutral or ionic species through recognition. Upper rim The rim containing the groups present at the para-position in a calixarene.

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Encyclopedia of Nanoscience and Nanotechnology

www.aspbs.com/enn

Nanoassembly for Polymer Electronics Tianhong Cui University of Minnesota, Minneapolis, Minnesota, USA

Yuri Lvov, Jingshi Shi, Feng Hua Louisiana Tech University, Ruston, Louisiana, USA

CONTENTS 1. Introduction 2. Polycation/Polyanion Layer-by-Layer Assembly 3. Nanoparticle/Polyion Multilayers 4. Spin-Coating for Layer-by-Layer Assembly 5. Soft Lithography to Pattern 2D Patterns on Polyion Multilayers 6. Lithographic Approach to Pattern Layer-by-Layer Thin Films 7. Nanofabrication for Nanoelectronics 8. Polymer Microelectronics 9. Potential Applications of Nano Self-Assembly 10. Conclusions Glossary References

1. INTRODUCTION The self-assembly (SA) of nanoparticles in an organized array has become increasingly important. The current methods used for the design of ultra-thin films include: spin-coating and solution-casting, thermal deposition, polyion layerby-layer assembly, chemical self-assembly, the Langmuir– Blodgett technique, and free-standing films. The optimal combination of molecular order and stability of films determines the practical usefulness of these technologies [1–6]. The most ordered macromolecular films are free-standing liquid crystalline films, but they are very unstable. The Langmuir–Blodgett method allows to construct lipid multilayers with a thickness from 5 to 500 nm, but only flat substrates can be covered by this film and it has intrinsic defects at the lipid grain borders. Another method that can be ISBN: 1-58883-062-4/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

applied to surface modification is a monolayer self-assembly, based on thiol or silane compounds [1]. By this method, one can achieve self-assembly of 2–5 nm thick organic layers on silicon or gold surfaces, but there is no simple means for thicker film construction. Other widely used methods for the industrial manufacture of thin films are spin-coating and thermal deposition of macromolecules onto a substrate. Unfortunately, unlike the methods considered above, these methods do not allow one to control a film composition in the direction perpendicular to the surface. Finally, there is a newer method for film self-assembly that makes use of the alternate adsorption of oppositely charged components (polymers, nanoparticles, and proteins) [2–9]. The assembly of alternating layers of oppositely charged linear or branched polyions and nanoparticles is simple and provides the means to form 5–500-nm thick films with monolayers of various substances growing in a preset sequence on any substrate at a growth step of about 1 nm. Mallouk [4] has called this technique “molecular beaker epitaxy,” meaning that with simple instruments (exploiting the materials’ self-assembly tendency), one can produce molecularly organized films similar to the ones obtained with sophisticated and expensive molecular beam epitaxy technology. One can assemble on a standard silicon wafer, multilayers containing different nanoparticles and polymers and then apply lithography to manufacture microdevices with nanostructured elements. Such a combination of nano-assembly with traditional micromanufacturing is the topic of this review.

2. POLYCATION/POLYANION LAYER-BY-LAYER ASSEMBLY 2.1. General Procedure A cleaned substrate of any shape and dimension is immersed into a dilute solution of a cationic polyelectrolyte, for a time optimized for the adsorption of a single monolayer Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 6: Pages (23–51)

Nanoassembly for Polymer Electronics

24 (ca 1 nm thick), and then it is rinsed and dried. The next step is the immersion of the polycation-covered substrate into a dilute dispersion of polyanions or negatively charged nanoparticles (or any other nanosize-charged species) also for a time optimized for the adsorption of a monolayer; then it is rinsed and dried. These operations complete the self-assembly of a polyelectrolyte monolayer and monoparticulate layer sandwich unit onto the substrate (Fig. 1). Subsequent sandwich units are self-assembled analogously. Different nanoparticles, enzymes, and polyions may be assembled in a preplanned order in a single film. The forces between nanoparticles and binder layers govern the spontaneous layer-by-layer self-assembly of ultrathin films. These forces are primarily electrostatic and covalent in nature, but they can also involve hydrogen bonding, hydrophobic, and other types of interactions. The properties of the self-assembled multilayers depend on the choice of building blocks used and their rational organization and integration along the axis perpendicular to the substrate. The sequential adsorption of oppositely charged colloids was reported in a seminal paper in 1966 by Iler [2]. The electrostatic self-assembly was subsequently “rediscovered” in the mid-nineties and extended to the preparation of multilayers of polycations and phosphonate ions, as well as to the layering of linear polyions, proteins, and nanoparticles by Decher, Mallouk, Möhwald, Lvov, Rubner, Fendler, Hammond, Kunitake, Schlenoff, Kotov, and others. This selfassembly is now employed in the fabrication of ultra-thin films from charged polymers (polyions) [3–47], dyes [48–51], nanoparticles (metallic, semiconducting, magnetic, insulating) and clay nanoplates [52–75], proteins [76–96], and other supramolecular species [79]. The greatest advantage of this self-assembly is that any of these species can be absorbed layer-by-layer in any order. The oppositely charged species Layer-by-layer electrostatic assembly by alternate adsorption of oppositely charged nanoparticles, polyions and proteins

Solid substrate

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are held together by strong ionic bonds and they form longlasting, uniform, and stable films. Self-assembly is economical and readily amenable to scaling-up for the fabrication of large-area, defect-free devices on any kind and shape of surfaces. The main idea of this method is the resaturation of polyion adsorption, which results in the alternation of the terminal charge after each layer is deposited. This idea is general and implies that there are no major restrictions in the choice of polyelectrolytes. It is possible to design composite polymeric films in the range of 5 to 1000 nm, with a definite knowledge of their composition. For the successful assembly of nanoparticle or protein multilayers, the alternation with linear polyion layers is important. Flexible linear polyions penetrate between nanoparticles and act as electrostatic glue. The concept of “electrostatic polyion glue,” which keeps together neighboring arrays of nanoparticles, is central to this approach [77, 79]. The self-assembled film contains amorphous polyion interlayers, and this organization “heals” defects that arise because of the introduction of foreign particles during the process of film formation (dust, microbes) [13, 79].

2.1.1. Standard Assembly Procedure As a standard approach to film preparation, we employ the following steps: 1. Take aqueous solutions of polyion, nanoparticles, or protein at a concentration of 0.1–1 mg/mL and adjust the pH in such a way that the components are oppositely charged. 2. Take a substrate carrying a surface charge (e.g., plates or polymer films covered by a layer of cationic poly(ethylenimine) that may be readily attached to many surfaces). 3. Carry out alternate immersion of the substrate in the component’s solutions for 10 min with 1 min intermediate water rinsing. To rinse a sample, use a solution with pH that keeps the polyions ionized. 4. Dry the sample using a stream of nitrogen (Note: drying may hinder the assembly process and it is not necessary for the procedure). Linear polyions predominately used in the assembly are as follows: polycations—poly(ethylenimine) (PEI), poly(dimethyldiallylammonium chloride) (PDDA), poly(allylamine) (PAH), polylysine, chitosan, polyanions—poly(styrenesulfonate) (PSS), poly(vinylsulfate), poly(acrylic acid), dextran sulfate, sodium alginate, heparin, and DNA. One can grow polymer nanocomposite films by means of the sequential adsorption of different material monolayers that employ hundreds of commercially available polyions. The only requirement is that there be a proper (positive/negative) alternation of the component charges.

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2.2. Kinetics of Polyion Adsorption Nanoparticle/polyion (or protein) bilayer, D = 5–50 nm

Figure 1. A scheme of the layer-by-layer assembly.

For the time-dependent control of adsorption and monitoring of the assembly in-situ, the quartz crystal microbalance method is quite suitable [23, 46, 86]. The kinetics of

Nanoassembly for Polymer Electronics

the adsorption process could be delineated by the QCMtechnique, which is indispensable for establishing proper assembly conditions (e.g., a saturation adsorption time). The multilayer assemblies are characterized by means of a quartz crystal microbalance technique in two ways: 1. After drying a sample in a nitrogen stream, we measured the resonance frequency shift and calculated an adsorbed mass by the Sauerbrey equation; or 2. By monitoring the resonator frequency during the adsorption process onto one side of the resonator, which was in permanent contact with polyion solutions. While performing experiments in permanent contact with the polyion solution, we touched the surface of solutions with one side of the resonator, while the upper electrode was kept open to air and the upper contact wire was insulated from the solution by a silicone paint covering. The fitting of adsorption to an exponential law yields a first-order rate of adsorption for PSS
= 25 ± 02 min and for PAH
= 21 ± 02 min. This means that during the first 5 min ca 87% of the material is adsorbed onto the charged support and t = 8 min (t = 3
) gives 95% full coverage. Typically, in most publications on polyion assembly, adsorption times of 5 to 20 min are used. One does not need to maintain an adsorption time with great precision: a minute more or less does not influence the layer thickness if we are at the saturation region. For other species, PDDA, PEI, montmorillonite clay, myoglobin, lysozyme, and glucose oxidase, the first-order rate of adsorption onto an oppositely charged surface was found to be 2, 3, 1.8, 3, 4, and 5 min, respectively. Interestingly, 5–20 min is essentially greater than the diffusion-limited time (mass transport limitation), which is necessary for complete surface covering (for the used linear polyion concentrations it is a few seconds). Only for 45-nm silica/PDDA assembly do we have an example when 2 s time corresponds to the diffusion limited time for the SiO2 monolayer adsorption. One could suppose that linear polyion adsorption occurs in two stages: quick anchoring to a surface and slow relaxation. To reach a surface-charge reversion during linear polyion adsorption, one needs a concentration greater than 10−5 M [23]. The dependence of polyion layer thickness on concentration is not great: thus, in the concentration range of 0.1–5 mg/mL PSS/PAH pair yielded a similar bilayer thickness. A further decrease in polyion concentration (using 0.01 mg/mL) decreases the layer thickness of the adsorbed polyion. An increase in the component concentrations to 20–30 mg/ml may result in the nonlinear (exponential) enlargement of the growth rate with adsorption steps, especially if an intermediate sample rinsing is not long enough [47].

2.3. First Layers and Precursor Film At the very beginning of the alternate assembly process, one often sees nonlinear film growth [13, 23, 41]. At the first 2–3 layers, smaller amounts of polyion are adsorbed as compared with further assembly, when the film mass and thickness increase linearly with the number of adsorption cycles. Tsukruk et al. [41] explained this as an island-type

25 adsorption of the first polyion layer on a weakly charged solid support. In the following two-three adsorption cycles, these islands spread and cover the entire surface, and further multilayer growth occurs linearly. If a substrate is well charged, then a linear growth with repeatable steps begins earlier. In studying the possibility of using new compound in approach [6, 13, 23]. On a substrate (silver electrode of quartz crystal microbalance (QCM) resonator or quartz slide), we deposited 2–3 layers of polyions, and on this “polyion blanket,” with a well-defined charge of the outermost layer, an assembly of proteins, nanoparticles, or other compounds was produced. In a typical procedure, precursor films were assembled by repeating two or three alternate adsorptions of PEI and PSS. The outermost layer became “negative,” or “positive,” respectively. Quartz crystal microbalance monitoring of multilayer growth was often the first stage of the assembly procedure elaboration. Initially, we estimated the time needed for a component’s saturated adsorption in a kinetic experiment. Then we performed the assembly typically with 10 min alternate adsorption. After every other adsorption step, a layer was dried by a nitrogen stream and the QCM resonator frequency was registered. The frequency shift with adsorption cycles gave us the adsorbed mass at every assembly step. A linear film mass increase with the number of assembly steps indicated a successful procedure. The following relationship is obtained between adsorbed mass M (g) and frequency shift F (Hz) by taking into account the characteristics of the 9 MHz quartz resonators used [23]: F = −183 × 108 M/A, where A = 016 ± 001 cm2 is the surface area of the resonator. One finds that a 1 Hz change in F corresponds to 0.9 ng, and the thickness of a film may be calculated from its mass. The adsorbed film thickness at both faces of the electrodes (d) is obtainable from the density of the protein/polyion film (ca 1.3 g/cm3 ) and the real film area: d (nm) = −0016 ± 002F (Hz). The scanning electron microscopy data from a number of protein/polyion and linear polycation/polyanion film cross-sections permitted us to confirm the validity of this equation. Another powerful method for polyion film characterization was small-angle X-ray and neutron reflectivity.

2.4. Multilayer Structure X-ray or neutron reflectivity measurements of polyion films show patterns with profound intensity oscillations, as demonstrated in Figure 2. They are so-called Kiessig fringes, due to the interference of radiation beams reflected from interfaces solid support/film and air/film. From the periodicity of these oscillations, one can calculate the film thickness (with the help of the Bragg-like equation and taking into account refraction phenomena that are essential at small angles). Growth steps for a bilayer of 1.1–2.0 nm are typical for alternate linear polyion assembly, and a thickness of one layer often equals to half of this value [6–14]. These values correspond to a polyion cross-section and show that in one cycle of excessive adsorption we have approximately one monolayer coverage of the substrate. The nanoparticle/polyion bilayer thickness is determined by the diameter of the particle. Model fitting of X-ray data gives

Nanoassembly for Polymer Electronics

26 X-ray (λ=1.54 A) and neutron (λ=2.37 A) reflectivity from PEI+(PSS/PEI)2+{PSS/Mb/PSS-d/Mb}8 multilayer, film thickness is 940 A, four-unit cell thickness is 111 A 10

Bragg

Intensity, Arb. units

8

peak

6

in a smaller step of film growth (1–2 nm) and lower ionization gives a larger growth step (3–6 nm). It can be reached either by adding salt to a polyion solution (as previously discussed for strong polyelectrolytes, such as PDDA and PSS), or by varying the pH for weak polyelectrolytes (e.g., polyacrylic acid (PAA) and PAH, as was analyzed by Yoo et al. [30]). Direct zeta-potential measurements confirmed a symmetric positive/negative alternation of the polycation/polyanion multilayer’s outermost charge with adsorption cycles [34].

neutrons

2.5. Stoichiometry of the Components and Polyion Molecular Weight

4

2

X-ray

0

0.02

0.04

0.06

0.08

0.1

0.12

Q, A-1 Figure 2. Small-angle X-ray and neutron reflectivity curves from (PSS/myoglobin/deuterated PSS/myoglobin)8 multilayer.

a surface roughness of the polyion film on an order of 1 nm. Atomic force microscopy (AFM) and scanning electron microscopy (SEM) data revealed a surface roughness of 1–2 nm [42]. Polyion films are insoluble in water and in many organic solvents and are stable to 280
C [38, 95]. Neutron reflectivity analysis of the films composed of alternate layers of deuterated PSS and hydrogen containing PAH has proved that polyanion/polycation films possess not only a high uniform thickness but a multilayer structure, too [19–22]. The interfaces between layers in polyion films are not sharp and partial interpenetration (30–40% of their thickness) between neighboring polymeric layers takes place [21–22]. A distinct spatial component separation may be reached between the first and the third or fourth neighboring polyion layers. In the neutron reflectivity experiments with the selectively deuterated component (usually d-PSS), it was possible to observe 1–3 Bragg reflections in addition to Kiessig fringes. This was not possible in the X-ray reflectivity experiments because of a small scattering contrast of neighboring polycations and polyanions, and because of their large interpenetration. X-ray Bragg reflections from the alternate gold nanoparticle/poly(allylamine) multilayers were observed by Schmitt et al. [55]. They demonstrated that in order to have good spatial separation between gold layers in the film, one needs to make a thicker polyion interlayer (of 3–4 PSS/PAH bilayers). In a similar approach, we formed the four-step unit cell multilayers of myoglobin, deuterated, and “usual” poly(styrenesulfonate): (myoglobin/deuteratedPSS/myoglobin/PSS)9 . A Bragg reflection in the neutron reflectivity curve of this four-step unit cell multilayer was observed (Fig. 2). The film’s total thickness was calculated at 94.0 nm, and the four-unit cell thickness was 11.1 nm. The polycation/polyanion bilayer thickness depends on the charge density of the polyions. It was shown that more than 10% of polyion side groups have to be ionized for a stable reproducible multilayer assembly via alternate electrostatic adsorption [34]. High ionization of polyions results

A multilayer film has to be totally neutral, that is, a stoichiometry of charged groups in neighboring polycation and polyanion layers has to be 1:1. In many cases, we confirmed this (for PSS/PDDA, PSS/PEI, PSS/chitosan, DNA/PAH multilayers), but for PSS/PAH a deviation from 1:1 stoichiometry was found [34]. This is probably due to the incomplete dissociation of the polyions. It is difficult to control polyion dissociation because it depends on a concentration and on the presence of oppositely charged compounds in solution [97]. The complex stoichiometry did not depend on the ionic strength of polyion solutions, which indicates an absence of low molecular weight ions (K+ , Na+ , Cl−  in the films. For deposition from water solutions, the PSS/PAH growth step was similar for PSS molecular weights varying from 40,000 to 1,000,000 [21]. The influence of the polymerization degree on the formation of stable interpolyelectrolyte bulk complexes was analyzed by Kabanov [97]. He found that such complexes were stable when a polyion contained more than 20 charged groups in the sequence. We used polyions, such as PSS, PVS, PDDA, PEI with molecular weights of 50,000–200,000. They contain hundreds of ionized groups in the pH range from 3 to 9. A cooperative electrostatic interaction between the polycations and polyanions used is strong and prevents the dissolution of the multilayers even in high ionic strength solvents.

2.6. Nonequilibrium Growth and Admixed Polyion Complexes When the polyion assembly was performed at equilibrium conditions, a saturated adsorption was achieved at every deposition step and a careful intermediate sample washing removed all nonspecific polyion adsorption. Next, one has the permanent increment of the multilayer growth (i.e., the film mass and thickness increased linearly with the cycles of adsorption). In some cases, we encountered the situation when the film growth step exponentially increased with the number of adsorbed layers. We recognized such conditions as nonstable and usually reached a stable growth step by optimizing the solution pH or by decreasing the polyion concentration. As we previously discussed, one can increase the speed of growth from 1–2 nm to 5–10 nm in 10 min by increasing the ionic strength of the polyion solutions. Another way to increase the assembly speed is by using preformed interpolyelectrolyte complexes (coacervates) [92]. The formation of

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water-soluble polyelectrolyte complexes has been intensively studied by means of turbidity measurements [58]. Aqueous mixtures of oppositely charged polyelectrolytes are usually homogenous at the stoichiometry far from the neutralization point. First, such complexes permit an increase in the size of the assembly construction blocks. Second, they make it possible to immobilize with polyion, which were impossible to use in the assembly directly (poor charged nanoparticles, dyes, and proteins).

2.7. Polyion Films for Biocompatible Coverage Multilayer assemblies of natural polyions, such as DNA, polynucleotides, polylysine, and polysaccharides (e.g., heparin, chondroitine, and chitosan) are interesting for biological and medical applications. DNA and polynucleotides (polyuridylic and polyadenylic acids) can be readily assembled in alternation with polycations (PEI, PAH, polylysine). The assembly of polysaccharides with oppositely charged polyions is possible as a means of biocompatible surface preparation. A chitosan and albumin/heparin multilayer assembly for such coatings has been developed [42–44].

2.8. Multipolar Dye and Liposome Assembly The layer-by-layer assembly by alternate adsorption of oppositely charged molecules was applicable for multipolar dyes with symmetric charges possessing conjugated rings and other hydrophobic fragments [48–51]. Hydrophobic fragments probably enhance dye stacking. Interestingly, the dye/polyion bilayer has the same thickness in a wide range of dye concentrations. For Congo Red/PDDA films, the bilayer thickness was 1.5 nm for dye concentrations from 0.01 up to 10 mg/mL, that is, below and above the critical micelle concentration (CMC) of the dye. The characteristic feature of the assembly of some dye multilayers was greater than the monolayer adsorption at the dye adsorption cycle followed by a depletion of the material during the following linear polyion adsorption step. In this process, we have substantial nonspecific adsorption at the dye adsorption step, and then the removal of nonspecific bond material by complexation with an oppositely charged polyion (at the next assembly step). The graph of the film mass against the number of adsorption steps, such as a growth mode, looks like “a large step up followed by a small step down” [46, 50]. A similar growth mode was observed for protein/polyion and nanoparticle/polyion assemblies, especially with a short intermediate sample washing time [58, 77].

3. NANOPARTICLE/POLYION MULTILAYERS The construction of organic/inorganic nanostructured materials is an important goal of modern materials research. An alternate adsorption procedure was used for the following charged nanoparticles: clay and ceramic plates, nanotubules, 10, 20, 45, 75-nm silica spheres, 50, 150, 300-nm latex, 15-nm gold, 30-nm magnetic Fe3 O4 , 20–30 nm CeO2 , MnO2 , ZrO2 , SnO2 , TiO2 particles [23, 52–71], as well as

27 34-nm diameter spherical plant viruses [12]. Many oxide particles have a zero-charge point at pH 4–5. They are negatively charged at pH 7–8, and can be readily assembled by means of alternate adsorption with such polycations as PEI or PDDA. The number of particle monolayers in such “sandwich” multilayers is exactly known, and any profile across the film can be constructed with a resolution of 5–10 nm. Using a “soft” polymeric interlayer was important for the composite multilayers formation: flexible linear or branched polyions optimize electrostatic attraction. An organic component can change electrical properties of nanostructured material. Therefore, after the assembly is completed, organic interlayers can be removed by a 2-hour thermal treatment above 320
C in air (calcination process), which results in direct contacts between the nanoparticles needed for improved electric or magnetic properties. Nanoparticles, such as gold, silver, and fullerenes may be “sandwiched” in multilayers with proteins providing electrically or optically induced electron donor-acceptor properties. Semiconductor nanoparticles, such as PbS, CdS, and CdSe, were used in this assembly [54, 67–69]. An assembly of coreshell nanoparticles, such as Ag/TiO2 or Fe3 O4 /Au, was also possible [71, 73].

3.1. Silica Multilayers As an example of the nanoparticle architecture, let us analyze a 45-nm silica assembly by alternate adsorption with PDDA [58–59]. In-situ QCM monitoring of alternate PDDA and SiO2 adsorption gave the kinetics of the assembly process. In the first step, PDDA was adsorbed onto a Agelectrode. The QCM frequency decreased during the first 60 s, after which a slower change was observed as adsorption saturation set in. Then the resonator was immersed in pure water for washing. Next, the film was immersed in SiO2 dispersion and silica adsorption saturation occurred within several seconds. After subsequent water rinsing, the film was immersed again in a PDDA solution, and so on. Each growth step was reproducible, and the adsorption process reached 90% saturation in 10 s for SiO2 and 30 s for PDDA. The film assembly was not possible simply by the multiple immersion of the substrate in the silica solution. An alternation with an oppositely charged polyion was necessary. At every assembly step, the component monolayers were formed, as was recorded by QCM, SEM (Fig. 3). The average density of SiO2 /PDDA multilayers is  = 143 ± 005 g/cm3 . SiO2 /PDDA film volume composition is: 60% SiO2 + 10% polycation + 30% air-filled pores. These pores are formed by closely packed 45-nm SiO2 and have a typical dimension of 20 nm. The films have controlled pores, which can be varied by the selection of the nanoparticle diameter. We estimated the diffusion limitation for surface coverage At by adsorption from solution of parti√ cles with the diffusion coefficient D from At = 2/C Dt. For t = 2 s, C = 10 mg/cm3 , and assuming for 45-nm silica D = 11 × 0−7 cm2 /s, A ≈ 3 × 10−6 g/cm2 and the layer thickness: L = At/ ≈ 21 nm. This is reasonably close to the experimental silica monolayer thickness of 24.6 nm. Thus, 2 s corresponds roughly to the diffusion-limited time for the SiO2 monolayer adsorption; this time is the fastest nanoparticle monolayer formation rate that we have achieved.

28

Nanoassembly for Polymer Electronics

Figure 4. (a–b) SEM cross-sectional images of (MnO2 /PDDA)9 and, on right, (12-nm diameter SnO2 /PDDA)18 films. The films formed on a silver electrode.

Figure 3. SEM image of multilayer containing 18 monolayers of 45-nmdiameter silica alternated with polycation PDDA.

3.2. Latex Assembly Charged latex is a good building block for an electrostatic layer-by-layer assembly. Positively or negatively charged monodisperse lattices with diameters of 30, 40, 45, 50, or 75-nm and with different colors are commercially available, for example, from Seradyn Inc. or IDC-Ultraclean Uniform Latex Inc. For the first time, a multilayer assembly of negative latex spheres (carboxyl-modified or sulfate polystyrene) in alternation with positive latex (amidinemodified polystyrene) was reported by Bliznyuk and Tsukruk [57]. They have described a strong tethering of charged nanoparticles to the surface, which prevents surface diffusion and the rearrangement required for formation of perfect lateral ordering. This situation is different from the one with the formation of the ordered 3D-mesocrystals by slow crystallization of the monodispersed aqueous colloids [72]. In the nanoparticle/polyion multilayers, one loses the crystallike ordering, but gains control of the process, preparing multilayers of close-packed nanoparticles with a precisely known number of monolayers. We demonstrated a regular layer-by-layer assembly of carboxylated 45-nm diameter Seradyn latex in alternation with PEI.

3.3. Compact Nanoparticle/ Poly(ethyleneimine) Multilayers Figure 4 shows the assembly QCM monitoring and scanning electron micrographs of film cross-sections and a partial top view of a film with architecture PDDA/PSS/PDDA + (MnO2 /PDDA)9 and 190 nm thick SnO2 /PDDA multilayer. MnO2 -film has a remarkably smooth surface and uniform thickness. The total frequency shift by QCM was 11,000 Hz and film thickness from SEM was 170 nm. Dividing the film

thickness by the number of manganese oxide/PDDA bilayers, we obtain values slightly less than the 23-nm bilayer thickness found above from QCM because the first two layers of manganese oxide are thinner. We cannot detect separate layers in the film by SEM, but individual structures of about 20 nm dimensions are clearly visible and may be attached to nanoparticles. We analyzed the chemical composition and the chemical state of Mn and N atoms on the surface of a film with architecture PDDA/PSS/PDDA + (MnO2 /PDDA)9 by XPS. Spectra revealed a surface rich in carbon and oxygen with manganese and nitrogen present in concentrations less than 7% and trace amounts of chlorine. The Mn (2p) region consists of a spin-orbit doublet with a Mn (2p1/2) binding energy of 653.30 eV and Mn (2p3/2) binding energy of 641.63 eV. This doublet can be assigned to a mixed valent manganese system, most likely Mn (4+) and Mn (3+) since the average oxidation state of Mn in the nanoparticles is 3.7. The N 1s region showed two peaks at 402.04 eV and 399.12 eV, indicating two different chemical environments for the nitrogen atoms. The difference in the chemical environment may reflect the formation of contact ion pairs and long-distance charge pairs between the MnO2 particles and the polycation PDDA.

3.4. Open-Structured TiO2 -Nanoparticle/ Poly(styrenesulfonate) Films The assembly of 35-nm diameter TiO2 (Degussa P25) was possible at pH 3.8 (when the particles were positive) in alternation with PSS. TiO2 assembly with polycation PDDA at this pH was not possible. The saturation adsorption time for TiO2 nanoparticles was 5 min. The growth step of the TiO2 /PDDA multilayer was stable and linear, with the mass adsorption increment corresponding to the monolayer surface coverage. The SEM of the TiO2 /PSS multilayer shows not a close-packed but an open structure of the film. It was possible to vary the porosity of the film by changing the ionic strength of nanoparticle dispersions. Such porous structures can be useful for catalytic applications.

3.5. Organized Gold/Polycation Multilayers In [55–56], the self-assembly of 15-nm-diameter gold particles in alternation with polycation PAH was demonstrated. Gold alternation with the polycation was possible because

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of negative nanoparticle charge (surface potential −35 mV) due to the synthesis procedure. The saturation time needed for the formation of close-packed gold nanoparticle monolayer (full coverage) was 2 h because of the low particle concentration in solution [55]. An approach to a spatial separation of nanoparticle layers in such sandwich-like films was elaborated: three- to five polycation/polyanion interlayers were assembled between gold layers (e.g., Au/{PAH + (PSS/PAH)3−5 }/Au). The gold surface (with a roughness of the order of the radius of nanoparticles) was covered and smoothed by the 6–10 nm polyion layer. Further “sandwiching” of gold nanoparticles with the thick polyion interlayers resulted in the ordered gold/polymer heterostructure. The low-angle, X-ray reflectivity of these samples gave 2–3 orders of Bragg reflections with the spacing corresponding to such a complex unit cell. We think that this is a general approach to creating ordered inorganic/organic heterostructure multilayers, and we have used it also for the formation of protein/polyion heterostructures [77, 79].

3.6. Layered Ceramics Mica-type layered silicates can bear a natural negative charge because of the isomorphous substitution of silicon in octahedral sheets by aluminum or magnesium. The charge is generally balanced by potassium cations that reside in the galleries between layers. The intercalation of organic polymers between sheets of layered ceramics provides access to novel polymer-ceramic nanocomposites. These nanocomposites exhibit unique physical and mechanical properties attributable to the synergism of the individual components. The build-up of the multilayers in a stepwise manner rather than in the bulk “all-at-once” manner is of special interest. Kleinfeld and Ferguson [52] were first to apply the electrostatic layer-by-layer adsorption to produce multilayers of anionic synthetic silicate—hectorite and cationic PDDA. We used the polyion assembly to build up multilayers with alternating 1-nm-thick montmorillonite sheets and cationic PEI or PDDA [64–65]. The film thickness increase for the montmorillonite adsorption cycle was 1.1 nm and for PEI 2 nm. After 20 cycles, the resultant film had a permanent thickness of 63 nm.

29 modulation with a few nanometer-resolution across the polymeric films is possible by selective synthesis of heavy atom nanoparticles. A simple process to convert multilayers of weak polyelectrolytes (e.g., poly(acrylic acid) and poly(allylamine)) into uniform microporous films has been developed by Mendelsohn et al. [76]. These multilayers were immersed briefly into acidic solution (pH 2.4) to effect an irreversible transformation of the film morphology. The resulting microporous structure thickness is 2–3 times less than the thickness of the original films, and possesses reduced relative density of 1/2 to 1/3. The interconnected pores ranging in size from 100 to 500 nm. A refractive index of the porous PAA/PAH film was n = 118 ± 001. It is much less than the origin n = 154 for the untreated polyion multilayer. Correspondingly, a dielectric constant of the porous PAA/PAH film dropped to ′ = 2 from the initial ′ = 5–7.

3.8. Protein Multilayers In many cases, one can consider proteins as hard monodisperse nanoparticles with dimensions of 2–10 nm. Taking protein solution at pH well apart from its isoelectric point, one can provide 10–60 elemental charges for a protein globule due to ionization of its carboxyl or amine groups [77]. Multilayer films that contain ordered layers of protein species were assembled by means of alternate electrostatic adsorption mostly with positively charged PEI, PAH, PDDA, and chitosan or with negatively charged PSS, DNA, and heparin [77–96]. The pH of the protein solutions was set apart from the isoelectric point so that proteins were sufficiently charged under the experimental conditions. The assembly of 20 different proteins was successfully achieved (including cytochrome, carbonic anhydrase, myoglobin, hemoglobin, bacteriorhodopsin, pepsin, peroxidase, alcohol dehydrogenase, glucoamylase, glucose oxidase, immunoglobulin, catalase, and urease) (Fig. 5) [79]. The mass increment at each

3.7. Multilayer Reactors for Metallic and Semiconducting Particles. Microporous Films This process was recently introduced by Joly et al. [75]. First, polyelectrolyte multilayers with controlled content of free nonionized carboxylic acid groups were fabricated with weak polyions (e.g., poly(acrylic acid) via suitable pH-adjustments of the processing solutions). These groups were then used to bind various inorganic ions that were subsequently converted into 2-nm diameter particles (e.g., Ag, Pb, or PbS). The spatial control over the growth of the nanoparticles was achieved by the use of multilayer heterostructures which also contain bilayer blocks that are not able to bind inorganic ions. These nonbonding bilayers were fabricated from strong polyions, such as poly(styrenesulfonate). A density

Figure 5. SEM image of cross-section of glucose oxidase/PEI multilayer (24 bilayers, thickness 270 nm) on quartz support.

30 step was quite reproducible. Proteins immobilized in multilayers with strong polyions such as PSS, PEI, and PDDA were insoluble in buffer for a pH range between 3 and 10. The assembled proteins are in most cases not denaturated [77–78, 82, 87–88]. Moreover, the layer-by-layer immobilization with linear or branched polyions enhanced the enzymatic stability [95]. The enzymatic activity in multilayers increased linearly with the number of layers up to 10–15 protein layers, at which point the film bioactivity became saturated. This saturation was probably due to substrate diffusion limitations into the film, that is, accessibility to the protein requires a substrate transport through the multilayer [95]. For the antigen-antibody reaction in immunoglobulin (IgG)/PSS multilayers, the activity increased up to five immunoglobulin layers. Compactness or openness of protein multilayers may be regulated. Thus, glucose oxidase, myoglobin, and albumin multilayer films were compact, but immunoglobulin/PSS multilayers had an open structure with areas as large as 100-nm in diameter unfilled in the upper layers of the film [87]. Drying of polyion films exerts unclear influences on the structure. We do not need drying for the assembly process; samples were dried for control of the assembly. From the other hand, the importance of film drying (as a separate process) is still not fully understood. The assembly with a regular film, drying at every other adsorption step, gave polar multilayers with nonlinear optical properties [99]. A similarly prepared Photosynthetic Reaction Center/PDDA multilayer demonstrated second harmonic light generation [89]. Regular immunoglobulin/PSS assembly with the film drying at every adsorption cycle was possible at a pH close to the IgG isoelectric point, which again indicates an importance of hydrophobic interactions [87].

3.9. Different Proteins in Alternation with Polyions An elaboration of the assembly technique for a variety of proteins makes it possible to construct multicomponent protein films (superlattices) [77, 79, 83]. We have described the formation of two types of superlattices: 1. The alternation of similarly charged proteins at identical pH conditions; both positively charged myoglobin and lysozyme in alternation with polyannegatively ion {myoglobin+ /PSS/lysozyme+ /PSS}; charged glucose oxidase (GOx) and glucoamylase (GA) with polycation {glucose oxidase− /PDDA/glucoamylase− /PDDA}. 2. The combination of negative and positive proteins in the two-block film with the insertion of an additional polyion layer to change the assembly mode: {(lysozyme/PSS)3 + PEI + (glucose oxidase/PEI)6 }. The protein multicomponent films are extremely interesting as novel biologically active materials. One can arrange given protein layers according to a specific biological activity. Sequential enzymatic reactions and vectorial transfer of electrons and energy become feasible targets by the preparation of anisotropic protein layers with the precise control of the distances of active layers.

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4. SPIN-COATING FOR LAYER-BY-LAYER ASSEMBLY Spin coating, a technique used for casting chemical layers onto a rotating substrate, has been used extensively to prepare thin films for diverse industrial applications such as photolithography [100], light emission [101, 102], nuclear track detection [103], and gas sensing [104, 105]. Since the 1950s, monolayer film formation dynamics by spin-coating has been studied both experimentally and theoretically. Recently, ultra-thin multiplayer films have attracted much interest because of their wide applications as sensors, integrated optics, friction-reducing coatings, biological surfaces, light emitting devices (LEDs), or surface-orientation layers [106–110]. Most of these applications require preparation of stable and well-organized films with fast fabrication. The simplicity, time-efficiency, and cost-effectiveness of spincoating have made it a practical method for the deposition of polymer thin films. Spin-assembly is a specialized application of spin-coating, in which a polyelectrolyte multilayered thin film is self-assembled onto a spinning substrate. The spin self-assembly method as an alternative for making wellorganized multiplayer films in a very short process time has been described [111–113].

4.1. The Concentration and Spinning Rate Effect Deposition of organic material by spin-coating has been done for almost a century [114]. Solution flow dynamics [115–117], film surface topography [118–120], and evaporate effects [121–123] has been explored both theoretically and experimentally. The two main parameters that control the amount of polyelectrolyte adsorbed onto the substrate are solute concentration and spin rate. These have been shown to directly influence the thickness of monolayer films [125, 126]. Dubas and Schlenoff have fabricated multiplayer polyelectrolyte films by immersing spinning substrate into polyelectrolyte solution. Peter and Malkiat investigated those variables in multiplayer polyelectrolyte films that are spinassembled by dropping a solution onto a spinning substrate [113]. The materials used include the polyanion PAZO and polycation PEI. The thickness of a film of a single polyelectrolyte can be easily controlled by varying the concentration of polyelctrolyte and spin rates. Higher concentrations of PEI most likely lead to a greater amount of adsorbed PEI, and therefore lead to greater amounts of PAZO deposited on the film. At faster spin rates, the films experience increased mechanical forces, which lead to shorter contact time between the polyelectrolyte [115]. The forces acting on a spinning film have been studied in detail [127, 128]. The effects of spin rate on both monolayer thickness [124, 125] and multiplayer thickness [113] have been studied.

4.2. Comparison of Spin SA Method and Dip SA Method 4.2.1. The Adsorbed Amount Mechanism The adsorbed amount between the dipping and the spinning methods is significantly different [113]. This is caused by different adsorption mechanisms. Fast elimination of water

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in the spinning process significantly increased the molar concentration of the polyelectrolyte solution during the short deposition time [129] and this increases in the polyelectroyte concentration yields of thick layers, despite the thin film formation typically provided by the centrifugal force and air shear force [130–132]. It also increases the electrostatic attraction between oppositely charged polymers because the presence of water molecules in the assemblies generally screens the electrostatic attraction. When water molecules are adsorbed onto the substrate, the preadsorbed water molecules may block polyelectrolyte adsorption onto the surface, and thus the surface coverage with polyelectrolyte chains may be incomplete. However, if polymer adsorption and water drainage are almost simultaneously realized in a short time, as in the case of the spin SA process, there would be more room for polyelectrolyte to adsorb onto the substrate.

4.2.2. The Structure The spin SA method has been found to have a significant effect on the surface roughness of prepared multiplayer films, presumably because of the air shear force caused by the spinning process [110]. It was proved that the internal structure of the spin SA films is highly ordered and the film prepared with the spin process contains rather distinct interfaces between respective layers in contrast to the film obtained by the dipping method. The distinct difference in the dip and spin SA multiplayer structure indicates that the spin SA method can easily provide the well-ordered internal structure, which cannot be achieved with the dip SA even containing a high ionic strength of the polyelectrolyte solution or multiple organic layers between inorganic particle layers [112].

4.2.3. Single-Species Deposition Another important advantage of spin assembly is that the film formation process is not solely dependent on electrostatics to induce deposition. The linear growth of a PAZO layer over 10 deposition cycles on top of a single positively charged PEI underlayer has been reported [113]. A thick PEI layer on a bare, negatively charged substrate using 10 deposition cycles of 10 Mm PEI was also built [111]. Whereas film formation in the case of ionic self-assembly is governed by electrostatics and entropy; the underlying mechanism for film formation in spin-assembly involves the mechanically induced entanglement between polyelectrolyte chains of different layers. Electrostatics, therefore, takes a supplementary role in spin-assembly, enhancing the deposition process when alternating charges are used. Singlespecies multiple deposition do not show linear growth when carried out using conventional dipping techniques [111]. In summary, a new ultra-thin film-forming process, spinassembly, is an excellent method for controlling the amount and thickness of adsorbed polyelectrolyte in fabricating multiplayer thin film with highly ordered internal structure far superior to the structure obtained with the dip SA process. It also allows us to build multiplayer polyelectrolyte multilayered films without the absolute requirement of alternating charges.

31

5. SOFT LITHOGRAPHY TO PATTERN 2D PATTERNS ON POLYION MULTILAYERS Soft lithography is an alternative, nonphotolithographic set of microfabrication methods [134–136]. All of its members share the common feature of using a patterned elastomer as the stamp, mold, or mask (rather than a rigid photomask) to generate micropatterns and microstructures. Such techniques include: microcontact printing ( CP) [137], replica molding (REM) [138], microtransfer molding ( TM) [139], micromolding in capillaries (MIMIC) [140], solvent-assisted micromolding (SAMIM) [141], phase-shift photolithography [142], cast molding [143, 144], embossing [145, 146], and injection molding [147–149]. These techniques have been explored and developed by The Whitesides Group and several other groups. The key element of soft lithography is an elastomeric block with a patterned relief structure on its surface and poly(dimethylsiloxane) (PDMS) elastomers (or silicone rubbers) are used in most demonstrations. Poly(dimethylsiloxanes) have a unique combination of properties resulting from the presence of an inorganic siloxane backbone and organic methyl groups attached to silicon [150]. These liquid materials can be poured over a master having a relief structure on its surface, then easily converted into solid elastomer by curing and peeling off. Poly(dimethylsiloxane) has been widely used because they can make conformal contact with surfaces over relatively large areas and they can be released easily from rigid masters or from complex structures. The formulation, fabrication, and applications of PDMS elastomers have been extensively studied and are well-documented in the literature [150]. The master is, in turn, fabricated using microlithography techniques such as photolithography, micromachining, e-beam writing, or from available relief structures such as diffraction gratings [151], and relief structures etched in metals or Si [151, 152], or even by directly printing. Figure 6 illustrates the procedure for fabricating PDMS stamps. Microcontact printing ( CP) is a flexible, nonphotolithographic method that routinely forms patterned SAMs containing regions terminated by different chemical functionalities with submicron lateral dimensions [153–158]. An elastomeric PDMS stamp is used to transfer molecules of the “ink” to the surface of the substrate by contact. After printing, a different SAM can be formed on the relief pattern on the surface of a PDMS stamp to form patterns. However, it differs from other printing methods [159] in the use of self-assembly (especially, the use of SAMS) to form micropatterns and microstructures of various materials. Self-assembly is the spontaneous aggregation and organization of subunits (molecule or meso-scale objects) into a stable, well-defined structure via nonconvalent interactions. The information that guides the assembly is coded in the properties (e.g., topologies, shapes, and surface functionalities) of the subunits; the individual subunits will reach the final structure simply by equilibrating to the lowest energy form. Self-assembled monolayers are one of the most intensively studied examples of nonbiological self-assembling systems [161]. Self-assembled monolayers can be easily prepared by

Nanoassembly for Polymer Electronics

32 Fabrication and silanization of master l0

SiO2, Si3N4, metals, photoresists or wax Si

Pouring of PDMS over master

PDMS Si

Curing, and releasing of PDMS

PDMS h l

d

(l=0.99In)

Deformation of PDMS Pairing

PDMS

Sagging

PDMS substrate

(h>>d)

(d0 in all nonequilibrium systems. 8. Adiabatic theorem of quantum mechanics. 9. Considerations 6 and 8 taken together.

10. Gravity, as per Einstein’s theory of general relativity.

Limits on computational capabilities 1a. Lower bound on communications latency across systems of given diameter [12, 17]. 2a. Upper bound on information capacity for systems of given diameter and energy [15, 16]. 3a. Upper bound on rate of bits communicated per unit area, with given power [4, 15]. 3b. Lower bound for average random access time for a memory of given size and energy density. 4a. Upper bound on rate of useful bit operations per second in systems containing a given amount of free energy [16, 18]. 5a. Lower bound on energy wasted per irreversible bit operation, given external temperature [19]. 5b. Upper bound on rate of irreversible bit operations performed per watt of power consumption, given external temperature [4]. 6a. Upper bound on sustainable rate of irreversible bit operations within an enclosure of given area and external temperature [20]. 7a. >0 rate of energy waste per bit stored. 7b. Upper bound on number of bits stably stored, given rate of heat removal and rate of entropy generation per bit [21]. 8a. Energy waste proportional to speed in reversible bit-operations [22]. 9a. Upper bound on rate of reversible operations given system diameter, device quality, heat flux or power limits, and external temperature [21]. 10a. Upper bounds on internal energy of computers of given diameter, in turn limiting their speed and capacity [4].

Note: Many older models of computation fail to respect all of these limits and therefore are physically unrealistic, except in restricted regimes in which these constraints are far away. Constraint 1 already affects communication delays and computer performance today. Constraints 2–9 are still far from being reached today, but they are all expected to become important limiting factors over the course of the next 50 years. Larger scale analogs to these fundamental considerations are also important today. In contrast, constraint 10 requires extremely high energy densities (near black hole density) in order to become relevant and therefore is not expected to be a concern any time in the near future (the next 100 years, for example).

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253

Table 2. Summary of ways in which physics offers opportunities for more cost-efficient computing than would have been thought possible using earlier, physically realistic (but overly conservative) models of computation that ignored those opportunities. Physical observations 1. Events can occur in different places at the same time. 2. Our universe has three (and only three) usable spatial dimensions.

3. Some types of physical transformations can occur in a way that generates an amount of entropy approaching zero.

4. Quantum mechanics allows a system to be in a superposition (weighted sum) of many distinct states simultaneously.

Opportunities for computing Parallel computation; a machine can perform different operations in different devices simultaneously [23]. The number of bit locations accessible within a given time delay can scale up as quickly as (at most) the third power of the delay; this fact can help performance of some parallel algorithms, compared to the 2D or 1D cases [17, 23]. Such nearly reversible transformations can perform computations with less loss of free energy, and as a result less total cost in many situations, compared to irreversible methods. This is called reversible computing [4]. Carefully controlled systems that use superposition states can take shortcuts to arrive at solutions to some problems in many fewer steps than is known to be possible using other methods. This is called quantum computing [3].

Note: Parallelism is already heavily used at many levels, from logic circuits to wide-area distributed computing, as are architectural configurations that take some advantage of all three dimensions of space, though to a limited extent (constraint 6 in Table 1 is an important limit on three-dimensional computing today). Reversible computing and quantum computing, in contrast, are still very much in the research stage today, but they are both expected to become increasingly important for competitive computing as device sizes approach the nanoscale. Reversible computing is important because it directly alleviates constraints 5 and 6 from Table 1 (which are already relevant, in a scaled-up way, today), and quantum computing offers a totally new class of algorithms that will be important in and of themselves for certain problems, regardless of whether quantum computing turns out to be useful for general-purpose algorithms, or whether general-purpose nanocomputing itself even becomes feasible.

[25]. Fundamentally, this is because not all pairs of quantum states are totally mutually exclusive with each other. Rather, states can overlap, in a certain mathematically well-defined way, which results in the phenomenon that a system that is prepared in a certain state has a necessarily diffuse sort of presence, so to speak, a presence that extends to partly include other, sufficiently nearby states as well.

expressed in different (though still compatible) units, such as Joules per Kelvin, or kilocalories per mole per Kelvin, and are usually also reserved specifically for discussing information that happens to be entropy. Note that the total amount of information contained in any system is constant over time, so long as its maximum number of states is also. This is the case for any system with constant total energy and volume.

2.1.2. State Space The state space of a system is the set of all of its possible states. In quantum theory, a state space has the mathematical structure of a Hilbert space (a complex vector space having an inner product operation).

2.1.3. Dimensionality The dimensionality of a system’s state space is simply the number of states in a maximum-sized set of states that are all mutually exclusive (mutually orthogonal vectors). For example, the spin orientation of a single spin one-half subatomic particle has two distinguishable states and thus has a state space of dimensionality 2. Two such particles together have four distinct states, and a four-dimensional state space.

2.1.4. Amount of Information The total amount of information contained in a system is just the logarithm of the dimensionality of its state space, that is, the logarithm of its maximum number of mutually distinguishable states [26]. The base of the logarithm is arbitrary and yields a corresponding unit of information. Taking the log base 2 measures the information in units of bits (binary digits). Using the natural logarithm (base e ≈ 2.717,


), the corresponding information unit is called the nat. The physical quantities that are traditionally known as Boltzmann’s constant kB and the ideal gas constant R are simply different names for 1 nat of information, but they are usually

2.1.5. Information The specific information that is in a system (as opposed to the amount of information) is the particular choice of state, itself. We can say that the actual state of a system is the information in the system.

2.1.6. Entropy Entropy S was originally just an unnamed, abstract quantity (the ratio between heat and temperature) of unknown physical significance when its usefulness in thermodynamic calculations was first recognized by Rudolph Clausius in 1850. But entropy is now understood to simply represent that portion of the information in a system that is not redundant (correlated) with the information in other parts; that is, it cannot be derived from the other information. As such, the distinction between which pieces of physical information are effectively entropy, and which are not, depends, to some extent, on the information-processing capabilities of the entity that might be doing the deriving. A specific body of information may appear at first to be haphazard and random, but with sufficient processing, we may eventually notice an underlying order to it. Right now, the amount of information that is under explicit control within our computers is just a tiny fraction of the total physical information in the world around us,

Nanocomputers: Theoretical Models

254 and so we do not notice the effect that information processing capabilities can have on entropy. But, as computation approaches the nanoscale, an increasingly large fraction of the information inherent in the physical material making up our computer circuits will be explicitly manipulated for computational purposes, and as a result, the ultimate computational nature of entropy will start to become more and more apparent. As we will see, it turns out that the amount of entropy that a nanocomputer produces actually depends heavily on whether its design recognizes that all of the information that it deterministically computes is actually not entropy, since it was derived from other information in the machine and therefore is redundant with it. Current machine designs ignore this fact and simply discard intermediate results after they are no longer needed, irreversibly committing them to the great entropy dump in the sky. (Literally: the discarded information flows out of the machine and eventually out into space.) So, to sum up, entropy is defined as simply any and all information whose identity (as opposed to amount) happens to unknown by a given entity of interest, an entity whose interactions with the system we are concerned with describing. (This entity in question can itself be any kind of system, from a human to a logic gate.) The state of knowing can itself be defined in terms of the presence of accessible correlations between the state of the knower and the state of the system in question, but we will not get into that here.

2.1.7. Subsystems Consider a maximal set of distinguishable states of a system. If this set is partitioned into N equal-sized subsets, then the selection of one subset from the partition can be considered a part of the state of the whole system. It corresponds to a subsystem of the original system. The amount of information in the subsystem is log N . This much of the whole system’s information can be considered to be located in the subsystem. Two subsystems are independent if they partition the state space along independent (orthogonal) directions, so to speak. (This concept can be made more precise but we will not do so here.) A set of mutually independent subsystems is complete if specifying the state of each subsystem is enough to specify the state of the whole system exactly. A minimal-sized subsystem (one that cannot be further broken down into independent subsystems) is sometimes also called a degree of freedom.

2.1.8. Bit Systems A bit system or just bit is any degree of freedom that contains only 1 bit of information, that is, a bit is a partition of the state set into two equal sized parts. Note the dual usage of the word bit to refer to both a unit for an amount of information and to a system containing an amount of information that is equal to that unit. These uses should not be confused. Systems of sizes other than 1 bit can also be defined, for example bytes, words, etc.

mechanics (and all Hamiltonian mechanical theories, more generally) that the transformations corresponding to the passage of time are reversible (that is, one-to-one, invertible, bijective). The size of a given transformation can be described in terms of the average distance between old states and new states, by some appropriate metric.

2.1.10. Operations A primitive orthogonalizing operation (or just operation for short) is a transformation that maps at least one state to some new state that is distinguishable from the original state, and that cannot be composed of smaller operations. An operation is on a particular subsystem if it does not change the state of any independent subsystem. An operation on a bit system is called a bit operation (and similarly for other sizes of systems). Two operations commute if performing them in either order has the same net effect. Operations on independent systems always commute.

2.1.11. Transformation Trajectory A transformation trajectory is a transformation expressed as a sequence of (primitive orthogonalizing) operations, or pieces of such operations, operating on individual degrees of freedom (e.g., a quantum logic network Nielsen and Chuang [3]).

2.1.12. Number of Operations The total number of operations that take place along a given transformation trajectory can be defined. Planck’s constant h def (or
= h/2) can be viewed as a unit for expressing a number of operations. The unreduced Planck’s constant h represents two primitive operations (for example, a complete rotation of a particle spin through an angle of 360 ), while the reduced constant
represents a fraction 1/ of a primitive operation, for example, a rotation of a spin through an angle of only 1 radian.

2.1.13. Steps A complete parallel update step or just step is a transformation of a system that can be described by composing operations on each subsystem in some maximal, complete set of subsystems, such that the total number of operations in bitops is equal to the amount of information in bits. In other words, it is a complete overhaul of all of the state information in the system, whereas an operation on the system only potentially changes some part of the state.

2.1.14. Dynamics The dynamics of a system specifies a transformation trajectory that is followed as the system evolves in time.

2.1.9. Transformations

2.1.15. Amount of Time

A transformation is an operation on the state space, mapping each state to the corresponding state resulting from the transformation. It is a fundamental fact of quantum

Given the dynamics, the amount of time itself can be defined in terms of the number of steps taken by some fixed reference subsystem, during a given trajectory taken by the

Nanocomputers: Theoretical Models

system. Note that if the system and the reference subsystem are both taken to be just the whole universe, then time just represents the total “amount of change” in the universe, in terms of number of parallel update steps performed. (Such concepts hearken back to the relativist philosophies of Leibniz and Mach which helped inspire Einstein’s general relativity [27].)

2.1.16. Energy Now, the energy in a subsystem is the rate at which primitive operations are taking place in that subsystem, according to its dynamics. In other words, energy is activity; it is computing itself. This can be proven from basic quantum theory [16, 18, 28]. As a simple way to see this, consider any quantum system with any subsystem whose physical Hamiltonian induces any two energy eigenstates of distinct energies; call these states 0 and 2E arbitrarily. Now, if the subsystem happens to be in the state 0 + 2E, which has (expected) energy E, then the quantum time evolution given by the system’s Hamiltonian takes it to the orthogonal state 0 − 2E in time (h/4)/E. Margolus and Levitin [18] show that a system with energy E can never change to an orthogonal state any faster than this, no matter what its initial state. Therefore, we can say that any E-sized chunk of energy is, every h/4E time, “performing” the operation “If I am in this subsystem and its state is 0 + 2E, make its state 0 − 2E, otherwise


.” This transformation counts as an operation, by our definition, because it does orthogonalize some states. However, this particular operation is somewhat limited in its power, because the subsystem in question subsequently immediately cycles right back to its original state. We call this special case an inverting op (iop); its magnitude in terms of Planck’s constant is (h/4). Margolus and Levitin show that an op that instead takes a system to the next state in a repeating cycle of N states requires more iops worth of time, in fact, 2(N −1)/N times more ops, or [(N −1)/2N h. In the limit as the cycle length N approaches infinity (as it does in any complex system), the time per orthogonal transition approaches 2 iops worth, or (h/2), so we define this as the magnitude of a generic “op” as previously. Incidentally, when applying the Margolus–Levitin relation to the example of a simple freely rotating system, N can be argued to be equal to the system’s total angular momentum quantum number l plus 1, and with a few more steps, it turns out that the relation can be used to independently confirm the usual angular momentum quantization formula (L/
2 = ll + 1, much more easily than by the usual derivation found in quantum physics textbooks.

2.1.17. Heat Heat is just the energy in those subsystems whose state information is entirely unknown (entropy).

2.1.18. Temperature The temperature of a subsystem is the average rate at which complete update steps are taking place in that subsystem (i.e., the average rate of operations per bit) [28]. Note that energy divided by temperature gives the amount of information in the subsystem. This is, historically, how physical

255 information (in the form of entropy) was first noticed as an important thermodynamic quantity (by Rudolph Clausius, in 1850), even before the fact that it was really just information was understood. Note that the reciprocal of temperature is just the time required for a complete step that, on average, updates all parts of the state information, once each. This definition of temperature, in contrast to traditional ones, is general enough that it applies not just to systems in a maximum-entropy equilibrium state (all of whose information is entropy), but more generally to any system, even systems in a completely known state with no entropy, which according to traditional definitions of temperature would always be at absolute zero. However, for any system we can also identify a thermal temperature which is the average temperature of any of its subsystems whose state information is entropy, and then consistently define that the thermal temperature of a system having no entropy is zero. Thermal temperature is, then, just the traditional thermodynamic concept of temperature. But our more general temperature concept is somewhat more flexible. Note also that energy spontaneously flows from “hot” subsystems to “cold” ones, rather than vice versa, simply because the fast-changing pieces of energy in the hot system more frequently traverse the trajectories through state space that cross over the boundary between the two systems. These are enough definitions to support our later discussions in this chapter. A more complete discussion of the relationships between physics and information processing can be found in [24] (in progress). Discussions of quantum information and how it extends the classical concepts of information can be found in [3].

3. TRADITIONAL MODELS OF COMPUTATION In this section, we systematically survey a wide variety of early models of computing and identify exactly which of the limits or opportunities listed in the previous section each one fails to account for, which result in the model’s lacking one or the other of the properties of PR or UMS. Furthermore, we consider what types of costs are respected in the model. In the next section, we will present the newer models which may actually come close to being both PR and UMS for all practical purposes in the foreseeable future. Here are some contributions to real-world costs that an economically thorough cost model ought to take into account: 1. Manufacturing cost to build a machine that can perform a given computation. We may expect this to be roughly proportional to its total information capacity. However, if the machine can be reused for more than one computation, then the cost model should account for this properly (cf. item 3a below). 2. Costs that may be considered to scale roughly proportionally to the execution time of programs, but not to the machine’s manufacturing cost, such as, for example, the inconvenience cost to the user of waiting to receive a desired result.

Nanocomputers: Theoretical Models

256 3. Costs that can be expected to scale proportionally to both execution time and manufacturing cost, such as:

to spacetime cost but still does not quite hit the mark, since there are real costs even associated with those bits that are just sitting statically and not being operated on at all (hardware rental cost, maintenance cost, opportunity cost). Newer models such as VLSI theory (very large scale integrated circuits cf. [30]) address these problems somewhat by considering the hardware efficiency of algorithms, which is essentially the reciprocal of their spacetime usage. However, these models still do not usually integrate the cost of energy into the analysis in a way that treats it as somewhat independent from spacetime cost, which it is, as we will see. Table 3 summarizes how a variety of existing theoretical models of computation fare with respect to the fundamental limits and opportunities discussed in Section 2, and the costs discussed previously. A discussion follows.

a. Hardware rental cost, or essentially manufacturing cost amortized per unit time, given some fixed expected lifetime for the machine. b. Maintenance and operation costs for the machine per unit time, including cost of energy used by components that are operating at constant power levels. c. Opportunity cost foregone by not applying the machine’s capacity toward some alternative useful purpose. 4. Total cost of energy spent for the computation. We list this separately from item 3b because later we will see that there are significant components of energy that are not necessarily proportional to spacetime usage.

3.1. Turing Machines

Traditional computational complexity theory (cf. [29]) considers purely time-proportional costs like item 2, simplified to just the total number of discrete time-steps (clock ticks) performed (i.e., assuming a fixed rate of steps per unit time), and dubbed time complexity. It also considers a rough measure of manufacturing cost, in the form of the total number of bits of storage required to perform the computation and calls this space complexity. However, most work in complexity theory does not combine the two in the natural way suggested by items 2b–2e, which is that real costs are usually proportional to both space and time, or in other words to the spacetime utilized, that is to say, the cost to rent the required amount of hardware for the amount of time needed to perform the computation, and to other costs that can be assumed to scale proportionally to this quantity, such as maintenance cost, opportunity cost, and energy used (typically). Some cost models in complexity theory count the number of fixed-size computational operations that are performed, rather than the number of parallel steps. This comes closer

The Turing machine [31] was the first universal, physically evocative (as opposed to totally abstract and formal) model of computation. It has a single fixed-size processor (the head) and a memory laid out in one dimension that is accessed in serial fashion (the tape). The Turing machine model does not violate any of the fundamental physical limits on information processing, and therefore it is physically realistic. However, since a Turing machine has only a single, fixedsize “processor” (the tape head), it does not leverage the possibility of parallelism. Multitape and multihead Turing machines provide limited parallelism, but true parallelism in the model requires that the number of processors must be scaled up in proportion to the information capacity of the machine. Turing machine models usually do not try to do this, but later we will see other models that do. It is possible to analyze space and time costs in a Turing machine model, but the joint spacetime cost is not usually a concern, since the model has such understated efficiency in any case. Due to its drastic suboptimality, the Turing

Table 3. We can compare various models of computation as to which fundamental physical limits they violate (see Table 1), which opportunities for more efficient computing they leverage (Table 2), and which aspects of cost they take into account. Opportunities leveraged

Fundamental limits violated Model Turing machine [31] RAM machine [32] PRAMs, etc. 1D cellular automata [33] 2D cellular automata [33] 3D cellular automata [33] Reversible logic networks [34] Quantum logic networks [35] Reversible 3D mesh [4] Quantum R3M [4]

1

2

3

4

5

6

7

8

9

10

× (b) × (b)

× × (b) × (b)

× ×

× × ×

1

2

✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓

1   1 2 3   2–3 2–3

3

✓ ✓ ✓ ✓

Costs considered 4

✓ ✓

1

2

3

✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓

✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓

1/2 1/2 1/2 ✓ ✓ ✓ ✓ ✓ ✓ ✓

4

✓ ✓ ✓

Note: Opportunity #2 gives the number of dimensions explicitly or implicitly assumed by the model; three or more is unrealistic, two or less is underambitious. Cost measure #3 (spacetime) is denoted “half-way considered” if spacetime cost could be easily measured in the model but is typically ignored instead. Note that the quantum reversible 3D mesh model described in Section 6 (first introduced in [4]) strictly dominates all earlier models in realism and comprehensiveness, so long as gravity (limit #10) is not a concern, which we can expect to remain true for very long time. (This limit would only become relevant if/when we come to build computer systems of near black-hole density, e.g., by building them out of several suns’ worth of matter, or alternatively by somehow achieving an average device-pitch scale nearly as small as the Planck length scale of fundamental particles. Both of these possibilities seem extremely distant at present, to say the least.)

Nanocomputers: Theoretical Models

machine and related models are primarily only suitable for the following purposes: • Determining whether a desired class of computations is possible to do at all, even given unlimited resources (its computability). • Proving that other models of computation are universal, by showing that they are capable of simulating a Turing machine. • Determining the time required to perform a computation to a very rough degree of accuracy, that is, to within a polynomial factor (a factor growing as ∼nk where n is the size of the input data set and k is any constant). The strong Church’s thesis [36] is the hypothesis that Turing machines are satisfactory for this purpose. However, results in quantum computing suggest strongly that ordinary nonquantum Turing machines may actually overstate the physically required minimum time to solve some problems by exponentially large factors (that is, factors growing roughly like en ) [3], in which case the strong Church’s thesis would be false. • Determining the space (measured as number of bits) required to perform a computation within a constant factor. These concerns are generic ones in computing and are not tied to nanocomputing specifically but can be used in that context as well. However, if one wishes a more precise model of costs to perform a desired computation than can be provided by Turing machines, one must turn to other models.

257 worse than this, because the time to access today’s commercial memory technologies is much greater than the speedof-light travel time.) And, when considering a wide-area distributed computation, communication halfway around the Earth (i.e., ∼20,000 km) requires at least 200 million clock cycles! Delays like these can be worked around somewhat by using architectural latency hiding techniques in processor architectures and parallel algorithms, but only to a very limited extent [12, 37]. Furthermore, these problems are only going to get worse as clock speeds continue to increase. Communication time is no longer insignificant, except for the restricted class of parallel computations that require only very infrequent communication between processors, or for serial computations that require only small amounts of memory. For more general purposes, the RAM-type model is no longer tenable. Slightly more realistic than the RAM are models that explicitly take communication time into account, to some extent, by describing a network of processing nodes or logic gates that pass information to each other along explicit communication links. However, depending on the topology of the interconnection network, these models may not be physically realistic either. Binary trees, fat trees, hypercubes, and butterfly or omega networks are all examples of interconnection patterns in which the number of locations accessible within n hops grows much faster than n3 , and therefore, these networks are impossible to implement with unit-time hops above a certain scale within ordinary 3D space. The only scalable networks in 3D space are the locally connected or mesh-type networks, and subgraphs of these [12, 17].

3.2. RAM Machine

3.3. Cellular Automata

One limitation of the Turing machine was that since the memory tape was laid out serially in only one dimension, merely traversing it to arrive at a desired item consumed a large portion of the machine’s time. For early electronic memories, in contrast, the time required for a signal to traverse the distance through the machine was negligible in comparison to the time taken to perform logic operations. Therefore, it was useful to model memory access as requiring only a single step, regardless of the physical distance to the desired memory location. This fast memory access model is the defining characteristic of the RAM or random-access machine model of computation [32]. The RAM model is occasionally called the von Neumann machine model, after the inventor of architectures having a central processing unit (CPU) with a separate random-access memory for storing programs and data. The RAM model is also sometimes extended to a parallel model called the PRAM. Today, however, individual transistors have become so fast that the speed-of-light travel time across an ordinarysized machine is becoming a significant limiting factor on the time required to access memory, especially for computations requiring large-scale supercomputers having large numbers of processors. For example, at the 3 GHz processor clock speeds that are now routinely available in commercial off-the-shelf microprocessors, light can only travel 10 cm in one clock cycle, so the memory accessible within a round-trip latency of one cycle is limited to, at most, the amount that will fit within a 5-cm radius sphere centered on the processor. (In practice, at present, the situation is even

Cellular automaton (CA) models, also originally due to von Neumann [33], improve upon theRAM-type or abstractnetwork model in that they explicitly recognize the constraints imposed by communication delays through ordinary Euclidean space. CAs are essentially equivalent to meshinterconnected networks of fixed-capacity processors. The one-dimensional and two-dimensional CA variations are entirely physically realistic, and the 2D CA can be used as a starting point for developing a more detailed theoretical or engineering model of today’s planar circuits, such as, for example, the VLSI theory of Leiserson [30]. However, ordinary CAs break down physically when one tries to extend them to three dimensions, because the entropy that is inevitably produced by irreversible operations within a 3D volume cannot escape quickly enough through the 2D surface. To circumvent this constraint while still making some use of the third dimension requires avoiding entropy production using reversible models, such as we will discuss in Section 4.1. These models can be shown to have better cost-efficiency scaling than any physically possible nonreversible models, even when taking the overheads associated with reversibility into account [4]. Finally, all of these models, in their traditional form, miss the opportunity afforded by quantum mechanics of allowing machine states that are superpositions (weighted combinations) of many possible states, within a single piece of hardware, which apparently opens up drastic shortcuts to the solution of at least certain specialized types of problems. We will discuss quantum models further in Section 4.2.

258

4. NEW MODELS OF NANOCOMPUTERS Computer technology already is forced to contend with the limits to communication delays imposed by the speed-oflight limit. Over the next 20–50 years, we can expect the limits that thermodynamics and quantum mechanics place on bit energies, sizes, and bit-device speeds to become plainly manifest as well. Other fundamental constraints, such as the one that gravity imposes on machine size (namely, that any sufficiently large 3D computer with a fixed energy density will collapse under its own gravity to form a black hole) are still very far away (probably many centuries) from being relevant. So what we want is to have a model of computation that is physically realistic, at least with respect to the relatively near-term constraints, and that also provides a cost efficiency that scales as well as possible with increasing computation size, for all classes of computations. We can argue that there is an existence proof that such a model must be possible, for the laws of physics themselves comprise such a model, when looked at from a computational perspective. However, raw physics does not provide a very convenient programming model, so our task is to develop a higher level programming model that scales as well as possible, while also providing a relatively easy-to-understand, comprehensible framework for programming. In Sections 4.1 and 4.2 we survey a couple of new classes of models which attempt to make progress toward this goal, namely the reversible and quantum models.

4.1. Reversible Computing The fundamental insight of reversible computing is that there is absolutely nothing about fundamental physics that in any way requires that the free energy that goes into bit manipulations must be discarded after each operation, in the form of waste heat. This is because bits that have been computed are not (yet) entropy, because they are derived from, and thus correlated with, other bits that are present in the machine. Present-day computers constantly discard temporary results that are no longer needed, in order to free up storage space for newer information. This act of wanton erasure causes the old information and energy associated with those bits to be relegated to the degraded status of effectively becoming entropy and heat, respectively. Once this is done, it cannot be undone, since the second law of thermodynamics tells us that entropy can never be destroyed. Information erasure is irreversible [19]. However, we can avoid this act of “trashification” of bits by instead recycling bits that are no longer needed, by taking advantage of their redundancy with other bits present in the machine to restore the unneeded bits to a standard state (say “0” for an empty memory cell), while leaving the bit’s associated energy (or most of it, anyway) in the machine, in the form of free energy which can go on to perform another useful computational operation [38].

4.1.1. Adiabatic Principle Of course, no machine is perfect, so even in a reversible machine, some of the kinetic energy associated with the performance of each operation goes astray. Such events are

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called adiabatic losses. The detailed accounting of adiabatic losses can be proven from basic quantum theory as in the adiabatic theorem [39], which tells us that as a system proceeds along a given trajectory under the influence of slowly changing externally applied forces, the total energy dissipation is proportional to the speed with which the external forces change; however, rather than getting into the technical mathematical details of this theorem here, we discuss some more intuitive ways to understand it. First, the amount of adiabatic loss is roughly proportional to the number of elementary quantum operations performed, and thus to the energy involved in carrying out transition times the time over which it is performed, divided by a technology-dependent constant that specifies the quantum quality factor of the system, that is, how many quantum operations can be performed on average without an error (decoherence event). As the speed of carrying out a given transformation is decreased, the kinetic energy associated with the system’s motion along the desired trajectory through configuration space decreases quadratically (in proportion to the square of the speed, since as we all know, kinetic energy is 21 mv2 ), and so the total adiabatic losses over the entire motion decrease in inverse proportion to the time taken for the transformation. However, when the kinetic energy involved in carrying out transformations decreases to a level that is close to the static bit energies themselves, further decreases in speed do not help, because entropy generation from degradation of the static bits comes to dominate the total dissipation. That is, some of the energy whose job it is to maintain the very structure of the machine, and/or the state of its stored information, also leaks out, in a continual slow departure from the desired configuration (this is called decay), which must be periodically repaired using correction mechanisms if the computation is to continue indefinitely. For example, all of the following phenomena can be considered as simply different examples of decay processes: • Charge leakage from DRAM (dynamic RAM) cells, requiring periodic refreshing. • Bit errors due to thermal noise, cosmic ray impacts, etc., requiring the use of error-correction algorithms. • Decoherence of quantum bits from various unwanted modes of interaction with a noisy, uncontrolled environment, requiring quantum error correction. • Gradual diffusion of the atoms of the devices into each other (e.g., from electromigration), leading to eventual failure requiring remanufacture and replacement of all or part of the machine. All of these kinds of decay processes incur a cost in terms of free energy (to periodically correct errors, or to repair or replace the machine) that is proportional to the spacetime usage, or space to hold bits, times time occupied, of the computation. This spacetime usage cannot be adequately reduced to time alone, space alone, or even to the number of logical operations alone, since, depending on the computation to be performed, not all bits may be actively manipulated on every time step, and so the spacetime usage may not be simply proportional to the number of operations.

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Adiabatic (or kinetic) losses, on the other hand, do effectively count the number of operations performed, but these are quantum operations, whose number is not necessarily directly proportional to the number of classical bit operations, even when the algorithm being carried out is a classical one. This is because the number of quantum operations involved in carrying out a given classical bit operation increases in proportion to the speed with which the desired trajectory through state space is followed. There are two ways to see this. First, the de Broglie wavelength  of the “particle” wave packet representing the system’s state in configuration space is inversely proportional to its momentum, according to the formula  = h/p. Momentum is proportional to velocity, so following a given trajectory will involve a larger number of distinct transitions of the system’s wave packet (i.e., translations through about a wavelength) the faster it is done; each of these can be considered a orthogonalizing quantum operation. Second, recall that kinetic energy increases with the square of velocity, whereas the frequency or quickness with which a fixed-length classical trajectory is followed increases only linearly with velocity. Therefore, the interpretation of energy as the rate of quantum operations requires that the number of operations on a given trajectory must increase with the speed at which that trajectory is followed. With this interpretation, the technology-dependent coefficients (such as frictional coefficients, etc.) that express the energy dissipation per unit quickness for an adiabatic process can be seen as simply giving the decoherence times for those qubits whose transitioning corresponds to kinetic energy. The decoherence of qubits carrying energy causes the dissipation of that energy. The adiabatic principle (which states that the total energy dissipation of an adiabatic process is proportional to its speed) can be derived from the postulate that a fixed fraction of kinetic energy is dissipated each time unit [22]. Adiabatic coefficients are therefore lower bounded by the decoherence rates that can be achieved for qubits whose transitions carry us from one logical machine state to another. The adiabatic principle also tells us that whenever logical transitions are carried out by a process that uses multiple quantum operations (in place of a single one), we are doing extra unnecessary work, and thus generating more entropy (and energy dissipation) than necessary. This happens whenever we try to do a process faster than strictly necessary. As a simple example, consider a hollow cylinder of radius r and mass m, rotating with rim velocity v. Let us consider a rotation of this wheel to carry out a “cycle” in our computer, a complete transition from one logical state to another. A simple calculation shows that the number of quantum orthogonal transitions (angle /2 rotations of the state vector in Hilbert space) that occur during one complete rotation is given by 4L/
, where L = mvr is the wheel’s angular momentum about its axis, and
is Planck’s (reduced) constant, h/2. Total angular momentum for any system is quantized, and the minimum possible rotation speed occurs when L =
. At this speed, the kinetic energy is just enough to carry out one quantum logic operation (an iop, for example, a bit toggle) per quarter-cycle. At this rate, the rotation of the wheel through a quarter-turn is, from a quantum mechanical

259 perspective, a bit flip. The decoherence rate of this spin qubit determines the rate at which the wheel’s energy dissipates. In contrast, if the wheel were spun faster (L were higher), there would be proportionally more distinct rotational positions around 1 complete rotation, and the total energy is quadratically higher, so the average energy per location (or the generalized temperature) is proportional to L. With order L more locations, each carrying order L more energy, a fixed decoherence rate per location yields a quadratically higher total rate of energy dissipation, and thus a linearly higher amount of entropy generation per complete cycle. This is an example of why the dissipation of an adiabatic process is proportional to the speed at which it is carried out. Simply put, a faster process has quadratically greater kinetic energy and so, given a fixed mean-free time or decoherence time for that energy, energy dissipates to heat at a quadratically faster rate, for linearly more energy dissipation during the time of the operation. The minimum energy dissipation of an adiabatic process occurs when the speed of the transition is slow enough that the dissipation of kinetic energy is not much greater than the dissipation of static (potential) energy. If the decoherence rates are comparable for the two types of energy, then the kinetic energy for bit change should be of the same order as the static energy in the bits themselves, as in our previous wheel example. This makes sense, since if energy is computing, we want as much as possible of our available energy to be actively engaged in carrying out transitions at all times. Having a kinetic energy that is much larger than bit energy would mean that there was a lot of extra energy in the system that was not directly occupied in carrying out bit transitions. In such cases, a more direct and economical design would be preferable. This is what a good optimized adiabatic design attempts to accomplish.

4.1.2. Device Implementation Technologies Reversible, adiabatic logical mechanisms can be implemented in a wide variety of physical systems; indeed, nearly every type of bit-device technology that has been proposed (whether electrical, mechanical, or chemical) admits some sort of reversible variant. Virtually all of these technologies can be usefully characterized in terms of the bistable potential-well paradigm introduced by Landauer [19]. In this framework, a bit is encoded by a physical system having two distinct meta-stable states. The relative energies of these states, and the height of a potential barrier between them, is adjustable by interactions with nearby bits. Figure 1 illustrates this model. Irreversible erasure of a bit in this model corresponds to lowering a potential-energy barrier (e.g., by turning on a transistor between two circuit nodes) regardless of the state of the bit under consideration (say, the voltage on one of the nodes). Due to the energy difference between biased states, this in general leads to large, nonadiabatic losses (thick red arrows in the diagram), which reversible logic must avoid. Even the lowering of a barrier between two states of equal energy still creates at least 1 bit’s worth of entropy, even when done infinitesimally slowly, if the state of the bit was not already entropy (medium red arrows).

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260 Possible Adiabatic Transitions (Ignoring superposition states.)

1

leak

1

1

leak

0

0

leak

0

leak

Barrier Height

0

N

“1” states “0” states

1

Direction of Bias Force

Figure 1. Possible adiabatic (green) and nonadiabatic (red) transitions between states of any device technology that provides a generic bistable potential well. Each box indicates a different abstract configuration of the system. Within each box, the x axis is some continuous state variable in the system (such as the position of a mechanical component or a charge packet), and the y axis is potential energy for the given value of the state variable. Small black horizontal lines show the energy level occupied (or the surface of a set of occupied levels). The x position of the occupied state encodes the value of the bit. Device configurations encoding logical values of 0, 1, and an in-between neutral level “N” are shown. Thick arrows between configurations indicate nonadiabatic active transitions, while thin arrows indicate possible leakage pathways (activated thermally or by tunneling). Note the lower three boxes show the potential barrier lowered, while the upper three show it raised. The left–right position of the box in the diagram corresponds roughly to the direction of an external force (e.g., from a neighboring device) that is applied to the system.

Of course, even in reversible logic systems, we must still contend with the smaller losses due to thermally excited transitions or tunneling of the bit system’s state over the potential energy barriers (thin red arrows labeled “leak”) Now, a number of different reversible logical and storage mechanisms are possible within this single framework. We can categorize these as follows: 1. Input-bias, clocked-barrier latching logic (type I): In this method, the device barriers are initially lowered, and input data to the device apply a bias, pulling the device toward a specific bit value. Optionally in this stage, forces applied by several input bits can be combined together to carry out majority logic (or switch gates can be used to do logic, as in [40]). Next, a timing signal raises the barrier between the two states. This step can also serve to amplify and restore the input signal. After the barrier is raised, the input data can be removed, and the computed stated of the device remains stored. Later, the stored data can be reversibly unlatched, if desired, by the reverse sequence of steps. Specific physical examples of the type I technique include the adiabatic quantum dot cellular automaton of Lent and Tougaw [41], the complementary metaloxide semiconductor (CMOS) transmission-gate latch of Younis and Knight [42], the reversible rod logic latch of Drexler [43], the reversible superconducting Parametric Quantron logic of Likharev [44], the mechanical buckled logic of Merkle [45], and the electronic helical logic of Merkle and Drexler [40]. 2. Input-barrier, clocked-bias retractile logic (type II): In this technique, the input data, rather than applying a bias force, conditionally raise or lower the potential energy

barrier. Arbitrary AND/OR logic can be done in this stage, by using series/parallel combinations of several barriers along the path between bit states. Then, a timing signal unconditionally applies the bias force, which either pushes the system to a new state, or not (depending on whether the barrier between states was raised). Since the output state is not inherently latched by this timing signal, the input signal cannot then be removed (if this would lower the barriers) until other “downstream” devices have either latched a copy of the output or have finished using it. So these gates cannot by themselves perform sequential logic (e.g., memory, networks with feedback, or pipelined logic), although they can be used in combination with latching gates to do so. Examples of the type II technique are Hall’s retractile electronic logic [46], the nonlatching portions of Younis and Knight’s CMOS SCRL gates [42], and Drexler’s rod logic interlocks [47]. 3. Input-barrier, clocked-bias latching logic (type III): Finally, from Figure 1, one can immediately see that there is a third possibility, one that has not previously been considered. It is more efficient than either (1) or (2), in the sense that it combines AND/OR logic with latching in a single operation. In this scheme, as with the previous one, the input signal sets the barrier height, doing logic in series/parallel networks, and then a timing signal applies an unconditional bias force. But we note that the input signal can now be immediately removed, if in doing so we restore the barriers to a null state that consists of barriers unconditionally raised. Then, when the bias timing signal is removed, the output bit remains latched in to its new state. The bit can be unlatched using the reverse sequence along the same path, or a different one. This general method for doing reversible logic apparently has not been previously described in the literature, but we have developed a straightforward technique for implementing this model in standard CMOS technology. It is significantly more efficient than previous truly adiabatic logic families, by several different metrics. The bistable potential-well model is basically one in which we model one subsystem (the output bit) as being subject to a time-varying Hamiltonian (essentially, a matrix representing the forces on the system) that is provided by the device’s interaction with some other subsystems (the input and clock bits). However, one must stay aware that a closer look at the situation would reveal that there is really just a single system that evolves according to an actual underlying Hamiltonian which is time-independent, being itself just an expression of the unchanging laws of physics. So, in general, one cannot ignore the back-reaction of the controlled system (the output bit) on the system that is doing the controlling (the input bit), especially if we want to be accurate about the total energy consumption in the entire system, including the controlling system, which in practice is just some other logic element within the computer. For example, it is easy to design adiabatic gates using transistors that dissipate almost no energy internally, whose transitions are

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controlled by some large external signal generator. But it is much harder to integrate the signal generator and design a complete, self-timed system that is nevertheless almost reversible. For this reason, some authors have unjustly criticized the concept of adiabatic circuits in general, solely on the basis of the poor quality of the particular signal generators that were assumed to be used in the author’s particular analysis. But the failure of a single short-sighted designer to imagine an efficient resonator does not mean that such a thing is impossible, or that alternative designs that avoid these timing-system inefficiencies are impossible to build. For example, Bennett [2] illustrated a proof-of-concept mechanical model of a self-contained reversible computer by doing away with directed kinetic energy entirely, and instead letting the system take a random walk, forward or backward, along its nonbranching path through configuration space. Unfortunately, doing away with kinetic energy entirely is not such a good thing, because random walks are very slow; they take expected time that increases quadratically with the distance traveled. (Chemical computing techniques in which communication relies primarily on molecular diffusion in solution also have performance problems, for the same reason.) Thus, we would prefer to stick with designs in which the system does have a substantial net kinetic energy and momentum along the “forward” direction of its motion through configuration space, while yet dissipating ≪kT energy per logic operation performed, due to a high quality factor for the individual logic interactions. We call such trajectories ballistic. I emphasize that we still know of absolutely no fundamental reasons why ballistic reversible computation cannot be done, and with arbitrarily high quality factors. A series of increasingly realistic models have been proposed that illustrate steps along the path toward actually doing this. Fredkin and Toffoli [34] described a ballistic “billiard ball model” (BBM) of reversible computation based on collisions between idealized elastic spheres. Their original model contained chaotic instabilities, although these can be easily fixed by confining the balls to travel along valleys in configuration space, and by keeping them time-synchronized through a few additional mechanical interactions. A concrete example of an electronic model similar to the BBM that avoids these instability problems entirely is described in [40]. Puremechanical equivalents of the same synchronization mechanism are also straightforward to design. Now, the BBM was primarily just a classical model. Richard Feynman and Norm Margolus made some initial theoretical progress in devising a totally quantum-mechanical model of ballistic reversible computation, Feynman with a serial model [48], and Margolus with a self-synchronized parallel model [49]. However, Margolus’ model was restricted to allowing parallelism in only one dimension, that is, with only a linear chain of active processors at any time. As of this writing, we do not yet have an explicit, fully detailed, quantum physical model of totally three-dimensional parallel reversible computing. But we know that it must be possible, because we can straightforwardly design simple classical-mechanical models that already do the job (essentially, reversible “clockwork”) and that do not suffer from any instability or timing-system inefficiency problems. Since these models are manifestly physically realizable (obviously

261 buildable, once you have conceived them), and since all real mechanical systems are, at root, quantum mechanical, a detailed quantum-mechanical fleshing out of these classical-mechanical models, if mapped to the nanoscale, would fit the bill. But significant work is still needed to actually do this translation. Finally, in general, we should not assume that the best reversible designs in the long run necessarily must be based on the adiabatic bistable-potential-well-type model, which may be unnecessarily restrictive. A more general sort of model of reversible computing consists simply of a dynamic quantum state of the machine’s “moving parts” (which may be just spinning electrons) that evolves autonomously according to its own built-in physical interactions between its various subparts. As long as the evolution is highly coherent (almost unitary), and we can accurately keep track of how the quantum state evolves over time, the dissipation will be kept small. The devil is in figuring out the details of how to build a quantum system whose built-in, internal physical interactions and natural evolution will automatically carry out the desired functions of logic, communication, and synchronization, without needing a full irreversible reset of the state upon each operation. But as I stated earlier, we can be confident that this is possible, because we can devise simple mechanical models that already do the job. Our goal is just to translate these models to smaller sized and higher frequency physical implementations.

4.1.3. Algorithmic Issues For now, we take it as given that we will eventually be able to build bit devices that can operate with a high degree of thermodynamic reversibility (i.e., very small entropy generation per operation), and that the details of ballistic signal propagation and timing synchronization can also be worked out. What, then, can we do with these devices? One key constraint is that physically reversible devices are necessarily also logically reversible; that is, they perform invertible (one-to-one, bijective) transformations of the (local) logical machine state. Debunking Some Misunderstandings First, the preceding statement (physical reversibility requires logical reversibility) has occasionally been questioned by various authors, due to some misunderstanding either of physics, or of the meaning of the statement, but it is not really open to question! It is absolutely as certain as our most certain knowledge about physical law. The reversibility of physics (which follows from the unitarity of quantum mechanics, or from the mathematical form of all Hamiltonian dynamical systems in general) guarantees that physics is reverse-deterministic, that is, that a given (pure, quantum) state of a closed system can only have been arrived at along a specific, unique trajectory. Given this fact, any time we have a mechanism that unconditionally erases a bit (i.e., maps both of two distinct initial logical states onto a single final logical state), without regard to any other knowledge that may be correlated to that bit’s state, there must be a compensatory splitting of some other adjoining system from one state into two distinct states, to carry off the “erased” information, so that no merging of possible state trajectories happens in the system overall. If the state distinction happens to become lost

262 somewhere, then it is, by definition, entropy. If the erased bit was itself not already entropy before the erasure, then this entropy is furthermore newly generated entropy, and the mechanism is then by definition not physically reversible. In contrast, if the state information remains explicitly present in the logical state that is transformed in the operation, then the mechanism is by definition logically reversible. If you think that you have found a way to unconditionally erase known logical bits without generating new entropy (without having also disproved quantum mechanics in the process), then check your work again, a lot more carefully! Such a device would be exactly equivalent to the longdebunked perpetual motion machine [50]. I will personally stake my reputation on your having made a mistake somewhere. For example, did you analyze the “erasure” of a logical bit that was uncorrelated with any other bits and thus was already entropy? No new entropy need be generated in that case. Or did you just reversibly decrement a long counter until it was zero, but you forgot that an exactly equal amount of timing information about when you finished counting, relative to other subsystems, is still present and still must be got rid of in order to interact with outside systems? Or did you rely on an exponential number of high-energy states all “decaying” to a single slightly lower energy state, while forgetting that the exponentially larger number of higher energy states and slow decay rate will mean that there is an exactly equal chance to go the other way and make a transition to occupy the high-energy state instead, excited by thermal noise? These issues are rather subtle, and it is easy to make mistakes when proposing a complicated new mechanism. In contrast, the impossibility proof from basic, uncontroversial axioms of physics is straightforward and easily verified to be correct. If you want to erase logical bits without generating entropy, you will first have to go back and show why most of the basic physics that has been learned in the last 150 years (such as statistical mechanics and quantum mechanics) must be totally wrong, despite agreeing perfectly with all our myriad experiments! Algorithmic Overheads Now, those misconceptions aside, let us take a clear look at the algorithmic issues that result from the need for logical reversibility. (These issues apply equally whether the logic of the particular computation is implemented in hardware or in software.) Apparently, the requirement of logical reversibility imposes a nontrivial constraint on the types of algorithms we can carry out. Fortunately, it turns out that any desired computation can be emulated by a reversible one [38], although apparently with some algorithmic overheads, that is, with some increases in the number of bits or ops required to carry out a given computation. First, some history: Rolf Landauer of IBM realized, as early as 1961 [19], that information-“destroying” operations such as bit erasure, destructive (in-place) AND, and so forth can be replaced by analogous reversible operations that just move the “erased” information somewhere else rather than really erasing it. This idea is now known as a Landauer embedding of an irreversible computation into a reversible one. But, at the time, Landauer thought this approach would pointlessly lead to an accumulation of unwanted information in storage that would still have to be irreversibly erased

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eventually. In 1963, Yves Lecerf [51], working independently on a related group theory problem, reinvented the Landauer embedding and furthermore noted that the intermediate results could also be reversibly uncomputed by undoing the original computation. We call this idea Lecerf reversal. In 1973, Charles Bennett independently rediscovered Lecerf reversal [38], along with the observation that desired results could be reversibly copied (known as a Bennett copy) before undoing the computation. Simple as it was, this was the final key insight showing that computation did not necessarily require entropy generation, as it revealed that a given area of working storage could indeed be reversibly reused for multiple computations that produce useful results. All of these ideas were independently rediscovered in a Boolean logic circuit context by Ed Fredkin and Tom Toffoli during their work on information mechanics at MIT in the late 1970s [34]. Unfortunately, although the extra storage taken up by the Landauer embedding can be reused, it does still at least temporarily take up space in the computation and thus contributes to economic spacetime costs. Even this temporary usage was shown not to be technically necessary by Lange et al. [52], who showed how to compute reversibly in general using virtually no extra space, essentially by iterating through all possible machine histories. (The technique is very similar to earlier complexity theory proofs showing that deterministic machines can simulate nondeterministic machines in-place, using the same space [53].) But unfortunately, the Lange et al. technique is not at all close to being practical, as it generally requires taking an exponentially longer time to do the computation. Today, we know of a continuous spectrum of possible trade-offs between algorithmic space and time overheads for doing reversible computation. In 1989, Bennett described a space of trade-offs between his original technique and a somewhat more space-efficient one [54], and later work by Williams [55] and Burhman et al. [56] showed some ways to extrapolate between the Bennett-89 approach and the Lange et al. one. However, these latter approaches are apparently not significantly more efficient in terms of overall spacetime cost than the older Bennett-89 one. It is, however, possible to reduce the spacetime cost of the Bennett-89 algorithm by simply increasing its degree of parallelization (activity factor, hardware efficiency) so that less time is spent waiting for various subcomputations. But this apparently gives only a small improvement also. At present, we do not know how to reversibly emulate arbitrary computations on reversible machines without, at least, a small polynomial amount of spacetime overhead. It has been conjectured that we cannot do better than this in general, but attempts (such as [57]) at a rigorous proof of this conjecture have so far been inconclusive. So, as far as we know right now, it is conceivable that better algorithms may yet be discovered. Certainly, we know that much more efficient algorithms do exist for many specific computations, sometimes with no overhead at all for reversible operation [4]. But Bennett’s algorithm and its variations are the best we can do currently for arbitrary computations. Given the apparent algorithmic inefficiencies of reversible computing at some problems, as well as the limited quality factor of reversible devices even for ideal problems, it does not presently make sense to do all computations in a totally

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reversible fashion. Instead, the computation should be broken into pieces that are internally done reversibly, but with occasional irreversible logical operations in between them. The size of the reversible pieces should be chosen so as to maximize the overall cost efficiency, taking into account both the algorithmic overheads and the energy savings, while optimizing the parameters of the emulation algorithms used. Examples of how to do this via analytical and numerical methods are illustrated in [5, 21, 58]. That work shows that reversible computing remains advantageous for overall cost efficiency, despite its algorithmic overheads, even for worstcase types of computations, for which we do not know of any better reversible algorithm than Bennett’s. In cases where the reversible devices have a high quantum quality q, it turns out to make sense to do a substantial amount of reversible computing in between irreversible operations. Since the most efficient use of these reversible computing resources may, in some cases, call for a handoptimized reversible algorithm, the architecture and programming model should best include directives that directly expose the underlying reversibility of the hardware to the programmer, so that the programmer (as algorithm designer) can perform such optimizations [4]. In other words, the algorithm designer should be able to write code that the architecture guarantees will be run reversibly, with no unnecessary overheads. Some examples of architectures and programming languages that allow for this can be found in [4, 59, 60]. Can the machine’s potential reversibility be totally hidden from the programmer while still preserving asymptotic efficiency? Apparently not. This is because the best reversible algorithm for a given problem may in general have a very different form than the best irreversible algorithm [4]. So we cannot count on the compiler to automatically map irreversible code to the best reversible code, at least, given any compiler technology short of a very smart general-purpose artificial intelligence which we could rely on to invent optimal reversible algorithms for us. How hard is it to program in reversible languages? At first it seems a little bit strange, but I can attest from my own experience that one can very quickly become used to it. It turns out that most traditional programming concepts can be mapped straightforwardly to corresponding reversible language constructs, with little modification. I have little doubt that shortly after reversibility begins to confer significant benefits to the cost efficiency of general-purpose computation, large numbers of programmers, compiler writers, etc. will rush to acquire the new skills that will be needed to harness this new domain, of computing at the edge of physics. However, even reversible computing does not yet harness all of the potential computational power offered by physics. For that, we must turn our sights a bit further beyond the reversible paradigm, toward quantum computing.

4.2. Quantum Computing 4.2.1. Generalizing Classical Computing Concepts to Match Quantum Reality The core fact of quantum mechanics is that not all of the conceivable states of a physical system are actually operationally distinguishable from each other. However, in the

263 past, computer scientists artificially constrained our notion of what a computation fundamentally is, by insisting that a computation be a trajectory made up of primitive operations, each of which takes any given legal state of the machine and changes it (if at all) to a state that is required to be operationally distinguishable from the original state (at least, with very high probability). For example, a traditional Boolean NOT gate, or logical inverter, is designed to either leave its output node unchanged (if its input remains the same), or to change its output to a new state that is clearly distinct from what it was previously. But really this distinguishability restriction on operations was an extra restriction that was, in a sense, arbitrarily imposed by early computer designers, because this type of operation is not the only type that exists in quantum mechanics. For example, when a subatomic particle’s spin is rotated 180 around its x axis, if the spin vector was originally pointing up (+z), it will afterward be pointing down (−z), and this state is completely distinct from the up state. But if the spin was originally pointing at an angle halfway between the x and z axes, then this operation will rotate it to an angle that is only 90 away from its original angle (namely, halfway between the x and z axes). This spin state is not reliably distinguishable from the original. Although it is at right angles to the original state in 3D space, its state vector is not orthogonal to the original state in the Hilbert space of possible quantum state vectors. Orthogonality in Hilbert space is the technical quantum-mechanical requirement for distinguishability of states. Thus, the operation “rotate a spin by 180 around a given axis” does not change all states by orthogonalizing amounts, only some of them. What if we allow a computation to be composed of operations that do not necessarily change all legal states by an orthogonalizing amount? Then the new state after the operation, although possibly different from the original state, will not necessarily be reliably observationally distinguishable from it. However, if we do not try to observe the state but instead just let it continue to be processed by subsequent operations in the machine, then this lack of distinguishability is not necessarily a concern. It can simply be the situation that is intended. In essence, by loosening our requirement that every state of the computation be distinguishable from the previous one, we open up the possibility of performing new types of operations, and thus traversing new kinds of trajectories through state space, ones that were not previously considered to be legal computations. Does this new possibility confer additional computational power on the model? We cannot prove that it does, but it is currently strongly believed to. Why? Because specific, well-defined algorithms have been found that use these new types of trajectories to perform certain kinds of computational tasks using exponentially fewer operations than with the best classical algorithms that we know of [3]. In other words, opening up this larger space of operations reveals drastic “shortcuts” through state space; that is, transformation trajectories that get us to where we want to go using exponentially fewer steps than the shortest classical paths that we know of. The two most important examples of these apparent exponential shortcuts that have been found so far are the

264 following: (1) Shor’s quantum factoring algorithm [61] and (2) simulations of quantum systems [62]. Shor’s factoring algorithm can factor n-digit numbers using a number of quantum operations that increases only quadratically with the number of digits n, whereas the best known classical algorithms require time that increases exponentially in the number of digits. The primary application of Shor’s algorithm would be to break the public-key cryptosystems such as RSA [63] that are popularly used today for encryption and authentication of data for e-commerce and other purposes over the internet. For example, someone armed with a good-sized quantum computer and eavesdropping on your internet connection could steal your account information whenever you do home banking or credit-card purchases over a supposedly secure https: or secure socket layer connection that uses RSA for security. In other words, that little padlock icon in your web browser gives you no protection against a quantum computer! However, perhaps a more widely useful application for quantum computers is to simulate quantum physics. This was the original motivation for quantum computers that was proposed by Feynman [64]. We now know that the statistical behavior of any quantum-mechanical system can be accurately simulated in polynomial time on a quantum computer [62], even though quantum systems in general seem to require exponential time to simulate accurately on classical (nonquantum) computers. Another quantum algorithm that is useful, but that provides a less-than-exponential speedup, is Grover’s quantum “database search” algorithm that can locate a specified item, out of n items, in n1/2  lookup steps [65]. However, Grover’s algorithm is, unfortunately, misnamed, since it is not really useful at all for real database searches, in the usual sense of the term “database,” meaning an explicit table of arbitrary data. First, such a table, in general, requires just as much space to store in a quantum system as in a classical one (see “Myth #1”). Also, real commercial databases always include the capability to index the table by the most commonly used types of search keys, in which case a lookup, even on a classical computer, already requires only 1 lookup step. More precisely, the time required scales like n1/3  or n1/2 , if the speed-of-light travel time to the desired search item in 3D space or on a 2D surface is taken into account. But this is still less than in Grover’s algorithm. Also, even if the database is not indexed by the desired type of search key, if the data are stored in a processingin-memory architecture, in which each area of storage of some constant size has an associated processor, then lookup can be done in parallel, achieving the same light-limited n1/3  time, or at least n1/2  time, if the machine must be laid out in two dimensions, rather than three. Anyway, in random-data-lookup applications where the speed-of-light travel time to the data is the limiting factor, Grover’s algorithm cannot help us. However, Grover’s algorithm is still useful, not for database search, but rather for a different kind of application called unstructured search of computed (not tabulated) search spaces. This is because a search space can be much larger than the physical size of the machine if the “data values” (really, function values) are computed as a function

Nanocomputers: Theoretical Models

of the data’s index, rather than being explicitly stored. In cases where no more efficient algorithm is known for “inverting” the function (that is, finding an index that maps to a given value), Grover’s algorithm can still be used to obtain a speedup, although not one that is so large as is traditionally claimed. A simple classical parallel search can still outperform the serial Grover’s algorithm in terms of time alone; for example, if n3/4  processors simultaneously each search a different n1/4 -size piece of the search space, the search can be completed in n1/4  time classically in 3D space. However, given Grover’s algorithm, we can use a smaller number n3/5  of processors, each searching n2/5  items in n1/5  time. But note that the speedup is now only n1/4 /n1/5  = n1/20 )! However, the benefit in terms of spacetime cost can be still as great as n1/2 , since a single quantum processor searching for n1/2  time consumes only n1/2  spacetime, whereas the best classical unstructured search through n items requires n spacetime.

4.2.2. Dispelling Some Myths In addition to the misconceptions arising from the inappropriate association of Grover’s algorithm with database search, there are a few other popular myths about quantum computers that, although widely repeated, are entirely false, and we would like to dispense with them here and now. Myth #1 “Quantum computers with a given number of bits can store exponentially more information than classical computers having the same number of bits.” This is patently false, because the maximum amount of information that can be stored in any physical system is just the logarithm of its number of distinguishable states. Although an n-bit quantum computer can be put into an infinite number of different quantum states, only 2n of these states can be reliably differentiated from each other by any physical means whatsoever, no matter how cleverly you try to design your measurement apparatus. In other words, the presence of all those extra, “in-between” superposition states can have zero causal impact on the total amount of information you can reliably extract from the system. This basic feature (or “bug” if you prefer) of all physical systems was demonstrated convincingly by Heisenberg long ago [25]. Myth #2 “Quantum computers can perform operations at an exponentially faster rate than classical computers.” This is also false, because the Margolus–Levitin bound on processing speed [18] applies to quantum computers as well as classical ones. Operations (if defined as transformations that orthogonally transform some states) can only be performed, at best, at the rate 4E/h, or 2E/h for nontrivial ops, for a system of average energy E above its ground state. Small pieces of operations (small transformations that do not orthogonally transform any states) may be done more often [66], but these pieces arguably also perform correspondingly less computational work than do complete operations. Why? Note that a small piece of a (primitive orthogonalizing) operation (which transforms every state into a new state that is almost completely indistinguishable from the original) can be omitted entirely from a computation, and the end result of the computation will necessarily be almost completely indistinguishable from the case where

Nanocomputers: Theoretical Models

that small “operation piece” was included. (This is because the property of the near-indistinguishability of the two states must be preserved by any subsequent operations on the system—otherwise, the states would not be indistinguishable! Mathematically, this is ensured by the linearity of quantum evolution.) So it is fair to count the computational work performed by a transformation by counting the number of complete operations, as we have defined them (transformations that at least orthogonalize some states). Whether or not a given operation orthogonalizes the actual computational state that is presented to it as its input in a specific situation is another question altogether. It need not do so in order for the operation to be considered useful. For example, an ordinary “AND” gate, upon receiving new inputs, is considered to be doing useful work even when its output does not change. Namely, it is doing the work of determining that its output should not change.1 Similarly, a quantum operation that does not orthogonalize its actual initial state, but that might orthogonalize others, is, at least, doing the work of determining that that specific input is not one of the ones that was supposed to have been orthogonalized. Therefore, the Margolus–Levitin bound does indeed give a valid limit on the rate of useful operations that can be performed in any computer (classical or quantum). The correct interpretation of why a quantum computer provides exponentially faster algorithms for some problems (such as factoring, and simulating quantum physics) is not that the quantum computer is carrying out operations at an exponentially more frequent rate, but rather that the new types of operations that can be performed by the quantum computer make use of the fact that there actually exist exponentially shorter paths (requiring exponentially fewer total operations to traverse) leading from the input state to the desired final state than was previously recognized. As an analogy: Suppose you have a computer with integer registers, but the only arithmetic operation provided is “decrement/increment,” which subtracts 1 from one register, while adding 1 to another register. With this operation, you could still add two registers together, by repeatedly performing this operation on the two registers, until the first one equals zero. But this would generally take exponential time in the length of the registers. Now, suppose we introduce a new operation, which is the standard direct bitwise ripple-carry add of one register into the other. Then, the add only takes time proportional to the length of the registers. Thus we have gained an “exponential speedup” for the add operation, but not by doing increment/decrement operations exponentially more frequently, but rather by choosing a type of operation that allows us to do an exponentially smaller number of steps in order to get to the result that we want. The key insight of quantum computing was that nature provides for us a type of operation (namely, operations that might incompletely orthogonalize some input states) that was not previously recognized in any of our early computing models and that, moreover, adding this kind of operation allows some problems to be solved using exponentially fewer total operations than was previously realized. Therefore, omitting the capability of performing quantum operations from our future computer designs is, in a sense, 1

Seth Lloyd pointed out this analogy to me in personal discussions.

265 just as foolish as omitting the capability for bitwise addition (as opposed to just decrement/increment) from the design of our arithmetic units! One caveat is that, at present, only a few kinds of problems (such as those mentioned previously) have been found so far for which quantum operations provide a drastic speedup. However, since a low decoherence rate will eventually be needed anyway, in order to allow for highspeed reversible operations that avoid excessive dissipation, it makes sense for us to aim toward a full quantum computing technology in the long run. Also, quantum computing is still only in its infancy, and many useful new quantum algorithms may yet be discovered. Myth #3 “Quantum computers are known to be able to solve nondeterministic polynomial (NP)-complete problems in polynomial time.” If this were true, it would be wonderful, because all problems whose solutions can be checked in polynomial time (this is the definition of the NP problems) could then also be solved in polynomial time using a quantum computer. Among other applications, this would revolutionize the way we do mathematics, because very complex proofs of difficult mathematical theorems could be found very quickly by computer, that is, in time only polynomial in the length of the proof. Unfortunately, no one has shown a way to use quantum computers to solve NP-hard problems efficiently, and furthermore, a result due to Bennett et al. [67] provides some mild theoretical evidence suggesting that it is not possible. The factoring problem and other problems that apparently do have exponential shortcuts from using quantum computing have never been proven to be NP-complete, so they do not constitute examples of NP-complete problems that can be efficiently solved on a quantum computer. However, more research on this question is needed. Myth #4 “Quantum computers have been proven to be far more powerful than classical computers.” First, we know that a quantum computer can be perfectly simulated by a classical computer, though most likely this requires exponential slowdown. So any problem solvable on a quantum computer can be eventually solved on a classical computer, given unbounded resources. So quantum computers are not any more powerful in terms of the kinds of problems that they can solve at all in principle; rather, at best, they are just exponentially more efficient at solving some problems. But even the exponential efficiency advantage has never really been proven. For all we know for sure today, there could still exist a (not yet discovered) polynomial-time classical algorithm for simulating all quantum computers, in which case every efficient quantum algorithm could be translated to a similarly efficient classical one. Other than in various artificial oracle scenarios, we still have no rock-solid proof that quantum computers confer any extra computational power, although most researchers expect that they do. Moreover, for practical purposes today, they would effectively confer that exponential extra power, because of the existing problems for which the best quantum algorithm we know is far more efficient than the best classical algorithm we know. But this situation could change someday, if equally efficient classical algorithms were eventually to be discovered, which has not (yet) been proven to be impossible.

266 Myth #5 “Quantum computers require exponential space to simulate on a classical computer.” This myth is often quoted as the “reason” simulating a quantum computer on a classical one must also take exponential time. But the myth is simply not true; it has been recognized since at least 1992 [68] that a polynomial-space simulation of quantum computers on classical ones is easy. The technique used is pretty obvious to anyone who is familiar with Feynman’s path-integral formulation of quantum mechanics, which has been around much longer. It tells us that the amplitude of a given final basis state can be computed via a sum over trajectories (here, sequences of basis states) that terminate at that final state. A given sequence requires only polynomial space to store, and we can just iterate serially through all possible sequences, accumulating the final state’s net amplitude. This is all that is needed to compute the statistical behavior of the quantum system (e.g., quantum computer) being simulated.

Nanocomputers: Theoretical Models

4.2.3. Implementation Technologies Many potential implementation technologies for quantum computers have been proposed and are being experimented on. These include nuclear spin systems [70], electron spin systems [71], superconducting current states of various sorts [72], and even mechanical vibrational systems [73]. To date, all of these approaches rely on an externally supplied signal for control and timing of operations. (As Lloyd says, “Almost anything becomes a quantum computer if you shine the right kind of light on it.”) But really, there seems to be no fundamental reason why the generator of the programmed control signal could not eventually be integrated with the actual devices, in a more tightly coupled fashion. For scalability to large arrays of self-timed processors, synchronization becomes a concern but can presumably be handled in much the same ways as we discussed for the case of reversible processors earlier.

4.2.4. Architectures and Programming Models Myth #6 “Large-scale quantum computers are fundamentally impossible to build, due to the phenomenon of decoherence.” Our best models to date tell us that this is not so. We only require a quantum device technology that has a quality factor q that is above a certain finite threshold (currently estimated to be around 103 –104 ) [69] that allows known robust, fault-tolerant quantum error-correction algorithms to be applied, thereby allowing the scale of the achievable computations to be scaled up arbitrarily, just as classical error correction techniques allow classical computations to be scaled up arbitrarily, despite the small but not perfectly zero error rates in current-day bit devices. A high quality factor like this will be required anyway, if we wish to ever perform computation at rates well beyond those planned in the present semiconductor roadmap, which would imply computational temperatures that would quickly melt the computer’s structure, if the computational degrees of freedom were not extraordinarily well isolated from interactions with structural ones. So quantum computing is, in a sense, no harder than any technology that aims at capabilities well beyond the present semiconductor roadmap. Of course, many important engineering details remain to be worked out. However, for a densely packed, 3D parallel quantum computer to be able to handle a noticeable rate of decoherence using fault-tolerant error correction techniques may require hardware implementation of the error correction algorithms, internally to the processor’s architecture, rather than just in software. Because of this, a quantum computer requires a somewhat different and more elaborate hardware architecture, as compared with a simple reversible computer, which would not need to maintain superposition states and so could make do with simple classical approaches to error correction, such as encoding computational bits redundantly in numerous physical bits, whose values can be “replenished” to stay locked with their nominal value by more trivial mechanisms (e.g., by connecting a voltage-coded circuit node statically to a reference power supply, as is done in ordinary static CMOS logic circuits today).

A self-contained quantum computer architecture looks very similar to a classical reversible architecture, but with some added instructions that can perform quantum operations that might not orthogonalize the input state. In principle, it suffices to include a single quantum instruction operating on a one-bit register, while keeping all other instructions simply coherent classical reversible [74], but a larger variety of quantum operations would probably also be useful. A self-contained, stored-program quantum architecture should probably have built-in support for fault-tolerant error correction algorithms, to avoid the overheads of implementing these in software. However, it is important to note that the entire architecture need not be coherent at all times, only the parts that are directly storing and manipulating the quantum data of interest. It may be beneficial to design each processor as a classical reversible processor (kept reversible and mildly coherent for speed and energy efficiency) paired with a relatively small quantum subprocessor whose state is kept highly coherent through the use of quantum error correction. The quantum component might be kept at a relatively low temperature to help avoid decoherence, since its speedups come from the use of superpositions in quantum algorithms, not from a fast operation rate (high computational temperature). Meanwhile, the classical part of the processor can perform in software, at relatively much higher frequencies, the meta-computation needed to determine which quantum operation should be performed next on the quantum subprocessor. However, if a much wider range of useful quantum algorithms is eventually discovered, we may eventually find ourselves wishing to do quantum operations more pervasively throughout a wider range of applications, and also at higher frequencies, in which case the quantum functions might be integrated more thoroughly into the primary reversible processor. Without the availability of a classical processor running at higher speed, more of the low-level quantum algorithms such as error correction would need to be done “in hardware,” incorporated directly into the design, arrangement, and interactions of the individual quantum devices. The technique of using decoherence-free subspaces [75] provides one example of how to cope with errors

Nanocomputers: Theoretical Models

directly in the hardware design. Other methods may eventually be discovered. Now, given our recognition of the need to incorporate the possibility of reversibility and quantum computing into our nanocomputer models, while respecting fundamental physical constraints as well, what will the resulting nanocomputer models look like? Let us take a look.

5. GENERIC REALISTIC MODEL OF NANOCOMPUTERS In this section, we give a detailed example of what we consider to be a reasonably simple, realistic, and efficient model of computing which remains valid at the nanoscale. It is realistic in that it respects all of the important fundamental constraints on information processing except for gravity, which, unlike the other constraints, is not expected to become relevant yet within the coming half-century of technological development. The model is efficient in that it is not expected to be asymptotically less cost efficient (by more than a constant factor) than any other model that respects all of the same fundamental physical constraints. To achieve this, it must recognize the possibility of reversible and quantum computing. The focus of this particular model is on enabling the analysis of the complete cost-efficiency optimization of parallel computer systems, when simultaneously taking into account thermodynamic constraints, communications delays, and the algorithmic overheads of reversible computing.

5.1. Device Model A machine instance can be subdivided into logical devices. The total number of devices in the machine can be scaled up with the memory requirement of the given application. Each device has a logical state, which is an encoded, desired classical or quantum state (possibly entangled with the state of other devices) for purposes of carrying out a classical or quantum computation. The logical state is encoded by a coding physical state, which is the portion of the device’s physical state that encodes (possibly redundantly) the desired logical state. The device will probably also have a noncoding physical state, which is the rest of the device’s physical state, which is not used for encoding computational information. The noncoding state can be further subdivided into a structural state, which is the part of the state that is required to remain constant in order for the device to work properly (if it is changed, the device becomes defective), and the thermal state, which is the unknown part of the device’s physical state that is free to change because it is independent of the logical and structural state and so is not required to remain constant in order to maintain proper operation. The device mechanism can be characterized by the following important parameters. In any given technology, the value of each of these parameters is assumed to be designed or required to fall within some limited range, for all devices in the machine. • Amount of logical information, Ilog , that is, information in the logical subsystem.

267 • Amount of coding information, Icod , that is, information in the coding subsystem (in which the logical subsystem is represented). • Amount of thermal information, Itherm , that is, information in the thermal subsystem, given the device’s allowed range of thermal temperatures. • Computational temperature Tcod of the coding state. This is the rate at which minimal desired changes to the entire coding state (steps) take place, that is, transitions which change all parts of the coding state in a desired way. Its reciprocal tcod = 1/Tcod is the time for a step of updating the coding state to take place. • Decoherence temperature Tdec . The rate at which undesired coding-state steps take place due to unwanted, parasitic interactions between the coding state and the thermal/structural state of the device or its environment. Its reciprocal tdec = 1/Tdec is the decoherence time, the characteristic time for coding state information to be randomized. Of course, it is desirable to select the coding subsystem in a way that minimizes the decoherence rate; one way to do this is to choose a subsystem whose state space is a decoherence-free subspace [75], or one that is based on pointer states, which are those states that are unaffected by the dominant modes of interaction with the environment [76]. The stable, “classical” states that we encounter in everyday life are examples of pointer states. Of course, even in nominal pointer states, some residual rate of unwanted interactions with the environment always still occurs; that is, entropy always increases, however slowly. • Thermal temperature Ttherm . The rate at which the entire thermal state of the device transforms. This is what we normally think of as the ordinary thermodynamic operating temperature of the device. • Decay temperature Tstruc . The rate at which decay of the device’s structural state information takes place. It depends on the thermal temperature and on how well the structural subsystem’s design isolates its state from that of the thermal degrees of freedom in the device. Its reciprocal tstruc is the expected time for the device structure to break down. • Device pitch lp . For simplicity, we can assume, if we wish, that the pitch is the same in orthogonal directions, so the device occupies a cube-shaped volume Vd = lp3 . (This assumption can be made without loss of generality, since devices of other shapes can always be approximated by a conglomeration of smaller cubes. However, allowing alternative device shapes may give a simpler model overall in some cases.) We are also assuming here that the region of space occupied by distinct devices is, at least, nonoverlapping, as opposed to (for example) different devices just corresponding to different degrees of freedom (e.g., photonic vs electronic vs vibrational modes) within the same region. Again, this is not really a restriction, since such overlapping phenomena could be declared to be just internal implementation details of a single device whose operation comprises all of them simultaneously. However, we can loosen this no-overlap restriction if we wish. But if we do so, care should be taken not to

268 thereby violate any of the fundamental physical limits on entropy density, etc. • Information flux density IAt (rate of information per unit area) through the sides of the device. This includes all physical information such as thermal entropy (flux SAt ) or redundant physical coding information (flux IAtcod ) of logical bits (flux IAtlog ). Note that since the motion of information across the device boundary constitutes a complete update step for the location of that information, we know that IAt ℓ2p ≤ IT where I is the information of a given type within the device, and T is the temperature (rate of updating) of the location information for that type of information. Additionally, one of course also needs to define the specifics of the internal functionality of the device. Namely, what intentional transformation does the device perform on the incoming and internal coding information, to update the device’s internal coding information and produce outgoing coding information? To support reversible and quantum computing, at least some devices must reversibly transform the coding information, and at least some of these devices must perform nonorthogonalizing transformations of some input states. The device definition may also provide a means to (irreversibly) transfer the content of some or all of its coding information directly to the thermal subsystem, causing that information to become entropy. For example, a node in static or dynamic CMOS circuit effectively does this whenever we dump its old voltage state information by connecting it to a new fixed-voltage power supply. However, a metal-oxide-semiconductor field effect transistor’s (MOSFET) built-in dynamics can also be used to transform coding states adiabatically, thereby avoiding transformation of all of the coding information to entropy. Most generally, the device’s operation is defined by some reversible, unitary transformation of its entire state (coding, thermal, and structural), or, if the transform is not completely known, a statistical mixture of such. The actual transformation that occurs is, ultimately, predetermined solely by the laws of quantum mechanics and the state of the device and its immediate surroundings. So device design, fundamentally, is just an exercise of “programming” the “machine” that is our universe, by configuring a piece of it into a specific initial state (the device structure) whose builtin evolution over time automatically carries out a manipulation of coding information in such a way that it corresponds to a desired classical or quantum operation on the encoded logical information. As we will see, this notion of a device is general enough that not only logic devices but also interconnects, timing sources, and power supply/cooling systems can be defined in terms of it.

5.2. Technology Scaling Model The technology scaling model tells us how functional characteristics of devices change as the underlying technology improves. Just from basic physical knowledge, we already know some things about the technological characteristics of

Nanocomputers: Theoretical Models

our device model: First, Ilog ≤ Icod . That is, the amount of logical information represented cannot be greater than the amount of physical information used to do so. We can thus define the redundef dancy factor Nr = Icod /Ilog ≥ 1. Next, note that for devices that are occupied by information of interest (that is, actively maintaining a desired logical state), the rate Sdt of standby entropy generation is at least Icod Tdec as coding information decays. The coding state of devices that are not occupied (not currently allocated for holding information) can be allowed to sit at equilibrium with their thermal environment, so their rate of standby entropy generation can be zero (or more precisely, some extremely low rate determined by the rate of structural decay Tstruc ). Next, if we assume that changing a logical bit is going to in general require changing all Nr of the physical bits used to redundantly encode it, we can immediately derive that logical bits, as well as physical bits, change at most at the rate Tcod [77]. If the computational temperature were only room temperature (300 K), then, expressed in terms of ops (h/2) per bit (kB ln 2), this temperature would allow a maximum rate of only one bit-op per 0.115 ps, that is, a bit-device operating frequency of at most 10 THz. Note that this operating frequency is only about a factor of 3000 times faster than the actual ∼3 GHz working clock speeds in the fastest microprocessors that are currently commercially available, and furthermore it is only about a factor of 10 faster than the fastest present-day NMOS switches (which already have minimum transition times of ∼1 ps [6]) are theoretically capable of. By 2016, minimum transition times are planned to be almost as small as 0.1 ps, according to the semiconductor industry’s roadmap [6]. So, in other words, taking device speeds significantly beyond the end of the present semiconductor roadmap will require temperatures in the computational degrees of freedom that are significantly above room temperature. This does not conflict with having structural temperatures that are relatively close to room temperature (to prevent the computer from melting), insofar as the computational degrees of freedom can be well isolated from interactions with the thermal and structural ones. But such isolation is desired anyway, in order to reduce decoherence rates for quantum computations and entropy generation rates for reversible classical computations. Looking at the situation another way, given that increasing operating frequency significantly beyond the end of the semiconductor roadmap would require computational temperatures at significant multiples of room temperature, and given that solid structures melt at only moderate multiples of room temperature, the computational degrees of freedom must become increasingly well isolated from interactions with the rest of the system. This high-quality isolation, in turn, in principle enables reversible and quantum computation techniques to be applied. In other words, going well beyond the semiconductor roadmap requires entering the regime where these alternative techniques should become viable. Let us look more carefully now at entropy generation rates. Since a step’s worth of desired computation is carried out each tcod = 1/Tcod time, whereas a step of unwanted

Nanocomputers: Theoretical Models

state modifications occurs each tdec = 1/Tdec time, a key measure of the quality of the device technology is given by q = tdec /tcod = Tcod /Tdec , the ratio between decoherence time and state-update time, or in other words between state update rate and rate of state decay. Since the unwanted decay of a bit effectively transforms that bit into entropy, the entropy generated per desired logical bit operation must be at least Nr /q ≥ 1/q bits, even for logically reversible operations. Note that our q is, effectively, just another equivalent definition for the quality ratio Q (the fraction of energy transferred that is dissipated by a process) that is already commonly used in electronics. We use lower case here to indicate our alternative definition in terms of quantum decoherence rates. Now, for specific types of devices, we can derive even more stringent lower bounds on entropy generation in terms of q. For example, in [77], we show that for field-effect based switches such as MOSFETs, the entropy generated must be at least ∼q 0
9 , with the optimal redundancy factor Nr to achieve this minimum growing logarithmically, being ∼1
12 lg q. However, it is reassuring that in this more specific device model, entropy generation can still go down almost as quickly as 1/q. It may be the case that all reversible device models will have similar scaling. The key assumption made in that analysis is just that the amount of energy transfer required to change the height of a potential energy barrier between two states is of the same magnitude as the effected amount of change in height of the barrier. If this is true in all classes of reversible logic devices, and not just in field-effect-based devices, then the results of [77] hold more generally. See Figures 2 and 3. However, in contrast to the reversible case, irreversible erasure of a bit of logical information by direct means (e.g., grounding a voltage node) in general requires discarding all Nr of the redundant bits of physical information that are associated with that bit, and thus generating Nr bits of physical entropy which must be removed from the machine. At best, at least 1 bit of physical entropy must be generated for each logical bit that is irreversibly erased (see discussion in Section 5.2.5). Thus, when the device quality factor q is large (as must become the case when computational rates far exceed room temperature), the reversible mode of operation is strongly favored.

5.3. Interconnection Model For simplicity, we can adopt an interconnection model in which interconnects are just another type of device, or are considered to be a part of the logic devices, and so are subject to the same types of characterization parameters as in our general device model. The machine need not be perfectly homogeneous in terms of its device contents, so interconnects could have different parameter settings than other types of devices. Indeed, they could be physically very different types of structures. However, it is critical that the interconnection model, however it is described, should at least accurately reflect the actual delay for a signal to traverse the interconnect. To save space we will not develop the interconnection model in detail here.

269

1.8 1.6 1.4

Minimum entropy Sop generated per operation, nats/bit-op

1.2 1 0.8 0.6 0.4 0.2 0 -1 -2 5 -3

Logarithm of relative decoherence rate, ln 1/q = ln Tdec/Tcod

4 3 -4 2 -5

1

Redundancy Nr of coding information, nats/bit

Figure 2. Minimum entropy generation per bit-op in field-effect devices, as a function of quality factor q and redundancy Nr of physical encoding of logical information. When q ≤ e2 , the function is monotonically nondecreasing in Nr , but for larger q, it has a local minimum which first appears at Nr = 2 nats per bit. The black line curving horizontally across the figure traces this local minimum from its first appearance as q increases. This local minimum becomes the absolute minimum when 1/q ≤ 0
0862651


(numerically calculated), when the black line dips below the surface that we have visualized by sweeping the left edge of the figure (where Nr = ln 2 nats/bit, its minimum) through the x direction. (The white line is there only to help visualize how far above or below that surface the black line lies at a given q.) The other black line, along the left edge of the figure, marks the approximate range of q values for which Nr = ln 2 nats/bit is indeed the optimal choice. Note that as q increases, ever-lower entropy generation per bit-op becomes possible, but only by increasing the redundancy of the encoding (which raises energy barriers and improves the achievable on/off power transfer ratios).

5.4. Timing System Model Again, for simplicity, we can assume that timing synchronization functions are just carried out in special devices designated for this purpose or are integrated into the logical devices. Timing synchronization (correction of errors in timing information) can be carried out in an entirely local fashion. This is illustrated by the extensive literature on clockless (self-timed, or asynchronous) logic circuits. Reversible circuits cannot be allowed to operate in a completely asynchronous mode, in which substantial-size timing errors are constantly appearing and being corrected, since each synchronization operation would be irreversible and thus lossy, but they can be maintained in a closely synchronized state via local interactions only. Margolus showed explicitly how to do this in a simple 1D quantum model in [49]. But it is also clear that locally synchronized reversible operation can be generalized to three dimensions, just by considering simple mechanical models in which arrays of high-quality mechanical oscillators (e.g., springs or wheels) are mechanically coupled to their neighbors (e.g., via rigid interconnecting rods like those between the wheels on an old steam locomotive). An interesting research problem is to develop analogous reversible local-synchronization mechanisms that are entirely electronic rather than mechanical or, if this is impossible, prove it.

Nanocomputers: Theoretical Models

270 25

20

Nopt -ln Smin ~Nopt ~-lnSmin

15

Optimal redundancy factor Nr, in nats/bit

10

Exponent of factor reduction of entropy generated per bit-op, ln (1 nat/∆Sop)

5

0 1

0.1

0.01

0.001

0.0001

0.00001

0.000001 0.0000001

Relative decoherence rate (inverse quality factor), 1/q = Tdec/Tcod = tcod/ tdec

Figure 3. Scaling of optimal redundancy factor and maximum entropy reduction with decreasing relative decoherence rate. In the graph, the horizontal axis sweeps across different q factors (decreasing values of 1/q), and we show the corresponding optimal choice of Nr (found via a numerical optimization) and the natural logarithm of the maximum entropy reduction factor (factor of entropy reduction below the reference 1 kB = 1 nat) that may be obtained using this choice. The thin, straight trend lines show that for large q (small 1/q), the optimal Nb (for minimizing S) scales as roughly 1.1248(ln q), while the minimum

S itself scales as about q 0
9039 .

5.5. Processor Architecture Model For purposes of analyzing fundamental trade-offs, this need not be particularly restrictive. A processor should contain some memory, with a low standby rate of entropy generation for bits that are occupied but are not being actively manipulated, and zero standby rate of entropy generation in unallocated, powered-down bits (after they equilibrate with their environment). The processor should contain some logic that can actively process information in some way that can be programmed universally (any desired program can be written, given sufficiently many processors). It should be able to perform fully logically reversible operations which are carried out via reversible transformations of the coding state. Some examples of reversible architectures can be found in [4, 59, 60, 78, 79]. For convenience, the architecture should also permit irreversible operations which treat the information in the coding state as entropy and transfer it to a noncoding subsystem that is basically just a heat flow carrying entropy out of the machine. (There is no point in keeping unwanted information in a coded state and wasting error correction resources on it.) However, the reversible operations provided by the architecture should also allow an alternative, of uncomputing the undesired information, so as to return the coding state to a standard state that can be reused for other computations, without needing to ever treat the coding information as if it were entropy. The architecture should be able to be programmed to efficiently carry out any reversible algorithm. Ideally, the architecture should also support performing nonorthogonalizing quantum operations (that is, operations

that create quantum superpositions of logical basis states), so that, in combination with classical coherent reversible operations, arbitrary quantum computations can be programmed. If quantum computation is to be supported, simply using classical pointer basis states in the device is no longer sufficient for representing the logical state, and full quantum superpositions of logical basis states (spanning some relatively decoherence-free subspace) should be permitted. The key criteria are that the architecture should be both physically realistic and universally maximally scalable. These goals, together with ease of programmability, imply that it should look something like we described previously.

5.6. Capacity Scaling Model An ordinary multiprocessor model can be adopted, scaling up total machine capacity (both memory and performance) by just increasing the number of processors. However, we must be careful to be realistic in specifying the interconnection network between the processors. It has been shown that no physically realizable interconnection model can perform significantly better than a 3D mesh model, in which all interconnections are local (i.e., between processors that are physically close to each other) [17]. Moreover, although the planar width of the whole machine can be unlimited, the effective thickness or depth of the machine along the third dimension is inevitably limited by heat removal constraints [4]. However, insofar as reversible operation can be used to reduce the total entropy generated per useful logical operation, it can also increase the effective thickness of the machine, that is, the rate of useful processing per unit of planar area [20]. This, in turn, can improve the performance of parallel computations per unit machine cost, since a thicker machine configuration with a given number of processors has a lower average distance between processors, which reduces communication delays in parallel algorithms [4, 58].

5.7. Energy Transfer Model The flow of energy through the model should, ideally, be explicitly represented in the model, to ensure that thermodynamic constraints such as conservation of energy are not somewhere implicitly violated. A piece of energy E that is changing state at average rate (temperature) T contains I = E/T amount of information, by our definitions of energy and temperature. Likewise, for I amount of information to be transitioning at rate T requires that energy E = IT be invested in holding that information. Entropy S is just information whose content happens to be unknown, so ejecting it into an external atmosphere where it will transition at room temperature, or ∼300 K, always requires that an accompanying S(300 K) energy (heat) also be ejected into the atmosphere. (Or, if the cosmic microwave background is used as a waste heat reservoir, an ambient temperature of 2.73 K applies instead.) The same relation between energy, information, and temperature of course applies throughout the system: Whenever an amount of information I is added to any subsystem that is maintained at a specific, uniform temperature T , an amount E = IT of energy must also be added to that subsystem.

Nanocomputers: Theoretical Models

Thus, the continual removal of unwanted entropy from all parts of the machine by an outward flow of energy (heat) requires that this lost energy be replenished by an inwardflowing energy supply going to all parts of the machine, complementing the outward heat flow. This inward-flowing supply also has a generalized temperature Tsup and carries information, which must be known information in a standard state, or at least contain less entropy than the outward flow (otherwise we could not impress any newly generated entropy onto the energy flow). The total rate of energy flow to the machine’s innards and back might be greater than the minimum rate needed for the entropy internally generated to be emitted, if the heat is being moved actively (e.g. by a directed flow of some coolant material). This may be required to keep the thermal temperature of internal components low enough to maintain their structure. If the coolant is flowing at such a speed that the effective temperature of its motion is greater than the desired internal structural temperature, then we must isolate this flow from direct thermal contact with the structure, in order to avoid its raising the structural temperature rather than lowering it. Nevertheless, a well-isolated coolant flow can still be used to remove heat, if the unwanted heat is sent to join the coolant stream by a directed motion. Note that the extra, directed energy flow in an active cooling system (its moving matter and kinetic energy) can be recycled (unlike the heat) and directed back into the machine (after being cooled externally) to carry out additional rounds of heat removal. So all the energy contained in the inward coolant flow does not necessarily represent a permanent loss of free energy. To minimize the total rate of free-energy loss needed to achieve a given internal processing rate, we should minimize the rate at which entropy is produced internally, the inefficiencies (extra entropy generation) introduced by the cooling system, and the temperature of the external thermal reservoir (for example, by placing the computer in primary thermal contact with outer space, if possible). One way to approach the energy transfer model treats the energy flow pathways as just yet another type of information-processing device, subject to the same type of characterization as we discussed earlier in Section 6.1. The only difference is that there need be no coding information present or error correction taking place in a device whose only purpose is to carry waste entropy out of the machine to be externally dissipated.

5.8. Programming Model For purposes of this discussion, we do not particularly care about the details of the specific programming model, so long as it meets the following goals: • Power. Harnesses the full power of the underlying hardware (i.e., does not impose any asymptotic inefficiencies). In the long run, this implies further that it supports doing the following types of operations, if/when desired and requested by the programmer:  Parallel operations.  Reversible classical operations (implemented with as little entropy generation as the underlying device quality permits in the given technology).

271  Quantum coherent operations (with as little decoherence as the device quality permits). • Flexibility. The efficiency of the machine will be further improved if it provides several alternative programming models, so that whichever one that is most efficient for a particular application can be used. For example, each processor might provide both a CPU running a fairly conventional style of instruction set architecture (although augmented by reversible and quantum instructions) which efficiently maps the most common operations (such as integer and floating-point calculations) to device hardware, as well a section of reconfigurable logic (also offering reversible and quantum operation), so that specialized, custom application kernels can be programmed at a level that is closer to the hardware than if we could only express them using traditional software methods. • Usability. The programming model should be as straightforward and intuitive to use by the programmer (and/or compiler writer) as can be arranged, while remaining subject to the previous criteria, which are more important for overall efficiency in the long run. At present, programmer productivity is arguably more immediately important than program execution efficiency for many kinds of applications (for example, in coding business logic for e-commerce applications), but in the long run, we can expect this situation to reverse itself, as fundamental physical limits are more closely approached, and it becomes more difficult to extract better performance from hardware improvements alone. When this happens, the efficiency of our programming models will become much more critical. Also, there may be a period where our choice of programming models is constrained somewhat by the type of hardware that we can build cost-effectively. For example, processors might be forced to be extremely fine-grained, if it is initially infeasible to build very complex (coarse-grained) structures at the nanoscale. Papers on NanoFabrics [80] and the Cell Matrix [81] describe examples of fine-grained parallel models based on very simple processing elements. In the case of [80], the processing elements are ones that can be built by making heavy use of certain chemical self-assembly techniques that are deemed more feasible by the authors than other fabrication methods. However, my own opinion is that the need for such finegrained architectures, if there ever is one, will only be a short-term phenomenon, needed at most only until manufacturing capabilities improve further. In the longer run, we will want direct hardware support (i.e., closer to the physics) for very common operations such as arithmetic, and so eventually our nanoarchitectures will also contain prefabricated coarse-grained elements similar to the integer and floating-point ALUs (arithmetic-logic units) which are common today, which will be naturally programmed using instruction sets that are, in large measure, similar to those of today’s processors. To see why, consider this: The cost efficiency of a very fine-grained architecture, such as the Cell Matrix, on any application is reduced by at most a factor of 2 if we take

Nanocomputers: Theoretical Models

272 half of the area that is devoted to these fine-grained reconfigurable cells and use it to build fixed 128-bit ALUs (say) directly in hardware instead, even in the worst case where those ALUs are never used. But those general applications that can use the ALUs (which is probably most of them) will run hundreds of times more cost-efficiently if the ALUs are directly available in hardware than if they have to be emulated by a much larger assemblage of simple reconfigurable cells. However, including some amount of reconfigurable circuitry is probably also desirable, since there are some specialized applications that will probably run more costefficiently on top of that circuitry than in a traditional instruction set. The most basic law of computer architecture, Amdahl’s law (in its generalized form [82] which applies to all engineering fields, and to any measure of cost efficiency), can be used to show that so long as the costs spent on both reconfigurable circuitry and traditional hardwired ALUs are comparable in a given design, and both are useful for a large number of applications, there will be little cost– performance benefit to be gained from eliminating either one of them entirely. Furthermore, it seems likely that the business advantages of having a single processor design that can be marketed for use for either kind of application (ALU-oriented vs more special-purpose) will probably outweigh the small constant-factor cost efficiency advantage that might be gained on one class of application by killing the cost efficiency of the other class. Since arithmetic-intensive computing drives most of the market for computers and will probably continue to do so, I personally think it most likely that we will follow a evolutionary (not revolutionary) manufacturing pathway that continues to make smaller and smaller ALUs, which continue to be programmed with fairly traditional (CISC/RISC/DSP) instruction-set styles, and that gradually evolves toward the point where these ALUs are composed of truly nanoscale devices. The alternative scenario promoted by these authors, that the majority of computing will suddenly change over to using some radically different alternative architecture which lacks efficient low-level hardware support for such application-critical operations as “add,” does not seem very plausible. Now, of course, above the instruction-set level, higher level programming models (languages) may take a variety of forms. For example, Skillicorn [83] discusses issues in the design of high-level parallel models that map efficiently to hardware. Some discussion of reversible programming languages can be found in [4, 84, 85], and some examples of quantum programming languages are [86–91].

5.9. Error Handling Model Typically, the physical coding state will be chosen in such a way that any errors that appear in the coding state can be detected and corrected, before enough of them accumulate to cause the logical state information to be lost. Ordinary static CMOS logic provides a simple example of this. The coding state is the analog voltage on a circuit node. A fairly wide range of possible voltages (thus, a relatively large amount of coding state information) is taken

to effectively represent a given logical value (0 or 1). The ideal coding state is some power-supply reference voltage, GND or Vdd . If, through leakage, a node voltage should drift away from the ideal level, in a static CMOS circuit, the level will be immediately replenished through a connection with the appropriate power supply. A simple static CMOS storage cell, for example, may include two inverter logic gates that continuously sense and correct each other’s state. This can be viewed as a simple hardware-level form of error correction. In dynamic digital circuits, such as a standard DRAM chip, a similar process of error detection and correction of logic signals takes place, although periodically (during refresh cycles) rather than continuously. Of course, many other coding schemes other than voltagelevel coding are possible. Electron spin states [71], current direction states [72], AC current phase states [92], electron position states [41], and atomic position states are just some of the examples. Whatever the coding scheme used, a similar concept applies, of redundantly representing each logical bit with many physical bits, so that errors in physical bits can be detected and corrected before enough of them change to change the logical bit. This idea applies equally well to quantum computing [93]. If the architecture does support quantum computing and is self-contained, then, for efficiency, fault-tolerant quantum error correction algorithms [69] should probably eventually be implemented at the architectural level in the long term, rather than just (as currently) in software. Note that to correct an error is by definition to remove the “syndrome” information that characterizes the error. Insofar as we do not know precisely how the error was caused, and thus how or whether it might be correlated with any other accessible information, this syndrome information is effectively entropy, and so we can do nothing sensible with it except expel it from the machine. Unless the error rate is negligibly small, the resources required for removal of this error information must be explicitly included in any realistic model of computing that takes energy costs or heat-flux constraints into account.

5.10. Performance Model Given the care we have taken to recognize fundamental physical constraints in our model components, a correct performance model will fall out automatically, as the architectural details are filled in. As we compose a large machine out of individual devices characterized as described, our device model forces us to pay attention to how energy and information flow through the machine. An algorithm, specified by an initial coding state of all of the devices, runs at a rate that is determined by the device dynamics, while respecting the time required for signals to propagate along interconnects throughout the machine, and for generated entropy to flow out along cooling pathways.

5.11. Cost Model As we described earlier, a good cost model should include both spacetime-proportional costs (which include manufacturing cost, amortized over device lifetime), and energyproportional costs. The energy costs can easily be dominant,

Nanocomputers: Theoretical Models

if the machine is to be operated for a long lifetime, or in an environment where energy is hard to come by and thereof expensive (or, complementarily, where heat is hard to get rid of). As a pragmatic example, suppose a battery in a 30-W laptop lasts 5 hours, thus supplying 0.15 kW-hrs of energy. Assuming the recharge process can be done very efficiently, the raw cost of energy for a recharge, at typical current U.S. electric utility rates, is therefore less than one cent (US$0.01). However, the inconvenience to a business traveler of having to charge and carry extra batteries in order to make it through a long international flight could well be worth tens of dollars, or more, to him or her. Also, having a particularly hot laptop sitting on one’s lap can be a significant discomfort that users may be willing to pay a significant amount of money to reduce. The effective cost of energy can thus be many orders of magnitude higher than usual in these scenarios. As additional examples, think of the cost to supply fresh fuel for energy to soldiers in the field, or to wireless transponders that may mounted on autonomous sensors, or on goods during warehousing and shipping, for electronic inventory and tracking systems. Or, think of the cost to supply extra energy to an interstellar probe in deep space. Moreover, space vehicles also can have difficulty getting rid of waste heat, due to the absence of convective or conductive modes of heat transport. These examples serve to illustrate the general point that circumstances in particular application scenarios can inflate the effective cost of energy by a large factor, perhaps hundreds or thousands of times over what it would be normally. Even at normal wall-outlet electricity rates, a 200-W high-performance multiprocessor desktop workstation that remained in continuous service would use up ∼US$1,700 worth of electricity over 10 years, which may be comparable to the cost of the machine itself. (However, for as long as Moore’s law continues, the computer would probably be replaced about every 3 years anyway, due to obsolescence.) Also, the cost of energy could increase further if and when the rate of fossil fuel extraction peaks before energy demand does, if more cost-effective energy technologies do not become available sooner than this. However, such variations in the cost of energy may not affect the trade-off between manufacturing cost and energy cost much, because manufacturing costs are, probably, ultimately also dominated by the cost of energy, either directly or indirectly through the manufacturing tool supply chain. Also, offsetting the fossil fuel situation, nanotechnology itself may eventually provide us new and much cheaper energy technologies, in which case the cost of energy might never be significantly higher than it is at present. However, even if the cost of energy always remains low, or even goes much lower than at present, the discomfort to a human user of holding or wearing a computer that is dissipating much more than ∼100 W will always remain an important concern for as long as there remain biological humans who want to carry their computers around with them, and who comprise a significant part of the market for computing.

273 5.12. Some Implications of the Model In some previous work that did a complete system-level analysis based on a model highly similar to the one just described [21], we demonstrated (based on some straightforward technology scaling assumptions) that the costefficiency advantages of reversible computing, compared to irreversible computing, for general-purpose applications in a 100 W, US$1,000 machine could rise to a factor of ∼1000 by the middle of this century, even if no more efficient algorithms for general-purpose reversible computing are found than those (specifically, [54]) that are already known. In the best case, for special-purpose applications, or if ideal general purpose reversiblization algorithms are discovered, the cost-efficiency benefits from reversibility could rise to a level ∼100,000 × beyond irreversible technology. See Figure 4. However, that particular analysis assumed that a very high q value of ∼1012 could be achieved at that time and, further, that it could be maintained as manufacturing costs per device continued to decrease. If this does not happen, then the gains from reversibility will not be so great. Unfortunately, the exponentially increasing rate at which electrons tunnel out of structures as distances shrink [94] makes it seem that very high q’s—corresponding to very strongly confined electron states—will be very hard to achieve in any technology at the deep nanoscale (1014  · nm. However, even this would not permit gate voltage swings greater than about 1.23 V, since at that level, even pure water conducts, via electrolysis. And even a 1.23 V barrier in the channel would still not allow channel lengths less than roughly 2–3 nm (depending on the particular semiconductor’s effective electron mass) without significant tunneling occurring between the source and drain electrodes. But if we widen our perspective a bit, we can note that there are other ways to control a potential-energy barrier between two electron-position states, besides just the field effect, which, at root, is only a simple application of ordinary Coulombic repulsion, together with the carrierdepletion phenomenon in semiconductors. For example, one could mechanically widen or narrow the separation between two conductive regions—this is the principle used in old electromechanical relays. Or a piece of conductive material could be inserted and removed from the space between the source and drain—ordinary toggle switches work this way. One can easily imagine performing the same general types of electromechanical interactions at the molecular level, and thereby perhaps obtaining device sizes closer to 1 nm. Vacuum gaps between conductors constitute fairly high energy

277 barriers, due to the multi-eV electron affinities (work functions) of most conductive materials, and therefore such gaps can be made significantly smaller than semiconductor channel lengths, while still avoiding the electron tunneling problem. So, ironically, electromechanical devices, which today we think of as being terribly antiquated, might, in the nanomolecular realm, turn out to scale to higher device densities than can our vaunted field-effect devices of today. However, whether this potentially higher device density may be enough to compensate for the relatively sluggish inertia of entire atoms, compared to electrons, when switching a gate, is still dubious. Nevertheless, one fortunate coincidence is that the relative slowness of the mechanical motions seems to be exactly what is needed anyway for efficient adiabatic operation in the electronics, which is necessary to maintain high performance in the face of heat flow constraints. So my tentative (and ironic) nomination for the “most likely contender” to be the dominant nanocomputing technology a few decades hence is nanoscale electrostatic relays using a dry-switching discipline. “Dry-switching” is an old term from electromechanical relay technology, meaning “do not open (resp. close) a switch when there is a significant current through (resp. voltage across) it.” Historically, this was done to prevent corrosion of the relay contacts due to air-sparking. But this is also exactly the key rule for adiabatic operation of any switch-based circuitry. The thought of using electromechanical relays sounds slow at first, until you consider that, at the nanoscale, their characteristic speeds will be on the order of the rates at which chemical reactions occur between neighboring molecules—since both processes will consist of essentially the same kinds of operations, namely molecule-sized objects bumping up against each other, and interacting both electrostatically via conformational changes and via actual exchange of electrons. The molecule-size gate, moved into place by an impinging electrostatic signal, can be thought of as the “catalyst” whose presence enables a source–drain electron-exchange “reaction.” In other words, this technology could be thought of as a sort of “controlled chemistry,” in which the “chemical” interactions happen at predetermined places at predetermined times, and information flows not randomly, via a slow diffusive random walk through solution, but instead at nearlightspeed along hard-wired electrically conductive paths to specific destinations where it is needed. This NEMS vision of computing does not yet specifically include quantum computing capabilities, but it might be modified to do so by including some spintronic device elements [102]. We briefly discuss some of the other alternative switching principles that have been considered. See also [103] for an excellent review of most of these.

6.2.2. Coulomb-Blockade Effect Single-Electron Transistors These devices are based on the quantum principle of charge quantization. They typically consist of a conductive island (although semiconductors may also be used) surrounded by insulator and accessed via some fairly narrow (typically 5– 10 nm) tunnel junctions. The Coulomb blockade effect is

278 the observation that the presence of a single extra electron on these small, low-capacitance structures may have a significant effect on their voltage, which, if greater than thermal voltage, thereby suppresses additional electrons from simultaneously occupying the structure. The Coulomb blockade effect may be significant even in cases where the number of electron energy levels is not itself noticeably quantized. In these devices, a voltage applied to a nearby gate allows one to choose the number of electrons (in excess of the neutral state) that occupy the island to a precision of just a single electron out of the millions of conduction electrons that may be present in, say, a 20 nm cube of material. The Coulomb blockade effect has also been demonstrated on a molecular and even atomic [104] scale, at which even roomtemperature manifestation of the effect is permitted.

6.2.3. Quantum Wells/Wires/Dots These are typically made of semiconductor materials. They are based on confinement of electron position in one, two, or three dimensions, respectively. Increased confinement of electron position in a particular direction has the effect of increasing the separation between the quantized momentum states that are oriented along that direction. When all three components of electron momentum are thus highly quantized, its total energy is also; this leads to the quantum dot, which has discrete energy levels. In quantum dots, the total number of activated conduction electrons may be as small as 1! Based on a thorough understanding of the quantum behavior of electrons, some researchers have developed alternative, non-transistor-like quantum-dot logics. A notable example is the paradigm of quantum dot cellular automata (QDCA) introduced by the group at Notre Dame [105]. The name QCA is also sometimes used for these structures, but I dislike that abbreviation, because it can be confused with quantum cellular automata, which is a more general and technology-independent class of abstract models of computation, whereas the QDCA, on the other hand, comprise just one very specific choice of device and circuit architecture, based on quantum dots, of the many possible physical implementations of the more general QCA concept. Also worth mentioning are the quantum computing technologies that are based on externally controlling the interaction of single-electron spins between neighboring quantum dots [71].

6.2.4. Resonant Tunneling Diodes/Transistors These structures are usually based on quantum wells or wires, and therefore may still have 2 or 1 (resp.) effectively “classical” degrees of freedom. In these structures, a narrow-bandgap (conductive) island is sandwiched between two wide-bandgap (insulating) layers separating the island from neighboring source and drain terminals. When the quantized momentum state directed across the device is aligned in energy with the (occupied) conduction band of the source terminal, electrons tunnel from the source onto the island, and then to unoccupied above-band states in the drain terminal. But a small bias applied to the device can cause the quantized momentum state in the island to no

Nanocomputers: Theoretical Models

longer be aligned in energy with the source terminal’s conduction band, in which case tunneling across that barrier is suppressed, and less current flows. Since multiple harmonics of the lowest momentum state also appear in the spectrum of the device, these devices typically have a periodic dependence of current on bias voltage. Resonant tunneling transistors are just like resonant tunneling diodes, except that there is an additional gate terminal near the island that provides an additional means for adjusting the energy levels in the island.

6.2.5. Electromechanical Devices Several kinds of nanoscale devices have been proposed which use mechanical changes (movements of atoms or assemblages of atoms) to control electrons, or vice versa. The molecular switches of [106] fall in this category, as would NEMS switches and relays based on nanoscale solidstate structures. Electromechanical structures offer somewhat of a design advantage in that the mechanism of their operation is relatively easy to visualize, due to the explicit change in their structural configuration. But the primary disadvantage of electromechanical operation is that atoms are many thousands of times as massive as electrons and therefore accelerate many thousands of times more gradually in response to a given force. As a result, the characteristic frequencies for oscillation of mechanical components tend to be many thousands of times less than those of similar-sized electrical ones. However, this disadvantage might conceivably be offset if it turns out that we can design NEMS devices that have much higher quality factors than we manage to obtain using electronics alone. This is suggested by the very high Q’s (in the billions) for a perfect diamond crystal vibrating in vacuum, and by the practical Q’s in the tens of thousands that are achievable today for MEMS mechanical resonators (essentially, springs) in vacuum. In contrast, the Q’s that have been obtained in simple microelectronic circuits such as LC oscillators tend to be much lower, usually in the tens or at most hundreds. We (or more precisely, I) do not (yet) know any fundamental reasons why a high-Q all-electronic nanoscale oscillator cannot be built, but it is not yet clear how to do so. In the meantime, hybrid electromechanical approaches might take up some of the slack. Resistive elements such as transistors naturally have high Q when they are operated at relatively slow speeds (i.e., adiabatically). If these are coupled to high-Q electromechanical oscillators, a high overall Q might be obtained for the complete self-contained system, thereby enabling ≪kT energy dissipation per bit operation. For example, if a mechanical oscillator with Q = 10000 is coupled to an adiabatic electronic FET which has a similarly high Q at the low frequency of the oscillator, so that the overall Q of the system is still 10,000, and if tunneling currents are kept negligible, then if we use a redundancy factor in the logic encoding of ∼11.5 nats/bit (i.e., on the order of 0.3 eV switching energy per minimum-sized transistor gate at room temperature), then one could theoretically achieve an on/off ratio of order e11
5 ≈ 100,000 and a best-case minimum entropy generation per bit-op on the order of e7 nat ≈ 0.001 kB (refer to Fig. 3). This could be advantageous in

Nanocomputers: Theoretical Models

that it would permit a ∼700 × higher total rate of computation per watt of power consumption (and per unit area, given heat-flux constraints) than in any physically possible fully irreversible technology (even if all-electronic), in which the entropy generated per bit-op must be at least ∼0
7kB . Another potential advantage of electromechanical operation is that mechanically actuated switches for electricity may be able to change electron currents by relatively large factors while using a relatively small amount of energy transfer. This is because a mechanical change may significantly widen a tunneling barrier for electrons, which has an exponential effect on electron tunneling rates. Therefore, it is not clear that an electromechanical system must be subject to the same kind of lower bound on entropy generation for given quality index as we discussed in Section 6.12. Thus, an electromechanical system with a Q of 10,000 might be able to achieve an even lower rate of entropy generation than we described in the previous paragraph, perhaps of the order of 1/10,000th of a bit of entropy generated per bit-op. An interesting corollary to this electromechanical line of thought is this: If the operating frequency of the logic is going to be set at the relatively low frequency of nanomechanical oscillators anyway, in order to achieve low power consumption, then is there any remaining benefit to having the actual logic be carried out by electrons? Why not just do the logic, as well as the oscillation, mechanically? This leads back to the idea of using all-mechanical logic at the nanoscale, an idea that was first promoted by Drexler [47]. We will discuss this possibility further in Section 7.3. However, there is still one clear advantage to be gained by using electrons for logic signals, and that is simply that the propagation speed of electronic signals can easily be made close to the speed of light, while mechanical signals are limited to about the speed of sound in the given material, which is much lower. Thus, communication delays over relatively long distances would be expected to be much lower in electromechanical nanocomputers than in all-mechanical ones. This is an important consideration for the performance of communication-dominated parallel algorithms.

6.2.6. Superconductive Devices Complex integrated circuits using high-speed (∼100 GHz) digital logic based on superconductive wires and Josephson junctions have already existed for many years [107], although they are unpopular commercially due to the requirement to maintain deep cryogenic (liquid helium) temperatures. Another problem for these technologies is that their speed cannot be further increased by a very large factor unless much higher temperature superconducting material can be effectively integrated. This is because flipping bits at a rate of 100 GHz already implies an effective coding-state temperature of at least 3.5 K; thus increasing speed by another factor of 100, to 10 THz, would require room-temperature superconductors, which have not yet been discovered. Superconductive devices therefore might never have an opportunity to become competitive for general-purpose computing, since traditional semiconductor devices are expected to reach ∼100 GHz frequencies in only about another 15 years. Also, it appears that it may be difficult to scale superconducting technology to the nanoscale, because ordinary

279 superconductivity is based on Cooper pairs of electrons, which have a relatively large spacing (order of 1 micrometer) in the usual superconducting materials [108]. However, this may turn out not really be a problem, since even carbon nanotubes have already been found to superconduct under the right conditions [109]. Even if superconductive technologies turn out not to achieve extremely high densities, they may still be useful at relatively low densities, for those particular applications that happen to require the special-purpose features of quantum computing. Superconductor-based devices for quantum computing are currently being aggressively explored [72], and this may turn out to be a viable technology for creating large scale integrated quantum computer circuits. But if the technology is not also simultaneously dense, low power, and high frequency, then it will likely be relegated to a “quantum coprocessor,” while the main CPU of the computer (used for more general-purpose applications) remains nonsuperconducting.

6.2.7. Spintronic Devices Spintronics [102] is based on the encoding of information into the spin orientation states of electrons, rather than the usual approach of using energy (voltage) states. Spin information typically persists for nanoseconds in conduction electrons, compared with the typical ∼10 fs lifetime for decay of momentum information (except in superconductors). Spintronics requires various technologies for spin control, propagation of spins along wires, selection of electrons based on their spin, and detection of electrons. Some examples of spintronic devices are the Datta–Das [110] and Johnson [111] spin-based transistors. Electron spins are also a potential medium for quantum computation, as is illustrated by the spin-based quantum dot quantum computers being explored by Friesen et al. [71]. Nuclear spins have already been used for quantum computing experiments for some time [70]. It is currently still unclear whether spintronic nanoelectronic technologies might eventually outperform nanoelectronics based on other properties.

6.3. Nanomechanical Logic Technologies Way back in the late 1980s and early 1990s, Drexler and Merkle proposed a number of all-mechanical technologies for doing logic at the nanoscale [43, 45, 47]. There is an argument why technologies like these might actually be viable in the long run, despite the slow speed of mechanical (atomic) signals. That is, if all-mechanical nanotechnologies turn out (for some reason) to be able to be engineered with much higher Q’s than electronic or electromechanical nanotechnologies can be, then the all-mechanical technologies would be able to operate with greater parallel performance per unit power consumed, or per unit surface area available for cooling. Presently, it is not yet clear whether this is the case. One approach called “buckled logic” [45] was specifically designed by Merkle to have very high Q, because it completely eliminates sliding interfaces, rotary bearings, stiction-prone contacts, moving charges, etc. and instead consists of an electrically neutral one-piece mesh of rods that simply flexes internally in a pattern of vibrational motions that is designed to be isomorphic to a desired

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280 (reversible) computation. If the computational vibrational modes can all be well insulated from other, noncomputational ones, then in principle, the Q’s obtainable by such structures, suspended in vacuum, might even approach that of pure crystal vibrations, that is, on the order of billions. This may enable a level of entropy generation per bit-op that is so low (maybe billionths of a nat per bit-op) that a vastly higher overall rate of bit-ops might be packed into a given volume than by using any of the feasible alternatives. However, until many more of the engineering details of these interesting alternatives have been worked out, the all-mechanical approach remains, for now, as speculative as the others.

6.4. Optical and Optoelectronic Technologies For purposes of high-performance, general-purpose parallel nanocomputing, all purely optical (photonic) logic and storage technologies are apparently doomed to failure, for the simple reason that photons, being massless, at reasonable temperatures have wavelengths that are a thousand times too large, that is, on the order of 1 micrometer, rather than 1 nanometer. Therefore, the information density achievable with normal-temperature (infrared, optical) photons in 3D space is roughly 10003 or a billion times lower than what could be achieved using electronic or atomic states, which can be confined to spaces on the order of 1 nm3 . Light with comparable 1 nm wavelengths has a generalized temperature on the order of 1000 × room temperature, or hundreds of thousands of Kelvins! These 1-nm photons would have to be extremely stringently confined while remaining somehow isolated from interaction with the computer’s material structure, in order to keep the computer from immediately exploding into vapor, unless a solid structure could somehow still be maintained despite these temperatures by (for example) applying extremely high pressures. The only exception to this problem might be if mutually entangled photons can be used, as these behave like a single, more massive object and thus have a lower effective wavelength at a given temperature. This wavelength reduction effect has recently been directly observed experimentally [112]. However, we presently have no idea how to produce a conglomeration of 1000 mutually entangled photons, let alone store it in a box or perform useful logic with it. Even if this problem were solved, photons by themselves cannot perform universal computation, since under normal conditions they are noninteracting, and thus only linearly superpose with each other (they cannot, for example, carry out nonlinear operations such as logical AND). However, photons may interact with each other indirectly through an intermediary of a material, as in the nonlinear photonic materials currently used in fiber optics [113]. Also, extremely high-energy photons (MeV scale or larger, i.e., picometer wavelength or smaller) may interact nonlinearly even in vacuum, without any intermediary material, due to exchange of virtual electrons [15], but the temperatures at which this happens seem so high as to be completely unreasonable. To deal with the problem of low information density and photon noninteraction, hybrid optoelectronic technologies have been proposed, in which electron states are used to

store information and do logic, while photons are used only for communication purposes. However, even in this case, we have the problem that the bit flux that is achievable with photons at reasonable temperatures is still apparently far lower than with electrons or atoms [114]. Therefore, it seems that light is not suitable for communication between densely packed nanoscale devices at bit rates commensurate with the operating speeds of those devices. This is again due to the limit on the information density of cool, nonentangled light. Communicating with (unentangled) photons therefore only makes sense for communications that are needed only relatively rarely, or between larger scale or widely separated components, for example, between the processors in a loosely coupled distributed multiprocessor.

6.5. Fluid (Chemical, Fluidic, Biological) Technologies 6.5.1. Chemical Computing Not all proposed nanotechnologies rely primarily on solidstate materials. Computing can also be done in molecular liquids, via chemical interactions. Much work has been done on chemical computing, especially using DNA molecules as the information-carrying component, since it is naturally designed by evolution for the purpose of information storage. Universal computing in DNA appears to be possible; for example, see [115]. Unfortunately, it seems that chemical techniques in a uniform vat of solution can never really be viable for large-scale, general-purpose parallel nanocomputing, for the simple reason that the interconnects are much too slow. Information is propagated in 3D space only by molecular diffusion, which is inherently slow, since it is based on a random walk of relatively slow, massive entities (molecules). Information transmission is thus many orders of magnitude slower than could be achieved in, say, a solid-state nanoelectronic technology in which signals travel straight down predetermined pathways at near the speed of light. Chemical methods also tend to be difficult to control and prone to errors, due to the generally large numbers of possible unwanted side-reactions.

6.5.2. Fluidics However, the situation may be improved slightly in fluidic systems, in which the chemicals in question are actively moved around through microchannels. Desired materials may be moved in a consistent speed and direction and brought together and combined at just the desired time. This more direct method gives a much finer degree of control and improves the interconnect problem a bit, although transmission speeds are still limited by fluid viscosity in the channel. One can also dispense with the chemical interactions and just use pressure signals in fluidic pipes to transmit information. Pressure-controlled values can serve as switches. This technique is highly analogous to ordinary voltage-state, transistor-based electronics, with pressure in place of voltage, and fluid flow in place of electric current. Fluidic control and computation systems are actually used today in some military applications, for example, those that cannot use electronics because of its vulnerability to the electromagnetic pulse that would result from a nearby nuclear blast.

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However, insofar as all fluid-based techniques require the motion of entire atoms or molecules for the transmission of information, one does not anticipate that any of these techniques will ever offer higher computational densities than the solid-state all-mechanical technologies, in which state changes are much more well controlled, or than the electromechanical or pure-electronic technologies in which signals travel at much faster speeds.

the human brain. Of course, it is another matter entirely whether software people will have figured out by then how to effectively harness this power to provide (for example) an automated office assistant that is anywhere close to being as generally useful as a good human assistant, although this seems rather doubtful, given our present relative lack of understanding of the organization and function of the brain, and of human cognition in general.

6.5.3. Biological Computing

6.6. Very Long-Term Considerations

Computing based on chemical interactions is, at best, likely to only be useful in contexts where a chemical type of input/output (I/O) interface to the computer is needed anyway, such as inside a living cell, and where the performance requirements are not extremely high. Indeed, a biological organism itself can be viewed as a complex fluidic chemical computer. In fact, it is one that can be programmed. For example, Knight and Sussman at MIT are currently experimenting with reengineering the genetic regulatory networks of simple bacteria to carry out desired logic operations [116]. Notice, however, that even in biology, the need for quick transmission and very fast, complex processing of information in fact fostered the evolution of a nervous system that was based on transmission of signals that were partly electrical, and not purely chemical, in nature. And today, our existing electronic computers are far faster than any biological system at carrying out complex yet very precisely controlled algorithms. For less precisely controlled algorithms that nevertheless seem to perform well at a wide variety of tasks (vision, natural language processing, etc.), the brain is still superior, even quantitatively in terms of its raw information processing rate. But by the time we have nanocomputers, the raw information-processing capacity of even a $1,000 desktop computer is expected to exceed the estimated raw information-processing capacity of the human brain [117]. One attempt at a generous overestimate of the raw information-processing capacity of the brain is as follows. There are at most ∼100 billion neurons, with at most ∼10,000 synapses/neuron on average, each of which can transmit at most ∼1000 pulses per second. If each pulse can be viewed as a useful computational “operation,” this gives a rough maximum of ∼1018 operations per second. Conservatively, today’s largest microprocessors have on the order of ∼100 million transistors (Intel’s Itanium 2 processor actually has 220 million) and operate on the order of ∼1 GHz (although 3 GHz processors now can be bought off-the-shelf, in early 2003). Such densities and clock speeds permit ∼1015 transistor switching operations to be performed every second. This is only a 1000 × slower raw rate than the human brain, assuming that the transistor “ops” are roughly comparable to synaptic pulses, in terms of the amount of computational work that is performed as a result. The historical Moore’s law trend has raw performance nearly doubling about every 1.5–2 years, so we would expect a factor of 1000 speedup to only take around 15– 20 years. So the nanocomputer that will be sitting on your desk in the year 2020 or so (just a little way beyond the end of today’s roadmap for traditional semiconductor technology) may well have as much raw computational power as

What are the ultimate limits of computing? As we have seen, to maximize rates of computation, both high computational temperatures and very precise control and isolation of the computation from the environment are simultaneously required. However, as computational temperatures increase, it becomes increasingly difficult to isolate these fastchanging, thus “hot,” computational degrees of freedom from the relatively cool degrees of freedom inherent in ordinary matter having stable structure (e.g., solids, molecules, atoms, nuclei). At some point, it may be best not to try to keep these structures stable anymore, but rather to let them dissolve away into fluids, and just harness their internal fluid transitions as an intentional part of the computation. In other words, it may eventually be necessary to take some of the energy that is normally tied up in the binding energy of particles, and thus is not doing useful computational work (other than continually computing that a given structure should remain in its current state), and release that energy to actively perform more useful computations. Smith [15] and later Lloyd [16] explored this hypothetical concept of a plasma-state computer and quantitatively analyzed the limits on its performance and memory capacity, which are determined by fundamental considerations from quantum field theory. As expected, performance is dependent on temperature. If material having the mass density of water is converted entirely to energy with no change in volume, it forms a plasma of fundamental particles (mostly photons) with a temperature on the order of 109 kelvins, hotter than the highest temperatures reached at the core of an exploding thermonuclear (hydrogen fusion) bomb. How can such a violent, high-temperature state possibly be configured in such a way as to perform a desired computation? Of course, this is totally impractical at present. However, in principle, if one prepares a system of particles in a known initial quantum state and thoroughly isolates the system from external interactions, then the unitary quantum evolution of the system is, at least, deterministic and can be considered to be carrying out a quantum computation of sorts. In theory, this fact applies to hot plasmas, as well as to the relatively cool computers we have today. However, even if the required exquisite precision of state preparation and isolation can someday be achieved, the question of how and whether any desired program can be actually “compiled” into a corresponding initial state of a plasma has not yet even begun to be explored. For the remainder of this section, we will pretend that all these issues have been solved, but alternatively, it may well be the case that we are never able to organize stable computation, without relying on an underlying infrastructure made of normal solid (or at least atomic) matter.

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282 Lloyd [16] points out that at normal mass-energy densities (such as that of water), a plasma computer would be highly communication-limited, that is, heavily limited by the speed-of-light limit, rather than by the speed of processing. But in principle the communication delays could be reduced by compressing the computer’s material beyond normal densities. As the energy density increases, the entropy density increases also, though more slowly (specifically, as energy density to the 43 power), and so energy per unit entropy is increased; that is, the temperature goes up. The logical (if extreme) conclusion of this process, for a given-size body of matter, is reached when the ratio of the system’s mass-energy to its diameter exceeds the critical value c 2 /4G, at which point the system comprises a black hole, disappearing into an event horizon, and the effects of any further compression cannot be observed. For a 1-kgmass computer, the critical size is extremely small, about 10−27 m, or roughly a trillionth of the diameter of an atomic nucleus. (Needless to say, this degree of compression would be very difficult to achieve.) Due to gravitational time dilation (redshifting), although the compressed matter would be very hot in its own frame of reference, it appears somewhat cooler than this to the outside world. In other words, the system’s output bandwidth is decreased by gravitational effects. This is because, simply stated, the outgoing information tends to be pulled back by gravity. Classically, in general relativity, the temperature of a black hole as measured from outside would by definition always be zero (no information can leave the hole), but, as shown in the now-famous work by Stephen Hawking [118], the temperature of a black hole is actually not zero when quantum uncertainty is taken into account. Effectively, particles can tunnel out of black holes (“Hawking radiation”), and the smaller the black hole, the quicker this rate of tunneling becomes. So smaller black holes have higher output temperatures and thus effectively make faster “computers,” at least from an I/O bandwidth point of view. A 1-kg-mass black hole would have a temperature of about 1023 K, and a presumed minimum-mass (Planck mass) black hole would have a temperature of ∼1032 K. This last temperature, the Planck temperature, may be a fundamental maximum temperature. It corresponds to a maximum rate of operation of ∼1043 parallel update steps per second, or 1 step per Planck time. This may be considered the fastest possible “clock speed” or maximum rate of operation for serial computation. It is interesting to note that if processor frequencies continue doubling every 2 years, as per the historical trend, then this ultimate quantumgravitational limit on clock frequency would be reached in only about 200 more years. At this point, the only possible improvements in performance would be through increased parallelism. Moreover, the parallel machine would have to be very loosely coupled, since Planck-mass black holes could not be packed together very densely without merging into a larger black hole, whose temperature, and output communication bandwidth, would be proportionately lower. The problem is that a black hole outputs information in only a single quantum channel, with bandwidth proportional to its

temperature [119]. However, its internal rate of operations can be considered to still be given by its total mass-energy. It is interesting to note that within a black-hole computer, the interconnection problem becomes a nonissue, since the time to communicate across the hole is comparable to the time to flip a bit [16]. Of course, all of these considerations remain extremely speculative, because we do not yet have a complete theory of quantum gravity that might be able to tell us exactly what happens inside a black hole, in particular, near the presumably Planck-scale sized “singularity” at its center. Conceivably, at the center is a busy froth of very hot fundamental particles, perhaps near the Planck temperature, which occasionally tunnel (although greatly gravitationally redshifted) out beyond the horizon. But we do not know for certain. Regardless of the precise situation with black holes, another speculative long-term consideration is the potential computational capacity of the entire universe, in bits and in ops. Lloyd has estimated upper bounds on these quantities, over the history of the universe so far [28]. Other papers by Dyson [120], and more recently by Krauss and Starkman [121], attempt to characterize the total amount of future computation that an intelligent civilization such as ours might eventually harness toward desired purposes. Significantly, it is still a matter for debate whether the total number of future ops that we may be able to perform over all future time is finite or infinite. Krauss and Starkman present arguments that it is finite, but they do not seem to take all possible considerations into account. For example, it may be the case that, by engineering reversible computational systems having ever-higher quality factors as time goes on, an infinite number of operations might be performed even if only a finite total supply of energy can be gathered, a possibility which they do not consider. Memory capacity is not necessarily limited either, since as the universe expands and cools, our energy stores might be allowed to expand and cool along with it, thereby increasing without bound the amount of information that may be represented within them. In any event, whether the total number of future ops that we may perform is infinite or not, it is undoubtedly very large, which bodes well for the future of computing.

7. CONCLUSION To conclude, we already have an arguably valid, if still rather rough, idea of what the most cost-effective general-purpose future nanocomputer architectures over the coming century should look like. Most concretely, high-performance nanocomputers will generally be flattened slabs of densely packed computing “material” (of limited thickness), consisting of 3D locally connected meshes of processors that include local memory and both traditional hardwired arithmetic-logic units and reconfigurable logic blocks, built from nanoscale, probably solid-state, electronic, or electromechanical devices. The device technology and architecture must also support both mostly reversible classical operation and fault-tolerant quantum algorithms, if it aspires to be universally maximally scalable.

Nanocomputers: Theoretical Models

Devices must be well insulated from their environment, that is, designed to have a very high quantum quality factor (i.e., low relative decoherence rate) which allows their internal coding state to transition reversibly and coherently at a fast rate (thus, a high effective temperature) relative to the rate of undesired interactions between the coding state and the (probably cooler) thermal state of the machine’s physical structure. Even when an application does not need to use quantum superposition states, well-isolated, high-Q reversible operation remains particularly critical for general-purpose parallel computation, in order to maximize the effective computation rate and number of active processors per unit area enclosed, and thereby to minimize the communication delays in communication-limited parallel algorithms. In these parallel architectures, the processors will be kept synchronized with each other via local interactions. Meanwhile, free energy will be supplied, and waste heat removed, by active flows of energy and/or coolant material which pass perpendicularly through the computing slab, and which are recirculated back through the machine to be reused, after their entropy and the accompanying waste heat are deposited in some external reservoir. This vision, although it places a number of constraints on what nanocomputing will look like, still provides a lot of flexibility for device physicists to do creative engineering design and optimization of the specific device mechanisms to be used for logic, memory, interconnect, timing, energy transfer, and cooling, and it leaves a lot of room for computer engineers and computer scientists to come up with more efficient new processor organizations and programming models that recognize the need to support reversible and quantum, as well as parallel, modes of operation and that respect fundamental physical constraints. Finally, if we are successful in converging on a nanocomputing technology that indeed approaches the quantum limits discussed in Section 2, and if our civilization’s demand for computational power continues to increase beyond that point, then we can expect that the fraction of the available material (mass-energy) that is devoted toward nanocomputing will increase as well. If our civilization continues to thrive and grow, then eventually, in the extremely long term (perhaps hundreds or thousands of years hence), we may find ourselves wanting to build nanocomputers that are so massive (using many planets’ or stars’ worth of raw material) that their self-gravitation becomes a significant concern. This will bring a new fundamental physical concern into play, namely general relativity, which this chapter has not yet thoroughly considered. At that distant future time, the form of our computer models may need to change yet again, as we figure out how best to maximize cost-efficiency of computing in the face of this new, gravitational constraint. But in the meantime, until that happens, the simpler type of nanocomputer model that we discussed in Section 6 is expected to last us for a very long time. The primary goal for the current generation of nanocomputer engineers is, then, to flesh out and optimize the technological and architectural details of the general class of models that we have outlined, guided by our rapidly improving understanding of the basic principles of nanoscale science and technology, as documented throughout this encyclopedia.

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GLOSSARY Å Standard abbreviation for Ångstrom. Adiabatic A process is adiabatic to the extent that it can take place with arbitrarily little generation of entropy. Originally in thermodynamics, “adiabatic” literally meant “without flow of heat” and applied to any physical process in where there was no (or negligibly little) heat flow. However, today in applied physics, “adiabatic” means “asymptotically isentropic,” that is, approaching zero total entropy generation, in the limit of performing the process more slowly, and/or with diminished parasitic interactions with its environment. The old and new definitions are not equivalent. Adiabatic losses Energy that is dissipated to heat due to the imperfections present in a nominally adiabatic process, as opposed to energy that is necessarily dissipated due to logical irreversibility. Adiabatic principle The total adiabatic losses of a given process scale down in proportion to quickness as the process is carried out more slowly. Adiabatic theorem A theorem of basic quantum theory that says that so long as the forces on a system (expressed in its Hamiltonian) are changed sufficiently slowly, and some additional technical conditions on the spectrum of energy eigenstates are met, a system that is initially in a pure state will remain in an almost pure state, that is, with a total generation of entropy that is inversely proportional to the quickness of the transition. The theorem is very general; adiabatic processes are therefore nearly ubiquitously available, that is, in almost any reasonable nanodevice technology. Adjoint A term from matrix algebra. The adjoint of a matrix is its conjugate transpose. Algorithm A precise description of a particular type of computation, abstracted away from the specific inputs, and often also abstracted away from the machine architecture and the details of the programming model. Amplitude Complex number giving the value of a quantum wavefunction at a given state. It can be broken into phase and magnitude components. The squared magnitude of the amplitude corresponds to the probability density at the given state. Amu Unified atomic mass unit, equal to 1
6605402 × 10−24 g. About the mass of a proton or neutron. Originally defined as 1/12 the mass of a carbon-12 atom. In computational units, equal to 450 zettapops per second. Ångstrom A unit of length equal to 10−10 meters, or 0.1 nm. One Ångstrom is the approximate radius of a hydrogen atom. Angular momentum In computational terms, this is the ratio between the number of quantum operations required to rotate an object by a given angle around a point, and the magnitude of the angle. It is quantized, so that a rotation by 180 or  radians always involves an integer number of -ops (ops of magnitude size h/2), and a rotation by 1 radian involves an integer number of -ops (ops of magnitude
). Architecture An activity, namely, the functional and structural design of any complex artifact, such as a skyscraper or a computer. Within the field of computer architecture, a specific architecture refers to a particular computer design, which may include any levels of design from the logic circuits

284 up through the interconnection networks of a multiprocessor computer. Architecture family A class of architectures of unbounded capacity (a specific architecture may have only constant capacity). That is, a recipe for creating architectures of any desired capacity. I also frequently use the phrase capacity scaling model rather than architecture family, since it is more descriptive. ASCII American Standard Code for Information Exchange; a widely used standard for representing Latin alphabet characters, digits, and simple punctuation marks using 8-bit numbers. Ballistic An adiabatic process that also has a nonzero net “forward” momentum along the desired trajectory through configuration space. This is an opposed to adiabatic processes that have zero net momentum and progress only via a random walk (Brownian motion). Bandgap In condensed matter theory, the bandgap in a semiconducting or insulating material is the magnitude of separation in energy level between the top of the valence band and the bottom of the conduction band. Insulators have a large bandgap; semiconductors have a relatively small one. In metals the bandgap is negative (meaning the bands overlap). Bandwidth In computer science, a rate of information transfer (e.g., in bits per second). This meaning is closely related to the original, literal meaning, which was the width (in Hertz) of a frequency band used for wave-based communications. In communications theory, a single classical wave-based communication channel with a given frequency bandwidth can be shown to have a proportional maximum rate of information transfer. Basis A term from linear algebra. A complete set of (often orthogonal, but at least linearly independent) vectors, sufficient to define a given vector space. In quantum theory, a complete set of distinguishable states forms a basis. Basis state Any single state that is aligned along one of the axes of a given basis. Bennett’s algorithm A reversiblization algorithm discovered by Bennett. The 1973 version of the algorithm (which takes linear time but polynomial space) is a special case of a more general version of the algorithm described in 1989. Bennett copy To rescue desired information from being uncomputed during Lecerf reversal by reversibly copying it before performing the reversal. Binary number A number represented in base-2 notation, using a series of bit systems. Binary tree An interconnection network structure in which each node is connected to 1 “parent” node and 2 “child” nodes. Binary trees are not physically realistic with unit-time hops. Bistable Having two stable states. Bit Shorthand for binary digit, this is the log-base-2 unit of information or entropy. (The abbreviation bit for this concept was coined by John Tukey in 1946.) An amount of information can be counted by a number of bits. In addition, the word bit can also be used to mean a bit system; in this usage, a bit denotes not only a measure of amount of information, but also a specific piece of information.

Nanocomputers: Theoretical Models

Bit device Any device that is designed for storing and/or processing a single logical bit, or a small constant-size collection of logical bits, at any given time. For example, a transistor or a logic gate could be considered to be a bit device, but an n-bit adder is larger than that. (We sometimes use the term bit device when we wish to be clear that we are referring to individual logic devices, rather than to more complex “devices” such as CPUs or laptop computers.) Bit operation An operation that manipulates only 1 or at most a small constant number of (physical or logical) bits. Bit system A system or subsystem containing exactly 1 bit of physical information. That is, a specific instance of a type of system or subsystem having exactly two distinguishable states (see qubit) or with a particular pair of distinguishable states for the subsystem (i.e., a particular partition of a set of distinguishable states for the entire system into two equal sized parts). Bitwise ripple-carry add In computer arithmetic, a hardware or software algorithm for adding two binary numbers using the base-2 equivalent of the traditional grade-school algorithm, with a carry from each place to the next. Black box Name applied to a device, function, process, or transformation when one is allowed to use the entity to produce outputs from inputs but is not allowed to “open the box,” to directly determine anything about its internal structure. Black hole An object whose escape velocity (due to its gravity) exceeds the speed of light. Boltzmann’s constant See nat. Butterfly network An interconnection network similar to a sort of unfolded hypercube. Butterfly networks are not physically realistic (see PR) given unit-time hops. Byte Usually, 8 bits. Sufficient to denote 1 Latin character, number, or punctuation symbol in the ASCII character set. c See speed of light. CA (cellular automaton) The cellular automaton is a model of computation, first envisioned by von Neumann [33], consisting of a regular mesh of finite-capacity processing elements operating in parallel. Two-dimensional cellular automata have the maximum scalability among fully irreversible models of computing. Three-dimensional reversible cellular automata are conjectured to be a universally maximally scalable model of computation, up to the gravitational limit. Calorie Unit of energy originally defined as the heat required to increase the temperature of 1 g of water by 1 degree Kelvin. Equal to 4.1868 J. CAM (cellular automata machine) A type of parallel computer architecture in which the programming model is based upon the cellular automaton model of computation. A number of CAMs were designed and built by the information mechanics group at MIT in the 1980s and 1990s. (See [122].) Capacity The computational capacity or just capacity of a computer is measured by two parameters: (1) How many bits of logical information can it store? (2) How many bit operations per second can it perform? Carbon nanotube Sometimes called buckytubes (for Buckminster Fuller), these are nanometer-scale (in diameter)

Nanocomputers: Theoretical Models

hollow tubes made out of pure carbon, consisting essentially of a graphene (graphite-like) sheet rolled into a cylinder. They have a higher strength-to-weight ratio than steel, conduct electricity better than copper, and have a high thermal conductivity, making them a promising component for future nanomechanical and nanoelectronic applications. Cellular automaton, cellular automata See CA. Channel The region of a transistor through which current flows (between source and drain) when the transistor is turned on. Characteristic length scale For any engineered system, its characteristic length scale is defined as the average distance between neighboring instances of the smallest custom-designed functional components of the system (for example, the average distance between neighboring transistors in a densely packed electronic circuit). The characteristic length scale of a traditional semiconductorbased computer is determined by the minimum wire pitch (distance between center lines of neighboring wires) in integrated circuits, which in early 2003 is roughly 0.2 micrometers. Church’s thesis Also known as the Church–Turing thesis. This physical postulate claims that any reasonable (physically realizable) model of computation yields the same set of computable functions as does recursive function theory (Church’s original model of computing) or (equivalently) the Turing machine model. See also the strong Church’s thesis and the tight Church’s thesis. Circuit node In lumped models of electronic circuits, a node is a region of the circuit that is modeled as being at a uniform voltage level. Classical computing Computing in which the only coding states used are pointer states. Classical information Information that is sufficient to pick out a single basis state from a given basis, but that does not itself specify the basis. CMOS Complementary metal–oxide–semiconductor, the dominant process/device technology for digital electronic computing today, involving PFET and NFET field-effect transistors, which complement each other (the PFETs conduct the high-voltage signals, and the NFETs conduct the low-voltage ones). Coding state Also coding physical state. This is the state of the coding subsystem of a given system, that is, the physical information that represents (perhaps very redundantly) the logical information that is intended to be encoded. Coherent Term for a quantum system that can remain in a superposition of pointer states for long periods, which requires a very low decoherence rate. Because of the low decoherence rate, a coherent system undergoing a definite evolution produces no entropy and evolves adiabatically, even ballistically. (In contrast, noncoherent adiabatic evolution occurs when the evolution is restricted to a trajectory consisting of only pointer states; superpositions of these must be avoided in order to achieve adiabatic operation if the system is decoherent.) Combinational logic Digital logic in which outputs are produced by a combination of Boolean operators applied

285 to inputs, as soon as inputs are available, as fast as possible. Less general than sequential logic, because intermediate results cannot feed back into the inputs to be reused, and data cannot be stored. Communication The movement of information from one physical system to another. Commute Mathematical term. Two operators commute with each other if performing them in either order always gives the same result. Measurements in quantum theory are represented by observables, that is, Hermitian operators, which leave the eigenstates unchanged, except for scaling by the measured value. Two observables commute if one can measure them in either order and always obtain the same result. If this is not the case, then we can say that one measurement has disturbed the value that would have been obtained for the other, and vice versa. This fact is the origin of Heisenberg’s uncertainty principle. Complete (parallel) update step See step. Complex number When the theory of the real numbers is extended by closing it under exponentiation, the result is a unique theory in which numbers correspond to real vectors (called complex numbers) in a 2D vector space over the reals, and the vectors corresponding to reals themselves all lie along a given axis. The other orthogonal axis is called the imaginary axis. The imaginary unit vector i is defined as i = −11/2 . In complex vector spaces, complex numbers themselves are considered as being just scalar coefficients of vectors, rather than as vectors themselves. Complexity In computational complexity theory, a major branch of theoretical computer science, “complexity” is simply a fancy name for cost by some measure. There are other definitions of complexity, such as the algorithmic or Kolmogorov complexity of objects, often defined as the length of the shortest program than can generate the given object. However, we do not make use of these concepts in this chapter. Compute To compute some information is to transform some existing information that is in a known, standard state (e.g., empty memory cells), in a deterministic or partially randomized fashion, based on some existing information, in such a way that the “new” information is at least somewhat correlated with the preexisting information, so that from a context that includes the old information, the new information is not entirely entropy. See also uncompute. Computable A function is considered computable if it can be computed in principle given unlimited resources. Computation The act of computing. When we refer to computation in general, it is synonymous with computing, but when we reify it (talk about it as a thing, as in “a computation”), we are referring to a particular episode or session of information processing. Computational temperature Also coding temperature. The temperature (update rate) of the coding state in a machine. Computing Information processing. The manipulation and/or transformation of information. Computer Any entity that processes (manipulates, transforms) information. Conductance The ratio between the current flowing between two nodes and the voltage between them. A single

286 quantum channel has a fundamental quantum unit of conductance, 2e2 /h, where e is the electron charge and h is Planck’s constant. Conduction band In condensed matter theory, the conduction band is the range of energies available to electrons that are free to move throughout the material. Conductor An electrical conductor is a material in which the valence and conduction bands overlap, so that a significant fraction of electrons in the material occupy unbound states with wavefunctions that spread throughout the material. The electrons in the highest energy of these states can very easily move to other states to conduct charge. However, they have a minimum velocity called the Fermi velocity. Conjugate The conjugate of a complex number is found by inverting the sign of its imaginary part. The conjugate of a matrix is found by conjugating each element. Cost Amount of resources consumed. To the extent that multiple types of resources can be interconverted to each other (e.g., by trade, or by indifference in decision-making behavior), cost for all types of resources can be expressed in common units (e.g., some currency, or utility scale). This should be done when possible, because it greatly simplifies analysis. Cost measure A way of quantifying cost of a process based on one or more simpler characteristics of the process (e.g., time or spacetime used). Cost efficiency The cost efficiency of any way of performing a task is the ratio between the minimum possible cost of resources that could have been consumed to perform that task using the best (least costly) alternative method, and the cost of resources consumed by the method actually used. It is inversely proportional to actual cost. COTS Commercial off-the-shelf; a currently commercially available, noncustom component. Coulomb blockade effect The phenomenon, due to charge quantization, whereby the voltage on a sufficiently lowcapacitance node can change dramatically from the addition or removal of just a single electron. This effect can be utilized to obtain nonlinear, transistorlike characteristics in nanoscale electronic devices. Coulombic attraction/repulsion The electrostatic force, via which like charges repel and unlike charges attract, first carefully characterized by Coulomb. CPU Central processing unit. The processor of a computer, as opposed to its peripheral devices, enclosure, etc. Today’s popular CPUs (such as Intel’s Pentium 4) reside on single semiconductor chips. However, the future trend is toward having increasing numbers of parallel CPUs residing on a single chip. Current In electronics, the current is a rate of flow of charge; it is measured in units of charge per unit of time. The SI unit of current is the Ampere. Database In the real world, a database means an explicit table listing arbitrary data (perhaps in a constrained format), or a collection of such tables. With this standard definition, quantum “database search” is misnamed; it is not actually beneficial for searching such databases. (See Section 5.2.) de Broglie wavelength In quantum mechanics, a fundamental particle (or entangled collection of fundamental

Nanocomputers: Theoretical Models

particles) having total momentum p is described by a quantum wavefunction over position states having an associated wavelength  = h/p, with the wave vector oriented in the same direction of the momentum vector. The wavelength is called the de Broglie wavelength of the particle. Decay temperature The rate of decay of structural information. Decoherence A quantum system decoheres (increasing the entropy of its density matrix) when it undergoes either an unknown unitary transformation, or a known interaction with an environment whose state is itself unknown. Maximum decoherence occurs when the state has become a Boltzmann maximum-entropy state (uniform distribution). Continuous decoherence can be factored into a superposition of discrete quantum decoherence events, each of which changes the sign or value of an individual qubit. Decoherence-free subspace Some quantum systems that as a whole are highly decoherent may include natural subsystems (perhaps internally redundant ones) that are highly coherent, due to cancellation or interference effects that naturally suppress the subsystem’s interactions with the environment. Quantum error correction is the algorithmic construction and maintenance of a decoherence-free subspace, achieved through explicit coding schemes. Decoherent Having a high decoherence rate. Decoherence rate A measure of the rate at which the offdiagonal elements of the density matrix approach zero, meaning that the quantum state is approaching a plain statistical mixture of pointer states. Can be characterized in terms of number of discrete quantum decoherence events per unit time. Decoherence temperature The temperature (step rate) of decoherence interactions. Same thing as (one measure of) decoherence rate. The reciprocal of decoherence time. Density matrix A representation of mixed states, generated by right-multiplying the state vector by its adjoint. Device In general, this means any physical mechanism; however, in the context of computer architecture, it usually refers to the lowest level functional components of the design, such as (in electrical circuits) transistors, capacitors, resistors, and diodes, although sometimes even interconnecting wires are also explicitly considered as devices (since they do have physical characteristics that affect their functionality). In this chapter, I use the phase bit device instead of just device when I wish to emphasize the primitive components of digital systems. Device pitch The pitch between devices. See device, pitch. Dimensionality A term from linear algebra. The maximum number of mutually orthogonal vectors in a given vector space. Distinguishable states Two quantum states are considered to be entirely distinguishable from each other if and only if their state vectors are orthogonal (perpendicular to each other). Dopants Impurities (sparse atoms) that are added to a semiconductor to adjust its equilibrium concentration of mobile charge carriers, and their dominant type (electrons vs holes).

Nanocomputers: Theoretical Models

Dynamics The dynamics of a system specifies a transformation trajectory that applies to the system over time. Effective mass In condensed matter theory, it is found that an electron of given velocity has a longer wavelength than the de Broglie wavelength of a free electron with the same velocity. This phenomenon is concisely handled by ascribing an effective mass to the electron in matter that is smaller than the actual rest mass of the particle. Eigenstate A state of a quantum system that remains unchanged by a given measurement, interaction, or time evolution. An eigenvector of the measurement observable, interaction Hamiltonian, or the unitary time-evolution matrix. Eigenvalue A term from linear algebra. An eigenvalue of an eigenvector of a particular linear transformation is the scalar value that the vector gets multiplied by under that specific transformation. The eigenvalue of a measurement observable is the numerical value of the measured quantity. Eigenvector A term from linear algebra. An eigenvector of a particular linear transformation is any vector that remains unchanged by the transformation apart from multiplication by a scalar (the corresponding eigenvalue). Electromigration When the motion of a current through a solid material causes gradual rearrangement of the atoms of the material. A problem in today’s microcircuitry. If a wire happens to be narrower than intended at some point, electromigration can accelerate the wire’s degradation until it breaks. Note: adiabatic operation can help prevent this. Emulate Simulate exactly (with complete digital precision). Energy Energy (of all kinds) can be interpreted, at a fundamental level, as just the performing of physical computation at a certain rate in terms of quantum bit operations per second, according to the formula E = 14 hR, where h is Planck’s (unreduced) constant and R is the rate of complete bit operations [16, 18]. For most forms of energy, we do not notice the computation that is associated with it, because that computation is only performing such familiar, everyday sorts of information processing as shifting a physical object through space (kinetic energy) or exchanging force particles between two objects (binding energy, a.k.a. potential energy). Also, depending on the state, much of the energy may have a null effect. Only a miniscule part of the energy in most computers is actually directed toward performing information transformations that are of interest for carrying out the logic of the application. As technology advances, we learn to harness an increasing fraction of systems’ energy content for computational purposes. The first law of thermodynamics expresses the observation that total energy is conserved (i.e., that the total physical computation taking place within a closed system proceeds at a constant rate), which we know from Noether’s theorem is equivalent to the postulate that the laws of physics (as embodied in the global Hamiltonian) are unchanging in time. Energy eigenstate An eigenstate of the energy observable. Energy transfer model In a model of computation, the model of the flow of energy and information (including entropy) through the machine. Entangle Two quantum systems are entangled if their joint state cannot be expressed as the tensor product (essentially,

287 a concatenation) of simple pure or mixed states of the two systems considered separately. This is really nothing more than a straightforward generalization to quantum systems of the simple classical idea of a correlation. For example, if I flip a coin and then, without looking at it or turning it over, chop it in half, then I may know nothing about the state of either half by itself, but I do know that the two halves will show the same face when I look at them. Entropy Information that is unknown to some particular entity (unknown in the sense that the amount of information in the system can be known, but the specific content of the information is not). Equilibrium A given system is considered to be at equilibrium if all of its physical information is entropy, that is, if it has maximum entropy given the constraints implicit in the system’s definition. Due to the second law of thermodynamics, the equilibrium state (a mixed state) is the only truly stable state; all other states are at best meta-stable. Error correction Through decay/decoherence interactions, the logical or coding state of an information-processing system may gradually accumulate unwanted departures away from the desired state. The information in these unwanted variations represents a form of entropy. Error correction is the removal of this entropy and recovery of the original, desired logical and coding state. Being an entropy removal process, it is just a special case of refrigeration. Error correction can be implemented physically (e.g., by connecting a circuit node to a high-capacitance power supply reference node with a stable voltage), or algorithmically, by using redundant error correction codes and explicitly detecting and correcting bit errors one by one. Error correction techniques exist for quantum superposition states, as well as for classical state spaces. Euclidean space A space in which the metric is flat, and classical flat-plane geometry like Euclid’s remains valid. Measurements show that the physical spacetime that we live in is very nearly Euclidean. Far nanoscale The range of pitch values between 0.032 and 1 nm. Contrast near nanoscale. Fat tree Another interconnection network stricture similar to a binary tree, except that each node is connected to several parent nodes for additional communication bandwidth and redundancy. Fat trees are not physically realistic with unit-time hops. Fermi level The average energy of electrons at the “surface” of the Fermi sea. Fermi velocity The average velocity of electrons having sufficient energy to be at the Fermi level. Fermi wavelength The de Broglie wavelength of electrons moving at the Fermi velocity, that is, having enough kinetic energy to put them at the Fermi level (the surface of the Fermi sea of electrons). Fermi sea Electrons, being Fermions, obey the Pauli exclusion principle (no two can occupy the same state at the same time), and therefore, given a set of available states, electrons will “fill up” the available states, from lowest to highest energy. This is called the “Fermi sea.” The surface of the Fermi sea may be called the “Fermi surface”; it is at the Fermi level of energy. All the action (transitions of electrons

288 and holes to new states) happens near the Fermi surface, because the deeper electrons have no available states nearby to transition to. FET Field-effect transistor; a transistor (voltage controlled current switch) whose operation is based on the field effect. Field effect An effect seen in semiconductors where an applied electrostatic field significantly changes the mobile charge-carrier concentration in a material, as a result of moving the Fermi level farther toward or into the valence band or the conduction band. Flux In general, for our purposes, a rate of transfer of some conserved substance or material per unit area of some surface it is passing through. Sometimes called flux density or flux rate. In nanocomputer systems engineering, we consider key quantities such as information flux (bandwidth density), entropy flux, energy flux, and heat flux. The former two are fundamentally limited as a function of the latter two. FPGA (field-programmable gate array) A type of processor consisting of a regular array of low-level functional units or logic gates, which is programmed by configuring the function and interconnection of the individual elements. Commonly used today in embedded applications; major commercial manufacturers in 2003 include Xilinx and Altera. Many future general-purpose processors will likely include an FPGA-like module that can be reconfigured for efficient special-purpose processing. Free energy For our purposes, the free energy in a system is its total energy minus the spent energy, that is, the amount of energy ST that would be needed to move all of the system’s entropy S to the lowest temperature available thermal reservoir, at temperature T . Compare to Gibbs free energy and Helmholtz free energy. Frequency The quickness of a process that continually repeats itself. In other words, periods or cycles per time unit. Typical unit: the Hertz (inverse second). G Newton’s gravitational constant, 6
67259 × 1011 Nm2 /kg2 . Still used in Einstein’s general relativity, the modern theory of gravity. g Abbreviation for gram (the mass unit). Gate There are two meanings used in this document. The gate of a transistor is the circuit node that controls its conductance. A logic gate is a bit device that carries out a specified Boolean logic operation. A logic gate today consists of several transistors and may contain several transistor gates. General-purpose processor A processor that can be programmed to carry out any algorithm (up to the limit set by its storage capacity). General Theory of Relativity Also just general relativity (GR), Einstein’s theory of gravity, based on the principle that gravity is equivalent to an accelerated reference frame. GR predicts a number of surprising phenomena, such as curved spacetime, black holes, and gravity waves, all of which have been (at least indirectly) confirmed by experiment. Eventually GR needs to be unified with the Standard Model. GR provides the only fundamental physical limit to computer scaling that is not already incorporated into the model described in this chapter. Gibbs free energy The Helmholtz free energy, plus the energy of interaction with a surrounding medium at pressure

Nanocomputers: Theoretical Models

p given by pV where V is the volume of the system. See free energy for an even more comprehensive concept that includes all energies that are not clearly spent energy. Gram SI mass unit originally defined as the mass of 1 cubic centimeter of water at a certain standard temperature and pressure. Ground state The lowest energy state of a given system of variable energy. That is, the energy eigenstate having the lowest (most negative) possible energy eigenvalue. Grover’s algorithm A quantum algorithm originally characterized as a database search algorithm that is (more usefully) really an algorithm for the unstructured search problem. Hamiltonian This is a term from classical mechanics that remains valid in quantum mechanics. The Hamiltonian is a function that gives a system’s energy as a function of its state variables. The Hamiltonian incorporates all of the interactions between the subsystems of a given system. All of the dynamical laws of mechanics can be expressed in terms of the system’s Hamiltonian. In quantum mechanics, this remains true; the dynamics is given by Schrödinger’s equation. The Hamiltonian is an observable, an Hermitian transformation of state vectors. In quantum field theory, the Hamiltonian can be expressed as a sum of local interactions, which makes it consistent with special relativity. Hardware efficiency The reciprocal of the spacetime cost of a computation. A figure of merit used in VLSI theory that is appropriate for some nanocomputer system optimizations, in limited contexts. However, in general, it is incomplete, because it ignores energy costs, as well as costs that are proportional to time alone (such as inconvenience to the user). Heat Heat is simply that part of a system’s total energy that resides in subsystems whose physical information is entirely unknown (entropy). Heisenberg’s uncertainty principle The most general form of this principle is that two quantum states that are not orthogonal to each other are not operationally distinguishable, by any physical possible means whatsoever. It manifests itself frequently in statements that two observables that do not commute with each other (e.g., position and momentum of a particle) cannot both be precisely measured for the same system. Helical logic A reversible logic scheme proposed by Merkle and Drexler in which a rotating electromagnetic field adiabatically shuttles charge packets around a network of wires in which they steer each other via Coulombic interaction. Helmholtz free energy The free energy (see our definition) of a system, minus that portion that is not considered to be internal energy. To the extent that internal energy is less well defined than is total energy (for instance, how much of the rest mass-energy does it include?), Helmholtz free energy is less well defined than is our free energy. Hermitian operator An operator on quantum states that is equal to its adjoint (conjugate transpose). Hermitian operators have real-valued eigenvalues. In quantum mechanics, Hermitian operators represent both measurements of observable characteristics and interactions (Hamiltonians)

Nanocomputers: Theoretical Models

between systems (which makes sense, since a measurement is just a type of interaction). Hilbert space This is a term from linear algebra. A Hilbert space is simply a complex vector space that supports an inner product (dot product) operation between vectors. In quantum mechanics, the set of possible quantum states of a system is described mathematically as a Hilbert space. Not all states in the Hilbert space are operationally distinguishable from each other. Two states are distinguishable if and only if their state vectors are orthogonal. Hole The absence of an electron in a state below the Fermi surface. (Think of it as a bubble in the Fermi sea.) Hop The propagation of information from one node in an interconnection network to another node to which it is directly connected. Https Hyper text transfer protocol, secure: a protocol for secure communication of web pages and form data based on the transport layer security (TLS) protocol, which may use RSA internally (thus being vulnerable to cracking by a quantum computer). Hypercube An d-dimensional interconnection network formed by connecting corresponding nodes of a (d − 1)dimensional hypercube. Hypercubes are not physically realistic with unit-time hops. Ideal gas constant See nat. Information That which distinguishes one thing from another, in particular, different (distinguishable) states of a physical system. We say that a system in a particular state contains the information specifying its state. An amount of information can be quantified in terms of the number of (equally probable) distinct states that it suffices to distinguish. The natural convention is that the information corresponds to the logarithm of the number of distinguishable states; this measure has the advantage of being additive whenever multiple independent systems are considered together as one system. Any real number r > 1, when used as the base of the logarithm, yields a corresponding unit of information. The unit of information corresponding to the choice r = 2 is called the bit, whereas the unit corresponding to r = e (the base of the natural logarithms) is called the nat. (Boltzmann’s constant kB and the ideal gas constant R turn out to be simply alternative names for 1 nat.) Instruction set architecture (ISA) A traditional type of programming model in which serial computations are expressed by a sequence of low-level instructions which tell the computer to do a simple arithmetic or logical operation (such as adding two numbers), or to transfer control to a different point in the instruction sequence. Other, very different types of programming models are also possible, such as models used in FPGAs and cellular automata machines. Insulator An insulator is a material in which the bandgap between the valence band and the conduction band is so large that there is negligible charge-carrier concentration and therefore negligible conductivity. (Compare semiconductor.) Integrated circuit A complex circuit manufactured as a single solid-state component.

289 Interference In any wave-based process, waves interfere when they add linearly in superposition; this interference can be either constructive with two waves have the same sign or destructive when they have opposite sign. Since everything is a wave in quantum mechanics, two different trajectories in a quantum computer can interfere destructively if they arrive at a given state out of phase with each other. Such interference between trajectories is necessary to get added power from quantum algorithms. Interconnect A pathway for communication. Internal energy Energy in a system other than the kinetic energy of its overall motion and energies of interaction with other external systems. Sometimes in the traditional thermodynamics definitions of this concept, rest mass-energy is also omitted from the definition, although this is an arbitrary and artificial step, since internal potential energy (which is usually included in internal energy) is technically (in relativity) an indistinguishable concept from rest mass-energy, which necessarily includes the binding energies (which are internal potential energies) of, for example, atoms, protons, and neutrons. Internal ops Operations that are concerned with updating the internal state of an object, as opposed to propagating the object through space translationally or rotationally. The rate of internal ops is the rest mass-energy or internal energy of an object. The total number of internal steps taken, relative to that of a comoving reference object (clock), is the proper time experienced by the system. Invertible A mathematical term. A function is invertible if its inverse relation is also a function, that is, if the original function is one-to-one. Iop Short for “inverting op,” a unit of computational work equal to one-half of a pop. Irreversible computing The traditional computing paradigm, in which every computational operation erases some amount of known information and therefore necessarily generates a corresponding amount of new physical entropy. Isentropic Literally, “at the same entropy.” A process is isentropic if it takes place with no new generation of physical entropy. J Abbreviation for Joule (the energy unit). Josephson effect, Josephson junction A superconducting current can even pass through a sufficiently narrow tunnel barrier (Josephson junction) without resistance, up to some critical current at which the junction abruptly switches off (Josephson effect). This phenomenon is the basis for some superconducting logic technologies, such as the fairly successful rapid single-flux quantum technology developed by Konstantin Likharev’s group at SUNY. Joule A unit of energy defined as 1 N · m. In computational units, a Joule is equal to a potential computing rate of 6
036 × 1033 primitive operations (pops) per second. k In Roman font, k, an abbreviation for kilo-. In italic font k, often used to represent Boltzmann’s constant. kT Called the thermal energy, this product of Boltzmann’s constant k and the thermal temperature T is the average energy (or rate or operations) per nat’s worth of state information in a thermal system. However, it also applies just as well to nonthermal systems at generalized temperature T .

290 Kelvin SI unit of absolute temperature, defined originally as 1/100th the absolute temperature difference between the freezing and boiling points of water at atmospheric pressure. In computational units, 1 Kelvin is equal to an average rate of state change of 28.9 billion steps (pops per bit) per second, that is, an update frequency of 28.9 GHz. Kilo SI unit prefix meaning 1000. Kinetic energy Energy associated with the overall motion of a system as a whole. Known A given piece of information is known by a given entity (which can be any kind of entity, a human, organization, computer, or logic gate) to the extent that it is correlated with other information that is accessible by that entity, in a such a way that the entity can make use of this correlation in a well-defined way. Landauer embedding The technique of embedding a desired logically irreversible computation into a logically reversible computation by simply keeping a copy of all information that would otherwise be thrown away. Latch To store a copy of an input signal so that it remains available when the signal is removed. Conceptually, the information is “latched into place,” like a mechanical part can be. Latency In computer architecture, the amount of time that passes while waiting for something. Latency hiding A computer architecture trick of “hiding” delays to high-latency operations (e.g., communicating with memory or distant processors) by finding other useful work to do in the meantime. Unfortunately, there are limits to the extent to which the technique can improve the overall cost efficiency of a computation. LC oscillator A simple electrical circuit in which an inductance (L) is connected to a capacitance (C). In this circuit, energy oscillates between the magnetic field of the inductor and the electric field of the capacitor. Unfortunately, the Q’s obtainable in nanoelectronic inductors are quite limited. Lithography Literally, “stone writing,” this refers generically to any technique for forming a patterned structure on a solid surface. Photolithography is a photochemical technique for etching specific patterns using projected light; it is the most widely used technique today. However, it is limited by the wavelengths of easily manipulated light. Other emerging lithography techniques such as electron-beam lithography, deep reactive ion etching (DRIE), and direct-imprint lithography are helping extend minimum feature sizes to the nanometer realm. Logical basis The particular basis of a qubit’s state space, chosen by convention, in which the two orthogonal basis vectors are taken represent a pure logic 0 and 1 respectively. If the qubit system contains natural pointer states, these may conveniently be selected as the basis (especially if the system is not highly coherent). Sometimes, it may be more convenient to use an alternative description of quantum architectures in which the logical basis is considered to change over time. Logical bit Also coded bit, computational bit. This is a bit that the logical or coding state of a bit device is intended to represent. Note: Every logical bit that we can actually manipulate is also a physical bit!

Nanocomputers: Theoretical Models

Lecerf reversal To reversibly clear temporary storage used up by a reversible computation by running the steps of the computation in reverse. Used in Bennett’s algorithm and in retractile cascade circuits. Logically reversible A computational process is logically reversible if every logic operation performs an invertible transformation of the logical state. Logical state The part of a bit device’s state that corresponds to the intended digital information to be stored. May be determined redundantly by a large amount of physical coding-state information. Logic gate A bit device that operates on logical bits of interest in a computation. Logic operation A transformation that takes a logical state to a distinguishable logical state. May be implemented by a collection (in series or in parallel) of operations carried out on coding state information. Loop Quantum Gravity The leading competitor to String Theory as a potential path toward the unification of the Standard Model and general relativity. Interestingly, in Loop Quantum Gravity, spatial area and volume are quantized, and the exact maximum number of quantum states (and thus the exact maximum information content) of any region of space can be counted and matches the limit found earlier by Bekenstein and Mayo [119]. In this limit, the maximum information capacity within a given surface is given by the surface area in Planck units. This suggests that a limiting model of computing in the high-density regime may be only two-dimensional. But it is still too early to tell. m Abbreviation for meter (the length unit). Machine language The language in which algorithms are expressed when they can be directly processed by a given machine. The instruction set architecture of a conventional machine specifies the rules of its machine language. Magnitude The complex number c has magnitude m ≥ 0 if and only if c = mei for some real number. An equivalent definition: If c = a + bi for real numbers a b, then m = a2 + b 2 1/2 . Majority logic A type of logic operation in which the value of an output bit is set to the majority value of an odd number of input bits. Mass Relativistic mass is total energy, converted to mass units (by dividing by c 2 ). See also rest mass. MEMS Microelectromechanical systems. Denotes a lithography-based technology for fabrication of mechanical or electromechanical structures and systems on surfaces. MEMS technologies are available today. Mesh An interconnection network based on local (bounded-length) connections between nodes located in a space having (if realistic) three or fewer dimensions. Mesoscale Literally, “middle scale,” an intermediate scale between the nanoscale and the microscale at which surface effects and quantum effects begin to become important but do not yet entirely dominate the physics of materials and devices. Meta-stable A state is called meta-stable if it has a relatively slow rate of decay toward an equilibrium (maximumentropy) state.

Nanocomputers: Theoretical Models

Meter Unit of length originally defined as ten-millionth of the distance from the Earth’s equator to its north pole. Metric A function that gives the distance, according to some method of measurement, between any two given points. Microcomputer For our purposes, a computer whose characteristic length scale is anywhere between 10−4
5 and 10−7
5 meters (i.e., between 32 and 0.032 m; i.e., closer to 1 micrometer than to 1 millimeter or 1 nanometer on a logarithmic scale). Micrometer A unit of length equal to 10−6 meters. Typical length of a bacterial cell. Micron Shorthand name for micrometer. Mixed state A statistical mixture of (pure) quantum states, which may be represented by a density matrix, which can always be diagonalized or transformed to an alternative basis in which it consists of a mixture of orthogonal states. Therefore a mixed state can be understood as nothing more than a classical statistical mixture of pure quantum states. Mole Quantity of molecules (or other objects) such that the collection’s mass in grams is equal to the individual object’s mass in atomic mass units (amu). Number of amus per gram. Equal to Avagadro’s number, 6
0221367 × 1023 . Momentum In computational terms, the physical momentum p is the total number of operations per distance required to translating a system spatially in a given direction. Such a transformation is orthogonal to any internal transformations, whose rate is given by the system’s rest mass, so the total rate of operations E for a system of rest mass m0 with momentum p is given by the Pythagorean theorem as E 2 = m20 + p2 , the correct relativistic formula. MOSFET Metal–oxide–semiconductor field-effect transistor. A field-effect transistor structure constructed by sandwiching a layer of insulating material (usually silicon dioxide or another oxide) in between a metallic (or actually, often polysilicon) gate electrode and a semiconducting substrate. M-theory A generalization and unification of several leading string theories in which d-dimensional membranes, rather than one-dimensional strings, are the fundamental entities. Like the individual string theories themselves, Mtheory has made no confirmed predictions and therefore remains fairly speculative. Even if true, I do not expect it to radically change our understanding of the physical limits of computing.
m Standard abbreviation for micrometer. N Abbreviation for Newton (the force unit). Nano- SI unit prefix, denoting multiplication of the unit by 10−9 . Abbreviated n. Nanocomputer A computer whose characteristic length scale is between 10−7
5 and 10−10
5 meters (i.e., between ∼32 and ∼0
32 nm, i.e., closer to 1 nanometer than to 1 micrometer or 1 picometer on a logarithmic scale). Nanocomputing Computing using nanocomputers. Nanometer A unit of length equal to 10−9 meters, or 10 Å. A typical length for a small molecule, such as an amino acid. About five carbon–carbon bond lengths. About the radius of the smallest carbon nanotubes.

291 Nanoscale Although definitions vary, for purposes of this chapter, we define nanoscale as meaning a characteristic length scale that falls anywhere in the three-order-ofmagnitude range between ∼30 and ∼0
03 nm. That is, the logarithm of the characteristic length scale is closer to 1 nm than to either 1 m or 1 pm. Nanowire A wire (made of conductive or semiconductive material) that has a nanoscale diameter. Nat The natural-log unit of information or entropy. Also known as Boltzmann’s constant kB or the ideal gas constant R. Near nanoscale The range of pitch values between 1 and 32 nanometers. Contrast far nanoscale. NEMS Nanoelectromechanical systems. Basically, just MEMS technology scaled down to the nanoscale. More generically, NEMS could be used to refer to any nanoscale technology for building integrated electromechanical systems. Newton A unit of force equal to 1 kg m/s2 . NFET A field-effect transistor in which the dominant charge carriers are negative (electrons). nm Standard abbreviation for nanometer. NMR Nuclear magnetic resonance, a technology used in chemical NMR spectrometers and modern medical (magnetic resonance imaging) scanning machines. In the mid 1990s, NMR technology was used to implement simple spinbased quantum computing (massively redundantly encoded) using nuclear spins of selected atoms of a molecular compound in solution. Noncoding physical state The part of the physical state of a computing system or device that is uncorrelated with its logical state, for example the detailed state of unconstrained thermal degrees of freedom (see thermal state). However, another part of the noncoding state (the structural state) is correlated with the system’s ability to have a well-defined logical state. For example, if a transistor gate is in a state of being shorted out then its nodes may no longer be able to maintain a valid logic level. Nondeterministic models of computing The adjective “nondeterministic” is used misleadingly in computer science theory as jargon for models of computation in which not only is the computer’s operation at each step nondeterministic, in the sense of not being determined directly by the machine’s current state, but furthermore it is assumed to be magically selected to take the machine directly to the desired solution, if it exists (or equivalently, all solutions are magically tried in parallel, and the correct one is then selected). Computer scientists really ought to rename “nondeterministic” models as magical models of computing, to emphasize their total lack of realism. Probably this was not done historically for fear of scaring off potential funding agencies. In any case, the name seems intentionally misleading. NP Nondeterministic polynomial-time, the set of problem classes in which a proposed solution can be checked or verified within an amount of time that is polynomial in the length n of the problem description in bits, that is, in which the time to check the solution grows as nk  for some constant k.

292 NP-hard The set of problems such that any problem in NP can be reduced (in polynomial time) to an instance of that problem. If any NP-hard problem can be solved in polynomial time, then all of them can. NP-complete The set of problems that are both in NP and in NP-hard. Number of operations A characteristic of a transformation trajectory that counts the total number of primitive orthogonalizing operations that occur along that trajectory. The number of operations can be counted in units of Planck’s constant or pops. Observable In quantum theory, an observable is just any Hermitian operator on states. The eigenstates of an observable are orthogonal (distinguishable), and its eigenvalues are real-valued (zero imaginary component). The eigenstates of the observable have a definite value of the measured quantity, and its numerical value is given by the eigenvalue. Omega network Similar to a butterfly network. Omega networks are not physically realistic for unit-time hops. Op Short for operation, or pop. We also sometimes use ops to refer to operation units of other sizes besides pops, such as rops and iops. Operation In this document, shorthand for primitive orthogonalizing operation. Also used sometimes to mean the special case of logic operation, a primitive orthogonalizing operation, or series of such, that effects a single change in the logical state. Operational In the scientific method, a defined characteristic of a system is called operational in nature if there exists a reliable, physically realizable procedure for measuring or confirming that characteristic. For example, two states are operationally distinguishable if there exists a definite experiment that can reliably distinguish them from each other. Operator In mathematics, a function that operates on a sequence of a prespecified number of members of a given set and returns a member of that same set. Functions that operate on sequences of length 1 are called unary operators or transformations. Opportunity cost In economics, the implicit cost of consumption of resources that results from foregoing the best alternative use of those same resources. Orthogonal A term from vector mathematics. Two vectors are orthogonal if and only if, considered as lines, they are perpendicular, or (equivalently) if their inner product (dot product) is zero. Orthogonality is the requirement for two quantum state vectors to be operationally distinguishable from each other. Orthogonalize To transform a vector (such as a quantum state vector) to another vector that is orthogonal to the original one. Parallel Two processes are parallel if they take place simultaneously. p− Short for pico, SI unit prefix meaning 1012 . Performance Performance is a figure of merit for computing. It is equal to the quickness of a reference computation. PFET A field-effect transistor in which the dominant charge carriers are positive (holes).

Nanocomputers: Theoretical Models

Phase The complex number c has phase 0 ≤ < 2 if and only if c = m · ei for some real number m. Physical bit Any bit of physical information. Physical entropy Physical information that is entropy (unknown to a particular observer). Physical information Information contained in a physical system, defining that system’s state. Of course, all the information that we can access and manipulate is, ultimately, physical information. Physically reversible Synonym for adiabatic, isentropic, and thermodynamically reversible. Physical realism In this chapter, a property had by a model of computation when it does not significantly (by unboundedly large factors) overstate the performance or understate the cost for executing any algorithm on top of physically possible implementations of the architecture. WARNING: Many models of computing that are studied by computer scientists lack this important property and therefore can be very misleading as guides for computer engineering and algorithm design. Physical system In essence this is an undefined term, based on intuition. But we can distinguish between abstract types of physical systems, constrained by their descriptions, and specific instances of physical systems embedded within our actual universe. For a specific instance of a system, we may in general have incomplete knowledge about its actual state. We should emphasize that a particular system might be defined to consist of only specified state variables within a particular region of space, as opposed to the entirety of the physical information within that region. Pico- SI unit prefix, denoting multiplication of the unit by 10−12 . Abbreviated p. Picometer A unit of length equal to 10−12 meters, or 0.01 Å. Roughly 1/100 the radius of a hydrogen atom, or 100 times the diameter of an atomic nucleus. Pipelined logic A deep combinational network can be broken into a series of shorter stages which can be used simultaneously to process different sequential inputs, resulting in a higher overall hardware and cost efficiency for most irreversible computations. However, pipelined reversible logic is not always more cost efficient than is nonpipelined reversible logic. Pitch The distance between the center lines of neighboring wires in a circuit. Planck energy The fundamental constants h G c can be combined to give an energy unit, EP = 
c 5 /G−1/2 ≃ 1
956 GJ. This energy, or something close to it, is believed to be a fundamental maximum energy for a fundamental particle in whatever turns out to be the current unified theory of quantum gravity. It is the energy of a particle when traveling at a velocity so high that that its de Broglie wavelength is equal to the Planck length. Planck length The fundamental constants h G c can be combined to give a length unit, ℓP = 
G/c 3 −1/2 ≃ 1
616 × 10−35 m. This length, or something close to it, is believed to be a fundamental minimum length scale in whatever turns out to be the correct unified theory of quantum gravity. For example, it is already known that the maximum information

Nanocomputers: Theoretical Models

in any region, in nats, is given by the area of the smallest enclosing surface around that region, in units of 2ℓP 2 . Planck mass The fundamental constants h G c can be combined to give a mass unit, mP = 
c/G−1/2 ≈ 2
177 × 10−8 kg. This mass, or something close to it, is believed to likely be a maximum mass for a fundamental particle, and perhaps the minimum mass of a black hole, in whatever turns out to be the current unified theory of quantum gravity. It is the mass of a particle when traveling at a velocity so high that that its de Broglie wavelength is equal to the Planck length. Planck’s constant Expresses the fundamental quantum relationship between frequency and energy. Comes in two common forms, Planck’s unreduced constant, h = 6
6260755 × 1034 Js, and Planck’s reduced constant,
= h/2. In computational terms, Planck’s constant is a fundamental unit of computational work; h can be viewed as equal to two primitive orthogonalizing operations. Planck temperature Dividing the Planck energy by Boltzmann’s constant k, we get a temperature TP ≃ 1
417 × 10−32 K. This temperature, or something close to it, is believed to be a fundamental maximum temperature in whatever turns out to be the correct unified theory of quantum gravity. It is the temperature of a Planck-mass (minimum-sized) black hole, or a single photon of Planck energy. In computational terms it corresponds to 1 radianop per Planck time, or 1 pop per  Planck times, which gives a maximum possible frequency of complete state update steps in a computational process of ∼5
9 × 1042 steps per second. Planck time The fundamental constants h G c can be combined to give a time unit, tP = G
/c 5 −1/2 ≃ 5
391 × 10−43 s. This time, or something close to it, is believed to be a fundamental minimum time unit in whatever turns out to be the correct unified theory of quantum gravity. It is the time for light to travel 1 Planck length and is the reciprocal of the angular phase velocity of a quantum wavefunction of a Planck-mass particle, or in other words the minimum time per rop. The minimum time for a primitive orthogonalizing operation is tP ≃ 1
69 × 10−42 s. pm Standard abbreviation for picometer. Polynomial time In computational complexity theory, having a time complexity that grows as nk  in input length n for some constant k. Pop Abbreviation for primitive orthogonalizing operation -op. Pointer state A state of a quantum system that remains stable under the most frequent modes of interaction with the environment, that is, an eigenstate of the observable that characterizes the interaction. The states chosen to represent logical bits in a classical (nonquantum) computer are usually pointer states. Quantum computers, however, are not restricted to using only pointer states. This is what gives them additional power. However, it requires a high degree of isolation from unwanted interactions with the environment, which will destroy (decohere) nonpointer states. Polysilicon Sometimes abbreviated just poly, this is polycrystalline silicon, a quasi-amorphous state of solid silicon, made of numerous nanoscale crystal grains. Often used for

293 local interconnect layers, in contrast with the single-crystal silicon forming the chip substrate. Power Rate of energy transfer, often measured in Watts. PR See physical realism. PRAM Parallel variant of the RAM machine model of computation. There are several varieties of PRAM model. One simply has n RAMs accessing the same shared memory in parallel. PRAM models are not physically realistic, in the sense used in this chapter. Primitive orthogonalizing operation Also pop, -op. In this chapter, a unitary transformation that takes some quantum states to new states that are orthogonal to the original state. A -op is equal to  rops or to 
= h/2. Principle of locality Casual effects can only happen through local interactions in space. This is a consequence of special relativity, and it is obeyed by modern quantum field theory, in which the global Hamiltonian is composed from local interaction terms only. Einstein thought that quantum mechanics was nonlocal, but it turned out he was wrong. Processor Short for information processor, this refers either to a computer or to a part of a computer (e.g., a CPU) that is large and complex enough to be programmed to perform different types of computations. Program Information specifying in complete detail an algorithm that a computer will perform. Relates to a specific programming language or to a computer’s specific programming model. Programming model Specifies how a given architecture can be programmed to carry out whatever computation is desired. Most computers today have a specific type of programming model called an instruction set architecture. Other kinds of programming models exist, such as those used in FPGAs, CAMs, and dataflow machines. Programming language A standard language, usually textual (although graphical languages are also possible) for representing algorithms. A compiler translates a program from an easily human-readable programming language into a form that can be utilized by a given machine’s programming model. Proper time In relativity, this is the amount of time (number of reference-system update steps) to pass, as experienced in a reference frame moving along with a given object, rather than in some other arbitrarily chosen reference frame. Public-key cryptography An approach to cryptography and authentication based on a complementary pair of keys, a public key and a private key, each of which decrypts the code that the other encrypts. The most popular known public-key cryptography algorithms are vulnerable to being broken by quantum computing. Pure state See quantum state. Q3M Quantum 3D mesh, a model of computing consisting of a three-dimensional mesh-connected network of fixedsize, arbitrarily reversible, and quantum-coherent processing elements. The Q3M is postulated by the author to be a UMS model. See tight Church’s thesis. Quality In this chapter, the quality or q factor of a device or process is defined as the ratio of energy transferred to energy dissipated, or (quantum) bit operations

294 performed to entropy generated, or quantum bit operations performed to decoherence events. It is also the ratio between the coding-state temperature and the temperature of the decoherence interaction, or the ratio between the coherence time and the operation time. Quantum algorithms Algorithms for a quantum computer, which use superpositions of states and interference effects in an essential way. Quantum algorithms must be reversible to avoid decoherence. Quantum computer A computer that uses superpositions of pointer states as intended intermediate states in a computation. Ordinary classical computers are restricted to only using pointer states. The less-constrained state space available in a quantum computer opens up exponentially shorter trajectories toward the solution of certain problems, such as the factoring problem. The more constrained state space available to a classical computer appears to require exponentially more steps to arrive at solutions to this problem. Quantum dot A mesoscale or nanoscale structure in which conduction-electron energies are quantized. Quantum dot cellular automaton Abbreviated QDCA or just QCA, this is a particular logic scheme using quantum dots which was invented at Notre Dame. Involves “cells” (made of four dots) which interact with each other locally; in this respect, it roughly resembles the cellular automaton model of computing. QDCA also includes adiabatic variants. Quantum electrodynamics Abbreviated QED, this is the quantum field theory that deals with charged particles, photons, and the electromagnetic field. Now subsumed by the Standard Model of particle physics. Quantum field theory When quantum mechanics is unified with special relativity, the result is a field theory. The Standard Model of particle physics is the modern working quantum field theory. Other, simplified models, which omit some details of the Standard Model, including quantum electrodynamics, the quantum field theory of electric charge and electromagnetism, and quantum chromodynamics, the quantum field theory of “color” charge (carried by quarks and gluons) and the strong nuclear force. Quantum information The specific quantum information contained in a system can be identified with the actual quantum state of the system, itself. The total amount of quantum information is the same as the amount of classical information—namely, the logarithm of the number of orthogonal states—except it is measured in qubits rather than bits. The quantum information can be thought of as a choice of basis, together with the classical information inherent in the selection of one of the basis states. The classical information is only the selection of basis state, with the basis itself being fixed. Quantum mechanics Modern theory of mechanics, initiated by Planck’s discovery of the fundamental relationship between frequency and energy, namely that a system performing transitions between distinguishable states at a given rate or frequency must contain a corresponding minimum amount of energy. (This fact was first discovered by Planck in the context of blackbody radiation.) Quantum state Also called a pure state, the state of a quantum system is identified with a vector (normalized to

Nanocomputers: Theoretical Models

unit length) in the system’s many-dimensional Hilbert space. Two states are distinguishable if and only if their state vectors are orthogonal (perpendicular to each other). Qubit A unit of quantum information, as well as a name for any particular instance of a physical system or subsystem that contains this amount of quantum information. A system that contains one qubit of information has only two distinguishable states. A qubit may be in a state that is superposition of pointer states, and this state may be entangled (correlated) with the states of other systems. Quickness The quickness of any process is the reciprocal of the total real time from the beginning of that process to the end of the process. Quickness is measured in units of Hertz (inverse seconds). R3M Reversible 3D mesh, a model of computing consisting of a three-dimensionally connected mesh network of fixed-size, arbitrarily reversible processors. The R3M is postulated to be a UMS model for nonquantum computations. See also Q3M. RAM Random access memory, a memory in which any random element can be accessed (read or written) equally easily, by supplying its numeric address. Also stands for random access machine, an early non-PR, non-UMS model of computation in which any random element of an unboundedly large memory can be accessed within a small constant amount of time. Radian-op See rop. Random access To access (read or write) a bit of memory selected at random (i.e., arbitrarily). Resonant tunneling diodes/transistors Structures in which the rate of tunneling between source and drain electrodes is controlled by the resonant alignment of electron energy levels in an intervening island with the Fermi energies of free conduction electrons in the source terminal. Rest mass Computationally, the rate of ops in a sytem that are concerned with the internal updating of the system’s state, rather than with net translation of the system in a particular direction (i.e., that portion of a system’s total energy that is not kinetic energy). Retractile cascade logic Or just retractile logic. A reversible combinational logic style in which inputs are presented and intermediate results computed and then (after use) are uncomputed by “retracting” the operations that produced the results, in reverse order. Reversibility A process or dynamical law is reversible if the function mapping initial state to final state is one-to-one (that is, its inverse is a function). Reversible is synonymous with reverse-deterministic (deterministic looking backwards in time). It is not synonymous with time-reversal symmetric. A dynamical law is time-reversal symmetric if it has the identical form under negation of the time component. Modern particle physics actually has a slightly changed form under time reversal (namely, charges and handedness must also be changed), but it is still reverse-deterministic, thus still reversible. Reversible algorithms Algorithms composed of reversible operations.

Nanocomputers: Theoretical Models

Reversible operations An operation is reversible if it transforms initial states to final states according to a one-to-one (bijective) transformation. Reversible computing A paradigm for computing in which most logical operations perform a logically reversible (bijective) transformation of the local logical state; this transformation can then be carried out adiabatically (nearly thermodynamically reversibly). Reversiblize To translate a computation described as an irreversible algorithm to an equivalent but reversible form, often by reversibly emulating the steps of the irreversible algorithm. Rop Short for radian-op, a unit of computational work equal to Planck’s reduced constant
. Equal to 1/ of a -op (pop). An example would be the rotation of a quantum spin by an angle of 1 radian. RSA Rivest, Shamir, Adleman, the abbreviation for a popular public-key cryptography algorithm whose security depends on the assumed hardness of factoring large numbers. The advent of large-scale quantum computing would falsify this assumption and permit RSA codes to be broken. RTD See resonant tunneling diode. s Abbreviation for second (the time unit). SI Standard abbreviation for Système Internationale d’Unites, the International System of Units, adopted by the 11th General Conference on Weights and Measures (1960). Second law of thermodynamics The law that entropy always increases in closed systems. The law can be proven trivially from the unitarity of quantum theory, together with von Neumann’s definition of entropy for a mixed quantum state, by analyzing the effect when a quantum system evolves according to a Hamiltonian that is not precisely known or interacts with an environment whose state is not precisely known. Semiconductor A semiconductor is a material in which there is (small but positive) gap (called the bandgap) between the highest energy levels of valence electrons that are bound to specific atoms, and the lowest energy levels of conduction electrons, electrons that are freely moving through the material. Due to the bandgap, only a small number of electrons will be free to move, and the material will not conduct electricity well. However, addition of dopants, applied fields, etc., can significantly change the concentration of charge carriers in the material. The ease of manipulation of carrier concentration is what makes a semiconductor a useful material for controlling conductance in transistors. Contrast conductor and insulator. Sequential logic Digital logic with feedback loops and storage capability, in which new results are produced sequentially, one at a time in definite steps, and in which a given piece of hardware is reused, in sequence, for calculating results of subsequent steps. Compare combinational logic. Shannon entropy The appropriate definition of entropy for a situation in which not all possible states are considered equally probable. The Shannon entropy is the expected amount of information gain from learning the actual state.

295 Single-electron transistor A transistor whose conductance changes significantly upon the addition or removal of a single electron to/from its gate electrode. Can be built today. Space complexity In traditional computational complexity theory, this is the machine capacity (in bits) required to perform a computation. In physical computing theory, this is seen as an inaccurate measure of the true economic cost of a computation; spacetime cost is a more accurate substitute. Spacetime A volume of physical spacetime is measured as the physical volume of a region of space, integrated over an interval of time. Computational spacetime reflects the same idea, for the region of space actually utilized to perform computations or store intermediate results during a computation. It may be approximated in restricted contexts by just integrating the number of bits in use over the number of parallel update steps performed. Special relativity Einstein’s theory based on the principle that the speed of light is independent of the observer’s velocity. It revolutionized mechanics with the discovery that space and time are interwoven with each other, and that moving objects slow down, shorten, and become more massive, and that mass itself is nothing but a bound form of energy. It predicts that nothing can go faster than light. Its predictions have been exhaustively confirmed to high accuracy by myriad experiments. It was later generalized to incorporate gravity and accelerated motion in the General Theory of Relativity. Speed of light Denoted by c ≃ 3 × 108 m/s, the speed of light is the maximum propagation velocity of information and energy through space, as was discovered by Einstein in his theory of relativity. Computationally speaking, the speed of light is that speed at which all of the quantum operations taking place in a system are spatial-translation ops, which makes it clear why this speed cannot be exceeded and why nonzero rest-mass systems (which have a nonzero rate of internal ops) cannot achieve it. We should emphasize that modern quantum field theory, being entirely local, definitely and explicitly obeys the constraint that information (both classical and quantum information) can travel at most at the speed of light. Spent energy The spent energy in a system is defined as the system’s entropy S times the temperature T of the coolest available thermal reservoir of effectively unlimited capacity. At least ST energy must be permanently dedicated in order to remove the entropy to the reservoir (unless a cooler reservoir later becomes available). Spent energy is total energy minus free energy. Spin Fundamental particles in quantum field theory have a spin, an inherent angular momentum whose absolute numerical value is always an integer multiple of
/2. (This prediction arose from the unification of quantum theory and special relativity and was subsequently confirmed.) Spin states have an orientation; oppositely oriented spins are distinguishable, but other pairs of orientations are not. A spin can hold only 1 qubit of quantum information, and only 1 bit of classical information. Spintronics Electronic technology in which electron and/or nuclear spin states (instead of or in addition to the position and momentum states of electric charges) are used to store, transmit, or process information. Magnetic storage

296 technology can be considered an early example of spintronics. NMR quantum computing is a more recent example. Spintronic diodes and switches are also being developed. Standard Model of particle physics This is the consensus bedrock of modern physics. It treats electromagnetism and the strong and weak nuclear forces together in a single quantum field-theoretic framework. It encompasses all known fundamental particles, and all forces except for gravity. Its predictions have been verified to many decimal places. Aside from an eventual unification with general relativity, which would modify the theory’s predictions only at extremely high-energy scales, there is no indication that any future developments in physics would change the Standard Model’s ramifications for nanoscale engineering. In other words, the Standard Model seems to be a totally complete model so far as nanotechnology is concerned. This allows us to make confident predictions about the fundamental limits of computing based on the Standard Model. State An exact configuration of a given type of physical system. States of quantum systems are identified with mathematical vectors. (See quantum state.) State space The set of all possible states of a system. Statistical mechanics Branch of mechanics dealing with the statistical behavior of large numbers of simple systems. The foundation of thermodynamics. Modern statistical mechanics is based on quantum-mechanical counting of distinguishable states and is sometimes called quantum statistical mechanics. Statistical mixture An ensemble of systems, characterized by a probability distribution, that is, a function from states to their probability. Step A complete parallel update step or just step of a quantum system or subsystem is a transformation that can be expressed as a trajectory (sequence) of quantum bit operations totaling an average amount of computational work performed of 1 pop per bit of physical information contained in the system. Physical temperature is just a measure of the rate at which steps are performed. Stored-program computer A computer in which the program to be executed can be stored in the computer’s memory along with the data to be manipulated. String Theory A hypothetical extension of the Standard Model of particle physics in which fundamental particles of different masses are explained as different modes of vibration of tiny strings and closed loops. String Theory is not yet a complete theory that yields testable predictions, and so it has not yet been experimentally confirmed. It does, however, predict a number of surprising things such as the existence of extra “hidden” spatial dimensions. However, these are not expected to have a major bearing on the physical limits of computing beyond what we already know based on the Standard Model and general relativity. Strong Church’s thesis This early expectation of computer science theory claimed that any physically realizable model of computation has a time cost for all problems that is within at most a polynomially growing factor above or below the minimum time to solve the same problem on a Turing machine. However, if quantum computers can be built on arbitrarily large scales, and if no polynomial-time classical

Nanocomputers: Theoretical Models

algorithm exists for emulating them to arbitrarily precision, then the strong Church’s thesis is false. See also Church’s thesis, tight Church’s thesis. Structural state The part of the noncoding physical state of a computer/device that is required to remain unchanged in order for the machine to even continue functioning as intended. For example, for a given circuit to function as intended, its wires must remain unbroken, although in practice they may actually break occasionally, due to electromigration effects, an example of state decay. Superposition of states A superposition of states in a quantum system is a linear combination (with complexvalued coefficients) of those states, considered as vectors. The coefficients are normalized so that their squared magnitudes sum to 1. A superposition of states is therefore another vector and therefore is a quantum state, just as much as the states being superposed. However, a superposition of pointer states will not generally be a pointer state and thus may be subject to decay (decoherence) to a statistical mixture of pointer states upon interaction with the environment. Subsystem Informally, a piece of a larger (physical) system. Often (but not always) identified with a particular region of space. May include some degrees of freedom but not others. Superconductor In a superconducting material, pure electron momentum states occupy a decoherence-free subspace and therefore constitute pointer states that are immune from decoherence via ordinary modes of interaction with the environment. A current in a superconductor is therefore maintained indefinitely (with zero resistance). In the more well-understood superconductors, this occurs as a result of a pairing-up of electrons (into Cooper pairs) due to indirect mutually attractive interactions intermediated by phonon exchange through the material’s crystal lattice. Syndrome In error correction, when an error occurs, the syndrome is the information contained in the exact identity of the error (when/where/what/how it occurred). This information is entropy from the perspective of the designer of the error-correction mechanism and so must be removed from the device in question in order to free up space for desired computational purposes. Technology For purposes of this chapter, a technology refers to a device-level technology, for example a specific fabrication process for circuits of electronic or electromechanical devices, or to another low-level physical mechanism used for communication, cooling, etc. Higher level design elements such as processor architecture or software algorithms also represent technology, in the broader sense of the word, but we will reserve the word for lower level technology in this chapter (the parts that are not traditionally the domain of the computer scientist). Technology scaling model A part of a model of computing that describes how key characteristics of devices and systems change as the parameters of the underlying manufacturing process technology are varied, for example by scaling devices to smaller sizes, or by scaling cooling technology to effect higher or lower operating temperatures. Temperature The physical temperature of any system can be interpreted as the average rate of quantum operations

Nanocomputers: Theoretical Models

per bit of physical information, that is, the average rate at which the system’s quantum information is (potentially) completely updated. Usually in thermodynamics we are only interested in the temperature of an entropic subsystem (that is, a subsystem whose state information is all unknown); however, the temperature of the known information in a system (that is, of the subsystems whose state information is known) is related and also important. If the known information is transitioning at a much faster rate than is the entropy, then an increasing degree of thermal insulation of the known information from the entropy is necessary in order to prevent the entropic subsystem from becoming too hot (and causing the computer to melt). Tensor product A term from vector algebra. The tensor product of two vectors of dimensionality d1 and d2 is a new vector of dimensionality d1 d2 whose components in a given basis are obtained by pairwise multiplying components of d1 and d2 . Thermal energy See kT . Thermal state That part of the state of a physical system that is entirely entropy, and whose exact state under normal circumstances and intended operating temperatures is expected to fluctuate constantly and unpredictably. For example, a circuit node may be at a fairly definite average voltage level, and so its logic state (high or low) may have low entropy, but at the same time, the detailed occupancy numbers of all of the electron states within a few kT ’s of the Fermi surface will be rapidly and unpredictably fluctuating, and so will constitute another, high-entropy part of the state. Thermal temperature The temperature of those subsystems whose physical information happens to be entropy (i.e., whose energy is heat). Thermal temperature is the traditional thermodynamic concept of temperature, but it is subsumed by the more general, modern definition of temperature given previously. Thermodynamically reversible Synonym for adiabatic or isentropic. A process is thermodynamically reversible to the extent that it does not produce any new entropy, that is, to the extent that the modeler does not become increasingly uncertain about the identity of the actual state. Even though quantum physics itself is reversible, a quantum process can still be thermodynamically irreversible, to the extent that the state of known parts of the system become mixed up with and affected by the state of unknown parts. Theta f  is a mathematical order-of-growth notation denoting any function that is constrained to be within a constant factor of the given function f , for all sufficiently large inputs. Tight Church’s thesis This thesis (by the author) postulates that a reversible, quantum 3D mesh (Q3M) is a UMS model of computing, that is, that the minimum time cost to solve any problem in any physically realizable machine lies within a constant factor of the time cost in the Q3M model. See also Church’s thesis, strong Church’s thesis. Time A quantity of physical time itself (specifically, relativistic proper time) can be defined computationally, in terms of the number of (parallel complete update) steps taken by a fixed reference subsystem (perhaps, a Planckmass photon) over the course of a particular transformation

297 trajectory that is undergone by an entire system as it follows its dynamics. Time complexity In traditional computational complexity theory, this is the number of update steps of the logical state of a computation. In physical computing theory, this quantity is seen as an insufficient basis for a correct engineering optimization, and we prefer to use the actual physical time cost, together with other components of true economic cost, instead. In an optimized family of adiabatic architectures, it turns out that time and number of logical steps are not always proportional to each other, since the optimum frequency varies with the machine capacity as well as the algorithm to be performed. Total energy The total energy of all kinds in a system can be measured by weighing the mass of the system in a gravitational field and converting to energy units using E = mc 2 . This includes rest mass-energy as well as thermodynamic internal energy. Transformation A unary operator on a state space (or any other set), mapping states to states. The transformation corresponding to time evolution in quantum mechanics is unitary. Transformation trajectory A transformation expressed as a sequence of simpler, irreducible local transformations (e.g., bit operations). A quantum logic network is a description of transformation trajectories in a particular graphical language. Transistor An electronic device that is a voltage-controlled current switch. That is, the conductance between two nodes is determined by the level of voltage (relative to some threshold) on a third gate node. Transmission gate A circuit element buildable from parallel NFET and PFET transistors that conducts at any voltage level between logic high and low levels when turned on. Tunneling Quantum mechanical phenomenon in which an electron of given energy can penetrate a potential energy barrier that would be too high for it to penetrate classically. This occurs because the inherent indistinguishability of nearby quantum states means that if a barrier is narrow enough, the electron wavefunction can have significant amplitude even on the other side of the barrier. Turing machine A simple early mathematical model of computing due to Alan Turing, in which a fixed-size processor serially traverses an unbounded, one-dimensional memory. The Turing machine is a physically realistic model, but it is not universally maximally scalable. UMS See universal maximum scalability. Uncompute To uncompute some information that is correlated with other information is to remove the correlation, by undoing (performing in reverse) a transformation that could have computed the information to begin with. Uncomputing and related operations provide the only physically and logically reversible way to remove known information so as to return a memory cell to a standard state that can be reused for later computations. The ability to uncompute is a key capability for reversible algorithms. (However, uncomputing an old result and computing a new one can sometimes be combined in a single operation, so uncomputing by itself is not always strictly necessary for reversible operation.)

Nanocomputers: Theoretical Models

298 Unitary transformation A term from linear algebra. An invertible, length-preserving linear transformation of a vector space. All quantum systems evolve over time via a unitary transformation U = expiHt/h of their state vector in each unit of time t, where i2 = −1, H is the system’s Hamiltonian, and
is Plank’s reduced constant. Universal A model of computation is called universal if it can emulate any Turing machine, given sufficient resources. Universal maximal scalability (UMS) A model of computation has this property if there is no physically realizable algorithm that is asymptotically more cost efficient (by unboundedly large factors) than all algorithms possible in a physical realization of the given model. None of the models of computation that have been traditionally studied by computer scientists in the past have this property. Nevertheless, it is a desirable property to have, from a computer engineering and algorithm-design standpoint. A reversible 3D mesh that supports quantum operations is conjectured to be a physically realistic, UMS model. Unstructured search A class of problems characterized by the following general description: Given a black-box function f over some domain, and a target element y, find a value x in the domain such that f x = y. Valence band In condensed matter theory, the valence band is the range of energies accessible to electrons that are bound to specific atoms and therefore not free to move throughout the material. Velocity Computationally speaking, velocity is a dimensionless quantity whose square gives the fraction of ops taking place in a system that are devoted to the spatial translation of the system in a particular direction. There is therefore a maximum velocity for all systems of 1, which is equal to the speed of light. Only systems with zero rest mass can actually attain this speed. Of course, we all know that velocity also expresses the distance traversed per unit time. Virtual particles In quantum field theories, fundamental forces are transmitted via the exchange of “virtual” particles (called such because they are not directly observed). For example, the electromagnetic force is transmitted via the exchange of virtual photons. VLSI Very large scale integrated circuits. That is, monolithic chips fabricated with tens of thousands to millions of devices. VLSI theory A model of computation, invented by Charles Leiserson of MIT, that is appropriate for a wide variety of VLSI design applications that focuses on concerns with circuit area and hardware efficiency. It is more suitable for engineering purposes than is traditional computational complexity theory. However, VLSI theory is still not the most comprehensive possible model, because it does not take energy costs and heat-dissipation considerations into account and also does not always account adequately for communications delays. The example model presented in this chapter removes these limitations. Voltage The voltage between two circuit nodes or points is the electrostatic potential energy difference between those points per unit charge, for an imaginary infinitesimal test charge located at either point.

Voltage coding A simple physical logic coding scheme (the one used today in digital electronics) that considers all voltage states above a certain threshold to represent a logic 1, and all voltage states below a certain threshold to represent a logic 0. However, many other coding schemes are possible (e.g., using superconducting current states, or electron spin states). von Neumann entropy The appropriate definition of entropy for an uncertain quantum state, or mixed state. It is equal to the Shannon entropy of the mixed state when expressed in the diagonalized basis, as a statistical mixture of orthogonal pure states. von Neumann machine A simple computer architecture often attributed to von Neumann, consisting of a single fixed-capacity serial processor that accesses an external memory of arbitrary capacity. Closely related to the RAM machine model of computation. Watt A unit of power (rate of energy transfer) equal to 1 Joule per second. Wavefunction A particular quantum state can be identified with a function that maps all state vectors to the corresponding complex number that arises when the given state vector is combined by a dot product with the state vector of the particular state in question. This function is called the state’s wavefunction. The wave has nonzero amplitude for most states (all except the ones that are orthogonal to the particular state). It is a consequence of this wave aspect of quantum mechanics that states can never be totally localized with infinite precision; any system of finite size and energy can have only a certain finite number of distinguishable states, corresponding to different normal modes of vibration of the given wave [15, 16] up to the maximum energy. Wave packet A wavefunction whose magnitude approaches zero for all position states outside of a given region of space. A system whose position is localized is in a wave packet state. Zetta SI unit prefix meaning 1021 .

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300 78. A. Ressler, The Design of a Conservative Logic Computer and a Graphical Editor Simulator, MIT Master’s Thesis, 1981. 79. J. Storrs Hall, in “PhysComp ’94: Proceedings of the Workshop on Physics and Computation,” 17–20 November 1994, Dallas, TX, pp. 128–134. IEEE Computer Society Press, Los Alamitos, CA, 1994. 80. S. Goldstein and M. Budiu, NanoFabrics: Spatial computing using molecular electronics, in “28th Annual International Symposium on Computer Architecture (ISCA’01),” June 2001. 81. L. Durbeck and N. Macias, Nanotechnology 12, 217 (2001). 82. M. P. Frank, Computer Architecture Principles, course lecture slides, http://www.cise.ufl.edu/class/cda5155fa02/, 2002. 83. D. B. Skillicorn, Parallelism and the Bird–Meertens Formalism, Dept. of Computing and Information Science, Queen’s University, Kingston, Canada, http://citeseer.nj.nec.com/ skillicorn92parallelism.html, 1992. 84. C. Lutz and H. Derby, Janus: A Time-Reversible Language, CalTech class project, http://www.cise.ufl.edu/∼mpf/rc/janus.html, 1982. 85. H. Baker, NREVERSAL of fortune—the thermodynamics of garbage collection, in “Proceedings of the International Workshop on Memory Management,” St. Malo, France, 1992. Also in Lecture Notes in Computer Science, Vol. 637, New York, Springer, 1992. 86. S. Bettelli et al., Toward an Architecture for Quantum Programming, IRST technical report 0103-010, 2001. 87. B. Ömer, A Procedural Formalism for Quantum Computing, Master’s Thesis, Dept. of Theoretical Physics, Technical University of Vienna, 1998. 88. B. Ömer, QCL—A Programming Language for Quantum Computers, Master’s Thesis, Institute of Information Systems, Technical University of Vienna, 2000. 89. J. W. Sanders and P. Zuliani, Quantum Programming, TR-5-99, Programming Research Group, OUCL, Oxford, 1999. 90. P. Selinger, Towards a Quantum Programming Language, Dept. of Mathematics, University of Ottawa, 2002. 91. G. Baker, “Qgol”: A System for Simulating Quantum Computations: Theory, Implementation and Insights, Honors Thesis, Macquarie University, 1996. 92. R. L. Wigington, Proc. IRE 47, 516 (1961). 93. P. Shor, Phys. Rev. A 52, 2493 (1995). 94. D. Frank, IBM J. Res. Dev. 46, 235 (2002). 95. J. M. Rabaey, “Digital Integrated Circuits: A Design Perspective.” Prentice Hall, New York, 1995.

Nanocomputers: Theoretical Models 96. R. Chau, 30nm and 20nm physical gate length CMOS transistors, in “Silicon Nanoelectronics Workshop,” 2001. 97. B. Doris et al., Extreme scaling with ultra-thin silicon channel MOSFET’s (XFET), in “2003 International Electron Devices Meeting (IEDM),” San Francisco, 9–11 December 2002. 98. Y. Huang et al., Science 294, 9 (2001). 99. V. Derycke et al., Nano Lett. 1, 9 (2001); A. Bachtold et al., Science 294, 9 (2001). 100. T. Yamada, Doping scheme of semiconducting atomic chain, in “Fifth Foresight Conference on Molecular Nanotechnology,” Palo Alto, CA, 5–8 November 1997. 101. R. Eisberg and R. Resnick, “Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles,” 2nd ed. Wiley, New York, 1985. 102. S. Das Sarma, Am. Sci. Nov.–Dec. (2001). 103. D. Goldhaber-Gordon et al., Proc. IEEE (1997). 104. J. Park et al., Nature 417, 6890 (2002). 105. G. L. Snider et al., J. Appl. Phys. 85, 4283 (1999). 106. C. P. Collier et al., Science 285, 391 (1999). 107. K. K. Likharev, Rapid Single-Flux-Quantum Logic, Dept. of Physics, State University of New York, http://pavel.physics.sunysb. edu/RSFQ/Research/WhatIs/rsfqre2m.html, 1992 108. T. van Duzer and C. W. Turner, “Principles of Superconductive Devices and Circuits,” 2nd ed. Prentice Hall, New York, 1999. 109. Z. K. Tang et al., Science 292, 2462 (2001). 110. S. Datta and B. Das, Appl. Phys. Lett. 56, 665 (1990). 111. M. Johnson, IEEE Spectrum 31, 47 (1994). 112. M. D’Angelo et al., Phys. Rev. Lett. 87, (2001). 113. G. He and S. Liu, “Physics of Nonlinear Optics.” World Scientific, Singapore, 2000. 114. M. Frank, Comput. Sci. Eng. 4, 16 (2002). 115. M. Frank, Cyclic Mixture Mutagenesis for DNA-Based Computing, Ph.D. Thesis proposal, MIT, http://www.cise.ufl.edu/∼mpf/ DNAprop/phd-proposal.html, 1995. 116. T. F. Knight, Jr. and G. J. Sussman, Cellular Gate Technology, MIT AI Lab, http://www.ai.mit.edu/people/tk/ce/cellgates.ps, 1997. 117. R. Kurzweil, “The Age of Spiritual Machines: When Computers Exceed Human Intelligence.” Penguin, Baltimore, 2000. 118. S. W. Hawking, Commun. Math. Phys. 43, 199 (1975). 119. J. D. Bekenstein and A. Mayo, Gen. Rel. Grav. 33, 2095 (2001). 120. F. J. Dyson, Rev. Modern Phys. 51, 447 (1979). 121. L. M. Krauss and G. D. Starkman, Astrophys. J. 531, 22 (2000). 122. T. Toffoli and N. Margolus, “Cellular Automata Machines: A New Environment for Modeling.” MIT Press, Cambridge, MA, 1987.

Encyclopedia of Nanoscience and Nanotechnology

www.aspbs.com/enn

Nanocontainers Samantha M. Benito, Marc Sauer Universität Basel, Klingelbergstrasse, Basel, Switzerland

Wolfgang Meier Universität Basel, Klingelbergstrasse, Basel, Switzerland, and International University of Bremen, Bremen, Germany

CONTENTS 1. Introduction 2. Natural Nanocontainers 3. Nanocontainers Formed by Self-Assembly 4. Template-Directed Preparation of Nanocontainers 5. Nanocontainers Prepared by Emulsion/Suspension Polymerization 6. Dendrimer Nanocontainers Glossary References

1. INTRODUCTION Design and synthesis of materials with micrometer (microscopic) and nanometer dimensions (mesoscopic) with welldefined structures in the sub-micrometer region have attracted increasing interest recently. The idea in this context is to tailor the composition, structure, and function of materials with control at the nanometer level, which may lead to new properties for well-known standard materials and hence to new applications. In addition, increasing progress has been attained in the last decade in nanostructured materials using block copolymers. The amount of research on this area is at constant growth, which makes a comprehensive or exhaustive review almost impossible; therefore, we intend here to give mainly the outlines of the field and some interesting illustrative examples. In the following we will focus on nanometer-sized hollow spheres, or so-called nanocontainers. Such particles produce great interest due to their potential for encapsulation of large quantities of guest molecules or large-sized guests within their empty core domain. They can be useful for applications in areas such as biological chemistry, synthesis, or catalysis. In this context monodispersity of the capsule’s

ISBN: 1-58883-062-4/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

size, stability of the particle, and permeability of the shell are key parameters in order to obtain materials with enhanced performance. Nature itself uses similar and very effective nanocontainers like micelles, vesicles, and viruses in biological systems, for example, for transport and delivery of sensitive compounds such as hormones or DNA [1]. However, these highly functionalized assemblies of proteins, nucleic acids, and other (macro)molecules perform very complicated tasks that are still too complex to be completely understood. Although the particles are perfectly designed to fulfill their tasks in biological environment after millions of years of evolution, their direct use in many technical applications is often not feasible. In many cases this is due to the non-covalent interactions responsible for their formation and hence their limited stability. This leads, for example, to a rapid clearance of conventional lipid vesicles (liposomes) from the blood after their intravasal administration [2]. Many applications require, however, more stable particles. Therefore, a great effort has been devoted within the last years to prepare sizeand shape-persistent nanocontainers and up to now a huge variety of different techniques has been described, each of them having its special advantages and of course also disadvantages. This chapter is divided into different subsections according to the different approaches that are commonly used to attain the desired particle morphology. This division is somewhat arbitrary, especially since a certain overlap between the different methods exists. However, the first part of the chapter gives a short introduction to natural nanocontainers, which, besides their limited technical applicability, are of major importance for the understanding of natural processes. Although they are naturally occurring substances, the use of lipids and liposomes will be considered together with polymer amphiphiles since both share analogous characteristics such as self-organization. The following three sections describe approaches in which mainly non-covalent interactions (i.e., van der Waals, electrostatic, or hydrophobic interactions) are used to imprint the characteristic shape

Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 6: Pages (301–319)

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onto the resulting particles. Once obtained, though, these self-assembled superstructures based on the aforementioned non-covalent interactions can be further stabilized by cross linking, thus obtaining shape-persistent particles. The last section deals with single polymers that have, by design of their architecture, intrinsic hollow-sphere morphology in the nanometer range.

2. NATURAL NANOCONTAINERS Although many naturally available nanocontainers are not suited for technical applications, much interesting research work has been published within the last years that describes the use of various natural systems in nanomaterial science [3]. Especially in the field of biomineralization a significant progress has been made with so-called bio-nanoreactors [4–7]. Among the different types of possible mineralization vessels, ferritin is probably the most intensively studied and best understood [8]. Nature uses ferritin as a storage device for iron, where it is encapsulated as hydrated iron (III) oxide within a multisubunit protein shell. After the iron has been removed from inside the protein shell, the remaining cavity has been successfully used to generate various nanometersized inorganic particles, such as, for example, manganese oxide or uranyl oxyhydroxide crystals [9]. Virus particles are another type of biological structures that can be applied as a template for biomineralization processes, like the tobacco mosaic virus (TMV) or the cowpea chlorottic mottle virus (CCMV). As indicated in Figure 1, several routes were explored for the synthesis of nanotubes composites that use TMV templates [10]. The spherical protein cage of the CCMV shows a completely reversible pH-induced swelling transition of approximately 10%, in case it is incubated in media of a pH value above 6.5 (Fig. 2) [11]. During this swelling, gated pores are opened along the viral shell that allow a free molecular exchange between the viruses interior and the surrounding bulk medium. In contrast, no exchange of larger molecules occurs at pH values lower than 6.5. This property has successfully been used for controlled host-guest encapsulation

pH 9 Fe|| /Fe||

pH 2.5 TEOS

TMV pH 7 Cd|| / H2S

pH 5 Pb|| / H2S

Figure 1. Synthesis of nanotubes composites by using TMV templates. (TEOS = tetraethoxysilane.) Reprinted with permission from [10], W. Shenton et al., Adv. Mater. 11, 253 (1999). © 1999, Wiley-VCH.

pH < 6.5

pH > 6.5

Figure 2. Cryoelectron microscopy and image reconstitution of the Cowpea chlorotic mottle virus (CCMV). Contracted structure at low pH values (left) and swollen structure at high pH values (right). Swelling results in the formation of 60 pores with a diameter of 2 nm. Reprinted with permission from [11], T. Douglas and M. Young, Nature 393, 152 (1998). © 1998, Macmillan Magazines Ltd.

and crystal growth of inorganic and organic materials within such virus [12]. These examples demonstrate clearly that biological nanocontainers are well suited for the formation of new materials. However, in addition to their low mechanical stability, it seems that their major drawbacks are the isolation and handling of larger quantities of such bioreactors.

3. NANOCONTAINERS FORMED BY SELF-ASSEMBLY 3.1. Lipids Due to their amphiphilic nature and molecular geometry, lipid molecules can aggregate in dilute aqueous solution into different morphologies, depending on many factors such as the molecular shape of the lipid, concentration, and temperature. Particularly spherical morphologies, micelles and vesicles, have attracted considerable interest in the scientific community. Micelles consist of aggregates in which the nonpolar chains of the lipid form a core surrounded by their polar heads [2]. In case of micellar structures in aqueous solutions, the inner core represents a hydrophobic domain capable of solubilizing hydrophobic substances. This solubilization of sparingly soluble substances is widely used, for example, in drug delivery [13, 14]. However, we will not discuss this here in detail. Spherically closed lipid bilayer structures enclosing an aqueous compartment are called vesicles or liposomes [2]. Here we reserve the term vesicle for polymer vesicular structures, while vesicles constituted from lipids are preferably referred to as liposomes. Owing to their similarity to the cell membrane, liposomes are widely employed as models and mimetic systems for biological membranes [15]. The aqueous volume entrapped within the liposome can serve as a reservoir for sensitive water-soluble compounds, protecting them from hostile environments. Enzymes, for instance, have been long protected by this procedure [16]. To make use of the catalytic activity, either the enzyme has to be released from the protecting vessel in order to enter into

Nanocontainers

contact with the substrates in the surrounding milieu, or the substrates have to permeate the membranes to be able to undergo the reactions catalyzed by such enzymes in the interior of the vesicular structure. Since the membrane acts as a diffusion barrier for the substrates, this usually decreases the turnover of the enzyme. A great deal of research has been devoted to the use of liposomes as drug carriers; it is not the intention to cover this area here in detail. The interested reader may consult some recent reviews [17–20]. The main disadvantage of liposomes is their inherent instability to both mechanical and environmental changes [19, 20]. One strategy to overcome this is to polymerize the constituent lipids within the membrane, thus producing robust entities. However, stabilizing the structure usually renders a decrease in its permeability, which is also a crucial parameter in the context of drug delivery [19]. Thus ways have to be found to overcome this. Lipid vesicles can be regarded as spherical capsules comprising a shell of the lipid bilayer and an aqueous core. Hence, it is straightforward to use them as precursors for the preparation of size- and shape-persistent nanocontainers. This can be achieved using different concepts. Figure 3 gives an overview of various methods. For example, lipids that are functionalized with polymerizable groups can be polymerized within such vesicular structures. As a result of the polymerization reaction, the individual lipid molecules are interconnected via covalent bonds, which stabilizes considerably the liposome membrane [21, 22]. In some sense the polymerized lipids can be regarded to mimic the role of the cytoskeleton or of the murein network (i.e., the polymer structures which Nature uses to stabilize biological cell membranes) [23]. In contrast to these natural polymer scaffolds that are simply attached to the lipid membrane via

COOH NH2

Figure 3. Schematic representation of the different possibilities for stabilizing lipid vesicles. Reprinted with permission from [21], H. Ringsdorf et al., Angew. Chemie 100, 117 (1988). © 1988, Wiley-VCH.

303 hydrophobic interactions, the polymerized lipids are, however, all covalently connected to each other. Cross-linking converts the structures held together solely by van der Waals forces into covalently bonded macromolecules. As a result of this procedure, a considerable obstruction of the lipid lateral mobility within the membrane is observed, leading to a reduced permeability of encapsulated substances [22]. Interestingly, the polymerization of reactive lipids in bilayers formed from mixtures of different lipids may induce phase separation phenomena within the membranes. This can be exploited to produce labile domains in a controlled manner in the shell of the polymerized vesicles. These domains can be plugged or unplugged using external stimuli, which renders such particles suitable for applications in the area of controlled or triggered release. Since the pioneering studies on polymerized vesicles derived in the late 1970s and early 1980s, this area has developed into a broad and active field of research. A detailed discussion of all its different aspects would lead too far here, all the more since several recommendable reviews and books have already appeared on this topic, to which the interested reader may refer [21, 22, 24, 25]. Even though liposomes are biocompatible and biodegradable materials and structurally and chemically closely related to cell membranes, they are recognized as foreign bodies in living systems. This recognition by the reticuloendothelial system (RES) accounts for their low circulation times after parenteral administration [2]. One important milestone in the development of liposome and liposome-related structures was the discovery of socalled stealth liposomes [26, 27]. These particles are ignored by the reticuloendothelial system and, hence, they show prolonged circulation times [28, 29]. Additionally, they are more stable towards oxidation, enzyme degradation, and reaction with plasma lipoproteins [2]. The stealth liposomes comprise “pegylated” lipids, that is, lipids covalently attached to poly(ethylene glycol) (PEG) chains [30]. This external brush of hydrophilic polymer chains at the surface of the lipid bilayer shields them from the recognition by opsonins and plasma lipoproteins. Additionally, the hydrophilic coating of the surface of the liposomes produces a steric repulsion towards adhesion to other surfaces (e.g., opsonins). In contrast to adsorbed polymers on liposomes, which also yield certain steric stabilization, the sterically stabilized liposomes are covalently bonded, thus increasing, for instance, the stability towards dilution. By the conjugation of lipids with polymers one obtains not only a more stable structure but also a very versatile system, that can easily be modified at its outer surface; that is, the system can be decorated with antibodies, receptors, and ligands, by using heterobifunctional PEG [26, 27]. A comprehensive collection of papers dealing with the theory and applications of liposome steric stabilization can be found in [26]. Recently an interesting application-relevant approach has been presented to release encapsulated material from liposomes under controlled conditions. Using a synthetic triplechain amphiphile to produce stable vesicles, pH-influenced release of encapsulated substrates was achieved. The artificial lipid used carried carboxylic end-groups. Interestingly, less than 10% of the encapsulated water-soluble probe was

304 released at pH 7.5 over a year of storage. However, by lowering the pH to 3.5, the vesicles were disrupted, thus expulsing their content into the surrounding medium [31]. Functional materials with enhanced properties can be obtained by properly combining different starting materials. Composite materials are a good example of this approach. For example, by inserting Prussian blue, a well-known ferromagnet at low temperatures, into a bilayer of photoresponsive azobencene containing vesicles, a very interesting kind of composite is obtained. The magnetic properties of such composites can be triggered by photoillumination. Upon irradiation the azobencene-containing vesicles undergo a cis-trans photoisomerization. This in turn has an effect on the electrostatic interactions between the incorporated Prussian blue and the lipid membrane, thus providing a tunable system [32].

3.2. Nanocontainers from Amphiphilic Block Copolymers Similarly to lipids, also synthetic amphiphilic block copolymers may form superstructures, like vesicles, in aqueous media [33–43]. The most simple block copolymer architecture consists of a sequence of repetitive units of the homopolymer A tethered to a sequence of repetitive units of homopolymer B. However, also more sophisticated polymer architectures are accessible, such as, for instance, triblock, multiblock, graft, and star copolymers, and combinations thereof. The characteristic molecular design of amphiphilic block copolymers consists of a minimum of two blocks of different chemical composition connected one to the other through a covalent bond. A good review of the synthetic pathways for the production of amphiphilic block copolymers can be found in [44, 45]. Block copolymers consisting of blocks with different solubility, that is, amphiphilic block copolymers, exhibit selfassembly behavior in solution. Within the self-assembled superstructures, the insoluble blocks are shielded as far as possible by the soluble ones from the surrounding solvent. Depending on block length ratio, the hydrophilicto-lipophilic balance (HLB), concentration, temperature, preparation method, etc., different morphologies can be observed in solution. Generally, the morphology of their self-assembled superstructures can be regarded as core-shell micellar structures in which the core and the shell consist of the insoluble block and the soluble one, respectively. It has been observed [34, 40] that in aqueous solutions, decreasing the relative length of the hydrophilic block leads to a transition from spherical (micelles) to cylindrical (rods) and later to lamellar (vesicular) structures. Generally, the self-assembly of amphiphilic block copolymers follows the same principles as that of low-molecularweight amphiphiles. However, block copolymer aggregates and particularly vesicles may be significantly more stable than those formed from conventional lipids due to the larger size and the slower dynamics of the underlying polymer molecules [46]. In contrast to lipid bilayers, the longer underlying polymeric chains with higher conformational freedom of

Nanocontainers

polymeric membranes gives the latter not only increased toughness, elasticity, and mechanical stability but also a considerably rather low permeability [46]. An excellent and very recent review on the field of polymeric vesicles can be found in [47]. Nanocontainers based on block copolymer vesicles possess great potential in a broad area of applications, such as controlled release systems [48–54], confined nanometersized reaction vessels, or templates for the design of new materials. In this context it is particularly interesting that the physical properties of their polymer shells can be controlled to a large extent by the block length ratio or the chemical constitution of the underlying polymer molecules [34, 45]. Furthermore, synthetic polymers provide a wide spectrum of alternatives to design materials with responsive behavior towards external stimuli. Similarly to conventional lipid self-assembled morphologies, block copolymer vesicles are held together solely by non-covalent interactions. Hence they can disintegrate under certain conditions (e.g., dilution or presence of detergent) and dissolve as individual block copolymer molecules. It is obvious that, analogous to the reactive lipids, also block copolymer molecules could be modified with polymerizable groups. A subsequent polymerization of the resulting “macromonomers” interconnects them via covalent bonds, which stabilizes the whole particle. Up to now, however, only a few papers dealing with such particles have appeared. In one reported case, using a diblock copolymer consisting of poly(1,2-butadiene)-bpoly(ethylene oxide), vesicular structures were locked in by
-irradiation in aqueous solutions. The resulting crosslinked vesicles could be dispersed in solvents that are good for both blocks, without losing the fixed vesicular structure [39]. In another paper, the formation of vesicles from a poly(isoprene)-b-poly(2-cinnamoyl methacrylate) (PIPCEMA) diblock copolymer in hexane-tetrahydrofuran mixtures has been exploited as a starting point [55]. Converting these vesicles into stable, water-soluble polymer nanocapsules requires, however, a rather costly procedure. The PCEMA blocks were photocross-linked and then, in a second step, the PI blocks had to be hydroxylated to make these hollow nanospheres water-soluble. The radii of the nanocapsules were about 50 to 60 nm and changed only very slightly during these conversions. After loading the nanocontainers with Rhodamine B, the dye could be quantitatively released in water and water-ethanol mixtures in a way that the release rate could be tuned by the composition of the water-ethanol mixtures. Ethanol seems to be a good solvent for the underlying block copolymers. Hence higher ethanol content in the solvent mixture increases the solvent quality and the cross-linked shell of the cross-linked particles swells increasingly. As a result, the shell permeability increases and release of the dye becomes faster. This feature makes such systems attractive for applications, since prefabricated particles can be loaded effectively in an organic solvent and subsequently the encapsulated material slowly released in water. In a similar approach, a rather simple one-step procedure has been used to prepare vesicular structures from

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Nanocontainers

poly(2-methyloxazoline)-b-poly(dimethylsiloxane)-b-poly(2methyl-oxazoline) (PMOXA-PDMS-PMOXA) triblock copolymers directly in aqueous solution. One remarkable characteristic of this type of triblock copolymers, in contrast to diblock copolymers, is that the resulting vesicles are composed of a single layer of polymer instead of a bilayer. The size of the resulting vesicles could be controlled from 50 nm to 100 m [33]. The underlying triblock copolymers were modified with polymerizable methacrylate end-groups without changing their aggregation behavior in water. These “macromonomers” were polymerized within the vesicles using a UV-induced free-radical polymerization, which did not lead to any measurable changes in size, size distribution, or even molecular weight of the particles [33]. Obviously the polymer chain reaction occurs mainly intravesicularly. Intervesicle reactions such as exchange of individual triblock copolymer molecules or a chain propagation reaction involving more than one vesicular aggregate play only a minor role on the time scale of the experiment. The covalently cross-linked polymer network structures result in particles that possess solid-state properties such as shape persistence. Therefore they are able to preserve their hollow-sphere morphology even after their isolation from the aqueous solution and redispersion in an organic solvent, such as chloroform, tetrahydrofuran, or ethanol. This is documented in Figure 4, which shows a transmission electron micrograph of polymerized triblock copolymer vesicles isolated from water and redispersed in ethanol. Ethanol is a good solvent for the whole underlying block copolymer molecule. Hence, nonpolymerized vesicles would immediately disintegrate under such conditions into singly dissolved polymer molecules. In contrast to their fluid-like, nonpolymerized precursors, a shear deformation of the polymerized vesicles may lead to cracks characteristic for solid materials [56]. This is directly demonstrated in the reflection intensity contrast micrographs of Figure 5 that show a giant polymerized triblock copolymer vesicle before and after shear-induced rupture. This shape-persistence allows the use of such vesicles as a delivery system since they can be loaded with guest molecules in an organic solvent. After isolation of the loaded polymer shells and redispersion in aqueous media, the encapsulated material can be subsequently released.

1. hν 2. shear

10 µm

10 µm

Figure 5. Reflection intensity contrast micrograph of a giant, polymerized PMOXA-PDMS-PMOXA triblock copolymer vesicle before (left) shear-induced rupture and after (right) shear-induced rupture.

A more specific uptake and release of substances could be achieved by reconstitution of membrane proteins in the completely artificial surrounding of the block copolymer membrane [57–59]. It has been shown that the functionality of the incorporated proteins is fully preserved even after polymerization of the vesicular membrane. With regard to the wide range of membrane proteins Nature provides, such copolymer-protein hybrid materials possess a great potential in many areas of application, such as, for example, gene therapy [60] or biomineralization [61]. By encapsulating an enzyme (-lactamase) in the aqueous core domain of the nanocapsule and reconstituting a membrane protein (OmpF) in the polymer shell, a novel kind of nanoreactor could be designed (see Fig. 6) [58]. Furthermore, the channels of this protein close reversibly above a critical transmembrane potential. By simply adding a large enough polyelectrolyte to the external solution, that cannot pass the protein channels, a Donnan potential is created across the vesicular membrane. If this potential exceeds

∆ϕ

= Polyelectrolyte = Channel Protein = Enzyme Figure 4. Transmission electron micrograph of polymerized ABAtriblock copolymer vesicles. The length of the bar corresponds to 1 m. Reprinted with permission from [33], C. Nardin et al., Langmuir 16, 1035 (2000). © 2000, American Chemical Society.

Figure 6. Schematic view of a PMOXA-PDMS-PMOXA nanoreactor with encapsulated -lactamase and of the Donnan potential induced by polyelectrolyte present in the external solution.

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Nanocontainers

the critical voltage necessary for closure of the protein, also small substrates can no longer enter the vesicular interior and the reactor is deactivated. Decreasing the potential below the critical voltage (e.g., by dilution) reactivates the reactor. The possibility to trigger the activation (or deactivation) of such systems is highly interesting for applications since it allows local and temporal control on the uptake and release of substrate. Very recently the use of polypeptide-based diblock copolymers, poly(butadiene)-b-poly(L-glutamate) (PB-PGA) for the preparation of vesicular structures has been described [62, 63], Figure 7. Particularly interesting here is that the solvating chains are polypeptides and form vesicles, or socalled “peptosomes,” composed of modified protein units. A subsequent polymerization of the poly(butadiene) block leads to shape-persistent nanocontainers that possess, due to their polypeptide block, a certain pH- and ionic strengthsensitivity [63]. By changing these parameters, the particles dimension changes reversibly as a result of the polypeptide block transition from a compact helical secondary structure at low pH values to a more extended random-coil conformation in basic media.

3.3. Nanocontainers Derived from Lipid Vesicles Alternatively to the stabilization of lipid vesicles via intrapolymerization of cross-linkable lipids [21, 22], also known as polymerization of vesicles [64], another strategy makes use of the vesicular morphology simply as a template to imprint its hollow structure to other materials. Here two main approaches can be differentiated. One concept uses just the geometry of the vesicular aggregates as a template [64–72]. In this case the amphiphilic molecules themselves are not polymerized to freeze in

200 nm

Figure 7. Freeze-fracture electron micrograph of a vesicular solution of poly(butadiene)85 -b-poly(glutamate)55 in pure water (pH ∼ 60). Reprinted with permission from [62], H. Kukula et al., J. Am. Chem. Soc. 124, 1658 (2002). © 2002, American Chemical Society.

the whole superstructure of the supramolecular aggregate; they just provide a geometrically restricted environment for dissolving and polymerizing conventional monomers. This approach is also known as polymerization in vesicles or morphosynthesis [64–73]. In a second approach, vesicular templates are used solely to impart a surface onto which materials are grown from. This is known as transcriptive synthesis, since the structure of the vesicle is transcripted onto the new material, or sometimes called vesicle directed growth [73]. It is well known that vesicles or liposomes are able to solubilize hydrophobic substances to a certain degree. Such compounds are usually dissolved in the hydrophobic part of the lipid bilayer. If such substances also carry polymerizable groups, their subsequent polymerization should lead to the formation of polymer chains entrapped in the interior of the membrane. In contrast to polymerizable lipids, the polymer chains are now simply dissolved within the alkane part of the bilayer forming lipids. Hence, they are of minor influence on the overall physical properties of the membranes. One special feature of vesicular polymerization of conventional hydrophilic or hydrophobic monomers is that the different compartments provided by the self-assembly of the lipid molecules generally serve only as a template, which determines size and shape of the resulting polymers. Thus, it is possible to use nearly every natural or synthetic lipid, without any modification. Although in most reported studies on vesicular polymerization of conventional monomers, synthetic lipids like dioctadecyl diammonium bromide (DODAB), chloride (DODAC), sodium di-2-ethylhexyl phosphate (SEHP), or even spontaneously formed vesicles prepared from mixtures of cationic and anionic surfactants have usually been used, any natural lipid would provide a suitable matrix. Moreover, a combination of polymerizable lipids and conventional monomers could be incorporated in templating vesicles to yield hybrids with interesting new polymer structures [64, 74, 75]. Of course, the incorporation of hydrophobic substances into lipid bilayers should not exceed certain saturation concentration [76]. Above this concentration the monomer is no longer homogeneously distributed within the bilayers. This has been shown for toluene in phospholipid vesicles at concentrations above the saturation level. Moreover, exceeding this saturation concentration may also disrupt the whole bilayer structure, thus converting the system into a conventional emulsion or even leading to the formation of a separate monomer phase in the presence of intact vesicles. It is obvious that the overall thickness of the lipid membranes has to increase upon the solubilization of hydrophobic substances. The maximum swelling of the membrane leads typically to an increase from about 3 to 5 nm [77]. This is, however, a negligible effect compared to the overall diameter of typical small unilamellar vesicles, which is about 100 nm. Therefore no dimensional changes of the underlying vesicles can usually be detected upon swelling the lipid bilayers of the vesicles, as long as the monomer concentration stays below the saturation value in the membranes. It has been shown that the hydrophobic portion of lipid bilayers can be selectively swollen by a variety of hydrophobic monomers, such as styrene [65, 66, 68, 69], alkyl(meth)acrylates [67, 70, 71], or even lipofullerenes

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Nanocontainers

carrying polymerizable octadecadiine side chains [72]. A cross-linking polymerization of such monomers leads to the formation of two-dimensional polymer networks in the interior of the membranes. Such networks can act as a polymeric scaffold that increases the mechanical stability of lipid membranes considerably without impeding the mobility of the lipid molecules within the aggregates. The free-radical polymerization of the hydrophobic monomers incorporated into the lipid membranes of vesicles can be initiated, similarly to the polymerization of reactive lipids, by UV irradiation, thermal, or redox chemical radical generation. The polymerization process itself seems, however, to be rather sensitive towards the composition of the system, that is, the chemical constitution of the monomer and the lipid and the concentration of the monomers in the bilayer, which, of course, limits its possible applications. While polymerization of alkyl (meth)acrylates in dioctadecyl-ammonium chloride vesicles [70, 71], the reaction of lipofullerenes in dipalmitoyl-phosphatidylcholine vesicles [72], or styrene/divinyl benzene mixtures in equilibrium vesicles formed by CTAT/SDBI or CTAB/SOS mixtures [79] clearly lead to the formation of polymer hollow spheres, in case of styrene/divinylbenzene in dioctadecyl-ammonium bromide vesicles, an intravesicular phase separation occurs during polymerization, thus leading to the formation of so-called parachute-like structures [69, 78]. An interesting aspect of the formation of cross-linked polymer particles in vesicular dispersions arises from the fact that, in contrast to linear polymers, they should be able to retain their structure even after their isolation from the lipid matrix [70, 79]. Although the particles contract considerably after their isolation from the lipid membrane, they preserve their spherical shape. Their dimensions always remain, however, directly proportional to those of the underlying vesicles. This is not too surprising since the polymer chains are expected to be forced into a nearly two-dimensional conformation in the interior of the lipid membrane. After their liberation from the membrane, the polymer chains can gain entropy by adopting a three-dimensional conformation. To do this, such spherically closed polymer shells have to shrink and the thickness of their shells increases. The extent of the observed contraction of the particles depends sensitively on the cross-linking density of the polymer network structure. The contraction increases with increasing cross-linking density, thereby showing the same scaling behavior as branched polymers upon variation of their number of branches. For the highest cross-linking densities, the particles contract to about 1/10 of the original size of the templating vesicles. In context with possible applications, it would be of great interest to have detailed information about the permeability of these polymer hollow spheres. It has to be expected that, besides the chemical constitution of the polymer backbone, the mesh size, that is, the cross-linking density of the polymer network structure, also plays an important role. Only molecules that are smaller than this mesh size should be able to diffuse across the polymer shell. Molecules which are larger cannot pass the polymer membrane for geometrical reasons. Whereas the templating vesicles directly determine the size and shape of the resulting polymer particles, the

polymer scaffold can be modified rather easily using conventional chemical reactions. This allows, for example, sulfonation of poly(styrene) containers [79] or the conversion of poly(tert-butyl acrylate) hollow spheres into poly(acrylic acid) hollow spheres. The resulting polyelectrolyte nanocapsules can swell as a response to changes in the pH of their environment [80]. This pH-dependent transition influences considerably the permeability of such polyelectrolyte shells and can be used to selectively entrap and release specific substances. Although such a vesicular polymerization represents a rather elegant approach to produce polymeric nanocontainers, their possible technical application is expected to be rather limited. The reason for this lies in the low economical efficiency of this method. Apart from the often energyconsuming vesicle preparation procedure, the synthesis of one gram of pure polymer nanocapsules already requires approximately 1.5–2 times their weight of lipid, a reaction volume of about 300–400 milliliters of water, and additionally several liters of organic solvents (for purification).

3.4. Nanocontainers Derived from Polymer Micelles Since block copolymers are very versatile materials, they are broadly used as scaffold structures to construct sophisticated and complex materials with new properties. The richness of the block copolymer field relies on the fact that by choosing different repeating units to form each of the blocks, a great variety of starting materials is at hand. Additionally, synthetic polymers provide a wide spectrum of alternatives to design materials with responsive behavior towards external stimuli; this combined with their supramolecular aggregation makes polymers very interesting raw materials. Not only vesicular structures but also micelles can be used for the controlled formation of nanocontainers. It is, for example, well known that block copolymers may assemble into polymeric micelles with diameters in the 10- to 100-nm range. An important issue in making these self-assembled systems useful for specific applications is again their capability to respond to external stimuli, that is, to interact with their surrounding environment. Very recently the formation of three-layer micelles in water from polystyreneb-poly(2-vinylpyridine)-b-poly(ethylene oxide) (PS-b-P2VPb-PEO) triblock copolymers was reported [81]. It was demonstrated that the pH sensitivity of the P2VP shell can be used to tune the micelle size from a hydrodynamic diameter (Dh  of 75 nm at pH > 5 to 135 nm at pH < 5. This effect is based on the electrostatic repulsion between the charged P2VP blocks and is not completely reversible because of the formation of salt with each pH cycle. Although this feature makes this system useful for encapsulation and release of active species and has already been used for the synthesis of well-defined gold nanoparticles, its long-term stability is still questionable. One major aspect of block copolymers is that they can be modified so that either the interior or the exterior blocks within the micelles contain polymerizable groups. For example, poly(isoprene)-b-poly(acrylic acid) (PI-PAA) diblock copolymers form micelles in aqueous solution with a PI core and a PAA shell. It has been shown that the PAA

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Nanocontainers

shell can be cross-linked with , -diamino-poly(ethylene glycol), giving shell-cross-linked nanoparticles also known as shell-cross-linked knedels (SCK) [82, 83]. Similarly, a poly(isoprene)-b-poly(2-cinnamoylethyl methacrylate)-bpoly(tert-butyl acrylate)(PI-PCEMA-PTBA) triblock copolymer forms micelles with a PTBA corona, PCEMA shell, and a PI core in THF-methanol mixtures [84]. In this case the micellar structure could be locked in by UV-cross-linking of the PCEMA within the micelles. Subsequently the PI cores of both the cross-linked PI-PAA and the PI-PCEMAPTBA micelles could be degraded by ozonolysis into small fragments that could diffuse into solution and leave nanospheres with a central cavity. A schematic representation of the whole process is given in Figure 8. The potential of such systems for encapsulation of small molecules has been demonstrated by loading the cross-linked PCEMA-PTBA capsules with Rhodamine B [84]. The incorporation of the dye into the central cavity of the particles could readily be visualized by transmission electron microscopy (TEM). The degradation of the shell-cross-linked PI-PAA micelles leads to water-soluble cross-linked poly(acrylamide) hollow spheres which considerably increase the Dh of their shells after removal of the core [83]. The increase of Dh from 27 to 133 nm has been explained by the fact that the cross-linked poly(acrylamide) shells can be regarded as a hydrogel that swells when the core domain fills with water after the PI core has been removed. The diameter of the hollow-sphere products depends sensitively on both the degree of polymerization of the block copolymers originally used to form the micelle and the nature of the cross-linking diamine used to prepare the shell-cross-linked micelles. By the same approach, poly( -caprolactone)-b-poly (acrylic acid)-co-poly(acrylamide) SCKs with a biodegradable core were prepared [85]. The synthetic approach included initially the hydrolysis of poly( -caprolactone)b-poly(tert butyl acrylate) to give poly( -caprolactone)-bpoly(acrylic acid), followed by micellization. Cross-linking sec-Bu 130 Ph Ph O

H 170 OH

Self-assembly in an Aqueous Solution

PI-block-PAA PI

PAA Polymer Micelle H2N

O

O n NH2

n = 1 or 70

Amidation of PAA to Give Shell Crosslinking

Ozonolysis to Degrade the PI Core

Nanocage 3. n = 1 4. n = 70

SCK O NH

O

NH O n O

1. n = 1 2. n = 70

Figure 8. Procedure for the preparation of nanocages from amphiphilic diblock copolymers. The shell of the final nanocages consists of cross-linked poly(acrylamide). Reprinted with permission from [83], H. Huang et al., J. Am. Chem. Soc. 121, 3805 (1999). © 1999, American Chemical Society.

of the carboxylic groups present in their corona was performed with 2,2′ -(ethylenedioxy)bis(ethylamine) to render finally the poly( -caprolactone)-b-poly(acrylic acid)-co-poly (acrylamide) SCK, while hydrolysis of the core was achieved by either acidic-or basic-promoted degradation of the ester linkages to produce the hollow capsules. Such mild core removal is of particular interest in biological applications, especially since the monomers released are biocompatible [85]. Moreover, these shell-cross-linked particles were surface functionalized to promote cell binding [86] via conjugation with a peptide sequence. Using also the SCK technique as above but without removal of the core, such shell-cross-linked particles have been modified in order to respond to environmental stimuli [87]. Interestingly, here the hydrophobic core consisting of poly(methyl acrylate) is hydrolyzed to give hydrophilic poly(acrylate) chains. The nanoparticles thus obtained, although not completely hollow, have a nanocage-like structure, due to the fact that the shell swells considerably after the hydrolysis of the core chains. Additionally, the nanocagelike particles undergo a pH-controllable swelling, due to electrostatic repulsive forces acting among the ionized core chains [87]. The extent of swelling depends on the percentage of cross-linking of the shell. In contrast with the initial core-shell particles, the particles with modified core are capable of encapsulating hydrophilic guest molecules. One can produce hollow capsules not only by degradation of the core to monomer or oligomers, but also by selectively detaching both core- and shell-forming block copolymer chains. Obviously, the particles have to be previously stabilized in some way, to prevent disruption of the whole self-assembled superstructure. For example, this concept has been used to prepare SCK in which the core was cleaved by thermolysis of the bond connecting it to the shell. Surprisingly, the polymeric chains are able to permeate the cross-linked shell membrane, and this permeability is found to be inversely dependent on the degree of cross-linking of the shell. Nevertheless, the removal of the core by this approach is not complete, since less than 30% of the total poly(styrene) chains were released even for the lower crosslinking densities [88]. One “block-copolymer free strategy” to prepare micelles solely by hydrophobic interactions between the core and the shell of the structures instead of using covalent attachment, has been described by Liu et al. [89]. They report the preparation of hollow capsules via self-directed assembly of a homopolymer (poly( -caprolactone)) and a random graft copolymer comprising a hydrophilic backbone of poly(methylmethacrylate) and poly(methylacrylic acid) and hydrophobic branches of poly( -caprolactone). Upon addition of water to a DMF solution of the above mentioned polymers, micelles form in which the poly( -caprolactone) constitutes the core and the graft copolymer arranges as the shell. The structure is achieved only by the anchoring of the branches of the graft copolymer into the poly( -caprolactone) core; thus, no covalent or hydrogen bonding is needed. Although they report a block-copolymer free approach with no need of covalent bonding between the core and the shell, they use a further stabilization of the system by (covalent) cross-linking the carboxylic and amino groups present in the shell, via a carbodiimide derivative.

Nanocontainers

309

The structures thus obtained resemble the shell-cross-linked micelles described by Wooley and co-workers [82]. Removal of the core to give the hollow counterparts was achieved by enzymatic degradation of the poly( -caprolactone) with a lipase [89]. Another approach used self-assembled superstructures as templates for the production of inorganic MoO3 nanospheres. A micelle forming triblock-copolymer, comprising poly(oxyethylene)-b-poly(oxybutylene)-b-poly(oxyethylene), served as the templating matrix for the formation of thin-layered hollow nanospheres. The latter were obtained with MoO2 (OH)-(OOH) which upon decomposition affords MoO3 and O2 , a precipitation crystallization process taking at least two weeks for completion. The template forming triblock-copolymer was removed by solubilization in excess water. Apparently and against expectation, the crystallization of MoO3 occurs at the interface between the core and the shell of the micellar scaffolds. This follows from the observation of smaller radii for the inorganic cages obtained in comparison with the external radius of the micellar templates used [90].

4. TEMPLATE-DIRECTED PREPARATION OF NANOCONTAINERS Another possibility for generating polymer nanocapsules is to form a polymer shell around a preformed template particle that can subsequently be removed, thus leaving an empty polymer shell. There are several methods of conducting such a template synthesis of hollow polymer particles. Different templates have been used so far, including silica micro and nanoparticles (usually prepared by Stober synthesis) [91], colloidal or latex particles, gold nanoparticles, etc.

4.1. LbL Deposition A convenient way to produce nanocapsules is to exploit the well-known polyelectrolyte self-assembly at charged surfaces. This chemistry uses a series of layer-by-layer (LbL) deposition steps of oppositely charged polyelectrolytes [92]. The driving force behind the LbL method at each step of the assembly is the electrostatic attraction between the added polymer and the surface. One starts with colloidal particles carrying surface charges, for example, a negative surface charge. Polyelectrolyte molecules having the opposite charge (e.g., polycations) are readily adsorbed due to electrostatic interactions with the surface. Not all of the ionic groups of the adsorbed polyelectrolyte are consumed by the electrostatic interactions with the surface. As a result, the original surface charge is usually overcompensated by the adsorbed polymer. Hence, the surface charge of the coated particle changes its sign and is now available for the adsorption of a polyelectrolyte of again opposite charge (i.e., a polyanion). As sketched in Figure 9, such sequential deposition produces ordered polyelectrolyte multilayers. The size and shape of the resulting core-shell particles is determined by the template colloidal particle, where the formation of particles with diameters ranging from 0.2 to 10 m has been reported. The thickness of the layered shell is determined by the number of polyelectrolyte layers and can be adjusted in the nanometer range.

Figure 9. Illustration of the procedure for preparing hollow spheres using layer-by-layer deposition of oppositely charged polyelectrolytes on colloidal particles. Reprinted with permission from [92], E. Donath et al., Angew. Chem. Int. Ed. 37, 2201 (1998). © 1998, Wiley-VCH.

Up to now, a variety of charged substances, such as synthetic polyelectrolytes, biopolymers, lipids, and inorganic particles have been incorporated as layer constituents to build the multilayer shell on colloidal particles [93–95]. As templates for this approach, mainly colloids consisting of polystyrene latexes or melamine formaldehyde particles [96] have been used, but also gold [97] and proteins [98] have been tested. To avoid, however, a polyelectrolyte-induced particle flocculation, one has to work at rather low particle concentrations and excess polyelectrolyte not adsorbed to the surface has to be removed carefully after each step by washing, which makes this technique rather tedious. After completed deposition of a predefined number of layers, the colloidal core can be dissolved and removed. If one uses human erythrocytes as colloidal templates, they can be oxidatively decomposed in an aqueous solution of sodium hypochlorite. When using weakly cross-linked melamineformaldehyde particles, the core is dissolved upon exposure to an acidic solution of pH < 16. Products of both decomposition methods are expelled through the shell wall and removed by several centrifugation and washing cycles. Although the core removal takes place under harsh conditions, neither the acid treatment nor the oxidative decomposition affects the polyelectrolyte layer shells, as can be seen in Figure 10 [92]. They clearly preserve their hollow-sphere

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1 µm

Figure 10. Transmission electron micrograph of polyelectrolyte hollow spheres. The shell of the particle consists of 9 layers ((poly (styrene sulfonate)poly(allylamine hydrochloride))4 /poly(styrene sulfonate)). Reprinted with permission from [92], E. Donath et al., Angew. Chem. Int. Ed. 37, 2201 (1998). © 1998, Wiley-VCH.

morphology and are shape-persistent. It has been shown that small dye molecules can readily permeate such layered polyelectrolyte shells while larger-sized polymers with molecular weights larger than 4000 Da obviously do not [99–101]. Nevertheless, it has to be expected that their long-term stability will depend sensitively on the surrounding environment of the particles. Especially in biological fluids (e.g., blood plasma), or in media of high ionic strength, which may screen the ionic interactions responsible for maintaining their integrity, the long-term stability of such polyelectrolyte shells may be rather limited. However, this sensitivity towards the physico-chemical conditions of the surrounding medium, in particular to pH and ionic strength changes, was successfully used to get control over the permeability of multilayer shells consisting of poly(styrene sulfonate) and poly(allylamine) hydrochloride [103, 104]. By this control it is possible to release from these capsules in a controlled manner prior encapsulated biomacromolecules or fluorescent probes, even with molecular weights of 70,000 Da, or to use them as templates for the selective crystallization of various dyes [102, 103, 105]. Even loading and releasing of substances was accomplished by pH-induced or salt-triggered permeability of the mentioned polyelectrolyte capsules. Another interesting point is that the capsules could be filled with oils by sequential exchange of the solvent. These oil-filled capsules could be dispersed in water due to their amphiphilic nature, thus leading to a stable, surfactant-free oil-in-water emulsion [106, 107]. Additionally, applying this concept of polyelectrolyte layering onto substrates, a protein aggregate has been encapsulated in a process similar to that already described for other templates such as latex particles. Although the hybrid aggregates obtained were amorphous and removal of the core-forming template was not attempted, this shows the potential of the LbL approach, where, for instance, the encapsulating substrate and templating material can be the same and one [98, 102]. Functionalized polystyrene latex particles carrying surface charges are also suitable substrates for the polyelectrolyte self-assembly technique. In one case, inorganic particles

were incorporated into the adsorbed shells by a sequential adsorption of nanometer-sized SiO2 particles with negative surface charge and cationic poly(diallyldimethyl-ammonium chloride) (PDAD-MAC) [96, 108]. Layers with a thickness ranging from tens to hundreds of nanometers could be prepared by this procedure. Removing the polystyrene core, either with acid solutions or with solvents such as THF or DMSO, leaves SiO2 /PDAD-MAC hybrid nanocomposite shells and after calcination even pure SiO2 hollow spheres. Both the inorganic-organic composite and the pure inorganic capsules can be expected to show interesting physical properties such as enhanced mechanical stability or exceptional permeability behavior. By exactly the same strategy but using melamine formaldehyde as templates, micrometersize hollow hybrid organic-inorganic capsules and hollow silica spheres were also obtained [96]. With a similar approach, void spheres of titania, iron oxide (magnetic hollow nanocapsules), zeolite, clay, and their respective composites were also prepared [109–112]. Using the LbL technique, gold nanoparticles were used as templates for the production of polymer multilayer shells [97]. In the first reported case of metal particles as templates using the LbL method, the particles had to be surface modified to allow good deposition of the polyelectrolyte. Such functionalization of the gold particles was achieved by covalent bonding of alkanethiols, which also possessed ionic moieties that promoted the adsorption of the layers of polyelectrolytes. In this context, core dissolution via etching with cyanide produced the desired hollow polymeric nanoparticles, with reported diameters ranging from 15 to 50 nm. Not only stabilization due to electrostatic interactions of the polyelectrolyte forming shells may be used but also their stability can be enhanced by a subsequent cross-linking procedure. For example, by using diazoresins and alternating its deposition with poly(styrenesulfonate) or poly(acrylic acid) onto a sacrificial core, followed by UV irradiation to covalently cross-link the shells, and subsequent removal of the core, hollow polymeric capsules with enhanced stability were obtained [113]. Comparison of ionically crosslinked and covalently cross-linked capsules upon exposure to organic solvents and high-ionic-strength solutions shows a considerable increase of the stability of the latter ones, which is attributed to the covalent attachment. Although the capsules seem to retain to some extent their permeability, since removal of the core could be done either prior to the cross-linking step or after it, their permeability appears to be lower than in other polyelectrolyte capsules. Moreover, in contrast to poly(allylamine hydrochloride)poly(styrenesulfonate) containers, osmotic pressure resulted in almost no deformation for both polymerized and nonpolymerized diazoresin-poly(styrenesulfonate) capsules [113]. As already mentioned, one of the main interests in this field is to control the permeability and encapsulation of substrates. One way to achieve this is to modify the capsules’ shells, particularly their internal walls. With this aim in view, polymerization of monomers was carried out in the void volume of such polyelectrolyte capsules. While polymers cannot, monomers easily permeate the shell [99– 101]. If monomers are introduced in the empty volume of the containers, followed by a polymerization reaction, the resulting macromolecules are entrapped inside the capsules.

311

Nanocontainers

By using this approach to encapsulate a polyelectrolyte macromolecule, it was possible to obtain a pH of about 2 in the interior of the spheres. This is of interest, for example, in the context of nanoreactors, to carry out acid catalyzed reactions within the capsules. Interestingly, swelling and shrinking of the shells could be tuned by changing the osmotic pressure. Moreover, it was observed that the polymerization of encapsulated monomers took place mainly within the walls of the capsules which gave, for poly(styrenesulfonate), the possibility to modify the ionic selectivity of the shells. Thus, fluorescent anions could not translocate the functionalized walls, while cationic probes did. Surprisingly, the adsorption of oppositely charged ions on the walls resulted in an increase of the permeability of the shell, through the formation of pores which finally released the encapsulated macromolecules into the bulk of the solution. Therefore a tunable control of the permeability is achieved [114].

4.2. In-Situ Polymerization Similarly, poly(N-vinylpyrrolidone)-stabilized polystyrene latex particles were coated with thin overlayers of poly(aniline) to produce electrically conductive core-shell particles [115]. In contrast to the LbL deposition method where preformed polymers are adsorbed to a surface, here the polymer is formed in-situ by oxidative coupling of monomers at the particle surface. The poly(aniline) layers had, however, a rather nonuniform and inhomogeneous morphology. Therefore extraction of the polystyrene core left poly(aniline) shells that displayed a so-called “broken egg-shell morphology”; that is, they were largely disrupted. Also gold nanoparticles have successfully been used as templates for nucleation and growth of surrounding poly(pyrrole) and poly(N-methylpyrrole) shells [116, 117]. Etching the gold leaves structurally intact hollow polymer particles with a shell thickness governed by the polymerization time. This formation of polymer-coated colloids involves trapping and aligning the particles in the pores of membranes by vacuum filtration and a subsequent polymerization of a conducting polymer inside the pores (Fig. 11). In a first step, the gold nanoparticles are being filtered into a porous Al2 O3 support membrane with a pore size of 200 nm. After an initiator (Fe(ClO4 3 ) has been poured into the top of the membrane, monomer (pyrrole or N-methylpyrrole) is placed underneath the membrane. Upon diffusion of the monomer vapor into the membrane, it contacts the initiator to form polymer, preferentially at the surface at the gold particles. The resulting polymerencapsulated nanoparticles can be isolated by dissolution of the membrane in basic media. The shell thickness depends on the polymerization time and can be controlled in a range from 5 to 100 nm. In order to obtain hollow particles, the gold was etched, for example, with a KCN-K3 [Fe(CN)6 ] solution, prior to dissolution of the membrane material. Thus hollow cores with a diameter of 30 nm were seen by TEM, where the 30-nm Au particle was previously located, indicating that almost no reorganization, collapse, or shrinkage takes place when the empty shells are dried. Indeed, the diameter of the hollow core could be tuned by choosing an appropriate Au particle of different size. In this context it was shown that the gold particles are not only

Au nanoparticles Support membrane

Fe(ClO4)3(aq) polypyrrole

pyrrole (1) Vacuum Entrapment (1) Etch gold (2) Dissolve Membrane

Suspension of Hollow polypyrrole Nanocapsules

Dissolve Membrane (0.05 M KOH)

Suspension of polypyrrole-coated Gold Nanoparticles

Figure 11. Schematic diagram of the membrane-based method for synthesizing gold-core/polymer-shell nanoparticles. The particles are first trapped and aligned in the membrane pores by vacuum filtration and subsequently coated with poly(pyrrole), which occurs via polymerization of the monomer vapor when it diffuses into the membrane and interacts with the initiator (Fe(ClO4 )3 ). The membrane is then dissolved, leaving behind nanoparticle composites. The gold can also be etched first and the membrane then dissolved, resulting in hollow poly(pyrrole) nanocapsules. Reprinted with permission from [116], M. Marinakos et al., J. Am. Chem. Soc. 121, 8518 (1999). © 1999, American Chemical Society.

useful as a template material but can also be used to deliver guest molecules into the capsule core. For example, ligands attached to the gold surface, via alkanethiol-Au bonds or simply by physisorption, prior to polymerization remained trapped inside the hollow particles after gold etching, which demonstrates their potential as protective shells for sensitive compounds like enzymes. Indeed, the ability of the capsule to protect an encapsulated enzyme was studied [118]. Obviously the ions of the gold etchant were able to diffuse across the polymer shell, the permeability of which could even be tuned by the oxidation state of the polymer or the counter ion present during polymerization of the pyrroles. However, even rather small organic guest molecules like Rhodamine B [116] or anthraquinone-terminated hexanediol [118] were not released again from the interior of the particles, even over periods of up to three weeks. That means that there is only very restricted access to enclosed substances in the interior of the shells. In addition, the particle type appears to be limited to those that fit into the membrane supports used, which also restricts its applications. Nevertheless, it shows promise for coating of various templates like metals and biomacromolecules. One advantage in the use of conductive polymers, from the triggering or stimuli-response point of view, is that they could be interchanged from their cationic, anionic, and neutral forms, either chemically or electrochemically. Interestingly, quasi1D arrays of the Au-polymer composite and the hollow polymeric particles fabricated by this method could be obtained [117], which could be of advantage in the production of sensors, for example.

312 4.3. Surface Initiated Living Polymerization In another approach, hollow cross-linked polymeric nanoparticles are obtained by a template-assisted surface initiated living free-radical polymerization [119]. In this procedure, the surface silanol groups of silica nanoparticles, used as templates, are initially reacted with trichlorosilylsubstituted alkoxyamines as radical initiator groups. Subsequently, this layer of surface initiator groups is used to start linear polymer chains of poly(styrene) or poly(styrene-comaleic anhydride) by free-radical polymerization, thus leading to a hybrid core-shell morphology. In a following step, the shell is cross-linked and still covalently attached to the silica core; then removal of the core by HF treatment gives hollow polymeric particles, whereas the non-cross-linked particles after etching of the core gave linear polymers with loss of the capsular structure. Two different approaches were used to cross-link the shells; one involved thermal reaction of polystyrene with 4-vinylbenzocyclobutene, the other a two-step reaction in which a poly(styrene-co-maleic anhydride) is cross-linked with a diamine. This last cross-linking procedure resembles the one used by Wooley [82]. The obtained nanocapsules are stable against solvent dissolution and thermal treatment due to their cross-linked structure, although some disruption of the particles was observed and the solvent treatment followed by drying led to collapse of the spheres [119]. A similar approach was carried out [120] by using initiating sites for atom transfer radical polymerization (ATRP) [121] at the surface of silica microparticles, with a subsequent dissolution of the silica core to render hollow polymeric nanocapsules. Silica microspheres (3 m diameter) were used as templates to achieve hollow polymeric microspheres via surface initiated living radical polymerization of benzyl methacrylate followed by core dissolution. In a first step, living atom transfer radical polymerization was conducted via initiators attached to the surface of the template, leading thus to hybrid core-shell particles in which the template and the shell were covalently attached. In a following step, the sacrificial cores were dissolved, giving then hollow polymeric microcapsules. In this case control over the shell thickness was achieved by variation of the reaction time [120]. In both approaches the attained polymer chains are well defined in terms of polydispersity due to the living nature of the polymerization process [119, 120], thus leading to highly uniform shell thickness. Again cross-linking of the shells provides extra stabilization of the structures which otherwise would disintegrate upon dilution or during the subsequent manipulations necessary to obtain the hollow particles.

4.4. Nanocontainers from Inorganic Templates Taking into account the usually low permeability of nanocapsules and the difficulties encountered to load or to release molecules from them in a controlled way, some strategies have been proposed to overcome these disadvantages. For instance, Zha et al. [122] have used the well-known thermoresponsive poly(N-isopropylacrylamide) to obtain stimuli-responsive containers. Poly(Nisopropylacrylamide), which has a rather low (32 C) lower

Nanocontainers

critical solution temperature (LCST), undergoes a conformational change from coil to globule at its LCST [123]. The strategy used for obtaining the capsules was a colloid templated polymerization with a posterior removal of the core. As templates, silica particles (obtained by Stober synthesis [91]) with diameters from 10 to 100 nm were utilized, the surface of which was modified by 3-(trimethoxysilyl)propyl methacrylate, thus rendering a surface decorated with double bonds. In a seed precipitation polymerization, using the functionalized particles as seeds, N-isopropylacrylamide was polymerized in the presence of N,N′ -methylene bisacrylamide as cross-linker, in order to obtain hybrid particles, with a silica core and a cross-linked poly(N-isopropylacrylamide) shell structure. Hollow polymeric capsules were achieved by an etching step using HF. The hollow particles could maintain their shape after the dissolution of the core since they were cross-linked. While the size and shape obtained was found to be related to the templating particle, the shell thickness depended on different variables such as the amount of poly(N-isopropylacrylamide) and the size and concentration of the template particles. Also the degree of cross-linking influenced the morphology of the structures achieved. In this context, discs and dented structures, both due to collapsed capsules and intact spheres were observed. Most interestingly, the temperature dependence of the nanocapsules was investigated. In general, for all cross-linking densities, the capsules shrank as the temperature increased and their volume phase transition was 32  C. Additionally, the degree of shrinkage was found to be a function of the cross-linking density. Important is the fact that the swelling and shrinking cycles were repeatable and reproducible. Although it would be very interesting for applications like drug delivery, since the LCST of the polymer is close to biologically related applications, no attempt of encapsulation was reported [122]. Silica hollow spheres were synthesized by seeded polymerization of tetraethoxysilane on the surface of polystyrene particles followed by calcination [124]. Also microcapsules with magnetic interiors have been reported. By deposition of iron salts, coating of a crystalline shell of Fe3 O4 on polystyrene template particles was achieved. Following a posterior calcination of the core, hollow magnetic capsules were obtained. The stability of the spheres produced was low; nevertheless, this could be improved by additionally coating the spheres with a shell of silica nanoparticles via seeded polymerization of tetraethoxysilane according to the Stober technique [91]. Interestingly, these capsules are hydrophilic and thus can be dispersed in water, whereas heating to 100  C produces hydrophobic capsules by silica conversion to siloxane [124]. A similar approach to obtain submicron-sized hollow inorganic microcapsules consisting of yttrium was described by Kawahashi and Matijevic [125]. In this particular case, coating polystyrene latex with basic yttrium carbonate layers and subsequently calcining at elevated temperatures in air, resulted in the desired inorganic hollow particles. A self-aggregating polymer can be also used as a template for the formation of inorganic hollow spheres. Poly(L-lysine) in conjugation with hydrophobic amines was found to form

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Nanocontainers

aggregates in solution, and this was used to imprint their structure into silica [126]. Additionally, poly(L-lysine) is a well-known biocompatible polymer, which has the interesting property of showing strong pH-dependent behavior. In acidic solutions it adopts a random coil conformation, while at higher pH it undergoes a transition to -helix or -sheet conformations [127–129]. When tetraethyl ortosilicate was added to an aqueous solution of poly(L-lysine) in the presence of benzylamine, at pH 11.6, hybrid polymer core–silica shell capsules were formed with diameters from 100 nm to 1.5 m. The high polydispersity is a direct consequence of the broad size distribution of the template aggregates used, as confirmed by light-scattering techniques. Elimination of the core was achieved by subsequent calcination of the hybrid structures. Apparently both the poly(L-lysine) and the benzylamine are necessary to obtain the hollow silica structures, since attempts to use the individual components separately or other amines led only to the formation of silica particles or mixtures of particles and capsules. The advantages of this preparation method are the use of commercially available reactants, a biocompatible and biodegradable polymer, and a simple procedure in comparison with more established strategies like LbL in which many steps are required [126]. The advantages of inorganic hollow nanocapsules are their higher mechanical and thermal stabilities compared to the organic counterparts. However, encapsulation of molecules in their interior is quite challenging due to their rather impermeable shells. Zeolites have the advantage of imprinting micro pores on the shells of the nanospheres rendering readily permeable structures, and great research has been done in this area. We do not intend to cover this vast research field in detail. Nevertheless, it should be mentioned that very recently a new approach for the production of hollow zeolite microcapsules has been presented. Dong et al. [130] report the preparation of novel zeolite nanocapsules that comprise functionalized interiors. This is achieved by preencapsulating a specific substrate, followed by a vapor phase treatment (VPT). Mesoporous silica spheres (3–6 m) were coated with nano zeolite particle seeds (60 nm) and then these particles were treated with amine vapor in an autoclave (VPT). In this process the surface of the particle grows at expense of the silica core and finally once the silica is consumed, a hollow crystalline zeolite shell with a thickness on the order of 200 nm is obtained. Guest molecules, inorganic species like iron oxide (Fe2 O3 ), were encapsulated into the pores of the templating mesoporous silica, prior to the vapor phase treatment, thus rendering hollow capsules with an interior decorated by clusters of iron oxide [130]. Similarly, also porous carbon containers were prepared [131]. Using silica particles with solid core and mesoporous shell as templates, phenol resin or poly(divinylbenzene) was polymerized on their surface, thus giving a polymer-silica composite with the polymers being located inside the pores of the silica particles. A posterior carbonization of the polymer leads to carbon aluminosilicate nanocomposites. In a following step, hollow carbon capsules of 220 to 500 nm diameter and shell thickness of 55 to 90 nm were obtained by dissolution of the silica core with HF or NaOH when using phenol formaldehyde or poly(divinylbenzene), respectively.

Additionally, the diameter of the sphere and thickness of the capsule wall could be adjusted by careful choice of the silica templates. Interestingly, these carbon nanocapsules contain pores with size on the order of 2.8 to 4 nm, and constitute an inverse replica of the silica templates used [131]. One interesting approach using gold particles as templates has been reported by Sun et al. [132]. Hollow monolayerthick organic spheres were obtained by attaching thiolated -cyclodextrines to gold particle templates. The Au particles are synthesized in-situ by reduction of Au (III) in the presence of thiolated -cyclodextrines; this gives in turn particles coated with the thiolated substrate. Subsequent oxidation of the Au particles with iodine leads to dissolution of the gold and formation of disulfide bonds between the thiolated substrates. A key strategy in this approach is the use of molecules with many thiol groups to provide good crosslinking since, after dissolution of the Au core, the structure is held together solely by S S bonds. Confirmation of the hollow structures was done by solubility experiments; while the -cyclodextrines are insoluble in water, the hollow shells are soluble since they expose only their hydrophilic portions towards the bulk of the solution. The internal wall of the shells is hydrophobic, due to the disulfide bonds present, and to prove this, encapsulation of ferrocene was studied. As a result of disproportionation of the disulfide bonds, long storage in aqueous solution led to a precipitate of an insoluble disulfide polymer. This in turn could be used as a way of controlling the release of molecules encapsulated in such nanocontainers [132].

5. NANOCONTAINERS PREPARED BY EMULSION/SUSPENSION POLYMERIZATION In this section the formation of nanocontainers which can be achieved by several suspension and emulsion polymerization techniques is described. Although in most cases these methods have been shown to lead to particles with diameters of several micrometers, recent developments demonstrate that nanometer-sized polymer hollow spheres are also accessible. One example was described by Okubo et al. [133, 134] where the penetration and release behavior of various solvents from or into the interior of monodisperse cross-linked poly(styrene)/poly(divinylbenzene) composite particles could be investigated. The hollow structure of the particles is in this case achieved by a seeded polymerization utilizing the so-called dynamic swelling method. For example, the polymerization of divinylbenzene in toluene/divinylbenzene swollen polystyrene latex particles or in poly(styrene) containing toluene droplets leads to the formation of hollow poly(divinylbenzene) (PDVB) particles. This is a result of a micro phase separation due to the limited compatibility of the chemically different polymers in solution, which leads to the formation of a PDVB shell around a toluene-polystyrene core. After evaporation of the toluene, a cavity remains in the center of such particles. Another rather convenient method leading to hollow polymer particles proceeds via emulsion polymerization. Usually a two-stage process via seeded latex particles with physical or time separation between the two steps is applied.

314 In a first step, the core particles are synthesized by a conventional emulsion polymerization. Then in a second step, a different monomer or monomer mixture is added and a cross-linked shell is polymerized around the previously formed core particle. Although the preparation of such coreshell particles seems to be quite simple in theory, it is rather difficult in practice. This holds particularly if one is interested in well-defined and homogeneous particle morphologies, which is a basic requirement for the preparation of hollow polymer particles. It has been demonstrated that in this context both thermodynamic and kinetic factors are of crucial importance [135, 136]. The direct influence of many process parameters controlling the particle morphology, such as surface polarity, mode of monomer addition, role of surfactant and chain transfer agent, effect of polymer cross-linking and initiator, has already been demonstrated [137–143]. Additionally, to end up with a hollow polymer sphere one has finally to remove the core-forming material. Since core and shell are, however, frequently chemically rather similar, this is another critical step of the preparation procedure. Usually rather aggressive reaction conditions, like a prolonged alkali and acid treatment at high temperatures, are required to degrade the particle core [144, 145]. Although by using these methods clearly hollow particles can be formed, the question remains to what extent the polymer shells survive intact under these conditions. A rather elegant approach to remove the core under very mild conditions has recently been demonstrated. The authors report the synthesis and characterization of nanometer-sized hollow organosilicon particles [146]. The synthesis of these particles followed a two-step procedure similar to that described above. The core of the particles was formed by a rather low-molecular-weight poly(dimethylsiloxane) (PDMS) around which a cross-linked organosilicon shell was formed in a second step. The PDMS core-forming material from the interior of the particles could be removed quantitatively by ultrafiltration. The remaining organosilicon nanoboxes possess typical diameters of 50 nm and a shell thickness of about 6 nm (Fig. 12). Interestingly, they could be refilled with PDMS chains with a molecular weight of about 6000 Da, that is, rather large molecules, which reflects an obviously high porosity of the polymer shells. Hence, typical low-molecular-weight substances are expected to be released very quickly from such particles. Nevertheless, these organosilicon capsules represent a very promising system for applications in various areas. The formation of nanocontainers with a stimuli-sensitive permeability could be achieved in a slight variation of this approach. Here, a poly(ethyl-hexylmethacrylate) (PEtHMA) core was covered by a cross-linked poly(tertiary butylacrylate) shell. Due to their low molecular weight, that is, below 10,000 g/mol, the single PEtHMA chains are able to diffuse across the particles shell and can be removed by ultrafiltration. The isolated poly(tertiary butyl)acrylate spheres could successfully be used for encapsulation of dye molecules (Fig. 13) and converted into stimuli-responsive polyelectrolyte nanocapsules by selective saponification of the tertiary butyl ester groups [147]. The preparation of nanometer-sized hollow polymer particles as a one-step emulsion process was recently

Nanocontainers

M2

M3

Surfactant Ultrafiltration

1.M1/ M2

2.M3

HVN

Water

Toluene

Figure 12. Preparation of organosilicon nanocapsules. M1: MeSi (OMe)3 , M2: Me2 Si(OMe)2 , M3: Me3 SiOMe, HMN: hexamethyldisilazane. Reprinted with permission from [146], O. Emmerich et al., Adv. Mater. 11, 1299 (1999). © 1999, Wiley-VCH.

described by applying a miniemulsion technique [148]. Such miniemulsions are typically formed by subjecting an oil/water/surfactant/co surfactant system to a high shear field created by devices such as an ultrasonifier and a microfluidizer. The thereby-formed droplets generally range in size from 50 to 500 nm, in contrast to the thermodynamically stable microemulsions where the droplet sizes vary usually from 10 to 100 nm. When monomer is used as the oil phase, freeradical polymerization can be carried out after the phase has been broken by high shear into droplets. If one uses for the synthesis an oil and a monomer in such a way that the two components are miscible in the monomeric state, but immiscible as soon as polymerization takes place, phase separation occurs and results in an oily core surrounded by a polymer shell. Figure 14 shows an image of nanocontainers that encapsulated a liquid during their formation [149].

Figure 13. Transmission electron micrograph of nanocapsules before (left) and after (right) loading with pyrene. Reprinted with permission from [147], M. Sauer et al., Adv. Mater. 13, 1649 (2001). © 2001, Wiley-VCH.

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~5 µm

Figure 14. Encapsulation of liquid materials by the miniemulsion process to form nanocapsules. Reprinted with permission from [149], K. Landfester, Adv. Mater. 13, 765 (2001). © 2001, Wiley-VCH.

As already mentioned, one crucial step in emulsion polymerization is to obtain a reproducible formation of the particles structure and homogeneity. In conventional emulsion polymerization, this is mainly controlled by the concentration of surfactant and initiator. Although it was expected that in miniemulsions the particle formation would be independent of these parameters, this has been proven not to be the case [150]. However, the use of miniemulsions is of increasing interest and shows a great potential for the design of new materials, since it is not restricted to a single (radical) polymerization procedure and allows a low-cost reaction process (e.g., compared to microemulsions, considerably lower amounts of surfactant have to be employed).

From their topology it follows that at some stage in the synthesis of a dendrimer, the space available for formation of the next generation is not sufficient to accommodate all of the atoms required for complete conversion. That means, dendrimers that have internal cavities with a dense outer shell may be synthesized by controlling the chemistry of the last step. This has been demonstrated by the preparation of the fifth-generation poly(propylene imine) dendrimer [157] shown in Figure 15. Due to their dense outer shell, these molecules can be regarded as dendritic boxes [158] that are capable of retaining guest molecules trapped during synthesis. Subsequent guest diffusion out of the box was slow, since the dendrimer shell is close packed due to the bulky H-bonded surface groups. Guest molecules could diffuse out of the boxes if the tertiary butyl groups were removed, but only if the molecules were sufficiently small. Thus Rose Bengal remained in the containers while p-nitrobenzoic acid leaked out [157]. By synthetic design, dendrimers with tailored structures can be obtained. While the repeat units in the interior determine the solubilization characteristic of the dendrimer, that is, the capability to solubilize a molecule in the internal cavity, the outer units and functional terminal groups influence the solubility of the dendrimer itself in a given solvent. Thus by designing amphiphilic dendrimers, in which the interior is composed of hydrophobic moieties and the external groups consist of hydrophilic units, one can envision O

H

n

H

nO R NH2 64

O O

O CH2Cl2, Et2N

6. DENDRIMER NANOCONTAINERS Dendrimers are highly branched cascade molecules that emanate from a central core through a stepwise repetitive reaction sequence [151–156]. Dendritic macromolecules are also termed starbust dendrimers, denoting their characteristic radial symmetry. The question of the existence of a central cavity within dendrimers, that would make them a true nanocapsule, has been debated frequently. Indeed, molecules have been encapsulated within dendrimers, but this does not mean that dendrimers have a permanent and rigid cavity. However, by design such a molecule consists of three topologically different regions: first, a small initiator core of low density; second, the multiple repetitive branching units, whose density increases with increasing separation from the core, thus eventually leading to the third region, a rather densely packed shell constituted by the terminal functional groups. Characteristic of dendrimers are their welldefined structure, a three-dimensional globular shape, and a high density of terminal groups. In the context of dendrimer synthesis the term generation is used to describe each of the following stepwise reactions that give rise to the concentric growth of the macromolecule. Thus each of the subsequent layers of branched monomer units is termed a generation.

R=

Figure 15. A dendritic box capable of encapsulating small guest molecules during construction. Reprinted with permission from [157], J. F. G. A. Jansen et al., J. Am. Chem. Soc. 117, 4417 (1995). © 1995, American Chemical Society.

316

Nanocontainers O(CH2CH2O)16CH3 CH3(OCH2CH3)16O

Hydrophilic periphery

CH3(OCH2CH3)16O O

Hydrophobic interior Core

O

CH3(OCH2CH3)16O

O(CH2CH2O)16CH3

O

Me

O

O

Me

O

O

O

O O

O(CH CH O) CH 2

2

16

3

Me

Me

O

O

O

N CH3O

O Me

O

O

O(CH2CH2O)16CH3

O

O

O

O

O

Me

CH3(OCH2CH3)16O

Me

Me

Me

CH3

CH3(OCH2CH3)16O

O

Me

O(CH CH O) CH

O

2

2

16

3

CH2COOH

Indomethacin

CH3(OCH2CH3)16O

O(CH CH O) CH 2

2

16

3

Figure 16. Dendritic “unimolecular micelle” used for the slow release of indomethacin. Reprinted with permission from [166], J. M. Fréchet, Proc. Nat. Acad. Sci. USA 99, 4782 (2002). © 2002, National Academy of Science.

potential encapsulation devices resembling micellar structures. It is straightforward that an inverted polarity construction of such dendrimers can be also possible. Closely related to the already described dendritic boxes are amphiphilic dendrimers or hyperbranched molecules consisting of a hydrophobic (hydrophilic) core and a hydrophilic (hydrophobic) shell, so called unimolecular micelles [159–165]. In contrast to classical micelles that are aggregates of amphiphilic molecules and therefore dynamic assemblies of small molecules, these unimolecular micelles are static and retain their cohesion regardless of concentration. Due to their amphiphilic nature, these systems are able to solubilize selectively guest molecules within their core domain. For example, dendritic molecules with a hydrophobic interior and an oligoethylene glycol periphery have been used to entrap hydrophobic drugs, such as indomethacin (Fig. 16) [166]. For an overview of dendrimer application in diagnostics and therapy see [167]. A different type of encapsulation involving the formation of metal nanoparticles within dendrimers has been used to prepare inorganic-organic composite structures that are useful in catalytic applications. The formation of Cu-nanoparticles could be achieved by the use of poly(amidoamine) starburst dendrimers as a kind of nanoreactor. Due to the permeability of the outer shell for small molecules and ions, Cu2+ ions could diffuse into the interior of the dendritic boxes, where they were converted into Cu-nanoparticles upon reduction. Because of their rather large dimension, compared to single ions, with diameters of ca. 2 nm, the Cu-nanoparticles were too bulky to leak out of the dendritic cavity [168]. A different dendritic nanoreactor, a reverse micellar dendrimer, consists of a nonpolar aliphatic periphery and a polar inner functionality that has been used to catalyze the E1 elimination of a solution of tertiary alkyl halides in a nonpolar solvent. The alkyl halide has some polarity and becomes concentrated within the polar dendrimer, where it is converted into an alkene. As a result of its low polarity and the existence of a gradient of polarity between the dendrimer interior and the surrounding medium, the alkene product is readily expelled from the dendrimer back into the nonpolar solvent [169]. Recently also dendrimers with stimuli-response characteristics have been reported. Functionalization of the groups

Figure 17. Preparation of a cored dendrimer. Reprinted with permission from [171], M. S. Wendland and S. C. Zimmermann, J. Am. Chem. Soc. 121, 1389 (1999). © 1999, American Chemical Society.

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Nanocontainers

of amphiphilic dendrimers renders thus dendritic boxes with switchable permeabilities. The introduction of quaternary ammonium groups led to increased solubility in aqueous solutions and, due to the bulkiness of the added groups and their pH dependence, the desired release control of encapsulated molecules was achieved [170]. Although dendrimers show interesting and unique properties, they are, however, generally not real hollow particles, due to the fact that their core is covalently linked to the dendritic wedges of the molecule. It is obvious that this core is of crucial importance for the integrity of the whole molecule. Hence, removing the core requires another connection between the outer zones of the dendrimer. Indeed, applying similar concepts as shown in the approaches of Wooley [83] and Liu [84], it is also possible to produce real hollow structures from dendrimers. This has been recently demonstrated using a polyether dendrimer with a trimesic acid ester core. This polymer contains three cleavable ester bonds at its core and robust ether bonds throughout the rest of the molecule. As shown schematically in Figure 17 [171], the hollow particles were formed by selective cross-linking of homoallyl ether groups at their periphery and subsequent degradation of the core region by hydrolysis. An interesting possibility offered by this method is that the remaining functional groups in the interior of the container system could serve as endo-receptors available for molecular recognition. This approach allows a high control over the size and geometry of the formed nanocapsules. However, the preparation of the particles requires a rather costly and tedious procedure, which clearly presents a limiting factor for possible applications. Nevertheless, the quest for practical applications for dendrimers is becoming increasingly intense, but is still limited to highly specific areas.

GLOSSARY Amphiphilic Molecules consisting of two moieties, one hydrophobic (water-hating), the other hydrophilic (waterloving). Amphiphilic molecules show surfactant behavior. Block copolymer A polymer in which at least two different constituting repeating units are joint in a block fashion; that is, a sequence of monomer A linked together to give a block of homopolymer A is followed by a sequence of linked monomer B (homopolymer B). Copolymer A polymer in which the constituting units are two or more different ones. Critical micelle concentration (CMC) Lowest concentration above which micellization can occur. Dendrimer From dendro- branched and -mer part, a perfectly radial branched polymer molecule. Diblock copolymer A (usually) linear block copolymer with only two types of repeating units. Generation Each of the iterative reaction steps that give rise to a new layer of branched points in a dendrimer molecule. Graft copolymers One special kind of comblike branched polymer, consisting of a linear chain of homopolymer A (backbone) from which shorter side chains of a different type of repeating unit (homopolymer B) emanate.

Liposome A vesicle-like structure composed of one or more concentric phospholipid bilayers. Micelle Spherical or elongated aggregates of amphiphilic molecules, showing a core-shell structure. The hydrophobic inner core is shielded from the surrounding water media by the shell or corona formed by the hydrophilic part of the molecules that constitute the micelle. Polymer From poly- many and -mer part, that is, consisting of many parts. A macromolecule consisting of individual repeating units, monomers, covalently linked together. Vesicle Hollow aggregate consisting of a shell of one or more amphiphilic bilayers. Vesicles which have only one bilayer are termed unilamellar vesicles; if they show more bilayers, then they are called multilayered vesicles.

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Encyclopedia of Nanoscience and Nanotechnology

www.aspbs.com/enn

Nanocrystal Memories E. Kapetanakis, P. Normand Institute of Microelectronics, NCSR “Demokritos,” Aghia Paraskevi, Greece

K. Beltsios University of Ioannina, Greece

D. Tsoukalas NTUA, Athens, Greece

CONTENTS 1. Introduction 2. Nanocrystal Memory Approach 3. Nanocrystal Floating-Gate Technology 4. Nanocrystal Memory: Experimental Results 5. Conclusions Glossary References

1. INTRODUCTION The technologies that have been developed over the years in realizing data storage can be divided into semiconductor types (MOS, bipolar, and charge-coupled devices) and moving media types (magnetic disk, optical disk) which require mechanical equipment operation. Compared to disk devices, semiconductor memories exhibit superior characteristics in terms of cost and performance [1]. Furthermore, due to the advantages of MOS technology in device manufacturability and miniaturization, most ultralarge-scale integration (ULSI ≥ 107 transistors on a chip) memory circuits are made at the present time using MOS memories. The most important device for MOS memory technology today is the metal– oxide semiconductor (MOS) field-effect transistor (FET) [2, 3]. A simplified cross section of an n-channel MOS transistor is shown in Figure 1. It consists of a p (“positive”)type silicon substrate with a surplus of holes and a top gate electrode made of conducting material, between which an insulating dielectric (usually, a thermally grown silicon dioxide film) is formed. Two junctions, the source and the drain, that have an abundance of electrons are fabricated with a small overlap to the gate by n (“negative”)-doped ionized ISBN: 1-58883-062-4/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

regions. When a positive voltage is applied to the gate, an electric field is set up that penetrates through the insulator, attracting electrons toward the surface of the substrate. An inversion layer designated as the channel is formed, allowing current to flow between the source and the drain regions. Ideal memory devices ought to be low cost, nonvolatile, able to retain data without external power, have random access that features read–write access to any individual data location, high speed, high density, low power consumption, be easy to test, highly reliable, and compatible with established industrial manufacturing routes. Unfortunately a single type of memory device having all of these characteristics remains unfeasible to this day. Instead, the MOS memory devices that are used as the best alternatives in today’s electronics systems can be classified in terms of their volatility and access speed as volatile random-access memories (RAMs) and nonvolatile non-RAMs. Volatile RAMs permit data to be stored and retrieved at comparable speeds. They include the two most common memory types: dynamic RAM (DRAM) and static RAM (SRAM). DRAM has a small cell size and a reasonably short access (read) time (05 V). This is the reason why DRAM transistors have not scaled as fast as logic transistors, and generally have longer channel lengths, thicker gate oxides, and higher operating voltages. An additional constraint in DRAM cell scaling is imposed by the scaling of the storage capacitor. Because the voltage available to the sense amplifier for signal detection is proportional to the CS /CB ratio, the storage capacitance CS needs to be as large as possible in order to create a large enough signal (∼100 mV) on the bit line. CB is an unavoidable parasitic bit line capacitance coming from the transistor junction capacitance and bit-line wire capacitance. CS also must substantially remain large enough to minimize the sensitivity of the cell to soft errors that originate from high-energyparticle events. Typical CS values are in the range of 25– 30 fF, and these values have remained constant over many generations of DRAM technology. According to the equation for the memory cell capacitance, CS = 0 A/d, where  is the relative dielectric constant of the capacitor film material, 0 is the dielectric constant of free space, A is the capacitor area, and d is the thickness of the capacitor film, the approaches that have been used in order to maintain a constant CS are as follows. First, in the simple planar cell [Fig. 2(a)], the pure oxide capacitor film with a dielectric

Nanocrystal Memories

323

constant of 4 is replaced by a multilayer oxide/nitride/oxide (ONO) or nitride/oxide (NO) film with a dielectric constant of 7, followed by capacitor film thickness d scaling. Then, three-dimensional (3D) capacitor structures (stack or trench) in place of the conventional planar cell are developed to increase the capacitance per unit area. It is expected that future DRAM capacitors will need dielectric materials having high  values such as Ta2 O5 (tantalum pentoxide  = 25) and, eventually, materials with even higher  values such as BST (barium strontium titanate,  = 500) [6]. Although these exotic materials would significantly increase the capacitance per unit area, and thus the device integration density, they are not at this time compatible with the existing DRAM manufacturing process. All in all, it is unclear whether the DRAM memory cell will scale at gigabit densities due to the inherent constraints of low-leakage access transistors and the need for large storage capacitance.

1.2. Static RAM The SRAM memory cell is a bistable circuit utilizing a pair of inverters connected back to back, and is mostly used as on-chip cache memory on microprocessors because of its faster speed compared to the DRAM cell. The most common version of the SRAM memory cell is the full complementary MOS (CMOS) with PMOS loads illustrated in Figure 3. It is a six-transistor (6T) memory cell consisting of two cross-coupled inverters and two access transistors connected to complementary bit lines. Since the inverters are cross coupled, the SRAM memory cell is a two-state circuit with excellent stability; either the “1” or “0” state will be maintained indefinitely by a continuous small dissipation of power in the cell unless changed by another write operation. The access transistors are turned on when the word line is selected, and they connect the inverters to the bit lines, allowing the read and write operations to be performed. One important parameter for the stability of the SRAM cell and a serious concern in SRAM scaling is that the two cross-coupled inverters must have well-matched transistor characteristics. Random variations of the transistor properties, mainly fluctuations of the transistor threshold voltages (VTH ), result in an increased bit-fail rate of the memory

cell [7]. Such fluctuations of VTH MOSFETs are unavoidably caused by discrete dopant atoms or by the finite ability to control the fabrication process, and ultimately limit the number of devices which can be integrated on one chip. In addition, similar to the DRAM case, cosmic rays, mostly neutrons, can cause soft errors (temporary random errors) in SRAM cell operation, and thus impose another constraint in future cell scaling as the soft error rate increases as feature size and operating voltage decreases.

1.3. Flash EEPROM The Flash memory appeared in 1984 [8], and was designed to be the solution to the scaling problem of EEPROMs by trading off memory size with functionality. It has already become the largest market in nonvolatile technology due to a high competitive tradeoff between functionality and cost/bit, and it is expected to be the optimum choice for mass storage in personal mobile systems. The generic Flash memory cell is a single stacked-gate MOS transistor, as illustrated in Figure 4. The conductive polysilicon layer between the externally accessible gate (called a control gate) and the substrate is denoted as the floating gate. The dielectrics between the FG and the substrate (usually a thermal silicon oxide) and between the FG and the control gate are usually referred to as the tunneling and the interpoly or control dielectrics, respectively. The idea of using an FG device to obtain a nonvolatile memory device was suggested for the first time in 1967 by Kahng and Sze [9]. The basic operation principle of the FG device is the storage of charge in the FG [Fig. 5(a)]. During programming (writing), electrons (for the case of an n-channel device) from the silicon conduction band are injected through the tunneling oxide, and subsequently stored on the floating gate. The stored electrons in the FG screen the mobile charge in the underlying channel, thus inducing a change in the conductivity of the channel, allowing the transistor threshold voltage to be electrically altered between a low and a high value, conventionally defined as the “1” or erased state and the “0” or written state [Fig. 5(a)]. The threshold voltage shift VTH caused by the storage of the charge QFG is given by VTH = −QFG /CCG . CCG is the capacitance between the control and the floating gates, and is given by CCG = A/t,

VDD BL

BL

P

P

N

N

Word Line Figure 3. Circuit schematic of a six-transistor SRAM cell in a memory array configuration (one memory cell is shown).

Figure 4. Generic stacked-gate MOS transistor Flash memory cell cross section.

Nanocrystal Memories

324 (a)

Erase

Write CHE Injection

Channel Current

F-N Tunneling

≈ 12 V

VD Vs ≥ 12 V

≥5V

(open)

Source

Drain

Source

∆VTH

e

Drain

Substrate

Substrate

"1"

"0"

F-N Tunneling

Vread

Source

≥ 12 V

e

Drain

Substrate

VTH

VTH

Control Gate Voltage (b)

Figure 5. (a) Read and write/erase operation principles of a Flash memory. The schematic of the memory transistor illustrates the bias conditions that are employed for the case of CHE injection or F–N substrate electron injection write modes, and for the case of source-side electron extraction erase mode. (b) Circuit schematic of a one-transistor Flash memory cell in a memory array configuration (two memory cells are shown).

where A is the capacitor area, and  and t are the dielectric constant and thickness of the control dielectric, respectively. The information content of the cell is read by sensing the current through the bit line, while accessing the cell is achieved by applying a read voltage Vread , at the gate or word line with a value between the two possible threshold voltages. In one state, the transistor is ON (“1”) (conducting current), while in the other, the transistor is OFF (“0”). An erase operation involves removing electrons from the FG, hence returning the device VTH to a low state. The Flash memory cell can be erased electrically, but not selectively. The content of the whole memory chip is always cleared (Flash erase) in one step, and this design allows a single-transistor memory cell to be constructed [Fig. 5(b)]. In order to allow byte-selective write and erase, a select transistor, is added to the memory transistor, leading to the so-called two-transistor EEPROM memory cell. Therefore, Flash memories abandon the feature of single-cell erasability in favor of lower cost large-scale integration memory circuits. Once programmed, the cell is guaranteed to retain information for at least ten years (the industrial standard for nonvolatile memories), either under operation or with power turned off. Information can be lost if electron leak occurs, mainly through the tunneling dielectric. To maintain nonvolatility, relatively thick (about 10 nm) tunneling oxides are required, a feature that causes difficulty in charging the

FG as a very large amount of energy is needed for electrons to move into or from the FG. The physical mechanisms that are commonly used for this charge transfer are the fieldinduced (Fowler–Nordheim, F–N) tunneling [10] or channel hot-electron injection (CHE) [11] for the write operation and F–N tunneling for the erase operation. During CHE injection, a large drain VD bias causes the generation of highly energetic electrons at the drain side in the channel, while a large control gate VG bias, with VG > VD , generates an oxide field that favors the injection of the heated electrons over the Si–SiO2 energy barrier [Fig. 5(a)]. F–N tunneling is the flow of electrons through the energy barrier of the tunneling oxide that has been modified by a high electric field for effective narrowing of the oxide barrier width. During F–N programming, a high voltage applied to the top control gate causes electrons from the source, drain, or substrate (depending on the voltages at that terminals) to be injected into the FG. A schematic description of write by F–N tunneling for the case of electron injection from the whole channel region is shown in Figure 5(a). The erase process can be accomplished by applying a high voltage to the source, drain, or to the substrate of the well with the control gate grounded. It can also be accomplished by applying a negative voltage to the control gate with the other terminals connected at different positive voltages. Depending on the programming mechanism, Flash memory arrays have two different configurations: NAND and NOR. NAND cells use F–N tunneling to program the FG, while NOR cells use CHE injection for write operation. Both NOR and NAND cells utilize F–N tunneling to erase the cell. The generation of highly energetic carriers during both programming operations introduces permanent damage, referred to as degradation, due to charge trapping in the tunneling oxide. As a result, the Flash memory can withstand a limited number, typically 105 , of write/erase cycles (called its endurance). Additionally, due to the small currents flowing through the tunneling oxide during both the CHE injection and F–N tunneling processes, the charging times are slow, resulting in typical write times in the microsecond and millisecond ranges, respectively. Although Flash memories have been designed as a solution to the scaling problem of conventional EEPROM devices, aggressive scaling of the transistor dimensions and the dramatic increase in the memory array size demand a lower voltage memory cell design for the future. As the technology for the CHE injection or F–N tunneling process has to support relatively high voltages (e.g., 8–9 V minimum and >12 V for CHE and F–N tunneling programming, respectively), Flash memory cell scaling presents severe limitations. Constraints in vertical scaling of the memory cell, and therefore in scaling of the applied operating voltages, are imposed by the extreme requirements of incredibly low dielectric leakage (less than ∼10−14 A/cm2 ) to ensure a ten-year data retention time. In the case of the control dielectric, an ONO composite dielectric is typically used, and allows for thinner control layers compared to silicon oxide layers, with much lower leakage currents. In the case of the tunneling oxide, the requirements are even more stringent as it must be thin enough to allow a fast write/erase speed at reasonable voltage levels with negligible degradation after 105 programming cycles, and thick enough to avoid charge loss during read or normal

Nanocrystal Memories

operations. Thus, all scaling issues pertinent to Flash memories are ultimately related to the reliability of the tunneling oxide. Theoretically, in order to ensure ten-year data retention time, the tunneling oxide could be scaled until electron flow through the full oxide thickness becomes significant (i.e., down to ca. 5 nm). However, stress-induced leakage current (SILC) [12, 13] imposes a more stringent limitation on the tunneling oxide thickness as a single point of high leakage in the oxide can discharge the conducting polysilicon FG layer. This is the reason why the tunneling oxide of Flash memories was set as thin as about 10 nm from the beginning, and has scarcely been thinned over five successive generations to limit its thickness to 7–8 nm at the present state of nonvolatile memory technology. As a result, the dimensions of the FG transistor have been scaled much more slowly than those of the logic transistor, and therefore, the Flash memory performance in terms of access time, write/erase speeds, and operating voltages has not been substantially improved with device scaling. The increase in Flash memory capacity (thus, the decrease in the cost/Mbit) has been mainly achieved through different array architectures such as the NAND structure [14], which reduces the cell size by connecting the cells in series between a bit line and a source line. Another option for higher bit storage density without the need for aggressive technology scaling is the multilevel charge storage (MLCS) approach, where more than one bit is stored inside a single memory transistor [15].

2. NANOCRYSTAL MEMORY APPROACH In order to overcome the technological constraints imposed as the device size approach dimensions below the 100 nm range, new memory concepts are needed for ultrahighdensity, low-voltage, low-power, and fast write/erase data storage. For this reason, various memory alternatives are actively investigated. The ferroelectric RAM (FRAM) [16] that replaces the DRAM capacitor’s dielectric with ferroelectric material, and the one-transistor magnetic RAM (MRAM) [17] that replaces the capacitor with a magnetoresistor structure are two potential solutions. For such devices, the compatibility of the ferroelectric and magnetic materials with standard CMOS processes is an important technological issue that remains a subject of debate. Another promising alternative for low-cost ultradense data storage lies in the use of modified Flash memory structures. Nanocrystal memories are one particular implementation of this approach. In the subsections that follow, the operation principle and challenges of this new memory concept are reviewed, as well as the electrical characteristics of nanocrystal memory devices obtained through the use of various fabrication techniques of synthesizing nanocrystalline floating-gate layers.

2.1. Charge Storage in Spatially Isolated Trap Sites Two different approaches for improving the performance of “scaled-Flash” memory have been proposed. The first includes the nonvolatile RAM (referred to as NOVORAM) suggested by Likharev [18], and the phase-state lowelectron-number drive random (PLEDM) proposed by

325 Hitachi and the University of Cambridge [19]. NOVORAM uses a “crested” tunnel barrier that replaces the usual uniform oxide barrier (often called a “rectangular” barrier) with a stack of dielectric materials in order to create a special barrier shape for an effective F–N tunneling into/out of the floating gate. Thus, enhanced barrier height suppression is present during write/erase operations, while a higher barrier is present during the retention and read modes. In the PLEDM device, electrons are injected into the memory node through stacked multiple tunnel junctions. A second polysilicon gate that surrounds the memory cell is used to modulate the current flow through the tunnel junctions. For both devices, simulations have indicated write times potentially faster than DRAM and ∼ten-year retention time. NOVORAM and PLEDM devices are currently in the concept stage since no memory operation has been experimentally demonstrated. The second approach for overcoming scaling limitations of conventional Flash memory cells is based on the storage of charges in isolated charge-trapping sites in place of the conventional FG layer. Excellent immunity to oxide defects is thus ensured since, even if a pinhole exists in the tunneling oxide, leakage will only cause a few storage nodes to lose their charge. This allows the implementation of memory devices with thinner tunneling oxides, operating at lower voltages and/or faster programming speeds. In addition, compared to conventional FG memory devices, the single-transistor charge-trapping structure exhibits other important advantages such as: (1) the memory array requires only one level of polysilicon that simplifies the fabrication process and lowers the cost, (2) the memory cell permits further scaling (the cell size can be 2F 2 , where F is the minimum feature size), and (3) the absence of drain-to-FG coupling allows the use of higher drain reading voltages for faster memory access times, and also reduces the bit-line disturb as only storage nodes directly over the drain overlap region will be affected. Historically, the first charge-trapping device was introduced in 1967 by Wegener et al. [20], almost simultaneously with the FG memory cell, and was the metal–nitride– oxide–silicon (MNOS) cell, where the discrete chargestorage elements are traps distributed in the nitride layer. Today, two types of charge-trapping memory devices are actively investigated: the polysilicon-blocking oxide–nitridetunneling oxide–silicon (SONOS) device, including the most recent version of nitride read-only memory (NROM) and the nanocrystal memory. The SONOS [21] and NROM [22] storage transistors utilize an oxide–nitride–oxide trapping material instead of the normal gate dielectric of a conventional n-channel MOSFET. The difference between the two devices lies in the physical mechanisms involved during programming operations that are related to the thickness of the bottom tunneling oxide. For SONOS devices, charge injection (removal) into (from) the dielectric storage layer is performed by direct tunneling through thin tunneling oxide (∼2–3 nm in thickness), while for NROM devices with tunneling oxide greater than 5 nm, program (erase) operation takes place by localized charge trapping (removal) of channel hot-electron injection (tunnel-enhanced hot-hole injection) in the dielectric storage layer.

326

Nanocrystal Memories

The nanocrystal memory cell, proposed in the early 1990s by Tiwari’s team at IBM [23, 24], consists of a single MOS transistor with an array of laterally uncoupled crystalline silicon or germanium nanoparticles embedded in the gate oxide in close proximity to the channel. A schematic cross section of the memory cell is shown in Figure 6. A thin tunneling dielectric, usually thermal oxide (≤5 nm in thickness), separates the channel of an otherwise conventional MOSFET from a distributed charge-trapping layer that covers the entire transistor channel area. A thicker control oxide layer is used to electrically isolate the nanocrystal storage nodes from the control gate.

2.2. Operation Considerations and Challenges The storage of charges in a layer made of mutually isolated nanocrystals (in analogy to a conventional floatinggate device) is the basic operating principle of a nanocrystal memory. Stored charge changes the conductivity of the transistor by shifting the threshold voltage VTH of the device, for the case of negative stored charge, to more positive values. This single-transistor memory device has been introduced as an alternative structure to conventional DRAM for high-storage density and low-power operation, as well as to nonvolatile memories such as Flash EEPROMs for faster write/erase speed, lower write/erase bias, and better endurance [23]. There are, however, key issues to be solved before the practical implementation of this kind of memory. Of importance are: data retention, memory window, and device characteristic deviations. Here, we will briefly discuss the role of some of the main features that affect the operation of the device and its performance, as well as the progress in the area of nanocrystal memories.

2.2.1. Programming Mechanism Figure 7 shows schematic energy band diagrams for Si nanocrystal memories during: (a) write (electron injection), and (b) erase (electron removal). During write (erase) operation, electrons are injected (removed) to (from) the nanocrystals by applying a positive (negative) voltage bias to the gate with respect to source and drain electrodes. The thickness of the control oxide must be relatively thin for reasonable low voltage operation, but not so thin as to cause the charge to eventually leak to the control gate. These constraints make an optimum control oxide thickness on the order of 5–15 nm [25]. For the case of thin tunneling oxides with

Figure 6. Schematic cross-section representation of a one-transistor nanocrystal floating-gate memory cell.

Figure 7. Potential diagrams of the conduction bands for an Si nanocrystal memory device during: (a) write (nanocrystal electron injection) mode, (b) erase (nanocrystal electron extraction) mode, (c), (d) chargeretention mode (at a reading gate voltage) for the case of (c) electron storage in a quantized nanocrystal energy level, (d) electron storage in deep energy level located in the nanocrystal or/and at the nanocrystal/SiO2 interface.

thicknesses less than 3 nm, charge transfer takes place via direct tunneling (electron flow through the full oxide thickness, as illustrated in Fig. 7) instead of F–N tunneling. Since a large amount of current can pass through these thin oxides at low electric fields (5 nm) must be used Control Gate FG Tunneling Oxide

Substrate

Control Oxide Buried Channel Oxide Si

Threshold Voltage

the effect of quantized charge accumulation in ground-state energies of “few-electron” silicon dots have been experimentally demonstrated and discussed in [31–33]. The consequence of the Coulomb blockade and quantum confinement effects in a nanocrystal memory device is a reduction of the number of charged carriers used in the operation of the device that improves power and speed performance. To allow “few-electron” device operation, the charging energy must be greater than the thermal energy kB T (where kB is Boltzmann’s constant and T is the operation temperature). Room-temperature (kB T ca. 26 meV) “few-electron” operation can be accomplished if the semiconductor nanocrystals have dimensions below ca. 10 nm. However, for the programming voltage and write time of interest, a minimum dot size is required. Neglecting band bending of the substrate in the inversion region, the write voltage Vwrite needed for a channel electron to tunnel into a dot state is approximately given by EC /e1 + tcntl /ttun  + VTH , where tcntl  ttun are the control and tunneling oxide thickness respectively, and VTH is the threshold voltage. The large increase of the charging energy EC (through the increase of the eigenenergies and the electrostatic charging energy) with dot size reduction increases the amount of gate voltage needed for charging. In addition, the reduced density of states restricts the states available for electrons to tunnel at a given voltage, resulting in lower programming speed. Thus, for an efficient operation at write voltages of ∼3 V, an optimum nanocrystal size in between 3–10 nm is estimated (for reasonable control-to-tunneling-oxide-thickness ratio on the order of 3–5) [25].

327

3 el. 2 el. 1 el.

Control Gate Voltage

Figure 8. Schematic cross section of a self-aligned quantum-dot memory transistor, together with an illustration representing the discrete shifts in the device threshold voltage caused by the different number of electrons stored in the dot.

Nanocrystal Memories

328 in order to ensure a long data-retention time. Since high voltages are required for multiple-level memory storage, the tradeoff is between integration density and operation power. Note that, for the case of a multiple-dot device, the presence of a sufficient number of nanocrystals in the memory operation suppresses cell-to-cell variation. This is an important advantage of multiple-dot structures as it allows effective operation at a lower number of stored electrons per nanocrystal compared to quantum dot memory. However, although single-electron charging effects have been demonstrated in large-area channel multiple-dot memories [43], even at room temperature [44–45], there are important technological issues to be resolved, such as high dot density and extremely high uniformity in dot size and dot position from the channel, before the practical exploitation of singleelectron phenomena in nanocrystal memories.

2.2.5. Charge Storage A major challenge of nanocrystal memory using thin tunneling oxides lies in the realization of long charge-retention times. Because of the sharp increase of the direct tunneling current at arbitrarily low voltages, a tradeoff exists between the write/erase time and retention time. By making the injection oxide thicker for a long retention time, the advantages of high-speed write/erase at reasonable voltage levels and of high endurance are lost rapidly. For the case of Si nanocrystals, an additional constraint for long-term charge retention is introduced by quantum confinement. This can be understood by reference to Figure 7(c), which illustrates an energy band diagram of Si nanocrystal memory under charge storage condition. After write operation [Fig. 7(a)], injected electrons that may initially tunnel into higher nanocrystal energy levels eventually will fall into lower energy states. Due to energy quantization, the lowest energy level at flat-band condition is above the conduction band edge in the channel region. Thus, a finite probability exists for an electron to tunnel back into the channel, affecting the retention characteristics of the device. It should be noted that most experimental results to date have shown significantly longer erase times than write times, reflecting relatively longer retention times than what was theoretically expected if both the write and erase process are due to direct tunneling. Several works attempting to explain the charging/discharging phenomena involved in Si nanocrystal memories have been carried out. Theoretical approaches, based upon [46] a master equation including quantum confinement and Coulomb blockade effects in Si dots [46], or on a semiclassical current continuity model [47, 48], have been proposed to describe the observed time-dependent charging/discharging behavior. Other work has shown that the influence of channel-depletion effects on carrier charging characteristics is very important for long charge retention in Si dot memory [49]. The presence of traps inside the nanocrystal or/and at the nanocrystal/SiO2 interface [that causes electrons to be relaxed to lower trap states in the bandgap after injection, as illustrated in Fig. 7(d)] has been suggested to explain the observed relatively long-time charge-retention behavior [50]. However, the role of interface states on the charging/discharging phenomena in nanocrystal memories is still not entirely understood, and is possibly dependent

on the process conditions of nanocrystal formation. Experimental results related to the storage and erase process in these structures indicate two distinct time constants, which could be interpreted as fast nanocrystal-related emission followed by a slower interface state-related emission [51]. Another work has shown a small temperature dependence on the dynamic charging, at room/low temperatures, suggesting that Si-dot/SiO2 interface states do not dominate the charge exchange between the Si dot and the channel [48]. Similar results, but for the case of a single Si nanocrystal, supporting the nanocrystal-related emission process were obtained in another work [52]. Recently, simulation results concerning the charging time response in silicon nanocrystal memory (obtained from the self-consistent solutions of the three-dimensional Kohn–Sham and Poisson equations) have shown write, erase, and retention time characteristics that are very sensitive to the shape of the Si nanocrystal storage nodes [53].

2.2.6. Storage Dot Engineering In order to improve the performance of Si nanocrystal memory for high-speed nonvolatile applications, two different alternatives are actively investigated: a material and a structural engineering. Material engineering replaces the Si nanocrystal with a storage node composed of a material that allows long charge retention, while keeping the operation speed at acceptable levels. For example, this can be achieved if we use a storage node composed of a material having a conduction band edge (for the case of semiconductor material) or Fermi energy (for the case of metal) at least 26 meV (the room-temperature thermal energy) below the conduction band edge of the channel region [Fig. 9 (a)]. The energy band-edge difference creates an asymmetrical barrier (a)

Storage dot

Substrate

Control Gate

> kT

(b)

Control Gate

Double Si dot

Substrate

Figure 9. Potential diagrams of the conduction bands of a nanocrystal memory device during the charge-retention mode for the case of: (a) nanocrystalline material having a conduction band edge at least 26 meV below the conduction band edge of the channel region, and (b) double-stacked layer consisting of perfectly self-aligned (but different in size) Si nanocrystals.

Nanocrystal Memories

between the channel and the storage node that combines the high transparency necessary for fast write/erase times with the low transparency necessary for long retention times at low voltages. This can be achieved if the storage nodes are composed of a material that has a larger electron affinity than the silicon substrate (i.e., metal, semiconductor-like Ge nanocrystals, or semiconductor heterostructures such as Ge/Si nanocrystals). Operation of Au, Ag, and Pt nanocrystal memories working in the F–N tunneling regime (as in the case of relatively thick tunneling oxides) has been demonstrated [54–55]. However, metal contamination (especially for the case of thin tunneling oxides) and CMOS process integration compatibility are important technological issues for such structures. For the case of Ge nanocrystals, charge-storage advantages over the corresponding Si case are not clear, as similar results have been obtained for Ge and Si nanocrystal-based memory structures [56]. Up to now, only simulated charge-retention data exist for the case of Ge/Si storage nodes [57]. Another particular implementation of material engineering is a memory structure with silicon nitride (Si3 N4 ) storage dots proposed in 2001 [58]. Charge storage in Si3 N4 dot memory takes place, as in the case of a SONOS device, at nitride traps distributed in the Si3 N4 dot. However, due to restricted dot dimensions, a finite number of traps is expected (e.g., two or three traps for the case of a 10 nm diameter dot), allowing (as for the case of Si dot memory) small and controllable numbers of electrons to be involved in the memory operation. Moreover, the absence of Coulomb blockade and confinement effects in an Si3 N4 dot allows charging with more than one electron at a low write voltage, resulting in a larger memory window compared to the Si dot device [58]. The exact number of traps involved and a fabrication route of forming well-controlled, in terms of size and position, Si3 N4 dots are key issues for practical use of this new memory concept. Structural engineering replaces the single storage layer with a double-stacked layer consisting of perfectly selfaligned Si nanocrystals. The fabrication process and the memory characteristics of this structure are discussed in [59, 60]. For the case of a smaller dot at the lower stack with ultrathin tunneling oxides below and between the two stacks, fast write/erase speeds with a much better charge retention compared to single-dot memory have been demonstrated. Coulomb blockade and quantum confinement in lower dots [Fig. 9(b)] inhibit electrons in the upper dots to tunnel back into the channel. The smaller the size of the lower dots, the larger the improvement in data retention. An important point of this doubly stacked floating-dot memory device is its self-aligned structure. In addition, this concept is also applicable in the case of Si3 N4 dot memory for further improvement of data retention [58].

3. NANOCRYSTAL FLOATING-GATE TECHNOLOGY The atom-like behavior of semiconductor nanocrystals embedded in SiO2 matrices is expected to lead to interesting optical and electronic properties. As a result, many applications and synthesis techniques are being explored.

329 The possibility of using Si or Ge as a light source in optoelectronic devices is very attractive because of the compatibility of these materials with existing Si-based MOS technologies [61–62]. Luminescent SiO2 films consisting of Si or Ge nanocrystals have been fabricated through the use of various deposition techniques [63–68] or, more recently, through Si or Ge ion implantation [69–75]. Implanted impurities have been used to shift the emission wavelength of Si nanocrystals (i.e., absorption of the nanocrystal emission, 0.81
m luminescence peak, from implanted Er causes strong excitations of Er3+ at 1.54
m [76]), indicating the potential of Si nanocrystals as sensitizers for use in Erdoped waveguide amplifiers or lasers [77]. A major effort has been directed toward the understanding of the origin of luminescence and electroluminescence spectra obtained from these materials. The sources of visible-range luminescence are still not entirely clear, and continue to be a subject of debate. The recombination of quantum-confined exitons in nanocrystals, defects in the surrounding matrix, electronic states at the nanocrystal surface, and foreign compounds have been named as sources. The origin of optical emission in the nanocrystals should be well understood, and a fabrication route of forming well-controlled depth and size distributions of nanocrystals should be established in order to optimize and control the optical properties for device applications. Besides the attractive light-emitting property, semiconductor nanocrystals embedded in SiO2 matrices have regained interest due to their potential in future electronic devices. Resonant tunneling diodes [33, 78] and memory devices [23–24, 34–38] exploring quantum confinement and single-charge effects in Si nanocrystals have been demonstrated. For such applications, the nanocrystal characteristics have to satisfy certain specifications in order to provide reliable device operation. In particular, for multipledot memory applications, a fabrication route of forming high-density two-dimensional arrays of small, uniform size, noninteracting nanocrystals, and with well-controlled location without introducing defects at the SiO2 /Si interface or into the channel region, are important technological points. In addition, the synthesis technique should be as simple as possible (for low cost per bit) and compatible with existing CMOS processes. Because the optimum mean size of the storage dots is below the current lithography resolution, an attractive approach to fabricate a nanocrystal floating gate is through a self-assembling process [79]. This method also takes advantage of the whole-wafer nature of dot formation suitable for practical device implementation. Self-assembled semiconductor nanocrystal floating gates have been fabricated through various techniques, including Si-dot formation by low-pressure chemical vapor deposition (LPCVD) [24, 43], nanocrystal formation by a precipitation process during the annealing of a semiconductor-rich oxide layer (formed either by Si (Ge) ion implantation [56], or by deposition techniques such as LPCVD [80] or cosputtering of Si (Ge) and SiO2 [81–82]), rapid thermal oxidation either of a thin deposited amorphous Si [83] film or of amorphous silicon films deposited by ion-beam-assisted electron-beam deposition [84], molecular beam epitaxy combined with rapid thermal processing [85], aerosol deposition [86], and thermal oxidation of Si1−x Gex [87]. Nanocrystal memory transistors

Nanocrystal Memories

330 have been realized using these various self-assembling processes in combination with conventional MOS transistor fabrication steps. In the paragraphs below, nanocrystal synthesis through direct deposition techniques such as direct seeding on dielectric layers, or using a silicon-rich oxide layer, or through ion implantation techniques are briefly reviewed because of their advantages in terms of integration. In particular, we examine the case of the ion beam synthesis approach, as it is a simple and well-established technique within the semiconductor industry.

3.1. Direct Deposition Technique 3.1.1. Direct Nanocrystal Seeding on Dielectric Substrates Low-pressure chemical vapor deposition by pyrolysis of silane (SiH4 ) is a well-established technique within the microelectronic industry, and is commonly used for the fabrication of polycrystalline Si gates in MOS transistors and of thin-film transistors (TFTs). By controlling the early stages of Si film growth, a single layer of isolated Si nanocrystals a few nanometers in diameter can be formed on various dielectric substrates [88]. The size and density of the nanocrystals depend on the deposition parameters (pressure, temperature, and time) [77, 88, 89], as well as on the chemical treatments or on the chemical nature of the surface [77, 89–92]. Deposition on pure oxide substrates exhibits relatively low nanocrystal aerial density, while higher values have been observed for the case of deposition on nitride surfaces [89, 44]. The highest dot density, of 1012 cm−2 for optimized deposition conditions, has been obtained for the case of a pure Si3 N4 substrate [89] or, more recently, for an Al2 O3 surface [91]. A thermal oxidizing step after deposition is shown to improve dot size uniformity. A control oxide, formed by a second deposition step of SiO2 , covers the nanocrystals. The in-plane dot formation allows for excellent control of the tunneling oxide thickness without affecting the integrity of the oxide or of the oxide/channel interface. For these reasons, the LPCVD technique is an attractive option for nanocrystal memory device implementation. However, optimization of the deposition process (especially on SiO2 surfaces) and of the ultrathin tunneling dielectric formation step (especially for the case of SiO2 /Si3 N4 or SiO2 /Al2 O3 dielectric stacks) is still required in order to achieve high nanocrystal aerial density onto highly reliable dielectrics.

3.1.2. Deposition and Precipitation of SRO Silicon-rich oxide (SRO) or nonstoichiometric oxide is considered a solid solution of SiO2 and Si supersaturated in Si (SiOx  x < 2). SRO films are usually prepared through chemical vapor deposition (either LPCVD or plasmaenhanced CVD) using a mixture of silane and N2 O or SiH4 and O2 . Changing the gas flow ratio controls the excess Si content in the SRO film. Thermal annealing during preparation processing or during an additional annealing step causes excess Si to precipitate in the form of amorphous or crystalline Si nanoclusters, depending on the annealing conditions (time, temperature) and the amount of excess Si [93, 94]. The diffusion of Si atoms in the nonstoichiometric oxide matrix has been found to control the precipitation of

Si clusters [94]. SRO layers have been proposed as interpoly dielectrics for enhanced electron injection [95–98], or as ultrathin tunneling oxide alternatives [99] in conventional nonvolatile memory devices for low-voltage operation. In addition, the electron trapping characteristics of SRO make it useful as a charge-storage material for memory applications. The charge-storage properties and charge transport through these films have been related to the Si quantum dots of the SRO film [93, 100]. For memory applications, a thin SRO layer (1 week

109 s

Large

Write Voltage 3 3 3 4

VTH

V V V V

∼065 V ∼048 V ∼055 V ∼05 V

12 nm ∼2 nm

300 ns

∼10 ms/ −3 V ∼100 ms/ −8 V and Vsub = 8 V

>1 day

109

4V

∼03 V

>1 day

>105

8 V and Vsub = −5 V

∼23 V

5.5–6 nm

8 nm

∼50
s

Thermal Oxidation of Si-Ge [87]

1.5 nm

3 nm

∼100 ns

∼100 ns/ −4 V

>1 day

109

4V

∼04 V

SRO [101]

1.5 nm

5 nm

∼100 ns

∼100 ns/−5 V

∼1000 s

108

5V

∼05 V

Conventional Memory Technology DRAM NOR Flash

∼7–8 nm

∼15 nm

−12 V

No refresh is needed

>105

CHE write VG ∼ 12 V VD ∼ 8–9 V

3–4 V

Nanocrystal Memories

can be achieved to compete with Flash memory performance. For the case of tunneling oxide thicknesses comparable to, but still thinner than conventional Flash devices (e.g., ca. 6 nm), encouraging results in terms of disturb behavior and stress-induced leakage current have been obtained for aerosol deposition nanocrystal memory devices operating in the F–N tunneling regime [86]. In addition, the feasibility of hole-programming operation has been demonstrated for the case of p-channel deposited nanocrystal memory devices with 4 and 20 nm tunneling and control oxide thickness [92, 143]. Depending on the tunneling oxide thickness, nanocrystal memory devices have been introduced (similar to the case of scaled SONOS device [144]) as promising low-power operation candidates in applications ranging from Flash-like functions (slow programming in the millisecond range with long nonvolatile retention of years) to nonvolatile RAM (NVRAM)-like functions (fast programming in the microsecond range with limited nonvolatile retention). In addition, since the write/erase voltage pulses (for injection/extraction of charge into/from the nanocrystals) is not applied between the source or the drain of the memory cell, a reduced “punchthrough” effect can be achieved, allowing a shorter channel length and a smaller cell area than is possible in conventional floating-gate-type structures. Single-transistor nanocrystal arrays (organized in word lines, bit lines, and source lines, each connected to control gates, drains, and sources, respectively) with byteaddressable write/erase operations (or block-erase schemes for the case of very slow erase times) have been proposed for the incorporation of these structures into large-scale integration memory circuitry [56, 145]. However, the very stringent requirement for long-term charge retention (in particular, for the case of Flash functions) imposes serious constraints on the practical application of these structures in nonvolatile memory functions. Although promising chargeretention data have been published (e.g., retention times of hours have been measured at 200  C [146]), the ultimate goal of true nonvolatility (e.g., data retention > ten years) at low voltage and at acceptable write/erase speeds still remains an important issue to be verified for nanocrystal memory devices. Due to the inherent constraint of back tunneling charges through thin tunneling oxides, it is unclear whether nanocrystal memories will ever meet the industrial data-retention standard, and further effort and process optimization are necessary in order to demonstrate the feasibility of this target.

4.2. Volatile Behavior Long-Refresh-Time DRAM-Like Functions Besides the potential in nonvolatile functions, another application of nanocrystal memory device is for a dynamic RAM concept of lower power dissipation (long refresh time), simpler operation, smaller cell area, and lower cost fabrication process than the conventional DRAM structures. Since the information, or charge, is stored into the gate oxide of a single transistor, no additional storage capacitor is needed, thus minimizing the cell size for higher packing densities. For applications targeting DRAM-like functions, fast write and erase speeds (in the nanosecond range) at low voltages

335 and endurance cycles exceeding 1013 are important. In addition, for the case of the long (compared to conventional 1T–1C DRAM memory cell) refresh time requirement, data retention can be shortened to minutes or seconds; thus, quasinonvolatile retention is desired for DRAM functions, in contrast to the long-term retention of Flash and NVRAM functions. Hu and his co-workers at the University of Berkeley experimentally demonstrated the possibility of implementing DRAM functions by using single charge-trapping memory transistor structures with ultrathin tunneling oxides [101, 147]. For the case of SONOS devices with 1.2 nm tunneling oxide (the case of charge storage at traps distributed in the nitride layer), data-retention times as long as 1000 s are measured at 80  C after a 1011 cycle endurance test with 7 V/−7 V, 500 ns write/erase pulses [147]. For the case of nanocrystal-type memory with thin tunneling oxide (of ca. 1.5 nm) and a deposited SRO film as a charge-trapping layer, a fast write/erase speed that reaches 100 ns at 5 V write/erase voltage with a 0.5 V threshold voltage shift is reported [101]. In addition, a long refresh time of 1000 s is observed at room temperature after 108 write/erase cycles. Superior electrical characteristics in terms of write/erase speed/voltage and retention time (properties that also suggest the possibility of nanosecond programming range quasinonvolatile applications) have been recently reported for Ge nanocrystal memory devices obtained by thermal oxidation of S1−x Gex [87]. For this case, data retention longer than one day at room temperature and about 1 h at 85  C after a 109 cycle endurance test with 4 V/−4 V, 100 ns write/erase pulses are measured. Encouraging results suggest that DRAM-like functions also have been obtained for the simple and CMOS-compatible nanocrystal processing case of a very-low-energy Si nanocrystal memory device [148]. Fast write/erase characteristics at low electric fields with a large threshold voltage window under dynamic operation (using a gate-bias sine wave or pulsed signal) are measured in MOSFETs with embedded 2D arrays of Si nanocrystals at a distance ca. 3 nm from the channel obtained by 1 keV Si+ IBS in initially 8 nm thick gate oxides, and subsequently covered by 30 nm thick deposited control oxide. Endurance and retention-time characteristics of this memory cell using 15 V/−5 V, 100 ns write/erase pulses are shown in Figures 13 and 14. No degradation, even after a 1010 cycle endurance test (Fig. 13) and less than 5% (20%) reduction in the memory window (Fig. 14) after 1 s (10 s), is observed at room temperature. Further process optimization (e.g., adjustments of the deposited control oxide thickness and improvements of the implanted oxide quality) is expected to reduce operation voltage and to increase the refresh-time characteristics of such devices [135, 136].

4.3. Single-Electron Charging Effects Similar to the case of single-dot device structures, singleelectron charging phenomena also have been reported, and for the case of multiple-dot structures, consistent with the self-limiting charging process in nanocrystal storage nodes. However, in contrast to the former case, where a single dot is involved for screening the transistor channel, in the latter case (as discussed in Section 2), the uniformity of the size and depth distribution of the nanocrystals, as well as their density are critical parameters for

Nanocrystal Memories

336

– –

Figure 13. Endurance characteristic of a nanocrystal memory device obtained by implantation of 1 keV Si ions at a dose of 1 × 1016 cm−2 into 8 nm thick oxide and subsequent annealing at 950  C. A 30 nm thick oxide layer was deposited before annealing.

the observation of such discrete charging effects. Furthermore, concerning the magnitude of the threshold voltage shift caused by one stored electron in each nanocrystal, besides the nanocrystal size and the control oxide thickness (as in the single-dot case), the nanocrystal density is also very important for the case of a multidot memory device. Plateaus in the pulsed threshold voltage with static gate voltage characteristics have been observed at temperatures below 120 K in MOSFET structures with Si nanocrystals embedded in the gate oxide by deposition onto 1.9 nm thin tunneling oxide, and covered by a control oxide of ca. 9 nm in thickness [43]. The observation of threshold voltage plateaus in equidistant steps (of ca. 0.3 V) is found consistent with single-electron storage in the nanocrystals for the case of nanocrystal density of ca. 6 × 1011 cm−2 , a value within the error margins of that estimated by structural observations. In addition, the temperature range wherein this phenomenon becomes pronounced is in agreement with the relatively large observable nanocrystal size (>10 nm). Room-temperature discrete threshold voltage

shifts of 0.48 V have been observed for Si nanocrystal memories formed by LPCVD onto 2 nm in thickness oxide– nitride tunneling dielectric and covered by a 20 nm thick control oxide [44, 149–150]. The room-temperature singleelectron charging phenomena in these structures have been attributed to the extremely small size (ca. 4.5 nm in diameter), the good size uniformity, and the aerial density of 5 × 1011 cm−2 of the Si dots. Recently, Si-nanocrystal memory devices obtained by a high-dose (2 × 1016 Si+ /cm2 ) very-lowenergy (1 keV) IBS technique have been found to exhibit step-like source–drain current versus time (IDS –t) and periodic staircase plateau source–drain current versus gate voltage (IDS –VG ) characteristics, both in support of the notion of room-temperature discrete electron storage in Si nanocrystals [45]. Structural study for this case reveals the formation of well-crystallized Si grains of about 7–8 nm average linear dimensions in a dense arrangement. The observation of discrete threshold voltage shifts of ca. 2 V in the IDS – VG curves obtained during slow forward (Fig. 15)/fast backward (inset of Fig. 15) gate voltage sweeps is found to be consistent with successive single-electron injection/ejection into/from each nanocrystal for the case of nanocrystal density of ca. 1 × 1012 cm−2 . In spite of the inherent difficulties of controlling single-electron storage phenomena at a realistic level of integration, the experimental evidence of such effects at room temperature supports the pursuit of technologically practical large-channel devices operating on the basis of the Coulomb blockade principle. Successful exploitation of the discrete threshold voltage changes in multiple-dot structures may lead to the development of memory cells with a multilevel storage capability and current drive much higher than nanoscale Si channel FET devices with single (or few) nanocrystal storage nodes.

– –

–

–

Figure 14. Charge-retention time characteristics after 1010 cycle endurance test with +15 V/−5 V, 100 ns write/erase pulses of a nanocrystal memory device obtained by implantation of 1 keV Si ions at a dose of 1 × 1016 cm−2 into 8 nm thick oxide and subsequent annealing at 950  C. A 30 nm thick oxide layer was deposited before annealing.

Figure 15. Room-temperature transfer characteristics for the very-lowenergy Si nanocrystal memory devices (case of 1 keV/2 × 1016 cm−2 Si+ implants). With decreasing sweep rate, the IDS –VG curves show a clear staircase structure. The arrows indicate voltage regions VGS with one and two stored electrons per nanocrystal (n = 1 2), while the initial part of the fast swept IDS –VG curve corresponds to n = 0. VTH is the threshold voltage shift caused by the storage of a single electron per nanocrystal. Inset: VG is swept forward and backward after discharging at a rate of 0.8 V/s. The dot lines show IDS –VG curves with n = 1 and n = 2 stored electrons per nanocrystal and are obtained by shifting the forward swept curve (n = 0 stored electrons per nanocrystal) by 1.9 V and 3.8 V respectively.

Nanocrystal Memories

5. CONCLUSIONS Fundamental limits in (a) gate oxide thickness due to tunneling currents, (b) transistor channel length due to subthreshold leakage constraints, and (c) storage capacitor due to the need for large capacitance values, will become an important concern in the future scaling of conventional volatile and nonvolatile memory devices. Aggressive exploration of an alternate device architecture offers the best hope for continuing the current performance scaling trends seen in the last 20 years. A nanocrystal memory structure is one of the new promising memory concepts for overcoming the fastapproaching scaling limits of Flash and DRAM memories. In this short chapter, the current status and challenges of this approach for memory applications have been presented. The self-limiting charging process in laterally uncoupled nanocrystal storage nodes (due to the Coulomb blockade effect), together with the distributed nature of the storage nodes (in contrast to the conventional continuous poly-Si floating-gate layer) promise the implementation of memory devices with thinner tunneling oxides for ultrahigh-density, low-voltage, low-power, and fast write/erase data storage. The progress in the area of practical nanocrystal floatinggate technology has been reviewed, and the potential of the very-low-energy ion beam synthesis approach has particularly been discussed. Encouraging electrical results of prototype nanocrystal single-transistor memory structures have been presented, indicating an optimistic prospect for applications ranging from Flash to DRAM-like functions, with the exotic possibility of multilevel storage capability. However, the experimental memory characteristics up to now (e.g., data retention time, endurance, write/erase speed, programming voltages) span a very wide range of values, and definite conclusions concerning the scalability advantages of this type of memory device over the conventional DRAM or Flash ones cannot be fully evaluated at present. More extensive study and fabrication process optimization are required in order to realize the applicability of the nanocrystal memory concept. Important issues such as reliable low-voltage operation with long-term charge retention or fast write/erase speeds at low programming voltages with high endurance remain to be verified beyond doubt before the practical implementation of this device in nonvolatile or volatile memory circuitry, respectively. That is, it has yet to be clarified whether or not nanocrystal memories will be used for information data storage in place of the conventional memory devices.

GLOSSARY Charge-trapping devices Memory technology that stores binary information in the form of electric charge in discrete traps distributed in the gate insulator of a MOS transistor Coulomb blockade Phenomenon in which the flow of current through a metallic quantum dot is inhibited until the electrostatic energy needed to move an electron onto the dot is overcome through an applied bias. For the case of a semiconductor quantum dot (a system with much lower electron densities, and larger electron wavelengths at the Fermi energy), the kinetic energy of the added electron (due to

337 quantum confinement) also must be supplied for overcoming current suppression. Dynamic random access memory (DRAM) Memory technology that stores binary information in the form of presence and absence of electric charge on capacitors. The DRAM cell consists of a single capacitor and a single transistor to access the capacitor. This technology is considered dynamic because the stored charge degrades over time due to leakage mechanisms. Therefore, the cell data must be read and rewritten periodically (refresh operation), even when the memory cell is not accessed to replace the lost charge. Floating gate (FG) Conductive polysilicon layer, completely embedded inside the gate oxide of a MOS transistor. As it is not externally connected to any other part of the device (rather, it is left floating), it is appropriately called a floating gate. Ion beam synthesis (IBS) Method for synthesizing various types of quantum dots. In this technique, an appropriate number of selected ions are introduced into a given dielectric layer, and a subsequent thermal annealing can induce the implanted material to precipitate in the form of small particles dispersed within the host layer. Metal oxide semiconductor (MOS) Sandwich structure consisting of three layers: the metal gate electrode (usually made of polysilicon), the insulating oxide (SiO2 ) layer, and the bulk semiconductor (p- or n-type Si), called the substrate, that make up the MOS capacitors and MOS transistors. MOS field-effect transistor (MOSFET) (or briefly, MOS transistor) Synonym for insulated-gate FET. A fourterminal MOS device with the terminals designated as gate, source, drain, and substrate or body electrodes. Usually, the substrate terminal is connected to the source terminal. As a field-effect device, the electric field established by the voltage applied to the gate terminal controls the current flow in the transistor channel (the region between the source and drain electrodes). Nonvolatile memory (NVM) Type of memory device in which the stored data are not lost when the power supply is off, and refresh operation is not required. Nonvolatile memories are classified into two main categories: FG NVMs and charge-trapping devices. Quantum confinement (or briefly, confinement) Quantization of the kinetic energy of charge carriers, when their motion in a particular spatial dimension is confined to a region comparable to the de Broglie wavelength of the carriers. Quantum dot (or briefly, dot) Synonym for island. An electrically insulated object, for example, a metal or semiconductor nanocrystal, in which charge can be transferred only through a tunneling mechanism. The confinement in all three spatial directions completely confines the motion of charge carriers, giving rise to a discrete energy spectrum much like an isolated atom or molecule. This is, in particular, the case of very small dots with a size close to or less than the electron wavelength on the Fermi surface F . In semiconductors, F ∼ 50 nm, and in metals, F ∼ 1 nm.

338 Static random access memory (SRAM) Memory technology that utilizes the bistable characteristics of a two crosscoupled inverter circuit (a circuit with two stable operating points) to store binary information. The most popular SRAM cell consists of two cross-coupled CMOS inverters and two access transistors. The memory cell is considered static because the cell data are kept as long as the power is turned on and refresh operation is not required. Tunneling Quantum mechanical charge-transport process in which electrons are able to penetrate through a narrow potential energy barrier, when their energies happen to be smaller than the height of the potential energy barrier. Volatile memory Type of a memory device in which the stored data are lost when the power supply voltage is turned off. Volatile memories are classified into two main categories: DRAMs and SRAMs.

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Encyclopedia of Nanoscience and Nanotechnology

www.aspbs.com/enn

Nanocrystalline Aluminum Alloys Livio Battezzati, Simone Pozzovivo, Paola Rizzi Università di Torino, Torino, Italy

CONTENTS 1. Synthesis of Nanocrystalline Materials 2. Nanocrystalline Aluminum 3. Devitrification of Al Glasses 4. Al–TM–RE Alloys: Description and Properties 5. Ball Milling of Alloys 6. Nanoquasicrystalline Alloys 7. Nanocrystallization Induced by Deformation 8. Conclusions Glossary References

1. SYNTHESIS OF NANOCRYSTALLINE MATERIALS 1.1. Introduction In order for a material to be defined nanocrystalline the size of its grains must be of the order of less than 100 nm. Such materials can be constituted by one or more phases distributed in one, two, or three dimensions. Examples are nanowires, layers either deposited on top of a substrate as coatings or stacked in suitable sequences, and bulk objects. If the material is fully made of nanograins the number density of crystals scales with their size (e.g., it can range from 1025 to 1021 m−3 for sizes of 5 and 100 nm respectively). Correspondingly, a high density of grain boundaries (usually 6 × 1019 cm−3 ) is implied so a large quantity of the atoms constituting the material can be situated on interfaces (simple calculations provide estimates of 50% for grains of 5 nm; 30% for grains of 10 nm; 3% for grains of 100 nm) [1]. As a consequence, nanocrystalline systems can be looked at as if they contained two types of atoms: those resident on a crystal lattice and those belonging to interfaces. Analogous densities of crystals can be obtained in two-phase materials where the fine particles are dispersed in a matrix either crystalline or glassy. Here the interface and its properties have relevance in determining the rate of nucleation and of attachment kinetics during growth. ISBN: 1-58883-062-4/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

In classical physical metallurgy there are several examples of materials developed over several decades and owing their properties to the existence of extremely fine grains. Two obvious cases are those of Al alloys hardened by preprecipitates or metastable precipitates and high strength– low alloy steels where nitrides and carbonitrides act as grain refiners. Conventionally, these are not listed among nanomaterials and their science and technology are dealt with in well-established treatises. Other metallic materials have recently been discovered following the same leading idea of nanocrystal research (i.e., of producing very fine particles to improve properties). This chapter deals with a new class based on aluminum.

1.2. Techniques for the Production of Nanocrystalline Materials Nanocrystalline metals and alloys can be obtained essentially by means of four different techniques: (a) introducing a high number of defects (i.e., dislocations and grain boundaries) in initially perfect crystals by severe plastic deformation which is achieved by ball milling, extensive rolling, extrusion, and equichannel angular pressing; (b) condensation of clusters or deposition of atoms on a substrate by chemical or physical vapor deposition; (c) crystallization of metastable systems such as glassy metals or undercooled liquids or precipitation from supersaturated solid solutions; (d) two-step production routes in which nanocrystalline powders are consolidated in order to obtain a bulk material. In the following the essential features of each technique are described. Electro- and electroless deposition can be employed for some metals and alloys, but they will not be dealt with here since they are not appropriate for Al.

1.2.1. Production of Powders and Compaction Amorphous or nanocrystalline powders can be produced by ball milling. The technique has been considered as a tool for refining minerals for a long time. It gained more widespread application when it was realized that the mechanical action

Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 6: Pages (341–364)

342 can drive phase transformations (amorphization, disordering, etc.) and chemical reactions. The initial stage of ball milling invariably implies the introduction of disorder and defects in the material leading to the formation of crystals with size of the order of nanometers [2]. During the first stage of the process the deformation is localized in deformation bands of about 1
m thickness and grains of low dimension nucleate into these bands. For long treatment times grains of tens of nanometers are obtained in pure metals, without preferred orientation and with high-angle grain boundaries. The grain size approximately scales with the inverse of the melting point. In alloys and intermetallic compounds the grain refinement can be a precursor of phase transformations. Bulk materials can be obtained if the ball-milled powders are compacted by any powder metallurgy technique. Since these mostly imply hot pressing, the nanograins must resist growth enough to avoid coarsening to a large extent. Pure Al has been obtained in nanocrystalline form with an average size of 25.5 nm by cryogenic milling using liquid nitrogen as cooling agent. The powders were found to resist grain growth up to temperatures close to 0.78 Tm (Tm is the melting temperature) because of impurity pinning of grain boundaries [3]. Another technique for subjecting a sample to a very intense plastic deformation is equichannel angular pressing in which the material is forced to flow through an L-shaped die. A large amount of shear stress is experienced by the material with consequent grain refinement [4]. Inert gas condensation also results in Al particles of the order of 30 nm which were shown to remain fine sized up to the melting temperature if passivated with a small amount of oxygen [5].

1.2.2. Crystallization of Glassy Precursors The metastable systems used for the production of nanocrystalline materials are amorphous metals prepared by rapid solidification by means of melt spinning in order to obtain ribbons about 30–40
m thick. Powders of the same size can be produced by atomization. A careful control of the heat treatment and, as a consequence, of the crystallization kinetics allows either the complete crystallization of the amorphous precursors into a nanocrystalline structure, or a partial crystallization with nanocrystals dispersed in the remaining amorphous matrix [6]. Nanocrystalline materials obtained by crystallization of amorphous precursors have the advantage with respect to the other production techniques that the preparation procedure is simple, can be easily controlled, and allows one to obtain materials constituted by grains of different size, from a few nanometers to tens of microns, simply varying the heat treatment conditions. A large part of this chapter will deal with such alloys.

Nanocrystalline Aluminum Alloys

may appear to be ruled by very different alloy properties or even to be apparently contradictory. The requirements for amorphizing an alloy are: composition suited for high undercooling, high liquid viscosity, and relatively low tendency to crystal nucleation of both stable and metastable phases. For nanocrystallization the nucleation rate is expected to be high and atomic mobility low. All of these aspects will be treated in detail in the following with the aim of showing how each material parameter influences the processing steps and how the alloy composition can be chosen in order to reconcile possible discrepant tendencies.

2.1. The Reasons for Amorphization: Alloy Constitution and Size Effect It is well known that the presence of deep eutectics in the alloy phase diagram is indicative of the tendency to amorphization for the compositions around the eutectic point. The liquid of eutectic composition is relatively stable with respect to crystal phases and often displays strong resistance to crystallization. It, therefore, can be undercooled to the glass transition where it transforms to a glassy solid. A parameter useful for the evaluation of the glass forming ability is the reduced glass transition temperature, Tgr = Tg /Tl (Tg = glass transition temperature; Tl = liquidus temperature). Values of Tgr exceeding 0.5 are typical for metallic alloys. Values in excess of 0.6 are associated with good glass forming compositions and with formation of bulk metallic glasses. Since Tg does not present large variations as a function of composition, the most relevant parameter for evaluating the tendency to amorphize is Tl . The number of elements in the alloy is also relevant. In fact, in an alloy made of a high number of elements there is the possibility of crystallizing several phases. The short range order in the liquid may not correspond to that of any crystal phase implying that it is difficult for the system “to choose” a crystalline structure (the confusion principle). Therefore the tendency to give an amorphous structure will be increased. The atomic size effect on glass forming tendency was studied by Egami et al. [7] for binary alloys. The mismatch between the atomic radii of the constituent elements of the alloy, r, shows an inverse proportionality to the minimum solute concentration (CBmin ),






r


= 0 (1)
r
C min A B r r − rA = B = rA rA



rB rA

3

−1

(2)

where A and B are the solvent element and the solute element respectively. The minimum value of the parameter 0 necessary to obtain amorphous phases in binary alloys was empirically determined to be about 0.1.

2. NANOCRYSTALLINE ALUMINUM This chapter is devoted to the description of constitution, structure, and properties of nanocrystalline Al alloys. Most of them have been obtained by rapid solidification as amorphous solids and then heat treated. The two processing steps

2.2. Thermodynamic Aspects Alloys that are able to form amorphous phases by rapid solidification show a substantial degree of chemical order in the liquid state. Macroscopic evidence for preferential

Nanocrystalline Aluminum Alloys

T

where Sf is the entropy of fusion. Cp is approximated either by a fraction of the entropy of fusion (on average 0.8 Sf ) or by its value at the melting point. With this position, all the thermodynamic quantities can be calculated in the undercooled regime (Fig. 1). In particular the difference between the free energy of the liquid and crystal phases may be evaluated with some confidence and used in calculations of the nucleation frequency and growth rate of the crystals from the melt. For a liquid pure metal at the melting point the specific heat is close to that of the crystal, whereas it attains slightly higher values on undercooling. This means that pure metals lose little entropy on undercooling, so their reduced glass transition temperature will be low with respect to glassforming alloys. The isoentropic temperature for Al (i.e., the temperature at which the entropy of the undercooled liquid would equal that of the crystal) has been computed by Fecht and Johnson with Eq. (3) as 0.24·Tf and may be considered an ideal glass transition. This analysis has been pursued further to obtain trends for Tg as a function of composition.

∆ G/∆ Hf

0.5 0.4 0.3 0.2 0.1 0.0 0.5

0.6

0.7

0.8

0.9

1.0

0.5

0.6

0.7

0.8

0.9

1.0

0.5

0.6

0.7

0.8

0.9

1.0

1.0 ∆ H/∆ Hf

0.8 0.6 0.4 1.0 0.8 0.6 0.4 0.2 0.0

∆ S/∆ Sf

interaction between unlike elements is given by the strongly negative enthalpy of mixing which is a common characteristic of glass-forming liquid alloys [8]. Another peculiar feature of glass-forming metallic liquids is that their thermodynamic properties are temperature dependent: the degree of order increases with decreasing temperature. So the excess enthalpy and entropy of mixing become more negative as the temperature is lowered and the undercooling regime is entered. This gives rise to an excess heat capacity in the liquid state, the existence of which has been demonstrated for both metal–metal and metal–metalloid systems. The existing data show that the excess heat capacity can be substantial for some alloys and has often a maximum at compositions corresponding to a compound in the solid state. It is nil for pure components, which have liquid heat capacities very close to those of the crystal phases at the melting point. As crystalline alloys usually obey the additive Neumann–Kopp rule, the excess liquid specific heat for alloys may be approximated by the specific heat difference Cp between liquid and crystal phases. This quantity is measured easily at the melting point and more rarely on undercooling near the glass transition temperature. Cp is substantial in the temperature range from the melting point to the glass transition with values of the order of the entropy of fusion of the alloy. Cp for pure elements has been determined in the undercooled regime for a limited number of cases; in all of them it is close to zero. Therefore, it is reasonable to attribute the largest part of the specific heat difference between liquid and crystal phases in glass-forming alloys to topological and chemical effects produced on alloying and to use Cp as an appropriate approximation for the actual excess specific heat. A high value of the liquid specific heat with respect to the crystal lets the entropy of the liquid phase approach that of the solid quickly on decreasing the temperature according to  Tf S = Sf − Cp dln T  (3)

343

T/Tf Figure 1. Schematic trend of the extensive thermodynamic functions for an undercooled metallic glass-forming liquid. Reduced coordinates are used. The reference state is the equilibrium crystal. The enthalpy and free energy are plotted from the melting point to the glass transition temperature. The entropy curve is extended (dashed line) to the hypothetical ideal glass transition, TK . The enthalpy and entropy differences between liquid and crystals decrease on undercooling due to a positive Cp . Should Cp be zero, the free energy difference would follow the dashed line. The actual trend for a glass-former implies relative stabilization of the liquid, (i.e., a lower driving force for crystallization).

In a binary system an entropy balance can be established at every isoentropic temperature Tk . Since the entropy of fusion at Tk is nil, an entropy cycle is written Sfor − xA Sf  A − xB Sf  B − Smix = 0

(4)

where Sf  i is the entropy of fusion of the constituents at Tk . Smix is the entropy of mixing in the liquid state and Sfor is the entropy of formation of the crystalline solid at the same temperature. Sfor and Smix may be inserted either as experimental data or by derivation from suitable models. If Sf  A and Sf  B are expressed through Eq. (3), using an effective value for Cp of pure elements, the temperature Tk which satisfies Eq. (4) may be calculated for every alloy composition. The result will be a trend of Tk , which can approximate that of Tg across the phase diagram. An example is shown in Figure 2 for a simple eutectic system displaying regular miscibility in the liquid state and assuming Smix = 0 in the solid state. Among glass-formers, the analysis was applied to the Al–Ce system [9] showing agreement with Tg values obtained both from experiments and extrapolation of data collected in ternary alloys.

2.3. Kinetic Aspects: Viscosity of Melts and Glass Transition The glass transition is the phenomenon in which a viscous liquid passes continuously into the amorphous solid state during cooling [10]. In fact, when a liquid is cooled below its

344

Nanocrystalline Aluminum Alloys

The temperature dependence of viscosity for glassforming liquids is given by the empirical Vogel–Fulcher– Tammann relation,   D · T0  = 0 exp (6) T − T0 where D is the fragility parameter, T0 is the Vogel–Fulcher– Tammann temperature, and 0 is the high temperature limit of viscosity, determined according to the relationship 0 =

Figure 2. Hypothetical glass transition trends for a simple eutectic system. The lines refer to different positions for the entropy of mixing in the liquid state to be used in Eq. (4) where the entropy of formation of the crystal phases is taken as nil: (a) Smix ideal, (b) Smix = 0, (c) Smix negative. The actual trend for metallic glasses is reproduced by curve (c) which is computed with an amount of entropy implying that the liquid is ordered at short range. Reprinted with permission from [8], L. Battezzati, Phil. Mag. B 61, 511 (1990). © 1990, Taylor & Francis.

melting point, if nucleation and growth of crystalline phases are avoided, the viscosity increases until the liquid is frozen in a structurally still, glassy state. Therefore, liquid viscosity is a central parameter for glass formation. At the melting point the viscosity () is of the order of 10−2 –10−1 Pa s for glass-forming metals, whereas it is 10−3 Pa s for normal liquids. In general, viscosities of metallic liquids at the equilibrium melting point fit the Andrade formula:  mTm Tm = AC (5) V 2/3 where m is the molecular mass, Tm is the eutectic melting temperature, and V is the molar volume. The empirical quantity AC takes different values for metallic elements, intermetallic compounds, and normal eutectics 1 8 × 10−7 (JK−1 mol1/3 )1/2 } with respect to glass-forming eutectics {6 5 × 10−7 (JK−1 mol1/3 )1/2 } [11]. Conventionally, the viscosity at the glass transition is taken as 1012 Pa s for extremely slow cooling [12]. The viscosity behavior in the undercooling regime can differ markedly for various substances: for silica the viscosity during cooling increases continuously according to the Arrhenius equation, whereas for other substances (e.g., molecular, polymeric, ionic, and metallic materials) it shows deviations from the Arrhenius rate law. In all these cases the activation energy for viscosity is a temperature-dependent parameter. Since viscosity increases several orders of magnitude from the melting point to the glass transition, the more gradual the increase (i.e., that described as an Arrhenius behavior), the better the glass-forming ability of the liquid. Typical examples are silicate glasses. Marginal glass-formers present a rapid rise in viscosity during cooling when approaching the glass transition. Most metallic melts, including those based on Al, belong to this category.

h VA

(7)

where h is Planck’s constant and Va is the atomic volume of the liquid. The fragility parameter is useful to classify “strong” and “fragile” liquids according to Angell [10]. The former follow silica behavior while the latter show deviations from the Arrhenius equation. For silica, the fragility parameter is 100, to be compared with 2 for the most fragile liquids [13]. The fragility parameter is also a good indicator of the glass-forming ability: the larger the fragility parameter, the better the glass-forming ability of the liquid. In fact glasses with large fragility parameter have slow kinetics in the undercooled liquid regime, inhibiting crystallization of the liquid. The change in viscosity implies the change of thermodynamic properties as well: heat capacity and the expansion coefficient may decrease more than a factor of two with respect to their normal liquid state values. Thermodynamic and kinetic parameters are combined in the Adam–Gibbs theory, based on entropy. This theory uses the idea of a cooperatively rearranging region, that is, the smallest group of atoms that must move in concert to change configuration. The sizes of these cooperatively rearranging regions grow with decreasing temperature, decreasing the configurational entropy of the system. With this theory, the viscosity is expressed as   C (8)  = 0 exp T · Sc T  where 0 is the high temperature limit of viscosity, C is a constant related to the enthalpy barrier for a cooperative rearrangement, T is temperature, and Sc is the configurational entropy of the liquid. The Adam–Gibbs theory is in agreement with Angell’s fragility classification. In fact strong liquids, with a tendency to short range order, have configurational entropy that is not strongly dependent on temperature, instead of fragile liquids that show non-Arrhenius behavior. Viscosity is usually linked to atomic diffusivity, D, through the Stokes–Einstein equation: =

kT 6 rD

(9)

This relationship is useful in estimating the diffusion coefficient in the undercooled liquid state where any experimental measurement would be almost impossible. However, it has been recently verified for molecular liquids and confirmed for metallic melts and glasses that it breaks down at temperatures in the range 1.2–1.3 Tg [14–16]. Below

Nanocrystalline Aluminum Alloys

345

3. DEVITRIFICATION OF Al GLASSES 3.1. Thermodynamics of Phase Transformations Rapidly solidified materials contain usually metastable phases and/or microstructures which transform via nucleation and growth. The driving force is the difference between the free energy of the metastable and stable equilibrium states. A schematic free energy diagram is drawn in Figure 3 for devitrification. It is shown that a gain in free energy may involve three main types of transformations: primary, polymorphic, and eutectic transformation. A polymorphic transformation is defined as partitionless formation of a phase with different structure but the same composition as the matrix. During a eutectic transformation two crystalline phases grow cooperatively with a discontinuous reaction. There is no difference in the overall concentration across the reaction front, but diffusion takes place parallel to the reaction front and the two components must separate into two phases. A primary crystallization causes the formation of a phase with composition different from the original matrix which still remains as a major constituent of the material. During this reaction, a concentration gradient may be formed ahead of the particle interface with the matrix becoming enriched in a solute until a metastable equilibrium is reached. The driving forces can be computed with some confidence by means of approximate formulae which are available for the different transformations [16].

Free Energy

β

γ

α

Figure 4 represents a free energy versus composition scheme for primary crystallization. At the liquidus temperature a common tangent to the liquid and crystal free energy determines the composition of the nucleating phase. On undercooling, however, it is demonstrated that the maximum driving force for nucleation is determined by drawing a line parallel to the tangent originating from the crystal free energy curve. The free energy available for subsequent growth is determined by the line joining the free energy of the crystal of nucleating composition to that of the liquid of interfacial composition. The first approximated formula proposed to compute G for the most stable nucleus is    Gv = Tl − T SA f − R log xA l (10)

where Tl is the equilibrium liquidus temperature, SA f is the entropy of fusion of the pure nucleating component, and xA l is the A concentration at the liquidus temperature. It was derived under the assumption of regular solution behavior of the liquid phase and no miscibility in the crystalline phase. The former position does not hold for glassforming melts which are characterized by a dependence of the thermodynamic functions on temperature through a positive value of the liquid excess specific heat, Cpex . Could the excess free energy of the liquid phase be expressed by means of the subregular model? If the excess free energy of the liquid phase is expressed by means of the subregular model and there is no miscibility in the crystalline state, G would become   Gv = Tl − T SA f − R log xA l 2 + xB (11) l 4qxA l − p − q

where p and q are parameters expressing the temperature dependence of the excess free energy of the liquid phase. A more general approach, however, is to describe the thermodynamics of metastable and stable phases by means

Gibbs free energy

such temperatures it is suggested that the product  · D2 is constant at each temperature. The diffusion coefficient in the temperature range relevant for the formation of nanocrystals should be computed accordingly especially for Al alloys where no data are available for both viscosity and diffusivity in the liquid and glassy state. Below Tg the diffusivity can usually be described by the Arrhenius equation. For metallic alloys the temperature range of Tg is most often close to that where crystallization occurs and the two processes may overlap.

solid

liquid

xn

xs

xm

xl

composition 0

X1

X2

X3 A at. %

Figure 3. Schematic Gibbs free energy curves for , the undercooled phase, and and equilibrium phases. The arrows marks the extent of driving force for transformations: at x1 for polymorphic, at x2 for primary, and at x3 for eutectic.

Figure 4. Schematic Gibbs free energy curves for liquid and crystal phases at a temperature where the liquid of composition xm is in the undercooling regime. The line tangent to the liquid curve gives the chemical potential of the components. The arrows at xs and xn give the amount of variation in chemical potential of the components when a nucleus of these compositions is formed. The most probable nucleus has composition xn since Gxn  > Gxs .

Nanocrystalline Aluminum Alloys

346 of the optimization programs used to compute phase diagrams. This has been attempted in the case of the Al–Nd system for which the temperature- and compositiondependent driving forces for nucleation (Gv ) have been calculated after constructing free energy curves by means of the CALPHAD software [17]. In Figure 5 free energy curves are reported as a function of Nd content for the Al rich composition range at 700 K, a temperature in the undercooling regime. Note that the free energies of the metastable liquid and crystalline equilibrium phases are rather close due to the negative heat of mixing in the liquid being only slightly higher than the heat of formation of the stable intermetallic compound. After primary crystallization of Al the metastable equilibrium given by the dashed line will be established for compositions richer in Al than the tangent point to the liquid free energy. Since nucleation does not change significantly the composition of the matrix, the driving force for nucleation of primary Al, can be defined as the difference between the chemical potential of Al in the liquid and in the crystal phase, as shown by arrow a in Figure 5, for the Al97 Nd3 eutectic composition. Similarly, the driving force for primary nucleation of Al11 Nd3 is shown by arrow b. The driving force for the nucleation of Al is about twice as large as that for the nucleation of the Al11 Nd3 compound. Primary nucleation of facecentered-cubic (fcc)Al. Al will cause the rejection of Nd in the surroundings of primary precipitates reducing the driving forces for fcc-Al and enhancing that for Al11 Nd3 . So the intermetallic compound can nucleate beside fcc-Al leading to a eutectic crystallization. Once this has occurred growth is driven by the free energy difference indicated in Figure 5 by arrow c.

3.2. Kinetics of Primary Crystallization During primary crystallization, nanocrystals embedded in an amorphous matrix are formed. In rather wide temperature ranges their size increases quickly to a few nanometers and does not change significantly on further annealing. The usual requirements for obtaining this microstructure are high nucleation and growth rates in the very early stages of crystals formation and then both quantities must drop to negligible values. The two processes will now be described with reference to classical theories.

3.2.1. Nucleation Nucleation can be homogeneous or heterogeneous. It is homogeneous if each point in the volume has the same probability of generating the new crystal. It is heterogeneous if it starts at sites either predictable or recognized a posteriori. They may be unevenly distributed in the matrix, but the process remains stochastic in each of them. In heterogeneous nucleation the term site not only has the meaning of place where the new phase originates, but it also conveys the idea of catalyzing the transformation. In real systems there are interfaces, inclusions, or defects, so heterogeneous nucleation is extremely frequent. However, at times it is invoked also when the sites are unavoidable components (either known or unknown) of the matrix. If an impurity solute promotes the formation of a new phase, the nucleation may well be termed homogeneous since impurities are constituents of the material although being undesired. Analogously, point defects, such as vacancies, are intrinsic in solids and may occur in thermal equilibrium. Therefore, it would be preferable to consider them as components of the material instead of heterogeneities. A similar argument can apply to the free volume in liquids or glasses. On the other hand, excess vacancies, excess free volume, line defects, and interfaces introduce excess energy in the material and, as a consequence, are best considered as heterogeneities. Due to the excess energy associated with them, they can act as catalytic sites for transformations. The steady-state nucleation rate in a condensed system, Ivs , can be expressed as Ivs =

Figure 5. Gibbs energy versus composition for Al–Nd. The chemical driving force for crystallization are indicated: (a) primary Al, (b) primary Al11 Nd3 , (c) eutectic Al + Al11 Nd3 . Reference states are fcc-Al and hcp-Nd. Reprinted with permission from [17], M. Baricco et al., Mater. Sci. Forum, 269-272 553 (1998). © 1998, Trans Tech Publications.

24DN 2 n1/3 c



G∗ 3 kB T

1/2

  G∗ exp − kB T

(12)

where D is a diffusion coefficient for atomic species crossing the interface between the matrix and the new embryo, N is the number of atoms per unit volume,  is a diffusion distance, nc is the number of elemental particles in the nucleus of critical size, G∗ is the activation energy for the formation of a nucleus of critical size, and kB is the Boltzmann constant. The above equation contains the product of two exponential terms (the one containing G∗ is explicitly written; the other is D). On increasing undercooling G∗ decreases, favoring nucleation. If very low temperatures are reached, the nucleation rate decreases because the atomic mobility, D, is lower. The pre-exponential terms do not affect much the value of Iv when the temperature is changed. Two thermodynamic parameters are relevant for G∗ : the free energy difference between liquid (or glass) and crystals

Nanocrystalline Aluminum Alloys

347

and the interfacial free energy, , between the same phases. In fact, G∗ for a spherical nucleus is defined as G∗ =

16 3   3 Gv 2

(13)

Expressions for the driving energy G have been discussed in the previous section. It is difficult to evaluate . It is taken to a first approximation as a fraction of the enthalpy of fusion or as an adjustable parameter. Recent theories are based on the concept of the interface not being a geometrical dividing surface but a diffuse layer. A discussion can be found in [16]. The practical outcome is an expression of as a function of temperature which apparently fits a number of experimental data on homogeneous nucleation rate. The formula is 

T

T / Tf  = 0 48 + 0 52 · (14) Tf where Tf  is the interfacial free energy at the melting point. In most transformations the time scale is such that the time necessary to reach the steady-state condition, the transient period, , is negligible with respect to the overall transformation time. On the contrary, the time needed for quenching in rapid solidification experiments may become comparable to . Actually it has been suggested that vitrification of some compositions occurs because the process is shorter than the transient time. The nucleation frequency during the transient period is given by the Kashchiev expression [18]

  −n2 t It = Ist 1 + 2 −1n exp 

(15)

rc2

2D

Homogeneous Nucleation If steady-state homogeneous nucleation is operative during a transformation the following equation will give Ni : Ni = It1 − Xi−1 t

i = 1  t/t

(17)

where Xi−1 is the volume fraction transformed up to the (i − 1)-th time interval and (1 − Xi−1 ) accounts for the volume available for nucleation during the ith time interval. It is computed from Xi = 4 /3u3

i j=1

Nj ti + 1 − j3

(18)

where ul is the crystal growth rate. The resulting distribution has a decreasing number of crystals upon decreasing size because of the progressive reduction in the volume where nucleation is possible (Fig. 6a). Heterogeneous Nucleation Heterogeneous nucleation is promoted by a limited number of active sites per unit volume, Z, so Ni can be calculated with the expression   i−1   −1 Nj t Ni = I t 1 − Xi−1 1 − Z ∗

(19)

j=1

During the quenching of a metallic alloy to a glass the transient period can be estimated using the expression [19] =

Quenched in Nuclei Subcritical crystallike clusters are stochastically present in an undercooled melt. They are then frozen together with the matrix on rapid quenching [21]. Since the critical size decreases with decreasing temperature, a subcritical embryo may then become a nucleus and grow during an annealing treatment. Quenched-in nuclei are likely to have similar size, just above the critical one, and grow all at the same rate. Moreover there will be no other nucleus in the matrix since it will take time to induce further nucleation. Therefore it is expected that the crystal sizes are confined to a narrow range.

(16)

where rc is the radius of the nucleus of critical size. Heterogeneous nucleation is so frequent because most substrates can act as catalysts by reducing the activation barrier due to interfacial energy provided that the new phase wets the substrate. Information on the nucleation mechanism can be obtained by analyzing the distribution of dimensions of crystals in partially crystallized samples [20]. The model is based on the partition of the annealing time during an isothermal transformation in intervals, t. The number of crystals per unit volume (Ni ) formed in the time t depends on the nucleation mechanism. This approach provides a straightforward identification of the nucleation mechanism especially when applied to the initial stages of a polymorphic transformation and when the crystals are spherical and noninterfering. The expected distributions are described in the following.

where (1 − Z −1 Nj ) gives the fraction of available

sites at the ith time interval. Nuclei are formed when Nj < Z; Nj = 0 when all sites are consumed. In Figure 6b the distribution of the crystals diameters is reported. There is a steady decrease in the number of crystals with decreasing size due to the reduction in both number of available sites and volume and a sudden drop to zero when no new nuclei can be formed. Homogeneous and Heterogeneous Nucleation with a Transient In the transient period an increasing number of nuclei form during each time interval before reaching the steady state. Then either a homogeneous process or a heterogeneous one sets in. As a consequence, the distribution has a similar shape as for either case (ii) (Fig. 6c) or (iii) (Fig. 6d) but decreases smoothly when reaching the higher values of the measured crystal sizes. These crystals are those formed in limited amounts during the early transient period and which had more time for growth. For primary crystallization only a fraction of the alloy undergoes transformation so it is expected that a metastable equilibrium between crystals and amorphous matrix will be finally established and the amount of crystalline phase will

Nanocrystalline Aluminum Alloys

348

∆Ni

∆Ni

where G is substantial, then exp−G/RT  is negligible. Therefore at high undercoolings the growth rate follows an Arrhenius type equation: 

−Qs u1 = u0 exp RT crystal diameter

crystal diameter

(b)

∆Ni

∆Ni

(a)

crystal diameter

(c)

crystal diameter

(d)

Figure 6. (a) The distribution of sizes of crystals grown after the occurrence of a homogeneous nucleation process. (b) The distribution of sizes of crystals grown after the occurrence of a heterogeneous nucleation process. (c) The distribution of sizes of crystals grown after the occurrence of a transient and a homogeneous nucleation process. (d) The distribution of sizes of crystals grown after the occurrence of a transient and a heterogeneous nucleation process. A similar distribution may be found in case of primary crystallization when only a fraction of the alloy transforms. In fact, the amount of crystals having small sizes would reduce quickly because of the reduction of volume available for transformation.

be determined by the lever rule. Therefore, the available volume for nucleation will be quickly reduced during the progress of transformation so there will be less crystals of small size. The size distribution of crystals could result in one similar to that expected for heterogeneous nucleation with a transient as shown in Figure 6d.

3.2.2. Growth Considering a nucleus that starts to grow at the start of an isothermal anneal, different growth laws will be followed according to the transformation type (i.e., polymorphic, eutectic, or primary). Polymorphic Transformation When crystals and matrix have the same composition, the growth process needs only the movement of atoms through the crystal–matrix interface. The growth rate (u1 ) is constant and has the temperature dependence 

   −G −Qs · 1 − exp (20) u1 = u0 exp RT RT where Qs is the growth activation energy and u0 is a preexponential factor. The term in square brackets contains the free energy difference between melt and crystal, G, and is nil at the melting point. It expresses the need for limiting the growth rate in proximity to the equilibrium transformation temperature when the rate of detachment of atoms from the crystal becomes sizeable. If the crystallization takes place in metallic glasses at temperatures well below the melting point



(21)

Eutectic Transformation When a eutectic transformation takes place the average composition of the transformed region equals the composition of the matrix before the occurrence of transformation. However, partition of species between the new phases is needed which takes place via long range diffusion. As a consequence, the growth rate depends on the interparticle spacing (). In particular, if there is diffusion in the matrix ahead of the crystallization front, than ue is proportional to −1 ; if there is diffusion at the interface between matrix and crystals then the growth rate is proportional to −2 [22]. Considering a high level of undercooling (G > RT ) the growth rate can be expressed as follows when diffusion occurs in the bulk volume: ue = D

4D 

(22)

where D is the dimensionless supersaturation, a complex function of the elemental concentration in the matrix and the growing phase, D is a diffusion coefficient, and, when the diffusion occurs at the interface, ue = D

8··D 2

(23)

where  is the thickness of the crystallization front. Primary Crystallization When a crystal poor in solute grows in a multicomponent matrix there is rejection of solute in the matrix. If the crystal grows richer in solute there is a depletion of solute in regions of the matrix near the particle. In both cases the growth of the new particle requires homogenization of the concentration gradient built up in the surrounding matrix, that is, a diffusion controlled process. So the growth rate is controlled by the diffusion rate. If we assume that the diffusion coefficient is independent of concentration, the radius of a spherical particle during precipitation can be expressed as √ r =  Dt

(24)

up = 1/2 ·  · D · r −1

(25)

and the growth rate is

where  is a dimensionless parameter that depends on the composition of the material and on the composition of the crystal–amorphous interface.

Nanocrystalline Aluminum Alloys

3.3. Primary Nanocrystallization 3.3.1. Nucleation and Growth During Nanocrystallization At the very early stages of primary nanocrystallization high nucleation frequency and high growth rate occur on isothermal annealing at suitable temperatures. Soon after, both nucleation and growth slow down and in practical terms cease. During the formation of the Al nanocrystals a concentration gradient builds up in the amorphous phase at the crystal–matrix interface due to the rejection of solute from the crystal. The rare earth (RE) elements are slow diffusers in the alloy so their high content ahead of the interface reduces the rate of homogenization of the matrix and contributes to slowing of the growth rate of the Al crystals. In fact, when a high enough density of crystals is reached, impingement among their diffusional fields can become effective and change the growth law as described in the following section [23]. The ensemble of phenomena now described produce typical differential scanning calorimetry (DSC) results on continuous heating where the precipitation peak is rather sharp and then is followed by a long tail characteristic of the homogenization stage of the transformation.

During the early stages of primary crystallization from an amorphous matrix, the growing crystals can be considered isolated because their diffusion fields do not interfere with each other. In this case the growth follows the parabolic behavior reported in Section 2.3. On the contrary, when the number of crystals becomes large (a good estimate is 1014 m−3  the growth rate slows down due to soft impingement. The situation of two growing grains is represented in Figure 7 at two different times, t1 and t2 . At t1 every particle is considered isolated and the concentration of the solute far from the particle is the initial solute concentration in the metastable phase (c m . At a later time t2 the two grains are in competition for the solute (i.e., their diffusion fields overlap and the solute concentration far from the particles changes from the initial c m ). This implies that the quantity of solute available for growth is decreasing and the process is slowing down. As early as 1950, Wert and Zener [24] first modelled soft impingement, considering spherical particles of a phase

Concentration %

β

β

C

C

that grows with a parabolic law in an  matrix and assuming that all the crystals are already nucleated when the transformation starts. The volume fraction (Xi  was defined as Xi =



rI rf

3

(26)

where r I is the radius that identifies the position of the interface, r f is the final radius of the transformed region, and 1 − Xi =

ct − c  cm − c

(27)

where ct is the time-dependent concentration of solute far from the growing crystal, and c  is the concentration of solute in the  phase. Zener and Wert derived the following equation for the increase in the transformed volume fraction: dXi 3 = k2/3 DXi1/3 1 − Xi  dt 2

(28)

where k is k2/3 =

3.3.2. Soft Impingement

C

349

2c m − c   c − c  r f 2

(29)

and c is the concentration of solute in the phase. Equation (33) was solved numerically to obtain an expression for ct versus time and, as a consequence, of growth rate. Another model was proposed by Ham in 1958 [25]. He considered spherical particles distributed on a regular cubic lattice, obtaining an equation identical to that presented by Zener and Wert for which he provided an analytical solution. The model was shown to explain rather nicely the rate of heat evolution in DSC when applied to the devitrification of Al88 Y7 Fe5 [26].

4. Al–TM–RE ALLOYS: DESCRIPTION AND PROPERTIES This section reviews specific features of Al–TM–RE alloys with TM = transition metal and RE = rare earth element or Y which behaves similarly to RE in these materials. In the systems described below samples are all produced by melt spinning, using different wheel speeds that will be specified when possible. DSC, X-ray diffraction (XRD), and transmission electron microscopy (TEM) are the typical investigations adopted to study microstructural evolution during heat treatments.

α

4.1. Structural Aspects: Amorphous Structure

m

α

Distance Figure 7. The solute concentration profiles in the  matrix between two growing grains of phase at two annealing times.

X-ray diffraction patterns of glass-forming Al–TM–RE alloys present a broad signal, called a prepeak, at angles much lower than the halos typical of the amorphous phase. Further, an unusual shoulder of the main halo of the diffraction pattern is found. The intensity of both signals depends on composition. These particular features of the XRD pattern are shown in Figure 8 in the case of Al87 Ni7 Nd6 amorphous ribbons [27].

Nanocrystalline Aluminum Alloys

Intensity (a.u.)

350

20

40

60

80

100

120

2θ Figure 8. XRD pattern of the Al87 Ni7 Nd6 as-quenched alloy. It presents a prepeak at 2 ∼ 20 and a composite halo. The maximum of the main halo is close also to the angular position of the (111) reflection of Al pattern and has a shoulder at high angles. There are no evident scattering contributions close to the angular position of the other reflections of Al. The explanation for the main composite halo is controversial. It was attributed to a contribution to the total diffracted intensity from very short Al–TM distance [28], at variance to the possibility of amorphous phase separation [56], or to the presence of quenched-in Al nuclei [29]. The appearance of a glass transition in the DSC trace of this alloy shows that it is mostly constituted by a homogeneous amorphous phase ruling out phase separation in the liquid. Therefore, the halo in the pattern should be attributed to the local environment of the elements in the amorphous alloy and to the contribution of small Al crystals present in the matrix. Reprinted with permission from [27], L. Battezzati et al., Mater. Trans., 43, 2593 (2002). © 2002, The Japan Institute of Metals.

Amorphous ribbons of Al85 Yx Ni15−x , with 2 < x < 12, show two different patterns: Y-rich glasses (x ≥ 8) have a single main halo; Y-poor glasses have a shoulder on the high-angle side of the main halo close to the (200) Bragg reflection of Al [28]. It was suggested that the shoulder is due to scattering from fine quenched-in Al nuclei. The main halo should mask the broad (111) Bragg peak. Since the intensity of the shoulder increases with decreasing Y content, it was concluded that the number of Al nuclei of critical size depends on RE content in the alloy. The prepeak found at lower angles might suggest short range order due to Y–Y pairs. In fact, its intensity increases with Y content. This implies that the Y–Y distance is relevant for the prepeak and so most Y atoms must assume a definite configuration (Fig. 9), being all surrounded by Al atoms, so the Y–Y coordination number is zero. The prepeak shifts to higher angles as the Ni content is increased so this is attributed to the replacement of some of the Al atoms by the smaller Ni atoms. In the case of Al90 Fex Ce10−x (x = 5 7) [29] pulsed neutron diffraction indicates that the Al–Fe distances are anomalously short, while some Al–Al distances are anomalously long. The prepeak is present both in pulsed neutron and X-ray diffraction patterns. These results suggest a strong interaction between Al and Fe, leading to short range order. In neutron scattering experiments, the position of the prepeak shifts to higher Q on increasing Fe concentration. Analyzing the radial distribution functions, Ce atoms are basically randomly distributed in the glass. Fe atoms are

Figure 9. The most probable configuration of Al and Y atoms in an amorphous Al–Y–Ni alloy.

surrounded by about 10 Al atoms, with 6 of them in close contact with Fe, and the distance between Al–Fe in close contact is less than the sum of atomic radii, suggesting a strong interaction between Al and Fe more than Al and Ce with this alloy composition. This short range order, similar to the local order in quasicrystals, might explain the origin of the prepeak. The atomic structure of Al87 Y8 Ni5 alloy was investigated by both ordinary and environmental radial distribution functions around Y and by anomalous X-ray scattering around the Ni K-edge [30]. From the distances between pairs of atoms and coordination numbers collected in these measurements it resulted that the number of Y–Y pairs is insignificant; about 16% of the atoms surrounding a Y atom are Ni and, therefore, the rest of the coordination shell is mostly occupied by Al. A strong interaction also between Y and Ni is inferred from the number of Ni–Y pairs, higher than that expected from the alloy composition. A locally ordered structure of the three elements is present in the amorphous phase, thus favoring glass formation in this alloy. These results seem apparently to be in contrast with those derived above with considerations of XRD patterns. It should, however, be noted that the composition is changed by a few atomic percent. This suggests that these materials are very sensitive to alloy formulation as both structure and transformation behavior are concerned. In the following detailed analysis of various binary and ternary systems this feature will clearly appear. Whenever possible the properties of the materials (mechanical, chemical) will be reported stressing the effect of refined microstructures.

4.2. Al100−x Smx
8 < x < 12 A varied transformation mechanism was found in this series of binary alloys which serve as model materials. In the case of Al92 Sm8 , primary crystallization occurs with the formation of Al nanocrystals with a grain size of about 15 nm. A polymorphic crystallization is found in Al90 Sm10 , with the formation of a metastable intermetallic phase. For Al88 Sm12 and Al86 Sm14 a eutectic crystallization gives a mixture of stable (Al and Al11 Sm3  and metastable phases.

Nanocrystalline Aluminum Alloys

351

30

200

250 300 Temperature (°C)

350

Figure 10. A DSC trace showing the exothermal signals due to crystallization of an amorphous Al92 Sm8 .

45

60

75

90

2θ Figure 11. XRD pattern obtained with a Al92 Sm8 alloy after the first crystallization event shown in Figure 10.

the melt and causing the formation of a distribution in the size of quenched-in nuclei which have grown during the anneal or to heterogeneous nucleation.

4.2.2. Al90 Sm10 , Al88 Sm12 For Al90 Sm10 different phases were observed as a product of rapid solidification and, then, different transformation paths were found during heating [31, 35]. If a full amorphization is obtained, it transforms polymorphically to a metastable cubic phase having large unit cell which then decomposes in two steps to the equilibrium phase mixture, as represented by am → MS1 → Al + Al11 Sm3 + M1 → Al + o-Al4 Sm When crystalline phases are found in the as quenched ribbons then the transformation sequences are am + Al + M2 → am + Al + M2 (increase in crystalline fraction) → Al + Al11 Sm3 → Al + o-Al4 Sm The structure of all metastable phases (MS1, M1, M2) has been determined [36]. M2 forms only during undercooling and does not nucleate from the glass. It simply grows if already present. Different phases are obtained on annealing the single phase glass. This reveals the existence of a hierarchy in stability of phases occurring in different temperature ranges.

Crystalline fraction

Heat Flow 150

Intensity (a.u.)

4.2.1. Al92 Sm8 Both partially and completely amorphous ribbons can be produced by melt spinning. In partially crystalline ribbons, Al and Al11 Sm3 crystallize during rapid solidification [31,32]. Even in the case of apparently amorphous ribbons, tiny fractions of -Al were detected by XRD and TEM on the air side. The stability of the amorphous phase was checked with DSC (Fig. 10) [33]. Continuous heating experiments evidenced the presence of two transformations, the first of which starts at 180  C and the second at 266  C (heating rate of 40 K min−1 . XRD patterns of samples heated up to the end of the two transformations show the formation of Al nanograins of about 10 nm in size during the first transformation (Fig. 11) and, successively, the formation of Al and Al11 Sm3 . The kinetic of formation of the nanocrystals [34] was studied in isothermal conditions performing DSC measurements at various temperatures and annealing times. The evolution of the crystalline fraction of -Al (Fig. 12) versus time was determined for samples heated at 171  C by comparing the amount of heat released after the isothermal treatments to the amount of heat evolved from a totally amorphous sample. A sigmoidal shape is expected for a single stage process; however, the crystalline fraction displays a more complex behavior as a function of time, suggesting a sum of different processes. The variation of the density of Al nanocrystals and their size versus time of annealing are reported in Figure 13 as obtained from TEM observations (Fig. 14). The transformation can be described with nucleation and growth of a high density of Al nanocrystals. The clustering of Al atoms to form crystalline grains implies rejection of Sm into the matrix and the establishment of a concentration gradient at the crystal–matrix interface. This concentration gradient is hardly recovered during isothermal annealing, because of the low diffusivity of Sm. An example of such nanocrystals is shown in the TEM image of Figure 15. The size distribution of Al nanocrystals (a typical example is reported in Fig. 16) can be interpreted according to the classification described in Section 3.2.1. The frequency of crystal diameters has a tail at “high” values (>10 nm) indicating a transient effect. On decreasing size the number of crystals decreases with a shape which appears intermediate between Figure 6d and e. It may be due to homogeneous nucleation possibly occurring during quenching from

1,0 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0,0 0

200

400

600

800

1000 1200 1400

Annealing time (s) Figure 12. The evolution of the crystalline fraction of Al versus time for a Al92 Sm8 sample annealed at 171  C.

Nanocrystalline Aluminum Alloys

Density of cryst. (1021m-3)

352 16 14 12 10 171 166 150

8 6 4 2 0

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2000 3000 Annealing time (s)

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Figure 13. The number density of Al nanocrystals as a function of annealing time for the temperatures indicated in the insert for a Al92 Sm8 alloy.

Only partially crystallized samples were obtained for Al88 Sm12 alloy during rapid solidification. Al, Al11 Sm3 , and M1 compete with the formation of the amorphous phase and were found in the as quenched ribbons beside a little fraction of glassy phase.

4.2.3. Al–RE
RE = Y, La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, or Yb [37, 38] In these binary alloys the glass-forming ability is probably due to a strong attractive interaction of the constituent elements. This should result in the diffusion of the constituent atoms becoming difficult and the viscosity high in the strongly supercooled liquid. The composition range for the formation of the amorphous phase is 9–13% Y, 7–11% La or Ce, 10% Pr, 8–12% Nd or Gd, 8–16% Sm, 9–14% Tb, and 9–12% of Dy, Ho, Er, or Yb. Except for the Al–Nd system these ranges are situated between a shallow eutectic point and Al11 R3 (R=La,

Figure 15. High resolution TEM image of isolated Al nanocrystals in an Al92 Sm8 rapidly quenched alloy annealed at 150  C for 180 s. Lattice fringes correspond to the (111) lattice spacing of Al.

Ce, Pr, Nd, or Sm) or Al3 R (R=Y, Gd, Tb, Dy, Ho, Er, or Yb) compounds. The onset temperature of the first DSC peak (Tx  increases from 434 to 534 K with increasing RE content from 7 to 12 at%, but no further increase is seen in the concentration range 12–15 at%. Such a dependence is probably associated with different mechanisms of crystallization. Actually, DSC curves for Al91 Tb9 , Al90 Tb10 , and Al91 Dy9 show a first broad exothermic peak due to the precipitation of fine-grained fcc-Al and a second one due to a eutecticlike reaction involving Al, an unknown compound, and Al3 Tb or Al3 Dy. When the primary Al phase does not precipitate, Tx increases as seen in various Al–RE amorphous alloys with RE=Y, La, Ce, Nd, or Sm. So it is concluded that the strong compositional dependence of Tx is due to a change in crystallization process from Am → Am + Al → Al + Al3 R to Am → Al + X + Al3 R → Al + Al3 R or Am → Al + Al3 R.

4.3. Al–Ni–Ce Ternary and multinary alloys will be discussed in the following. For some systems there has not been a systematic work as a function of composition so each alloy will be reviewed separately. 0.30

frequency

0.25 0.20 0.15 0.10 0.05 0.00 4 Figure 14. Bright field TEM image of nanosized Al crystals embedded in an amorphous matrix in Al92 Sm8 alloy annealed at 171  C for 60 s. The corresponding diffraction pattern is also shown: there are crystalline reflections on top of amorphous halos.

6

8 10 crystal size (nm)

12

14

Figure 16. The distribution of the crystal sizes of Al in a Al92 Sm8 sample annealed at 171  C for 4 minutes. The shape of the histogram is intermediate between those shown in Figure 6c and d (see text).

Nanocrystalline Aluminum Alloys

4.3.1. Al88 Ni10 Ce2 [39] Rapidly solidified ribbons were found to be completely amorphous in XRD and TEM analysis. Two DSC exothermic signals were detected in the temperature ranges from 405 to 540 K and from 595 to 630 K (heating rate of 0.67 K s) and were assigned respectively to the precipitation of fcc-Al from the amorphous phase and to the transformation of the remaining amorphous matrix to Al3 Ni and Al11 Ce3 . The temperature dependences of nominal yield strength (y , nominal ultimate tensile strength (b , and elongation (f  of the amorphous alloy were investigated, pointing out that f increases from 1.8 to 45% at 465 K and then decreases rapidly. This behavior was attributed to the effect of elongation induced crystallization; in fact TEM observations of the sample subjected to tensile tests at 465 K showed fcc-Al nanoparticles (10–15 nm) dispersed homogeneously in the amorphous matrix. This phenomenon was attributed to the following processes: (a) preferential precipitation along the shear planes due to an increase in temperature resulting from deformation, (b) increase in the flow stress at the precipitation sites, and (c) propagation of the deformation to other regions along the tensile direction. This large elongation is very important for the processing of gas atomized amorphous powders to be consolidated in a bulk form, because it occurs in a temperature range well below the precipitation temperature of the compounds.

4.3.2. Al84 Ni10 Ce6 [40] This alloy shows an high glass-forming ability and fully amorphous powders are produced by high pressure gas atomization that can be compacted by a high pressure die casting process obtaining sheet and cylinder samples with thicknesses of 0.5 and 5 mm respectively. For sheet samples an amorphous surface layer of about 0.03–0.05 mm was obtained; for cylinder samples the layer was 0.18–0.20 mm thick. The hardness of the amorphous layer of the sheet samples was 370 Hv and the crystallization temperature was determined as 556 K. The corrosion resistance against NaOH solution for the amorphous layer was found to be better than the highest corrosion resistance in conventional alloys.

353 For Al87 Ni10 Ce3 amorphous ribbons, an atom probe analysis carried out to obtain a concentration depth profile (Fig. 17) provided the composition of the two phases of the alloy after heating up to the first crystallization peak. The -Al phase contains more than 95 at% Al and the remaining amorphous matrix has 25% Ni and 3% Ce. The -Al nanocrystals are evaluated to be about 15 nm in size by TEM. An enrichment in Ce content is found at the crystal–amorphous interfaces which is more evident when plotting the number of detected solute atoms versus the total number of detected atoms (Fig. 18a). The slope of the plot represents the local concentration of the alloy. Ni and Ce atoms are rejected from the growing Al crystals and an enrichment in Ce concentration is evident at the interface at a distance of about 3 nm. On the contrary, a similar enrichment is not observed for Ni atoms that display homogeneous concentration in the matrix. The concentration profile derived is schematically described in Figure 18b. It is concluded that faster homogenization is achieved for Ni than for Ce. This family of Al-based alloys shows good mechanical properties; for example yield strength up to 800 MPa can be reached in the amorphous state, which can increase up to 1500 MPa after partial crystallization (i.e., when nanocrystals are embedded in the amorphous matrix). Replacing Ni with Cu (Al87 Ni7 Cu3 Ce6  results in the increase in density of nanocrystalline particles formed during primary crystallization with the grain size becoming smaller (about 8 nm). Moreover Cu enriched clusters are present in the remaining amorphous phase, similar to Guinier–Preston zones in conventional crystalline alloys for precipitation hardening. These clusters may form in the early stage of annealing or even during cooling from the melt. They introduce a higher degree of heterogeneity in the local alloy composition and increase the density of nuclei during crystallization. The decrease in particle size of the Al phase causes an increase in tensile fracture strength with respect

4.3.3. Al87 Ni10 Ce3 , Al85 Ni10 Ce5 , Al80 Ni10 Ce10 , Al87 Ni7 Cu3 Ce6 [41–44] In these systems Ce plays an important role for the increase in glass-forming ability. The critical content in Ce for the formation of an amorphous phase was evaluated to be 3 at% since both partially and completely amorphous ribbons were produced with the Al87 Ni10 Ce3 alloy. The XRD diffraction patterns revealed a single symmetric halo for Al80 Ni10 Ce10 , whereas Al85 Ni10 Ce5 shows a halo with a shoulder as discussed in Section 4.1. Also the DSC trace for Al80 Ni10 Ce10 is different from the others; in fact it has only one exothermic peak. In the cases of Al87 Ni10 Ce3 and Al85 Ni10 Ce5 there are two exothermic peaks. The XRD patterns of samples annealed up to the first crystallization step show the reflections due to fcc-Al nanocrystals and an amorphous matrix in the case of Al87 Ni10 Ce3 and fcc-Al plus two compounds in Al85 Ni10 Ce5 .

Figure 17. Chemical analysis of a Al87 Ni10 Ce3 amorphous alloy heated up to the first crystallization DSC peak obtained with spatial resolution by means of the atom probe-field ion emission technique. The arrows mark the position of interfaces between Al nanocrystal and amorphous matrix. There is enrichment in Ce ahead of the interface. Reprinted with permission from [41], K. Hono et al., Scripta Metall. Mater. 32, 191 (1995). © 1995, Elsevier Science.

Nanocrystalline Aluminum Alloys

354

Heat Flow

b

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Figure 18. Total number of detected ions along a spatial direction in of a Al87 Ni10 Ce3 amorphous alloy heated up to the first crystallization DSC peak (a). The percentage of each element in the phases is reported. The slopes of the experimental traces suggest the concentration profile shown in (b). Reprinted with permission from [41], K. Hono et al., Scripta Metall. Mater. 32, 191 (1995). © 1995, Elsevier Science.

to the ternary alloy (from 1050 to 1250 MPa) and in hardness. Such an effect on mechanical properties was attributed by the authors to higher hardness of Al nanocrystals with respect to the amorphous phase. This statement was later questioned by others (see Section 4.4.2 below).

4.3.4. Al87 Ni10 Ce3 [45, 46] This composition was confirmed to be a marginal glassformer by rapid solidification since partially amorphous ribbons were obtained. It is interesting to remark that they contained nanosized Al crystals dispersed in an amorphous matrix so a two-phase microstructure was produced directly by quenching. It was also found that the devitrification behavior is very sensitive to changes in composition. In fact one of two samples, apparently identical in XRD analyzes, was found to contain less than 1% Si as a contaminant. The silicon contamination produces a change in devitrification behavior evidenced by DSC (Fig. 19a) in which three transformation steps are present instead of the two observed in the uncontaminated Al87 Ni10 Ce3 sample (Fig. 19b).

4.4. Al–Ni–Y 4.4.1. Al88 Ni10 Y2 , Al88 Ni8 Y4 [47] Ribbons of these alloys were produced by melt spinning, using different wheel speeds (20, 30, 40, 55, and 63 ms−1 . A two-phase microstructure, composed by Al nanocrystals homogeneously dispersed in the amorphous matrix, was obtained using wheel speeds greater than 30 ms−1 for Al88 Ni10 Y2 and 20 ms−1 for Al88 Ni8 Y4 . The crystallite size and volume fraction of fcc-Al increases with decreasing wheel speed. Al88 Ni10 Y2 shows a higher tendency to form a nanocrystalline structure, confirmed by X-ray diffraction analysis. Moreover, increasing Y content in place of Ni, the crystallite size decreases and the volume fraction of fcc-Al increases.

200

300 400 Temperature (°C)

500

600

Figure 19. DSC traces for two ribbons of nominal composition Al87 Ni10 Ce3 . The ribbon which provided curve (b) was later found contaminated with 1% Si. There is a clear effect of the contaminant on temperatures and mechanism of transformations. Reprinted with permission from [46], L. Battezzati, et al., in Proceedings of the 22nd Risø International Symposium on Material Science: Science of Metastable and Nanocrystalline Alloys, Structure, Properties and Modeling, 2001, (A. R. Dinesen, M. Eldrup, D. Juul Jensen, S. Linderoth, T. B. Petersen, N. H. Pryds, A. Schrøder Pedersen, and J. A. Wert, Eds.) Risø National Laboratory, Roskilde, Denmark, p. 211, 2001. © 2001, Risø National Laboratory.

TEM observations show that in Al88 Ni10 Y2 ribbons, produced with a wheel speed less than 30 ms−1 , some intermetallic compounds (i.e., Al3 Y) are present beside fcc-Al. The ribbons structure is fully crystalline when using a wheel speed of 20 ms−1 . On the contrary, Al88 Ni8 Y4 ribbons maintain a microstructure consisting of amorphous matrix and fcc-Al even at a wheel speed of 20 ms−1 . For both alloys the diameter of fcc-Al crystallites ranges from 10 to 90 nm, when wheel speed is decreased. DSC curves for Al88 Ni10 Y2 ribbons present three exothermic peaks in the temperature ranges from 437 to 446 K, from 600 to 603 K, and from 698 to 715 K, respectively (heating rate of 40 K min−1 . They are associated with (a) the precipitation of fcc-Al, (b) the transformation of the remaining amorphous matrix to fcc-Al plus an intermetallic compound (Al3 Y), and (c) the transformation of phases induced by crystallization. The area of the first peak decreases with decreasing wheel speed, but that of the second peak remains unchanged. This means that the volume fraction of the fcc-Al phase increases on decreasing cooling rate and so it is possible to control the amount of the fcc-Al phase by changing the wheel speed. On the contrary, with increasing wheel speed, the crystallization temperature tends to increase indicating a higher stability of the remaining amorphous phase. The microhardness of these alloys does not change linearly with wheel speed; its highest value is reached for a particle size of 10 nm and for volume fraction, Vf , of about 10%.

4.4.2. Al88 Ni10 Y2 , Al86 Ni1167 Y233 , Al84 Ni1333 Y267 , Al82 Ni15 Y3 [48] Different wheel speeds were used to produce ribbons by melt spinning. Samples with different compositions produced at 60 ms−1 are compared to obtain information on their respective glass forming ability. A fully amorphous

Nanocrystalline Aluminum Alloys

material was obtained for Al86 Ni11 67 Y2 33 and Al84 Ni13 33 Y2 67 alloys, while only partially crystalline ribbons are produced in the case of Al88 Ni10 Y2 and Al82 Ni15 Y3 systems. Analyzing XRD diffraction patterns of ribbons melt spun at different wheel speeds, it is concluded that for Al88 Ni10 Y2 there is a wide range of solidification rates in which a microstructure constituted by fcc-Al dispersed in the amorphous matrix is obtained. Using a wheel speed of 20 ms−1 a fully crystalline microstructure is evident. The same microstructural transitions were detected for Al86 Ni11 67 Y2 33 , but they occur at lower wheel speeds. In fact, a fully amorphous structure was obtained using a wheel speed of 60 ms−1 . In the case of Al84 Ni13 33 Y2 67 alloy, a limited range of wheel speeds can be used to obtain a nanocrystalline structure in which the presence of intermetallic compounds is evident. The results are similar for the Al82 Ni15 Y3 alloy, even if the glass-forming ability is lower than the previous case; in fact, fully amorphous ribbons are not obtained even using the highest wheel speed. When Al nanocrystals were obtained their dimensions, determined by Scherrer analysis, were about 10 nm; the result was confirmed by TEM observations. The as-quenched ribbons were also studied by DSC, using the area of the first devitrification peak to determine the volume fraction crystallized to fcc-Al. These measurements indicate that glass formation is easiest at around 15 at% total solute content, corresponding to the composition for which nanoscale fcc-Al particles are obtained at the lowest quenching rate. Furthermore, at this solute content and below, there is a wide range of quenching conditions for the direct synthesis of a two-phase microstructure (fcc-Al plus amorphous matrix). At higher solute content, the glassforming ability decreases and the two-phase structure is not obtained. Microhardness measurements have been made for the ribbons of all compositions and a linear increase in microhardness with solute content was detected. The trend in mechanical properties of Al–Ni–Y alloys indicates that the main cause of increase in hardness is the solute content in the amorphous matrix and not the amount of nanocrystalline Al.

4.4.3. Aly
Ni7/15 Y8/15 
100−y  [28, 49] These alloys can be divided into two distinct groups, based on their crystallization behavior. Compositions with y < 85 exhibit an endothermic glass transition just before the first exothermic peak. Tg ranges from 548 K (y = 84) to 660 K (y = 75). Similarly, the enthalpy of the first crystallization event increases from 44.8 to 73.2 J g−1 . On the contrary, for the alloys with y > 85 no glass transition is visible; the first exothermic peak has an enthalpy of about 24 J g−1 . The activation energy, Ea , for the first peak, computed by means of the Kissinger method, increases from 1 6 ± 0 1 eV (y = 81) to 2 1 ± 0 3 eV (y = 86). As for the mechanical properties, the Young modulus decreases from about 82 (y = 75) to about 52 GPa (y = 88).

4.4.4. Al85 Ni15−x Yx
3 < x < 12 [49] Al85 Ni15−x Yx 3 < x < 12 alloys can also be divided in two groups. For Y ≥ 8, DSC curves show a well-defined glass transition and XRD patterns show a single main halo. But if

355 Y content is less than 8 at%, DSC curves do not show a glass transition and in the XRD pattern the halo has a shoulder. Tg increases from 526 K for x = 8 to 538 K for x = 11 and the enthalpy for the first peak increases from 43.1 to 68.7 J g−1 respectively. The first crystallization temperature, Tx , is about 560 K for alloys with Y content less or equal to 8 at% and is about 520 K for Y-poor (x < 8) alloys, for which the enthalpy of the first crystallization increases from 22.4 to 26.6 J g−1 . The activation energy for the first peak increases from 2 8 ± 0 2 eV (x = 5) to 3 8 ± 0 5 eV (x = 10). For these alloys, the Young modulus decreases from 58 GPa (x = 3) to 48 GPa (x = 10). The highest tensile strength found is 930 MPa and corresponds to x = 4.

4.5. Al–Ni–Sm 4.5.1. Al85 Ni12−x Smx
2 < x < 10 [50] Only fully crystallized ribbons were obtained in the case of Al88 Ni10 Sm2 . On the contrary, Al88 Ni4 Sm8 ribbons were obtained fully amorphous and their DSC curves show four exothermic peaks: the first transformation starts at 250  C and is due to the precipitation of -Al from the amorphous matrix. The other transformations are due to the formation of several intermetallic compounds. Isothermal treatments were performed at 225  C for different times and the crystalline fraction of -Al nanocrystals was determined: it reaches about 70% after 120 minutes of annealing. Microhardness also changes as a function of annealing time and, as a consequence, of the fraction of Al nanocrystals: it increases rapidly from 280 Hv for as-quenched alloy to 370 Hv after 120 minutes of annealing, when it reaches a plateau. Wear measurements show a relevant increase in resistance for alloys annealed from 30 to 120 minutes.

4.5.2. Al88 Ni4 Sm8 [51] The structural evolution of this alloy during devitrification was studied using TEM and atom probe field-ion microscopy. TEM dark-field micrographs, together with the corresponding selected-area electron diffraction, of Al88 Ni4 Sm8 annealed at 200  C for 30 min show fine -Al nanoparticles embedded in an amorphous matrix. The average particle size is 20–25 nm and increases up to 30–35 nm in samples annealed at 225  C for 120 min. An increase in density of nanocrystals is also found for the latter heat treatment. High resolution TEM (HRTEM) observations show -Al nanoparticles composed of interconnected arms; such a shape suggests dendritic growth. The presence of an intermetallic compound in the partially crystallized alloy is evidenced by field-ion microscopy and TEM. Three-dimensional elemental maps are represented in Figure 20. The distribution of Sm atoms in the as-quenched alloy is random (Fig. 20a), confirming its fully amorphous state. Then, after an annealing treatment at 225  C for 15 min (Fig. 20b), some regions appear to contain a lower density of Sm atoms. Figure 20c shows an isoconcentration surface of 100 at% Al, which corresponds to -Al nanoparticles in dendritic shape. This is a further confirmation of

Nanocrystalline Aluminum Alloys

356 4.6. Al–Ni–Nd

4.6.1. Al96−x Nix Nd4
x = 2 4 6 12 [52] The XRD results for these alloys indicate a change from crystalline to fully amorphous ribbons on increasing the Ni content. DSC curves show that in the case of compositions with x = 2 and x = 4 two exothermic peaks are present, corresponding to the precipitation of Al and intermetallic compounds. When the Ni content is higher than 6 at%, the first broad peak disappears and a sharp exothermic reaction takes place, due to the eutectic formation of Al and intermetallic compounds. A change in mechanical properties is detected on increasing the Ni content. In fact f rises from 400 MPa (x = 0) to 1000 MPa (x = 2 4), when there is a coexistence of amorphous phase and nanocrystalline Al. It decreases to 850 MPa (x = 8) because of the presence of only amorphous phase and then rises again up to about 1000 MPa when the Ni content is raised further.

4.6.2. Al88 Ni10 Nd2 [53]

Figure 20. Three-dimensional map of the element concentrations in Al88 Ni4 Sm8 obtained by elaboration of atom probe data: (a) Sm in the amorphous alloy, (b) Sm in the partially crystalline ribbon, (c) Al in the partially crystalline ribbon. Reprinted with permission from [51], T. Gloriant et al., Mater. Sci. Eng. A 304–306, 315 (2001). © 2001, Elsevier Science.

the total rejection of the solutes from the crystallites during the nanocrystallization process. Analyzing an integrated concentration depth profile of Sm and Ni obtained from an Al-amorphous interface it is deduced that there is no enrichment in solute at the interface. It is interesting to note the difference with respect to Al87 Ni10 Ce3 alloy described above; in fact the diffusion-field impingement occurs later during the reaction and does not limit crystal growth so that the nanoparticles can grow in dendritic shape. The volume fraction of Al nanoparticles increases up to 35 (±5)% in the material annealed for 225  C for 30 min and, as a consequence, the Al content in the amorphous matrix passes from 88% in the as-quenched ribbon to 83.5%, the Ni content reduces to 3.5%, and the Sm content rises up to 13%.

Two crystallization stages are again detected by DSC. The volume fraction of Al nanocrystals, Vf , increases from 0% for the as-quenched ribbons to 32% for ribbons heated up to 525 K. Samples heated after the first crystallization peak show extraordinary values of tensile fracture strength (f , up to 1980 MPa, for alloys heated up to 430 K; this value is attributed to the microstructure constituted by Al nanoparticles dispersed in the amorphous matrix. In fact, in this annealing state Vf reaches 18% and correspondingly the maximum value of fracture elongation, f , of about 3% is obtained. The microhardness increases linearly from 220 to 400 Hv , when samples are annealed at 525 K. The size of Al particles in the two-phase state is about 8–10 nm.

4.7. Al–Ni–Gd 4.7.1. Al100−x Nix Gdy
5 < x < 11 12 < x + y < 18 [54] In this study Al100−x Nix Gdy alloys with a fixed concentration of 7 at% of Ni or Gd were studied and a composition area near Al87 Ni7 Gd6 was identified for the best glass-forming tendency. Here good intermediates for developing a twophase microstructure via thermal treatment should be found. DSC patterns show always three exothermic peaks. On increasing the Ni content, the first crystallization peak becomes sharper and shifts to higher temperature, from 488 K for Al88 Ni5 Gd7 to 577 K for Al82 Ni11 Gd7 . Similarly, on increasing the Gd content, the first crystallization peak shifts from 451 K for Al88 Ni7 Gd5 to 601 K for Al82 Ni7 Gd11 . The activation energy (calculated by means of the Kissinger method) increases monotonically when the content of either Ni or Gd is increased with the Gd being more effective. A higher activation energy for crystallization (or a higher crystallization temperature) means higher thermal stability; so for this ternary system it is concluded that Gd is more effective than Ni in increasing the glass-forming ability. This

Nanocrystalline Aluminum Alloys

357

was attributed to sluggish mobility of Gd with respect to Ni atoms.

4.8.1. Al86 Fe5 Nd9 , Al86 Fe9 Nd5 , Al88 Fe9 Nd3 [55] Al86 Fe5 Nd9 melt spun ribbons were found to be fully crystalline by XRD and TEM analysis. Their DSC curve has a principal exothermic peak and then two exothermic small signals. The first peak is due to the crystallization of fcc-Al and a metastable phase that transforms to the stable crystalline phases at higher temperatures. The equilibrium phases are Al, Al3 Fe, and a phase indicated as , which may be defined as Al10 Fe2 Nd. The Al86 Fe9 Nd5 alloy has a fraction of fcc-Al nanocrystals besides the amorphous phase after melt quenching. Its DSC trace has three exothermic peaks; the first one corresponds to the transformation of the amorphous matrix to fcc-Al and the same metastable phase as Al86 Fe5 Nd9 . The equilibrium phases are again reproduced as in Al86 Fe5 Nd9 .

4.8.2. Al88 Fe9 Nd3 [46] This composition is a good example to show the quenching sensitivity of this class of alloys. In fact various microstructures were observed after rapid solidification, depending on the solidification rates (Fig. 21): predominance of amorphous phase + Al, predominance of Al + amorphous phase, fully crystalline state made of Al + Al3 Fe + -Al11 Nd3 . Different transformation paths were found on heating these ribbons (Fig. 22) but the same crystalline products

Heat Flow

4.8. Al–Fe–Nd

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500

600

Figure 22. DSC traces obtained with the Al88 Fe9 Nd3 ribbons, the structure of which is shown in Figure 20. The differences in the exothermic signals show that various transformation paths are followed. Reprinted with permission from [46], L. Battezzati, E. Ambrosio, P. Rizzi, A. Garcia Escorial and K. R. Cardoso, in Proceedings of the 22nd Risø International Symposium on Material Science: Science of Metastable and Nanocrystalline Alloys, Structure, Properties and Modeling, 2001, (A. R. Dinesen, M. Eldrup, D. Juul Jensen, S. Linderoth, T. B. Petersen, N. H. Pryds, A. Schrøder Pedersen, and J. A. Wert, Eds.) Risø National Laboratory, Roskilde, Denmark, p. 211, 2001. © 2001, Risø National Laboratory.

were always recovered at 600  C. The transformation paths of the partially crystalline materials are amorphous phase + Al → Al + amorphous phase → Al + (Al,Fe)17 Nd2 + (Al,Fe)2 Nd → Al + Al3 Fe +  Al + amorphous phase → Al + unidentified metastable ternary phase

ϕ'

Al (Al,Fe)2Nd (Al,Fe)17Nd2

Intensity

d

→ Al + Al3 Fe +  It is apparent that several intermetallic phases can form in a limited range of compositions. The local metastable equilibria and concentration profiles dictate the phase selection on annealing.

c

20

40

60

b

4.9. Al–Fe–Y

a

4.9.1. Al90 Fe5 Y5 , Al85 Fe75 Y75 , Al80 Fe10 Y10 [56]

80

2θ Figure 21. XRD patterns obtained with Al88 Fe9 Nd3 ribbons of increasing thickness from (a) to (d) (i.e., quenched at decreasing rate). In (a) the material is almost fully constituted by Al and amorphous phase. In (b) and (c) the metastable crystalline compounds (Al, Fe)2 Nd and (Al, Fe)17 Nd2 also appear. In (d) the pattern of the equilibrium phases was obtained. Reprinted with permission from [46], L. Battezzati, et al., in Proceedings of the 22nd Risø International Symposium on Material Science: Science of Metastable and Nanocrystalline Alloys, Structure, Properties and Modeling, 2001, (A. R. Dinesen, M. Eldrup, D. Juul Jensen, S. Linderoth, T. B. Petersen, N. H. Pryds, A. Schrøder Pedersen, and J. A. Wert, Eds.) Risø National Laboratory, Roskilde, Denmark, p. 211, 2001. © 2001, Risø National Laboratory.

The XRD diffraction pattern of these ternary alloys shows a broad peak that indicates an amorphous material (result confirmed by TEM) and a prepeak due to local ordering of the Y–Y pair. The glass transition is evident in DSC curves followed by three exothermic peaks in all three alloys. There is no primary crystallization of -Al phase. In fact, on annealing the samples after the first DSC peak, partial crystallization of an intermetallic compound, Al9 (Fe,Y)2 , takes place that then transforms into -Al and Al70 Fe16 Y14 .

4.9.2. Al88 Fe5 Y7 [26] TEM analysis of the Al88 Fe5 Y7 melt spun ribbons reveals an amorphous structure with a random distribution of micrometer size intermetallic crystals.

Nanocrystalline Aluminum Alloys

358 The DSC thermogram shows three peaks. The first one corresponds to Al nanocrystal precipitation, with dimension of about 20–30 nm; the second one and the last one are partially overlapped and are due to the precipitation of intermetallic compounds.

4.9.3. Al85 Y10
Fe,Co,Ni,Cu5 [57] Completely amorphous ribbons were produced by melt spinning as confirmed by XRD and TEM analysis. A change in transition metal produces a corresponding change in the devitrification behavior of the material, evidenced by DSC studies: the alloy with Cu shows two exothermic peaks, the alloys with Fe and Co show three peaks, and the alloy with Ni presents five signals. Furthermore, the transition metals have different effects on the stability of the amorphous phase. Specifically, a decrease in crystallization temperature is observed in the following order: Fe > Co > Ni > Cu. The same scaling is found for the melting temperature, Tm , of the Al rich compounds. Ni addition is the most effective in improving the glass-formation ability. After heating samples through the first peak of crystallization, XRD patterns show a mixture of crystalline phases, consisting of a fcc solid solution possibly of Y and Ni, Cu, Fe, Co in Al. The other phases have not been identified. After heating through the second DSC peak fcc solid solutions and Al3 Y orthorhombic appear in all the ternary alloys. Al9 Co2 and Al3 Ni were identified in the respective alloys.

4.9.4. Al90 Fe7 Nb3 , Al87 Fe10 Nb3 [58] The rapidly solidified ribbons were found to be fully amorphous. DSC traces show two transformations; the first one corresponds to the precipitation of -Al nanocrystals with a size of 25–40 nm for Al87 Fe10 Nb3 and a size of about 200 nm for Al90 Fe7 Nb3 . The second peak is due to the precipitation of the equilibrium phases, Al3 Fe and Al3 Nb. An increase in Fe content implies higher temperatures of transformation and smaller size of -Al nanocrystals.

4.10. Al–Ni–Fe–Nd 4.10.1. Al88 Ni7 Fe3 Nd2 , Al88 Ni5 Fe5 Nd2 , Al88 Ni10 Nd2 [59] The melt-spun ribbons analyzed by TEM and XRD show only a single amorphous phase. Their DSC curves present two exothermic peaks. The first one is broad and corresponds to the precipitation of -Al nanocrystals. The second one is due to the precipitation of intermetallic compounds. The quaternary alloys present a shift to higher temperature of the transformations, due to a higher stability of the amorphous phase. The temperature increase is dependent on the Fe content. A complex behavior as a function of testing temperature was found for tensile strength (b ), yield strength (y ), and fracture elongation (f ). All three alloys have B higher than 800 MPa in the temperature range from room temperature to 580 K. This value is about 3 to 4 times higher than conventional heat resistant Al alloys. This is probably due to the Al nanoparticle dispersion and to the increase in thermal stability with solute enrichment of the amorphous matrix.

The elongation of Al88 Ni10 Nd2 , Al88 Ni7 Fe3 Nd2 , and Al88 Ni5 Fe5 Nd2 at room temperature is 2–3% and reaches values of 42, 29, and 22% respectively at the first peak and 54, 48, and 39% at the second one.

4.11. Al–Ni–Fe–Gd [60, 61] Twenty-four compositions were studied, containing 83, 85, and 87 at% Al. The best glass-forming ability was found for 85 at% Al, followed by 87 at% Al. In the latter series the compositions with the best glass-forming ability are Al87 Ni6 Fe1 Gd6 and Al87 Ni5 Fe1 Gd7 . Measurements gave the surprising result that the density of Al85 Ni5 Fe2 Gd8 exceeds the weighted average of its elemental densities by more than 5%, instead of less than 1% for Al85 Ni6 Fe3 Gd6 or Al87 Ni6 Fe1 Gd6 . This was attributed to a more closely packed atomic structure in the amorphous state and to stronger interactions between transition metal and rare-earth elements affecting glass-forming ability. DSC traces of Al85 Ni5 Fe2 Gd8 show a Tg signal and then four exothermic peaks; a glass transition is not observed for Al85 Ni6 Fe3 Gd6 that shows five transformations steps from the amorphous phase to stables crystalline phases. As for mechanical properties, tensile strength reaches values of 1280 and 1210 MPa for amorphous Al85 Ni6 Fe3 Gd6 and Al85 Ni5 Fe2 Gd8 , respectively, and Young’s modulus values are 72.7 and 75.3 GPa.

4.12. Al–Ni–Zr, Al–Ni–Hf [62] Melt-spun ribbons were completely amorphous as confirmed by TEM and XRD. In Al–Ni–Zr alloys with Zr > 5 at%, DSC curves show two exothermic peaks; the first one is due to the precipitation of a fcc-Al phase. The precipitation temperature increases with increasing Zr content. The second peak corresponds to the crystallization of the remaining amorphous matrix. The same behavior was observed in Al–Ni–Hf alloys. Probably the atomic radius of the solute elements plays an important role in determining the formation of the amorphous phase and the mechanism of crystallization. In fact, comparing the minimum solute concentration in the Al90−x Ni10 Mx systems for the single precipitation of fcc-Al particles, a critical concentration value was found of 5 at% for M = Ce and 7 at% for M = Zr. The minimum solute concentration necessary to form amorphous phases is 2 at% for Ce, 3 at% for Zr, and 4 at% for Ti. For these elements, the atomic radius is quite different: 1.83 Å for Ce, 1.62 Å for Zr, and 1.47 Å for Ti. This values are also relevant to determine the grain size of the Al nanoparticles. TEM analysis reveals a larger crystal size when using Zr: 20 nm for the partially crystallized Al87 Ni10 Zr3 and 15 nm for the same composition with Ce.

4.13. Al90 Fe5 Gd5 [63] The as-quenched ribbons are fully amorphous to XRD and HRTEM. After an isothermal anneal up to 445 K (i.e., just below the crystallization temperature), the material becomes partially crystallized. Alloys with a slightly higher aluminium

Nanocrystalline Aluminum Alloys

359

content, Al90 5 Fe4 75 Gd4 75 , are obtained partially crystallized directly after quenching. For both of them the volume fraction of fcc-Al is about 28%. The size of crystalline particles is about 8 nm. Tensile strength is shown to present a maximum for the annealed samples (1010 MPa), whereas Young’s modulus is higher for the fully amorphous material. The deformed materials were analyzed with scanning electron microscopy (SEM), which shown fracture surfaces typical of metallic glass materials, with vein patterns. More¯ the observations revealed that the distribution of macroover scopic plastic deformation is extremely inhomogeneous.

the first transformation temperature. Figure 23 is about Al88 TM12−x REx alloys. When TM = Ni a clear increase in temperatures is found. The two alloys containing 88 at% Al and TM = Fe have much higher transformation temperatures. They are, however, less easily quenched to a glassy state. In Figure 24 the onset temperature is reported as a function of rare-earth element in alloys of Al88 Ni7 RE6 composition [27, 65]. It is apparent that the temperature decreases on increasing atomic number of rare-earth elements.

4.14. Al–V–M (M=Fe, Co, or Ni) [64]

In the following systems the effect of the ball milling on the amorphization tendency and on devitrification behavior was studied.

The melt-spun ribbons present a nonequilibrium structure consisting of nanoscale amorphous particles surrounded by fcc-Al as revealed by XRD patterns and TEM images. The compositions which promote this structure are Al94 V4 Fe2 , Al94 V4 Co2 , and Al93 V5 Ni2 . The sizes of the coexistent amorphous and Al phases are about 10 to 25 nm and 7 to 20 nm, respectively. The as-quenched structure is composed of the Al and amorphous phases for the alloys containing Fe and Co and by the Al and icosahedral phases for the alloy containing Ni. Phase transitions take place through two stages, shown as exothermic signals in DSC traces. For Al94 V4 Fe2 the crystallization process may be described as amorphous → icosahedral phases → Al + Al11 V The mechanical properties are good. Measurements of tensile fracture stress, f , and microhardness, Hv , yielded high values in the series Al98−x Vx M2 at 4% V. In fact, for the asquenched structure values of 1350 MPa and 470 Hv , respectively, are obtained for the alloy with Fe, 1230 MPa and 460 Hv for that with Co, and 1090 MPa and 430 Hv for that with Ni. These values decrease after the first transition to icosahedral phase.

4.15. Concluding Remarks Although a large amount of information on Al–TM–RE alloys has been collected, there is some scatter in the data and there is still a lack of systematic representation of the results. For the ease of consultation the most relevant data discussed above are summarized in Table 1. For each alloy two temperatures are listed, as reported by the various authors, at the given heating rates: the onset of primary crystallization and that of the subsequent full devitrification of the matrix. Care should be taken in comparing the values since the microstructure of the rapidly solidified materials may differ from sample to sample. This information is provided in the Notes column detailing also the technique(s) used to study the sample structure, together with the value of the glass transition temperature when existing. The central column summarizes the most relevant mechanical properties of the ribbons either in the as-quenched state and/or after annealing. In Figures 23 and 24 data extracted from Table 1 are plotted to display the most prominent chemical effects on

5. BALL MILLING OF ALLOYS

5.1. Al–Ni–Co–Ti/Zr [66] Mechanical grinding of Al-based alloys with Al > 80 at% containing late transition metals such as Ni (6–9 at%) and Co (3–5 at%) with an atomic ratio Ni/Co equal to 2 leads to the formation of nanostructured materials made of fcc-Al solid solution and Al9 (Co,Ni)2 compound. Upon adding a few atomic percent of Zr or Ti there appear differences in the amorphization reactions. In fact, with (Al0 88 Ni0 08 Co0 04 100−x (Zr/Ti)x for x = 1 to 5%, partial to complete amorphization occurs via the following sequence: fcc-Al + Al9 (Co,Ni)2 + Al3 Zr / or Al3 Ti → fcc-Al + amorphous I → amorphous II. The experimental procedure consists of preparing by arc melting a mixture of pure elements under purified argon atmosphere, and then crashing them into fine powders. XRD patterns show complete amorphization after 100– 120 h of milling.

5.2. Al95 Cu5 Zr5 [67] Atomized powder of 100–200
m diameter were milled up to 140 h. The microhardness of the as-milled material is higher than that of the as-cast powders indicating that a degree of metastability has been introduced in the material during ball milling. It approaches that of the as-spun ribbons of the same composition. XRD patterns show only the presence of -Al, but SEM examinations also reveal other precipitates. After annealing at 500  C, XRD patterns indicate the presence of Al3 Zr + Al2 Cu and the milled material still retains a considerable hardness. It is suggested that extrusion of ball-milled powders may be performed to obtain bulk materials.

5.3. Al80 Ni8 Fe4 Gd8 [68] Amorphous powders of this alloy were produced using the ball-milling technique after a treatment for 80 hours. The composition range for easy amorphization is different for rapid quenching and mechanical alloying. It was necessary to reduce the Al content for mechanical alloying with respect to that presenting good glass-forming ability in the meltspinning process.

Nanocrystalline Aluminum Alloys

360

Table 1. A list of Al–TM–RE alloys produced by rapid solidification in the structural state given in the Notes column. The temperatures significant for phase transformations are provided at the given heating rate (glass transition temperature, Tg , onset of primary Al crystallization, T1 , onset of the second crystallization event, T2 . The most relevant mechanical properties are collected (tensile strength, b , Vickers hardness, Hv . Alloy

T1 (K)

T2 (K)

Rate (K min)−1

Al88 Ni10 Nd2 Al88 Ni7 Fe3 Nd2 Al88 Ni5 Fe5 Nd2 Al90 Ni8 Nd2

403 413 431 366

586 615 619 590

20 20 20 40

Al90 Ni6 Nd4

394

607

40

Al90 Ni4 Nd6

438

605

40

529 579.5 633 480 405 437 552–660 523 520 505 525 520 557 560 ∼ 525 577 ∼ 565 ∼ 550 542 ∼ 515 507 ∼ 475 601 ∼ 590 ∼ 565 550 ∼ 520 ∼ 470 ∼ 430 ∼ 445

∼ 615 ∼ 615 — 625 595 600 560–675 597 614 611 610 609 — — ∼ 595 ∼ 625 ∼ 580 ∼ 580 ∼ 580 ∼ 580 ∼ 580 ∼ 580 ∼ 615 ∼ 615 ∼ 585 ∼ 585 ∼ 585 ∼ 585 ∼ 585

20 20 20 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 5

Al85 Ni6 Fe3 Gd6 Al85 Ni5 Fe2 Gd8 Al80 Ni8 Fe4 Gd8 Al87 Ni10 Ce3 Al88 Ni10 Ce2 Al88 Ni10 Y2 Aly (Y8/15 Ni7/15 100−y Al85 Y3 Ni12 Al85 Y4 Ni11 Al85 Y5 Ni10 Al85 Y6 Ni9 Al85 Y7 Ni8 Al85 Y9 Ni6 Al85 Y10 Ni5 Al88 Ni4 Sm8 Al82 Ni11 Gd7 Al83 Ni10 Gd7 Al84 Ni9 Gd7 Al85 Ni8 Gd7 Al86 Ni7 Gd7 Al87 Ni6 Gd7 Al88 Ni5 Gd7 Al82 Ni7 Gd11 Al83 Ni7 Gd10 Al84 Ni7 Gd9 Al85 Ni7 Gd8 Al86 Ni7 Gd7 Al87 Ni7 Gd6 Al88 Ni7 Gd5 Al90 Fe5 Gd5 Al90 5 Fe4 75 Gd4 75 Al88 Fe5 Y7 Al88 Fe9 Nd3 Al94 Fe2 V4

553 500 579

649 618 ∼ 680

40 40

Al90 Fe7 Nb3 Al87 Fe10 Nb3 Al87 Ni7 La6

533 623 525

693 729 605

40 40 40

Al87 Ni7 Ce6

529

606

40

Al87 Ni7 Nd6

517

608

40

Al87 Ni7 Sm6

500

608

40

Mechanical Properties

Notes

= 1220 MPa ∼ 1250 MPa ∼ 1300 MPa = 1330 MPa; Hv ∼ 350 annealed up to 408 K for 60 s f = 1270 MPa; Hv ∼ 330 annealed up to 438 K for 60 s f = 1010 MPa; Hv ∼ 250 annealed up to 448 K for 60 s f = 1280 MPa; E = 72 7 GPa f = 1210 MPa; E = 75 3 GPa

Amorphous Amorphous Amorphous Amorphous

b b b f

 = 1100 Hv ∼ 3 25–5.25 GPa

 = 735 MPa a.q.; E = 50 7 GPa  = 1010MPa at 445 K, 20 min; E = 48 6 GPa  = 938 MPa E = 44 7 GPa f = 1350 MPa Hv = 470

Ref. to to to to

XRD XRD XRD XRD

and and and and

TEM TEM TEM TEM

[53] [59] [59] [52]

Amorphous to XRD and TEM

[52]

Amorphous to XRD and TEM

[52]

Amorphous Amorphous Tg = 570 K Amorphous Ball-milled powders A.q. ribbons contain Al nanocrystals Amorphous to XRD and TEM A.q. ribbons contain Al nanocrystals Amorphous Amorphous to XRD Amorphous to XRD Amorphous to XRD Amorphous to XRD Amorphous to XRD Amorphous to XRD Tg = 546 K Amorphous to XRD Tg = 551 K Amorphous to XRD and TEM Amorphous to XRD Tg ∼ 550 Amorphous to XRD Tg ∼ 540 Amorphous to XRD Tg ∼ 530 Amorphous to XRD Tg ∼ 520 Amorphous to XRD Tg ∼ 510 Amorphous to XRD Amorphous to XRD Amorphous to XRD Amorphous to XRD Tg ∼ 580 Amorphous to XRD Tg ∼ 555 Amorphous to XRD Tg ∼ 530 Amorphous to XRD Tg ∼ 505 Amorphous to XRD Amorphous to XRD Amorphous to XRD and TEM

[60, 61] [60, 61] [60, 61] [41–44] [39] [47] [28, 49] [49] [49] [49] [49] [49] [49] [49] [51] [54] [54] [54] [54] [54] [54] [54] [54] [54] [54] [54] [54] [54] [54] [63]

A.q. ribbons contain Al nanocrystals

[63]

Amorphous + intermetallic ( 0), Co75 Si10 B15 (s < 0), and Co68 Mn7 Si10 B15 (s ≈ 0) microwires. Reprinted with permission from [6], A. Zhukov et al., J. Mater. Res. 15, 2107 (2000). © 2000, Materials Research Society.

0

400

-400

0

400

d

0,0 -0,5

-2 4000

-400

0,5

0,0

0

-1,5

1,0

-0,5

-4000

b

0,5

-0,5

0,5

0

-8000

(13)

-400

0

400

-1,0

H(A/m) Figure 6. Effect of ratio  on hysteresis loop of Fe70 B15 Si10 C5 (s >0) microwire. (a)  = 063; (b)  = 062; (c)  = 048; (d)  = 026; (e)  = 016. Reprinted with permission from [4] M. Vázquez and A. Zhukov, J. Magn. Magn. Mater. 160, 223 (1996). © 1996, Elsevier Science.

Nanocrystalline and Amorphous Magnetic Microwires

- 5K - 100K - 250 K

55

0,6 0,3 0,0 -0,3 -0,6

- 40 K - 150K

50 45 40 70

75

80

85

90

95

H(A/m) Figure 7. Effect of temperature and magnetic field on velocity of domain wall propagation of Fe65 B15 Si15 C5 microwire. Reprinted with permission from [40], A. Zhukov, Appl. Phys. Lett. 78, 3106 (2001). © 2001, American Institute of Physics.

[42] but lower than in FeSiB amorphous wires prepared by quenching into water (150 ≤ v ≤ 500 m/s) [43]. Like in the case of Ni single crystals, significant deviations from the linear field dependencies vH  have been observed. The values of the magnetic field given on the horizontal axis in the Figure 7 are lower than the switching field. This means that after overcoming this first highest energy barrier corresponding to the domain wall nucleation, the domain wall propagates even in a field lower than the switching field (i.e., that the nucleation field is higher than the propagation field). The critical magnetic field, Hcr , actually can be obtained by the extrapolation of the curves that will be presented in Figure 9 at v = 0. This extrapolation gives values of Hcr around 5–10 A/m, which are one order of magnitude lower than the switching field. Hcr can be interpreted as the intrinsic coercivity of the material and characterizes the efficiency of the obstacles for the domain wall propagation. On the other hand, it was shown that the reversed domains already exist at the wire ends [44] due to the effect of the demagnetizing fields [45]. Therefore, one can assume that the appearance of the large Barkhausen jump should be related to the depinning of domain walls of such closure domains (i.e., to the critical size achieved by one of the reversed domains under the effect of the applied magnetic field).

3.1.2. Effect of Thermal Treatments (Tailoring of the Magnetic Properties) In the vicinity of the zero magnetostriction alloy composition the hysteretic magnetic properties depend strongly on the metallic alloy composition, such as shown in Figure 8. The shape of the hysteresis loop of the sample with x = 008 (Fig. 8a) suggests the presence of a transverse magnetic anisotropy. The initial magnetic permeability,
15 , estimated from the hysteresis loop is around 60 and the coercivity Hc ≈ 5 A/m. The sample with x = 009 (Fig. 8b) exhibits a rather good combination of relatively low values of coercivity (Hc ≈ 5 A/m) and relatively high initial magnetic permeability (
15 ≈ 2000). The sample with x = 010 (Fig. 8c) has a rectangular hysteresis loop (labeled as magnetic bistable behavior). This sample has Hc ≈ 25 A/m and relatively low magnetic permeability at magnetic field below coercivity (
15 ≈ 1–10).

(a)

-150 -100 -50

0

50 100 150

0,6 0,3 (b) 0,0 -0,3 -0,6 -150 -100 -50

0

50

µoM (T)

V (m/s)

60

371

0,6 0,3 0,0 -0,3 -0,6

100 150

(c) -40

-20

0

20

40

H(A/m) Figure 8. Effect of composition on hysteresis loop of (Co1−x Mnx 75 Si10 B15 (x = 008–0.11) microwires. Reprinted with permission from [7], A. Zhukov, J. Magn. Magn. Mater. 242–245, 216 (2002). © 2002, Elsevier Science.

It is worth mentioning that as in the case of amorphous ribbons heat treatment especially in the presence of the external magnetic field and/or applied stress significantly affects the magnetic behavior of amorphous magnetic materials [46, 47]. Therefore similar studies have been performed in glass coated microwires. Series of different treatments up to 473 K, such as conventional annealing (CA) and magnetic field annealing (FA), have been performed in the samples with x = 008 [37]. Figure 9a shows as an example the hysteresis loops obtained for the sample x = 008 after heat treatments at 373, 423, and 473 K. The conventional low-temperature thermal treatments (CA) (in the range of 373–473 K, 1 hour) produce small changes in the coercive field, which can be ascribed to the relaxation of internal stresses within the amorphous state. Nevertheless, when the thermal treatment was carried out under the presence of an axial magnetic field (FA), significant changes of the hysteresis loop were detected (see Fig. 9b). This change produces an increase of the initial permeability,
i , coercivity, Hc , and remanent magnetization,
0 Mr , and a decrease of the anisotropy field, HK (see Fig. 10a). The changes of the shape of the hysteresis loop with FA should be connected to the induction of magnetic anisotropy with easy axis along the longitudinal direction of the microwire. This anisotropy is developed by the combined effect of the high internal stress and the magnetic field applied during the treatment [37, 46, 47]. Similarly to conventional furnace annealing, current annealing could be used for the tailoring of the magnetic properties of amorphous microwires [48, 49]. Dependencies of coercivity on the annealing time, tann , for CA and FA with current density 227 A/mm2 for three microwires are shown in Figure 11. In the case of the Fe70 B15 Si10 C5 microwire, both treatments (CA, FA) at 30 mA (j = 227 A/mm2  caused a decrease of Hc with tann . In the case of FA, such a decrease of coercivity is more significant. In contrast, in the case of Co565 Fe65 Ni10 B16 Si11 samples, both treatments result in

Nanocrystalline and Amorphous Magnetic Microwires

0,6

373 K

0,0

0,0

-0,3

-0,3

-0,6

0,4

-150

0

150

300

tann= 0.5 hour

-300

-150

0

150

0,2

300

0,6

423 K

473 K

0,3

0,1

0,3

0,0

0,0

-0,3

-0,3

35 30

Hc, CA Hc, FA mr, CA mr, FA

0,3

-0,6

-300

40

(a)

µ0M(T)

µ0 M (T)

0,3

0,6

0,5

0,6

as-prepared 0,3

25

Hc(A/m)

372

20 15 10

0,0 250

300

350

400

450

500

0

-0,6

Tann( C)

-0,6 -300

-150

0

150

300

-300

-150

0

150

300

H(A/m) (a) as-prepared

0,3

0,0

0,0

-0,3

-0,3

µ0M(T)

0,3

8000

-300

-150

0

150

300

-300 0,6

423 K

0,3

0,0

0,0

-0,3

-0,3

-0,6

-150

0

150

-150

0

150

300

0,5 h 1,0 h 1,5 h

300

473 K

300

350

400 Tann(K)

450

250

-0,6 -300

CA:

4000

-0,6

-0,6 0,6

373 K

-300

-150

0

150

300

H(A/m) (b) Figure 9. Effect of conventional (a) and magnetic field annealing (b) on hysteresis loops of (Co092 Mn08 75 Si10 B15 microwire at different annealing temperatures. Reprinted with permission from [36], A. Zhukov et al., J. Appl Phys. 87, 1402 (2000). © 2000, American Institute of Physics.

200

Hk (A/m)

0,3

FA: 0,5h 1,0h 1,5h

(b)

µ15

0,6

0,6

12000

(c) CA 0.5 hour 1 hour 1.5 hour

150 FA

100 50 250

-0.5 hour - 1 hour - 1.5 hours

300

350

400

450

500

Tann( K) opposite effects [48]. CA treatment gives rise to a roughly monotonic decrease of the coercivity, while FA results in an increase of Hc , with a broad maximum at tann ≈ 10 min. Similarly to Fe70 B15 Si10 C5 samples, a monotonic decrease of Hc has been observed for the Co68 Mn7 Si10 B15 sample after both CA and FA treatments. Besides, as in the case of the Co565 Fe65 Ni10 B16 Si11 sample, the FA current annealing treatment results in higher Hc , as compared to the CA treatment. The observed difference between the CA and FA should be attributed to the effect of the stress+longitudinal field induced magnetic anisotropy in the last case, where the strong internal stresses contribute as the reinforcing factor. This feature implies that the application of the longitudinal magnetic field during annealing favors the formation of the internal axially magnetized core with longitudinal magnetic anisotropy. In the mean time, the CA results only in internal stress relaxation.

3.1.3. Soft Magnetic Behavior and GMI Effect Transformation of a rectangular hysteresis loop into a flat and almost unhysteretic loop is observed in nearly zero magnetostrictive compositions (Fig. 8) in the series of (Co1−x Mnx 75 Si10B15 (x = 008, 0.09, and 0.10) microwire compositions (Fig. 8 a–c) with x increasing from 0.08 to 0.10. Careful selection of the metallic alloy composition permits

Figure 10. Effect of magnetic field annealing on some magnetic properties of Co69 Mn6 Si10 B15 microwires: initial magnetic permeability,
15 (a), anisotropy field, Hk (b), and coercivity and remanent magnetization (c). Reprinted with permission from [36], A. Zhukov et al., J. Appl Phys. 87, 1402 (2000). © 2000. American Institute of Physics.

one to obtain the sample with enhanced magnetic softness and small magnetic anisotropy (the sample with x = 009 is an example). The very soft magnetic behavior of CoMnSiB microwires makes them very interesting to investigate the magnetoimpedance effect. A high GMI has been observed in Co685 Mn65 Si10 B15 microwire annealed at 100
C for 1 hour (see Fig. 12a). A maximum GMI ratio, (Z/Z)m , as well as a field of maximum, Hm , increases with the frequency of the driving current, f (see Fig. 12a) [50]. This GMI effect is extremely sensitive to the application of external tensile stresses: magnetic field, Hm , corresponding to the maximum of (Z/Z) shows a roughly linear increase with (Fig. 12b). The origin of this dependence should be related to the change of the domain structure inside the outer shell with circular orientation. As is well known, applied stress introduces a magnetoelastic anisotropy contribution which plays a very important role in the magnetization process of the metallic nucleus, even in this microwire

Nanocrystalline and Amorphous Magnetic Microwires

373 150

140 FA CA

∆Z/Z (%)

135

(a)

130 125 120 115

100 50 0

0

10

20

30

0

40

250

100

(b)

95

∆Z/Z (%)

Hc(A/m)

FA CA

85 80 75 0

10

20

30

40

50

40

500

750

H (A/m)

without stress σ=33 MPa σ=66 MPa σ=132 MPa

(b)

120

90

70

F = 1MHz F = 2MHz F = 4MHz F = 6 MHz F= 7 MHz F=10 MHz

(a)

90 60 30 0

60

0

(c)

200

400

H (A/m)

36

(c)

210

Hm/A/m)

28 24

0

10

20

30

∆Z/Zm

140

40

Hm 100

tann(min)

0

Figure 11. Comparative evolution of Hc with annealing time for CA and FA of Fe70 B15 Si10 C5 (a), Co56 5 Fe6 5 Ni10 B16 Si11 (b), and Co68 Mn7 Si10 B15 (c) microwires annealed at j ≈ 227 A/mm2 with the annealing time, tann , as a parameter. Reprinted with permission from [47], V. Zhukova et al., J. Non-Cryst. Solids 287, 31 (2001). © 2001, Elsevier Science.

exhibiting an extremely low magnetostriction constant (of around −3 × 10−7 ) [51–53]. It is remarkable to mention that according to [54, 55], the value of the dc axial field that corresponds to the maximum GMI ratio, Hm , should be attributed to the static circular anisotropy field, Hk . This argument allows us to estimate the magnetostriction constant using the dependence Hm   presented in Figure 12c and the well-known expression for the stress dependence of anisotropy field [56]: s = 
0 Ms /3dHk /d 

120

∆Z/Z(%)

FA CA

32

(14)

The Hm ( ) dependence (see Fig. 12c) is roughly linear with a slope of around 0.7 A/(m×MPa), which allows an estimation of the unstressed value of the saturation magnetostriction constant, s 0 . We have found that s 0 ≈ −2 × 10−7 , which is rather reasonable in comparison with the recently reported values measured from the stress dependence of initial magnetic susceptibility (s 0 ≈ −3×10−7 for such composition) [51, 53]. Both hysteresis loop and GMI effect also depend on the internal stresses induced by the glass coating. The strength of such internal stresses depends on the glass-coating thickness, increasing with an increase of the relative volume of

601 60

σ(MPa)

120 20

Figure 12. Effect of the frequency f (a) and applied stresses (b) on Z/Z ratio of Co685 Mn65 Si10 B15 amorphous microwire and dependence of Hm and Z/Z on applied stresses (c). Reprinted with permission from [7], A. Zhukov, J. Magn. Magn. Mater. 242–245, 216 (2002). © 2002, Elsevier Science.

the glass. Bulk hysteresis loops of three magnetically soft glass-coated Co67 Fe385 Ni145 B115 Si145 Mo17 microwires with different geometric ratios 0.78 ≤  ≤ 098 are shown in Figure 13a. As can be observed in this figure, the magnetic anisotropy field, Hk , increases with decreasing ratio  (i.e., with the increase of the glass-coating thickness). The (Z/Z)H  dependencies measured at f = 10 MHz and I = 075 mA for the samples with ratios  = 098, 0.816, and 0.789 are presented in Figure 13b. A maximum relative change in the GMI ratio, Z/Z, up to around 615% is observed at f = 10 MHz and I = 075 mA in the sample with  ≈ 098 (see Fig. 13b) [7, 57]. As may be seen from Figure 13, the field corresponding to the maximum of the GMI ratio, Hm , increases and (Z/Zm decreases with . Such Hm  dependence should be attributed to the effect of the above-mentioned internal stresses, , on the magnetic anisotropy field. Indeed, the value of the dc axial field corresponding to the maximum of the GMI ratio, Hm , should be attributed to the static circular anisotropy field, Hk [56]. The estimated values of the internal stresses in these amorphous microwires are of the order of 1000 MPa, depending strongly on the thickness of glass coating and metallic nucleus radius [5, 40]. Such elevated internal stresses give rise to a drastic change of the magnetoelastic energy, Kme ≈ 3/2s i , even for

Nanocrystalline and Amorphous Magnetic Microwires 0.6

240

0.4

200

0.2

160

0.0

120

(a) 1,5 1,0

µ0M(T)

0,0

-0,5 -1,0 -1,5 -300 -200 -100

0

100

200

H(A/m)

0

ρ=0.982 ρ=0.816 ρ=0.789

-0.4

-300

-150

0

150

300

300

(b)

70

0,6

60

450

0,3

axial magnetic field H, (A/m)

0,0

-0,3

50

(a)

500

16

3.1.4. Magnetoelastic Properties The behavior of coercivity and remanence with applied tensile stress depends strongly on the microwire composition and geometrical characteristics exhibiting a quite different character for Fe- and Co-rich compositions (Fig. 14). Generally, a proportionality of the switching field, Hs , to the square root of the applied stresses has been observed in Fe-rich compositions, as predicted by Eq. (20) (Fig. 14a). Hs   dependence in Co-rich (Co1−x Mnx 75 Si10 B15 (x = 008–011) microwires with small positive magnetostriction constant is quite different from Fe-rich microwires [7]. Besides, the evolution of Hs   depends also on the composition. In fact, some increase of the coercivity Hc with after initial roughly independent behavior has been observed for x = 011 (Fig. 14b). The sample (Co09 Mn01 75 Si10 B15 with an initially rectangular hysteresis loop shows a decrease of the coercivity and the remanent magnetization with and, finally, loses the magnetic bistability after application of certain (Fig. 14c). The estimations of the magnetostriction constant were based on the variation of the initial magnetic permeability

(c)

µ0M (T)

10

20

30

-0,3

-15

0

H(A/m)

15

50 100 150 200 250 300 350 0,6

(d)

0,3

οoM(T)

6

0,0

4

0,6

-0,3

0,3

-0,6

-15

2

0

H(A/m)

15

0,0

-0,3 -0,6 -30 -20 -10

0 -2

0

H(A/m)

0,0

8

λs

-0,6 -30 -20 -10

0,3

10

2000

small changes of the glass-coating thickness at fixed metallic nucleus diameter. Consequently, such change of the ratio  should be related to the change of the magnetostriction constant according to Eq. (14).

1500

-0,3

axial magnetic field H (A/m) (b)

Figure 13. Effect of the geometrical parameter  on hysteresis loop (a) and Z/ZH  dependencies (b) of Co6705 Fe385 Ni14 B1155 Si145 Mo165 microwires. Reprinted with permission from [57], V. Zhukova et al., IEEE Trans Magn. 38, 3090 (2002). © 2002. IEEE.

40

0,6

0

1500

20

0,0

12

0 1000

0

H(A/m)

0,3

14

-0,6

500

-20

0,6

8

0

-40

1000

µoM(T)

200

Hs(A/m)

ρ=0.98 ρ=0.816 ρ=0.789

400

-0,6

0

f=10MHz

600

300

600

µ0M (T)

-0.2

-0.6 -450

magnetoimpedance ratio ∆Z/Z, (%)

without stress

0,5

µ0M(T)

Magnetization, µoM(T)

374

0

10

H(A/m)

0

100

200

300

400

20

30

500

σ(MPa) Figure 14. Effect of microwire composition on stress dependence of coercivity: Fe65 B15 Si15 C5 (a); (Co1−x Mnx 75 Si10 B15 with x = 011 (b); x = 009 (c); and stress dependence of the magnetostriction constant for x = 009 (d). Reprinted with permission from [7], A. Zhukov, J. Magn. Magn. Mater. 242–245, 216 (2002). © 2002, Elsevier Science.

with tension in such microwires [56]. According to this method, the magnetostriction constant, s , can be evaluated from the relation s = −
0 Ms2 /3di−1 /d

(15)

where Ms is the saturation magnetization, i is the initial magnetic susceptibility, and is the applied tensile stress. The dependence of s   for the samples with 0.09 is shown in Figure 14d. It should be noted that the observed evolutions have mostly an illustrative character, since the level of the magnetic response from a single microwire is quite small. The sample with x = 009 exhibiting a positive magnetostriction constant shows also a decrease of the s with and even changes its sign at certain (around 200 MPa). The stress dependence of the magnetostriction constant, s (Fig. 14d), allows one to ascribe positive values of the

Nanocrystalline and Amorphous Magnetic Microwires

375

6

λs (x10 )

-0,4 -0,6 -0,8 -1,0 0

20

40

60

80

100

120

tann(min)

b

λs (x10 )

-0,4

6

-0,6 -0,8 30 mA 50 mA 60 mA 65 mA

-1,0 0

20

40

60

80

100

tann(min) -0,8

c

6

where 0 is the saturation magnetostriction constant without applied stresses and B is a positive coefficient of the order of 10−10 (MPa)−1 . For magnetostriction 0 of about 1 × 10−7 a stress of around 103 MPa needs to be applied to reach compensation of magnetostriction [56, 58, 59]. In fact, internal stresses induced during the preparation can reach values which indicate that high quenched-in internal stresses seem to be able to change effectively the value of the magnetostriction constant [60]. The small angle magnetization rotation method [61] also has been successfully applied to estimate the magnetostriction constant of Co-rich amorphous microwires exhibiting inclined hysteresis loops (i.e., with the magnetization rotation mechanism of the magnetization reversal) [60]. The microwires were submitted to current annealing at different annealing times, tann . The evolution of s with the annealing time (the current, i, as parameter) for selected glass-coated amorphous microwires is presented in Figure 15a–d. As can be observed, all samples exhibit negative s ranging between −09 × 10−6 and −03 × 10−6 . Under the effect of Joule heating, increasing both tann or i, s tends to increase approaching zero (see Fig. 15a–d). The general tendency of increasing of s with tann and i should be attributed to the relaxation of the internal stresses during the annealing and consequently [see Eq. (22)] with the stress dependence of the S . As has been mentioned, strong internal stresses have been predicted in glass-coated microwires due to a significant difference between the thermal expansion coefficients of the metallic nucleus and the glass coating [7]. Therefore one can expect an increase of the magnetostriction constant after annealing. Similarly to the magnetostrictive behavior widely reported [58, 59] for amorphous ribbons and conventional wires of similar compositions, rather low magnetostriction values exhibited by annealed microwire samples could be explained assuming the existence of two kind of short ordering, namely: an ordered highly anisotropic phase centered at Fe atoms with uniaxial shape and magnetic anisotropy and with positive magnetostriction, mainly due to anisotropic exchange mechanism, and a disordered phase at Co-rich atoms with negative magnetostriction. If we also assume that the positive magnetostriction phase (Fe atoms) undergoes a first order transformation from the uniaxial structural units (low temperature phase) toward a more symmetric and less anisotropic structural unit (high temperature phase), this allows us to explain the general behavior of macroscopic average magnetostriction, av s , of such Co-rich alloys. In fact, for pure Co the magnetostriction at room temperature is −4 × 10−6 and evolves with the temperature as expected from the single ion model. Therefore, the changes

71 mA 80 mA 90 mA

λs (x10 )

(16)

a

-0,2

-0,9 50 mA 60 mA

-1,0

0

20

40

60

80

100

120

80

100

120

tann(min) 0,00 -0,05 6

  = 0 − B

0,0

d

-0,10

30 mA 40 mA 50 mA

λs (x10 )

order of 10−7 for the magnetostriction constant in the sample with x ≥ 009. Such as was found in other amorphous materials, the application of tensile stresses results in a decrease of the s in the case of positive magnetostriction constant which even can change the sign of s in the sample with x = 009 when reaches some certain value (see Fig. 14d). In fact it was experimentally found in nearly zero magnetostrictive amorphous ribbons [58] that

-0,15 -0,20 -0,25 -0,30 -0,35 0

20

40 60 tann (min)

Figure 15. s tann  dependences for glass-coated amorphous Co57 Fe61 Ni10 B159 Si11 (a), Co675 Fe4 Ni15 B14 Si12 Mo1 (b), Co691 Fe52 Ni1 B148 Si99 (c), and Co695 Fe39 Ni1 B128 Si108 Mo2 (d) microwires. Reprinted with permission from [60], V. Zhukova et al., J. Phys. 34, L113 (2002). © 2002.

Nanocrystalline and Amorphous Magnetic Microwires

376

3.2. Nanocrystalline Microwires 3.2.1. Soft Nanocrystalline Microwires Properties of as-prepared microwires of “finemet”-type compositions Fe734 Cu1 Nb31 Six B225−x (x = 115, 13.5, and 16.5) significantly depend on their geometry [13, 62]. Hysteresis loops, of typically rectangular shape, have been observed in the as-prepared state. The coercivity of the sample Fe723 Cu1 Nb31 Si145 B91 strongly increases as the ratio  decreases. These results of Hc versus (d/D could be understood taking into account that the strength of internal stresses acting in the metallic nucleus increases with  [39, 40, 63]. The typical dependence of the coercive field, Hc , of Fe718 Cu10 Nb31 Si150 B91 alloy on annealing temperature with the ratio  as parameter is presented in Figure 16 [13]. Generally, a decrease of Hc has been observed at Tann below 400
C. A weak local minimum of Hc has been observed at about 400–450
C with the temperature of that minimum depending on both alloy composition and geometry. Such a decrease of Hc could be ascribed to the structural relaxation of the material remaining the amorphous character such as has been widely reported in metallic glass alloys. A small relative hardening (increase of coercivity) can be observed after annealing around 450–500
C, which could be ascribed to the very beginning of the first stage of devitrification [9–13]. It is interesting to note that the sample’s geometry affects the value and the position of the local extremes on the Hc Tann  dependence (see Fig. 16). A deeper softening (optimum softness) with a rather low value of Hc is obtained in samples treated at Tann = 500–600
C. Such magnetic softening is related to the nanocrystallization, related to precipitation of fine grains (10–15 nm) of -Fe(Si) phase within the amorphous matrix. Such interpretation has been confirmed by the X-ray diffraction studies of as-prepared and annealed at different temperatures samples [13, 14].

2500

ρ=0,282 ρ=0,359 ρ=0,41 ρ=0,467 ρ=0,646 ρ=0,871

Hc( A/m)

2000

1500

1000

500 300

400

500

600

700

800

900

1000

Tann(K)

(a) 450 400 350 300

σ (MPa) υ

of av s with the current annealing treatment repeated in this work on glass-coated amorphous microwires are assumed to be a consequence of the atomic rearrangements of topological character associated with both structural and stress relaxation processes. These processes would produce relative changes of the two mentioned volume fractions, so affecting the av s . In this way some peculiarities observed in Figure 15b–d can be roughly understood. It is worth mentioning that the high value of the internal stresses of these glass-coated microwires allows the thermal treatments to be considered as a stress annealing and, consequently, they could develop an uniaxial magnetic anisotropy [37, 53], which should play an important role on the magnetostrictive behavior. Particularly, the induction of a strong magnetic anisotropy at low annealing temperature has been observed in CoMnSiB microwires under the effect of applied axial magnetic field. Such peculiar behavior was interpreted as a reinforcing effect of the mentioned high internal stresses during field annealing of Co-rich microwires [37]. As reported previously, the magnetostriction constant can be also estimated from the stress dependence of GMI (see Fig. 12 and its description in Section 3.1.3).

250 200 150 100 50 0 0

100

200

300

400

500

600

700

800

T (ºC)

(b) Figure 16. (a) Dependence of coercivity on the annealing temperature, Tann , for Fe718 Cu1 Nb31 Si15 B91 with the ratio d/D ranging from 0.282 to 0.646. Reprinted with permission from [7], A. Zhukov J. Magn. Magn. Mater. 242–245, 216 (2002). © 2002, Elsevier Science. (b) Dependence of tensile yield on the annealing temperature in Fe718 Cu1 Nb31 Si15 B91 microwire. Reprinted with permission from [81], V. Zhukova et al., J. Magn. Magn. Mater. 249, 79 (2002). © 2002, Elsevier Science.

Excellent magnetic softness (coercivity of about 15 A/m) has been realized in Fe735 Cu1 Nb3 Six B225−x microwires with x = 135 [13, 14] at appropriate annealing conditions.

3.2.2. Semihard Magnetic Nanocrystalline Microwires An abrupt increase of Hc is shown by the samples treated at Tann above 600
C, indicating the beginning of the precipitation of second crystalline phase–iron borides (with grain size larger than 50 nm). Such beginning of the increase of Hc varies depending mainly on sample composition as well as geometry. It must be noted that for the thickest glass coating the increase of Hc appears at lower temperature, which could be related to the fact that the internal stresses induce some ordering to hinder the crystallization. It is important that the hysteresis loop in certain microwire compositions remains roughly rectangular in the whole range of annealing temperatures for certain compositions (Fig. 17) [14]. Such

15 as-prepared 10 5 0 -5 -10 -15 -500 -250 0

µ0M(T)

-4

M(e.m.u. x 10 )

Nanocrystalline and Amorphous Magnetic Microwires

10

0 -5 -10 250

500 -500 6

6 948 K

4

3

2

0

0

-3

-2

-6

-4 -250

673 K

5

9

-9 -500

377

0

250

500

-250

0

250

500

973 K

-6 -7000 -3500

0

3500 7000

H(A/m) Figure 17. Hysteresis loop of Fe718 Cu1 Nb31 Si15 B91 in as-prepared and annealed at different temperature microwires (b). Reprinted with permission from [7], A. Zhukov, J. Magn. Magn. Mater. 242–245, 216 (2002). © 2002, Elsevier Science.

temperature dependence of the hysteresis loops permits one to tailor the coercivity of microwires with rectangular hysteresis loops in a wide range of coercitivities. This fact is very important for some particular applications of glass-coated microwires (see Section 5). The effect of annealing temperature on the coercivity, Hc , of the alloy Fe723 Cu1 Nb31 Si145 B91 with ratio  as parameter is shown in Figure 18. A sharp magnetic hardening (increase of coercivity) can be observed after annealing around 500– 550
C. It should be indicated that such maximum takes place at the same range of the annealing temperature as the first small increase of Hc in Fe734 Cu1 Nb31 Six B225−x (x = 115 and 13.5) related to the first recrystallization process (compare with Fig. 16a) [3, 11, 12, 62, 64]. This strong magnetic hardening is followed by new magnetic softening with an increase of Tann above 550
C and consequent new magnetic hardening at Tann > 650
C which is accompanied by deterioration of mechanical properties.

In the case of Fe734 Cu1 Nb31 Si134 B91 samples such strong magnetic hardening is not observed (see Fig. 16). X-ray analysis of Fe723 Cu1 Nb31 Si145 B91 does not detect a presence of crystalline phases in as-prepared state as well as after annealing at 550
C. On the other hand, transmission electron microscopy (TEM) diagrams of the sample annealed at 550
C permit one to detect a small amount of fine grains of -Fe, -Fe, and -Fe(Si) [62]. The TEM image presented in Figure 19 shows that the average grain size of such crystallites is around 20–70 nm in annealed sample at 550
C. Observed structural features permit one to correlate observed magnetic hardening with precipitation of fine crystallites. Such a difference in magnetic behavior with conventional finemet-type microwires can be attributed to different alloy compositions as well as to high internal stresses. It is well known that the best magnetic softness is achieved when the nanocrystalline structure consisting of small -Fe(Si) grains and amorphous matrix has a vanishing magnetostriction constant. It is possible that even a small change of the alloy composition does not permit one to achieve such a vanishing magnetostriction constant. On the other hand, strong internals stresses due to glass coating can result in a change of structure of the precipitating fine grains. Thus, strong internal stresses (about 103 MPa or even more) are mainly induced by the difference in the thermal expansion coefficients of the glass and the metallic nucleus. It is well known that internal strains of different nature can be the origin of martensite-type transformation in alloys of Fe. Probably, the strong internal stresses induce a precipitation of the -Fe fine grains instead or apart from -Fe(Si) grains during the first stage of the crystallization process. Particularly, the presence of crystalline -Fe could be the reason for the observed magnetic hardening [62]. As a consequence, the origin of such strong magnetic hardening at low annealing temperatures without deterioration of mechanical properties could be ascribed to some peculiarities of the first recrystallization process under the effect of strong internal stresses induced by glass coating and differences in the alloy composition.

100 ρ= ρ= ρ= ρ= ρ=

HC (Oe)

80 60

0.385 0.333 0.136 0.093 0.047

40 20 0 0

200

400

600

800

Tann (˚C) Figure 18. Coercivity dependence with the annealing temperature of Fe723 Cu1 Nb31 Si145 B91 microwire. Reprinted with permission from [62], J. González et al., IEEE Trans. Magn. 36, 3015 (2000). © 2000, IEEE.

Figure 19. TEM diagram of Fe723 Cu1 Nb31 Si145 B91 microwire annealed at 550
C. Reprinted with permission from [62], J. González, IEEE Trans. Magn. 36, 3015 (2000). © 2000, IEEE.

Nanocrystalline and Amorphous Magnetic Microwires

3.3. Granular Glass-Coated Microwires 3.3.1. Structure and Phase Composition Granular systems formed by inmiscible elements (Co, Fe, Ni)–(Cu, Pt, Au, Ag) have been recently introduced [21, 65–67]. Such immiscible alloys exhibit unusual magnetic properties such as the GMR effect related to mixed ferromagnetic–paramagnetic microstructure and scattering of the electrons on grain boundaries between these two phases. A rapid quenching technique such as melt spinning has been employed recently for fabrication of Co–Cu ribbons [68]. The high quenching rate characteristic of the melt spinning method has been used for fabrication of metastable crystalline materials when the crystalline phases, stable at high temperature, can be quenched-in at room temperature. In this case the GMR and enhanced coercivity were obtained generally after recrystallization of such metastable phases. Recently, the Taylor–Ulitovsky technique has also been employed to obtain granular glass-coated microwires (km long) [21, 69] from inmiscible elements. Such granular structure has been achieved mainly by decomposition of metastable crystalline phases. A high quenching rate is also useful for fabrication of metastable crystalline materials when the crystalline phases, stable at high temperature, can be quenched-in at room temperature. Figure 20 shows the X-ray diffraction (XRD) analyses for the as-prepared Cox –Cu100−x microwires, which confirms the presence of a single phase for x = 10 with a lattice parameter a = 036 nm, while in the other compositions, with x > 10%, two phases were detected. It should be mentioned that Cox Cu100−x alloy ribbons obtained by rapid solidification were characterized by X-ray diffraction by various authors [67, 70, 71]. It was found by the XRD method that, in the as-quenched Cox Cu100−x ribbons, single phase facecentered cubic (fcc) peaks appear for x < 20% [67] (sometimes only for 35%. Since the lattice parameter was larger than for pure Co (a = 035447 nm) and smaller than that of pure Cu (a = 03615 nm), the same dissolution of Co atoms in the Cu matrix has been proposed. In any case, fcc Co particles were also reported in [72]. 500

1,0

as-prepared 0,5

0,0 1,0

o

700 C

0,5

0,0 1,0

o

o

800 C

∆

Intensity (a.u.)

x=50

The experimental data on X-ray diffraction of microwires from inmiscible elements are generally in agreement with those previously reported for ribbons with small Co concentrations, when single phase peaks have been observed at x < 10%. Indeed, the presence of two phases can be deduced from careful analysis of the maxima for x > 10%, with interatomic spacings of 0.209 nm (Cu) and 0.206 nm (Co). Nevertheless, it is important to mention that the coexistence of two phases is found even for x > 35%. Like in Cox –Cu100−x microwires with x > 10%, the XRD analyses for the as-prepared Cu–Fe microwires showed two maxima in the diffraction peak with the lowest diffraction angle corresponding to the Cu and the body-centered cubic -Fe phases. In some cases this granular structure is metastable at room temperature and the consequent heat treatment results in the recrystallization of this structure with the formation of stable phases. At certain conditions of such heat treatment this new granular structure can exhibit interesting magnetic and transport properties. As an example, Figure 21a–c shows the X-ray diffraction patterns for the Co29 Ni25 Cu45 Mn1 sample, in its asprepared state and after thermal treatment at two different temperatures Tann . In the as-prepared microwire, quenched from a high temperature, only a single phase, with a lattice parameter a = 03573 nm, was found (Fig. 21a). When the sample was heated at high temperatures, this metastable phase started to decompose. This can be seen in the sample treated at 973 K, where the segregation mechanism is

Relative Intensity (I/Imax)

378

250

x=15 0,5

x=10 0 30

0,0 40

60

45

70

80

90

100

90

Angle(2Θ)

Figure 20. X-ray diffraction pattern of Cox Cu100−x microwires with x = 10 15, and 50%. Reprinted with permission from [21], A. Zhukov et al., J. Appl Phys. 85, 4482 (1999). © 1999, American Institute of Physics.

Angle (2 θ ) Figure 21. X-ray scan of as-prepared and annealed Co29 Ni25 Cu45 Mn1 microwires. Reprinted with permission from [21], A. Zhukov et al., J. Appl. Phys. 85, 4482 (1999). © 1999, American Institute of Physics.

Nanocrystalline and Amorphous Magnetic Microwires

2000

Cu/d=2.09Å Co/d=1.25Å Co/d=2.05Å Cu/d=1.28Å Cu/d=1.81Å

1500

I (a. u.)

this peak allows the detection of a second small and broad maximum near this first peak which could be attributed to Co crystallites embedded in the Cu matrix. It can be observed that the higher the value of , the more intense this second peak. The observed second crystallization peak corresponds to fcc metastable Co, as has been previously observed in ribbons [67, 70, 71]. Similar behavior in the XRD patterns was observed for microwires of composition Co19 Cu80 Ni1 with different  values (see Fig. 23). Inside the diffraction peak with the lowest diffraction angle two maxima were detected: the first one can be attributed to an overlapping of two peaks corresponding to interatomic spacings of 0.209 nm (Cu) and 0.208 nm (Cu38 Ni) (the technique can hardly resolve these differences) and the second one corresponding to an interatomic spacing of 0.205 nm (Co) [74]. Figure 23 shows this first peak for the three values of the  parameter, which indicates its sensitivity to the geometry. This peak, ρ = 0.13

400

0 43

43.5

44

44.5

45

2θ

Co/d=1.77Å

1000

Cu80Co19Ni

1200

800

I (a. u.)

I (a. u.)

not yet complete (Fig. 21b). After annealing at 1073 K the sample shows the equilibrium phases, consisting of a copperrich matrix (a = 03591 nm) with Co-rich particles (a = 03545 nm) (Fig. 21c) [68, 69]. Annealing at higher temperature results in a very marked embrittlement of the glass coating. For alloys in the Co–Ni–Cu system containing more than 20% Ni a continuous series of (fcc) solid solutions is found to be stable at high temperatures [73]. When the alloy is quenched from the melt during the production of the microwire, a metastable cubic phase is found at room temperature. On heat treating this material, the segregation takes place and the metastable phase starts to decompose into a paramagnetic Cu-rich phase with a larger lattice parameter than the precursor phase, and a fine grained Corich phase with a smaller lattice parameter. It is well known that the presence of the glass coating introduces strong internal stresses inside the metallic nucleus due to the difference in the thermal expansion coefficients of metallic nucleus and glass coating [5, 38, 39]. The strength of such internal stresses depends on the metallic nucleus diameter as well as on the glass-coating thickness [38, 39]. Therefore, it is expected that the geometry affects the structural and magnetic features of glass-coated microwires. X-ray diffraction patterns for the as-prepared Co20 Cu80 microwires with different values of the  show peaks corresponding to two crystalline phases. Figure 22 shows these XRD patterns for the three microwires in this system with different values of . The diffraction peak with the lowest diffraction angle corresponds to the Cu matrix with an interatomic spacing, d, of 0.209 nm. A detailed examination of

379

Cu80Co19Ni

1200

ρ = 0.20

800

500

I (a. u.)

Cu80Co20 ρ = 0.09

400

0 6000

Cu80Co20 ρ = 0.51

0 43

43.5

44

44.5

45

2θ

4000

I (a. u.)

1500

I (a. u.)

2000

Cu80Co19Ni

ρ = 0.50

1000

0 5000

Cu80Co20 ρ = 0.67

4000

500

3000 2000 1000

0 43

0 40

45

50

55

60

65

70

75

80

43.5

44

44.5

45

45.5

46

2θ

2θ Figure 22. X-ray scan of Co20 Cu80 microwires with different ratios . Reprinted with permission from [72], J. González et al. J. Magn. Magn. Mater. 221, 196 (2000). © 2000, Elsevier Science.

Figure 23. First crystalline peak and the corresponding fittings to a sum of two Gaussian functions for Co19 Ni1 Cu80 microwires with different ratios . Reprinted with permission from [72], J. González et al., J. Magn. Magn. Mater. 221, 196 (2000). © 2000, Elsevier Science.

Nanocrystalline and Amorphous Magnetic Microwires

80

80

60

60

Hc(Oe)

% Co- phase

where Icorr denotes the total measured diffracted intensity corrected for background and Icorr Co Fe is the diffracted intensity corrected for background, corresponding to the peaks associated with Co or Fe phases. The dependence of the Co particle content (in percentage) on the  parameter for Co19 Cu80 Ni1 and Co20 Cu80 microwires is shown in Figure 24. An increase of the Co-phase content with  can be observed in the Co20 Cu80 microwires, particularly at high values of . This effect should be related to the strength and complexity of the internal stresses in the metallic core, arising from the insulating glass coating. It is reasonable to assume that these internal stresses increase as the  parameter decreases [38, 39] and, consequently, they could hinder the segregation of the magnetic Co phase. Surprisingly the Co19 Cu80 Ni1 alloy does not show such continuous behavior and the Co content is much higher than in CuCo microwires: this is evident in the raw diffraction patterns where the peak corresponding to the Co phase is much more intense. Figure 25 shows the variations in the mean diameter  of Cu and Co particles or grains as a function of the parameter  for Co20 Cu80 and Co19 Cu80 Ni1 alloys. From these results the dependence of the grain size seems to be quite insensitive to  in both alloys, although the presence of Ni increases significantly the size of such Co and Cu particles. The last two cases show that the presence of small amounts

Co80Cu19Ni1 40

Co80Cu20

20

40

20

3.5

Cu-phase Co-phase

3

Cu80Co19Ni 2.5

2

1.5

Cu80Co20 1 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

d/D Figure 25. Effect of geometry on average grain size of Co20 Cu80 and Co19 Ni1 Cu80 microwires. Reprinted with permission from [72], J. González et al., J. Magn. Magn. Mater. 221, 196 (2000). © 2000, Elsevier Science.

of Ni atoms drastically changes the structural characteristics of these alloys. The overview of Figures 20–25 indicates the sensitivity of the structure either to the composition (substitution of one atom of Co by Ni) or to the geometry (parameter ) or both. It must be pointed out here that the results for the  dependence of the Cu and Fe grain sizes and for the amount of Fe phase for the two different CuFe compositions is consistent with the fact that the different compositions show the same variations.

3.3.2. Effect of Composition and Geometry on Magnetic Behavior The hysteresis loops, at room temperature, for three different compositions in the series Cox -Cu100−x are presented in Figure 26. As can be observed, in as-prepared samples the saturation magnetization decreases and both the magnetic anisotropy field and the coercive field increase, as the Co content increases. As can be expected, the high saturation magnetic field of the samples with small Co content could be explained considering that Co precipitates behave as small superparamagnetic particles or as isolated spherical ferromagnetic particles. In the second case the magnetic

0,04

CoxCu1-x

X=70

0,02

M(e.m.u)

corresponding to the Cu38 Ni new phase in these samples, is accompanied by the presence of new peaks juxtaposed to the 0.181 and 0.128 nm (it is very clear in this last case) Cu spacings appearing in Figure 22 for the Co20 Cu80 system. The proportions of each phase were calculated, for each sample, from the relative area under all the peaks measured over all the 2 region of measurement. When relative peaks overlapped (which occurred in most cases), the experimental signal was fitted to the addition of two Gaussian functions in order to obtain the characterizing values of the position of the maximum and the width of the peak. Thus, the Co or Fe phase content in each sample was calculated as 80 Icorr Co Fe d2 (17) %Co Fe = 40 80 I d2 40 corr

log ∆ / nm

380

X=50 X=10

0,00

-0,02 -0,04

0,0

0,2

0,4

0,6

ratio ρ

-1000

-500

0

500

1000

H(Oe)

Figure 24. Effect of geometry on Co-phase content and coercivity in Co20 Cu80 and Co19 Ni1 Cu80 microwires. Reprinted with permission from [72], J. González et al., J. Magn. Magn. Mater. 221, 196 (2000). © 2000, Elsevier Science.

Figure 26. Hysteresis loops of Cox Cu100−x microwires. Reprinted with permission from [21], A. Zhukov et al., J. Appl. Phys. 85, 4482 (1999). © 1999, American Institute of Physics.

Nanocrystalline and Amorphous Magnetic Microwires

381

anisotropy field can be related to the demagnetizing factor of such particles, being in good accordance with experimental data for Co20 Cu80 particles (Hk =
o Ms /3). It should be also noted that the magnetization behavior of ribbons of similar composition is still a topic of discussion and sometimes it is interpreted as being superparamagnetic [67] and sometimes not [65]. It may be argued that the sample with x = 50 is not entirely superparamagnetic since its coercivity as well as the remanence shows nonzero values being, however, relatively small. The variations of the magnetization with the Co content can be explained on the basis of two contributions, namely: one coming from the superparamagnetic particles and other from the ferromagnetic contribution which originates from large Co grains or agglomerates of smaller Co particles [65–69]. The first contribution is negligible for a large Co content (that is, the x = 70 sample). Besides the large ferromagnetic grains, a source of the coercivity can also be, in the case of x = 10, the interactions between superparamagnetic particles. The shape of the hysteresis loop seems to be rather insensitive to the  parameter: the magnetic anisotropy field remains almost unmodified by changes of the  parameter. In contrast, considerable changes in the coercive field have been detected when the  parameter changes. These changes are shown in Figure 24, together with changes of average grain size with . Certain correlations, such as decrease of coercivity with increase of Co phase (Fig. 24) content and grain size (see Fig. 25), can be outlined. The hysteresis loops of as-prepared Fe30 Cu70 samples for two different  values can be seen in Figure 27. The reduction of the  parameter leads to important changes in the hysteresis behavior. In fact, for the lower value of  = 03 the hysteresis loop may indicate the presence of two magnetic phases with two different values of anisotropy field, one high and one low (see Fig. 27). On the other, hand, a single magnetic phase with enhanced anisotropy field can be deduced from the magnetization curve of the sample with the larger value of  = 06 [72]. The coercive field is smaller in the sample with the lower . As in Co–Cu microwires, an effect of internal stresses on the crystallization process can be deduced.

Comparison with structural analysis indicates that for Fe30 Cu70 microwires,  = 03, where the coexistence of two magnetic phases is suggested, corresponds to a maximum in the observed content of the Fe phase [74].

3.3.3. Effect of the Thermal Treatment on Magnetic Properties In order to achieve higher coercivity, the different families of microwires were submitted to thermal treatments (up to 800
C, for 1 hour). After the treatments, the magnetic properties of some samples underwent significant changes. Comparative results on the effects of annealing temperature, Tann , on coercivity of all studied microwires are shown in Figure 28. The annealing temperature dependence of the coercivity can be explained qualitatively, by taking into account the structure of the as-prepared samples. It is evident that for the samples having a two-phase structure in the as-prepared state, no significant changes of the magnetic properties were observed. But for single phase as-cast microwires (Co10 Cu90 and Co29 Ni25 Cu45 Mn1  a substantial increase of the coercivity is observed after annealing above 500
C [21]. Therefore, a precipitation of Co or Ni crystallites from the metastable Cu-rich solid solution can be responsible for the enhancement of the coercivity upon annealing [67]. The solubility of Co and Ni in Cu decreases as the temperature decreases and, at room temperature, it is quite small (less than 0.1% for Co). Consequently, these elements are almost inmiscible at room temperature. Therefore, a single phase solid solution is unstable at room temperature and the annealing results in its decomposition. A magnetic hardening (up to 200 Oe) is observed for the Cu90 Co10 microwires after annealing temperatures of around 500
C. Most significant magnetic hardening was observed for the Co29 Ni25 Cu45 Mn1 microwire. The room temperature hysteresis loop of Co–Ni–Cu–Mn microwires is presented, as an example, in Figure 29a, after annealing for one hour at various temperatures. The variation of the coercivity with the annealing temperature for the different microwires was obtained from such curves. The as-prepared Co29 Ni25 Cu45 Mn1 sample shows a relatively low coercivity (50–100 Oe). When raising the annealing temperature to 700
C, a strong increase in Hc is obtained, reaching 800

1,0

Co10Cu90 Co50Cu50 Co29Ni25Cu49Mn1 (FeSiBC)50Cu50

Cu70Fe30

600

Hc (Oe)

M(emu)

0,5

0,0

-0,5

ρ=0.6 ρ=0.3

400

200

-1,0

0 -10000

-5000

0

5000

10000

H(Oe) Figure 27. Hysteresis loop of Fe30 Cu70 microwires with different ratios. Reprinted with permission from [72], J. González et al., J. Magn. Magn. Mater. 221, 196 (2000). © 2000, Elsevier Science.

0

200

400

600

800

o

Tann( C) Figure 28. Effect of annealing temperature on coercivity of different microwires. Reprinted with permission from [21], A. Zhukov et al., J. Appl. Phys. 85, 4482 (1999). © 1999, American Institute of Physics.

Nanocrystalline and Amorphous Magnetic Microwires

382 1,0

o

600 C 0,5 0,0 -0,5

M / Ms

-1,0 1,0

o

700 C

0,5 0,0 -0,5 -1,0 1,0 o

800 C 0,5 0,0 -0,5 -1,0 -10

-8

-6

-4

-2

0

2

4

6

8

10

Applied Field (kOe) (a) 493

Resistance (Ψ)

492

491

As-prepared

4. MECHANICAL PROPERTIES

490

124.8

124.6

124.4

of a paramagnetic Cu-rich phase and a fine grained ferromagnetic Co phase; in this stage the coercivity increases quickly. Increasing the annealing temperature further, the equilibrium of phases is reached more rapidly, the grains start to grow, and the coercivity decreases. These results are in agreement with the magnetic hardening in bulk Co–Ni– Cu permanent magnet alloys, and the maximum value of the coercivity obtained after the annealing at 700
C for one hour agrees with that previously reported [73]. Magnetoresistance (MR), up to about 8% has been recently found in granular Fe, Ni, Co-rich microwires [75, 76]. This MR correlates quite well with the structure and the magnetization curves. Thus, the micro-X-ray absorption near edge structure (micro-XANES) spectroscopy reflects that the MR is related to fcc small grains of Fe–Ni ( 1 phase) embedded in fcc Cu ( 2 phase). By the microXANES method it was shown that Fe atoms remain in the fcc 1 phase even after the annealing. These data are consistent with the phase diagram of Fe–Ni–Cu alloys and with the similar results on the fcc small grain Co in Co–Cu and/or Co–Ni–Cu microwires. In the case of Co–Ni–Cu–Mn microwires field dependence of MR is quite different for the as-prepared and heat treated samples, reflecting also the difference of their structure and magnetization curves (see Figs. 21, 29a). Only small hysteresis correlated with low coercivity has been observed in as-prepared sample, while significant hysteresis with the MR maximum at around ±1200 Oe is observed in the sample annealed at 700
C. The relative change of the resistance under magnetic field in Co–Ni–Cu–Mn microwires is around 4% (Fig. 29b).

Annealed 0 at 700 C -2000

-1000

0

1000

2000

H(Oe) (b) Figure 29. Hysteresis loops of Co29 Ni25 Mn1 Cu45 microwires measured at different annealing temperatures (a) and magnetoresistance (b) measured at 100 K in as-prepared and annealed at 700
C microwires. Reprinted with permission from [72], J. González, et al., J. Magn. Magn. Mater. 221, 196 (2000). © 2000, Elsevier Science.

the maximum value of 700 Oe for the Co29 Ni25 Cu45 Mn1 microwire. A further increase of the annealing temperature results in a decrease of the coercivity. The largest reduced remanence ratio Mr /Ms = 05 is also found after annealing at 700
C and the estimated saturation magnetization for this sample is about 3.6 kG. As has been mentioned previously, the structure of these annealed samples consists

Most early reports on glass-coated microwires were devoted to their mechanical properties [77–80]. Thus, the effect of annealing and crystallization on tensile strength and Young modulus was studied in amorphous Fe-rich and stainless steel microwires produced by the Taylor–Ulitovsky technique [78, 79]. High tensile strength (around 250 kg/mm2  was observed in amorphous Fe80 P16 C3 B1 microwires as compared with the crystalline microwires (around 130 kg/mm2 . Such tensile strength is found to decrease, increasing the metallic nucleus diameter. This tendency has been attributed to the higher cooling rate with decreasing metallic nucleus diameter. On the other hand, the Young modulus of amorphous samples (8000 kg/mm2  is found to be much lower than that of crystalline (13,000 kg/mm2  samples of the same composition. Fracture surfaces of the amorphous microwires consist of a smooth region produced by shearing and a vein pattern [79]. It was observed later that additions of Si, Co, or Cr result in increasing averaged tensile strength [80]. Recently interest in studies of mechanical properties has been renewed mostly due to the promising technological applications of glass-coated microwires. In this way, tensile strength and fracture character have been recently studied in CoMnSiB microwires [53]. A wide number of samples of the CoMnSiB series have been studied and the average load for fracture has been found to range between 20 ± 3 g, with a maximum of 30 g and a minimum of 15 g. The tensile strength is then 624 ± 94 MPa, with maximum and minimum

Nanocrystalline and Amorphous Magnetic Microwires

values of 936 and 468 MPa, respectively. The tensile strength in the amorphous state seems to be due to the metallic nucleus of the microwire. The glass coating does not seem to contribute significantly in resistance to fracture. The glass around the point of fracture breaks, probably because of the sound wave produced by the rupture or the metallic nucleus, which is then visible. Moreover, samples with higher tensile strength seem to break in a slightly different mode than the ones breaking under lower stress. Thus sometimes the fracture plane is basically perpendicular to the axis of the microwire. On the other hand, another group of samples broken under stresses over the average show a more complex situation. These samples show some structure in the surface of the metallic nucleus of the microwire that could have improved the adhesion of the metallic nucleus to the coating and increased strength slightly. An interesting correlation of mechanical and magnetic properties has been observed in finemet-type microwires during the devitrification [81]. As mentioned previously, annealing of initially amorphous Fe734 Cu1 Nb31 Si134 B91 microwires results in the two-step crystallization process. First fine -Fe(Si) nanocrystals of grain size around 10 nm have been precipitated at temperatures around 550–600
C. At temperatures above 600
C, the beginning of the precipitation of iron borides (with grain size larger than 50 nm) has been found [81]. Such as described in Section 3.2 typically a decrease of coercivity has been observed at annealing temperatures below 650
C with two minimums of coercivity, Hc , at about 400–450 and at 550–650
C. Such soft magnetic behavior has been ascribed to the first crystallization process leading to the precipitation of fine nanocrystals -Fe(Si) of grain size around 10 nm with 70–80% of relative volume, as has been widely reported for finemet ribbons (see for example [9–12, 14]). An abrupt increase of the coercivity is shown by the samples treated at temperature above 600
C. The beginning of such an increase should be connected to the precipitation of iron borides (with grain size larger than 50 nm) which implies a magnetic hardening character. Tensile yield, y , has been measured for samples annealed at different temperatures. These results are presented in Figure 16b. Maximum y was found for the as-fabricated sample (402 MPa). Then, a certain correlation can be outlined with respect to the dependence of coercivity on annealing temperature. Like in the case of coercivity, tensile yield, y , decreases with Tann with a small local minimum around Tann = 450
C. Some increase of y has been observed at Tann = 575
C. Finally strong deterioration of the tensile yield has been observed at Tann > 650
C and a small increase at Tann = 700
C. The samples annealed at the two highest temperatures were extremely brittle. The y results in Figure 16b for these types of microwires correspond only to the maximum measurable value. In most opportunities, samples would fracture even under very careful handling. The character of the sample fracture has also been studied for the samples annealed at a few annealing temperatures by means of scanning electron microscopy. The annealing does not deteriorate significantly the glass coating as well as the metallic nucleus. The fracture character is complex.

383 The metallic nucleus seems to be responsible for the tensile yield, with the possible contribution of plasticity. It is possible that the thermal treatment deteriorates the glasscoating interface due to the difference in thermal expansion coefficients, having a slight effect on the tensile yield. For the annealing temperatures higher than 600
C, the character of the fracture is different. If the metal core is now brittle, the glass coating can be responsible for the sample fracture and the sample breaks immediately after the coating itself. The correlation of the mechanical properties with magnetic behavior is to be related to structural changes introduced by the annealing. The precipitation of the second crystalline phase leads to a completely crystalline structure, introducing strong internal stresses and change in the character of the chemical bonding. This crystallization process makes the sample brittle [9–12].

5. APPLICATIONS The latest advances in magnetic materials are based on the miniaturization of modern magnetic materials. In this sense tiny metallic wires (of the order of 3 to 30
m in diameter) covered by an insulating glass coating are quite suitable for the sensor applications. Such wires possess a number of excellent magnetic properties such as magnetic bistability with the extended range of the switching fields, enhanced magnetic permeability, GMI effect, and high stress sensitivity of the magnetic parameters (switching, field, GMI effect, magnetic permeability, etc.), which can be tailored by varying the metallic alloy composition, sample geometry (metallic nucleus diameter and glass coating thickness), and conditions of heat treatment. Several examples of applications of tiny glass-coated microwires will be reviewed. A magnetoelastic sensor of the level of liquid can be designed using the very sensible stress dependence of the hysteresis loop and particularly of the coercivity in nearly zero magnetostriction CoMnSiB microwires (see Fig. 14c). Such a sensor essentially consists of a piece of (Co09 Mn01 75 Si10 B15 microwire surrounded by primary and secondary coils [7, 82]. The sample is loaded with approximately 10 g and therefore exhibits a flat hysteresis loop. The weight is attached to the bottom of the sample. When a liquid arrives to cover the weight, the actual stress, affecting the sample, decreases giving rise to the appearance of the rectangular hysteresis loop. The principle of the work is based on the change of the voltage of the secondary coil, which increases drastically when the hysteresis loop of the sample C became rectangular after essential decrease of the stress. A simple circuit including the amplification of the signal and alarm set was used to detect changes of voltage in the secondary coil under the change of the tensile stresses due the floating effect of the weight on the liquid. The other example is based on the wide range of coercivity which can be obtained in microwires due to its strong dependence on the geometric dimensions and heat treatment. It was realized in the method of magnetic codification using magnetic tags [7, 83]. The tag contains several microwires with well-defined coercivities, all of them characterized by a rectangular hysteresis loop. Once the magnetic tag is submitted to the ac magnetic field, each particular

Nanocrystalline and Amorphous Magnetic Microwires

384

Air Microwire with GMI DC Magnetic field

V

Generator of AC current

DC output

A sail

(a) AC voltage (peak to peak) across the microwire (V)

microwire remagnetizes at a different magnetic field giving rise to an electrical signal on a detecting system (see Fig. 30). The extended range of switching fields obtained in Fe-rich microwires gives the possibility to use a large number of combinations for magnetic codification. The high sensitivity of the GMI ratio to quite small values of mechanical load makes this stress sensitive GMI effect very interesting for practical purposes. Figure 30 shows a magnetoelastic sensor of air flux based on GMI exhibited by nearly zero magnetostrictive Co685 Mn65 Si10 B15 microwire. The principle of work of this sensor device is briefly described [7, 84]. The microwire has a rather high dc electrical resistance per length owing to its tiny dimensions. Therefore, large changes (about 130%) of the magnetoimpedance could induce rather large changes of the ac voltage under mechanical loading. Indeed, under the effect of tensile stresses, the GMI ratio at fixed applied field, H , decreases giving rise to a significant change of the ac voltage between the sample’s ends. A dc magnetic field corresponding to the maximum ratio (Z/Zm without stresses has been applied by means of a small solenoid 7 cm in length and 1 cm in diameter. In the case of a driving current with frequency 10 MHz and amplitude 1.5 mA supplied by an ac current generator, the change of ac voltage (peak to peak) between the ends of the sample is around 3.5 V for small mechanical loads attached at the bottom of the microwire (see calibration curve in Fig. 31b). This huge change presented at the output permits one to use this kind of sensor in different technological applications related to the detection of small mechanical stress. The observed magnetic response on the external variable stresses can be used in many applications to detect different temporal changes of stresses, vibrations, etc. As an example we introduce a “magnetoelastic pen” which can be used for identification of signatures [7, 85]. It is well known that the signature of each person can be represented by typical series of the stresses. The sequence and strength of those stresses are characteristic features of any personal signature. So temporal changes of the stresses while signing can be used for the identification of signature itself. We have used this behavior and designed a setup consisting of a ferromagnetic bistable amorphous wire with positive magnetostriction, a miniaturized secondary coil, and a simple mechanical system inside the pen containing a spring, which transfers the applied stresses to the ferromagnetic wire (see Fig. 32).

10

9

8

7

6

0

1

2

3

4

P (g)

(b) Figure 31. Schematic representation of the magnetoelastic sensor based on stress dependence of GMI effect (a) and its calibration curve (b). Reprinted with permission from [7], A. Zhukov et al., J. Magn. Magn. Mater. 242–245, 216 (2002). © 2002, Elsevier Science.

The resulting temporal dependence of the stresses, corresponding to a signature, is reproducible for each individual person. The main characteristics of this dependence are time of signature, sign, and sequence of the detected peaks.

(a) Wire

Spring Pick up coil

(b) 1st signature

M

H Hc3 Hc2 Hc1

Hc2 Hc1

t1

t2

t3

t

H V Hc3

t

0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 10

Digital Codes

Voltage, V x 10

5

0.2

0.1

0.0 4 -0.2

2nd signature

6

-0.3 -0.4

t

Figure 30. Schematic representation of the encoding system based on magnetic bistability of the microwires. Reprinted with permission from [6], A. Zhukov et al., J. Mater. Res. 15, 2107 (2000). © 2000, Materials Research Society.

2

4

Time, s

Figure 32. Schematic representation of the magnetoelastic pen (a) and two magnetoelastic signatures (b). Reprinted with permission from [7], A. Zhukov et al., J. Magn. Magn. Mater. 242–245, 216 (2002). © 2002, Elsevier Science.

Nanocrystalline and Amorphous Magnetic Microwires

Examples of two magnetoelastic signatures corresponding to the same person are shown in Figure 32b.

6. CONCLUSIONS The following conclusions can be summarized: The Taylor–Ulitovsky technique can be fruitfully employed to fabricate technologically attractive ferromagnetic tiny amorphous, nanocrystalline, and granular system metallic wires covered by an insulating glass coating. A single and large Barkhausen jump is observed for soft magnetic microwires with positive magnetostriction. Negative magnetostriction microwires exhibit almost unhysteretic behavior. The origin of such magnetic bistability is explained in terms and nucleation and domain wall propagation mechanism. In this way the appearance of a single and large Barkhausen jump is related to the fact that the nucleation magnetic field is higher than the propagation field. The domain wall velocity measured at temperatures 5–300 K in the range of applied magnetic field of 65–100 A/m in amorphous Fe-rich microwire is found to be much higher than in Ni single crystals but slightly lower than in conventional amorphous wires due to the strong internal stresses. An increase of the domain wall velocity has been found with increasing temperature and magnetic field. The internal stresses frozen-in during the fabrication process are much stronger than for “in-rotating-water quenching.” As a result, the coercivity decreases with the ratio  = d/D. Significant changes of the soft magnetic properties have been observed in Fe- and Co-rich microwires after different treatments (conventional and current annealing with or without axial magnetic field). Upon heat treatment, FeSiBCuNb initially amorphous microwires devitrificate into nanocrystalline structure. Such devitrification permits one to obtain enhanced magnetic softness in microwires of certain compositions. On the other hand at certain conditions the magnetic bistability has been observed even after the second crystallization process, allowing one to increase the switching field by more than two orders of magnitude up to 5.5 kA/m. The experimental results on the soft magnetic properties obtained in Fe- and Co-rich microwires (submitted to conventional and current annealing with or without field) can be explained as a consequence of the induced magnetic anisotropy. This anisotropy is arising from the counterbalance between internal quenched-in stresses owing to the difference in thermal expansion coefficients of the metal and the glass. This induced anisotropy should be understood as originating from the simultaneous action of the large internal stresses and the axial applied magnetic field. A stress dependent GMI effect has been found under adequate treatment. Enhanced magnetic softness (initial permeability,
1 , up to 14,000) and GMI effect (up to 600%) were observed in amorphous Co-based microwires with nearly zero magnetostriction after adequate annealing. Large sensitivity of GMI and magnetic characteristics on the external tensile stresses have been observed. The correlations between their structures and magnetic properties and the geometry (ratio ) and compositions of Co–Cu, Fe–Cu, and Co–Ni–Cu microwires have been studied. The microstructural properties (interatomic distance,

385 lattice parameters, grain size, segregation, and relative percentage of phases) are strongly dependent on the geometrical parameters, that is, the relation rate of the diameter of the metallic core relative to the total diameter of the microwire. This effect should be attributed to the internal stresses within the metallic core arising from the different thermal expansion coefficients of the glass coating and the core. On the other hand high quenching rate permits one to obtain microwires from immiscible elements in a metastable state. These microwires can exhibit hard magnetic behavior and magnetoresistence. The coercivity depends both on the composition of the metallic nucleus and on the thermal treatment. It is worthy to note that elevated coercivity (up to 800 Oe) and GMR have been obtained by annealing Co29 Ni25 Cu45 Mn1 samples with a metastable single phase structure in the as-prepared state after the decomposition of this metastable phase.

GLOSSARY Coercivity The value of reverse driving field required to drive the magnetization to zero after being saturated. Giant magneto-impedance effect Large change of the electric impedance of a magnetic conductor when is subjected to an external dc magnetic field. Magnetic bistability Magnetic flux reversal a single and large Barkhausen jump between two stable remanent states. This results in a macroscopic squared hysteresis loop. Magnetoresistance Change of the electric resistance of a magnetic sample when is subjected to an external dc magnetic field. Saturation magnetostriction constant The fractional change in length as the magnetization increases from zero to its saturation value.

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Nanocrystalline and Amorphous Magnetic Microwires 48. V. Zhukova, A. F. Cobeño, A. Zhukov, J. M. Blanco, S. Puerta, J. González, and M. Vázquez, J. Non-Cryst. Solids 287, 31 (2001). 49. H. Chiriac, M. Knobel, and T. Ovari, Mater. Sci. Forum 302–303, 239 (1999). 50. A. F. Cobeño, A. Zhukov, J. M. Blanco, and J. González, J. Magn. Magn. Mater. 234, L359 (2001). 51. A. Zhukov, V. Zhukova, J. M. Blanco, A. F. Cobeño, M. Vázquez, and J. Gonzalez J. Magn. Magn. Mater. 258–259, 151 (2003). 52. V. Zhukova, J. M. Blanco, A. Zhukov, and J. Gonzalez, J. Phys. D 34, L113 (2001). 53. A. F. Cobeño, A. Zhukov, A. R. de Arellano-López, F. Elías, J. M. Blanco, V. Larin, and J. González, J. Mater. Res. 14, 3775 (1999). 54. L. V. Panina and K. Mohri, Appl. Phys. Lett. 65, 1189 (1994). 55. M. Knobel, C. Gómez-Polo, and M. Vázquez, J. Magn. Magn. Mater. 160, 243 (1996). 56. J. González, A. P. Zhukov, J. M. Blanco, A. F. Cobeño, M. Vázquez, and K. Kulakowski, J. Appl. Phys. 87, 5950 (2000). 57. V. Zhukova, A. Chizhik, A. Zhukov, A. Torcunov, V. Larin, and J. Gonzalez, IEEE Trans. Magn. 38, 3090 (2002). 58. J. M. Blanco, P. Aragoneses, J. González, A. Hernando, M. Vázquez, C. Gómez-Polo, P. T. Squire, and M. R. J. Gibbs, in “Magnetoelastic Effects and Applications” (L. Lanotte, Ed.), p. 253. Elsevier, New York, 1993. 59. J. M. Barandiarán, A. Hernando, V. Madurga, O. V. Nielsen, M. Vázquez, and M. Vázquez-López, Phys. Rev. B. 35, 5066 (1987). 60. V. Zhukova, J. M. Blanco, A. Zhukov, and J. González, J. Phys. D 34, L113 (2001). 61. K. Narita, J. Yamasaki, and H. Fukunaga, IEEE Trans. Magn. MAG16, 435 (1980). 62. J. González, A. Zhukov, V. Zhukova, A. F. Cobeño, J. M. Blanco, A. R. de Arellano-Lopez, S. Lopez-Pombero, J. MartínezFernández, V. Larin, and A. Torcunov, IEEE Trans. Magn. 36, 3015 (2000). 63. A. S. Antonov, V. T. Borisov, O. V. Borisov, A. F. Prokoshin, and N. A. Usov, J. Phys. D 33, 1161 (2000). 64. M. Vázquez, P. Marin, J. Arcas, A. Hernando, A. P. Zhukov, and J. González, Textures Microstruct. 32, 245 (1999). 65. M. N. Baibich, J. M. Broto, A. Fert, F. Nguyen Van Dau, F. Petroff, P. Etienne, G. Creucet, A. Friederich, and J. Chazelas, Phys. Rev. Lett. 61, 2472 (1988). 66. A. E. Berkowitz, J. R. Mitchell, M. J. Carey, A. P. Young, S. Zhang, F. E. Spada, F. T. Parker, A. Hutten, and G. Thomas, Phys. Rev. Lett. 68, 3745 (1992). 67. C. L. Chien, J. Q. Xiao, and J. S. Jiang, J. Appl. Phys. 73, 5309 (1993). 68. R. H. Yu, X. X. Zhang, J. Tejada, M. Knobel, P. Tiberto, and P. Allia, J. Appl. Phys. 78, 392 (1995). 69. E. H. C. P. Sinnecker, D. Páramo, V. Larin, A. Zhukov, M. Vázquez, A. Hernando, and J.González, J. Magn. Magn. Mater. 203, 54 (1999). 70. B. Busch, F. Gärtner, C. Borchers, P. Haasen, and R. Bormann, Acta Metall. Mater. 43, 3467 (1995). 71. V. Madurga, R. J. Ortega, V. N. Korenivski, H. Medelius, and K. V. Rao, J. Magn. Magn. Mater. 140–144, 465 (1995). 72. A. D. C. Viegas, J. Geshev, L. S. Domeles, J. E. Schmidt, and M. Knobel, J. Appl. Phys. 82, 3047 (1997). 73. R. M. Bozorth in “Ferromagnetism,” p. 402. Van Nostrand, New York, 1951. 74. J. González, V. Zhukova, A. P. Zhukov, J. J. Del Val, J. M. Blanco, E. Pina, and M. Vázquez, J. Magn. Magn. Mater. 221, 196 (2000). 75. J. Tang, K.-W. Wang, L. Spinu, H. Srikanath, P. J. Schilling, and N. Moelders, J. Magn. Magn. Mater. 249, 73 (2002). 76. A. Zhukov, M. Vázquez, and J. L. Martinez, J. Magn. Magn. Mat. (accepted). 77. J. Nixdorf, Draht-Welt 53, 696 (1967). 78. T. Goto, M. Nagano, and N. Wehara, Trans. JIM 18, 759 (1977).

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Encyclopedia of Nanoscience and Nanotechnology

www.aspbs.com/enn

Nanocrystalline Barium Titanate Jian Yu, Junhao Chu Chinese Academy of Sciences, Shanghai 200083, China

CONTENTS 1. Introduction 2. Syntheses of Nanocrystalline BaTiO3 3. Spectroscopic Characterization 4. Properties 5. Lattice Dynamics 6. Barium Strontium Titanate 7. Applications 8. Summary Glossary References

1. INTRODUCTION A ferroelectric is a system that exhibits a spontaneous polarization below the Curie temperature, Tc , which can be reversed by the application of an electric field. Conventionally, a ferroelectric is called displacive when the elementary dipoles strictly vanish in the paraelectric phase, and order– disorder when they are nonvanishing but thermally average out to 0 in the paraelectric phase. More rigorously, one may distinguish the two types on the basis of the dynamics of their phase transition and the nature of the soft mode involved, whether the frequency shifts to 0 or the linewidth becomes broad [1, 2]. To date, barium titanate (BaTiO3 ) is well accepted as a displacive and order–disorder mixed type of ferroelectric [3–5]. Since the discovery of ferroelectricity in BaTiO3 in the 1940s, it has been recognized as one of the most important functional materials and has been used in many practical applications in the form of single crystals and ceramics. At high temperature above Tc = 393 K, BaTiO3 is stabilized in a paraelectric cubic phase (space group Oh1 ). With decreasing temperature, it undergoes a sequence of structural phase transitions from the cubic to the ferroelectric tetragonal 1 14 (C4v ) at 393 K, orthorhombic (C2v ) at 278 K, and rhombohe5 dral (C3v ) at 183 K, in which the spontaneous polarization, ISBN: 1-58883-062-4/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

Ps , is along the prototype cube
001,
110, and
111 directions, respectively. Based on the temperature dependence of Ps , these three transitions are first-order transitions, the cubic-to-tetragonal phase transition being a first-order transition close to a second-order phase transition [1, 4–6]. In the three low-temperature ferroelectric phases, the existence of spontaneous polarization results in remarkable ferroelectric, dielectric, piezoelectric, pyroelectric, electrooptic, and nonlinear optical properties. As a result, the tetragonal and cubic phases are especially important for commercial technological applications. In ferroelectric BaTiO3 , the spontaneous polarization, the ferroelectric distortion (tetragonality c/a ratio), and the tetragonal–cubic transition temperature can be altered by external field changes in the temperature, applied field, stress, or chemical composition. The temperature dependence of Ps is referred to as a pyroelectric property, the electric field dependence of Ps as a dielectric property, and the stress dependence of Ps as a piezoelectric property. They all possess anomalous peaks near the phase transition, particularly the ferroelectric tetragonal– paraelectric cubic phase transition. By varying the chemical composition of BaTiO3 such as by the addition of strontium or calcium, the tetragonal–cubic phase transition temperature can be shifted downward so that the anomalous dielectric, piezoelectric, and pyroelectric properties can be used to build high-performance devices at ambient temperatures [1, 7]. For BaTiO3 bulk materials, the room-temperature structural and physical properties are summarized in Table 1. In the ferroelectric tetragonal phase, Ps = 26
C/cm2 with coervice field Ec = 15 kV/cm at room temperature; Ps = 18
C/cm2 at Tc and jumps to 0 above Tc . The dielectric constant is strongly anisotropic with c = 400 along the c axis and a = 4000 perpendicular to the c axis at room temperature. The piezoelectric coefficient is proportional to Ps , but the piezoelectric effect is 0 in the paraelectric phase above T [1, 2]. For conventional ceramics with a grain size of 20– 50
m, the room-temperature dielectric constant is around 2000 at 1 kHz. Previous investigations revealed that the spontaneous polarization, tetragonality, Curie temperature, and various properties related to the spontaneous polarization of the final BaTiO3 devices strongly depend on the Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 6: Pages (389–416)

Nanocrystalline Barium Titanate

390

Table 1. Structural and physical constants of ferroelectric BaTiO3 bulk materials and nanostructured materials in ambient environment except as noted. Property

Bulk value

Lattice parameter (Å)

a = 3996 at 398 K a = 3992, c = 4036, c/a = 1011

[1, 2]

Curie temperature ( C)

120

[1]

Ps = 26, Ps = 18 (393 K) Ec = 15

[1, 2]

d15 = 392, d31 = −345, d33 = 856 (single crystal) d15 = 260, d31 = −78, d33 = 190 (coarser ceramics)

[11]

2

Polarization (
C/cm ) Coercive field (kV/cm) Dielectric (1 kHz)

Piezoelectric (pC/N)

c = 400, a = 4000 ∼2000 (coarser ceramics) ∼5000 (fine ceramics)

Ref.

[8–10]

Ref.

a anomalous expansion c/a → 1000 at Rc

Tc = 128 −

700 R−110

Pr = 20–8.3 (50 nm) Ec = 27–50

[21, 22] [22] [23, 24]

120 (50 nm) (thin film) 430 (50 nm) (thick film) 230–401 (25 nm)

[24] [23] [25, 26]

2 × 1011 (50 nm)

[24]

[12]

dc resistivity ( cm)

>1010 (pure ceramic) 102 –103 (rare-earth-element doped)

[13, 14]

Mobility (cm2 /V s) (single crystal)


a = 05 (cubic at 126  C)
a = 12 ± 03,
c = 013 ± 003 (e)
a /
c = 92 ± 51 (e)
a /
c = 196 ± 06 (h)

[15]

Seebeck coefficient (
V/ C) (60 × 1018 cm−3 free e concentration)

Nano value

[16]

Sa = −600, Sc = −660

[15]

Thermal expansion co-efficient (10−6 / C)

a = 157, c = 62

[17]

Optical bandgap (eV)

3.2

[18]

3.68 (8 nm) 3.53 (35 nm)

[18]

Electrooptic (pm/V)

51 = 820 (632.8 nm)

[19]

[27]

Second-harmonic generation (pm/V) (1.064
m)

d15 ≈ 170, d31 ≈ 157, d33 ≈ 68

[20]

eff ∼ 50 ± 5 (dc) (154
m) eff ∼ 18 ± 2 (5 MHz) (154
m)

particle size. For example, the maximum room-temperature dielectric constant  ∼ 5000 was observed in fine ceramics with a grain size of about 1
m [8–10]. To elucidate the physical mechanism of the ferroelectric properties in reduced dimensions and to determine the ultimate level to which a microelectronic device based on such systems can be miniaturized, the grain size effects in ferroelectrics are most striking [21, 28–33]. These works pointed to prior studies on BaTiO3 nanostructured materials and also facilitated the application of ferroelectric nanoparticles in advanced technologies. In condensed-matter physics, many fundamental properties of materials are characterized by their feature length. For example, one of the feature lengths in a semiconductor is the exciton Bohr radius. Heath even stated that, if a crystal is fabricated such that at least one of its dimensions is comparable with the feature length of some property, the property is confined and becomes dependent on the size and shape of what is now called a quantum crystal [34]. In semiconductor nanosystems, the quantum size confinement effect, which establishes the physical fundamentals necessary to generate properties different from their bulk counterparts, has led to dipole-forbidden interband transitions,

deff = 213 c-oriented nc-film deff = 15 a-oriented nc-film

[20]

exciton level discretization, bandgap enhancement, and so on [34–36]. In perovskite-type ABO3 ferroelectric oxides (BaTiO3 and PbTiO3 ), the characterizations showed a fascinating dependence of the structural and dynamical behaviors on both details of the chemical composition and the delicate balance between the long-range Coulombic interaction and the short-range electric repulsive and covalent interactions [5, 37–40]. The long-range Coulombic interaction was found to play an important role in forming ferroelectric phases, of which the correlation length between polar units was estimated to be 10–50 nm parallel to the polar direction and 1–2 nm perpendicular to the polar direction [6, 21]. If the dimensionality of the ferroelectric nanomaterials were comparable to this correlation length, the long-range cooperative interaction would be reduced, leading to a phase transformation. Preliminary experimental investigations have revealed some major impact on the lattice vibration, phase transitions, and dielectric, ferroelectric, and optical properties. Some results are presented in Table 1. With decreasing ferroelectric nanocrystallite size below the submicrometer scale, there was a monotonic reduction in the tetragonal–cubic phase transition temperature, a decrease in tetragonality, and a grain size-induced

Nanocrystalline Barium Titanate

tetragonal to high-symmetry paraelectric phase transition at/below room temperature. The concept of a ferroelectric critical size, which is necessary to support the long-range cooperative ordering processes necessary for ferroelectricity, has been applied in ferroelectric BaTiO3 and PbTiO3 nanocrystals [21, 22, 32, 33, 41]. In this review, we summarize the wet chemical solution methods for producing crystalline BaTiO3 nanoparticles (nc-BaTiO3 ) with narrow size distributions and size tunability, the vapor deposition methods in particular for growing single crystal ultrathin films, and fabrications of nanoceramics and nanocomposites in Section 2. BaTiO3 nanoparticle and single-crystal thin films are also treated as building blocks to create nanostructured materials, one-dimensional (1D) and 3D superlattices. The spectroscopic characterizations of structural changes and defects are presented in Section 3. In this section, the surface, defect, and microscopic interaction models for understanding the mechanism of grain size–induced phase transformations are also discussed. The dielectric, ferroelectric, and optical properties of nanocrystalline BaTiO3 are summarized in Section 4. The lattice dynamic theory in ferroelectric nanocrystals is summarized and the present results on ABO3 ferroelectric nanoparticles are discussed in Section 5. In addition to BaTiO3 nanostructured materials, barium strontium titanate (Ba1−x Srx TiO3 ) nanostructured materials, including synthesization, dielectric, and nonlinear optical properties, are presented in Section 6. Some applications of BaTiO3 nanostructured materials in the fields of optical modulators, transducers and actuators, and thermal and chemical sensors are given in Section 7. Finally, a short summary is presented.

391 2.1. Chemical Solution Methods To date, various wet chemical methods have been developed to synthesize BaTiO3 nanostructured materials, including coprecipitation such as barium titanyl oxalate tetrahydrate (BTOT) and barium titanyl oxalate [42–44], freeze-dried nitrate method [45], alkoxide hydrolysis [46], stearic acid gel (SAG) [47, 48], sol–gel [21], hydrothermal methods [31, 49, 50], and solution phase decomposition [51]. The most important advantages of the wet chemical solution methods are easily controlling the chemical stoichiometry and producing particles of grain size on the nanometer scale with a relatively narrow distribution, coupled with low crystallization temperature owing to constituent mixing on the quasiatomic level in solution state [42]. Using these wet chemical solution methods, various BaTiO3 nanostructured materials have been successfully fabricated. For example, an ensemble of monodispersed BaTiO3 nanoparticles with grain size as small as 8 nm and a self-organization of BaTiO3 nanoparticles are illustrated in Figure 1. Owing to the wet chemical solution process, a dopant such as paramagnetic ions or rare-earth ions could be easily introduced during preparation of the precursor solution [52–54]. In the wet chemical solution processes for synthesizing nc-BaTiO3 , difficulties arise from the different behaviors of titanium and barium ions versus hydrolysis. To avoid the development of a highly cross-linked Ti–O network in the final structure, various methods were proposed to control the formation of Ti–O–Ti bonds. One method was to use titanium precursors with bidentate ligands (chelates, oxalate, citrate) attached to Ti4+ ions before reaction with Ba2+ ions [42, 46]. A second method was to employ organic solvent without water as the dispersing agent to realize the

2. SYNTHESES OF NANOCRYSTALLINE BaTiO3 Synthesizing crystalline BaTiO3 nanostructured materials (nanocrystalline particles, rods, films, and their superlattices) of high purity, stoichiometry, grain size with tunability, and narrow distribution is one of the basic requirements for BaTiO3 nanoscience and nanotechnology. Various wet chemical solution methods and vapor phase deposition methods have been developed to prepare BaTiO3 and related nanostructured materials. Using these nanocrystals as building blocks, attempts to fabricate complex superlattices, nanoceramics, and nanocomposites were also performed. In Section 2.1, wet chemical solution methods to prepare nanoparticles and fine microstructure thin films are reviewed, by which the grain size and grain shape have been separately controlled during growth. In Section 2.2, vapor phase deposition methods to grow epitaxial singlecrystal thin films and superlattices are discussed. In addition to nanoparticles of 0D nanocrystals and nanorods of 1D nanocrystals, single-crystal thin films with thickness on the nanometer scale form 2D nanocrystals. In Section 2.3, BaTiO3 nanoceramics fabricated with BaTiO3 nanopowders as starting materials are discussed. In Section 2.4, BaTiO3 nanoparticle dispersoids composites are discussed.

Figure 1. Transmission electron microscopy images of (a) a highresolution lattice image of an individual 8-nm-diameter nanoparticle and (b) an ensemble of discrete BaTiO3 8-nm nanoparticles. Inset: Selected area electron diffraction pattern of (c) self-organization of BaTiO3 nanoparticles and (d) superlattice of 8-nm-diameter BaTiO3 nanoparticles. Reprinted with permission from [51], S. O’Brien et al., J. Am. Chem. Soc. 123, 12085 (2001). © 2001 American Chemical Society.

392 uniform distribution of barium and titanium metalorganics in the gels [47, 48, 55]. These methods involved several reaction steps to deposit the precursor and required calcination at higher temperature to generate crystalline BaTiO3 nanopowders. Controlling the calcining temperature and time, BaTiO3 nanopowders with various grain sizes were obtained. For instance, using the SAG technique, Wang et al. and Qiu et al. reported that the average grain size of BaTiO3 nanopowders prepared at 600–950  C ranged from 25 to 60 nm [47, 48]. In these methods, a key point was to obtain a homogeneous precursor with uniform distribution of the different components. If not, a number of defects could occur in the nanocrystals [56]. In contrast to those coprecipitation processes, by which the nanopowders obtained were usually aggregate, sol– gel methods with metal alkoxides allowed for fabrication of monodispersed nanoparticles of barium titanate with improved homogeneity and purity. The low-temperature hydrothermal methods (LTHMs) not only allowed fabrication of monodispersed nanoparticles but also reduced the crystallization temperature of BaTiO3 to less than 100  C. In the following, these two methods are discussed in detail for fabricating BaTiO3 nanocrystals. Nanofabrication using mesoporous sieves and microemulsions are also reviewed. At the end of this section, the fabrication of nanocrystalline thin films using wet chemical solution methods is discussed.

2.1.1. Sol–Gel Method The sol–gel method was widely used to produce nanocrystalline BaTiO3 powders and films. This process involved dissolving the metal-containing compounds in the solvent, hydrolyzing to polymeric condensation, drying the resulting solution into various gels, and, finally, annealing the gels at high temperature to form BaTiO3 nanocrystals [21, 25, 54, 57, 58]. In this process, the choice of starting materials, concentration, pH value, and heat treatment schedule had a strong influence on the properties of the BaTiO3 nanoparticles. Barium acetate and titanium isopropoxide were often used as starting materials to generate BaTiO3 nanopowders. However, the different rates in the hydrolysis and condensation of Ba and Ti precursors often led to chemical component segregation in the obtained gels. To avoid this problem, acetic acid or acetylaceton was used to modify the hydrolysis rate of the Ti precursor, because these complexing agents act as chelating agents to coordinate with Ti species [23, 25, 54]. Compared with the case of mixed Ba and Ti alkoxides, Gablenz et al. and Yang et al. demonstrated that using barium titanium double alkoxides as the raw materials allowed one to produce BaTiO3 nanoparticles with a higher degree of homogeneity, a relatively narrow grain size distribution, and an exact [Ba/Ti] stoichiometry [59, 60]. In the case of double alkoxides, the absence of free barium alkoxide and titanium alkoxide led to relatively low hydrolysis and condensation rates, but the gelation time was remarkably increased, owing to the evolution of oligomeric structures. During the refluxing period, the oligomeric structures were found as a transition between noncrystalline and crystalline states. The shortest gelation time was observed near the crystalline state [60].

Nanocrystalline Barium Titanate

Furthermore, it was found that the pH value of the solvent had a great influence on colloid formation, gel structure, grain size distribution, and degree of aggregation [61, 62]. When the pH value was below 7, no gel formed and the obtained powder had a strong degree of aggregation. However, increasing the pH value above 8, the nanoparticles obtained at 600  C were homogeneous with an average grain size of 13 nm and a high specific surface area of 33.27 m2 /g. Luan and Gao analyzed the dependence of the zeta potential on the pH value and found that the hydrolysis was completed more rapidly than the polymerization as the hydrolysis speed was faster than that of polymerization under alkaline conditions. The hydroxide ions reacted with tetrabutyl titanate and water molecules to form the complexion [Ti(OH)6 ]2− , which neutralized with the Ba2+ ion and then polymerized to Ba2+ [Ti(OH)6 ]2− . At the same time, the high-repel potential energies among colloidal particles had reduced the degree of agglomeration, since the pH value was far away from the isoelectronic point (pH = 18). Therefore, the nanopowders obtained at high pH were homogeneous and ultrafine. In contrast, when the pH value was below 7, because the polymerization speed was much faster than the hydrolysis speed, polymerization had already started before the completion of hydrolysis. The product was hydrate TiO2 instead of the Ti complexion. Because the pH value was near the isoelectronic point, the gel particles were much more highly agglomerated. For the obtained gels, a high-temperature heat treatment above 600  C was required to remove unreacted organics and to crystallize the films. The following steps represented the transformation from the precursor to the crystalline BaTiO3 : transformation of the precursor to the amorphous barium titanate, three-dimensional nucleation of the crystalline barium titanate in the amorphous matrix, and crystal growth of BaTiO3 by a solid-state reaction [63]. The choice of heat treatment schedule, including postannealing temperature and time, and the increased rate of temperature during heating affected the nucleation and crystal growth processes of BaTiO3 and hence determined the nanocrystallite size and its distribution [62, 63]. The final annealing temperature played a dominant role in determining the grain size and its distribution in the obtained nanomaterials. Conventionally, the higher the annealing temperature or the longer the time, the larger the grain size obtained. In synthesizing ferroelectric Pb(Zr, Ti)O3 nanoparticles [62], the slow heating rate was found to inhibit the interparticle sintering—nanoparticle aggregation. Moreover, the annealing atmosphere also affected the quality of the nanoparticles; the inert atmosphere reduced the interparticle sintering in comparison with air or oxygen atmosphere. However, these heat treatment techniques were not reported for synthesizing BaTiO3 nanocrystalline particles and thin films. Because BaTiO3 is similar to Pb(Zr, Ti)O3 in its chemical qualities, these heat treatment techniques should be beneficial for synthesizing monodispersed freestanding BaTiO3 nanocrystalline particles and thin films. With these techniques, monodispersed BaTiO3 nanoparticles and related nanostructured materials have been successfully fabricated. The grain size was adjusted from a few nanometers up to micrometer size by combining solid-state polymerization and heat treatment [21, 53, 59–61, 63].

Nanocrystalline Barium Titanate

2.1.2. Low-Temperature Hydrothermal Method In contrast to sol–gel processing, the low-temperature (below 100  C) hydrothermal method with inorganic precursors offers a promising cost-effective approach to producing crystalline BaTiO3 nanoparticles and relevant nanomaterials. Thermodynamic calculations of the Ti–Ba– CO2 –H2 O system indicated that BaTiO3 is the thermodynamically favored phase at pH greater than 12 and high concentrations (2 M) of Ba2+ [64, 65]. Based on this prediction, BaTiO3 nanocrystals were produced by rapid hydrolysis of compounds such as TiCl4 , Ti alkoxides, or BaTi double alkoxides in an aqueous medium under strong alkaline conditions, and the grain size was tuned by controlling the reaction conditions such as concentration, pH, and temperature [31, 49, 52, 64–67]. Conventionally, the low-temperature hydrothermal synthesis of BaTiO3 nanoparticles was carried out in a batchtype reactor below 100  C under atmospheric pressure. There were two effective routes using synthesized titania gel or titania nanoparticles to produce BaTiO3 nanoparticles. For the case of titania gels, the raw materials were either inorganic such as barium chloride, titanium chloride, and sodium hydroxide base or organic salts such as barium acetate, titanium isopropoxide, and the organic base, tetramethylammonium hydroxide. A typical chemical reaction from inorganic salts can be written as BaCl2 + TiCl4 + 4NaOH → BaTiO3 + 4NaCl + 3H2 O where the ionic species react in an aqueous solution with a temperature of 80–95  C to form monodispersed crystalline nanoparticles with a grain size of 30–220 nm [31, 33, 52]. In a typical case, 164 mL NaOH solution of concentration 3.0 mol/L was preheated to 85  C in a beaker, and 96 mL BaCl2 –TiCl4 solution of 1 mol/L was then added under stirring. The entire system was kept at 85  C for 10 min. The nanoparticles obtained were determined to have an average grain size of approximately 80 nm and a specific surface area of 25 m2 /g. In this route, the stoichiometry in nc-BaTiO3 was achieved when the Ba/Ti molar ratio was 1.07 in the starting solution, and the aging time for full crystallization was as short as 4 min [31, 68]. Furthermore, Her et al. developed a controlled double-jet precipitation technique and realized continuous precipitation of monodispersed colloidal barium titanate nanopowders, for example, in a moderate-sized experimental reactor with about 50 pounds per day [31, 69]. The nanoparticle agglomeration could be avoided by controlling the flow rate and the volume of reactants. As known, one important source of contamination of nc-BaTiO3 is the formation of BaCO3 , through the reaction of Ba2+ with CO3 2− ions coming from air or dissolved in alkaline solutions. To reduce the final amount of this secondary phase, special care was taken in avoiding contact of NaOH solution with the atmosphere. Moreover, the crystalline BaTiO3 nanoparticles were directly formed by hydrolyzing the barium titanium double alkoxides at 60  C under a pH of 13 without any further calcination [60]. With barium titanium double alkoxides as the raw materials, a semicontinuous hydrothermal process was also designed to produce BaTiO3 nanopowders [70]. The grain size of the nanoparticles obtained by

393 hydrolyzing double alkoxides was around 10 nm. MacLaren and Ponton investigated the formation mechanisms of lowtemperature hydrothermal conversion of BaTiO3 nanoparticles from an amorphous hydrous TiO2 gel, which was derived from hydrolysis of titanium isopropoxide, in a solution of barium acetate and strong tetramethylammonium hydroxide base. On the basis of the fast reaction rate for the formation of nc-BaTiO3 , it was proposed that the BaTiO3 nanoparticles were formed by an in-situ transformation of amorphous TiO2 gel [67]. The second route was low-temperature hydrothermal conversion of titania nanoparticles in barium hydroxide solutions [65, 71, 72]. This route coupled two low-temperature hydrothermal steps: synthesis of monodispersed titania nanoparticles and hydrothermal conversion of the prepared titania nanoparticles to nanocrystalline BaTiO3 . At first, the morphology observations seemed to support a dissolution–precipitation mechanism—involving dissolution of TiO2 into TiOHx 4−x species, precipitative BaTiO3 nucleation by reaction with barium ions/complexes in solution, and recrystallization/growth—for the hydrothermal conversion of titania nanoparticles into nc-BaTiO3 [65, 71]. However, recent measurements indicated that the particle size and morphology of the BaTiO3 nanoparticles remained the same as the precursor titania nanoparticles. A shrinking-core in-situ transformation diffusion–reaction mechanism was proposed for this TiO2 -to-BaTiO3 conversion process [72]. In principle, the grain size of the BaTiO3 nanoparticles can be tuned by varying the size of the titania nanoparticles. In the development of nanocrystalline titania, TiO2 nanoparticles with a grain size as small as approximately 3 nm were successfully prepared [73]. Thus, monodispersed BaTiO3 nanoparticles with a grain size less than 10 nm can be prepared from titania nanoparticles by this low-temperature hydrothermal process. As discussed above, the low-temperature hydrothermal process provides an alternative to postannealing to control the phase structure of ferroelectric nanocrystals. Combining these two crystallization methods, two-phase coexisting barium titanate nanoparticles were synthesized with TiCl4 and BaCl2 as the raw materials, of which the second-phase clusters of the BaTiO3 hexagonal phase or BaTi2 O5 were embedded within the BaTiO3 nanoparticles [49, 74, 75]. To date, the low-temperature hydrothermal method has enjoyed considerable success for the production of monodispersed barium titanate spheric nanoparticles with a grain size ranging from 5 nm to the submicrometer, with a narrow distribution, and with a high purity. It has promise not only as a suitable laboratorial process but also as a suitable industrial process to produce barium titanate nanoparticles, starting from cheaper inorganic precursors (titanium oxide or chloride; barium hydroxide or chloride) [69, 70].

2.1.3. Nanofabrication Among the important characteristics of nanoparticle systems are facile manipulation and reversible assembly that allow for the possibility of incorporating nanoparticles into nanoscale electric, electronic, optical, and mechanical devices. Such bottom-up or self-assembly approaches have also been attempted in BaTiO3 nanofabrications.

394 The mesoporous silicate molecular sieve has uniform columnar periodic hexagonal mesopores ranging from 15 to 100 Å and separated by 8- to 9-Å walls, and is an important nanoreactor. BaTiO3 nanoparticles were embedded in the uniform mesopores by soaking a mesoporous silicate molecular sieve into a BaTiO3 precursor solution and with calcination at 700  C to crystallize BaTiO3 nanoparticles [76, 77]. Using sol–gel-type hydrolysis [46, 60], the crystalline BaTiO3 nanoparticles embedded in mesoporous sieves can also be directly fabricated without any calcination. Water-in-oil microemulsions are another important kind of nanoreactor, which are also used to synthesize BaTiO3 nanoparticles. The water droplet size in microemulsions can be tuned between 8 and 55 nm by varying the length of the hydrophilic part of the surfactant molecules, and, consequently, the size of the resulting BaTiO3 nanoparticles can be determined [78]. In these microemulsions, the crystalline BaTiO3 and SrTiO3 nanoparticles were directly prepared by a sol–gel-type hydrolysis reaction without calcination [78, 79]. In the synthesis of nanostructured materials, a general approach based on solution phase decomposition in a structured inverse micelle medium has been developed to separately control the shape and size of colloidal inorganic nanocrystals. The anisotropic growth is controlled by using a mixture of surfactants, where the different surfactants are used to selectively control the growth rates of different faces [80]. Of interest, this technique was successfully extended to synthesize BaTiO3 nanoparticles and nanorods. First, O’Brien et al. synthesized monodispersed perfect cubic BaTiO3 nanoparticles with diameters ranging from 6 to 12 nm. At the same time, the propensity of these BaTiO3 nanoparticles to self-assemble into superstructures was also demonstrated, as illustrated in Figure 1 [51]. In their typical synthesis, 1 mmol barium titanium ethyl hexanoisopropoxide was injected into a mixture of 50 mL diphenyl ether and 3 mmol stabilizing agent oleic acid at 140  C under argon or nitrogen. Excess 2-propanol was removed under vacuum. The mixture was cooled to 100  C and 30 wt% hydrogen peroxide solution (0.9 mL) was injected through the septum. The solution was maintained in a closed system and stirred at 100  C (under a mild reflux with the remaining water content) over 48 h to promote further hydrolysis and crystallization of the product in an inverse micelle condition. Recently, Urban et al. synthesized perfect singlecrystalline cubic BaTiO3 and SrTiO3 nanorods with diameters ranging from 5 to 60 nm and lengths in excess of 10
m [81, 82]. In their typical reaction, a 10-fold molar excess of 30% H2 O2 was added at 100  C to 10 mL heptadecane solution containing 10 mmol barium titanium isopropoxide alkoxide precursor and 1 mmol oleic acid. The reaction mixture was subsequently heated to 280  C for 6 h, and a white precipitate composed of nanorod aggregates was obtained. Anisotropic nanorod growth was due to precursor decomposition and crystallization in a structured inverse micelle medium formed by the precursor and oleic acid under these reaction conditions. This developing nanotechnology will provide more complex nanostructured systems for fundamental investigations on nanoscale ferroelectricity, piezoelectricity, and paraelectricity.

Nanocrystalline Barium Titanate

2.1.4. Nanocrystalline Film Deposition The microstructures of nanocrystalline BaTiO3 thin films are mainly composed of ultrafine grains (random or highly oriented) and epitaxial single crystals. The epitaxial singlecrystal thin films with thickness on the nanometer scale will be discussed in the next section. For ultrafine microstructured films, the sol–gel method is a good candidate for coating substrates with a large area or complex shape. Using the same precursors as in the preparation of nanoparticles, thin films were prepared by spin-coating, dip-coating, or spraycoating techniques [24]. For instance, BaTiO3 nanocrystalline films of thickness 200 nm–3
m were successfully produced on a Si single crystal or on platinum-coated Si single-crystal substrates, in which the average grain size was about 25 nm annealed at 750  C [25, 54, 83]. Studies of the film deposition mechanism revealed that the nanocrystalline granular microstructure was formed due to homogeneous nucleation in a layer-by-layer film process. When one limits the trend of homogeneous nucleation but enhances the heterogeneous nucleation at the substrate via some tricks such as lowering the thickness of each coating layer, a nanocrystalline columnar microstructure was obtained [24, 84, 85]. The conventional sol–gel process required heat treatment at temperatures above 600  C in order to crystallize the BaTiO3 films. This limited the practical application of ferroelectric thin films in integrated semiconductor circuits owing to severe interface diffusion at high crystallization temperature. To reduce the processing temperature, an alternative was to combine the merits of the sol–gel and low-temperature hydrothermal methods. In this so-called sol–gel–hydrothermal process, the as-dried BaTiO3 gel films were used as the precursor films for post hydrothermal treatment. Using this process, BaTiO3 nanocrystalline thin films have been obtained at temperatures below 100  C [86–88]. Alternatively, BaTiO3 nanocrystalline thin films were also fabricated in-situ by low-temperature hydrothermal– electrochemical methods [64, 89–91]. One method was to use titanium metal electrode contributing the Ti source within BaTiO3 thin films by anodic oxidation of Ti reacting with Ba2+ and OH− ions [64, 90]. Another method was to electrophoretically deposit BaTiO3 nuclei within solution on the substrates [89, 91]. With the latter technique, Tamaki et al. successfully obtained epitaxial nc-BaTiO3 thin films with a grain size less than 10 nm on La07 Sr03 MnO3 -coated SrTiO3 single-crystal substrate [91]. It should be noted that these films were usually characterized by partial substrate coverage or high surface roughness.

2.2. Vapor Phase Methods Besides wet chemical solution methods, BaTiO3 nanostructured materials were also prepared by vapor deposition methods, in which vapor and/or plasma were generated by electrical, optical, or chemical methods [18, 92–97]. Among those various physical vapor deposition processes such as thermal evaporation, magnetron sputtering, and laser ablation, the main difference is the interaction process used to generate a vapor and/or plasma by the removal of the target material. The type, density, energy, and excitation of atoms, molecules, clusters, and micro- and macroparticles

Nanocrystalline Barium Titanate

within the generated vapor (plasma) resulted in different microstructures of nanocrystalline particles and thin films. Compared with the wet chemical solution methods, the unique advantage of the vapor deposition methods was to grow epitaxial single-crystal thin films. At present, BaTiO3 epitaxial thin films have been achieved in an atomic scale layer-by-layer growth mode using metalorganic chemical vapor deposition (MOCVD) and laser molecular beam epitaxy (laser MBE) techniques [94–97]. In this section, the laser MBE technique for growing BaTiO3 epitaxial singlecrystal thin films and related superlattices is discussed in detail.

2.2.1. Epitaxial Thin Film Pulsed laser deposition performed in an ultrahigh vacuum, that is, laser MBE, has been verified as a suitable method for growing single-crystal thin films and artificial superlattices in an atomic scale two-dimensional layer-by-layer growth mode. It combines the merits of pulsed laser deposition and conventional MBE for growing epitaxial thin films, especially suitable for high-melting-point perovskite oxide ceramics such as BaTiO3 and multicomponent solids such as (Ba, Sr)TiO3 controlled in atomic scale [96–99]. The details of the laser MBE apparatus and processes are described in the literature [97, 98]. Using the laser MBE technique, Lu et al. and Yoneda et al. fabricated c-axis-oriented BaTiO3 ultrathin films of 1- to 50-unit-cell layers on SrTiO3 (001) and MgO (001) substrates [96, 97]. The epitaxial relationship of BaTiO3 films on both SrTiO3 and MgO substrates was determined to be [100] film[100] substrate (in the growth plane) and (001) film(001) substrate (along the growth direction). For the BaTiO3 single crystal, the thermal expansion coefficient is  = 157 × 10−6 / C along the a axis at room temperature [17]. In contrast, for the SrTiO3 substrate, the cubic lattice parameter is a = 3905 Å and  = 117 × 10−6 / C at 300 K, and for the cubic MgO substrate, a = 4213 Å and  = 148 × 10−6 / C at 300 K [100]. From the viewpoint of lattice mismatch, the magnitude of mismatch between the MgO substrate and the bulk BaTiO3 c axis is smaller than that between the MgO substrate and the bulk BaTiO3 a axis. If the epitaxial relationship depends only on the latticematched condition, the a axis of the BaTiO3 films on the MgO substrates should be oriented in the growth direction and the c axis in the growth plane. However, the BaTiO3 films obtained on MgO substrates were c-oriented. Therefore, the lattice mismatch strain is not the only factor that determines the orientation of the BaTiO3 films. Studying BaTiO3 epitaxial films on various substrates, it was found that, owing to lattice and thermal expansion coefficients between the thin film and the substrate, the net elastic strain in the film growth dictated the orientation of the epitaxial BaTiO3 thin films [100–102]. On the other hand, the magnitude of mismatch between the bulk BaTiO3 a axis and the SrTiO3 (+2.3%) was smaller than that between BaTiO3 and MgO (−5.2%). Owing to this different epitaxial strain, the BaTiO3 thin films had different crystal quality and tetragonality, for example, c/a = 1003 and 1018 for the 200-nmthick epitaxial film, respectively, on the SrTiO3 and MgO substrates [96]. For BaTiO3 epitaxial thin films on a MgO

395 substrate, the lattice parameter perpendicular to the surface was found to be nearly independent of the film thickness and close to the c-axis bulk value, while the in-plane lattice parameter was intermediate between the bulk a- and c-axis values and approached the bulk a-axis value with increasing film thickness to 2000 nm [102, 103]. In summary, the lattice strain in BaTiO3 epitaxial thin films could be tuned by choosing the substrate and controlling the film thickness. To eliminate the substrate clamping effect, preparing freestanding BaTiO3 single-crystal thin films is the next object. On the SrTiO3 substrates with various orientations, the surface morphology of BaTiO3 epitaxial films exhibited different roughness. For the typical perovskite oxides with formula ABO3 , there are two possible terminating atomic layers, AO (A-site plane) and BO2 (B-site plane), on the (100) surface. In the 10-nm-thick BaTiO3 (001) epitaxial thin film on a SrTiO3 (001) substrate, the in-situ reflection high-energy electron diffraction intensity oscillation indicated the BaTiO3 thin film to be in a unit-cell layer-by-layer growth. Angle-resolved X-ray photoelectron spectroscopy analysis revealed that the topmost surface atomic plane for this BaTiO3 ultrathin film was the TiO2 layer. Thus, the BaTiO3 film growth sequence was determined as TiO2 (substrate)/BaO/TiO2 /· · · /BaO/TiO2 . The root mean square surface roughness was 0.2 nm observed by atomic force microscopy [104]. In contrast, the topmost surface of BaTiO3 (001) epitaxial films with a thickness greater than 80 nm was determined as the BaO plane, even though the SrTiO3 (001) substrate had the dominant topmost surface of TiO2 [96, 99]. These facts also suggested that the film growth did not simply depend on the lattice-matched condition between the BaTiO3 films and the substrates [96, 105]. It should be noted that the substrate surface treatment was very important for the growth of high-quality epitaxial films in the layer-by-layer mode, especially for the ultrathin films of unitcell layers [97, 99]. To date, epitaxial BaTiO3 single-crystal thin films have been successfully deposited on various single-crystal substrates such as SrTiO3 , LaAlO3 , SrRuO3 , MgO, MgAl2 O4 , and sapphire [94, 97–99, 103]. These epitaxial films may provide a wide range of applications in microelectronics, integrated optics, and microsystem technology, such as sensors, microactuators, memories, and optical waveguide devices. Of interest, BaTiO3 is also a good candidate for the insulating layer in high-Tc oxide devices due to its similar perovskite structure and small lattice mismatch with the high-Tc oxide superconductors. The heteroepitaxial growth of BaTiO3 ultrathin films using the laser MBE technique creates a new way to fabricate superconductor–insulator– superconductor tunnel junction devices [97, 99]. In semiconductor nanotechnology, the MBE technique was widely used to fabricate ordered nanostructures through the self-organized growth mode. For Ce : BaTiO3 oxide, the strain-driven self-organized growth of nanoscale islands was also exploited using the laser MBE technique on MgO (100) substrates. The distributed coherent Ce : BaTiO3 square base pyramidal nanoislands were fabricated on top of a thicker wetting layer [106].

396 2.2.2. Strained Superlattice Synthetic superlattices are an essential approach to artificially controlling the crystal structures and ferroelectric properties. By changing the constituent layer thickness and stacking periodicity of the superlattice, the lattice strain stored in epitaxial thin films can be tuned [107]. With this approach, the dielectric constant, remanent polarization, Curie temperature, and/or lattice dynamics properties of BaTiO3 have been remarkably tuned [99, 108–110]. In addition to BaTiO3 , heteroepitaxial thin films of SrTiO3 , CaTiO3 , and BaZrO3 perovskite oxides were also achieved in the layer-by-layer growth mode using laser MBE. Thus, atoms of Ba and Ti in BaTiO3 can be replaced site selectively with atomic accuracy and lattice strain introduced by a combination of different layers. For instance, BaTiO3 /SrTiO3 artificial superlattices with periodicity of the BaTiO3 /SrTiO3 layers varying from 1 unit cell to 125 unit cells were obtained [98, 109]. In the BaTiO3 /SrTiO3 (BaTiO3 /CaTiO3 ) superlattices, there is a relatively large mismatch of 2.5% (5.5%) between the in-plane lattice parameters. When the film thickness reaches a critical thickness, misfit dislocations will form, which relax lattice mismatch strain and deteriorate the surface roughness [111]. The critical thickness for the strained superlattice has been experimentally determined as 220 Å for the BaTiO3 /SrTiO3 superlattice and 55 Å for the BaTiO3 /CaTiO3 superlattice [107, 112].

2.3. Nanoceramics For BaTiO3 ceramics, not only their dielectric properties but also their mechanical properties were found to depend strongly on the microstructures, such as grain size, grain geometry, and relative density. Using BaTiO3 nanoparticles as starting powders significantly lowers the sintering temperatures and enhances the mechanical and electrical properties of the final ceramics, due to improved homogeneity, purity, controlled grain size, and its distribution, and thus creates opportunity to develop better performing nanoceramic devices [79, 113–115]. With monodispersed BaTiO3 nanoparticles as the starting material, Her et al. obtained BaTiO3 fine ceramics using conventional ceramic processing. In a typical case, the polyvinyl alcohol was first added to BaTiO3 nanopowders approximately 100 nm in size as a binder to prepare green pellets. Second, the polyvinyl alcohol–containing BaTiO3 nanopowders were cold-pressed to form a pellet under 340 MPa. Then the pellet was sintered in air at a high temperature at a heating rate of 2 /min from room temperature to 600  C and then at a heating rate of 8 /min from 600  C to sintering temperature. Fine ceramics with a high density of 5.90 g/cm3 (98.2% of the theoretical density of 6.01 g/cm3 ) and 6.00 g/cm3 (99.8% of the theoretical density) were produced by sintering at temperature as low as 1200  C and 1250  C, respectively, in which the average grain size was over 1–2
m. The dielectric constant for the ceramics sintered at 1200  C was 9700 at 120  C and 5000 (with a dissipation factor of 2.0%) at room temperature [31]. Intensive investigations indicated that the maximum room-temperature dielectric constant of BaTiO3

Nanocrystalline Barium Titanate

ceramics was obtained with density near the theoretical density and optimal grain size near 1
m [10, 31, 113, 116, 117]. Moreover, using BaTiO3 nanoparticles allows thinner layers of ceramic in multilayer capacitors without loss of dielectric properties. BaTiO3 nanoceramics were also fabricated by using BaTiO3 nanoparticles with even smaller grain size and/or controlling the sintering schedule. Using nanopowders with a grain size of about 10 nm as the starting materials, Luan et al. fabricated BaTiO3 nanoceramics under hot pressing at uniaxial pressures in vacuum. It was found that both the density and the grain size increase quickly with increasing sintering temperature. The average grain size and relative density changed from 280 to 1800 nm and from 93.2 to 98.8%, respectively, when the sintering temperature increased from 1050 to 1150  C [118]. At 1250  C under atmospheric pressure, Bocquet et al. obtained BaTiO3 nanoceramics with a grain size of 200–800 nm and a relative density of 98%. The dielectric constant was measured as RT = 2780 at room temperature and max = 10 520 at Tc = 115  C [70]. Ragulya developed a rate-controlled sintering process, which controlled the densification rate instead of controlling the linear heating rate during sintering. Using this technique, he obtained BaTiO3 nanoceramics with a relative density up to 99.9% and the average grain size ranged from 100 to 300 nm for BaTiO3 nanopowders with a grain size of 20–25 nm. Two optimal rate-controlled temperature–time paths for preparing BaTiO3 nanoceramics were also reported [119]. In comparison with conventional temperature-controlled sintering, the rate-controlled sintering allowed one to obtain nanoceramics of smaller grain size and narrower distribution. Spark plasma sintering is a process that makes use of a microscopic electrical discharge between particles under mild pressure (30–50 MPa). This process enables a compact powder to be sintered to high density at relatively lower temperatures and in much shorter sintering times, typically a few minutes, compared with the conventional sintering process of cold isostatic pressing. Using the spark plasma sintering method, starting from BaTiO3 nanopowders with a grain size of 60 nm, Takeuchi et al. produced dense BaTiO3 nanoceramics with a relative density greater than 95% and an average grain size less than 500 nm under 1100  C for 5 min. The temperature increased from room temperature to sintering temperature at a heating rate of approximately 160  C/min, which was controlled by the applied current. It was found that the grain size of the initial nanopowders significantly affected the grain size of the resulting ceramics. For BaTiO3 nanoceramics with an average grain size of 300 nm, the room-temperature dielectric constant, spontaneous polarization, and remanent polarization were measured as 3000 at 100 kHz, 15
C/cm2 , and 2
C/cm2 , respectively [10]. In addition to suppressing exaggerated grain growth, the lower sintering temperature and/or shorter sintering time allow use of less expensive electrode materials in fabricating ceramic multilayer capacitors [10, 45, 120].

Nanocrystalline Barium Titanate

2.4. Nanocomposites 2.4.1. Ceramic Matrix Composites Since ceramic nanocomposites, materials reinforced by secondary dispersoids of a few tens to a few hundreds of nanometers in size (nanoparticles), were proposed in the field of engineering ceramics, significant improvements have been reported in their mechanical properties, such as fracture strength, hardness, and fracture toughness. From the viewpoint of mechanical properties, ferroelectricity or piezoelectricity shows an interesting property. By utilizing the electromotive force of the ferroelectric material, one is able to detect crack propagation. When the ferroelectric materials are subjected to an electric field, additional internal stresses are induced; since the internal stresses are anisotropic, they can increase or decrease fracture toughness, depending on the poling direction [121]. In this regard, ferroelectric nanoparticle-dispersed ceramic nanocomposites are expected to exhibit such intelligent functions as predicting fracture, controlling crack propagation, and so on. As one of the most important ceramic nanocomposites, BaTiO3 ferroelectric nanoparticle-dispersed MgO ceramic composites were developed through hot pressing or pulse electric current sintering (PECS) [122, 123]. Using nc-BaTiO3 with an average grain size of 100 nm as the starting material, Hwang et al. obtained highly densified nc-BaTiO3 /MgO ceramic nanocomposites and showed that these nc-BaTiO3 /MgO ceramic nanocomposites introduced ferroelectricity/piezoelectricity into the nanocomposites and still retained their mechanical properties. They also demonstrated that the PECS technique took advantage of shorter time and lower temperature to sinter ceramic nanocomposites in comparison with the hot-pressing technique, which increased the tetragonality of the BaTiO3 dispersoids because Mg2+ was not substituted for Ti4+ in the hot-pressed samples [123]. Compared with these two sintering methods, the PECS is a reasonably better sintering technique for fabricating various ceramic nanocomposites containing BaTiO3 nanoparticles with even smaller grain size.

2.4.2. Polymer Matrix Composites For ferroelectric nanoparticle dispersive nanocomposites, polymer is another kind of important matrix. The ferroelectricity impacted on polymeric nanocomposites could provide various applications in pyrosensors and piezosensors. In the 1990s, the considerable progress in nanotechnology rendered possible the fabrication of ferroelectric nanoparticle/polymeric nanocomposites. The basic process for fabricating polymer-based nanocomposites is to mix monodispersed ferroelectric nanoparticles into the polymer with the aid of suitable solvents [124–126]. The pyroelectric vinylidene fluoride/trifluoroethylene [P(VDF–TrFE)] copolymer is a useful matrix to form nanocomposites. P(VDF–TrFE) 70/30 mol% copolymer has a Curie temperature of 102  C upon heating and a melting temperature of 150  C. To prepare BaTiO3 nanoparticles/copolymer nanocomposites, the copolymer was first dissolved in methyl-ethyl-ketone solvent and ferroelectric BaTiO3 nanopowder was then blended into the solution to form a mixture. The powder in the mixture was dispersed

397 in an ultrasonic bath to produce a homogeneous suspension. The experiments revealed that the qualities of the BaTiO3 nanoparticles such as agglomeration and grain size limited the volume fraction of nanoparticles in the composite. Using small uniform monodispersed BaTiO3 nanoparticles can increase the volume fraction of nanoparticles in the composites. Thin films of ferroelectric nanoparticles/copolymer nanocomposites were also fabricated using the spin-coating technique. Finally, heat treatment at 120  C was performed to remove the solvent. Experimental measurements indicated that all three figures of merit (current, voltage, and detectivity) increased with increasing volume fractions of nanoparticles in the composite [124, 125]. Using this mixing technique, Yamamoto et al. prepared 40 vol% nc-BaTiO3 /chloroprene polymer composites and investigated the grain size effect on the piezoelectric properties of BaTiO3 /polymer nanocomposites. It was revealed that the piezoelectric constant was closely related to the crystallographic phase of nc-BaTiO3 . With BaTiO3 nanoparticles in the cubic phase, the piezoelectric coefficient d33 of BaTiO3 /polymer nanocomposites was very small (about 2 pC/N), but when the grain size was increased above the critical size, the d33 tetragonal nc-BaTiO3 dispersoids increased rapidly to 23 pC/N [126]. At the conventional crystallization temperature of BaTiO3 nanoparticles (>600  C), the polymer matrix was severely destroyed. As discussed in Section 2.1, low-temperature hydrothermal processing can reduce the crystallization temperature of BaTiO3 nanoparticles below 100  C. Taking advantage of this property, Collins and Slamovich extended it to directly prepare nc-BaTiO3 /polymer nanocomposite thin films. Thin-film composites of BaTiO3 nanoparticles in polymeric matrix were processed by hydrothermally treating a film of titanium alkoxide mixed within polybutadienepolystyrene triblock copolymer in an aqueous solution of 1.0 M Ba(OH)2 at a temperature ranging from 60 to 90  C. The subsurface growth of BaTiO3 proceeded through the percolating network of hydrolyzed titanium alkoxide, which enabled the reaction solution to permeate throughout the thin films. In their BaTiO3 /polymer nanocomposite thin films, the grain size of the subsurface BaTiO3 nanoparticles was approximately 5–10 nm, independent of the processing temperature, but the grain size of the surface nanoparticles was over 60–180 nm, depending on the processing temperature. The room-temperature dielectric constant of the 90 wt% BaTiO3 /polymer nanocomposite films was 10–15 at a frequency of 10 kHz. These ferroelectric nanoparticle/polymeric nanocomposite thin films could be used for applications ranging from nonlinear optics to abrasionresistant coatings [127].

3. SPECTROSCOPIC CHARACTERIZATION 3.1. Structural Changes In the BaTiO3 nanocrystals, the structural and physical properties were strongly dependent on the grain size. With decreasing grain size of the nanoparticles, the anomalous lattice expansion, tetragonality decrease, and tetragonal– cubic phase transition were experimentally observed at room temperature [21, 22, 33, 44, 49, 128]. Figure 2 presents one

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Table 2. Critical size of the tetragonal–cubic phase transition at room temperature for BaTiO3 nanoparticles. Synthesis method sol–gel Hydrothermal BTOT Alkoxide method LTHM

Critical size 50 90 ∼30 80 49

nm nm nm nm nm

Measurement method

Ref.

XRD SEM XRD XRD TEM TEM XRD

[21, 58] [22] [43, 44] [129] [49]

example of lattice constant variation in the sol–gel-derived BaTiO3 nanocrystalline particles as a function of heat treatment temperature, that is, nanoparticle grain size. It was clearly demonstrated that, with decreasing grain size, the lattice constant, a, of BaTiO3 nanoparticles increased anomalously in both the tetragonal and the cubic phases, while the lattice constant, c, decreased, which resulted in a decrease in tetragonality and tetragonal-to-cubic phase transition [21]. In the monodispersed BaTiO3 nanoparticles derived by the alkoxide method, the elongation of the lattice constant of a was measured to be greater than 2.5% in a 15-nm nanocrystallite using the electron diffraction technique [129]. In Figure 3, the room-temperature tetragonality as a function of grain size, which was determined using specific surface area data, is presented for hydrothermally derived BaTiO3 nanoparticles. Below 300 nm, the tetragonality decreased exponentially, and the tetragonality of nc-BaTiO3 became 1 at a critical size of approximately 120 nm, while a sizeinduced ferroelectric tetragonal–paraelectric cubic phase transition took place [22]. It should be noted that the reported critical size for the grain size–induced BaTiO3 tetragonal–cubic phase was closely correlated with the particular processing and the grain size determination methods. Some experimentally obtained critical sizes are listed in Table 2. It can be seen that they are on the order of 50 nm as

determined by the X-ray diffraction (XRD) technique [21, 22, 25, 44, 49, 58, 128, 130]. Thermal measurements on BaTiO3 polycrystals with a grain size ranging from 10
m to 35 nm were performed using differential scanning calorimetry (DSC) [21, 128]. The DSC data are presented in Figure 4. As illustrated in Figure 4, endothermic features near 125 and 5  C for larger grain specimens featured the first-order cubic–tetragonal and tetragonal–orthorhombic phase transformations, respectively. With decreasing grain size, the cubic–tetragonal and tetragonal–orthorhombic transformations shifted to lower and higher temperatures, respectively. For 35-nm nanocrystals, there was only a single very broad and weak endothermic peak, which featured BaTiO3 nanocrystals in a locally acentric distorted cubic phase. In contrast to the 211 J/mol of cubic–tetragonal transformation enthalpy for a single crystal, the transformation enthalpy was reduced to 183 J/mol for the 10-
m grains and 78 J/mol for the 100-nm grains [21]. The thermal features observed in BaTiO3 with finite grain size revealed the suppressed phase transformation characteristics. Dielectric measurements of BaTiO3 fine ceramics and nanocrystalline thin films showed also that the phase transitions were strongly dependent on the grain size [8–10, 23, 25]. Some experimental results are shown in Figure 5. It is obvious that, with decreasing grain size, the maximum value of the cubic–tetragonal phase transition decreased, and the dielectric peak became broader while the dielectric constant as a function of temperature deviated from the Curie–Weiss behavior above the ferroelectric phase transition and that the ferroelectric phase transformation at last disappeared over temperatures between −85  C and 200  C, as illustrated

Figure 3. Change in tetragonality c/a with particle size at room temperature. Reprinted with permission from [22], K. Uchino et al., J. Am. Ceram. Soc. 72, 1555 (1989). © 1989, American Ceramic Society.

Figure 4. DSC data for BaTiO3 polycrystals, illustrating the dependence of phase transition thermal characteristics on grain size. Reprinted with permission from [21], M. H. Frey and D. A. Payne, Phys. Rev. B 54, 3158 (1996). © 1996, American Physical Society.

Figure 2. Lattice parameters determined from the (200) XRD data and representing the room-temperature cubic-to-tetragonal structural transition with increasing processing temperature. Reprinted with permission from [21], M. H. Frey and D. A. Payne, Phys. Rev. B 54, 3158 (1996). © 1996, American Physical Society.

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399

Figure 5. (a) Dielectric constant vs. temperature of BaTiO3 fine ceramics with various grain sizes at 1 kHz. (b) Temperature dependence of dielectric constant and loss tangent for BaTiO3 thin films with an average grain size of 25 nm. (a) reprinted with permission from [9], G. Arlt et al., J. Appl. Phys. 58, 1619 (1985). (b) reprinted with permission from [25], M. H. Frey and D. A. Payne, Appl. Phys. Lett. 63, 2753 (1993). © 1993, American Institute of Physics.

in BaTiO3 nanocrystalline thin films with an average grain size of 25 nm. In most of the literature, the ferroelectric phase transition temperature Tc was observed to decrease with decreasing grain size [10, 22, 130]. It should be noted that, in Figure 5a, the cubic–tetragonal phase transition temperature for a 0.7-
m ceramic was slightly higher than that for a 6.8
m ceramic, which was attributed to the strong elastic constraint being correlated with the grain size effect in this sample [9]. In BaTiO3 fine ceramics and nanocrystalline thin films, the broadening of the ferroelectric–paraelectric phase transition as a function of grain size was even explained by an intrinsic grain size–induced diffuse phase transition model [131–133]. For the diffuse phase transition in ferroelectric perovskite solutions, the experimental data of dielectric constants above the phase transition were described by the empirical relationship: 1 1 1 − = T − Tc   max

(3.1)

where max is the maximum dielectric constant at the apparent transition temperature Tc , is a constant, and 1 ≤  ≤ 2.  = 1 is the a normal phase transition and  = 2 is the a pure diffuse phase transition [134, 135]. For BaTiO3 nanoceramics with various grain sizes, the experimental dielectric data

above the ferroelectric–paraelectric phase transition were successfully fitted with this relationship; the diffusivity, which was described by the critical exponent , was observed to increase with decreasing grain size [131, 132]. On the other hand, the room-temperature dielectric constant was strongly dependent on the grain size, which exhibited a maximum value for ceramics with a grain size around 1
m, but decreased dramatically with further decreasing grain size. The room-temperature dielectric constant was 230 for the sample with a grain size of 25 nm, which was one order of magnitude smaller than the maximum value of 5000 for fine ceramics with a grain size of 1
m [23, 25]. Of interest is to compare BaTiO3 with another important ferroelectric PbTiO3 system. A PbTiO3 single crystal has a tetragonal structure (a = 3899 Å, c = 4153 Å, c/a = 1065) at room temperature and is transformed to a cubic paraelectric phase (a = 396 Å) above Tc = 763 K. At present, the experimental results on PbTiO3 nanoparticles indicated that the lattice constant, tetragonality, Curie temperature, and phase transition latent heat changed similarly to nc-BaTiO3 with varying nanocrystallite size. When the grain size was below approximately 150 nm, the lattice parameter a increased and c decreased with decreasing grain size. The resulting tetragonal distortion decreases exponentially below 60 nm and becomes 1 at a grain size extrapolated to be between 7 and 12.6. The Curie temperature of the tetragonal–cubic phase transition in nc-PbTiO3 was also observed to decrease with decreasing grain size [32, 41, 136–139]. In the cases of BaTiO3 and PbTiO3 nanoparticles, the dielectric, thermal, and structural data indicated that the ferroelectric tetragonal–paraelectric cubic transition temperature, Tc , decreases monotonically and the transition peak becomes broad with decreasing grain size. The relationship between Tc and the nanocrystallite size, R, can be written as Tc = Tc   − D/R − Rc 

(3.2)

where Tc   denotes the value of the bulk crystals, Rc is the critical size, and D is a constant [22, 138, 139]. For BaTiO3 , Tc   = 128  C, D = 700, and Rc = 110 nm [22]. The broad tetragonal–cubic phase transition due to a reduction of grain size in nc-PbTiO3 was also explained in terms of a diffuse phase transition model [32, 134].

3.2. Hydroxyl Defects There were usually a lot of residual hydroxyl OH− defects within the BaTiO3 nanoparticles derived from wet chemical solution methods. In the BaTiO3 nanopowders prepared by the hydrothermal method, an absorption band near 3500 cm−1 was observed. In contrast, the band was measured near 3510 cm−1 in the sol–gel-derived nanopowders [21, 128]. This difference was attributed to different hydroxyl defect occupations within the nanoparticle matrix, since the hydrogen defects are very mobile in BaTiO3 perovskite and able to possess several configurations [140]. With increasing annealing temperature, this absorption intensity decreased and became 0 above 600  C, which demonstrated that the hydroxyl defects could be eliminated with heat treatment at high temperature and were totally removed

Nanocrystalline Barium Titanate

400

became negative when the tetragonality reached the value of the bulk materials. Therefore, the intensity of the 184-cm−1 mode was an effective probe to check the structural changes induced by grain size variation in nc-BaTiO3 [10, 21, 33].

3.3. Complex Defects In Section 2.1, it was pointed out that a homogeneous precursor played an important role in the chemical solution methods to obtain defect-free BaTiO3 nanocrystals. Using high-resolution transmission electron microscopy (HRTEM) Jiang et al. found many internal defect textures, including (111) nanoscale multiple twinning and complicated (111) intergrowth defects, in some barium titanate nanoparticles derived by the SAG and sol–gel methods [56]. As an illustration, Figure 7 presents an example of an SAG-derived BaTiO3 nanocrystal with a grain size of 10 nm, which contained a complex arrangement of defects on the (111) planes indicated by the arrow. At the same time, image processing showed a high density of small defects within the nanocrystal matrix. The density of small defects was estimated to be on the order of 1027 /m3 in the SAG BaTiO3 nanoparticles prepared at 600  C and decreased as the annealing temperature (i.e., particle size) increased. After annealing at high temperature (>1200  C), no hexagonal intergrowth structure and (111) multiple twinning defects were observed, but the small defect density was still high. In the sol–gel-derived BaTiO3 nanoparticles, the defect density was much lower than in the SAG-derived samples, but some still contained many internal defects, including the (111) multiple twinning. Based on the HRTEM results, the authors speculated that these defects of high density were the reason that the SAG BaTiO3 nanoparticles remained in the cubic phase even with grain size up to 3500 nm. In those cubic nc-BaTiO3 including (111) twinning planar and intergrowth defects, Raman scattering measurements recorded three novel peaks at 153, 640, and 1059 cm−1 besides the five modes of 184, 257, 308, 518, and 716 cm−1

716

518

806

Intensity (a.u.)

184

257 308

above 600  C [21, 128, 141]. On one hand, the release of hydroxyl induced the lattice distance contraction with increasing annealing temperature. However, in most cases where the crystalline nanoparticles were prepared with heat treatment above 600  C, the lattice contraction observed in nc-BaTiO3 was mainly caused by the variation in grain size [43, 44, 129]. In Raman measurements, it was found that these residual hydroxyl defects affected the behavior of the optical modes of nc-BaTiO3 , particularly the 257- and 308-cm−1 modes, which caused a mode shift in the frequency of the Raman mode of 257 cm−1 toward 297 cm−1 and inhibited the 308cm−1 mode in the as-prepared samples. With a decrease in the concentration of residual hydroxyl defects, the peak position shifted from 297 cm−1 toward 257 cm−1 with increasing annealing temperature to 600  C [21, 33, 58]. In contrast, the 308-cm−1 mode was unambiguously observed in two-phase coexisting barium titanate nanopowders, even in the LTHM as-prepared samples with a large concentration of hydroxyl defects [33, 49]. This different behavior of the 308-cm−1 mode in the single phase and in two-phase coexisting barium titanate nanoparticles also contributed to the different hydroxyl configurations within the nanocrystal lattice. Moreover, a new Raman mode at 806 cm−1 was observed owing to the hydroxyl absorbed on the nanoparticle boundary [21, 33]. Figure 6 presents typical Raman spectra for singlephase BaTiO3 nanoparticles derived by the low-temperature hydrothermal method. It can be seen that the peak position of the 257-cm−1 mode shifted upward to 297 cm−1 in the as-prepared sample and shifted downward with a reduction in hydroxyl concentration in the BaTiO3 nanoparticles. In the samples annealed above 600  C, the 308-cm−1 mode started to be clearly distinguished and the 806-cm−1 peak disappeared, in agreement with infrared measurements on the hydroxyl defects. In the pure cubic BaTiO3 nanoparticles, which were obtained with heat treatment above 600  C, five modes centered at 184, 257, 308, 518, and 716 cm−1 were recorded. In the tetragonal nc-BaTiO3 , the intensity of the 184-cm−1 mode decreased with increasing tetragonality and

o

1150 C o

900 C o

600 C o

500 C as-prep.

100 300 500 700 900 1100 -1

Raman Shift (cm ) Figure 6. Raman spectra of BaTiO3 nanoparticles derived by lowtemperature hydrothermal method and annealed at various temperatures. Reprinted with permission from [33], J. Yu et al., Mater. Res. Soc. Symp. Proc. 718, 177 (2002). © 2002, Materials Research Society.

Figure 7. High-resolution transmission electron microscopy image of a 10-nm SAG BaTiO3 nanocrystal with complex set of twins on (111) planes (prepared at 650  C). Reprinted with permission from [56], B. Jiang et al., Physica B 291, 203 (2000). © 2000, Elsevier Science.

Nanocrystalline Barium Titanate

characteristic of cubic nc-BaTiO3 . Although the 153- and 640-cm−1 modes were attributed to the nc-BaTiO3 hexagonal phase [142], the HRTEM measurements did not detect any hexagonal nanoparticles. The 153- and 1059-cm−1 modes were from BaCO3 contamination. These (111) twinning and intergrowth defects existing in SAG nc-BaTiO3 prepared below 950  C were attributed to the existence of the low oxidation state of Ti3+ [56, 63].

3.4. Phase Transformation Mechanism To understand the structural changes, in particular, the grain size–induced tetragonal–cubic phase transition in nc-BaTiO3 , three models were proposed.

3.4.1. Surface Model In nanoparticles, there are two significant factors affecting their physical properties: One is a macroscopic effect related to the surface tension of the nanoparticle, and the other concerns the grain size effect on microscopic interactions which induce ferroelectricity instability in perovskite oxides [5, 128, 143]. First, Zhong et al. developed a Landau phenomenological theory to treat the case of ferroelectric nanomaterials, in which a surface layer with degraded polarization was held responsible for the ferroelectric–paraelectric phase transition [144]. Numerical calculations showed that the spontaneous polarization decreased with decreasing particle size and eventually disappeared; that is, a size-driven phase transition took place. The ferroelectric critical size was defined as the size at which the ferroelectric tetragonal–paraelectric cubic phase transition takes place at Tc → 0 K. For BaTiO3 nanoparticles, the ferroelectric critical size was predicted to be 44 nm, and for nc-PbTiO3 to be 4.2 nm, which were on the same order as the experimental values. The size dependence of Tc was found to be inversely proportional to the grain size R  Tc ∝ 1/R. Second, Uchino et al. analyzed the surface tension effect on the Curie temperature and obtained the same inverse-proportion relationship between Tc and R, whereas the experimental relationship of (3.2) obtained in BaTiO3 and PbTiO3 nanoparticles included the critical size, Rc [22, 139]. On the other hand, for covalent crystals, surface tension-like forces would always lead to lattice contraction in small particles [136]. Obviously, this prediction was contrary to the experimental results in nc-BaTiO3 . So far, it can be seen that the surface model is insufficient to understand the Curie temperature change and lattice expansion in BaTiO3 ferroelectric nanoparticles. The grain size effect on the microscopic cooperative phenomenon must be taken into consideration [22]. The core–shell model was proposed to explain the anomalous dielectric behavior and the structural phase transition in fine BaTiO3 ceramics, in which each crystallite consisted of a regular ferroelectric core with a tetragonality gradient toward the outer surface range, surrounded by a cubic surface layer with low permittivity. The cubic surface layer was estimated to be approximately 5–15 nm thick [53, 117]. However, HRTEM measurements of lattice images of BaTiO3 and PbTiO3 nanoparticles did not reveal the existence of a cubic surface layer [56, 126].

401 3.4.2. Defect Model In the hydrothermal-derived BaTiO3 nanoparticles, it was found that the synthesized BaTiO3 nanoparticles were stabilized in the cubic phase by numerous residual hydroxyl defects, independent of grain size [126, 141, 145]. This stabilization was interpreted with the model of lattice defects, in which the dipoles were introduced by hydroxyl defects within the nanoparticles; the correlation size of the dipoles decreased greatly with increasing concentration of hydroxyl defects and, consequently, stabilized the cubic phase in the nc-BaTiO3 . Nevertheless, the hydroxyl defects derived from wet chemical solution methods could be totally eliminated from the nc-BaTiO3 matrix, while the cubic phase remained stable in nc-BaTiO3 with grain size below the ferroelectric critical size [21, 128]. Furthermore, the hydrothermal method was demonstrated to directly produce about 100-nm large tetragonal BaTiO3 nanocrystals, of which the hydroxyl concentration exceeded that in hydrothermal cubic BaTiO3 nanopowders [50, 128]. These facts indicated that the hydroxyl defect model is not responsible for the stabilization of the cubic nanophase.

3.4.3. Microscopic Interaction Model Before discussing the microscopic interaction model, let us recall the main results on the origin of ferroelectricity and the nature of the ferroelectric–paraelectric phase transition of ferroelectric titanates. The first-principle theoretical investigations revealed that the long-range Coulombic interactions favor the ferroelectric distortion, but the short-range electric repulsions favor the nonpolar cubic structure, and those ferroelectric phases result from softening of the shortrange electric repulsions by Ti 3d–O 2p hybridization [5, 6, 37, 38, 146–148]. Most recently, Kuroiwa et al. measured the charge density distributions of the tetragonal and cubic phases of BaTiO3 and PbTiO3 by the maximum entropy method/Rietveld analysis using synchrotron–radiation powder diffraction, and verified the hybridization between the Ti 3d states and O 2p states in the ferroelectric tetragonal phase. At the same time, a charge transfer was found between the Pb 6s states and O 2p states through the cubicto-tetragonal phase transition but the Ba–O bond was always ionic, which suggested that PbTiO3 has a larger ferroelectricity than BaTiO3 [39]. In ferroelectric nanomaterials, when the grain size of the nanoparticles was comparable to the correlation length describing the long-range Coulombic interaction, the longrange interaction remarkably decreased with a decrease in grain size. In creating balance, both the Ti–O hybridization and the short-range electric repulsion were correspondingly reduced [32, 33]. For the partially covalent–ionic crystals, the reduction in hybridization meant a loss in the directional character of the interionic bonds and the crystal tended to assume a structure with comparatively higher symmetry [136]. In the cubic nc-BaTiO3 , the reduction in Ti–O hybridization has been proved using X-ray photoelectron spectroscopy and ab initio simulation [129, 149]. In nc-BaTiO3 , the binding energy of the Ba 3d5/2 electron was measured as 779.3 eV, independent of nanocrystallite size, but the binding energy of the Ti 2p3/2 electron slightly decreased with decreasing grain size below the critical size and was the same as that in the bulk crystal, 458.5 eV,

402 above the critical size. This decrease reflected the character change of Ti–O bonds from covalent to ionic below the critical size [129]. In particular, for the covalent–ionic BaTiO3 nanoparticles, the reduction in Ti–O hybridization induced the lattice distance expansed and the ferroelectric tetragonal phase became unstable, then transformed to highsymmetrical cubic at some critical grain size. So far, it is seen that those structural changes caused by grain size in nc-BaTiO3 are well prescribed using the model of grain size effect on long-range interaction and its cooperative phenomena. In tetragonal PbTiO3 , owing to the additional Pb–O hybridization [39], the stronger covalent bonding resulted in a smaller ferroelectric critical size for the size-induced tetragonal–cubic phase transition than that for BaTiO3 . This further demonstrates that the hybridization change plays a dominant role in structural changes of ferroelectric nanomaterials. The first-principle calculations indicated that the tetragonal c/a lattice strain is quite significant for ferroelectric tetragonal distortion, which enhances the hybridization between the Ti 3d states and the O 2p states and helps stabilize the tetragonal phase. The ferroelectric–paraelectric phase transition in BaTiO3 arises from a complicated coupling of a displacive soft-mode, order–disorder hopping between wells and lattice strain. Under high pressure, the volume dependence of soft-mode potential surfaces is consistent with the loss of ferroelectricity in titanate. Under compression, the multiple-well structure disappears, and a continuous transition at zero temperature occurs at the pressure where the well depths vanish [5, 6, 37]. As indicated by (5.2), theoretical and experimental studies both revealed that the tetragonal strain scales with the spontaneous polarization (ferroelectricity) in BaTiO3 [150]. In the case of ferroelectric nanocrystals, the reduced tetragonality (as illustrated in Figs. 2 and 3) with decreasing grain size thus weakens the ferroelectricity in the tetragonal nanophase and reduces the hybridization, thereby driving the structure change to paraelectric cubic below the ferroelectric critical size. In nanomaterials of GaN [151] and a large majority of partially covalent oxides [32, 136, 152], which includes technologically important systems such as ferroelectrics, ferromagnets, superconductors, and structural ceramics, a structural change from low symmetry to high symmetry and lattice expansion were also observed with decreasing nanoparticle size. Similar to the case of nc-BaTiO3 , these results could also be well prescribed by the model of grain size effect on long-range interaction and its cooperative phenomena [33]. That is to say, the model of grain size effect on long-range interaction and its cooperative phenomena has universality for covalent–ionic nanomaterials. The reduction in electronic covalency intrinsically involved in this model may cause nanomaterials to possess some different properties from their corresponding bulk, such as superparaelectricity, quantum ferroelectricity (discussed below), superparamagnetism [153], and so on.

4. PROPERTIES Since the long-range Coulomb interaction is strongly reduced in BaTiO3 ferroelectric nanocrystals, it is quite natural that ferroelectric nanostructured materials exhibit

Nanocrystalline Barium Titanate

different electrical and optical properties from those of bulk crystals. In this section, the present results of the electrical and optical properties on BaTiO3 nanostructured materials are summarized in Sections 4.1 and 4.2, respectively.

4.1. Electrical Properties The grain size effect on the phase transitions and physical properties of ferroelectrics has been known since the 1950s. The properties of Curie temperature (Tc ), spontaneous polarization, coercive field, switching speed, dielectric constant, and so forth, were found to depend on the grain size [28, 144, 154]. As illustrated in Figure 5, the dielectric constant of BaTiO3 ceramics increased with decreasing grain size, and a maximum value of r ∼ 5000 was observed with a grain size around 1
m. With further decreasing grain size into the nanometer scale, r remarkably decreased [9, 10, 25, 31, 116, 117, 130]. For nanoceramics with an average grain size of 400 nm, the room-temperature dielectric constant was measured as 3500 at 100 kHz, but for a grain size of 300 nm, r = 3000 [10]. For sol–gel-derived 50-nm BaTiO3 nanocrystalline film on platinized silicon substrates with a thickness of 1.5
m, the dielectric constant and loss tangent were measured as 430 and 0.015, respectively, at 10 kHz under ambient conditions.  increased from 430 to 470, but tan remained unchanged as the measurement atmosphere was changed from air to vacuum [23]. In sol–gel-derived BaTiO3 nanocrystalline thick films with an average grain size in the range of 15–25 nm, the films with larger grain size exhibited stronger frequency dependence of the dielectric constant. For a film with a grain size of 25 nm, the roomtemperature dielectric constant decreased from 401 to 349 as the frequency was increased from 1 kHz to 10 MHz. When the grain size was increased from 15 to 25 nm, the relative dielectric constant increased from 207 to 401 at 1 kHz [26]. For sol–gel-derived BaTiO3 nanocrystalline thin films with a grain size of 25 nm, the dielectric constant and loss tangent were 230 and 0.02 at room temperature, respectively. The temperature coefficient of capacitance was 625 × 10−6 / C between −55 C and 125  C at 1 kHz, which exhibited a better temperature capacitance stability [25]. As discussed in the model of grain size effect on longrange Coulomb interactions and its cooperative phenomena, the reduced grain size in ferroelectric nanomaterials suppressed the long-range cooperative order process so that the temperature dependence of the dielectric properties exhibited different behaviors from their bulk counterparts. This grain size effect on the dielectric properties of nanostructured BaTiO3 was referred as to the superparaelectric effect [130]. For BaTiO3 nanoceramics with an average grain size of 400 nm, spontaneous polarization Ps = 17
C/cm2 and remanent polarization Pr = 4
C/cm2 were obtained from the polarization–electric field hysteresis loop at room temperature. For nanoceramics with a grain size of 300 nm, Ps = 15
C/cm2 and Pr = 2
C/cm2 . In contrast, BaTiO3 fine ceramics with a grain size of 1.2
m exhibited Ps = 19
C/cm2 and Pr = 6
C/cm2 . The coercive field was Ec ∼ 200 kV/cm for these nano- and fine ceramics [10]. For sol– gel-derived BaTiO3 nanocrystalline film on platinized silicon

Nanocrystalline Barium Titanate

substrates with a grain size of 50 nm and a thickness of 1.5
m, the observation of good capacitance–voltage butterfly curve and hysteresis loop indicated ferroelectricity behavior, while Pr = ∼20
C/cm2 with Ec = ∼27 kV/cm were obtained at room temperature. With increasing temperature, the dielectric constant increases and goes through a broad maximum around 125  C and then decreases with a further increase in temperature. This broad phase transition in the nc-BaTiO3 with a grain size of 50 nm was characterized by a diffuse phase transition feature. Regarding the low-temperature dielectric property, there was a lack of any anomalies at the phase transition temperatures corresponding to tetragonal–orthorhombic and orthorhombic– rhombohedal phase transitions, except for a change in the slope of the temperature dependence of the dielectric constant below about 50 K [23]. For 50-nm BaTiO3 nanocrystalline thin film on metallic LaNiO3 -coated LaAlO3 (100) single-crystal substrates, a good hysteresis loop with Pr = 83
C/cm2 and Ec = 50 kV/cm was observed. The dielectric constant slowly decreased from 127 to 117 and the loss tangent changed from 0.02 to 0.05 when the frequency was increased from 100 Hz to 1 MHz. The leakage current density for 400-nm-thick film was found to be less than 5 × 10−7 A/cm2 at an electrical field of 100 kV/cm [24]. In contrast, bulk single-crystal BaTiO3 has Ps = 26
C/cm2 and Ec = 15 kV/cm. Therefore, there occurred suppressed dielectric and ferroelectric behaviors but increased Ec in BaTiO3 nanostructured materials. In cubic BaTiO3 nanoparticles, the present electrical measurements indicated a lack of polarization–voltage hysteresis loops. It was found that this paraelectric cubic nanophase remained stable over a relatively large temperature range, preliminarily determined to be 80 up to 1000 K [25, 72, 128]. Surprisingly, using electrostatic force microscopy, a local polarization was induced and reversed repeatedly on cubic BaTiO3 nanorods as small as 10 nm in diameter. The retention time for induced polarization exceeded 5 days in an ultrahigh vacuum environment, which demonstrated the potential of nanorods for fabricating nonvolatile memory nanodevices [82]. Nevertheless, it should be noted that these electrical measurements on cubic BaTiO3 nanocrystals are just preliminary. The suppressed dielectric and ferroelectric behaviors but increased Ec in BaTiO3 nanostructured materials were attributed to the finite grain size effect and clamping of the film to the substrate. In the past, the finite grain size effect was widely investigated and has been determined to be an intrinsic resource for ferroelectric nanocrystals. Both theoretical and experimental studies revealed the structural changes of a multidomain–single-domain transformation, a decrease in tetragonal distortion, and a size-induced ferroelectric tetragonal–paraelectric cubic phase transition with decreasing grain size [9, 10, 22, 32]. Shaikh et al. measured the dielectric constant and spontaneous polarization of fine BaTiO3 ceramics with various grain size and estimated the critical size for the multidomain–single-domain transformation to be about 400 nm [116]. Using the thermodynamical free-energy method, Hsiang and Yen calculated this critical grain size to be about 80 nm, but their experimental measurements indicated it was larger than 100 nm [43].

403 The dielectric constant increment in fine BaTiO3 ceramics was attributed to the domain structure change from the multidomain to the single domain with decreasing grain size. In PbTiO3 , another important ferroelectric nanomaterial, transmission electron microscopy (TEM) measurements indicated it changed from the multidomain to the single domain when the grain size was less than 20 nm [137]. In perovskite-type oxide ferroelectrics, the tetragonal strain scales with the spontaneous polarization. Owing to the smaller strain of 1% in BaTiO3 bulk crystal compared to 6% in PbTiO3 , BaTiO3 has a weaker ferroelectricity than PbTiO3 [37]. In nc-BaTiO3 , the tetragonality changed from c/a = 101 to 1.00 with decreasing particle size, as illustrated in Figure 3. Compared with the bulk crystal, a reduction in the c/a ratio in nc-BaTiO3 implies a smaller strain and leads to a weakening of the ferroelectric tetragonal [33, 74]. These grain size–induced structural changes in the ferroelectricity and paraelectric cubic phase were the cause of the dielectric constant reduction observed in BaTiO3 nanocrystals. For BaTiO3 nanoceramics with a grain size of 300–400 nm, both XRD and Raman data indicated that the reduced electric properties were due to the reduced tetragonality; for example, the c/a ratio was measured as 1.008 in nanoceramics with a grain size of 400 nm [10]. In dense nanoceramics and films, the nanoparticles are elastically constrained by the surrounding environment, which makes the structural analysis complex. To understand the precise nature of ferroelectricity at the nanoscale, it is necessary to prepare freestanding BaTiO3 nanocrystalline particles and films [62]. In the BaTiO3 /SrTiO3 superlattices, Kim et al. observed an increase in both the dielectric constant and its nonlinearity (voltage tunability) with decreasing stacking periodicity within the critical thickness. A maximum zero-field dielectric constant of 1600 at 1 MHz and a large voltage tunability of 94% were observed at the periodicity of the (BaTiO3 )2-unit-cell /(SrTiO3 )2-unit-cell superlattice, in comparison with 74% in Bax Sr1−x TiO3 thin film [112]. The high dielectric constant and large voltage tunability make BaTiO3 /SrTiO3 strained superlattices very attractive for electrically tunable microwave devices. With varying layer thickness of the constituents, Tsurumi et al. found the [(BaTiO3 )10-unit-cell /(SrTiO3 )10-unit-cell ]4 and [(BaTiO3 )10-unit-cell /(BaZrO3 )10-unit-cell ]4 superlattices having much higher dielectric permittivities and refractive indices than other superlattices [98]. In contrast to symmetric superlattices, Shimuta et al. studied epitaxial asymmetric BaTiO3 /SrTiO3 strained superlattices that had unequal BaTiO3 and SrTiO3 layer thickness and found that the superlattice with a stacking periodicity of 15 unit cells BaTiO3 /3 unit cells SrTiO3 showed the largest remanent polarization 2Pr of 46
C/cm2 but the dielectric constant was 240 at 1 MHz [109]. These experiments demonstrated that the strained superlattice is an effective approach to enhance the properties of the constituents by controlling the stacking periodicity, the thickness of the alternative layers, and their thickness ratio. Playing the role of the pressure effect, the lattice strain in the superlattices affected not only the ionic polarization but also the electronic structure or chemical bonding nature of the superlattices [98, 107, 112].

Nanocrystalline Barium Titanate

404 4.2. Optical Properties In this section, second-harmonic generation, light emission, and up-conversion optical properties of BaTiO3 nanostructured materials are summarized.

4.2.1. Second-Harmonic Generation Owing to spontaneous polarization, pure or rare-earthdoped BaTiO3 single crystals have strong electrooptic, nonlinear optical, and photorefractive effects. In bulk barium titanate, the nonlinear coefficients for second-harmonic generation (SHG) were d15 ≈ 170 pm/V, d31 ≈ 157 pm/V, and d33 ≈ 68 pm/V. Theoretical calculations revealed that the nonlinear electronic polarizabilities are very sensitive to changes in electron covalency and electron correlation in the transition metal oxides [40]. Compared with BaTiO3 bulk crystals, the reduction in hybridization must decrease the optical nonlinear coefficients of BaTiO3 nanocrystalline particles and thin films. For epitaxial BaTiO3 nanocrystalline thin films with a grain size of 10–80 nm on MgO substrates, the SHG was investigated at an incident wavelength of 1.064
m. The effective d coefficient was measured as 2.13 pm/V for the c-oriented films and 1.5 pm/V for the a-oriented films [20]. Compared with the values of the bulk crystal, these values were much lower, in agreement with the theoretical prediction. Frey and Payne investigated the nanocrystallite grain size effect on SHG of BaTiO3 . In the cubic BaTiO3 nanoparticles, a measurable SHG signal was detected, but it was a factor of 103 weaker than that in the coarser grain of 10
m. When the nanocrystallite size increased above 50 nm, the SHG signal rose significantly. XRD and Raman scattering measurements indicated that the tetragonality increases with increasing grain size above 50 nm but only a local acentric lattice distortion occurs in the cubic nanoparticles [21]. From these facts, it was concluded that the SHG processes would be enhanced by large tetragonal distortion in BaTiO3 nanocrystals. As discussed in Section 2.2, the tetragonal distortion in epitaxial singlecrystal thin films can be tuned over a large range. Therefore, the strained epitaxial thin films are expected to exhibit better SHG performance with tunability.

crystal [18]. There are no reports in the literature on the light emission properties of BaTiO3 nanocrystals under excitation from the valence band to the conduction band. Under excitation by an Ar+ laser, a weak yellow luminescence around 570 nm was first observed in sol–gel-derived BaTiO3 nanoparticles [156]. Later, three photoluminescence bands centered at 543 nm (green), 574 nm (yellow), and 694 nm (red), respectively, were observed in the LTHM-processed slightly Ti-rich barium titanate nanoparticles with heat treatment at various temperatures; the results are reproduced in Figure 8 [49, 74, 75]. Yu et al. found that a hexagonal phase and BaTi2 O5 clusters embedded within BaTiO3 nanoparticles played the role of color centers for the 543- and 694-nm emission bands, respectively, but the Ti defects contributed to the yellow emission band. Under various annealing temperatures, the peak position of each luminescence band did not shift, despite the luminescent intensity. This phenomenon was understood by combining quantum size confinement and dielectric confinement effects, which had the opposite effect on the energy level of the color centers as a function of nanoparticle size and thus kept them unchanged within the band gap. In the experiments with excitation of various powers, all three light emission bands were found, characteristic of the self-trapped exciton emission mechanism [49]. The mechanism of self-trapped exciton light emissions in the cubic BaTiO3 nanophase can be understood by the embedded-molecular-cluster model [157], in which the local rhombohedral distortion and lattice expansion in cubic nc-BaTiO3 fulfill the requirements to make excitons self-trapped on second-phase clusters or defects. In particular, when the annealing temperature was increased to more than 900  C, the spectrum shape of the red band changed and could be fitted from one Gaussian distribution to two Lorentzian ones. This change was closely associated with the crystalline field change in the nc-BaTiO3 cubic–tetragonal phase transformation induced by the grain size [158]. In Er-doped BaTiO3 nanostructured materials with an average grain size of 25 nm, a typical erbium spontaneous luminescence, corresponding to the intra-4f transition from 4 I13/2 to 4 I15/2 , was observed at 1.54
m with a fine width

4.2.2. Light Emission 694

574

PL Intensity (a.u.)

Spontaneous light emission is one of the basic properties of nanocrystals due to the quantum size confinement effect, and it is a powerful tool to probe the electronic structure and impurity. In bulk ferroelectric BaTiO3 , a complex broad luminescence band around 500 nm was observed under valence band-to-conduction band excitation. With increasing temperature, the photoluminescent intensity decreased and was quenched above the tetragonal-to-cubic phase transition temperature [155]. The self-trapped exciton mechanism was proposed to understand this light emission band in ferroelectric phases. In nanocrystallites, the quantum size confinement effect would cause an increase in bandgap with decreasing grain size [18, 77]. Optical measurements indicated that the optical band edge blueshifted toward 3.68 eV for nc-BaTiO3 with a grain size of 8 nm, and 3.53 eV with a grain size of 35 nm, compared to the value of 3.2 eV for bulk single

574 o

600 C

543

o

1100 C

o

1000 C o

500 C

o

900 C o

800 C o

300 C

500

700

900 600

o

700 C

800

Wavelength (nm) Figure 8. Room-temperature photoluminescence spectra for nc-BaTiO3 annealed at various temperatures for 1 h. The photoexcitation line was 488.0 nm of Ar+ laser with an output power of 200 mW at header. Reprinted with permission from [49], J. Yu et al., Appl. Phys. Lett. 77, 2807 (2000). © 2000, American Institute of Physics.

Nanocrystalline Barium Titanate

at half-maximum of approximately 45 nm under excitation of both 514- and 980-nm lasers [159]. The luminescent intensity and the 1/e lifetime were closely dependent on the concentration of Er ions in the nanostructured materials. For the 3.0-mol% Er-doped BaTiO3 nanomaterials, the 1.54-
m emission decayed in a single exponential way with a 1/e lifetime of approximately 5 ms. When the concentration was more than 3.0 mol%, the 1.54-
m light emission was quenched. The quenching mechanism was explained by energy transfer and cross-relaxation processes between closely sited Er3+ ions within the BaTiO3 lattice, which are related to the up-conversion process discussed below.

4.2.3. Up-Conversion Up-conversion to the visible spectrum from the nearinfrared has been developing as an important approach for the generation of visible luminescence and shortwavelength lasing in some rare-earth-doped materials upon near-infrared excitation. Up-conversion is a nonlinear process, whereby two or more low-energy excitation photons are converted into one or two high-energy photons. It can find application in such as all-solid compact blue–green lasers pumped with near-infrared semiconductor laser diodes and infrared radiation detection by converting the invisible light into the visible range where conventional detectors are effective. In particular, Er3+ has a favorable energy level structure with two transitions of 4 I15/2 → 4 I11/2 (at 980 nm) and 4 I15/2 → 4 I9/2 (at 810 nm), which can be efficiently pumped with high-power near-infrared semiconductor lasers to yield blue, green, and red up-conversion emissions. Compared with glasses and fluoride crystals, in which blue and red up-conversion emission and lasing have been realized, BaTiO3 permits a high solid solubility of at least 10 at% at the Ti site of Er3+ ions [14]. In addition, Er3+ ions are homogeneously distributed throughout the depth of BaTiO3 films. Thus, much higher overlap between Er3+ distribution and optical field profile could be expected in the Er3+ : BaTiO3 film waveguides [54, 160]. In sol–gel-derived Er3+ : BaTiO3 nanocrystalline particles and thin films with an average grain size of 15–25 nm, three up-conversion emissions at 526 nm (2 H11/2 → 4 I15/2 ), at 549 nm (4 S3/2 → 4 I15/2 ), and at 670 nm (4 F9/2 → 4 I15/2 ) were observed under excitation at 980 and 810 nm from both laser diodes and a xenon lamp, among which the transition 4 S3/2 → 4 I15/2 is spin-allowed so that the 549-nm emission was bright even to the naked eye [54, 159–161]. The absorption measurements in the ranges from 805 to 825 nm (4 I15/2 → 4 I9/2 ) and from 960 to 1000 nm (4 I15/2 → 4 I11/2 ) indicated that the laser diodes operating at 810 and 980 nm are efficient pump sources for the 549-nm up-conversion emission. Upon excitation at 980 and 810 nm, the predominant 549-nm emission had a different intensity and lifetime. The lifetime of the 549-nm emission increased sixfold with 980-nm excitation compared to that with 810-nm excitation, which resulted from the different population mechanisms. With the 980-nm excitation, both the excited state absorption (ESA) of individual Er3+ ions and the cooperative energy transfer (CET) between two near Er3+ ions

405 contributed to the 549-nm up-conversion emission. In contrast, the up-conversion emission under the 810 nm excitation was just through an ESA process. Therefore, the excitation around 980 nm was more effective for the 549-nm up-conversion emission from the Er : BaTiO3 nanostructured materials [54, 160, 161]. For up-conversion lasing from Er : BaTiO3 nanostructured materials, research is currently underway.

5. LATTICE DYNAMICS 5.1. Raman-Active Optical Modes In the bulk BaTiO3 paraelectric cubic phase, the space group Oh1 transforms as 3T1u + T2u optical modes at the center of the Brillouin zone, which are triply degenerate. The longrange electrostatic forces split each of the optical modes into a doubly degenerate transverse optical (TO) mode and a singly degenerate longitudinal optical (LO) mode. The optical T1u modes are infrared active, but the T2u mode is neither infrared active nor Raman active [150, 162]. Nevertheless, two broad Raman modes centered around 250 and 515 cm−1 were recorded in bulk BaTiO3 single crystals and ceramics above T [95, 163, 164]. In the ferroelectric tetragonal phase, each cubic T1u mode transforms as the A1 + E irreducible 1 . The distinct Ramanrepresentation and T2u as B1 + E of C4v active optical vibrations, 3A1 TO + 3A1 LO + 3ETO + 3ELO + 1ELO + TO + 1B1 , were obtained for tetragonal BaTiO3 . In single crystals, the first-order Raman modes at 36, 180, 305, 463, 470, 486, 518, 715, and 727 cm−1 and two broad modes around 270 and 520 cm−1 were obtained, while four modes at 270, 305, 516, and 719 cm−1 and a negative intensity mode at 180 cm−1 were obtained in ceramics [95, 162–164]. As illustrated in Figure 6, the depolarized Raman scattering measurements recorded five modes centered at 184, 257, 308, 518, and 716 cm−1 in the single-phase cubic BaTiO3 nanoparticles [21, 33, 58, 63, 95, 126]. In the cubic nanocrystal, of major importance was that the three first-order modes at 184, 308, and 716 cm−1 were Raman active, even though these three modes typically conform to Raman selection rules in the bulk materials. These different lattice vibration properties indicated that the local structure of cubic nanocrystals was acentrically distorted, which relaxed the Raman selection rules. The second-harmonic generation and electron paramagnetic resonance spectroscopy measurements also revealed the occurrence of locally acentric distortion in the XRD-measured cubic nanoparticles [21, 53, 58]. Recent measurements showed that the change in the Ti–O bonding character of BaTiO3 nanoparticles leads to elongation of both the Ba–Ti and the Ba–O bond lengths from 3.47 Å and 2.83 Å to 3.60 Å and 2.94 Å, respectively, while the Ti–O bond length remains nearly constant (∼2.0 Å) [129]. Based on these bond lengths, the unit cell in cubic nc-BaTiO3 has local rhombohedral distortion, but not the tetragonal or orthorhombic distortion assigned by other authors [21, 33, 63]. In the quantum phase transformations, the zero-point fluctuation energy is closely associated with the property of lattice dynamics. The first-order phonons being Raman active would have a strong influence on the

Nanocrystalline Barium Titanate

406 zero-point energy of the BaTiO3 nanosystems and consequently, would shift the critical condition of phase transformation from classic to quantum [33, 158].

5.2. Soft-Mode Theory In 1960, Cochran and Anderson independently pointed out that the ferroelectric–paraelectric structural phase transition in ABO3 perovskite oxides was closely related to the dynamical behavior of the lowest frequency TO phonon mode, that is, the soft mode. Since then, the soft-mode theory has achieved great success in explaining ferroelectric phase transitions. In the lattice dynamic model of displacive ferroelectric structural phase transitions, the dynamical behavior of ferroelectricity is closely associated with the softening of the lowest frequency TO mode at the center of the Brillouin zone, and its freezing corresponds to paraelectric–ferroelectric phase transition. As each transition temperature is approached, the frequency of the soft mode generally decreases and is described by the following relationship:

2TO = AT − Tc 

′

(5.1)

where A is a constant: positive at T > Tc and negative at T < Tc . In cubic BaTiO3 , the soft mode is the lowest frequency T1u TO mode, whose freezing induces the generation of ferroelectricity, but in the tetragonal phase, the lowest frequencies E1TO and A1 1TO are the soft modes, whose freezing induces the disappearance of ferroelectricity [1, 150]. The temperature dependence of the ferroelectric soft mode in ABO3 reflects the variation of the anharmonic interactions due to the hybridization between transition metal d states and oxygen p states [165]. In the classical mean field region, the critical exponent  ′ = 1, but when the quantum zero-point fluctuation prevails at lowtemperature,  ′ approaches 2, close to the quantum limit, and becomes 0 at T → 0 K [165, 166]. In addition to explaining the sequence of phase transitions, the soft-mode theory has been successful in other ways. In the ferroelectric phase of ABO3 oxides, the spontaneous polarization Ps and spontaneous strain described by the tetragonality c/a are two important order parameters. In tetragonal BaTiO3 and PbTiO3 bulk materials, the connections between the temperature dependence of the soft-mode frequency A1 1TO and the spontaneous polarization and spontaneous strain were established [2, 150]:

A1 1TO ∝ Ps ∝ c/a − 11/2

(5.2)

The Curie–Weiss law characterizes the dielectric properties in the paraelectric phase of ferroelectric materials, and its general formulation is T  = CT − T0 −T

(5.3)

where C is the Curie–Weiss constant and T0 is the Curie– Weiss temperature. In the classical regime, the critical exponent T = 1 was found for the static dielectric constant, but at relatively low-temperatures where zero-point quantum fluctuations prevented long-range order phase,

T approached 2, close to the quantum limit. With T → 0 K, the saturation of the low-frequency dielectric constant corresponded to T = 0. These predictions have been experimentally demonstrated in incipient ferroelectrics such as SrTiO3 , KNbO3 , and KTaO3 and normal ferroelectrics such as BaTiO3 and PbTiO3 [1, 2, 7, 166, 167]. Through the Lyddane–Sachs–Teller (LST) relationship, the Curie–Weiss law intrinsically reduces to the soft-mode theory [7, 166]. In ionic crystals, the LST relationship is 0

2 = 2LO  

TO

(5.4)

which relates the static dielectric constant, 0, and the high-frequency dielectric constant,  , to the eigenfrequencies, LO and TO , of LO and TO phonons [1, 2]. The LST relationship has been proven quantitatively in the ferroelectric and paraelectric phases of ferroelectrics such as SrTiO3 , PbTiO3 , KNbO3 , and KTaO3 , and the dramatic change in the static dielectric constant is directly related to the soft-mode behavior [4, 150, 165, 166]. For example, in the case of tetragonal PbTiO3 , the dielectric constant along the ferroelectric axis c is determined primarily by the lowest frequency A1 1TO mode, and a perpendicular to the c axis by the lowest E1TO mode at all temperatures upto Tc [150]. To date, it is accepted that BaTiO3 is not a typical displacive ferroelectric [3, 4, 150]. In the tetragonal phase, the E1TO soft mode was found to be highly overdamped, but the A1 1TO soft mode was underdamped, both mixed with a certain amount of disorder character. Because of the large damping factor of the soft mode, it was very difficult to detect the soft modes by the conventional Raman spectroscopic method. At that time, the calculated LST from the soft mode was only about 25% of the experimentally determined c [150, 162]. In the 1990s, the femtosecond time-domain light-scattering spectroscopy technique was developed, which took advantage of determining the soft-mode frequency more accurately than conventional frequency-domain spectroscopy. Nevertheless, the static dielectric constant calculated via the LST relationship for BaTiO3 bulk crystals still did not quantitatively agree with the present experimental value [4]. Dougherty et al. suggested reperforming dielectric measurements of BaTiO3 to test the LST relationship, but the data are still lacking.

5.3. Finite-Size Effect In the microscopic theory of displacive ABO3 ferroelectrics, the dynamical behavior of the soft mode depends on the compensation of the long-range Coulomb force by the shortrange electric repulsive and covalent forces. The hybridization between transition metal B ion d states and oxygen p states softens the ferroelectric soft mode and thus ferroelectric displacement can take place [5, 165, 168]. In ferroelectric nanocrystalline particles and thin films, the finite-size effect on the behavior of the soft modes also plays a central role in these changes in the structural and physical properties. When the grain size is comparable to the correlation length, both the long-range Coulomb forces and the shortrange electric repulsive and covalent forces decrease with

Nanocrystalline Barium Titanate

407

decreasing nanocrystallite size, but the short-range forces decrease faster than the long-range Coulomb forces, and thus cause the A1 1TO and E1TO soft-mode frequencies to gradually decrease with decreasing grain size and finally to freeze out below a critical size. In accordance with (5.2), the reduction in soft-mode frequencies is accompanied by a weakening of the ferroelectricity and a decrease in tetragonality, and the soft mode freezing corresponds to the grain size-induced tetragonal–cubic phase transition [138, 139]. In PbTiO3 -based ferroelectric nanoparticles, with decreasing grain size, the room-temperature frequencies of the E1TO and A1 1TO soft modes were experimentally observed to decrease, but the linewidth increased, compared with those of the bulk materials [138, 169–171]. For example, in nc-PbTiO3 , the E1TO soft mode shifted from 83 cm−1 to 72 cm−1 in frequency and increased from 12 cm−1 to 31 cm−1 in linewidth with decreasing grain size from 50.5 nm to 20 nm [170]. For nc-PbTiO3 , with a grain size of 50.5 nm, the squared frequency of the E1TO soft mode deviated from the straight-line dependence of pressure above 4 GPa, which suggested that the PbTiO3 nanomaterials have a different phase transition from that of the bulk materials, where the E(1TO) soft-mode frequency decreased toward 0 as the pressure increased and all of the modes disappeared above 11.63 GPa [170]. Varying the temperature and/or pressure, the partial softening and superlinear broadening of the E1TO soft mode implied that nanocrystalline PbTiO3 is no longer an ideal displacive ferroelectric, but mixed with an order–disorder feature [172]. For each grain size of PbTiO3 ferroelectric nanoparticles, taking (3.2) into (5.1), the temperature dependence of the A1 1TO soft-mode frequency was determined by the equation:

2 = AT − Tc   + D/R − Rc 

(5.5)

On the other hand, the frequency of the soft mode decreased with decreasing nanocrystallite size, although they had the same dynamical behavior as described by (5.5) [138, 170]. This fact implies that the parameter A is a function of grain size, which decreases with decreasing grain size. Recently, the room-temperature spontaneous strain in nc-PbTiO3 as a function of nanoparticle size was experimentally obtained: c/a − 1 = E1 − expERc − R

(5.6)

where the constant E = 0065 [32]. Under the first approximation (1 − e−x ≈ 1/x), (5.6) can be simplified as c/a − 1 ≈ 1/R − Rc 

(5.7)

Comparing (5.5) with (5.7), the relationship 2 A1 1TO ∝ c/a − 1 does not exist in the case of nc-PbTiO3 . The reduced tetragonality (c/a) in ferroelectric nanoparticles only provides partial contributions to the reductions in the soft-mode-frequency, dielectric, and ferroelectric properties. So far, it is concluded that the reduced tetragonal distortion is partially responsible for the suppressed ferroelectricity and related properties in ferroelectric nanoparticles, and the intrinsic grain size effect on the electronic structure plays a dominant role, especially in the variation of parameter A.

In quantum paraelectric SrTiO3 nanocrystals, the reduced long-range Coulomb forces would cause the frequency of the T1u soft mode to increase with decreasing grain size, that is, soft-mode hardening. Raman and infrared spectroscopic measurements indicated that the zone center cubic T1u soft-mode frequencies of the small nanoparticles were higher than those of the larger ones at low temperature [166, 173, 174]. The dielectric constant was measured as 770 with a grain size of 44 nm but 350 with a grain size of 12 nm at 12 K and 100 kHz. Compared with SrTiO3 bulk crystal, of which the static dielectric constant was about 20,000 below 4 K, the quantum paraelectricity was strongly suppressed in SrTiO3 nanocrystals by the finite grain size. Through the LST relationship of (5.4), the soft-mode hardening observed in nanocrystals agreed with the dramatic reduction in the dielectric constant [173, 174]. For thick SrTiO3 films, the reduction in the dielectric constant was almost the consequence of the soft-mode hardening. But for thinner SrTiO3 films, the interfacial dead layer effect played a sifnificant role in the reduction in the dielectric constant, in addition to the finite-size effect [166]. Moreover, the deviation from the classical Curie–Weiss law started at a higher temperature for smaller nanocrystallite size. In ferroelectric BaTiO3 nanocrystals, the reduction in the p–d hybridization induced by the finite-size effect would no doubt influence the behavior of the soft mode [168]. Similar to PbTiO3 and SrTiO3 , the softening of the A1 1TO and E1TO soft modes in the tetragonal nanophase or the hardening of the T1u soft mode in the cubic nanophase is also reponsible for the reduction in the electrical properties of BaTiO3 nanocrystals. At present, there is a lack of experimental data on both the soft mode and the static dielectric constant with varying grain size for BaTiO3 nanocrystals.

5.4. Quantum Ferroelectricity For the displacive structural phase transitions in ferroelectrics such as BaTiO3 , the phase transition caused by variation of the parameters in a lattice dynamical system were investigated within the framework of both classical and quantum statistical mechanics [143]. For the ferroelectric– paraelectric transition Curie temperature Tc , it was found as a function of the interaction parameter S: Tc S ∝ Sc − S1/

(5.8)

where S is an interaction parameter—an external parameter such as pressure or chemical composition—that controls the interaction, and Sc is its value at Tc = 0. In the classical regime, the phase transitions were driven by thermal fluctuations, but when the Tc → 0 K, quantum zero-point fluctuations, instead of thermal fluctuations, played a dominant role. The theoretical treatment predicted that Tc varied with the critical exponent  ≡ 2, close to the quantum limit, and  ≡ 1, close to the classical limit. The relationship Tc = ASc − S1/2 is typical of quantum ferroelectricity, Tc = 0 at S = Sc being the quantum limit. Conventionally, BaTiO3 was a normal ferroelectric with a critical exponent  = 1 under low hydrostatic pressure or with a large concentration of strontium content. However, for BaTiO3 under a hydrostatic pressure of 4–8 GPa and Ba1−x Srx TiO3 with 08 < x < 0965,

408 the critical exponent  changed to 2 [7, 167, 175]. That is to say, under these conditions, BaTiO3 became a quantum ferroelectric and the nature of ferroelectric–paraelectric phase transition was controlled by quantum mechanics. For BaTiO3 , both theoretical and experimental results indicated the ferroelectric-paraelectric phase transformations change in nature from being controlled by classical mechanics to being controlled by quantum mechanics under high pressure (hydrostatic or chemical). In these pressure experiments, the interatomic distance played a crucial role in the pressure-established quantum ferroelectricity and paraelectricity. In the BaTiO3 nanocrystals, as shown by Figures 2 and 3, the lattice parameter was a function of grain size and the ferroelectricity decreased with decreasing grain size. As indicated by (3.2), with decreasing grain size, Tc was shifted downward through room temperature, eventually tending toward 0 K at some critical grain size [22]. According to the scaling theory of phase transitions, the properties of ferroelectrics and the nature of the phase transition would be controlled by quantum mechanics under the condition of the polar order parameter being comparable with zero-point fluctuation [143]. Similar to the pressure effect, the grain size effect in ferroelectric nanomaterials could induce the spontaneous polarization to be reduced to 0, in accordance with (5.2) and (5.5), so that it might shift the critical conditions of classical-to-quantum ferroelectric and paraelectric phase variations. From the viewpoint of microscopic interaction, the predominant change in these phase transformations was found to be the reduction in the Ti–O hybridization, despite different birthrights—hydrostatic pressure, chemical pressure, grain size effect in nanomaterials. Based on these facts, nc-BaTiO3 is expected in an analogous way to be quantum ferroelectric and paraelectric over some range of grain size [33, 158]. Equation (5.8) should also be suitable for nc-BaTiO3 , where the grain size R can be used as the interaction parameter. In addition, preliminary measurements showed that the grain size effect in nc-BaTiO3 plays an equivalent role of the pressure effect, spanning across the entire range of quantum ferroelectricity and paraelectricity of BaTiO3 [7, 128]. Compared with the pressure effect, the grain size effect in nc-BaTiO3 provides a method for stabilizing and utilizing those metastable phases in ambient environments. Of interest, in the experiments of pressureinduced phase transformation in CeO2 nanoparticles, the critical pressure was reduced 28.1% and there was a larger volume change of 9.4% in the phase transformation than that for the bulk CeO2 [176]. These facts supported in an experimental way the grain size effect in nanomaterials playing an equivalent role of the pressure effect. The prediction of quantum behavior in nc-BaTiO3 is significantly of interest for fundamental understanding of ferroelectric nanocrystals and technological applications, especially using its dielectric properties in such as infrared detection and electronic and photonic devices. However, in BaTiO3 and PbTiO3 nanoparticles with grain size above the critical size, the preliminary measurements revealed that the dependence of the Curie temperature on the grain size had a critical exponent  = −1 [22, 139]. Taking R−1 , rather than R, as the interaction parameter, this sign discrepancy in the critical exponent may disappear. In the near future the nanocrystallite size–temperature phase diagram and the

Nanocrystalline Barium Titanate

temperature dependence of dielectric properties with various nanocrystallite size will be required. In SrTiO3 nanocrystals, electrical and Raman spectroscopic measurements revealed that the finite-size effect suppressed the zero-point quantum fluctuations and shifted the classical-to-quantum crossover towards higher temperature [174]. Since the finite-size effect plays the role of suppressing quantum fluctuation, the chemical pressure necessary for quantum ferroelectricity in Ba1−x Srx TiO3 nanocrystals would be smaller than in the bulk case; that is, the critical composition xc increases with decreasing grain size.

6. BARIUM STRONTIUM TITANATE SrTiO3 is a well known quantum paraelectric or incipient ferroelectric. It is in the cubic phase (space group Pm3m) at room temperature and undergoes an antiferrodistortive structural phase transition to the tetragonal phase (space group I4/mcm) at 105 K. This transition results from the freezing of one of the triply degenerate R25 modes at the Brillouin zone boundary. With decreasing temperature, the dielectric constant increases but becomes saturate at 0 ≈ 20 000 below 4 K. Above 40 K, a zone center TO mode exhibits a softening behavior, which agrees with the temperature dependence of the static dielectric constant via the LST relationship. Below 40 K, zero-point quantum fluctuations preclude the freezing of this soft mode, and SrTiO3 remains in the tetragonal paraelectric phase even to absolute 0 K, which is known as the quantum paraelectric phase [166, 177]. Moreover, it is possible to suppress the quantum fluctuations and induce polar ordering in SrTiO3 by chemical substitutions of Ba, Ca, Pb, and 18 O, application of an electric field, or application of mechanical stress [167]. In Ba1−x Srx TiO3 solid solutions, three phase transition temperatures of BaTiO3 linearly decrease with increasing SrTiO3 concentration up to x = 08. For the tetragonal– cubic phase transition, the Curie temperature obeys Tc K = 410 − 360x. When 08 < x < 0965, there is only one paraelectric–ferroelectric phase transition with Tc = 3000965 − x1/2 (K). When x > 0965, the ferroelectric phase transition is precluded by zero-point quantum fluctuations while barium strontium titanate exhibits a glasslike behavior [167]. For quantum ferroelectric Ba1−x Srx TiO3 (08 < x < 0965) bulk crystals, the critical exponent T of the Curie–Weiss law at x near 0.8 is equal to 1 and then grows to about 1.5 when x increases. Lattice contraction as a function of Sr concentration obeys Vegard’s law, a = 3905x + 39921 − x. So the chemical pressure effect could be compared with the hydrostatic pressure effect, which has a similar pressure–temperature phase diagram [7, 167]. For Ba1−x Srx TiO3 solid solutions, of technological interest is the room-temperature ferroelectric–paraelectric boundary around x = 03. They exhibit high room-temperature dielectric constant, high pyroelectric coefficient, and low dielectric loss, which have attracted considerable attention for applications such as dynamic random access memory (DRAM), microwave, and pyroelectric devices [167, 178]. In the remaining part of this section, the syntheses of Ba1−x Srx TiO3 nanocrystalline thin film are reviewed. Then the dielectric and nonlinear properties are summarized.

Nanocrystalline Barium Titanate

409

Those factors affecting the film performance, including small grain size, film thickness, crystallographic orientation, lattice strain, and acceptor doping, are also discussed.

6.1. Syntheses In principle, all the synthesis methods for BaTiO3 nanostructured materials could be used without difficulty to prepare Ba1−x Srx TiO3 nanostructured materials. Owing to the strong application background of Ba1−x Srx TiO3 and the facility of the synthesis methods, the sol–gel [55, 178, 179], pulse laser deposition [180–184], and magnetron sputtering [185] methods were widely utilized to fabricate barium strontium titanate nanocrystalline thin films. In this section, the sol–gel methods are discussed and an alkoxide method proposed to prepare Ba1−x Srx TiO3 nanoparticles. Ba1−x Srx TiO3 nanocrystalline particles and thin films were widely synthesized using the same sol–gel method used for synthesizing nc-BaTiO3 , in which the desired stoichiometry was controlled by the ratio of strontium acetate to barium acetate. In a typical process, barium acetate and strontium acetate were mixed and then dissolved in acetic acid above 90 under stirring. 2-Methoxyethanol was utilized to adjust the viscosity of the solution. Titanium isopropoxide was then added to the solution. For films, the gel precursor was spincoated onto the substrates before heat treatment. Finally, the dried and solidified gel was heat-treated to obtain crystalline nanoparticles and thin films. The crystallization temperature for perovskite Ba1−x Srx TiO3 was 650  C. With this technique, nanocrystalline barium strontium titanate thin films with an average grain size of 50 nm were obtained [55, 178, 179]. BaTiO3 and SrTiO3 nanoparticles were successfully produced using bimetallic alkoxide as the starting material [60, 174, 186]. Because Sr(OCH3 OC2 H4 )2 has a similar chemical behavior as Ba(OCH3 OC2 H4 )2 , the alkoxide method could be extended to synthesize (Ba, Sr)TiO3 nanoparticles. Using Ti(i-OC3 H7 )4 , Sr(OCH3 OC2 H4 )2 , and Ba(OCH3 OC2 H4 )2 as the starting materials and 2-methoxyethanol as the solvent, their stoichiometric mixture is refluxed to form a trimetallic alkoxide homogeneous precursor solution. Then hydrolysis is carried out by adding a mixture of deionized water and 2-methoxyethanol to the obtained precursor solution. Finally, the gelated precursor is pyrolyzed and calcined at high temperatures to obtain crystalline barium strontium titanate nanoparticles. On the other hand, similar to the case of nc-BaTiO3 , crystalline barium strontium titanate nanoparticles may also be obtained by low temperature hydrolyzing of (Ba, Sr, Ti)-trimetallic alkoxides under highly alkaline condition [60, 186].

6.2. Low-Frequency Dielectric Properties Ba07 Sr03 TiO3 bulk material has a dielectric constant of approximately 5000 at 300 K. Parker et al. investigated the temperature and film thickness dependence of the dielectric constant of Ba07 Sr03 TiO3 films on the platinized silicon substrate with a thickness ranging from 15 to 580 nm; the results are given in Figure 9. As the film thickness decreased, the maximum dielectric constant decreased from 660 to 110 at 4 kHz, which was more than one order of magnitude less

Figure 9. Permittivity as a function of temperature for six film thicknesses. The data are denoted by closed circles; the diffuse phase transition feature fit by open circles. The arrows denote the maximum value of permittivity. Tabulated with the arrow was the film thickness, the maximum permittivity, and the temperature at which the maximum permittivity occurred. Reprinted with permission from [187], C. B. Parker et al., Appl. Phys. Lett. 81, 340 (2002). © 2002, American Institute of Physics.

than the bulk value. The temperature at which the maximum dielectric constant occurred decreased from room temperature to 269 K for the 580-nm-thick film and to 102 K for the 40-nm-thick film. With decreasing film thickness, the temperature dependence of the dielectric constant anomalous peak became more broad. The film thickness dependence of the dielectric properties was explained in terms of a diffuse phase transition, in which the diffusivity increased with decreasing film thickness [187]. In Ba08 Sr02 TiO3 nanocrystalline thin films on Pt/Ti/SiO2 /Si substrates with an average grain size of 100 nm and a thickness of 400 nm, a broad tetragonal-to-cubic phase transition was observed around 35  C, which was less than Tc = 80  C for the bulk material. Electrical measurements at room temperature showed a dielectric constant of 860 at 100 kHz, Pr = 65
C/cm2 , Ec = 41 kV/cm, and a leakage current density of 33 × 10−7 A/cm2 at 3 V [188]. In Ba08 Sr02 TiO3 thin films, the tetragonalto-cubic phase transition temperature was also observed to decrease with decreasing grain size [85, 188]. Similar to the case of BaTiO3 nanostructured materials, the tetragonal– cubic phase transition temperature and dielectric constants of (Ba, Sr)TiO3 nanocrystals were strongly suppressed by the reduced dimensionality, and an intrinsic finite-size effect and lattice strains introduced during film growth were proposed to understand these reductions in electrical properties [187, 189]. Owing to the strong anisotropy in ferroelectrics, the crystallographic orientation must influence the effective parameter normal to the film, as often reported in the literature. As an example, random and (100) oriented Ba1−x Srx TiO3 films with x = 033, 0.5, 0.67, and 1.0 were fabricated on base-metal (100) nickel tapes using a chemical solution deposition method. For randomly oriented films, zero-field room-temperature dielectric constants ranged from 250 to

410 420 at 100 kHz. But the films with enhanced (100) orientation exhibited zero-field dielectric constants of 980 to 1500, three times higher than the random films. The dielectric loss tangent was between 0.003 and 0.015 [190]. Taking advantage of the high dielectric constant, dynamic random access memories using barium strontium titanate thin film as the functional element were prepared for commercial use at the end of the 1990s.

6.3. Microwave Dielectric Properties In heteroepitaxial Ba1−x Srx TiO3 thin films, lattice strain was introduced during growth owing to lattice and thermal expansion mismatch between these films and the substrates, and the dielectric properties were able to be tuned by controlling the internal lattice strain [180, 181]. In the case of Ba05 Sr05 TiO3 , the bulk cubic lattice parameter is a = 395 Å and the thermal expansion coefficient  = 105 × 10−6 / C at 300 K. On the (001) MgO substrate, the inplane tensile stresses of heteroepitaxial Ba05 Sr05 TiO3 thin films were found to decrease with increasing film thickness from 14 to 130 nm and were fully relaxed above thickness 130 nm. The microwave dielectric constant dropped from 2350 for highly stressed thin films to 1700 for relaxed thicker films at 1 MHz [180]. For the pseudocubic LaAlO3 substrate, a = 379 Å and  = 10 × 10−6 / C at 300 K. Because of the different lattice match conditions between the MgO and LaAlO3 substrates, different lattice strains occurred in the epitaxial Ba05 Sr05 TiO3 thin films. In these epitaxial films, either a large dielectric tuning (75%) or a high dielectric Q = 1/ tan (100–250) but not both at the same time were typically observed [182]. To tune the lattice strain, various thin buffer layers were developed for epitaxially growing barium strontium titanate thin films. Using a thin (∼5 nm) amorphous Ba05 Sr05 TiO3 buffer layer, the strains in the crystalline films were relieved, and the films exhibited both high dielectric tunability and enhanced dielectric Q [182]. Alternatively, by inserting a very thin Ba1−x Srx TiO3 (x = 01–0.7) layer between the Ba06 Sr04 TiO3 thin film and the MgO (001) substrate, the lattice strain (described by the in-plane lattice constant/out-ofplane lattice constant ratio) in 400-nm-thick Ba06 Sr04 TiO3 epitaxial thin films was tuned from 0.9972 to 1.0051 by varying the interlayer composition. The dielectric constant varied between 512 and 1180 at a frequency of 1 MHz. On the Ba07 Sr03 TiO3 interlayer, Ba06 Sr04 TiO3 film showed a larger dielectric constant of 1180 and a tunability of 61% at a surface electric field of 80 kV/cm [181]. Silicon is a very technologically important substrate. Using a very thin yttria-stabilized zirconia buffer layer, epitaxial Ba05 Sr05 TiO3 thin films were successfully grown on the Si substrate using pulse laser deposition. The dielectric constant was as high as 1300 at 1 MHz when the lattice distortion of the in-plane lattice constant/out-of-plane lattice constant ratio was 1.007 [183]. For integrated film device applications, the better insulating (low leakage current density) quality is significantly attractive. In the metalorganic solution deposited Ba06 Sr04 TiO3 nanocrystalline thin films on a platinized silicon substrate, a typical resistivity was  = 004 × 1013  cm

Nanocrystalline Barium Titanate

at an electric field of 100 kV/cm. However, the small concentration of acceptor dopants could dramatically modify the properties of the ferroelectrics. For instance, the 1-mol% La-doped Ba06 Sr04 TiO3 film (average grain size 50 nm and film thickness 150 nm) exhibited an enhanced resistivity of  = 314 × 1013  cm at 100 kV/cm. The dielectric constant, loss tangent, and tunability of the 1-mol% La-doped Ba06 Sr04 TiO3 films were 283 at 100 kHz, 0.019, and 21% at 200 kV/cm, respectively. The improved dielectric properties, low leakage current, and good dielectric tunability of the acceptor-doped barium strontium titanate thin films suggest their use in fabricating high-performance tunable microwave devices [55]. Owing to their large dielectric tunability and low dielectric loss, barium strontium titanate nanocrystalline thin films were widely used to fabricate electrically tunable microwave devices, such as phase shifters and harmonic generators. As an example, using sol–gel-derived highly oriented Ba06 Sr04 TiO3 thin films on a LaAlO3 (100) substrate, eight element coupled microstrip phase shifters were fabricated. An insertion loss of 8.435 dB, phase shift on the order of 320 (2.6–14.5 V/
m), and factor (phase shift/decibel of loss) of about 38.0 /dB were demonstrated [191].

6.4. Nonlinear Optical Properties Similar to the dielectric properties, the nonlinear optical properties of Ba1−x Srx TiO3 thin films were also dependent on the strontium composition and the lattice strain. For a-oriented Ba1−x Srx TiO3 thin films of thickness 200 nm on a (100) LaAlO3 substrate, Li et al. investigated the composition dependence of electrooptic properties at  = 6328 nm of a He–Ne laser [184]. It was found that the linear electrooptic coefficient  had maximum at x = 035–0.4. The quadratic electrooptic coefficient s initially decreased as x increased and reached a small plateau around x = 05. Both  and s dropped to 0 when x > 07. For Ba07 Sr03 TiO3 film,  was determined as 110 pm/V in the case of increasing electric field and 230 pm/V in the case of decreasing electric field; s = 055 × 10−16 m2 /V2 . For Ba05 Sr05 TiO3 film,  was 70 pm/V in the case of increasing electric field and 115 pm/V in the case of decreasing electric field; s = 13 × 10−16 m2 /V2 . Compared with BaTiO3 , the large electrooptic coefficients of Ba1−x Srx TiO3 (x = 03– 0.5) films make them well suited to integrated optoelectronic devices [27, 184]. For cubic Ba1−x Srx TiO3 , second-harmonic generation is unexpected since the crystal structure is centrosymmetric under ambient conditions. However, due to large lattice and thermal expansion mismatches between the Ba1−x Srx TiO3 film and the MgO substrate, the introduced lattice strains destroyed the inversion symmetry and induced secondharmonic generation. In a 30-nm-thick Ba048 Sr052 TiO3 epitaxial film grown on (001) MgO substrate, a tetragonal distortion induced by film strain was determined to be c/a = 1015, and second-order nonlinear susceptibility was measured as d33 = 110 pm/V, d31 = 47 pm/V, and d15 = 22 pm/V at a fundamental wavelength of 1.064
m [185]. As the strain decreased from 2.7% to 0.7%, corresponding to a decrease in the film thickness from 30 nm to 165 nm, the

Nanocrystalline Barium Titanate

second-harmonic signal decreased by a factor of 10. Therefore, the strain was the dominant factor controlling secondharmonic generation in Ba1−x Srx TiO3 epitaxial thin films. Compared with BaTiO3 thin films [20], barium strontium titanate thin films have a large effective d coefficient, better chemical stability, and a higher dielectric constant as well.

7. APPLICATIONS As discussed above, the grain size effect plays an important role in controlling the structural phases and properties of BaTiO3 nanostructured materials. Due to the grain size– induced tetragonal–cubic phase transition, the nanocrystalline BaTiO3 thin films with various grain sizes could find possible applications in integrated high-density memories ranging from dynamic random access memory using high dielectric constant to nonvolatile memory with spontaneous polarization being reversed between two opposite directions, surface acoustic wave devices, microactuators, and various electrooptic devices [29, 154]. Nanocrystalline BaTiO3 thick films of thickness up to several micrometers have potential applications in pyroelectric infrared microsensors and ultrasonic high-frequency transducers [26]. In the following, BaTiO3 nanostructured material applications in the fields of optical modulators, transducers and actuators, and thermal, humidity, and CO2 sensors are discussed in detail.

7.1. Optical Modulators BaTiO3 crystals have the highest known electrooptic coefficient 51 = 820 pm/V at 632.8 nm [19]. In epitaxial BaTiO3 thin-film waveguides on a MgO (001) substrate, a large effective dc electrooptic coefficient of eff ∼ 50 ± 5 pm/V and an electrooptic coefficient of eff ∼ 18 ± 2 pm/V at 5 MHz for  = 154
m light were reported. The propagation loss in a 300-nm-thick planarized waveguide is typically 5 dB/cm for 1.5-
m light [27]. Compared with barium titanate epitaxial thin films, the barium strontium titanate (x = 03–0.5) epitaxial thin films exhibited a higher effective electrooptic coefficient, as discussed in Section 6.4. These experiments demonstrated the potential of BaTiO3 and (Ba, Sr)TiO3 epitaxial thin films for low-voltage, highly confining, guidedwave electrooptic modulator structures. Moreover, thin-film devices offer unique characteristics superior to diffused waveguides fabricated on bulk ferroelectric crystals. The large index difference between the film and the substrate enables a high confinement effect in the waveguides, which creates the potential for high-speed, low-voltage electrooptic switching and for high energy density to be produced at moderate incidence power [159]. In sol–gel Er : BaTiO3 nanocrystalline thin films, optical waveguide double modes were observed with effective refractive indices of 2.122 and 1.868, respectively, at 632.8 nm of He–Ne laser [159]. These results were encouraging for the investigation of planar Er : BaTiO3 film waveguides and devices for optical amplifiers and laser applications. In most cases, the sol–gel-derived films were high loss and random oriented in nature, which resulted in a smaller electrooptic response compared with oriented films. Compared with the sol–gel methods, the MOCVD and laser

411 MBE techniques have more potential to fabricate highquality optical waveguides with loss less than 1 dB/cm [54, 94, 192]. Epitaxial BaTiO3 optical waveguides and electrooptic modulators were fabricated with the MOCVD technique. Excellent modulation efficiency, frequency response, and losses as low as 3–4 dB/cm at 1.54
m were demonstrated [27, 94, 102, 192]. In the c-axis-oriented BaTiO3 epitaxial thin films on a MgO (001) substrate, the refractive index was 2378 ± 0002 at 632.8 nm, and the waveguide loss was 2.9 dB/cm [103]. Nevertheless, future integrated optical circuits will require BaTiO3 thin films to be integrated with silicon or III–V compounds. To date, it is still difficult to prepare epitaxial BaTiO3 films directly on bare silicon substrates due to large lattice mismatch and severe interface diffusion. To obtain high-quality epitaxial ferroelectric thin films on those substrates, the approach using yttria-stabilized zirconia (YSZ) and MgO buffer layers was developed, and then epitaxial BaTiO3 and (Ba, Sr)TiO3 thin films were obtained [183, 193, 194].

7.2. Transducers and Actuators Piezoelectricity is the property of acquiring electric polarization under external mechanical stresses, or the converse property of changing dimension when subjected to external electric fields. The large piezoelectric coefficient, especially near the phase transition temperature, makes ferroelectrics attractive for transducers, which convert mechanical changes to electrical changes or vice versa. In some cases, the purpose of the transducer is to convert ac fields, or sudden change of field, into corresponding mechanical motions, as in ultrasonic generators, actuators, louderspeakers, or pulse generators. In other cases, a transducer uses piezoelectric effects to convert small motions into electric changes, as in ultrasonic detectors, strain-gauge, microphones, and devices to measure vibrations [2]. As illustrated in Table 1, ferroelectric BaTiO3 exhibits high piezoelectric coefficient potential for transducer and actuator applications. According to (5.2), the spontaneous strain, which plays a dominant role in piezoelectricity, in ferroelectric BaTiO3 is proportional to the squared spontaneous polarization. Thus, the piezoelectric coefficient d31 in ferroelectrics is proportional to P [2, 150]. When the ferroelectrics are in the paraelectric cubic phase, Ps = 0, they have no piezoelectric effect. Therefore, cubic BaTiO3 nanostructured materials are precluded from application in transducers. The critical size of ferroelectricity is also the ultimate miniaturization level of piezoelectric BaTiO3 . In BaTiO3 nanoceramics with an average grain size of 300 nm, the spontaneous polarization Ps = 15
C/cm2 at room temperature [10]. Although it was less than the Ps for single crystals and ceramics with a grain size of 1.2
m, in accordance with (5.2), nanoceramics still possess sufficient piezoelectric coefficient. In comparison with conventional ceramics, dense nanoceramics, nanocomposites, and thick films, which make use of nanoparticles as starting materials, facilitated versatile shapes. For various transducers, the chosen shape depends on the utilization field and required frequency. For example, a complex shape is required for

Nanocrystalline Barium Titanate

412 actuators, but a simple slab is required for ultrasonic frequency [2]. On the other hand, the high-dielectric-constant BaTiO3 nanoceramics have a large electromechanical coupling factor—a measure of the proportion of electrical energy that can be stored elastically. Therefore, BaTiO3 nanoceramics with versatile shapes could be applied for transducers and actuators with controlled oscillator frequencies and bands.

7.3. Thermal Sensors The temperature dependence of spontaneous polarization, dielectric constant, or resistivity in ferroelectric BaTiO3 and (Ba, Sr)TiO3 was applied to fabricate bolometers for infrared detection, infrared imaging detection, and thermometers. For pyroelectric bolometers, based on (5.1) and (5.2), the temperature dependence of spontaneous polarization in the ferroelectric nanoparticles can be written as Ps ∝  A Tc − T /2

(7.1)

where under  = 1 ambient conditions. By differentiating (7.1) with respect to temperature and substituting (3.2) into it, the pyroelectric coefficient of ferroelectric nanoparticles is obtained: p = dPs /dT ∝ A 1/2 Tc   − D/R − Rc  − T −1/2 (7.2) From (7.2), it can be seen that the pyroelectric coefficient p could be enhanced by decreasing the ferroelectric nanoparticle size, owing to decreasing tetragonal–cubic phase transition temperature. But the parameter A was reduced greatly by decreasing grain size [138, 169–171]. Therefore, the resulting pyroelectric coefficient p was decreased in BaTiO3 ferroelectric nanocrystals. For dielectric bolometers, the bulk dielectric constant changes anomalously near the ferroelectric–paraelectric phase transition, which obeys the Curie–Weiss law. However, in ferroelectric nanocrystals, this anomalous dielectric peak was suppressed to become flat, and even disappeared below a critical size, as illustrated in Figure 5. The preliminary measurements have demonstrated that the figure of merits, which is proportional to p and inversely proportional to , in ferroelectric nanocrystalline BaTiO3 and (Ba, Sr)TiO3 was much lower than the value of bulk materials [85, 158, 187]. So the finite-grain-size effect precluded the small-grain-sized (Ba, Sr)TiO3 nanocrystalline thin-film application for uncooled monolithic integrated ferroelectric thin-film infrared focal plane arrays [195]. To avoid this limit of small-grain-size effect on pyroelectric properties, (Ba, Sr)TiO3 thin films with large grain size and columnar microstructure were prepared; they exhibited enhanced pyroelectric properties as expected [85, 188]. The vinylidene fluoride/trifluoroethylene [P(VDF-TrFE)] copolymers are useful pyroelectric organic materials without stretching and, thus, good candidates as solid-state imaging sensors. They have low thermal conductivity and can be fabricated into large-area thin films. Mixing ferroelectric nanoparticles and copolymer materials to form nanocomposites, improved pyroelectric performance was obtained [124, 125]. Because the piezoelectric coefficients

(d33 as well as d31 ) of the ferroelectric and polymer phases have opposite signs, while the pyroelectric coefficients have the same sign, the piezoelectric contributions in composites from the two phases are partially cancelled, but the pyroelectric contributions are reinforced. Therefore, the ferroelectric nanoparticle/copolymer composite exhibits high pyroelectric activity but no spurious electrical signal due to mechanical strain or vibration owing to the minimized piezoelectric microphone effect, and is a promising candidate in the application field of integrated pyroelectric sensor arrays on silicon-based readout integrated electronic circuits. Based on the relationship between pyroelectric property and ferroelectric nanocrystallite size, it is necessary to choose large BaTiO3 or (Ba, Sr)TiO3 nanoparticles with good pyroelectric property and with grain size significantly smaller than the thickness of the nanocomposite films for pyroelectric sensor applications. Usually, the pure BaTiO3 ceramics were highly resistive at room temperature. Some donor-doped BaTiO3 ceramics exhibited positive temperature coefficient of resistivity (PTCR) characteristics, which were used for infrared detection and temperature control [196, 197]. To optimize the sensor performance, the Ba or Ti elements were often substituted to tune the tetragonal–cubic phase transition temperature of BaTiO3 ceramics over a large temperature range, for example, between − 30  C and 400  C [197]. With nanotechnology, the grain size in the nanometer scale can cause the tetragonal–cubic phase transition temperature of BaTiO3 to decrease toward room temperature. On the other hand, the PTCR and anomalous dielectric properties were closely associated with the quality of grain boundaries [198, 199]. With low-temperature hydrothermal methods, the grain boundaries of BaTiO3 nanoparticles could be easily modified [75]. Therefore, BaTiO3 nanoceramics may find applications with the PTCR effect.

7.4. Humidity Sensor The electrical conductance and capacitance of BaTiO3 ceramics usually change in a humid environment due to water vapor chemisorption and physisorption and capillary condensation in the pores of the sensor element. Compared with conventional ceramics, BaTiO3 nanoceramics have better humidity-sensing properties, such as lower resistance and higher sensitivity. Qiu et al. observed the resistance of nc-BaTiO3 increasing with increasing grain size, for example, from 23 to 53 nm, while the linearity and slope in the highhumidity range were improved [48]. From the application point of view, the resistance for the resistive humidity sensor is better, ranging over 106 –103 , for minimizing humidity hysteresis and increasing sensitivity and repeatability. To further improve the performance of nc-BaTiO3 humidity sensors, Wang et al. proposed two methods of doping a certain amount of impurities into nc-BaTiO3 and mixing some polymer humidity sensing materials with nc-BaTiO3 to fabricate nanocomposite humidity sensors [47, 200, 201]. First, the experiments showed that doping Na2 CO3 , K2 CO3 , and sodium citrate modified the resistance of the nc-BaTiO3 humidity sensor from 106 to 103 , among which NaH2 PO4 was the best dopant for minimizing the humidity hysteresis of the BaTiO3 sensor. The maximum humidity hysteresis of the sensor was 3% relative humidity (RH)

Nanocrystalline Barium Titanate

in the region of 30–90% RH [200]. Second, some polymer materials also show good humidity sensitivities such as long-term stability, repeatability, precision, and so forth. However, the polymer materials do not behave as well as ceramic and nanocrystal materials in complex environments, for example, in air with organic gas. Combining inorganic (ceramic or nanocrystal) materials with organic polymers may be expected to obtain better humidity-sensing materials. One example was to use polymer material of quaternary acrylic resin [(R)n M+ X− ] mixed with nc-BaTiO3 to form a nanocomposite. These nanocomposite materials exhibited much better sensing properties: The sensitivity was higher than that of pure nc-BaTiO3 , and the maximum humidity hysteresis was about 3% RH in the range of 33–98% RH [47, 201].

413 The dielectric, ferroelectric, optical, and lattice dynamical properties of BaTiO3 nanostructured materials could be tuned or enhanced by controlling the grain size and lattice strains. The finite-size effect on structural and physical properties was well understood with the model of grain size effect on long-range interaction and its cooperative phenomena. The finite-grain-size effect not only extended the application fields BaTiO3 but also created some new fields such as optical modulators, transducers and actuators, and thermal and chemical sensors. Nevertheless, research is still needed to deepen our understanding of the grain size effect on those enhanced (novel) properties in BaTiO3 nanostructured materials, such as low-temperature quantum ferroelectricity and paraelectricity, electronic structure changes, and soft-mode behavior with varying nanocrystallite size.

7.5. CO2 Sensors In the fields of agricultural and biotechnological processes as well as air-conditioning systems and monitoring of exhaust gases, there is an increasing demand for CO2 sensors. In addition to optical and electrochemical sensors, a new generation of low-cost solid-state CO2 gas sensors based on nc-BaTiO3 thick films is being developed. Nanocrystalline BaTiO3 was used to fabricate CO2 sensors owing to the semiconducting character that the conductance or capacitance changes due to adsorbed CO2 . These sensors have the potential to further reduce production cost, increase sensor design versatility, and simplify integration with other gas sensors on the same substrate [202, 203]. Keller et al. systematically investigated the mechanical stability, sensitivity, reproducibility, detection limit, longterm stability, operating temperature, cross-sensitivity by interfering gases, and power consumption of nanocrystalline BaTiO3 -based sensors [202]. It was found that nanocrystalline BaTiO3 -based sensors had higher sensitivity to 0.01% CO2 concentration, lower detection limit, minor influence of interfering gases, and reduced power consumption than microcrystalline sensors. The nanocrystalline BaTiO3 thick films could also be applied as less power consuming CO2 solid-state sensor devices for mobile CO2 detection. In studying the CO2 -sensing mechanism, the sensitivity was found to be closely related to lattice defects in the sensing layers—defect structures rather than the concentration of lattice vacancies [203]. Nevertheless, before entering the market, major drawbacks of semiconducting solid-state layers such as small long-term stability and signal drift must be overcome.

8. SUMMARY In summary, perfect BaTiO3 nanocrystalline materials ranging from 0D nanoparticles to 2D single-crystal films have been successfully fabricated. With the benefit of generalized solution-phase decomposition nanotechnology [51, 80, 81], fabrications of complex BaTiO3 nanostructured systems (colloidal crystals) were also attempted, which would extend studying the properties and applications of nanostructured BaTiO3 . Using BaTiO3 nanocrystals as building block, strained superlattices, nanoceramics, and nanocomposites were also fabricated for technological applications.

GLOSSARY Ferroelectric critical grain size The minimum grain size, below which the ferroelectricity disappears. Ferroelectric phase transition A special class of structural phase transition where the transition from the high to the low symmetry phase is accompanied by the appearance of spontaneous polarization. They could be driven by external field applications of temperature, of pressure, of electric field, of composition substitution, and/or of grain size. Finite grain size effect When the dimension of crystal is comparable with the feature length of some property, this property becomes dependent on the grain size and shape, which is named as finite grain size effect. Perovskite oxide A family name of oxide materials having a chemical formula of ABO3 . In the prototype cubic structure, the ionic A is at the corner, B at the bulk center, and O at the face center. Quantum ferroelectric phase transition Instead of by thermal fluctuation, the ferroelectric phase transition from the paraelectric phase is driven by quantum fluctuation, of which the Curie temperature obeys the relation of Tc ∝ S − Sc 1/2 , changed from the classical law Tc ∝ S − Sc . S is external parameter controlling interaction, and S = Sc at Tc . Soft mode One of the lowest frequency transverse optical modes, of which the frequency is temperature dependent and reduces to zero as the transition temperature is approached, and at Curie temperature, the condensation of soft mode displacement determines the structure of the low temperature phase. Spontaneous polarization The existence of electrical momentum in the noncentrosymmetric phases, which can be reversed or reoriented by application of external electrical field.

ACKNOWLEDGMENTS This work was partially supported by National Climbing Project, National Natural Science Fund of China, and Shanghai Natural Science Fund (Grant 02ZE14113).

414

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Nanocrystalline Ceramics by Mechanical Activation J. M. Xue, Z. H. Zhou, J. Wang National University of Singapore, Singapore

CONTENTS 1. Introduction 2. Mechanically Activated Processes 3. Mechanical Activation Devices 4. Nanocrystalline Ceramic Materials 5. Nanocrystalline Ceramics by Mechanical Activation 6. Mechanical Crystallization and Precursor to Ceramic Conversions 7. Summary Glossary References

1. INTRODUCTION Ceramic materials are traditionally synthesized by solid-state reactions of the starting constituents (such as oxides, nonoxides, carbonates, and precursors) at elevated temperatures. It is, however, difficult to realize a nanocrystalline feature by the conventional ceramic process, as a high temperature calcination always leads to coarsening and aggregation of fine ceramic particles. Similarly, most of the wet-chemistrybased processing routes for ceramic materials have failed to deliver a true nanocrystalline structure, again due to the unwanted particle and crystallite coarsening and aggregation at the calcination temperature, which is unavoidably required for chemistry-derived ceramic precursors. In a fundamentally different approach, phase formation in mechanical activation is realized at room temperature, via one or more of the mechanically triggered chemical reactions, nucleation and growth from an amorphous state, decompositions, and phase transformations, depending on the specific ceramic material concerned. Little progress was made in synthesizing ceramic materials by mechanical activation until about 10 years ago when the potential of this novel ISBN: 1-58883-062-4/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

synthesis technique was demonstrated, although mechanical alloying for metals and intermetallics was devised more than 30 years ago. Over the past 5 years, there has been a surge in effort to employ mechanical activation for synthesis of a wide range of nanocrystalline ceramic materials including ceramic oxides, oxides of complex perovskite, spinel and layer structures, nonoxides, magnetic ceramics, electroceramics, and ceramic nanocomposites. While research focus on mechanical activation, on the one hand, is directed at synthesis of nanocrystalline ceramic materials, many of the underlying physical phenomena in association with mechanical activation have yet to be properly studied and made understood. On the other hand, mechanical activation promises a significant technological implication, whereby the currently employed multiple steps of phase-forming calcination/annealing at high temperatures for ceramic materials can be skipped, when the required nanocrystalline ceramic phases are realized at room temperature in an enclosed mechanical activation chamber. In this chapter, recent progress in mechanical activation for synthesis of nanocrystalline ceramic materials is reviewed and a number of new and unique phenomena brought about by mechanical activation in functional ceramics are discussed, together with a short discussion on the possible future development of this novel technique.

2. MECHANICALLY ACTIVATED PROCESSES Mechanically activated processes are among the earliest phenomena created by humankind and the use of flint to trigger fires is perhaps one of the best known examples [1]. Mechanochemical reactions were documented and date back as early as several hundred B.C., when a number of chemical reactions were noted under the influence of one or more types of mechanical actions. However, mechanochemistry was not developed in a systematic manner until late 19th century, along with solid state chemistry, when the

Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 6: Pages (417–433)

418 effects of high pressure, mechanical impact, and combination of high pressure and temperature on the rates of solid state chemical reactions and phase transitions were studied [2]. Following the steady establishment of physical metallurgy in the first half of 20th century and then materials science, the potential of mechanically activated processes for materials synthesis was first demonstrated by Benjamin [3], who devised “mechanically alloying” for oxide-dispersed nickel- and iron-based super alloys. This marked a new era of successfully employing mechanically activated process in materials synthesis, and it was followed by the extension and application of this novel technique to a wide range of structural and functional materials, including intermetallics and metal matrix composites in the early stage of development, and then magnetic materials, semiconductors, and more recently nanocrystalline ceramic materials and ceramic matrix composites. In the recent development history of mechanically activated processes, there existed a number of terminologies, each of which was adopted by the inventor of a specific fabrication technique [4]. In several cases, there is no clear boundary between two or more such terminologies. Mechanical alloying is used to describe a process where the powder mixture of different metals, alloys, or compounds is ultimately mixed together and the formation of a new alloy phase involves mass transfer. In comparison, mechanical milling refers to a milling process of homogenized compositions where mass transfer is not required. Therefore, it is often associated with milling of a pure metal or compound that is already in a state of thermodynamic equilibrium. Similarly, mechanical grinding refers to a milling process where mechanical milling is dominated by abrasion or shear stresses and chip formation. Mechanical disordering is specifically phrased for the milling process that is designed for destruction of the long-range order in intermetallics and production of either a disordered intermetallic or an amorphous phase. Mechanical crystallization describes the nucleation and crystallite growth triggered by a mechanical process from either an amorphous state or an amorphous precursor. Mechanochemical synthesis/process is the general phrase that has been widely given to any high energy milling process of powdered materials involving one or more chemical reactions occurring during milling [5, 6]. Most of the mechanically activated processes for synthesis of nanocrystalline ceramic materials fall into this category. In mechanochemical synthesis, mechanical activation is employed to trigger the chemical reaction, structural change, and nucleation and growth of nanocrystallites from an amorphous state, leading to a product phase, with or without the need of a further thermal treatment at elevated temperatures. In combination with mechanical alloying, mechanochemical synthesis has been used to describe majority of the mechanically activated processes that have been devised and utilized in materials synthesis, while several other terms, such as reactive milling [7], rod milling [8], and mechanically activated self-propagating high temperature synthesis [9], can easily be categorized into either of these two general categories. Reaction milling, for example, pertains to the mechanical alloying process that is accompanied by one or more solid state reactions. Rod milling is a specific technique that was

Nanocrystalline Ceramics by Mechanical Activation

developed in Japan to trigger the mechanochemical reaction by a predominant shear process, in order to reduce the level of contamination. Mechanically activated self-propagating high temperature synthesis refers to any mechanically activated reaction that is self-propagating in nature once triggered [10], which again can be categorized into the general terminology of mechanochemical synthesis. It must be pointed out that phase formation of several nanocrystalline ceramic materials, such as those via nucleation and subsequent crystallite growth from an amorphous state, is not a result of any chemical reactions that are described in the traditional mechanochemical process. Therefore, the terminology of mechanical activation is adopted in this chapter, which is aimed at covering most of the mechanically activated processes for synthesis of nanocrystalline ceramic materials.

3. MECHANICAL ACTIVATION DEVICES Although syntheses of ceramic materials and many other types of materials have been successfully realized by various mechanically activated processes, there has been little specification and standardization with the types of mechanical activation devices and setups [4]. Conventional ball milling, which is commonly employed for mixing and blending of raw materials and refinement in particle and agglomerate sizes in ceramic industry, is generally unsuitable for mechanochemical synthesis, although certain phase transformations (such as those in PbO) and a number of chemical reactions can occur in conventional ball milling. Generally speaking, mechanical activation devices are those of high energy milling and modifications of high energy milling, which were originally designed for mechanical alloying. SPEX shaker mills and planetary ball mills are among the very few choices of commercially available high energy mills. SPEX Shaker mills are designed for a relatively small capacity of up to 20 grams and are therefore popularly adopted for laboratory investigation. They typically consist of one vial, containing the sample composition and activation media (typically of one or more high density balls made of ceramics or stainless steel), secured in clamps and swung energetically back and forth up to several thousand times per minute. The back and forth shaking motion of the vial is also combined with lateral movements. By simple calculation, ball velocity in SPEX Shaker mills is up to the order of 5 m/s, generating an unusually high impact force at a very high frequency. Planetary mills, which are designed for relatively large quantities in the range up to a few hundred grams of powder per batch, are manufactured by Fritsch GmbH in Germany. Vials of planetary mills are arranged on a rotating support disk by a specifically designed drive mechanism to cause them to rotate around their own axes. There is a strong centrifugal force produced by the rotating vials around their own axes, together with that generated by the rotating support disk; both act on the vial contents and the activation balls. Because the vials and the supporting disk rotate in opposite directions, the centrifugal forces alternately act in like and opposite directions. This enables the activation balls to run against the internal walls of the vial, generating a friction effect, and at the same time the activation balls lift off and travel freely through the inner chamber of the vial and

Nanocrystalline Ceramics by Mechanical Activation

collide against the opposing inside wall generating a strong impact effect. An attrition mill, which is a modification of the conventional ball mill, consists of a vertically aligned drum with several impellers being set progressively at right angles to each other. The impellers energize the medium charge, causing impacts between activation media, between the medium and the drum wall, and between the medium, agitator shaft, and impeller. Attrition mills are capable of larger batch quantity (up to tens of kilos) than both planetary mills and shaker mills, although they are generally regarded as being of low energy type and unsuitable for successful mechanical activation syntheses in many cases. There have been several new designs of mechanical activation devices, including rod mills, vibrating mills, and those shaker and planetary mills in combination with the application of an electrical discharge, magnetic field, temperature, and hydrothermal conditions, in an effort to combine mechanical activation with other processing controls [11–14]. Typical processing parameters that can be controlled in mechanical activation include the activation (or mill) speed, activation time, choices, size and combination of vial and milling media, media to powder weight ratio, activation media and atmosphere, activation temperature, and pressure.

4. NANOCRYSTALLINE CERAMIC MATERIALS Performance and functional properties of ceramic materials are critically dependent on a number of compositional and structural parameters in atomic, nanometer, and microstructural scales. Over the past four decades starting from the 1960s following the wide application of electron microscopes in materials characterization, there has been a steady accumulation of knowledge and understanding on the microstructure and microstructure–property relationships in ceramic materials. At the same time, in particular over the past two decades, research focus on ceramic processing has been shifting from the traditional solid state reactions to wet-chemistry-based syntheses, in order to refine the microstructure into nanometer scales. There are two major driving forces behind the current surge in pursuit of a nanocrystalline structure for ceramic materials: (i) the unique physical and functional properties arising from a nanostructure and (ii) a much lowered processing temperature for ceramic materials. As a result of the significant refinement in particle size (for powdered ceramics) and grain size (for sintered bulk ceramics) into the nanometer range, surfaces, interfaces, and grain boundaries play a critically important role in determining the physical and functional behaviors of nanocrystalline and nanostructured ceramic materials, which can be considerably different from those of their counterparts with structural features in the micrometer scales. For example, a flexural strength of >2000 MPa and excellent superplasticity, which were traditionally considered as being impossible for brittle ceramic materials, have been demonstrated with both oxide ceramics (alumina and zirconia) and ceramic nanocomposites (e.g., alumina–SiC and Si3 N4 –SiC) [15–17].

419 Ultrafine ceramic powders consisting of well dispersed nanocrystalline particles of 800
C in the bulk growth regime, and to the full data set in the nucleation regime. The slopes of these lines yield the activation energies as shown. The broken line indicates a reproducible deviation from activated behavior. Reprinted with permission from [17], B. Hong et al., Diamond Relat. Mater. 6, 55 (1997). ©1997, Elsevier Science.

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3.2. Optical Emission Spectroscopy The diamond films were deposited on pretreated quartz substrates by the MPCVD technique as described in detail elsewhere [5]. In order to obtain information on plasma chemistry, OES was employed to monitor the H2 –CH4 plasma. A monochromater with a focal length of 500 mm and grating of 1200/mm, which gives a resolution of 0.05 nm and a precision of about ±02 nm/500 nm, was used for the OES measurements. Figure 4 [5] presents some typical optical emission spectra of the H2 –CH4 plasma used for the NCD film deposition. The H2 spectrum consists mainly of emission from atomic H Balmer lines (H and H lines at 656.3 and 486.1 nm, respectively) and excited H2 lines at around 460 and 590 nm. When methane was introduced into the system, C3 emission lines at around 400 nm, CH+ emission at 417 nm, CH lines at around 431 nm, and the C2 Swan bands around 469 and 515 nm appeared in the emission spectrum. Using the H2 line at 580.6 nm as reference, the relative intensities of emissions from the latter four species as a function of the methane fractions in the source gas are plotted in Figure 5 [5]. All emissions except that of C2 4500 4000

Intensity (a.u.)

3500 3000 2500

37.5% CH4

2000 1500

4% CH4

1000 500 0

H2

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400 500 600 Wavelength (nm)

IL-6301

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Figure 4. Some typical optical emission spectra of the H2 /CH4 plasma. Reprinted with permission from [5], L. C. Chen et al., J. Appl. Phys. 89, 753 (2001). © 2001, American Institute of Physics.

1.3 1.2 1.1

Relative Intensity

probability from 800 to 400
C, another order is due to the fraction of the substrate area from which initial nuclei can collect impinging flux, and factors of 4 and 2 are due to the reduction in the nucleus capture radius and nucleation density, respectively. Thus considerable gains can be achieved in preparing diamond at reasonable rates on nondiamond substrates at low T by enhancing the density and area of the nucleation centers and retaining these characteristics as T is reduced. It is most probable that disordered sp2 or sp3 C embedded within the silicon during seeding is converted to NCD nuclei by H exposure in the initial stages of nucleation and that this process becomes more effective as T increases. Although gains in diamond film can be made at low T by increasing the precursor flux, a primary limitation is the low capture cross-sectional area of nuclei at low density on the substrate.

CH*/H2 C2/H2 CH/H2 C3/H2

1.0 0.9 0.8 0.7 0.6 0.5 0.4

0

10

20 CH4 (%)

30

40

IL-6282

Figure 5. The relative intensity of the CH+ 
, C2 , CH •, and C3 + × emissions with respect to that of H2 as a function of the methane fraction in the source gas. Reprinted with permission from [5], L. C. Chen et al., J. Appl. Phys. 89, 753 (2001). © 2001, American Institute of Physics.

dimer increased with increasing methane content, reached a maximum at around 20%, and decreased at higher methane content. Emission from C2 dimer, however, showed a continuing increase above 20% methane content. It can be seen from Figure 4 that the 515 nm C2 emission line was very pronounced at high methane content. Due to the fact that the emission intensity is a function of many factors including Frank–Condon factor, the density of states, various quenching effects, etc., a quantitative description of the observation is very complicated and is beyond the scope of this chapter. The gas-phase analysis by OES or any other single technique is far from complete since it is not possible to detect some important growth species such as CH3 by this technique. It is observed from these studies that the gas phase experienced substantial change when the methane fraction went from below to above 20%, with which the optical transmittance and surface roughness data [5] also exhibited similar crossover behavior. Shown in Figure 6 [5] is the intensity ratio of two atomic hydrogen lines at 486.1 nm (H ) and 656.3 nm (H ) as a function of the methane fraction in the source gas. It is quite clear from the graph that the intensity ratio of H /H , which is related to the electronic temperature in the plasma, showed a maximum value at a methane fraction of 20% and declined rapidly with variation in methane content on either side. Once again, the electronic temperature exhibited a methane-fraction dependence similar to that of most emissions (except C2  as shown in Figure 5. From Figures 5 and 6, it is speculated that a change in major growth species might have occurred around a methane fraction of 20%. Most of the conventional PCD films were grown in low methane fraction. The major growth species C2 has been identified for the growth of NCD films using C60 as precursor under hydrogen-free or hydrogen-deficient environments [60]. For the conditions during this work [5], growth involving CH3 was expected since all depositions were carried out

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442 1.0

0.50 0.45 0.40 0.35

0.8

0.8

0.6

0.6 C2

0.4

0.4 C

0.2

0.2 OH (a)

0

0.30

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20 30 CH4 (%)

40

Figure 6. The relative intensity of H /H as a function of the methane fraction in the source gas. Reprinted with permission from [5], L. C. Chen et al., J. Appl. Phys. 89, 753 (2001). © 2001, American Institute of Physics.

in H2 –CH4 plasma. However, it is clear from OES studies that C2 dimer becomes the predominant growth species at methane fractions far above 20%.

3.3. Vacuum Ultraviolet Absorption Spectroscopy The deposition of NCD film by using a low-pressure inductively coupled plasma (ICP) was employed by Teii et al. [61]. NCD films were grown at a pressure of 80 mTorr using CO/CH4 /H2 and O2 /CH4 /H2 gas mixtures. The densities of C atoms in ground state are measured by vacuum ultraviolet absorption spectroscopy (VUVAS). CO is employed as one of the simple gases that yield C atoms, through the primary reaction: CO + e− → C + O + e− . The emissive species observed in the CO/CH4 /H2 plasmas in the wavelength range of 300–800 nm were OH, CH, H, C2 , and Ar. In addition to these species, pronounced emissions from O were observed in the O2 /CH4 /H2 plasmas. The normalized emission intensity of OH, CH, H , C2 , and O [62, 63] and the normalized absorption of C atoms as a function of XCO and XO2 for a fixed XCH4 of 5% are depicted in Figure 7 [61], respectively. It was very difficult to obtain sufficient absorption by C atoms when an emission line at 296.7 nm was initially used in (UVAS). It therefore follows from this that the absolute C atom density was lower than 1 × 1012 cm−3 , the lower detection limit in this UVAS system [64]. The trend of the C atom density as determined by VUVAS was consistent with that by OES under experimental conditions, indicating thereby that the influence of collisional excitation processes was small. In Figure 7a, the H and CH intensity ratios remain constant independent of XCO , while the C atom absorption and OH and C2 intensity ratios increase in proportion to XCO . To ensure that an increase in C and C2 was not due to an overall increase in the total carbon concentration in the feeding gas, a comparative experiment was performed by varying XCO with the sum of XCO + XCH4 kept constant at 5%. This experiment gave similar results except for a slight decrease in the CH

1.0

Normalized emission intensity ratio

0

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0 2 4 CO concentration (%)

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CH C2

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C 0.4

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Normalized absorption of C atoms

Relative Intensity Hβ/Hα

0.55

1.0 CH Hα

Normalized absorption of C atoms

Normalized emission intensity ratio

0.60

(b)

0

0 IL-6 28 6

0 2 4 O2 concentration (%)

Figure 7. Variations of the normalized emission intensity ratios of OH, CH, H , C2 , O, and the normalized absorption of C atoms (a) as a function of XCO for a XCH4 of 5%, and (b) as a function of XO2 for a XCH4 of 5%. Reprinted with permission from [61], K. Teii et al., J. Appl. Phys. 87, 4572 (2000). © 2000, American Institute of Physics.

intensity ratio probably due to a decrease in parent CH4 , informing thereby that the major origin of C and C2 is CO. In Figure 7b, the intensity ratios of OH, CH, H, C2 , and O as well as the C atom absorption increase with increasing XO2 . Emissions from O for XO2 = 0%, arising from the impurity from quartz windows, were as low as the noise level. An increase in C atom absorption is ascribed to the result of sequential reactions induced by O atoms. For the transition from upper state j to lower state i, the relationship between the emission line intensities Iji and excitation temperature Tex is given in detail elsewhere [65]. The relative excitational population of H atoms in the Balmer series as a function of excitation level for the three gas mixtures is shown in Figure 8 [61]. The emission line of H was not available because of its low signal-to-noise ratio. The distribution equilibrium of excitation levels of the H atom Balmer series is not satisfied because the three sets of plots do not produce straight lines, in accordance with the previous study in the same pressure range [66]. The energy distribution is almost equivalent in any gas mixture, suggesting a common excitation process of H atoms. Furthermore, the overall emission intensities are equivalent in any gas mixture, indicating that the H atom density was

Nanocrystalline Diamond

443

6

ln (λ/gA)

5 4 3

5%CH4-95%H2 5%CO-5%CH4-90%H2 5%CO-95%H2

2

19

20 Energy (0-19 J)

21

IL-62 87

Figure 8. Energy distribution of the H atom Balmer series as a function of excitation level for the three sets of data in the 5%CH4 –95%H2 , 5%CO–5%CH4 –90%H2 , and 5%CO–95%H2 plasmas. Reprinted with permission from [61], K. Teii et al., J. Appl. Phys. 87, 4572 (2000). © 2000, American Institute of Physics.

almost equivalent and the H atoms were produced mainly by dissociation of hydrogen molecules. These similarities for H atoms regardless of the gas mixtures imply that the H atoms were not responsible for the difference in the grown phases. Thus VUVAS analysis suggests that the C atoms resulting mainly from CO by electron impact dissociation increased the precursors to nondiamond phase by promoting gas-phase polymerization, while the OH radicals resulting predominantly by loss reactions of O atoms with H2 and CH4 were responsible for the enhancement of diamond growth. An excess amount of O atoms resulting from O2 interrupt the formation of nuclei at the initial stage of the growth. Besides, the production path of C atoms induced by O atoms is also possible.

4. SPECTROSCOPIC CHARACTERIZATION NCD films are materials of a great potential use in various fields such as tools, optical windows, microelectromechanical systems (MEMS), etc., due to their remarkable properties. In recent years, attempts have been made to develop NCD films with a smooth surface and special attention has been paid to NCD films with characteristics of a small crystallite size. In order to understand and improve the properties of NCD films, it is desirable to relate the remarkable properties of NCD with their microstructure. The various techniques used for characterization of NCD are discussed next.

4.1. Transmission Electron Microscopy Transmission electron microscopy has been the most powerful technique for characterizing the microstructure of NCD and is widely used to obtain bonding information. Figure 9 [5] depicts a typical TEM bright-field image of a diamond film deposited on a nanometer-scratched substrate with a methane fraction of 4% [5]. A typical selective-area diffraction pattern (not shown here) of a nanometer-scratched sample prepared with a methane fraction of 41% indicates

Figure 9. Bright-field TEM image of a NCD film grown on nanometerscratched quartz substrate with a methane fraction of 4%. Reprinted with permission from [5], L. C. Chen et al., J. Appl. Phys. 89, 753 (2001). © 2001, American Institute of Physics.

high degree of diamond phase. All the sharp diffraction rings can be indexed to the diamond structure. It is observed that diamond films consist of randomly oriented grains and that the substrate pretreatment has a strong effect on the average grain size of the resulting films. With a methane fraction of 4%, the average grain size of the micrometerscratched sample was about 200 nm, whereas the corresponding value of the nanometer-scratched sample was only about 4 nm. As the methane fraction was increased from 4% to 41%, the grains of the micrometer-scratched samples became coarser and coarser. In fact, it is noted that the average grain size of the nanometer-scratched sample prepared at a methane fraction of 41% is quite similar to that of its micrometer-scratched counterpart. High-resolution transmission electron microscopy has been utilized to understand the initial stages of diamond film growth [12, 67–69]. The detailed electron microscopic study [70] of NCD films grown from C60 fullerene precursors showed that various planar defects such as twinning boundaries and stacking faults were observed in large crystallites found in the films. Similarly, measurements of the diamond crystallite size distribution using diffraction contrast TEM followed a gamma distribution with an average grain size of 15 nm [71]. Since the resolution of the TEM technique is limited by the small objective aperture, HRTEM has a great edge for reliable grain size measurements [72]. In addition, the TEM imaging techniques give additional information that can be used to determine the phase purity of NCD films. The selected-area electron diffraction is a powerful method to examine the phase composition of these films as short-range order in either sp2 -bonded glassy carbon or predominantly sp3 -bonded diamondlike amorphous carbon as they provide different diffraction intensities. Gruen et al. have grown NCD films on (100) surfaces of n-doped silicon wafers using electrical biasing of the silicon substrate to initiate nucleation [4]. Growth was carried out at a rate of about 0.5–1
m/h. Although NCD films have uniform morphology, two additional factors mandate the use of the HRTEM technique. When the packing density is high, the diffraction contrast due to orientational differences of the diffracting crystallites appears weak for

Nanocrystalline Diamond

444 bright-field images. Also, the resolution of the diffractioncontrast method is quite low, and, therefore, it is difficult to resolve nanosized crystallite boundaries. For all the reasons mentioned above, reliable information on grain size could be determined from lattice images of nanodiamond crystallites. Mostly the (111) lattice planes are resolvable in the microscopes. Hence, the lattice images from those crystallites are oriented such that at least one set of their (111) lattice planes is parallel to the incident imaging electron beam. The crystallite size with high accuracy can be measured because of the low contrast from surrounding structures is close to random white noise. Although lattice images reveal individual crystallites at atomic resolution, the presence of amorphous carbons cannot be determined. When the crystallite size is reduced to the nanometer scale, the percentage of atoms located at the grain boundaries increases drastically with decrease of grain size. It is estimated that for NCD films, the fraction of atoms residing at grain boundaries can be as high as 10% when the average crystallite size becomes 3 to 5 nm. On the other hand, electron microscopy observations show that there is no graphitic phase between the grain boundaries. The presence of sp2 bonds suggests that carbons are -bonded across sharply delineated grain boundaries limited to widths of 0.2–0.5 nm [73].

4.2. Electron Energy Loss Spectroscopy Shown in Figure 10 [74] are high-resolution electron energy loss spectroscopy (EELS) spectra of the plasmon for C60 fullerene, amorphous, nanocrystalline, and polycrystalline diamond [74]. C60 fullerene shows peaks around 6.5 eV which are -plasmons due to the – ∗ band transition

[75, 76]; such peaks are not observed in the amorphous diamond, indicating thereby the absence of -plasmons. Among the three diamond materials, -plasmon peaks that appear around 30–34 eV [77] are different in peak position and shape. Plasmon excitation of valence band electrons of EELS spectra is related to the dielectric function by an equation [78]. Applying the Kramers–Kronig equation, the real and imaginary parts of the dielectric function, 1 and 2 , can be estimated from the plasmon of EELS. The calculated

2 for the diamond materials is shown in Figure 11 [74]. The rise-up position of 2 corresponds to the bandgap. For the natural crystalline diamond, the rise-up position is 5.5 eV, indicating excellent agreement with the established bandgap of diamond (5.5 eV). Two peaks appear at 8.2 and 12.7 eV, and the former is assigned to direct excitation of an electron at the  point, the latter being assigned to X and L positions, respectively [79]. For the amorphous diamond, the rise in peak is gradual and the rise-up position changes with the sample from 3.5 to 4.5 eV. In any case, the magnitude of the bandgap is smaller than that of crystalline diamond. A large peak at 7.2 eV, corresponding to point  , is observed. For the nanocrystalline powder, the rise-up position is at 3.0 eV and occurs very gradually. This implies that the present method of estimating 2 from the EELS plasmon is reliable. For the amorphous diamond, the magnitude of the bandgap is 3.5 to 4.5 eV, smaller than that of diamond. The variation in magnitude of the bandgap may be caused by the temperature distribution during the synthesis. In addition, the amorphous diamond exhibited the characteristic distribution in 2 and only  excitation at the point

7.2

C60 fullerene

π-π*

30

Intensity (arb. units)

nanocrystalline powder

3.3

7.2

ε2

20 amorphous diamond

amorphous diamond

4.5 nanocrystalline powder

12.7

10 8.2

cystalline diamond

5.5 IL-6298

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5

10

15

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25

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crystalline diamond

35

40

45

50

Energy Loss (eV)

Figure 10. High-resolution EELS plasmon spectra for C60 fullerene, amorphous diamond, nanocrystalline powder, and crystalline diamond. Reprinted with permission from [74], H. Hirai et al., Diamond Relat. Mater. 8, 1703 (1999). © 1999, Elsevier Science.

0

IL-6288

0

5

10 Energy Loss (eV)

15

20

Figure 11. Imaginary part of the dielectric function obtained from EELS spectra for diamond materials, showing different rise-up manners. Reprinted with permission from [74], H. Hirai et al., Diamond Relat. Mater. 8, 1703 (1999). © 1999, Elsevier Science.

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appeared, while excitations at X and L points were not noticed or considerably weakened. X and L points, where the wave number vector has a certain value, are defined when the direction and periodicity exit in the material, whereas the  point is independent of direction and periodicity. The observed characteristics might have originated from the short-range structure of the amorphous diamond. For the nanocrystalline powder the small bandgap of 3.3 eV and the gradual increase in 2 are probably generated from the disordered carbon layer surrounding individual nanometer-sized crystallites observed under high resolution TEM. It is quite likely to tailor the bandgap of diamond films by controlling the synthesis parameters.

4.3. X-Ray Photoelectron Spectroscopy The NCD films with a thickness of 800 nm were grown by MPCVD and these films were implanted with nitrogen ions at energy of 110 keV [80]. During the implantation process, the temperature of the samples was controlled below 80
C using a water-cooling device. X-ray photoelectron spectroscopy (XPS) was used to analyze the changes in surface structure and chemical state of the films before and after implantation. Figure 12 [80] presents the XPS spectra for C 1s and O 1s states of the as-deposited film. The C 1s envelope has been deconvoluted into three components (Fig. 12a). The main peak at 284.5 eV can be attributed to contribution from C–C and C–H bonds [81]. The peak signals at 285.8 and 286.9 eV are indications of the presence of C–O

and C O [82], respectively. Figure 12b is the O 1s spectra of the as-deposited film. A single-peak signal centered at 532.8 eV is evident, which may be assigned to the C–O bond [83]. The surfaces of as-grown CVD diamond films are typically terminated with hydrogen atoms [84]. However, the film grown as previously stated indicates that the O concentration on the surface reaches 9.83%, which implies that the terminals of dangling bonds of sp3 C–C atoms on the surface are occupied not only by hydrogen atoms but also by some oxygen atoms and absorption of hydrogen and oxygen may also exit on the surface [85]. Shown in Figure 13 [80] are the XPS spectra for C 1s and O 1s states of the film implanted with 1 × 1017 ions cm−2 . As compared with the unimplanted sample, distinct changes in the C 1s and O 1s spectra are observed. The C 1s core-level spectrum shifts to a higher binding energy, and the intensity of peaks for C–O and C O shows an obvious increase (Fig. 13a). The O 1s lines are asymmetric, and more than one binding state is presented. Absorbed oxygen (529.6 eV), C O (531.5 eV), C–O (532.8 eV), and absorbed H2 O (534.9 eV) [86] are shown in the O 1s spectrum of Figure 13b. These studies show that nitrogen-ion implantation changes the surface chemical state of the NCD film. The C–H and C–O bonds on the surface of as-deposited films were broken by highly energetic nitrogen ions. Hydrogen and oxygen desorb from the diamond surface and yield unoccupied surface states, which cause the change in the surface state of the as-deposited film. These chemically unsaturated surface carbon atoms have free valences that may be saturated by chemisorption of foreign elements or may react with foreign elements to form bonded surface functional groups [87]. When the implanted samples are exposed in ambient atmosphere, the dangling bonds can be quickly

10 C-H C-C

(a)

10 (a)

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C-O

8

4 2

N(E)/E

N(E)/E

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C-O C=O

0 294

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286

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C-C, C-H

4 C=O

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Binding Energy (ev)

π-π*

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10

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(b)

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N(E)/E

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N(E)/E

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6

C-O

6

C=O

4

4 2 H2 O

2 0

0 540

IL-6 29 0

538

536

534 532 530 Binding Energy (ev)

528

526

Figure 12. XPS spectra for: (a) C 1s and (b) O 1s states for the as-deposited film. Reprinted with permission from [80], T. Xu et al., Diamond Relat. Mater. 10, 1441 (2001). © 2001, Elsevier Science.

IL-6292

538

536

534

532 530 Binding Energy (ev)

528

526

Figure 13. XPS spectra for (a) C 1s and (b) O 1s states for the film implanted with 1 × 1017 ions cm−2 . Reprinted with permission from [80], T. Xu et al., Diamond Relat. Mater. 10, 1441 (2001). © 2001, Elsevier Science.

Nanocrystalline Diamond

446 occupied by OH, CO2 , or H2 O molecules and ions in air. In this way the surfaces of NCD films are covered by a layer of oxygen-containing groups after high fluence implantation, thereby resulting into the change in chemical state of oxygen on the surface.

4.4. Raman Spectroscopy It is well known that Raman spectra, that are sensitive to changes in translational symmetry, are very powerful for the study of disorder and crystalline formation in thin carbon films [88]. In Raman spectroscopy, a visible laser is used for excitation, and a sharp peak at 1333 cm−1 appears in the spectrum. For NCD films, with decreasing the grain size, the grain surface area and grain boundary that mainly consist of amorphous sp2 C phases increase. In the Raman spectrum, a broad D peak (disorder-induced mode) at 1350 cm−1 will appear and possibly overlap the diamond peak at 1333 cm−1 with increasing sp2 C bonding. The high frequency stretch modes of sp2 C atoms are overemphasized due to the – ∗ transition resonance effects [89], and the sp2 C network exhibits resonance enhancement in the Raman cross-section since the local sp2 C energy gap of approximately 2 eV is comparable to the energy of the incident photons. The sp3 C atoms do not exhibit such a resonance effect because of the higher local gap of approximately 5.5 eV. Hence the Raman spectra obtained with visible excitation are completely dominated by the sp2 C atoms [90]. Raman scattering in the UV region is promising for vibrational studies of sp3 bonded C phase [91]. Advantages of using UV over visible photons include the suppression of the dominant resonance Raman scattering from sp2 C atoms and increase in the intensity from sp3 C bonding [92]. Figure 14 [93] is the Raman spectra of NCD films grown by the MPCVD technique at different temperatures [93]. The Raman spectrum of the NCD films mainly exhibits three features near 1150, 1350, and 1580 cm−1 . The bands in the Raman spectra of these films near 1350 and 1580 cm−1 , popularly known as D and G bands, are related to graphitic

islands [90]. The D band appears due to small domain size in graphite. The band near 1150 cm−1 is shown to be related to the calculated photon density of states of diamond and has been assigned to the presence of a nanocrystalline phase of diamond [94, 95]. It is observed from Figure 14 that the NCD feature is almost missing in the film grown at 400
C, and this feature increases with temperature in the film grown at 500
C and becomes quite pronounced in the films grown at 600
C followed by a drastic decrease in its intensity at higher temperature. It has also been observed as a weak band in the microcrystalline diamond films along with a sharp peak near 1332 cm−1 giving thereby the signature of crystalline cubic diamond [21, 96]. It is interesting to note that though the film grown at 600
C shows an intense band related to NCD, it does not show any peak near 1332 cm−1 . This is mostly due to uniformly distributed short-range sp3 crystallites in the films [96, 97]. However, the higher intensities of the graphitic bands in the films grown at 600
C, as compared to the intensity of NCD features, do not represent high amounts of sp2 carbon in the film. This is because the cross-section of Raman scattering is 50–60 times higher for sp2 -bonded carbon in comparison to sp3 -bonded carbon [98]. This small amount of graphitic carbon in the film may exit between the nanodiamond grains [99]. The variation in the intensity of NCD peak can be taken as a qualitative measure of concentration of NCD grain in the film. It appears that the growth of NCD starts at 500
C, becomes a maximum at 600
C, and decreases at higher temperatures.

4.5. Infrared NCD films deposited by CVD of camphor on Si substrate were analyzed by infrared (IR) spectroscopy [38]. Figure 15 [38] shows the variation of transmittance with wave number of thermal CVD of diamond (curve a) and by rf + dc plasma CVD of CH4 and hydrogen (curve b). It is observed from these figures that over the IR region, the transmittance of NCD is comparable to that of PCD film [100]. The transmittance of bulk diamond (curve c) is also shown

2.86

3.3

λ (µm)

5

6.6 8 10

1.0 0.9

Transmittance

0.8 0.7 0.6

diamond bulk (c)

0.5 0.4

(b)

0.3

(a)

0.2

CO2

SiO2

0.1 0.0 I L-6327 4000 3500 3000 2500 2000 1500 1000 Wave number (cm-1) Figure 14. Raman spectra of the films deposited at different temperatures: (a) 400
C, (b) 500
C, (c) 600
C and (d) 700
C. The samples were excited by a 488-mm Ar+ laser. The three positions 1150, 1350 and 1580 cm−1 correspond to nanocrystalline diamond, graphitic D and G bands, respectively. Reprinted with permission from [93], T. Sharda et al., Diamond Relat. Mater. 10, 1592 (2001). © 2001, Elsevier Science.

Figure 15. IR spectra of two representative films deposited on Si substrates: (a) deposited by CVD of camphor and hydrogen, (b) deposited by rf + dc plasma CVD of CH4 + H2 , (c) the spectrum of bulk diamond for comparison. Reprinted with permission from [38], K. Chakrabarti et al., Diamond Relat. Mater. 7, 845 (1998). © 1998, Elsevier Science.

Nanocrystalline Diamond

in Figure 15. Clearly, the transmittance of bulk diamond is higher than that of NCD and PCD film. The reduction in transmittance of the CVD diamond is related to the formation of the initial layer of silicon carbide on Si substrate, while for bulk diamond the transmittance is higher as no such substrate effect is observed in this case. In addition, the two-phonon absorption is prominent in bulk diamond. The IR spectrum of CVD film exhibits two small peaks at wave numbers ∼2325 and 1050 cm−1 that are due to CO2 and SiO2 absorptions. The CVD diamond films deposited by CVD of camphor + H2 have much lower average grain size of 0.1
m and smoother surface whereas the films deposited by rf + dc plasma CVD have large polycrystals with average grain size of ∼3.2
m. No prominent C–H absorption peak around 2900 cm−1 was noticed in IR spectra indicating thereby a good quality of NCD films. On the other hand, the IR spectra of diamond films grown on Si substrates by MPCVD exhibit predominant C–H bands [101]. In particular, sp3 -CH2 symmetric stretch at 2850 cm−1 and sp3 -CH2 asymmetric stretch at 2925 cm−1 were identified.

5. PHYSICAL PROPERTIES Diamond has unique and remarkable properties, for instance high hardness, low friction coefficient [102], high thermal conductivity [103], high chemical stability, and low or negative electron affinity (NEA) [104]. NEA enables electrons at the conduction band minimum to escape from the diamond without an energy barrier at the surface. However, diamond is a good insulator and therefore it is difficult to deliver electrons to the surface. Similarly diamond is a potential material for wear-resistant applications due to its excellent physical and chemical properties. However, conventional CVD diamond coatings that are deposited at high temperatures possess rough surfaces. The high surface roughness is a major problem when these diamond films are used for machining and wear applications. The successful growth of thin films of NCD at low deposition pressures opens up their large scale uses in tribological applications and field emission display devices.

5.1. Mechanical Properties 5.1.1. Surface Roughness The surface of PCD films is often very rough and hinders their use for optical and tribological applications. The consensus is that efficient ways must be developed to produce smooth diamond films wherein high sp3 content can be maintained. The NCD films appear promising toward this goal. It is well known that the key parameter to obtain smooth NCD films is the primary nucleation density of diamond nuclei on the substrate. Nucleation densities exceeding 1010 cm−2 can be achieved by ultrasonically scratching the substrate surface with fine-grained diamond powder [9, 105, 106]. A direct relationship between the grain size of diamond powder and primary nucleation density on the substrates, and consequently the optical transparency, has been observed. Other parameters such as the methane fraction in the source gas and the substrate temperature can also affect the morphology and the size of the crystallites. However, previous studies

447 have only focused on the variations in grain size of the diamond powder, keeping the methane fraction in the source gas either constant or varying it over only a small range. The optimized value of the optical transparency at 700 nm and beyond was about 60% and the surface roughness was about 20 nm [9, 105, 106]. The effects of both the grain size of diamond powder and methane fraction in the source gas over a wide range on the microstructure and the optical transmittance of the films have been investigated by these researchers. The substrate pretreatment involved ultrasonic polishing of the substrates with diamond powder of two different grain sizes, 4 nm and 0.1
m, for 8 h, followed by standard chemical cleaning with acetone and de-ionized water. For convenience, hereafter the substrates treated with 4 nm diamond powder will be designated as nanometerscratched and those treated with 0.1
m diamond powder as micrometer-scratched. Both types of substrates were placed together in the deposition chamber. Notably, for no ultrasonic polishing at all or polishing for less than 8 h with either of the powders, the resulting films were not continuous, indicating that the substrates were not uniformly and entirely scratched for less than 8 h of treatment. The substrates were also cleaned in pure hydrogen plasma at 1.5 kW for 30 min before the depositions. Typical deposition time was about 3–4 h to give a film thickness of about 0.5
m. Typical surface profiles of NCD films grown at two methane fractions on nanometer- and micrometer-scratched substrates are presented in Figure 16 [5]. At low methane fraction, the micrometer-scratched sample had a rough surface whereas the nanometer-scratched sample was smooth. Under this specific condition, the average surface roughness is comparable to the respective average grain size, which in turn is directly related with the powder size used for substrate pretreatment. Surprisingly, this correlation between the average grain size and the surface roughness was not observed in the samples prepared at high methane fraction. For films deposited at 31% methane fraction, despite the similarity in the grain size distribution and the average grain size (∼30 nm), the nanometer-scratched sample has a much rougher surface [root mean square (rms) of roughness ∼100 nm] than its micrometer-scratched counterpart with rms of roughness ∼8 nm. Shown in Figure 17 [5] are some typical transmission spectra of these NCD films. It is observed that the transparency of NCD film is strongly dependent not only on the methane fraction but also on the pretreatment of the substrate. The optical absorption edge for most of the NCD films was quite similar to that for type IIa diamond. However, detail tailing near the absorption edge varied from sample to sample, presumably due to the structural imperfections of the films, as well as the internal light scattering at the grain boundaries. Optical transparency over 60% in the spectral range of 0.6–2.0
m is considered sufficiently high for most practical applications [105]. For comparison, a variation in the transmittance at 700 nm as a function of the methane content of the source gas is depicted in Figure 18 [5]. Since most of the optical transmittance spectrum showed the influence of interference of the light in the film, the value of a smooth curve that represented the average behavior has been used. At lower methane fractions, the films grown on nanometer-scratched

Nanocrystalline Diamond 100 100 0

-100 0

4

8

12 length (µm)

16

20

(b)

100

Transparency (%)

(a)

(a)

80

4%

60

13%

40 37.5% 20

0 -100

0 0

4

8

12 length (µm)

16

20

(c)

100

200

300

400 500 600 700 Wavelength (nm)

800

100

0 -100 0

4

8

12 length (µm)

16

20

(d)

100 0

Transparency (%)

Surface profile (nm) Surface profile (nm) Surface profile (nm) Surface profile (nm)

448

(b)

80

37.5% 60 13%

40

4%

20

-100 IL-6293

4

8

12 length (µm)

16

20

Figure 16. Surface profiles of NCD films grown at (a), (b) methane fraction of 4%, nanometer- and micrometer-scratched substrates, respectively; (c), (d) methane fraction of 31%, nanometer- and micrometer-scratched substrates, respectively. Both pairs of films have similar thickness of about 0.55 (±0.05)
m. Reprinted with permission from [5], L. C. Chen et al., J. Appl. Phys. 89, 753 (2001). © 2001, American Institute of Physics.

substrates were considerably more transparent than those on micrometer-scratched substrates. However, as the methane fraction increased, the difference between the transmittance of these two types of films diminished and actually reversed at a methane fraction of 20%, such that beyond this methane fraction, the films grown on micrometer-scratched substrates were more transparent than those on nanometer-scratched substrates. The films grown on micrometer-scratched substrates remained highly transparent until a methane fraction of 42%, while those on nanometer-scratched substrates became fairly opaque for methane fractions beyond 25%. Figure 19 [5] shows the plot between the optical transmittance at 700 nm and the inverse surface roughness and clearly reveals the existence of a region showing a linear relationship between the two parameters. In a second region, saturation of the optical transmittance of the films to 80% to 84% occurred despite continuing reduction in their surface roughness. Thus, the major factor that dictates the optical transmittance of NCD films is the surface roughness, instead of the grain size, provided that the contents of the sp2 -bonded carbon and the structural disorder were negligible.

5.1.2. Hardness The indentation technique has been most widely used for the determination of hardness. This technique is suitable for films with higher thickness since the method requires

0

IL-6 28 4

200

300

400 500 600 Wavelength (nm)

700

800

Figure 17. Optical transmittance spectra of the NCD films grown on (a) nanometer-scratched and (b) micrometer-scratched and substrates at various methane fractions. Reprinted with permission from [5], L. C. Chen et al., J. Appl. Phys. 89, 753 (2001). © 2001, American Institute of Physics.

a penetration depth (h) so that h < 01d, where d is the film thickness [107]. The stress/strain and hardness in thin films may be evaluated indirectly by measuring the physical properties that are influenced by the mechanical properties. 90

Optical Transmittance at 700 nm (%)

0

80 70 60 50 40 30 IL-6280

0

10

20 30 Methane Fraction (%)

40

Figure 18. Variations in optical transmittance at 700 nm as a function of methane fraction for NCD films grown on nanometer-scratched () and micrometer scratched (O) substrates. Reprinted with permission from [5], L. C. Chen et al., J. Appl. Phys. 89, 753 (2001). © 2001, American Institute of Physics.

Nanocrystalline Diamond

449

Optical Transmittance at 700 nm (%)

90

80

70

60

50

40

30 0

2

4

6

8

10

12

14

16

1/Ra (x10-3 )

18 IL-6279

Figure 19. Correlation between optical transmittance at 700 nm and average surface roughness for NCD films grown on nanometerscratched () and micron-scratched (O) substrates. The asterisk (∗) denotes the data from Reference 9. Reprinted with permission from [5], L. C. Chen et al., J. Appl. Phys. 89, 753 (2001). © 2001, American Institute of Physics.

Chakrabarti et al. [38] studied the effect of mechanical stress on the optical absorption band tail to determine the strain (a/a) from the theoretical curve-fitting method. This being a nondestructive technique is often very useful since the film may be utilized for other applications. If  and 0 are the absorption coefficients at any wavelength () and at the band edge, respectively, then a plot of /0 vs (Eg − h, as shown in Figure 20 [38], may be used to obtain the strain (a/a) in the film by using the curvefitting procedure [108]. The stresses (S) in the films were obtained from the relation

Figure 20. Plot of /0 vs (Eg − h) for four representative films deposited on quartz substrates, 0 being the absorption coefficient at the band edge Eg. Reprinted with permission from [38], K. Chakrabarti et al., Diamond Relat. Mater. 7, 845 (1998). © 1998, Elsevier Science.

mechanical properties of as-grown and annealed NCD films were evaluated. Shown in Figure 21 [110] are the Raman spectra of the as-grown and annealed samples of NCD films. The spectra consist of bands near 1150, 1350, 1500, and 1580 cm−1 . The bands near 1350 and 1580 cm−1 are D and G bands, respectively, and are related to graphitic islands. Another band near 1150 cm−1 is assigned mainly to the presence of the nanocrystalline phase of diamond [15, 88, 90]. The band intensity near 1500 cm−1 varies proportionally with

S = Y a/a/1 −  with Young’s modulus Y = 600 GPa and Poisson’s ratio  = 011. The hardness (Hv) in the films were obtained from [109] Hv = 29Y /1 − 1000/x−nc a/a1−nc where nc is the strain-hardening coefficient and x is the indentational strain. The values of S, (a/a), and Hv, for NCD films grown from CVD of camphor at various temperatures, were obtained and are in the range 1.9–8.4 GPa, (2–12)×10−3 , and 47–62 GPa, respectively [38].

5.2. Thermal Properties 5.2.1. Thermal Stability To investigate the thermal stability of NCD films grown on mirror-polished Si substrates by biased enhanced MPCVD, the NCD films were annealed in an ambient Ar atmosphere at 200, 400, 600, and 800
C [110]. The structural and

Figure 21. Raman spectra of the (a) as-grown and annealed samples at (b) 200
C, (c) 400
C, (d) 600
C, and (e) 800
C. Reprinted with permission from [110], T. Sharda et al., J. Nanosci. Nanotech. 1, 287 (2001). © 2001, American Scientific Publishers.

Nanocrystalline Diamond

450 the band intensity near 1150 cm−1 and is related to the disordered sp3 carbon in the films [12, 15]. The Raman results in this case indicate association of these Raman features closer to NCD. If these features were related to hydrogen, their intensity should have decreased with annealing temperature, because the hydrogen should have started to evolve from the samples after 200
C [111]. On the other hand, if these features are related to sp2 -bonded carbon, their intensities should have increased with annealing temperature as the concentration of sp2 carbon increases with annealing temperature [111, 112]. Figure 22 [110] depicts the plot of the intensity ratio of the Raman features near 1150 cm−1 to the graphitic G band as a function of annealing temperature. The ratio does not change significantly as a function of annealing temperature and shows an increasing trend up to 400
C but saturates at higher temperatures to a lower value, which is identical to the value of the as-grown sample. Figure 23 [110] depicts the cubic crystalline diamond features in the XRD patterns of the NCD films, which also support to some extent the conjecture that the Raman feature near 1150 cm−1 is related to NCD. In addition, the calculated interplanar spacings corresponding to the peaks at 2 ∼ 4405
and 7525
± 020
in XRD patterns of the films closely match the interplanar d-values of (111) and (220) planes of cubic diamond, respectively. The full width at half maximum of diamond peaks in the films is high as compared to the CVD grown microcrystalline films and these observations are well correlated with that of diamond nanocrystallites [21]. It should be noted that no XRD peaks associated with graphite or features related to amorphous carbon could be identified either in the as-grown films or in the annealed films. These results support the assignment of the Raman feature near 1150 cm−1 to the presence of NCD. Similarly, the intensity ratio of the Raman NCD to the graphitic G band does not change much with annealing temperature, indicating thereby the structural stability of NCD films to temperatures as high as 800
C.

Figure 23. XRD patterns of the (a) as-grown and annealed samples at (b) 200
C, (c) 400
C, (d) 600
C, and (e) 800
C. Reprinted with permission from [110], T. Sharda et al., J. Nanosci. Nanotech. 1, 287 (2001). © 2001, American Scientific Publishers.

5.2.2. Specific Heat Capacity The specific heat capacity bears important implications on various parameters like thermal conductivity, diffusivity, and thermal expansion. The independent measurement of this quantity is important to gain an understanding of the thermodynamic behavior of NCD. The specific heat capacity of NCD samples has been measured by differential scanning calorimetry [113]. Shown in Figure 24 [113] is the plot of the specific heat at constant pressure Cp for the type IIb diamond stone, coarse-grained diamond, NCD, amorphous carbon, and reference data (solid line [114]) vs temperature. The Cp values of the coarse-grained sample are found to be lower than the reference data by less than 10% but are consistent with the measured Cp of the diamond single 2.0

1.2

reference data single crystal coarse grained nanocrystalline amorphous carbon

1.5

0.8 Cp [J/g K]

Intensity Ratio (ln /lg)

1.0

0.6 0.4

1.0

as grown

0.2

0.5

0.0

IL-6330

0

200

400

600

800 IL-6331

Annealing Temperature (oC)

Figure 22. Plot of the Raman intensity ratio of NCD (In) to the graphitic G band (Ig) as a function of annealing temperature. The error bar is the standard error in fitting the individual Raman curves. Reprinted with permission from [110], T. Sharda et al., J. Nanosci. Nanotech. 1, 287 (2001). © 2001, American Scientific Publishers.

0

100

200 Temperature [ oC]

300

Figure 24. Specific heat Cp of poly- and nanocrystalline CVD diamond, amorphous carbon and single-crystalline diamond (solid line: [114]) versus temperature. Reprinted with permission from [113], C. Moelle et al., Diamond Relat. Mater. 7, 499 (1998). © 1998, Elsevier Science.

Nanocrystalline Diamond 100

75

Tr (%)

Ts = 713 K (13θ) Ts = 673 K (13θ) Ts = 573 K (13θ) 25

0 200

400

600 800 λ (nm)

I L-6332

1000

Figure 25. Transmittance (Tr  vs wavelength ( of three representative films deposited on fused silica at different substrate temperature (Ts . Reprinted with permission from [38], K. Chakrabarti et al., Diamond Relat. Mater. 7, 845 (1998). © 1998, Elsevier Science.

10

5.3. Optical Properties

400

9 8 300 7

(α hν)2 x 10-9 (eV/cm)2

Figure 25 [38] presents the optical transmittance (Tr ) versus wavelength () traces of three NCD films deposited at different substrate temperature (Ts ) on quartz. It may be observed that the transmittance (Tr ) had a high value (∼93%) for Ts > 673 K. The direct and indirect bandgaps (Egd and Egi ), estimated from the corresponding plots of (h2 vs h and (h1/2 vs h is presented in Figure 26 [38], where Egd = 484 eV and Egi = 218 eV. It may be noted that both the direct and indirect bandgaps were high and their values increased with increasing Ts . The surfaces of the as-deposited films were generally sp2 rich. The sp2 phases from the surfaces of the films could be removed either by etching in oxygen plasma or by using a chemical process [116, 117]. After etching, the absorption edge of the optical spectra became sharper than that of the asdeposited film as presented in Figure 27 [38]. There was also a substantial increase in the direct bandgap (Egd ) due to the removal of the sp2 phase from the film surface by etching, although the change of indirect bandgap (Egi ) was insignificant. The variation of bandgap energy due to removal of the sp2 phase etching was similar to that reported earlier for NCD films deposited by high pressure sputtering of vitreous carbon target [118] and for diamond films deposited by CVD of freon-22 and hydrogen [119]. In fact, the etching characteristics of diamond films may provide the information of sp2 graphitic and sp3 diamond structure in the film because the trigonal sp2 phase can be more easily etched than the tetragonal sp3 [120, 121]. The etch rate will be higher in films

50

Sample = 12θ Ts = 673 K

6 5

200

4

α hεν(eV/cm) 1/2

crystal. The NCD sample exhibits a higher Cp at 50
C and slightly lower values for T > 100
C. The accuracy of the experimental values for the NCD and amorphous sample is limited by the very small sample amount and is estimated to be about 15% based on repeated test runs. The Cp values of the amorphous carbon films are found to be increased by 0.5 J g−1 K−1 compared to the reference data and are due to the different atomic short-range order and the sp2 :sp3 bonding composition in the amorphous structure. Additionally, the large amount of hydrogen homogeneously incorporated in the amorphous structure contributes to the increase of Cp . The Cp data of the coarse-grained diamond and NCD sample deviate from the reference data by a maximum of 15%. Since the microstructure and hydrogen concentration considerably differ between them, it can be concluded that these properties have a negligible impact on the specific heat. These results are in good agreement with those of large-grained thick CVD diamond films [115]. The impact of nondiamond phases on the specific heat appears to be small. A residual volume fraction of amorphous carbon in the nanocrystalline sample should make a small contribution to Cp , with Cp of the second amorphous phase being increased by a factor of about 2. The fact that the specific heat data of the CVD diamond samples fall within a 15% interval around the reference data up to 300
C implies that the temperature dependence of the thermal expansion coefficient should be the same as that of single-crystalline diamond.

451

3 100 2 Egi = 2.10 eV

1

Egd = 4.80 eV 0

2.0

4.0

6.0

I L-6334

0

hν (eV) Figure 26. Plots of (h2 vs h and (h1/2 vs h for a representative film deposited on quartz. Reprinted with permission from [38], K. Chakrabarti et al., Diamond Relat. Mater. 7, 845 (1998). © 1998, Elsevier Science.

Nanocrystalline Diamond

452

CAM-4Q etched

75

CAM-4Q

Tr (%)

unetched

2.0 x 1020

100

(a)

10 1.5 x 1020 1 1.0 x

1020 0.1

5.0 x 1019

50

Conductivity (Ω cm)-1

3

Nitrogen concentration (atoms/cm )

100

0.01

0

5 10 15 20 N2 in gas phase (%)

(b)

20% N2 NCD

25

0

I L-6328

200

400

600 λ (nm)

800

1000

Figure 27. Variation of transmittance (Tr  with wavelength ( for a representative film before and after removal of sp2 -rich surface layer by chemical etching. Reprinted with permission from [38], K. Chakrabarti et al., Diamond Relat. Mater. 7, 845 (1998). © 1998, Elsevier Science.

having low sp3 /sp2 ratio and also the effect of the etching on the optical absorption edge will be higher in sp2 -rich film. The refractive index (n) of the films was estimated from the transmittance spectra. n varied within 1.3 to 1.5 in most of the as-deposited nanodiamond films showing practically no significant change with the variation of wavelength. The low value of n may be due to the presence of a significant amount of sp2 phases in the surface of the as-deposited film. Removal of sp2 by surface etching resulted in higher n values (i.e., within 1.8–2.2).

5.4. Electrical Conductivity Nitrogen doped ultrananocrystalline diamond (UNCD) films with 0.2% of total nitrogen content were synthesized by MPCVD, and temperature dependences of electrical conductivity of these films are reported [122]. These results are shown in Figure 28 [122]. In addition, Figure 28a shows secondary ion mass spectroscopy (SIMS) data for the total nitrogen content in the films as a function of the percentage of N2 gas added to the plasma. Along with these data is a plot of the room temperature conductivities for the same. The graph shows that the nitrogen content in the films initially increases but then saturates at ∼2 × 1020 atoms/cm−3 for 5% N2 in the plasma, which is ∼0.2% total nitrogen content. The increase in room temperature conductivity is dramatic and represents an increase by roughly five orders of magnitude over undoped UNCD films. The value of conductivity increases from 0.016 −1 cm−1 for 1% N2 to 143 −1 cm−1 for 20% N2 . The latter value is much higher than n-type diamond [123, 124] and is comparable to heavily boron-doped p-type diamond [125].

Conductivity (Ω cm)-1

100.00

20% N2

10% N2

0.10

5% N2 1% N2

0.01 0

40

80

120

160

1000/T (K-1 )

200

240 IL-6341

Figure 28. (a) Total nitrogen content (left axis) and room temperature conductivity (right axis) as a function of nitrogen in the plasma. (b) Arrhenius plot of conductivity data obtained in the temperature range 300–4.2 K for a series of films synthesized using different nitrogen concentrations in the plasma as shown. Reprinted with permission from [122], S. Bhattacharya et al., Appl. Phys. Lett. 79, 1441 (2001). © 2001, American Institute of Physics.

Figure 28b depicts the temperature dependent conductivity of nitrogen doped UNCD film over the temperature range of 300 to 4.2 K. This graph clearly exhibits finite conduction for temperatures even as low as 4.2 K. This behavior is also seen in heavily boron-doped diamond thin films. These graphs are indicative of multiple, thermally activated conduction mechanisms with different activation energies. Hall measurements have been carried on two samples. The carrier concentrations for the 10% and 20% N2 sample were found to be 20 × 1019 and 15 × 1020 cm−3 , respectively, and the carrier mobility of 5 and 10 cm2 /V s for 10% and 20% N2 samples, respectively. The negative value of the Hall coefficients indicates that electrons are the majority carriers in these films. It is proposed that conduction occurs via the grain boundaries. Nitrogen in microcrystalline diamond thin films usually forms a deep donor level with an activation energy of 1.7 eV [123]. It is therefore likely that the enhanced conductivity in UNCD is due to nitrogen doping

Nanocrystalline Diamond

6. APPLICATIONS The high optical transmittance, mechanical, and electrical properties of NCD films offer ample opportunities for applications in electron emitting cold cathodes, tribology, MEMS, electrochemical electrodes, surface acoustic wave (SAW) devices, and NCD coatings. A brief discussion of the results of research in these areas is provided.

6.1. Electron Emission Field electron emission, which has important applications in the field of flat panel displays and high performance electron guns, has been a subject of extensive studies for many years. Early studies used sharp geometry [126] to attain the local field enhancement necessary to extract electron from materials with high work functions, such as Mo or W. This requires complex and expensive patterning and fabricating process. Another approach is to explore new materials with lower emission thresholds. In the past few years, diamond [125, 127] has attracted much attention. It is widely recognized that the property of NEA that can be displayed by diamond does not alone make this material ideal for low field electron emission applications. Few electrons exit in the conduction band of diamond, which is difficult to dope n-type, making transport of electrons from metallic contacts and emission of electrons from the diamond surface difficult. However, fine grain, highly defective diamond films have shown more promise, presumably due to the presence of a network of grain boundaries and a higher level of nondiamond carbon, which can increase the material’s conductivity. These films, often called NCD films, are being investigated for field emission display devices [4]. The development of field emission flat panel displays (FEDs) has triggered very intense research especially in various kinds of carbon thin films because one of their properties is to emit electrons at relatively low applied electric field [127, 128]. A wide range of carbon films, such as amorphous and diamondlike carbon [129, 130], CVD diamond [125, 131], and single and multiwalled carbon nanotubes [132, 133], have shown field emission current in the mA range for applied fields below 10 V/
m. Cold cathode field emission has been demonstrated in CVD PCD films. In the undoped CVD diamond films, the space-charge-limited current limits the conductance of the bulk. As a result, grain boundaries, which are highly disordered and may contain codeposited graphitic impurities, have been suggested as the main conducting pathway. Because reduction in diamond grain size may increase the conducting pathways, it is possible to improve diamond field emission by depositing size controlled diamond films. The field emission of CVD grown diamond films shows very analogous behavior to the emission of diamondlike carbon films. CVD diamond films of good quality characterized by a sharp and intense 1332 cm−1 Raman peak seem to exhibit poor field emission properties. Zhu et al. [134] reported a relation between the quality of the diamond films measured by the full width at half maximum (FWHM) of

the Raman 1332 cm−1 line and the field emission properties. By decreasing the crystalline quality and monitoring it by the FWHM of the 1332 cm−1 Raman line, the threshold field to get an emission current of 1 nA decreases [134]. The NCD films show a very weak Raman line or even its absence and exhibit threshold field below 5 V/
m. Numerous models such as classical tip emission [135], emission from the conduction band due to a negative electron affinity [136], defect band emission [134], and field enhancement at conducting channels in an insulating matrix [137] have been suggested to explain the low field electron emission of CVD diamond films. The current–voltage characteristics of NCD films were measured at a base pressure of 10−8 Torr. The field emission measurements were performed using a Keithley 237 instrument with an incorporated high voltage. The emission current is collected by a graphite counter electrode placed 30
m above the anode. The experimental procedures for current density measurements were described in detail elsewhere [138]. Figure 29 [139] shows the typical electron emission characteristics of a NCD film deposited on nanometer-scratched (4 nm) substrate with methane of 20%. These films were grown for 4 h at 900
C and demonstrate an emission current density of 15 mA/cm2 at an applied field of 17 V/
m with turn-on field of 12 V/
m. Here the turn-on field expresses a value of field at emission current density of 0.01 mA/cm2 . The field emission characteristics of the NCD films are further analyzed by the Fowler–Nordheim (FN) plot, a plot of log I/V 2 vs 1/V , as depicted in Figure 30 [139]. The plot yields a straight line according to the FN equation [140], 

 A V 2 −B3/2 J = exp  d Vd where A and B are constants, current density J is in A/m2 , voltage V is in volts, anode-to-cathode distance d is in meters,  is the effective barrier height for electrons in eV, and is the field enhancement factor that depends on the 0.02

Current Density (A/cm2)

of the grains. The nitrogen in these films is present predominantly in the grain boundaries and not within the grains.

453

0.015 0.01 0.005 0 -0.005

IL-6303

0

5

10

15

20

Electric Field (V/µm) Figure 29. Electron emission characteristics of a NCD film deposited on nanometer-scratched substrate with methane of 20%. Reprinted with permission from [139], P. D. Kichambare, Center for Applied Energy Research, University of Kentucky, Lexington, KY, unpublished work, 2001.

Nanocrystalline Diamond

454

will make it insufficient to form conducting channels; thus the emission properties will be rapidly degraded. Recently, field emission from nitrogen-incorporated NCD films has also been reported [143]. All these studies indicate that NCD will be an excellent candidate for cold cathode materials for field emission devices.

-8.8

Log (I/V2 ) [(A/V2)]

-9.0 -9.2 -9.4 -9.6 -9.8

6.2. Electrochemical Electrodes

-10.0 -10.2 -10.4 0.8

0.9

1.0 1000/V (1/V)

1.1

IL-6294

1.2

Figure 30. The Fowler–Nordheim plot depicting field emission characteristics of NCD film. Reprinted with permission from [139], P. D. Kichambare, Center for Applied Energy Research, University of Kentucky, Lexington, KY, unpublished work, 2001.

emitter geometry. Consequently, a plot of logJ /V 2  vs 1/V yields a straight line with slope B3/2 d/ indicating that the field emission property can be explained by a tunneling mechanism. The slope of the FN plot can be used to determine the work function of the emitter. These studies indicate that the NCD films would be suitable for application in electron emission devices as these devices operate at 10 mA/cm2 . The field emission properties of the NCD films [138] can be explained by a conducting–tunneling mechanism. A model based on the graphite/nanodiamond mix-phase structure reported earlier [141] is considered. The NCD films used for field emission measurements were grown on silicon substrates. In such a structure, graphite plays the role of conducting channels from the silicon substrate to the film surface. While on the surface, it is assumed that the nanodiamond has a relatively low or even NEA as that of bulk. Thus electron will first tunnel through the nearby diamond edges and then emit from the diamond surface [127, 142]. There are two main parameters deciding the field emission. The first is the diamond grain size and the other is graphite content in the film. As electrons from the diamond/graphite interface must tunnel through a barrier between them, the diamond grain size is a critical factor determining the tunneling probability. For large-size diamond grains, electrons can only be emitted from regions close to crystal edges, which are thin enough for electrons to tunnel through. In contrast, for small-size diamond grains, electrons can be effectively emitted from a larger surface area, or even the whole diamond surface, thus greatly increasing the emission site density. The graphite content is another critical factor as the emission starts from the diamond/graphite interface. There is an optimum graphite content for maximizing the graphite/diamond interface area on the film surface. The optimal value of the graphite content is just enough to fill the gaps between the densely agglomerated diamond grains. Above this value, a decrease in graphite content will increase the diamond/graphite interface area and thus enhance field emission. But when the graphite content is below this value, a decrease in graphite content will decrease the interface area at the surface, and the field emission properties will drop. Moreover, a further decrease of the graphite content

The use of diamond in electrochemistry is a relatively new field of research that has begun to blossom in recent years [144, 145]. Conductive diamond possesses several properties that distinguish it from conventional sp2 carbon electrode, like glassy carbon, and makes it most promising for electroanalysis [146–148]. These distinguishing properties are (i) background current densities an order of magnitude lower than freshly polished glassy carbon, (ii) a working potential window of 3 to 4 V in aqueous media, (iii) an extremely stable surface structure resulting in better response precision and long-term response stability, (iv) a high degree of response activity for several aqueous-based analytes, and (v) weak adsorption of polar adsorbates such that the electrode material resists fouling and passivation. It has been demonstrated that untreated diamond outperforms freshly polished glassy carbon in terms of limit of quantitation, response precision, and response stability [146–148]. It is therefore necessary to understand the factors that influence electron transfer at conducting diamond thin film electrode. These electrode materials are challenging to investigate because these are typically polycrystalline with multiple crystallographic orientations, and because they contain extended and point defects, grain boundaries, and low levels of nondiamond carbon impurity. The multiple crystallites, defects, and possible nondiamond carbon phases could provide discrete sites for heterogeneous electron transfer. Within this context, NCD films are challenging as it is nearly pure diamond. Recently, the electrochemical properties of NCD thin films deposited from C60 /Ar and methane/nitrogen gas mixture were investigated [149]. Figure 31 [149] depicts the cyclic voltammetric i–E curve for a nanocrystalline diamond film deposited from a C60 /Ar mixture and a boron-doped, microcrystalline diamond film deposited from a CH4 /H2 mixture. The voltammograms were obtained in 1 M H2 SO4 at 50 mV/s. The open circuit potential of the untreated nanocrystalline film was +174 mV (vs saturated calornel electrode (SCE)). Figure 31a shows voltammograms for nanocrystalline and microcrystalline film between −05 and 1.0 V (vs SCE). The curve for the nanocrystalline film is basically featureless within this potential range, and after the initial scan, the curves are reproducible in shape. The anodic current at 0.1 V is 2.5
A/cm2 , and this is significantly smaller than the cathodic current, 20
A/cm2 observed for polished glassy carbon. The open circuit potential for the untreated microcrystalline film was +205 mV (vs SCE). The voltammogram for this film between −05 and 1.0 V is not quite as featureless, as there are two small anodic and cathodic peaks at 0.75 and 0 V, respectively. These features are associated with a quasi-irreversible but as yet unknown surface redox process, probably at the nondiamond carbon impurities in the grain boundaries. The peak current ratio is near 1, so the

Nanocrystalline Diamond

Figure 31. Cyclic voltammetric i–E curves for a nanocrystalline diamond film deposited from a 1% C60 /Ar gas mixture and a boron-doped microcrystalline diamond film deposited from a 0.3% CH4 /H2 gas mixture over (a) a potential range from −05 to 1.0 V (vs. SCE) and (b) a potential range from −16 to 2.0 V (vs. SCE). The electrolyte was 1 M H2 SO4 and the potential sweep rate for (a) was 50 mV/s and for (b) was 25 mV/s. Reprinted with permission from [149], B. Fausett et al., Electroanalysis 12, 7 (2000). © 2000, Wiley-VCH.

surface sites that are being oxidized on the forward sweep are fully reduced on the reverse sweep. The anodic current at 0.1 V is 0.7
A/cm2 , which is a factor of 4 lower than the value observed for the NCD. It should be noted that the microcrystalline films show no evidence for any surface redox processes. The slightly higher background current for this particular nanocrystalline film has been mentioned due to the increased fraction of grain boundary carbon. Figure 31b shows voltammograms for the nanocrystalline and microcrystalline films between −14 and 2.0 V (vs SCE). The electrolyte was 1 M H2 SO4 and the potential sweep rate was 25 mV/s. The working potential window in this medium for the NCD film is ca. 3 V (±250
A/cm2  and is larger than the ca. 2.5 V window observed for freshly polished glassy carbon. The response shows a large anodic peak at 1.5 V and a smaller cathodic peak at 0.4 V. The anodic peak at 1.5 V is likely due to redox-active carbon in the grain boundaries. This indicates that some reduction of these surface carbon–oxygen functionalities must occur during the cathodic potential sweep in order to allow for their reoxidation on the subsequent forward sweep. The voltammogram for the boron-doped microcrystalline film, between −14 and 2.0 V, reveals a working potential window of 3.3 V, which is slightly wider than observed for NCD films. The voltammogram shows an anodic peak at 1.8 V just prior to oxygen evolution; however, the peak charge is significantly less than that for the NCD films. This reflects the reduced coverage of redox-active grain boundary carbon on the microcrystalline films. These studies indicate that NCD films prepared from C60 /Ar gas mixtures appear to have basic electrochemical properties similar to boron-doped microcrystalline diamond films with a wide working potential window and a low voltammetric background current. The potential application of NCD in electroanalysis seems to be due its nanocrystalline structure.

6.3. Tribology The unique properties of diamond (i.e. the highest hardness, stiffness, and thermal conductivity as well as imper-

455 viousness to acidic and saline media) are exceptional and far exceed those of any other known material. The cleaved diamond surfaces exhibit one of the lowest friction coefficients of any known material. The combination of these qualities in a material is ideal for highly demanding tribological applications. The prospects for large-scale uses of diamond in tribology increased sharply when it was discovered that diamond can be grown as thin films at low deposition pressures by various methods [150–153]. High quality microcrystalline diamond films exhibit most of the desired properties of the natural diamonds. They are made up of large columnar grains that are highly faceted and generally rough. They tend to grow continuously rougher as the thickness of the deposited films increases. The generally rough surface finish of these films precludes their immediate uses for most machining and wear applications. When used in sliding-wear applications, such rough films cause high friction and very high wear losses on mating surfaces [154–156]. The rough surface can be polished by laser beams and fine diamond powders or by rubbing against a hot iron plate [157]. Despite the high interest in using diamond films for diverse tribological applications, their widespread utilization in the industrial world has not yet met expectations [158–160]. Recently, new methods have been developed for deposition of smooth NCD films [161] and the films afford ultralow friction and wear in sliding tribological applications. As elaborated above, conventional diamond films are generally rough and consist of large grains. Depending on deposition conditions, these grains exhibit 111 or 100 crystallographic growth orientations. Figure 32 [162] depicts the friction coefficients of microcrystalline diamond films (surface roughness: 0.35
m, rms) and NCD (surface roughness: 30 nm, rms) films against Si3 N4 balls in open air and dry N2 [162]. After an initial run-in period during which friction is relatively high, the friction coefficient of the NCD film decreases rapidly to ∼0.1 in open air and to ∼0.05 in dry N2 , whereas the friction coefficient of the microcrystalline diamond film remains high and unsteady in both test environments. Wear rates of Si3 N4 balls slid against the smooth NCD and rough microcrystalline diamond films in air and dry N2 are shown in Figure 33 [162] which clearly shows that the wear rates of balls slid against the NCD films are more than two orders of magnitude lower than the wear rates of balls slid against the rough microcrystalline diamond (MCD) films. The high friction coefficients of rough diamond films can be attributed to the abrasive cutting and plowing effects of sharp asperity tips on softer counterface pins, whereas the plowing effects created by smooth NCD films on counterface balls are minimal and thus exhibit lower friction. Previous studies also demonstrated a close correlation between higher surface roughness and greater frictional losses [155, 163, 164]. When the rough MCD films were polished and then used in sliding-contact experiments, very low friction coefficients were obtained [161, 163, 164]. Apart from physical roughness, surface chemistry and tribo-induced adhesive interactions can also occur and play a dominant role in the friction and wear performance of all diamond films [165]. The nature and extent of interactions may be controlled by the environmental species or by ambient temperature [166]. Mechanistically, the low-friction

Nanocrystalline Diamond

456

a combination of low friction and high wear resistance under a wide range of sliding-contact conditions. NCD coatings have been applied to seals using dc-biased substrates and an oxyacetylene torch [161, 169].

1.0 Rough Diamond Smooth Diamond

Friction Coefficient

0.8 0.6

6.4. Superhard Nanocrystalline Composites

0.4 0.2 0

0

1,000

2,000

(a)

3,000

4,000 5,000

6,000

7,000

8,000

Number of Sliding Cycles 1.0 Smooth Diamond Rough Diamond

Friction Coefficient

0.8 0.6 0.4 0.2 0

IL-62 97

0 (b)

1,000

2,000 3,000 Number of Sliding Cycles

4,000

5,000

Figure 32. Friction coefficients for rough MCD and smooth NCD films against Si3 N4 balls in (a) open air and (b) in dry N2 . (Test conditions: load, 2 N; velocity, 0.05 m s−1 ; relative humidity, 37%, sliding distance, 40 m, ball diameter, 9.55 mm.) Reprinted with permission from [162], A. Erdemir et al., Surf. Coat. Technol. 120–121, 565 (1999). © 1999, Elsevier Science.

nature of smooth or cleaved diamond surfaces has long been attributed to the highly passive nature of their surfaces [167, 168]. Specifically, it has been postulated that gaseous adsorbates, such as hydrogen, oxygen, or water vapor, can effectively passivate the dangling surface bonds of diamond. When the dangling bonds become highly passive, the adhesion component of friction is diminished [162]. Thus, unlike most other engineering materials, NCD offers

Figure 33. Wear rates of Si3 N4 balls slid against smooth NCD and rough MCD in air and dry N2 (test conditions: load, 2 N; velocity, 0.05 m s−1 ; relative humidity, 37%; sliding distance, 40 m; ball diameter, 9.55 mm). Reprinted with permission from [162], A. Erdemir et al., Surf. Coat. Technol. 120–121, 565 (1999). © 1999, Elsevier Science.

Materials with Vickers hardness of ≥40 GPa are called superhard materials. The hardness of diamond depends on its quality and is typically in the range of 70 to 90 GPa. It is limited by dislocation sliding and crack propagation along the 111 crystallographic direction [170, 171]. The theoretical strength of ideal single crystalline materials can be easily estimated from the critical stress, which is needed to cause shear sliding of lattice planes [172]. However, the practically achievable strength of single crystals and engineering materials is orders of magnitude smaller because plastic deformation and fracture occur due to inherent flaws, such as multiplication and propagation of dislocations and crack growth, which are present in the materials. The design of novel superhard materials is based on the formation of stable nanocomposite consisting of two or more phases, for example nanocrystals of hard transition metal nitride imbedded in an amorphous phase [173–175]. When such a nanostructure is formed by a thermodynamically driven segregation of transition metal nitride and silicon or boron nitride, it is fairly stable against recrystallization even at high temperatures of ≥1000
C [176, 177]. The resulting strong interface and compact grain boundaries avoid grain boundary sliding, which would otherwise limit the strength and hardness of nanocrystalline materials [178–181]. Beside the hardness, the nanocomposites also show a very high elastic recovery of 80% to 90% and toughness. The nanocrystalline diamond seems to be one of the promising superhard nanocomposite materials if the properties of NCD are properly tailored. The superhardness combined with a high elastic recovery and toughness will be very important for many practical applications. Hardness of a material is a measure of its ability to resist deformation upon load. Hence, the meaning of hardness depends on the exact nature of that load resulting in various kinds of engineering scales of hardness, such as scratch, static contact indentation, or dynamic ones. The most universal measure of the hardness is the energy of the plastic or pseudoplastic deformation, which is calculated from the ratio of the applied load to the area of that deformation. Depending on the shape of the indenter used, various scales of the static hardness result. For the characterization of thin films the Vickers or alternatively Knoop hardness is most commonly used. During the measurement a diamond indenter of pyramidal shape with an angle between the opposite faces of 136
is pressed into a material with a given load L and after unloading, the area of the remaining plastic deformation A is measured. The hardness in GPa or kg/mm2 is then calculated from the equation H = ∝L/A, where the constant ∝ depends on the type of the indenter which differs by the angles between the opposite faces of the diamond pyramid. Figure 34 [175] shows examples of indentation into a NCD and into ultrahard nc-TiN/a- and nc-TiSix , x ≈ 2. It should be noted that the measurements on super- and ultrahard materials including diamond show large scattering and, therefore,

Nanocrystalline Diamond

indentation depth [µm]

0.25

457

nc - diamond Hv = 88 GPa E = 534.3 GPa HU = 1879 kg/mm2

0.20 0.15 0.10 0.05

(a) 0.00

0

5

10

15 20 load [mN]

25

30

0.40 nc - TiN/a-& nc - TiSi2 Hv = 138.9 GPa E = 607.4 GPa HU = 1914.4 kg/mm2

indentation depth [µm]

0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00

(b) 0

10

20

30 40 load [mN]

50

60

IL-6338

70

Figure 34. Example of indentation into (a) NCD and (b) nc-TiN/a- & nc-TiSix (x ∼ 2) coatings. The area between the lower (loading) and upper (unloading) curve corresponds to the energy of pseudoplastic deformation, the area between the loading curve and the y-axis corresponds to the total energy of deformation. Reprinted with permission from [175], P. Nesladek and S. Veprek, Phys. Status Solidi A 177, 53 (2000). © 2000, Wiley-VCH.

the obtained values of hardness should be considered as relative ones. Therefore, one can conclude from Figure 34 that the microhardness of the nc-TiN/a- and nc-TiSix films is at least equal to that of the hardest diamond.

6.5. Conformal Coatings The excellent mechanical properties of diamond suggest that diamond is one of the best materials for MEMS applications. In addition, the chemical inertness of diamond makes it a suitable as a corrosion protection material. Recently, NCD film growth has been demonstrated on various substrates of engineering interest [182]. The substrate of choice in most diamond deposition studies has been silicon while for metals, the thermal expansion mismatch between the diamond film and substrate gives rise to thermal stress, which often results in delamination of the film. Thus, one of the major barriers in obtaining a diamond film that is resistant to delamination is the inherent difference between the coefficient of thermal expansion between the diamond film and a metal substrate. The desirable mechanical properties with coating containing NCD and/or amorphous carbon have been reported [183]. The combination of nanocrystalline and amorphous carbon components can result in coatings with high toughness, high hardness, and low surface roughness [183, 184]. These films are believed to consist of NCD grains imbedded in a primarily amorphous carbon matrix, which itself

has some sp3 -bonded carbon content. These coatings have been produced with hardness up to 80% that of natural diamond and yet still exhibit appreciable toughness uncharacteristic of a pure ceramic material [182]. NCD coatings can be tailored in their coating structure and mechanical properties by appropriate changes in CVD feed gas chemistry [182]. The relative concentration of CH4 and N2 is shown to strongly influence coating structure, hardness, and adhesion. This can provide an opportunity to choose a balance between coating hardness and toughness as required for a particular application. There is general agreement that diamond film growth occurs most readily on pure metal that supports the formation of a stable carbide layer. There has been controversy as to whether the formation of a surface carbide film was a prerequisite for diamond growth. Ramanthan et al. [185] have studied the transition metals and found that diamond growth is supported by those metals that tend to produce stabilized sp3 carbon structures. Diamond film adhesion is critically linked to the thermal expansion mismatch between diamond and metal. At higher deposition temperatures more stress may be induced in the film, providing a higher driving force for film buckling or delamination. Ager and Drory [186] measured a residual compressive stress of about 7 GPa for a diamond film on Ti–6Al–4V that was in excellent agreement with the stress predicted from calculation. With such large residual film stresses it would be advantageous to be able to deposit diamond at low substrate temperature. It has been well established that adding small quantities of oxygen can lower the temperature range for which diamond can grow [187, 188]. A small amount of CO and O2 diluted in H2 has also resulted in high quality diamond growth at substrate temperatures in the range of 411 to 750
C [189]. However, in high H2 -dilution conditions, the deposition rate decreases rapidly with temperature. This is because the precursor radical that is widely believed to be responsible for diamond growth under high H2 dilution is thermally activated [190, 191]. An interlayer can be used as a barrier to the diffusion of carbon into the substrate, thus providing sufficient carbon concentrations at the surface to nucleate diamond. The interlayer may also be used in order to minimize interfacial stresses and to provide an intermediate layer for bonding. Diamond deposition onto WC–Co and steel substrates has been achieved using a multiplayer structure of silver and refractory metals with a resulting improvement in adhesion [192]. Such coating is typical of that required for good WC–Co cutting tool properties. Figure 35 [182] shows a thick NCD film grown on WC–Co that was prepared with a chemical treatment prior to coating and it depicts an extremely smooth and flat surface. Similarly, results of conformal coatings of NCD are very encouraging and a good degree of coating conformality has been reported wherein a hexagonal shaped silicon needle ∼5
m in diameter was successfully coated with ∼2000 Å NCD [4].

6.6. SAW Devices SAW devices have found several key applications in radio frequency and microwave electronics [193]. They offer a high degree of frequency selectivity with low insertion loss,

Nanocrystalline Diamond

458 electrodes ZnO

Nanocrystalline diamond

Si substrate IL-6337

Figure 36. Schematic diagram of the surface acoustic wave device multiplayer structure. Reprinted with permission from [200], B. Bi et al., Diamond Relat. Mater. 11, 677 (2002). © 2002, Elsevier Science.

making them highly suitable for use as narrow band filters. SAW devices are particularly well adapted to microwave integrated circuits since they can provide a significant size reduction over purely electromagnetic devices. These devices are most typically implemented on piezoelectric substrates on which thin metal film interdigitated transducers (IDTs) are fabricated using photolithography. The use of diamond as a SAW substrate offers an attractive means for relaxing the lithographic criteria [194]. With a surface wave velocity  ∼ 1 × 1014 m s−1 , diamond allows SAW device operation near 2.5 GHz with nominal 1
m linewidths. Since diamond is not piezoelectric, additional complexity is introduced by a requisite overlayer of a piezoelectric thin film, typically ZnO. Sound propagation in layered media may be highly dispersive and in general admits a multiplicity of allowed modes. Nevertheless, highly successful devices based on ZnO/polycrystalline diamond/Si layered structures have been reported [195–199]. NCD is a new form of diamond and differs from diamondlike carbon in that it contains relatively little hydrogen or sp2 -bonded carbon. The properties of NCD films like smooth surfaces and small crystallite size are most attractive and relevant for SAW applications, since standard PCD on Si is quite rough and must be smoothed by mechanical polishing before photolithographic processing can be attempted. Furthermore, one expects acoustic scattering at large angle grain boundaries in PCD, especially if lateral grain dimensions exist on length scales between acoustic wavelength and SAW device apertures and transducer separations. The use of NCD eliminates these concerns. SAW devices based on NCD have been fabricated [200] as shown schematically in Figure 36 [200]. This device was studied using a frequency and time domain method. Phase velocities were obtained from device resonant frequencies measured with a network analyzer. Figure 37 [200] presents a compilation of experimental results and calculations of the phase velocity  as a function of khZnO . It is evident that several modes are allowed for a given value of khZnO . The modes

6.7. MEMS Devices Thin film ferroelectrics are important for MEMS because of their strong piezoelectric effect and high energy density originating from the very high dielectric constant of ferroelectric materials [201, 202]. Further, these MEMS devices are fabricated primarily in silicon because of the available surface machining technology. A major problem with Si-based

Dispersion Curves of ZnO/Diamond/Si Structure kh(diamond) = 4 12000 1st

2nd

10000

Phase Velocity (m/s)

Figure 35. Thick NCD coating made on chemically treated surface of WC–Co cutting tool insert. Edge shown is a cutting edge of the tool. Reprinted with permission from [182], R. Thompson et al., in “Proceedings of the 1st ASM International Surface Engineering and the 13th IFHTSE Congress and Exposition” (O. Popoola et al., Eds.), 7–10 October 2002, Columbus, OH. © 2002, ASM International.

are highly dispersive at small values of khZnO (i.e., the phase velocity is strongly dependent on khZnO ). As expected, the lowest order mode tends toward the phase velocity of the Rayleigh wave on (0001) ZnO at large khZnO but approaches the diamond Rayleigh wave velocity as khZnO → 0. It should be noted that the large phase velocity suggests that carbon within the grain boundaries is strongly bonded. Since surface waves are dominated by elastic shear strains, the grain boundary carbon is highly resistant to bond-bending forces. This indicates that most of the carbon is highly coordinated.

8000 0th 6000

4000 VR (ZnO) 2000

IL-6336

0

1

2 kh(ZnO)

3

4

Figure 37. Phase velocities as measured for surface waves on NCD, diamond (
⋆) and on large-grain polycrystalline diamond ( ). The solid line represent calculations of phase velocities based on single crystal diamond material parameters. The label denotes the Rayleigh mode indices for the layered medium. The dashed line shows the Rayleigh wave velocity on ZnO. Reprinted with permission from [200], B. Bi et al., Diamond Relat. Mater. 11, 677 (2002). © 2002, Elsevier Science.

Nanocrystalline Diamond

459 Table 2. Electrical properties of diamond thin films. Thin films

Figure 38. Combined lithographic patterning and selective deposition methods. Reprinted with permission from [207], A. R. Krauss et al., Diamond Relat. Mater. 10, 1952 (2001). © 2001, Elsevier Science.

MEMS technology is that Si has poor mechanical and tribological properties [203, 204]. On the other hand, diamond is an ultrahard material with high mechanical strength, exceptional chemical inertness, and outstanding thermal stability. The friction coefficient of diamond is exceptionally low and the projected wear life is 10,000 times greater than that of Si, making diamond an ideal tribomaterial for MEMS components [205, 206]. Lubrication poses a major limitation on the design of MEMS devices since the usual methods of delivering lubricant to the interface between contacting parts are very difficult to implement. There are a number of ways in which diamond components can be fabricated for MEMS applications using thin film deposition methods [207]. One of the methods of obtaining the tribological benefits of diamond while exploiting the availability of Si fabrication technology is to produce Si components to near-net shape and then to provide a thin, low wear, low friction diamond coating [208–213]. This approach only works if the diamond film can be produced as a thin, continuous, conformal coating with exceptional low roughness on the Si component. Conventional diamond CVD deposition methods result in discontinuous films with a low density of large grains and poor ability to form thin conformal coatings on Si microstructures [214]. Recently, Krauss et al. successfully developed a fabrication technique [207] for conformal UNCD coating that is comparable to the lithography, galvanoformung, Abformung (LIGA) method and permits fabrication of complex three-dimensional shapes as opposed to the two-dimensional structures produced by Si microfabrication methods. The selective deposition represents a second method that may be used for the production of UNCD microstructures but has no analog in Si microfabrication technology. All diamond films require a nucleation layer, usually achieved by exposing the substrate to a suspension Table 1. Mechanical properties of diamond thin films. Thin films Grain size Specific heat (J g k−1 ) Friction coefficient Surface roughness Young’s modulus Hardness

NCD

UNCD

PCD

Ref.

50–100 nm 0.68

2–5 nm —

0.5–10
m 0.54

[113] [113]

0.06

—

0.35

[168, 207]

50–100 nm

20–40 nm

400 nm–1
m

[207]

600 GPa

—

1200 GPa

[38, 207]

62 GPa

—

100 GPa

[10, 38]

Direct bandgap Indirect bandgap Field emission threshold field Electronic bonding H content

NCD

UNCD

PCD

Ref.

4.84 eV 2.18 eV 1 V/
m

— — 3.2 V/
m

5.45 eV — 22 V/
m

[38, 74] [38] [8, 140]

up to 50% sp2

2–5% sp2

sp3

[207]

1.7 eV. The observed broadening of the PL spectra has triggered a search for another technique that is able to separate different possible contributions to the luminescence in nc-Si superlattices. To our surprise, the most interesting results with a very clear interpretation have been found in studies of the PL spectral response as a function of external magnetic and electric fields. Following the initial report that an external magnetic field increases the gap between singlet and triplet states in Si nanocrystals, the fact that the PL lifetime increases and intensity decreases in Si nanocrystals is quite well understood [64–66]. However, our studies show that in nc-Si superlattices this PL quenching is selective and

PL intensity (arb. un.)

T = 4.2 K

104

50 mW/cm mW/cm22 Ecxitation Ecxitation 2.8 2.8eV eVnm nm 103

1.3

1.5

1.7

1.9

Energy (eV) Figure 21. PL spectra in a nc-Si/a-SiO2 superlattice with 42-Å-diameter Si nanocrystals under different excitation intensity.

affects only PL at wavelengths longer than ∼750 nm. The PL intensity at shorter wavelength does not show any quenching under an applied magnetic field as high as 9 T (Fig. 22). The observed selective quenching of PL in nc-Si superlattices proves that the PL origin is more complex than just a single mechanism based on the quantum confinement effect in Si nanocrystals. The application of an external electric field is also an informative experiment due to quite different mechanisms of PL quenching, including direct exciton deformation and dissociation under an external electric field and exciton impact ionization. Different electric-field-induced PL quenching mechanisms have very different thresholds and field dependences. Therefore, we studied the PL dependence as a function of the applied electric field in nc-Si/a-SiO2 superlattices. Our technique is based on the application of an AC

100 B=0T

T=4.2 K 10-1 T=10K τ=3.3ms

T=300K τ=130µs

10-2

10-3 0

0.002

0.004

0.006

42Å Si

PL intensity (arb. un.)

Normalized PL intensity (arb. un.)

514.5 nm excitation

0.008

Time (s) Figure 20. PL decay time in a fully crystallized nc-Si/a-SiO2 superlattice with 42-Å-diameter Si nanocrystals showing a single exponential decay and a strong PL lifetime temperature dependence.

3T 9T

650

750

850

6T

950

Wavelength (nm) Figure 22. PL spectra in a nc-Si/a-SiO2 superlattice with 42-Å-diameter Si nanocrystals in an applied magnetic field of different strengths. A selective quench of PL intensity is clearly shown.

Nanocrystalline Silicon Superlattices

489

electric field and detection of a modulated PL component using a lock-in amplifier. This technique is more sensitive compared to the standard technique where CW PL is influenced by an applied dc electric field. We have found that an electric-field-dependent PL spectral component is strongly correlated with magneto-PL measurements: the modulated PL component is red-shifted compared to CW PL at zero electric field, and the electric field modulates only the PL at wavelengths longer than 750 nm (Fig. 23). These data are in complete agreement with the magneto-PL measurements. Therefore, we can conclude that a portion of the PL in ncSi superlattices at shorter wavelengths does not depend on the electric or magnetic field and most likely has a different origin than PL associated with confined excitons in Si nanocrystals. Additional support for this conclusion can be found in early work on porous Si showing that the PL peak follows the ratio between the numbers of Si-O and Si-H bonds in samples with different degrees of oxidation [67].

6. RESONANT CARRIER TUNNELING IN NANOCRYSTALLINE SILICON–SILICON DIOXIDE SUPERLATTICES Amongst a wide variety of phenomena exhibited in semiconductor quantum transport, resonant carrier tunneling (RCT) and negative differential conductivity (NDC) due to a nonmonotonic dependence of the carrier tunnel transmission through potential barriers has always been associated with nearly perfect semiconductor heterostructures and superlattices with a long carrier mean free path [68–70]. The question as to how RCT can be preserved in a structure with a partial disorder is important both for the physics of quantum structures and for practical quantum device applications [71–76]. A system with a controlled degree of disorder, combining for example a periodic potential in the z direction (i.e., the growth direction) with the presence of grain boundaries separating nanocrystals laterally in the xy plane, is a special case of general interest. A nc-Si superlattice fabricated by controlled crystallization of amorphous Si/SiO2 layered structures forms a perfect example of such a system.

Normalized PL intensity (arb. un.)

T = 20 K

CW PL ext 457 nm EM PL ext. 457 nm

650

700

750

800

850

900

950

Wavelength (nm) Figure 23. Strong red shift of the electric-field-modulated PL spectrum in a 20-period nc-Si/a-SiO2 superlattice with 42-Å-diameter Si nanocrystals measured using a lock-in amplifier and an ac voltage of 15 V.

The flat and chemically abrupt SiO2 layers of low defect density [77] separate the Si nanocrystals and provide vertical carrier confinement, which is a key condition for functional quantum devices. This structure has a well-defined order in the z direction, but is partially disordered laterally due to the nanograin boundaries and the limited degree of Si nanograin crystallographic orientation, as discussed earlier in this chapter. Using such a novel structure, the vertical carrier transport has been investigated and entirely unexpected effects such as narrow resonances in the conductivity, stable self-oscillations, and the strong influence of a low magnetic field applied in the z direction have been observed [13]. The surprising results show that even though there is significant carrier scattering, resonant tunneling and the formation of electron standing waves is still possible. A typical sample for this work was prepared in the form of a 10-period nc-Si superlattice on an n-type, highresistivity ( > 1 k cm) c-Si substrate, with a Si nanocrystal diameter of ∼45 Å and with ∼15-Å-thick SiO2 layers. The low-temperature (4.2 K) hole transport measurements were performed in the sandwich geometry. A He-Ne laser (632.8 nm) was used to generate electron-hole pairs, mostly within the depletion region of the positively biased Si substrate, and holes were extracted through the superlattice structure toward the negatively biased top Al contact. Standard direct current (dc) current-voltage (I-V) measurements were performed using a Keithley 595 electrometer. Measurements of alternating current (ac) differential conductivity were obtained using an HP 4192A impedance analyzer. The experiments were carefully designed to avoid a nonuniform electric field, which may destroy the symmetry of barriers and reduce the effects of resonances. Using a superlattice-type structure confined in a p-i-n diode or Schottky barrier minimizes these effects. In addition, the use of light to generate carriers is a relatively nondestructive way to manipulate the carrier density without significant screening and distortion of the electric field uniformity. Finally, special attention was paid to transient conductivity characteristics. Resonant carrier tunneling in a structure with large (Si/SiO2
barriers is not an immediate phenomenon. In a practical device, resonant tunneling is time-dependent and needs a non-negligible time to become fully established. This process mainly requires the accumulation of tunneling carriers within the resonant well. Each electron localized within the well modifies the local potential, and a feedback mechanism, which often can be limited (at least in part) by the circuit resistance-capacitance time constant, increases the time of the resonant transition [78]. In the extreme case, this process may generate an oscillating current. Therefore, the dc current measurement should be accompanied by frequencyand phase-sensitive ac conductivity measurements. Figure 24 shows a TEM micrograph of the investigated structure and a set of dc I-V characteristics measured under different levels of photoexcitation. The I-V curves clearly exhibit a step-like structure between 1 and 3 V of the applied reverse bias, with current steps shifted to slightly higher voltage as the excitation power increases (shown in the figure by the arrows). The observation of a step-like structure indicates the expected RCT in a multibarrier structure, which results from a non-monotonic dependence of the barrier tunnel transmission on the applied bias. However, in dc

Nanocrystalline Silicon Superlattices

490 (a)

5 µW

Current (A)

10-8

1 µW

10-9

T = 4.2 K ν= 465 Hz

25 µW

11 µW

Differential Conductivity (arb. un.)

20 µW

T=4.2 K λ = 632.8 nm

SiO2

(b) T = 4.2 K; W=10 µW 7 µW 5 µW

4 µW

1 µW

nc-Si SiO2 -1000

10-10

0

1000

2000

Voltage (mV)

0

1000

2000

3000

4000

Voltage (mV)

Figure 24. Step-like direct current (dc) current-voltage (I-V) characteristics in a Si (45 Å)/SiO2 (15 Å) 10-period superlattice with different levels of photoexcitation. The inset shows a TEM of a fragment of the sample. Reprinted with permission from [13], L. Tsybeskov et al., Europhys. Lett. 55, 552 (2001).© 2001, EDP Sciences.

conductivity measurements no fine structure was observed, which can be used in the identification of particular resonant transitions. Also, no NDC was found in these experiments, showing that carrier scattering in the structures is not negligible. The measurements of ac differential conductivity ac (V) proved to be much more sensitive. Figure 25a shows several traces of ac (V) with different levels of photoexcitation (corresponding to different levels of carrier concentration) recorded at a frequency of 465 Hz. At the lowest level of excitation we detect a broad peak at V ≈ 850 mV with a full width at half maximum of about 600 meV. On increasing the carrier concentration, the peak is split and another peak rises near 1.3–1.5 V, which quickly becomes dominant. With further increase of carrier concentration, a sharp (≤100 mV) asymmetric peak, the NDC regime, and an oscillating behavior near 2 V applied bias are found. At an even higher level of photoexcitation, the sharp peak and NDC regime could disappear, leaving a remnant in the form of a broad feature near 1.6 V and a sharp minimum at 2 V. The rich structure becomes less pronounced for temperatures above 20 K and practically cannot be detected at temperatures much greater than 60 K. The expected time dependence of carrier tunneling in a barrier structure is demonstrated by the frequency dependence of the ac differential conductivity under experimental conditions close to the resonance condition (see Fig. 25b). The NDC regime has not been found for biases lower than 1.0 V. On increasing the applied bias (V ≥ 18 V), NDC is observed localized near 1 kHz. When a larger bias is applied, the NDC regime may occupy a broad frequency range, anywhere from 10 Hz to 106 Hz. Finally, at a large bias (V ≥ 35 V) NDC is no longer observed, which indicates that the system is out of resonance. The observed step-like dc I-V characteristics, rich structure, and the NDC regime in the ac differential conductiv-

3000

Normalized conductivity (arb. un.)

10-7

V = 3.5 V

V = 2.2 V

V = 1.8 V

V = 1.0 V

1

102

104

106

Frequency (Hz)

Figure 25. (a) Differential alternating current (ac) conductivity as a function of the applied bias measured under different levels of photoexcitation. The NDC regime is shown by arrows. (b) Frequency dependence of the ac differential conductivity measured at the specified applied bias and light intensity. The traces are shifted for clarity and the zero level is indicated by dashed lines. Reprinted with permission from [13], L. Tsybeskov et al., Europhys. Lett. 55, 552 (2001). © 2001, EDP Sciences.

ity measurements convincingly show that the conductivity in nc-Si/SiO2 samples exhibits a non-monotonic dependence as a function of the applied bias. However, the conductivity  = en, where e is the electron charge, is a function of the carrier mobility  and carrier concentration n. It is well known that a non-monotonic carrier density dependence on the applied electric field also causes NDC, and an example of such a process is the electric field ionization of the Si/SiO2 interface traps [79]. In general, the observation of NDC does not imply a resonant tunneling mechanism, and a test, independently probing tunnel transmission through the barriers, is necessary to prove the existence of RCT. This test can be performed using measurements of the longitudinal magnetoresistance for low applied magnetic fields. Figure 26 shows that at nearly resonant conditions, the ac conductivity at low frequency (300) are normally necessary to obtain a good statistic] and to determine an equivalent particle size based on these areas. Figure 9b shows an example of particle size distribution of Ni nanoparticles in a Ni–SiO2 EDP nanocomposite built from dark field TEM images. In addition to morphological information, TEM provides crystallographic and chemical information. The crystallographic information can be obtained from the diffraction pattern of a selected area, using the so-called select area electron diffraction (SAED) technique. This technique allows for the indexation of crystallographic structures of small or even nanometric regions in the samples. Besides SAED, HRTEM can generate lattice images of the crystalline material, allowing for the direct characterization of a sample’s atomic structure. Figures 4b and 5 contain examples of HRTEM images. HRTEM images are particularly sensitive to changes in a phase of the incoming parallel electron wave as it passes through the sample. The atomic structure can also be characterized by scanning transmission electron microscopy (STEM), using a high angle annular dark field detector (HAADF). In fact, the image generated by a HAADF detector, which is sensitive to the atomic number (Z), is also known as a Z-contrast image [188]. The high-resolution image generated by HAADF detector is sensitive to the chemical composition. In TEM, the chemical information is provided by the X-rays generated through the interaction of the electronic

Figure 9. (a) Dark field TEM image of an EDP nanocomposite consisting of Ni nanoparticles embedded in an amorphous silica matrix. The bright points represent the Ni nanoparticles. (b) Particle size distribution of Ni nanoparticles in a Ni–SiO2 EDP nanocomposite built from dark field TEM images.

Nanocrystals Assembled from the Bottom Up

beam with the sample. This technique, known as energy dispersive X-ray spectroscopy (EDS), allows regions as small as 2 nm in a TEM configuration or lower than 0.8 nm to be chemically characterized, using STEM equipment. In addition to EDS analyses, nanostructured materials can also be chemically characterized by electron energy loss spectroscopy (EELS), which allows for a better characterization of light elements, which usually pose a major problem in X-ray spectroscopy-based characterization. Another advantage of EELS spectroscopy is the fact that it is sensitive to the element’s chemical environment, allowing information to be obtained on the local structure of the analyzed element. EDS analysis is insensitive to the chemical environment. Detailed information about TEM characterization is given in the book by William and Carter [189]. TEM characterization as been used more recently for in-situ studies of materials in the nanoscale range [190, 191]. Using in-situ TEM characterization to obtain atom-resolved images of copper nanocrystals on different supports, Hansen and co-workers [190] found that Cu nanocrystals undergo dynamic reversible shape changes in response to changes in the gaseous environment. SEM is carried out by scanning an electron beam over the sample’s surface and detecting the yield of low energy electrons (secondary electrons) and high-energy electrons (backscattered electrons) according to the position of the primary beam. The secondary electrons, which are responsible for the topologic contrast, provide mainly information about the surface morphology. The backscattered electrons, which are responsible for the atomic number contrast (Z-contrast), carry information on the sample’s composition. Regarding this type of contrast, because the heavy elements (high Z value) have the ability to scatter the electrons more efficiently, an image composed of bright areas (consisting of high Z elements) and dark ones (consisting of low Z elements) is generated. A new generation of SEM has recently emerged as an important tool to characterize nanostructured materials. This state-of-the-art equipment, called a field emission gun (FEG)-SEM, has a FEG that provides the electron beam, and it uses in-lens or semi-in-lens secondary electron detectors to obtain images with a low acceleration voltage and a resolution as high as 1 nm. A STEM detector can be used in the FEG-SEM device, enabling one to obtain the transmitted dark and bright field images of thin specimens or nanoparticles, similar to images obtained with a dedicated STEM. Figure 10 shows images of SnO2 nanoparticles, with rather good bright and dark field images, which were taken with a FEG-SEM instrument, using a STEM detector. SEM can provide not only morphological but also chemical information about the sample; however, the spatial resolution is only about 1 m3 . This limitation has rendered the chemical characterization of nanostructured materials using SEM practically useless. The second characterization technique to be analyzed is X-ray diffraction (XRD). XRD is the most popular technique for structural characterization, providing information about the phases present in the material, as well as refined crystallographic parameters and morphological information. XRD consists of the elastic scattering of X-ray photons by

549

Figure 10. STEM images of SnO2 nanoparticles, which were taken with a FEG-SEM instrument, using a STEM detector. (a) Bright field image; (b) dark field image.

atoms in a periodic lattice. The scattered X-rays (monochromatic) that are in phases provide constructive interference. The lattice space (dhkl , or the distance between two lattice planes in a crystal, is described by the Bragg relation 2 dhkl sin  = n

(11)

where is the X-ray wavelength,  is the diffracted angle, and n is the integer called order of the reflection. A dhkl set is characteristic of a given compound. Powder XRD has been used extensively to characterize nanoparticles; however, due to the small particle size, broadening of the diffraction lines occurs at the usual X-ray wavelengths, rendering analyses more complex. These analyses are more difficult if structural parameters are required. In such cases, special X-ray surges like synchrotron radiation and special fit analyses are required to achieve a good structural characterization [192]. X-ray line broadening analysis provides a fast and usually reliable estimate of the particle size [153, 154, 183, 184, 193]. The particle size or, more precisely, the crystallite size (Dhkl ), can be calculated based on Scherer’s equation, Dhkl  = K / cos 

(12)

where K is a constant (0 9 ≤ K ≤ 1 0), and  is the corrected full width at half maximum of the diffraction peak. This method of determining the crystallite size takes into account only the X-ray line broadening promoted by the

Nanocrystals Assembled from the Bottom Up

550

Raman Intensity (counts/s)

0,005

a)

SnO 2 5% La

A1g

0,004

Bands associated to superficial disorder

Eg

0,003

0,002

0,001

0,000 400

500

600

700

800

900

-1

Raman shift (cm )

3,0

Raman Intensity (counts/s)

size effect. Other effects, such as the broadening induced by lattice strain, are not considered. However, considerable discrepancies can occur in metallic nanocrystalline systems [194], even in metal oxide nanoparticles [154]. In such situations, correction of the strain broadening is indispensable for a reliable characterization of the crystallite size. XRD refinement methods, such as the Rietveld method, can be used to correct the strain broadening [195]. Electron microscopy and XRD can provide good morphological, chemical, and structural characterization of nanocrystals; however, these techniques do not provide information about the disordered part of nanocrystals, such as their surfaces. An alternative technique to obtain information about structural disorder in nanocrystals, including surface information of nanocrystals, is X-ray absorption spectroscopy (XAS). This technique is based on the absorption of X-rays and the creation of photoelectrons that are scattered by nearby atoms in a structure. This technique provides information about local structures, such as distance and the number and type of neighbors of the absorbing atom, and can be used to characterize the bulk and surface of solid-state materials, including amorphous materials and catalysts [196, 197]. XAS techniques [X-ray absorption near-edge spectroscopy and extended X-ray absorption fine structure (EXAFS)] have been used to study the size dependence of structural disorder in semiconductors and metal oxide nanocrystals. The results of these techniques have demonstrated that this spectroscopic analysis is sensitive to the structure of the entire nanocrystal, including the surface [198, 199]. By EXAFS analyses of CdS nanoparticles (1.3–12 nm diameter), Rockenberger et al. [200] showed that the stabilization of nanoparticles influences the mean Cd–S distance. Thiol-capped nanoparticles display an expansion of their mean interatomic Cd–S distance, whereas polyphosphate-stabilized particles contract in terms of their CdS bulk. EXAFS has also proved to be highly sensitive in the identification of the surface segregation of foreign cations [201, 202]. Raman spectroscopy can also provide information about the overall nanocrystal structure. Raman spectroscopy is based on the inelastic scattering of photons, which lose energy by exciting vibration in the sample. This technique is very sensitive to the crystal’s symmetry and any change can cause modifications in the spectrum, such as shift of the line position, broadening of the line, and new lines. The crystal symmetry of the nanocrystal surface must present differences in relation to the symmetry of the nanocrystal core. Hence, the Raman spectrum of a nanostructured material must be different from the Raman spectrum of the same material with bulk characteristics. In fact, several reports have described the influence of particle size on the Raman spectrum [203–206]. Figure 11a shows Raman spectra of a SnO2 nanocrystal processed by the IPC process (particle size ∼9 nm) compared with a spectrum of a SnO2 single crystal (Fig. 11b). In addition to the classic modes of the rutilelike structure, the figure clearly shows bands associated with superficial disorder. A detailed discussion of the influence of particle size on the Raman spectrum of SnO2 is given in the literature [205]. In that work, Dieguez and co-workers proposed a model in which the additional band is due to a

A1g

b)

2,5

2,0

B2g

1,5

Eg

1,0

0,5 200

300

400

500

600

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800

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Raman Shift (cm )

Figure 11. Raman spectra of a SnO2 : (a) nanocrystal processed by the IPC process (particle size ∼9 nm); (b) SnO2 single crystal spectrum.

surface layer of SnO2 with a dissimilar symmetry. The thickness of this layer was calculated at ∼1.1 nm. Analyses of the Raman line can provide important information about lattice disorder. Such analyses can be performed using the spatial correlation model described by Parayanthal and Pollak [207]. Basically, this model describes the crystal’s quality by introducing a parameter called correlation length (L), which can be interpreted as the average size of the region of homogeneous materials. According to this model, the Raman line intensity [I] can be written as I =




1 0

exp −q2L2/4 d 3 q/  − q2 + 0 /22  (13)

where  is the frequency, q is the wave vector, 0 is the halfwidth of the Raman line, and q is the Raman phonon dispersion. Based on the spatial correlation model, Kosacki et al. [208] demonstrated that the Raman spectra of CeO2 and Y-doped ZrO2 thin film are influenced by defects attributed to grain size-controlled nonstoichiometry. Indeed, they proved that Raman spectroscopy could be an effective method to determine the concentration of oxygen vacancies in fluorite-structured oxides.

6. SUMMARY An analysis of the various synthesization routes described above leads to the conclusion that the development of new synthesization routes or the improvement of routes currently under study are necessary to achieve greater control over

Nanocrystals Assembled from the Bottom Up

the synthesis of nanocrystals, particularly of metal oxide nanocrystals. The advances achieved over the last year in expanding our understanding of the synthesis and control of metal nanocrystals have led to the development of nanoparticles with strictly controlled particle size and particle size distribution, and good control of particle shape. Part of this progress can be attributed to the application of concepts used in the synthesis of semiconductor nanocrystals, such as the thermal decomposition of organometallic compounds and the use of surfactants for the control of particle growth and shape. The same progress, however, has not been achieved in the synthesis of metal oxide nanocrystals, particularly of metal oxides composed of two or more cations. Part of the reason for this lack of progress is the fact that, during the process of hydrolysis and precipitation, a hydrated amorphous metal oxide phase is formed, requiring heat treatment or a hydrothermal process to promote crystallization of the desired phase. This crystallization step may lead to particle growth, particle shape modification, and particle agglomeration. The use of dopants and surface modifying agents during the synthesis of metal oxide nanoparticles may offer a good alternative to increase the thermal stability of nanocrystals, thus preventing particle growth. The use of nanocomposites to prevent the growth of nanocrystals, particularly in the case of materials for use at high temperature, appears to be a good strategy. This approach can be combined with the synergism between phases to design nanocomposite materials with superior performance. There is no doubt that considerable progress has been made in nanocrystal synthesis over the last few years. However, further studies are necessary to achieve improved control over particle size, particle shape, and particle size distribution, as well as to obtain nanoparticles with greater stability against particle growth at high temperatures.

GLOSSARY Nanocomposite Nanostructured material formed by two or more phases with nanometric scale (1–100 nm). Nanocrystal Crystalline particle with size in the 1–100 nm range. Particle growth Physical–chemical process promoted by the high superficial energy of the particles. Self-assembled Controlled (ordered) particle deposition governed by particle–particle and particle–substrate interaction. Sol–gel Chemical synthesis process in which a sol (often defined as a suspension of small particles or molecules in a liquid phase) undergoes a transition to a gel (a threedimensional network structure spreading throughout the liquid medium).

ACKNOWLEDGMENTS The author thanks many colleagues for stimulating discussions and collaboration, especially Elson Longo, J. A. Varela, Carlos A. Paskocimas, Emersom R. Camargo, Fenelon M. Pontes, N. L. V. Carreño, and Adeilton

551 P. Maciel. The following Brazilian agencies have provided support for my work: FAPESP, CNPq, and CAPES.

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Nanocrystals Assembled from the Bottom Up 194. J. Weissmüller, “Characterization by Scattering Techniques and EXAFS in Nanomaterials: Synthesis, Properties and Applications” (A. S. Edelstein and R. C. Cammarata, Eds.), p. 219. IOP, Bristol, 1996. 195. C. O. Paiva-Santos, H. Gouveia, W. C. Las, and J. A. Varela, Mater. Struct. 2, 111 (1999). 196. R. F. Pettifer, “X-ray absorption studies of glass structure, in Glasses and Glass-Ceramics” (M. H. Lewis, Ed.), p. 41. Chapman and Hall, London, 1989. 197. J. W. Niemantsverdriet, “Spectroscopy in Catalysis, An Introduction,” p. 137. VCH, Weinhein, 1993. 198. K. S. Hamad, R. Roth, J. Rockenberger, T. van Buuren, and A. P. Alivisatos, Phys. Rev. Lett. 83, 3474 (1999). 199. T. Shido and R. Prins, J. Phys. Chem. B 102, 8426 (1998). 200. J. Rockenberger, L. Tröger, A. Kornowski, T. Vossmeyer, A. Eychmüller, J. Feldhaus, and H. Weller, J. Phys. Chem. B 101, 2691 (1997). 201. C. V. Santilli, S. H. Pulcinelli, G. E. S. Brito, and V. Briois, J. Phys. Chem. B 103, 2660 (1999). 202. C. M. Wang, G. S. Cargill, H. M. Chan, and M. P. Harmer, J. Am. Ceram. Soc. 85, 2492 (2002). 203. M. Yoshikawa, Y. Mori, H. Obata, M. Maegawa, G. Katagiri, H. Ishida, and A. Ishitani, Appl. Phys. Lett. 67, 694 (1995). 204. A. Dieguez, A. Romano-Rodriguez, J. R. Morante, N. Barsan, U. Weimar, and W. Göpel, Appl. Phys. Lett. 71, 1957 (1997). 205. A. Dieguez, A. Romano-Rodriguez, A. Vila, and J. R. Morante, J. Appl. Phys. 90, 1550 (2001). 206. J.-M. Jehng and I. E. Wachs, Chem. Mater. 3, 100 (1991). 207. P. Parayanthal and F. H. Pollak, Phys. Rev. Lett. 52, 1822 (1984). 208. I. Kosacki, V. Petrovsky, and H. U. Anderson, J. Am. Ceram. Soc. 85, 2646 (2002).

Encyclopedia of Nanoscience and Nanotechnology

www.aspbs.com/enn

Nanocrystals from Solutions and Gels Marc Henry Université Louis Pasteur, Institut Le Bel, Strasbourg, France

CONTENTS 1. Introduction 2. Nucleation 3. Crystalline Growth 4. Limited and Secondary Growth 5. Aggregation 6. Conclusion Glossary References

1. INTRODUCTION The interest in nanocrystalline materials comes from the occurrence of a large interface with a surrounding liquid or gaseous medium. A very elementary calculation is helpful here to grasp this importance of size. Any solid matter may be characterized by its molar volume Mv (cm3 mol−1
and its molar surface Ms (cm2 mol−1
. For a sphere of radius R, the number of bulk atoms Nv should be such that Nv × Mv = NA 4/3
R3 , whereas the number of surface atoms would be given by Ns × Ms = NA × 4R2 (with NA the Avogadro number). Consequently, we may define the atomic surface to volume ratio f = Ns /Nv = 3/R
× Mv /Ms
. As typical values for condensed solid matter would be Mv ∼ 20 cm3 mol−1 and Ms ∼ 6 × 108 cm2 mol−1 , it follows the very simple rule of thumb that f ∼ 1/R (nm). This analysis shows that for R = 1 nm there could exist no core atoms (the nanocrystal is a pure surface as f ∼ 100%), while for R = 1000 nm only one atom over 1000 remains accessible. The nanometer range 2–10 nm is thus particularly interesting as in this domain we have enough atoms (at least 50%) into the bulk to insure the existence of some useful mechanical, electrical, optical, magnetic, or chemical property. On the other hand we also have enough atoms (at most 50%) exposed to the outer space, creating an active interface able to deeply modulate the bulk properties. In fact, one may even hope for the appearance of a new property. A very nice example is provided by a quite old but very instructive paper ISBN: 1-58883-062-4/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

by Gortner concerning the state of water in colloidal and living systems [1]. The author was interested in the difference in mass between a fresh opaque jellyfish (weighting 500 g) and the dried transparent animal (weighting 0.45 g). As the volatile matter at room temperature is water, the conclusion of this simple experience is that the jellyfish was made of 99.9 wt% of water and only 0.1 wt% of solid matter. This solid matter includes all proteins, lipids, carbohydrates, and mineral salts needed to get a living animal. However, just take a glass containing 499.55 g of water and add 0.45 g of a well-dosed amount of organic and inorganic matter. You do not get a living animal, but just an inert more or less stable colloidal solution. Life is here really a new property not shared by a glass of water nor by a piece of sugar nor by a drop of oil nor by a chain of amino acids nor by sodium chloride crystals. The key to life apparition in this system is to create a nanosized solid/water interface, where the bulk, the surface, and the solution interact, leading to a system qualitatively different from the sum of its constituents. This simple example shows that making nanometric sized objects may be quite rewarding. However, in order to remain quite concise we will limit ourselves to the possible mechanisms allowing growing nanocrystalline dispersions and to their stability toward aging and/or aggregation processes. Even if several well-documented reviews already exist covering all these “well-known” aspects, it appears that none take into explicit account the chemical dimension of the problem. This complete absence of chemistry from nucleation, growth, and aggregation equations has the consequence that it is very difficult to establish a causal link between the final equilibrium size of the crystals and the growth conditions. In fact every crystal maker knows that playing with concentration, temperature, pressure, or ionic strength is not enough to fully control crystalline growth. The key to the success of controlled crystal growing lies in the wise use of chemical additives or suitable complexing reagents. It is the aim of this chapter to fully review an often quite old literature and bring to light all the hidden points where chemistry has a role to play. For each important step (nucleation, growth, aging, aggregation) we will put down for the first time a new analytical expression, linking the equilibrium final sizes to growth conditions. With these equations in hand crystal

Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 6: Pages (555–586)

556 scientists may then understand, on a quantitative basis, why the change in such physical or chemical parameter alters the final equilibrium size.

2. NUCLEATION 2.1. Physicochemical Parameters Nanocrystal formation from solutions and gels is ruled by several factors gathered in Figure 1 [2–4]. From the classical nucleation theory (CNT) viewpoint, five parameters are needed to fully characterize the state of the solution. These are the concentration of solute species c (mol l−1
, assumed to bear an electrical charge eq and moving with diffusion coefficient D, the dielectric constant of the solvent , and the temperature T . Recall that for typical molecular solute species we should have a constant value D ∼ 10−5 cm2 s−1 . For the growing solid phase, three parameters may be identified: its solubility cs (mol l−1
, its density  (g cm−3
, or molecular volume v = M/NA (with M molar mass of one structural motif and NA the Avogadro number). Notice that another useful way to express the molecular volume is to think to the characteristic molecular size of the structural repeating unit: d ∼ v1/3 . For typical binary compounds this value is roughly constant and may be taken approximately equal to v ∼ d 3 ∼ 10−285 m3 .

2.2. Interfacial Energy The interfacial energy  (J m−2
is finally the last critical parameter that remains to be introduced. Its physical meaning is perfectly clear if one refers to the top left diagram of Figure 1. In a growing crystal, two kinds of atoms may be identified. At the bottom, buried inside the core of crystal

Nanocrystals from Solutions and Gels

are atoms that interact with other similar atoms. The net force acting on these atoms is thus just zero. At the top, exposed to the surface are atoms displaying a clear force unbalance. On one side they are attracted by atoms buried within the bulk of the crystal, but on the other side they are involved in usually much weaker interactions (van der Waals or hydrogen bonds) with solvent molecules. In fact, the highest asymmetric situation is encountered when there is no solvent at all (i.e., crystals are placed under vacuum), leading to a maximum interfacial or surface energy. Consequently, in the presence of a given solvent, this interfacial energy may be strongly reduced. The stronger the interaction with the solvent, the lower the interfacial energy should be. This is just what is expressed by the Gibbs equation: d = − × d
P T

(1)

Here,  stands for the density in adsorption sites (sites nm−2
and refers to the electrochemical potential of adsorbed species. Table 1 gives some typical values of interfacial energies for aqueous solutions [3, 5–8]. This shows that expected values for this parameter should be in the range 50 ≤  ≤ 400 mJ m−2 . Let us notice that it has been very recently shown that vacuum surface energies may also be derived directly from the knowledge of the crystal structure [9]. In this last study, it was also proved that the surface energy concept remains valid even at a molecular scale. This last observation is important in a relation with the justified criticism that may be lodged against CNT that assumes constant surface tension for nucleation [10]. The first principles approach in [9] clearly shows that this criticism is not justified. For each crystal, one may define a characteristic vacuum surface energy averaged over a sphere whose value may be fixed (for most simple structures of course) by the relative spatial disposition of less than five atoms!!! Nevertheless, the most serious criticism remains as nucleation is an irreversible process that just cannot be handled by equilibrium thermodynamics. A more correct approach for this review would have then been to use entropy-based nucleation theory [10] instead of CNT. This was, however, not possible as analytical solutions exists only for liquid–vapor interfaces and not for solid–liquid or solid– solid interfaces, the subject of this chapter.

2.3. Nucleation Rate J From a macroscopic point of view, the most important quantity governing the final size and number of nanocrystals is the nucleation rate J (number of nuclei formed per unit volume and per unit time). A detailed analysis of the nucleation phenomenon [6] leads to the following expression for this nucleation rate:
 GN D (2) J = 5/3 × exp − v kT

Figure 1. A graphical overview of some factors ruling nucleation, growth, and spinodal decomposition processes. See text for details and explanations.

In this equation, k is the Boltzmann constant (k ∼ 138 × 10−23 J K−1 ) and GN is the energetic barrier to nucleation. The value of the pre-exponential factor J0 = J GN = 0
= D/v5/3 ∼ 10325 cm−3 s−1 has a clear physical interpretation. Accordingly, in the absence of any energetic barrier

Nanocrystals from Solutions and Gels

557

Table 1. Interfacial energies for water/solute interfaces derived from nucleation studies in aqueous solutions.  (mJ m−2 ) Halogens KCl KBr KI NH4 Cl NH4 Br NH4 I AgCl AgBr MgF2 CaF2 TlCl TlBr TlIO3

30 24 17 27 19 8 90 65 300 280 92 92 87

S, Se BaSO4 SrSO4 CaSO4 · 2H2 O PbSO4 Ag2 SO4 Na2 S2 O3 · 5H2 O BaSeO4 PbSeO4 TlSCN

135 85 117 100 96 16 88 71 65

Carbon BaCO3 PbCO3 CH3 COOAg SrC2 O4 · H2 O PbC2 O4

115 125 113 76 145

Oxides SiO2 TiO2 Mg(OH)2 Ca(OH)2

45 270 123 66

Cr, Mo, W PbCrO4 BaCrO4 Tl2 CrO4 Ag2 CrO4 SrMoO4 BaMoO4 CaMoO4 SrWO4 CaWO4 BaWO4

170 120 108 107 100 103 118 62 151 94

for incorporation into a crystalline embryo, the limiting step should be the diffusion of the solute species toward the embryo/solution interface. Consequently, the frequency of incorporation inc should scale like D/d 2 . This is because the solute species have just to diffuse over an area of size d × d to be immediately incorporated (recall that v ∼ d 3 and that GN ∼ 0). As the number of structural repeating units per unit volume is just 1/v ∼ 1/d 3 , the nucleation rate should scale like J0 ∼ inc /v ∼ D/d 5 ∼ D/v5/3 , in good agreement with Eq. (2). Obviously, J0 ∼ 10325 cm−3 s−1 is an incredibly high value and in most cases GN > 0, leading to a strongly reduced value. In fact, from a practical point of view,

nucleation rates can be experimentally measured only when 1 ≤ J ≤ 1015 cm−3 s−1 . Consequently, at room temperature, the nucleation barrier GN should be at least 80 kJ mol−1 and at most 170 kJ mol−1 .

2.4. Thermodynamic Barrier
G∗ Two terms are expected to contribute to the nucleation barrier. The first one G∗ has a thermodynamic origin. It corresponds to the energetic competition existing between reduction of the sursaturation ratio S = c/cs when S > 1 and the necessary increase in area A of the growing solid phase (energetic cost  × A). Identifying activities a to concentrations c ( = kT × Ln a ∼ kT × Ln c), one may write for the transfer of n moles of solute species from the solution to the crystal GnS → nC
= n ×  C − S
+  × A ≈  × A − nkT × ln S

(3)

The variation of G with n is visualized at the top right corner of Figure 1. If C ∼ S (i.e., c ∼ cs or S ∼ 1), the dominant contribution comes from the positive interfacial term (first monotonic curve in Figure 1). On the other hand, when S ≫ 1, the negative chemical contribution insures that a maximum should be reached for a given number n∗ of solute precursors (second curve in Figure 1). According to this analysis, only embryos such that n > n∗ are able to reach a macroscopic size as G < 0 for the n → n + 1
addition (growth). For other embryos such as n < n∗ the n → n + 1
association is characterized by G > 0, meaning that such species should dissolve back into the solution. Embryos such that n = n∗ are called critical nuclei, and the corresponding positive G∗ value defines the first thermodynamic contribution to the nucleation barrier GN . The magnitude of G∗ may be readily derived under the assumption that embryos undergo no change in shape (only the mean size is changing among similar bodies) during nucleation. Consequently, the ratio K = A/V 2/3 should remain invariant, and if the total volume of a given embryo is V ∼ n × v then the associated area A may be written A = K × n × v
2/3 . Inserting this value into Eq. (3) and looking for a maximum by setting dG
/dn = 0 leads to the following thermodynamic barrier G∗ =

=

n∗ × kT Ln S 2 A/3
3 V /2
2

n∗ = 2

 3 v2 kT Ln S
3 (4)

Table 2 gives the values of the dimensionless shape factor for some ideal geometries. As evidenced in Eq. (4) the only way to get G∗ = 0 is to have a vanishing interfacial energy. Such a condition ( ∼ 0) is easily met in polymer chemistry or in metallic alloys, and in this case phase segregation cannot lead to the sharp boundaries characterizing systems with  ≫ 0 (bottom left picture in Figure 1). Instead, for this spinodal decomposition scheme, deeply interconnected patterns

Nanocrystals from Solutions and Gels

558 Table 2. Dimensionless shape factors, for some common regular 3D geometries. Shape

Area A

Sphere

4a2

Volume V

= 4A3 /27V 2 16o¨ = 167552 3 √ 16 3 = 202162 4  √ 80 o¨ 5 = 222012 4

Cube

6a2

4 3 a 3 5a3 2 6 √ a3 o¨ 4 5 2 √ 2 a3 3 a3

Parallelepiped 4a × 2a × a

28a2

8a3

Regular icosahedron Regular dodecahedron Regular octahedron

√ 5a2 3 √ 15a2 o¨ 3 √ 5 √ 2a2 3

√

2 12

Regular tetrahedron

√ a2 3

Rod 10a × a × a

42a2

10a3

Plate 10a × 10a × a

240a2

100a3

a3

√ 16 3 = 277128 8 × 4 = 32
3 7 = 508148 4× 3 √ 32 3 = 554256 143 = 10976 25 5 4 = 2048 5

Note: Shapes are characterized by one size a and classified by increasing value. Here  stands for the golden √ ratio defined as the positive root of the 2 x = x + 1 equation, viz.  = 1 + 5
/2.

with rather diffuse boundaries are typically observed (bottom right picture in Figure 1).

2.5. Kinetic Barrier
G′ As indicated, the thermodynamic barrier G∗ is not the only contribution to the nucleation barrier GN . Another kinetic barrier G′ associated with chemical reactions occurring during jumps across the nucleus–solution interface should also be considered. Obviously, for a solid metallic alloy nucleating from a melt one may expect G′ ∼ 0 as the system undergoes only a disorder → order phase transition on going from the liquid to the solid state. During this transition local metallic chemical bonds between atoms are not fundamentally changed, explaining the low kinetic cost G′ ∼ 0. Such would not, however, be the case in other systems.

2.5.1. Quartz versus Glass Consider for instance the growth of quartz crystals from a silica melt. Besides the thermodynamic barrier associated with the quartz/fused silica interface and difference in chemical potentials, one has to take into account the fact that the local structure of both phases is very different. In the quartz crystal, SiO4 tetrahedra are strongly engaged into spiral chains, whereas in the melt small oligomeric species (which may be chains, cycles, or cages) are encountered. In order to be able to jump across the nucleus/liquid interface and fit inside the crystalline network, oligomeric species must first be reduced to monomeric SiO4 tetrahedra. This means that rather strong Si–O–Si bonds have to be broken, and that a corresponding activation energy G′ > 0 has to be provided before nucleation and growth of quartz crystals can occur.

Let us remark that this activation energy G′ has absolutely nothing to do with thermodynamics as almost the same Si–O–Si bonds are found before (oligomeric species) and after nucleation (spiral chains). This term is a true kinetic barrier inevitably associated with any kind of reconstructive transformation [11]. Accordingly, glass formation is intimately linked to the existence of a large kinetic barrier G′ which renders the cost of nucleation quite prohibitive just because GN = G∗ + G′ . If G∗ were the only contribution to nucleation, glasses would never be formed and should not exist.

2.5.2. Sodium Chloride: A Case Study The same kind of kinetic barrier G′ is expected when crystallization occurs from solutions or gels. First consider the simplest case: nucleation of a crystalline salt (NaCl for instance) from an aqueous solution. In solution we find ionic species such as [Na(OH2
x ]+ and [Cl(H2 O)x ]− . The precise value of the coordination number x does not matter here as it depends on the molar fraction of sodium chloride. Consequently, variation in x is well reflected by variation of the chemical potential S and should influence only the thermodynamic term G∗ . Our point of interest is rather how such solute species should be transformed in order to allow them to jump across the NaCl/water interface for further incorporation into the NaCl crystalline network. As this crystal is built from a regular stacking of naked Na+ and Cl− ions, it is clear that ion pairing should be the very first step: [Na(OH2
x ]+ + [Cl(H2 O)x ]− → [NaCl(OH2
2x ]. Having formed a neutral species, water removal may then occur: [NaCl(OH2
2x  → [NaCl] + 2x H2 O, and only after that incorporation into the network becomes possible. The origin of the kinetic barrier G′ lies here in the lability of water molecules around cations and anions.

2.5.3. Aquo Cations For the NaCl case, it is obvious that the lability around Na+ or Cl− ions is rather high (Fig. 2), meaning that G′ ∼ 0. But this clearly would not be the case for more charged cations, as it is well known that the kinetics of water splitting, [M(OH2
N ]z+ → [M(OH2
N −1 ]z+ + H2 O, is considerably slowed down if z increases or if the ionic radius of the metallic element decreases [12]. Also, for some transition metal elements such as Cr3+ , crystal field stabilization energies may be so high (leading to G′ ≫ 0) that nucleation of the corresponding hydroxide Cr(OH)3 cannot occur anymore. In such a case, gelation (the equivalent for solutions of glass formation from melts) instead of precipitation is usually observed. Figure 2 shows how the kinetic constant kw characterizing the removal of aquo ligand from the metal coordination sphere varies for usual ionic species. It was found that, at room temperature, it lies above 10−6 s−1 (V2+ or Cr3+ ions) and below 1010 s−1 (Ba2+ or Cs+ cations) [12, 13]. Now, if h stands for the Planck constant, the activated complex kinetic theory says that the rate constant may be written kw = kT /h
× exp−G0 /kT ) or for T = 300 K (G0 /kJ mol−1
= 73 − 571 × logkw /s−1
. Consequently, assuming that G′ ∼ G0 , the kinetic barrier for nucleation of a metallic salt or hydroxide should be in the range

Nanocrystals from Solutions and Gels

559 2.5.5. Metal Alkoxides The same kinetic barrier is encountered when the nanocrystal nucleates after decomposition of metallo-organic complexes in nonaqueous media. Figure 2 shows that, at least in the case of metallic alkoxides precursors, a considerable rearrangement of chemical bonds should also occur. As before, with hydrolysis of the metal alkoxide requiring a proton transfer, the kinetics depends strongly on the amount of acid or base added with the water. As shown in Table 3 for silicon alkoxides [17–22], the height of the kinetic barrier G′ is at least 90 kJ mol−1 explaining the difficulty to nucleate quartz directly from the solution at room temperature. Unfortunately, there is a paucity of kinetic data for other metallic cations. To the best of our knowledge, only a global kinetic constant k ∼ 30 s−1 is available concerning the nucleation of titanium or aluminum oxides from Ti(OEt)4 and Al(OBus
3 respectively [23]. This would mean that octahedral species may have significantly lower kinetic barriers (G′ ∼ 65 kJ mol−1
relative to tetrahedral silicate species.

2.6. Applications Figure 2. Chemical origin of the kinetic barrier G′ for oxide, hydroxide, or metallic salt nulceation. Top left: type of ligand expected around a metallic cation Mz+ in aqueous solutions as a function of pH. Top right: chemical bonds rearragements expected for oxy ions or metal alkoxides in the case of oxide nucleation. Bottom: techniques used for measuring lability of water molecules around metallic cations Mz+ (z ≤ 3, i.e., hydroxide or metallic salt nucleation).

15 < G′ < 110 kJ mol−1 , depending on the electronic configuration, ionic radius, or total charge of the metallic cation.

2.5.4. Oxo Anions Obviously this picture can be valid only for metallic cations having a low formal oxidation state (typically z ≤ 3) allowing them to keep the aquo ligand within their coordination sphere. As shown in Figure 2, cations displaying higher formal oxidation states z are on the contrary extensively hydrolyzed in aqueous solutions. These cations should then lead to oxide rather hydroxide precipitation [14]. Silicon (z = +4) is a good example of this behavior, as it is found under low pH conditions under the silanol form Si(OH)4 . As this form does not display any aquo ligand in its coordination sphere, a considerable rearrangement of chemical bonds is necessary (Fig. 2) in order to incorporate it in a network based on corner-sharing SiO4 tetrahedra (Si– O–Si bridges). However, as a proton transfer is needed in the transition state to form a good leaving group (water), the kinetics of condensation is expected to depend strongly on the solution pH. Accordingly, experiments [15] shows that the kinetic constants for silanol condensation vary from 1018 M−2 s−1 at pH ∼ 7 up to 1034 M−2 s−1 at pH ∼ 10. Proceeding as before, this corresponds to a kinetic barrier 50 kJ mol−1 < G′ < 70 kJ mol−1 . Another possibility of estimating this kinetic barrier G′ for nucleation from aqua and oxo ions is to use 18 O exchange studies [16] nH2 O∗ + MOH2
n z+ → nH2 O + M∗ OH2
n z+ nH2 O∗ + XOn z− → nH2 O + X∗ On z−

After this rapid outline of the classical nucleation theory, we may take time to see some typical examples, the relative orders of magnitude of the two kinetic barriers G∗ and G′ .

2.6.1. Ionic Crystals Consider first the case of a simple crystalline salt such as KCl for instance (M = 7455 g mol−1 ,  = 1984 g cm−3 , i.e., v = 10−282 m3 ). Referring to Figure 2, the characteristic residence time of water molecules around the potassium cation is  < 10−10 s. Consequently we may suppose that G′ ≤ 16 kJ mol−1 . A look at Table 1 shows that for the KCl/H2 O interface we have  ∼ 30 mJ m−2 . Consequently, at T = 300 K (kT = 41 × 10−21 J, or RT = 248 kJ mol−1
, we may write n∗ = 025

log S
3

and G∗ = 0714

kJ mol−1 log S
2 (5)

Owing to its cubic structure one may further assume a cube-shaped nucleus ( = 32); that is, n∗ = 8/log S
3 and Table 3. Measured rate constants and associated kinetic barrier G′ for the chemical reaction (RO)3 Si–OX + HOY → (RO)3 SiOY + HOX. XR


Y

Rate constant

pH

G′ kJ mol−1


Ref.

CH3 C2 H5 C4 H9 C6 H13 H(Me) H(Me) CH3 H(Me) CH3 C2 H5 H(Et)

H H H H Si Si Si Si2 Si2 H Si

10 M s 10−13 M−1 s−1 H+ −1 10−17 M−1 s−1 H+ −1 10−21 M−1 s−1 H+ −1 10−4 M−1 s−1 10−21 M−1 s−1 10−48 M−1 s−1 10−47 M−1 s−1 10−49 M−1 s−1 10−42 M−1 s−1 10−53 M−1 s−1

5.5 7–2 7–2 7–2

104 120–92 123–94 125–96 96 85 100 100 101 97 103

[17] [18] [19] [19] [20] [17] [20] [21] [21] [22] [22]

−55

−1 −1

5.5 2.8 2.8 3.1 3.1

Note: Y = Si2 refers to the (RO)3 SiOSi(OH)(OR)2 dimer.

Nanocrystals from Solutions and Gels

560 G∗ = 228 kJ mol−1
/(log S
2 . Now for S = 2 (two times the solubility of KCl, cs ∼ 347 wt% at 20 C), it transpires that about 300 KCl pairs have to meet together, forming a sphere of radius r ∗ ∼ n∗ v
1/3 ∼ 26 Å, in order to nucleate the KCl network. The very low probability of such an event is easily understood by looking at the nucleation rate J . With G∗ = 252 kJ mol−1 and making the conservative choice G′ = 16 kJ mol−1 , it comes that GN = 268 kJ mol−1 leading to J = 1032 × exp−268/248
∼ 10−15 nuclei per cm3 and per second. Another statement of this matter of fact is to say that in order to see one such nucleus appear in 1 cm3 of solution, one has to wait about 32 Myr!!! Let us now see what would happen by just doubling the sursaturation ratio S. Now, with S = 4 the same equations tell us that n∗ = 37 (critical nucleus with radius ∼13 Å). If the thermodynamic barrier is still dominant, it has nevertheless been reduced down to G∗ = 63 kJ mol−1 . The new barrier to nucleation is thus GN = 79 kJ mol−1 leading to J = 1032 × exp−79/248
∼ 1018 cm−3 s−1 . Consequently, instead of waiting a virtual eternity to see just one nanocrystal, everything is finished (i.e., c ∼ cs corresponding to about 1022 nanocrystals with radius 13 Å) in about 8400 s or less than 3 hours.

2.6.2. Critical Sursaturation Ratio S∗ This example clearly demonstrates that nucleation is basically a critical phenomenon, as a mere doubling of one parameter S leads to a variation in J of about 33 orders of magnitude. These considerations are shown graphically at the bottom of Figure 1 (two middle diagrams). Below a critical value S ∗ , nothing can happen, while slightly just above this threshold, the nucleation rate displays a very fast divergence (middle left diagram). The main consequence of this burst of nuclei is that the sursaturation is strongly and rapidly reduced and may instantaneously become smaller than S ∗ (middle right diagram). This condition is usually met in moderately dilute solutions leading to just one burst of nuclei. Further removal of the remaining sursaturation would only be removed by growth processes (vide infra). This is the classical picture for the formation of monodisperse nanocrystals under homogeneous nucleation conditions [24, 25]. On the contrary, for strongly concentrated solutions, the first birth of nuclei is not able to reduce the sursaturation ratio below S ∗ , meaning that J > 0 during all the precipitation process. Under such circumstances, a polydispersed system is usually obtained and aggregation phenomena may become competitive for determining the final particle size or shape. From a practical viewpoint, the critical sursaturation ratio S ∗ may be defined as the value of S leading to J = 1 or log J = 0 [26] Ln S = ∗



kT
3

 3 v2 LnDv−5/3 gN
/1

(6)

2.6.3. Silica This example also illustrates the crucial role played by the kinetic barrier G′ . It is just because the thermodynamic term is dominant and the kinetic one negligible that it is so difficult to keep control over the nucleation

rate. To see that, let us consider the nucleation of silica SiO2 · 2H2 O (M = 7808 g mol−1 ,  = 22 g cm−3 , i.e., v = 10−282 m3 and  ∼ 45 mJ m−2 ) [8, 27]. For nuclei displaying spherical shapes, we may write n∗ = 14/log S
3 and G∗ = (40 kJ mol−1
/(log S
2 . Now, let us choose G′ ∼ 100 kJ mol−1 as a typical value characterizing the interfacial oxolation reaction (see Table 3): Si–OH + HO– Si → Si–O–Si + H2 O. This choice then leads to GN ∼ 540 kJ mol−1 for S = 2 and GN ∼ 210 kJ mol−1 for S = 4. Converting these values into nucleation rates according to J cm−3 s−1
= 1032 × exp−GN (kJ mol−1 )/2.48] leads to J ∼ 3 × 10−63 cm−3 s−1 (S = 2) and for S = 4, to only J ∼ 2 × 10−5 cm−3 s−1 . Consequently, doubling the sursaturation ratio as before has here no practical consequences, as the nucleation rate remains quite negligible (about 1 nucleus per cm3 after one day). Notice that even for S = 10 (10 times the solubility of amorphous silica, or c[Si(OH)4 ] ∼ 10−2 M) the nucleation rate is only J ∼ 3 × 107 cm−3 s−1 , a perfectly measurable value. The presence of a reasonable kinetic barrier then provides an efficient healing mechanism against the otherwise pathological behavior of the nucleation rate versus sursaturation variation. For oxide or hydroxide precipitation, the kinetic term is provided by the inertness of the metallic cation toward water substitution. It is thus possible to control the nucleation process under dilute conditions through thermal hydrolysis for instance [28].

2.6.4. Metallic Salts For metallic salts (such as carbonates, sulfates, or phosphates for instance) the kinetic barrier should be provided by the slow decomposition of a suitable preformed metallic complex [29]. Only in this case do we get a chance to keep some control over the nucleation process. Among the numerous chemical methods available to control the nucleation stage for sparingly soluble substances, we may cite [29–34]: (i) Variation of pH induced by temperature elevation (thermal solvolysis) is a method well suited for acidic media. In order to generate basic conditions a suitable organic reagent able to decompose into ammonia (urea, hexamethylene tetramine) upon heating should be added. (ii) Some anions such as [CO3 ]2− , [C2 O4 ]2− , [SO4 ]2− , [PO4 ]3− or S2− may also be generated in-situ after decomposition of various esters or amides. (iii) Metallic cations may be masked by formation of a suitable complex that may be carefully destroyed through pH changes or through exchange with another complex. (iv) The use of mixed solvents with one volatile component is another useful strategy. Upon aging or heating the volatile species will be evaporated inducing controlled precipitation. (v) For transition metals displaying several oxidation states, one may add a reducing reagent for highvalency forms or an oxidizing one for low-valency forms. (vi) Finally, if the temperature of the medium cannot be changed, the possibility remains to use a light sensitive molecule that should release one of the

Nanocrystals from Solutions and Gels

561

nucleating species upon irradiation with ultravioletvisible light or even -rays.

2.7. Heterogeneous Nucleation It is a well known experimental fact that nucleation from a vapor, melt, or solution is affected considerably by traces of impurities in the system. Indeed, some authors even say that true examples of homogeneous nucleation in the condensed state should be indeed very rare [26]. One may then wonder about the practical utility of this treatment. In fact, it has been shown [35] that if R is the radius of the foreign nucleating particle and if  stands for the contact angle with the foreign surface, then G∗ (hetero) = G∗ (homo) × cos  R/r ∗
with  ∼ 1 when R < 10 nm or when  = 180 . Above 100 nm  becomes independent of R (with  < 1) leading to [26]
 2−3cos +cos3  R → ⇒ G∗H = G∗ × 4 r∗ =

 2v sin kT lnS 2

(7)

The important point is that due to the existence of a kinetic barrier G′ , homogeneous nucleation is already governed by a sticking probability gN = exp−G′ /kT
J ∼ Dv−5/3 gN × exp−G∗ /kT


various mechanisms of these competing processes. Kinetically speaking, the dominant process just after nucleation has occurred should be crystal growth. Accordingly, Ostwald ripening is ruled by the Ostwald–Freundlich equation for two spheres with radii (a1 a2
characterized by their solubility (c1 and c2 respectively) [36] 
c 1 1 kT × ln 1 = 2v − (9) c2 a1 a2 It is then expected to become important only when a2 ≫ a1 in order to have c1 ≫ c2 (disappearance of small crystals and growth of larger ones). On the other hand, aggregation implies that nuclei have to move through diffusion in order to meet together. According to the Einstein equation D = kT /6a
, D should be, for a given solution viscosity , smaller for a nuclei displaying a size a much larger than that of active solute species for crystal growth. In the following, we consider a solution containing N nanocrystals per unit volume, all built from incorporation of nt
solute species. As n is changing with time, this means that some characteristic linear size rt
increases with time according to a given growth law drt
/dt = f c r
. Writing the volume V of each nanocrystal as V =  × r 3 , where  is a shape factor ( = 4/3 for spheres,  = 8 for cubes, etc.) means that nt
=  × rt
3 /v. According to literature [3, 5], four main mechanisms may be recognized for crystalline growth (see Fig. 1).

(8)

Now as we know that 0 ≤  ≤ 1 we may rewrite (7) as G∗ (hetero) = G∗ (homo) − Ecos  R/r ∗ ), with E the energetic correction that should be applied and such that E = 0 if R = 0 or  = 180 . As far as the nucleation rate is concerned, we then just have to define a modified sticking probability gH = expE − G′
/kT showing that only the pre-exponential term is affected. These two terms gN and gH could then help to understand the considerable spreading of the measured kinetic constant J0 = J G∗ = 0
observed in literature (10 ≤ J0 ≤ 1032 cm−3 s−1
[26]. Obviously, this spreading is no more surprising in view of the earlier analysis but just reflects the importance of the competition between the kinetic barrier G′ and the heterogeneous activation E. For this chapeter, we will still use (8) as the correct expression for the nucleation rate. However, the gN term should be interpreted as a nucleation probability whose value depends on at least three physicochemical parameters: G′ , cos , and R. With this new interpretation of the kinetic constant J0 , the exact nature of the nucleating event (either homogeneous or heterogeneous) becomes immaterial as soon as gN reflects the exact physicochemical state of the solution.

3. CRYSTALLINE GROWTH 3.1. Competitive Growth Ideally, it is desirable that the nucleation stage should be the whole story of nanocrystal formation from solutions and gels. From a practical point of view, one has then to ensure that other stages such as growth, Ostwald ripening, or aggregation should be avoided. In the following, we will try to understand how this should be possible by studying the

3.2. Diffusion Controlled Growth In this first mechanism, each partner is characterized by a linear size [rm for solute species and rt
for nanocrystals] and a diffusion coefficient (D for solute species and Dr for nanocrystals). If the solute species can be incorporated into the crystalline network immediately after sticking to a crystal, the limiting step should be diffusion of solute species toward the solid/liquid interface.

3.2.1. Growth Law Let d be the solid angle spanning the direction in which a sticking event has been observed. The rate for mass increase of the nanocrystals may be written d 2 n/dt d = k × c − cs
with k a kinetic constant which may be approximated by k ∼ Dr + D
r + rm
. As Dr ≪ D and r ≫ rm , it comes k ∼ D × r, or after integration over all the possible sticking directions: dn/dt = 4Dc − cs
r. But as nt
=  × r 3 /v
, we should also have dn/dt = 3 × r 2 /v
× dr/dt
. The final growth law for pure diffusion may thus be written

  dr 4 4 Dvc − cs
dr 2 = ⇐⇒ = Dvc − cs
dt 3 r dt 3 (10) An interesting point is that irrespective of the original size r0 at nucleation time (t = 0) and provided that c ∼ c0 , then the square of the radius of all particles increases at the same rate [37]. Consequently, calling the absolute width of the distribution r for radius r and r0 for radius r0 , we have r × r ∼ r0 × r0 . This means that the absolute width of the distribution becomes narrower with time (r ∼ r0 /r × r0 ) while the relative width will decrease even faster (r/r ∼ r0 /r2 × r0 /r0 
.

Nanocrystals from Solutions and Gels

562 3.2.2. Chronomals From a practical point of view, one way to decide if such a rate law applies is to measure how the concentration in solute species ct
changes with time. Knowing ct
and the initial concentration c0 , one may write for spherical shapes  = 4/3
ct
= c0 − N × 4r 3 /3v
and compute the following quantity xD =

c0 − ct c0 − c s

⇐⇒

√ r = re 3 xD

(11)

Here re is the equilibrium size of the nanocrystals given by cs = c0 − N × 4re3 /3v
. Inserting (11) into (10) then leads to the characteristic t = KD ID law [5] with KD = re2 /3 Dvc0 − cs
 and ID =



xD 0

√ √ dx 1−xD 3 1 −1 3 tan − Ln = √ √ −1/3 1− 3 xD
3 1−x
3 x 2 2+xD (12)

A decisive test (named chronomal analysis) for validating this mechanism would be to observe a straight line for an ID = f t
plot leading to a diffusion coefficient D (computed from the observed slope KD ) close to 10−5 cm2 s−1 . Also notice that for crystals large enough the growth rate through diffusion may be increased by convection according to Dvc − cs
dr =F dt r

(13)

Here F is a complex hydrodynamic factor function of the solution viscosity [3].

3.2.3. Characteristic Time Besides knowing the growth law, one may also be interested in relating the final equilibrium size re to initial concentration in solution c0 . Let tD be the characteristic time below which the condition S > S ∗ remains satisfied. In this time domain J > 0 and if the initial concentration is high enough, we are allowed to write J c
∼ J c0
. When the condition S < S ∗ is reached due to solute species consumption during nucleation and growth (t > tD ), one should expect that J drops suddenly from J c0
down to zero. Further matter consumption should then be attributed to crystalline growth only. Now, from the growth law, we know that a nanocrystal nucleated at time  has reached, at time t, a size r t
=





t

f c r
× d

 ≤  ≤ t


(14)

Consequently, the concentration in solute species at time t should be given by t J c
r t
3 d v 0 t vc0 − ct
≈  J c0
r t
3 d

ct = c0 − ⇒

0

(15)

For diffusion growth, the magnitude of tD may be evaluated from (10) and (14) by setting c ∼ c0 , leading to  8Dvc0 r t
= t −
1/2 3  
 2J c0
8Dvc0 3/2 5/2 ⇒ vc0 −ct
≈ ×t (16) × 5 3 This shows that concentration of solute species decreases with time according ct = c0 1 − t/tD
5/2 ] with tD given by
2 1/5
  
1 5  1/5 3 3 tD ≈ × × 8 2 vc0 J c0
2/5 D3/5 
1 2  1/5 × 2/5 ≈ (17) 5 vc0 J0 D3/5

3.2.4. Equilibrium Size The next problem t is now to compute the total number of particles N ≈ 0 D J × dt formed during time tD . To do this, one may notice that from (8) and (4) that if n∗ changes slowly with time
n∗  Ln J c  3 v2 ∗ = n ⇒ J ≈ J c
= 2 0 3  Ln c kT Ln S
c0 (18) Thus, for the particular case of diffusion growth 
5/2  t c = c0 1 − ⇒ N ≈ J c0
tD f n∗
tD  1 n∗ 

k ∗ 1 − x5/2
n dx = (19) f n∗
= k + 2/5
0 k=1

Then, from the mass conservation law Nre 3 = c0 − cs
v ∼ c0 v, it becomes possible to get an analytical expression linking the average equilibrium size re  of the nanocrystals to the solid phase and solution properties  
1/5 1 94 vc0 3 re  ≈ = v11/5 c06/5 gN−3/5 N f n∗
 
3  3 v2 (20) × exp 5kT
3 Ln S0
2 Figure 3 shows the typical variation of re  with concentration in solute species c for several values of the dimensionless nucleation constant N =  3 v2 /kT Ln 10)3 . This fundamental curve shows that when N is low, re  remains roughly constant above S = 10, with typical sizes close to 1 nm. On the other hand, when N is high, nanocrystals with typical sizes close to 10 nm can be formed from concentrated solutions. In all cases, there is a critical concentration domain where average size suddenly drops from the millimetric range down to the nanoscopic one. One may also notice that for given physical conditions (sursaturation ratio S and nucleation constant N kept constant), chemistry can still play a determinant role on particle size through the sticking probability term (or kinetic barrier) gN . As seen in (20), decreasing the sticking probability (i.e., increasing the kinetic barrier) should lead to larger nanocrystals.

Nanocrystals from Solutions and Gels

563

concentration 100cs

10cs

1000cs

160

0

1.0

0,1 M ID

2

3

1M 4

5

6

1m

dr Dv(c - cs) r dt

0.6

-2

log re (m)

1

0.8

-1

xD

-3

0.4

-4

0.2

1 mm

0.0 -2

-5 -6

-1

log ID

0

1

re 1 µm

80

-7

60

-8 20

-9 -10

0

3.3.2. Thermodynamic
G ′ ∗ and Kinetic Barrier
G ′′

40 1 nm

10 23

1Å 24

25

26

27

log c (m-3) Figure 3. Crystalline growth controlled by diffusion. Boxed curve shows the shape of the chronomal function ID given by Eq. (9). Other decreasing curves were plotted according to Eq. (20) assuming a spherical shape ( = 4/3 = 4) with f n∗
 = 1/3 for six typical values of the nucleation constant N =  3 v2 /kT Ln 10
3 leading to log re = 1/3
log18v11/5 /4
+ 6/15
log c − 1/5
log gN + N /5log c/cs
2 . Other parameters were v = 10−285 m−3 , cS = 1022 m−3 , and g = exp−G′ /kT
= 10−5 . The key point is the final nanometer size of the crystal when precipitation occurs in concentrated solutions.

3.3. Interface-Limited Growth One has to remember that (20) applies only when diffusion in solution is the rate limiting step for crystalline growth. Physically, this means that if a sticking probability exists for nucleation (gN ≪ 1), the corresponding growth sticking probability gC should be close to unity. Obviously, systems satisfying simultaneously these two conditions are not very common, and in most experimental situations if gN ≪ 1, then gC ≪ 1 too. Consequently, we must look for a possible generalization of (20) in order to be able to cover the widest range of chemical systems.

3.3.1. Surface Nucleation Rate In this mechanism it is supposed that in order to form a new layer, solute species have to be adsorbed onto the crystal surface and make, through surface diffusion, a critical two-dimensional nucleus. As some chemical reactions must occur to lead to this new 2D nucleus, bulk diffusion in the solution cannot be the rate-determining step. As before, one may define a surface nucleation rate J ′ ∼ Dv−4/3 × exp−Gc /kT
with Gc = G′ ∗ + G′′ . Here, the preexponential factor has been written by taking into account that for Gc ∼ 0, the surface nucleation rate may be approximated by J ′ ∼ 1/d 2
× inc = Dv−4/3 ∼ 1025 cm−2 s−1 . Con′ cerning the thermodynamic barrier G ∗ , the prime symbol is a reminder for the fact that we are now treating a twodimensional (2D) problem instead of a 3D one. Similarly, the double prime symbol refers to the kinetic barrier associated with all chemical reactions needed to transfer a structural motif from the surface into the crystalline lattice.

At first sight, one may think that as the solute species responsible for crystalline growth are the same as those responsible for bulk nucleation, one should have G′′ ∼ G′ . In fact, this cannot be true. For bulk nucleation a crystal/solution interface first has to be created in order to initiate crystalline growth. For interface-limited growth, the solid interface is already there and by its mere presence may catalyze or inhibit the incorporation of the solute species inside the crystalline network. Consequently, in the most general case G′′ = G′ , the equality being realized only in the case of a completely neutral crystalline interface. As before, we should define gC = exp−G′′ /kT
as the growth sticking probability. Concerning the associated thermodynamic barrier to surface nucleation, it should depends on a frontier energy  ′ = G/L
p T (mJ m−1
similar to the surface energy concept  = G/A
p T (mJ m−2
. In order to simplify the problem we will assume that  ′ ∼ d = v1/3 . With this simplification the free energy variation for incorporation of m moles of surface species inside the crystal may be written GS mS → mC
= m ×  C − S
+  ′ × L ≈  ′ × L − mkT × Ln S

(21)

As for 3D nucleation, the magnitude of G′ ∗ may be readily derived under the assumption that surface embryos undergo no change in shape (only the mean size is changing among similar bodies) during surface nucleation. Consequently, the ratio K ′ = L/A1/2 should remain invariant, and if the total area of a given embryo is A ∼ m × a then its frontier L may be written L = K ′ × m
1/2 × v1/3 . Inserting this value into Eq. (21) and looking for a maximum by setting dGS
/dm = 0 leads to the following thermodynamic barrier ∗

G′ = m∗ ×kT LnS

m∗ = ′

 2 v4/3 kT LnS
2

′ =

L2 4A (22)

Table 4 gives the values of the dimensionless shape factor ′ for some ideal 2D geometries. Table 4. Dimensionless shape factors, for some common regular 2D geometries. Shape

Length L

Area A

′ = L2 /4A

Circle

2a

a√2 3a2 3 2 a2 2 2a √ a2 3 4 10a2

 = 31416 √ 2 3 = 34641

Regular hexagon

6a

Square Rectangle 2a × a

4a 6a

Equilateral triangle

3a

Rectangle 10a × a

22a

4.0000 9/2 = 45000 √ 3 3 = 51962

121/10 = 121000

Note: Shapes are characterized by one size a and classified by increasing ′ value.

Nanocrystals from Solutions and Gels

564 3.3.3. Timing Events Having a suitable expression for the rate of surface nucleation J ′ ∼ Dv−4/3 gC × exp−G′ ∗ /kT
, two characteristic times have to be considered: (i) The time N = J ′ Ai
−1 needed to nucleate a new layer on a perfectly planar interface displaying area Ai . (ii) The time C = ai /k′ needed to get a full coverage of the area Ai just after surface nucleation. Here ai stands for the largest linear size found on surface Ai and k′ = da/dt is the linear growth rate of surface nuclei. This rate should be proportional to the frequency of arrival of solute species at any edge of the surface times a sticking probability ( ′ ∼ D × gc /d) and should also depend on their average number at the interface [n′ ∼ c − cs
v]. Consequently, with d ∼ v1/3 , we should have k′ ∼ n′ × ′ ∼ Dgc v2/3 c − cs
. Now, depending on the relative values of N and C two limiting cases may be encountered.

3.3.4. Mononuclear Growth Law For mononuclear crystalline growth, the rate limiting step is the apparition of a new 2D nucleus on the surface (N ≫ C ). In this case, the linear growth rate dr/dt may be written dr d = ∼ J ′ ′ r 2 v1/3 dt N 
G′ ∗ 2 ′ −1 r = km × r 2 =  DgC v exp kT

(23)

Here ′ stands for the shape factor of the surface nucleus. It should be obvious that such a mechanism cannot be the whole story as if r with a size r0 , then at time t one tone starts would have km 0 dt = r0t dr/r 2 ; that is, rt = r0 /1 − km tr 0
]. It thus appears that rt → + for a finite time t → 1/km r0
. Such a divergence being unacceptable from a physical standpoint, this means that this mechanism should be valid only for very small sizes.

= vkp c p

Accordingly, when the exposed surface becomes large enough, the probability to observe several nucleation events on the same area Ai cannot be neglected and one has to switch to the polynuclear growth. In this alternative mechanism, the rate limiting step is the coverage of a surface by all its surface nuclei (N ≪ C ). If the whole area is covered at time t = C , then dr/dt = d/C for the linear growth rate. In order to find a reasonable value for this time one should consider that at any time 0 ≤  ≤ C , a certain amount of surface nuclei dn = N
−1 d = J ′ Ai
d have appeared. First assume an independent for each germ so that a growth if da/dt = k′ then a = 0 da = k′  C dt = k′  − 
. The total area covered by germs that have appeared at t =  may then be written

(24)

m∗ + 2 3

(25)

3.3.6. Chronomals and Equilibrium Size As for the diffusion law, one may introduce a chronomal analysis in order to find the order p for crystalline growth. Setting c = c0 1 − xp
and r = re xp1/3 then leads to t = Kp Ip , with  xp re and Ip = x−2/3 1 − x
−p dx (26) Kp = p 3vc0 kp 0 Figure 4 shows the variation of Ip with xp for increasing values of p. Concerning the integrated form of the polynuclear growth law, let tP be the characteristic time below which the condition S > S ∗ remains satisfied. From (14) and (15) it comes that ct = c0 1 − t/tP
4 ] with tP given by


12 ′ 

1/4

−1/4

J c0


D−3/4 gC−3/4 c0−1/4

G′ ∗ exp 4kT




(27)

As done, this induction time may be used to evaluate the number of nanocrystals N formed per unit volume 
4  t ⇒ N ≈ J c0
tP F n∗
c = c0 1 − tP  1 n∗ 

k (28) 1 − x4
n∗ dx = F n∗
= k + 1/4
0 k=1

This in turn leads to an analytical expression linking the average equilibrium size re  of the nanocrystals to the solid phase and solution properties re 3 =

2

p=

The expression in the right hand side of (25) comes from an alternative evaluation of J ′ based on the observation that from (22): Ln J ′
/Ln S
= m∗ ⇔ J ′ ∼ kC c m∗ . It is interesting to compare relations (10) and (25). In both cases, the growth rate depends on the diffusion coefficient D, and on the difference (c − cs ). The differences are that we have a power law for the concentration dependence with a growth rate independent of crystal size in the case of polynuclear growth. According to this last mechanism this means that the absolute width of the size distribution should be constant (r ∼ r0 ) at all times and that only the relative width may decrease with time (r/r ∼ r0 /r × r0 /r0 ).

tP =

3.3.5. Polynuclear Growth Law

dA = ′ a2 dn = ′ J ′ Ai k′  − 
2  C ′ 2 dA = J ′ Ai k′ C3 ⇒ Ai = 3 0

Taking into account that in fact germs may overlap during growth we may write C = ′ J ′ k′ 2 /3
−1/3 , where  is the numerical geometric correction describing the geometric details of the various overlaps. For disk-shaped 2D germs it may be shown that  ∼ 06 [5]. This gives our final polynuclear growth law 
d G′ ∗ dr = = ′ v/3
1/3 DgC c − cs
2/3 exp − dt C 3kT


 
 1 ′  1/4 9/4 5/4 gC 3/4 v c 0 F n∗
12 gN 
′ 2 4/3 3 2

 v 3  v (29) − × exp 4kT
3 Ln S0
2 4kT
2 Ln S0



Nanocrystals from Solutions and Gels

565

Concentration 10cs

100cs

1000cs

log re (m)

0

0.8 0.6

-2

0.4

-3

0.2

-4

0.0

-5

p=1

p=2 p=3 p=4

dr = vk cp p dt 2

4

6

8

10

12

14

re

8 σc = 16

4

-7

1m

1 mm

Ip

0

-6

1 µm

2

-8 -9

1M

xp

1.0

-1

3.4.1. Growth Law 0,1M

1 nm

1

-10

1Å 23

24

25

26

27

log c (m-3) Figure 4. Crystalline growth controlled by the interface. Boxed curve shows the shape of the chronomal functions IP given by Eq. (24). Other decreasing curves were plotted according to Eq. (29) assuming a spherical shape ( = 4/3 = 4) for 3D nuclei and a disk shape (′ = ′ =   = 06) with F n∗
 = 3/8 for five typical values of the growth constant C = ′  2 v4/3 /kT Ln 10
2 . For these particular shapes we have N ∼ 3C
3/2 leading to log re = 1/3
log6v9/4 /4
+ 5/12
log c + √ 1/4
loggC /gN
+ C 9 C − logc/cs
/12log c/cs
2 . Other param−285 eters were v = 10 m−3 , cs = 1022 m−3 , and gC /gN = 10−6 . As for diffusion controlled growth, nanometer sized nanocrystals are formed when precipitation occurs in concentrated solutions.

Figure 4 shows the typical variation of re  with concentration in solute species c for several values of the dimensionless growth constant C = ′  2 v4/3 /kT Ln 10
2 . One 3 2 3 may notice  that as N =  v /kT P Ln 10
, the link N = ′ ′

C /
C /
exists between growth and nucleation constants. As in the case of diffusion, these curves show that when N is low, re  remains roughly constant above S = 10, with typical sizes close to 100 nm. On the other hand, when N is high, nanocrystals with typical sizes close to 1 m can be formed from concentrated solutions. Again, in all cases, there is a critical concentration domain where average size suddenly drops from the millimetric range down to the nanoscopic one. One may also see that nucleation and growth terms have antagonist effects on the equilibrium size. Concerning the role of chemistry at the interface larger crystals are expected when g ′ > g (i.e., when G′′ < G′ ).

3.4. Dislocation Controlled Growth When the sursaturation ratio S is smaller than about 2, the rate of surface nucleation may become so slow that the crystal growth rate becomes practically nil. In fact there are numerous examples in literature where crystalline growth is easily observed even when S = 101. In such cases, it has been shown [2] that growth may be initiated on crystalline defaults (dislocations or stacking faults). Among the possible defaults, it appears that the most efficient ones are screw dislocations leading to the formation of typical Archimedean spirals on the surface [2, 3].

In this mechanism, we have to estimate the normal velocity of advancement u for the leading step of the growing spiral. For a spiral of radius R, this rate should be proportional to the frequency of arrival of solute species at the leading edge times a sticking probability ( ′ ∼ D × gc /d) and should also depend on their average number at the interface [n′ ∼ c − cR
v]. Consequently, with d ∼ v1/3 , we should have u ∼ n′ × ′ ∼ Dcgc v2/3 1 − cR /c
. Now, from (22) with ′ = , it is possible to relate the concentration just outside the crystal surface c to a critical germ radius r ′ ∗ according to r ′ ∗
2 = m∗ × v2/3 ; that is, r ′ ∗ = v/kT Ln S
. Moreover, applying (9) with r2 → + (i.e., c2 → cs
and r1 = R or r ′ ∗ allows one to express the ratio cR /c as 

  cR v 1 1 1 v 1 = exp − − ≈1+ c kT R r ′ ∗ kT R r ′ ∗ ⇒

lim u =

R→+

Dv5/3 c g kT r ′ ∗ C

(30)

Assuming a spiral displaying a stationary shape and rotating with a constant angular velocity S rad s−1
, it may be shown that S = u /r ′ ∗
[38]. Consequently, each spiral turn should deposit a layer of thickness d ∼ v1/3 leading to the following linear rate of growth
 dr S DkTc ∼ Ln S
2 (31) × v1/3 = gC dt 2 2 2 

3.4.2. Two Limit Cases Two important limiting cases may be discussed. When c ∼ cs (i.e., S = 1 + ), then Ln S = Lnc/cs
∼ c − cs
/cs , and we get a nonvanishing growth rate dr/dt = gC DkT /2 2 cs
 × c − cs
2 . This explains the possibility of growing large single crystals from solutions even when S ∼ 1. On the other hand, when c ≫ cs the growth rate may become quite large, but very soon the diffusion of solute species toward the spiral leading edge will become rate determining. As both rate laws are known, it is possible to see for which value of S both processes should contribute equally to the crystalline growth gC

Dv1 − S −1
DkTc Ln S
2 ≈ 2 2  r
 2 2 2 v SLn S
≈ ⇒ S−1 gC kTr

(32)

Using  ∼ 01 J m−2 , v ∼ 10−285 m3 , and T = 300 K as typical values leads to the following condition: [gC rnm
 × SLn S
2 ≈ 152S − 1
. Setting gC ∼ 1 and r = 1 nm as reasonable limits leads to S = 47338. Under these conditions, diffusion should become the rate limiting step as soon as S > 50. However, if one considers a millimetersized single crystal (r ∼ 106 nm) with rather low kinetic barrier (gC ∼ 1 for purely ionic crystals such as NaCl or KCl) well developed spirals should be evidenced only if S ≈ 1 + 152/gc r
< 100001. However, if gC ∼ 10−7 (i.e., G′′ ∼ 40 kJ mol−1
, then for the same single crystal size diffusion toward  the interface will be rate determining only when S ≈ exp 152/gc r
 > 105 . A direct consequence of this fact is that nanocrystal formation (r ∼ 10 nm) should never be under diffusion control, unless gC > 01.

Nanocrystals from Solutions and Gels

566 3.4.3. Chronomals Interestingly enough, when spiral growth is the rate limiting step, the chronomal analysis shows that it would be rather difficult to distinguish between the spiral and the polynuclear growth. Proceeding as before by setting c = c0 1 − xS
p and r = re xS1/3 leads to t = KS Ip , where Ip is the polynuclear p chronomal limited to values of p = 1 or 2 and KS stands for two time constants given by 2 2  re × with 3gC DkTfp c0
 xS x−2/3 1 − x
−p dx p = 1 or 2 Ip =

xs

1.0

p=1 p=z

0.8 0.6 0.4 0.2 0.0

Ip 0

2

4

6

8

10 12 14

p

KS =

0

(33)

The two p-values correspond to the two previously described limiting cases. When c ≫ cs , then c ∼ c − cs and Ln S ∼ Lnc0 /cs ) leading to t = KS1 I1 with f1 c0
= c0 Lnc0 /cs
2 . For the other limiting case c ∼ cs , we have t = KS2 I2 with f2 c0
= cs /c0 − cs
2 . On the other hand, if diffusion is the rate limiting step, then one should follow the ID chronomal given by (12). This analysis shows that observing a crystalline growth law following ID , I1 , or I2 chronomals does not rule out the spiral mechanism. In fact the only clear evidence for the occurrence of the polynuclear mechanism would be to follow chronomals IP characterized by p > 2. To the best of our knowledge such a situation has been scarcely reported in literature as most precipitation processes follow either ID or I1 chronomals. This result may just be a direct consequence of the very high efficiency of the spiral growth for nanocrystals which bypassing the bottleneck of surface nucleation run directly into the one of diffusion toward the interface. If this is true, then all nanocrystals grown using concentrated solutions should in fact be formed from numerous interpenetrating nanospirals and not from overlapping surface nuclei.

3.4.4. Equilibrium Sizes At last, we may consider the integrated form of the spiral growth law, characterized by a time tS below which the condition S > S ∗ remains satisfied. From (14) and (15) it comes that ct = c0 1 − t/tS
4 ] with tS given by
1/4  3/4 1/4  4 v 2 2  (34) tS =  gC DkT Ln S0
2 c02 J c0
As the power dependence of concentration with time is similar than that observed for polynuclear growth, (28) holds with tP replaced by tS , leading to  
1/4
3/4   1  kT Ln S0
2 3/4 2 3/2 gC v c re 3 = 0 F n∗
4 gN 2 2  
3  3 v2 (35) × exp 4kT
3 Ln S0
2

3.5. Discussion At this stage a comparison between Figures 3, 4, and 5 may be useful. All curves display the same characteristic L-shaped aspect, the decreasing left part coming from an exponential term and the increasing right part from a power

2

Figure 5. Spiral crystal growth controlled by screw dislocations. Boxed curve shows the shape of the two chronomal functions I1 and I2 given by Eq. (26). Other decreasing curves were plotted according to Eq. (35) assuming a spherical shape ( = 4/3 = 4) for 3D nuclei with F n∗
 = 1/2 for five typical values of the nucleation constant N =

 3 v2 /kT Ln 10
3 leading to log re = 1/3
log6v2 /4
+ 1/2
log c + 1/4
loggC /gN
+ 1/4
logkTLn S0
2 /2 2  + N /4log c/cs
2 . Other parameters were T = 300 K, v = 10−285 m−3 ,  = 01 J m−2 , cs = 1022 m−3 , and gC /gN = 105 . As for other growth mechanisms, nanometer sized nanocrystals are formed when precipitation occurs in concentrated solutions.

of the total concentration c0 . In these drawings the two sticking probabilities gN and gC (linked to the occurrence of kinetic barriers G′ and G′′ for nucleation and growth) have been adjusted in order to have re > 01 nm in all the investigated concentration range. In the case of diffusion controlled growth, one should have gC ∼ 1 and the size of the nanocrystals will be fixed by the relative values of N and gN . This is no more the case for the two other mechanisms, where the two competing terms are N and the (gC /gN
ratio. However, a clear difference exists between polynuclear and spiral growth as one must set (gC /gN
= 10−6 for the first mechanism and (gC /gN
= 10+5 for the second one in order to get reasonable sizes. The chemical interpretation of this phenomenon is straightforward. Polynuclear (or mononuclear at low S-values) growth should be suspected as soon as gC < gN , that is, when solute species are more easily incorporated when the nanocrystal has not yet appeared (embryo stage). Chemically speaking, we are in a situation where crystal growth is poisoned by the decomposition products of the solute precursors. In this case, it seems obvious that the highly reactive leading edge of a growing spiral will be much more affected by the poisonous material than a less reactive flat layer. Owing to the presence of the poison, the surface nucleation bottleneck is unavoidable and the polynuclear picture dominates crystallin growth. In the reverse situation, gC > gN , the decomposition products of solute precursors are expected to show no affinity for the crystal/solution interface. In this case, solute species absorption should occur at the most reactive sites, and one may expect a crossover between polynuclear and spiral growth. It then appears that Eqs. (20), (29), and (35) should cover both qualitatively and quantitatively all the pertinent physical and chemical aspects of nucleation and crystalline growth from solutions.

Nanocrystals from Solutions and Gels

4. LIMITED AND SECONDARY GROWTH It should be noticed that the previous equations have been reached without any explicit description of the structure of the solution/crystal interface. One should then expect that some other important aspects remain yet hidden, particularly in the interfacial energy . In the previous treatment, it was tacitly assumed that the interfacial energy  was a constant characterizing the solution/crystal interface. In this section, we will consider what should happen to the final equilibrium size of a nanocrystalline dispersion when  may change owing to variations in pH or ionic strength. To do this we must dispose of a faithful model of the crystal/solution interface. In the following, we will consider mainly oxide/water interfaces that are by far the most commonly encountered experimental cases. Generalizations for nonaqueous or nonoxide interfaces will not be discussed in this chapter.

4.1. Solute–Solvent Interface The best way to understand what the structure of an oxide water interface should be is to start from the molecular scale (Frank and Wen model [39]). Accordingly, X-ray or neutron diffraction studies of aqueous solutions [13, 40] have shown that the molecular environment around a given solute is not a random medium. At less than 0.3 nm, a first shell of frozen solvent molecules is very often found in close contact with the solute species. After this coordination shell, other more or less immobilized shells may be found. The spatial extension of this zone is typically between 0.3 and 0.5 nm. In this critical zone, it may be observed that the local order characterizing the solvent in a pure state may either be broken or strengthened. This comes from the fact that on one side solvent molecules are under the influence of the more or less rigid coordination shell around the solute. On the other side, they are under the influence of the random motions of their congeners that are far from any solute (this holds for sufficiently diluted solutions). When the solute coordination shell is highly structured and rigid, this orderliness tends to be propagated at longer distances. One then speaks of a structure-forming solute. Conversely, if the coordination shell is highly labile and disordered, the disorder will also be more or less transmitted to the neighboring shells breaking the original structure of the pure solvent. In this case, one may speak of structure-breaking species.

4.2. Oxide–Water Interface This classical picture of the solvent–solute interaction may serve as a faithful basis for a realistic model of the solid/liquid interface. As explained in previous sections, nucleation is an irreversible phenomenon by which several solute precursors meet together in a limited volume (thermodynamic barrier G∗ ). Within this confined state, they may further expel partly or fully their coordination shell (kinetic barrier G′ ) in order to build a new solid phase. Chemically speaking, the solid phase may be viewed as the result of a giant polymerization process of solute species. On this basis, one may expect that their respective coordination shells should also merge together defining the solid/liquid

567 interface. This merging process should, however, also apply to secondary coordination shells leading to a more or less compact layer, tightly bonded to the interface (called hereafter the “Stern” layer). Finally, just outside this more or less immobilized Stern layer a slipping plane for solvent molecules should exist, that may be identified as the “outer Helmholtz plane” (OHP). Adopting this “natural” model for the solid/liquid interface allows us to zoom more deeply into the crystalline growth process. For instance, the quite vague statement of “diffusion toward the solid/liquid interface” may then acquire an accurate formulation. Accordingly, diffusing solute species may be identified as any kind of fully solvated chemical entity not able to go beyond the OHP. One must realize that the last statement is not an assumption, but a logical consequence of the chosen model. Accordingly, assume that some kind of solute species has been able to jump over the OHP landing inside the Stern layer. The chemical consequence of this hopping should be that some spatial reorganization of the surrounding solvating shell was possible in order to fit the local structure of the Stern layer. If the energetic cost of this reorganization were too expensive, the jumping would have been a very unlikely process. Consequently, the solute species would show no tendency to cross the OHP, preferring to diffuse quietly far away from this unfriendly disturbing spatial zone. Conversely, it may happen that some otherwise quietly diffusing solute species may experience a very high structural affinity for the Stern layer. Such a species is then expected to cross the OHP ending up right inside the Stern layer. As a result of this jump, a quite new solvating shell more adapted to the local structure of the Stern layer should be adopted, leaving with no regret the older one more adapted to the structure of the bulk solvent. The automatic consequence of fact is the existence of a second kind of molecular plane, named the “inner Helmholtz plane” (IHP). By its very definition this plane lies somewhere outside the solid surface and well below the OHP. From a chemical standpoint, it is formed by the locus of all strongly adsorbed species that are not allowed to diffuse freely into the solution due to their particular affinity for the Stern layer. At last, chemical entities already localized within the Stern layer may exist and could display rather high chemical affinity for the crystalline surface. For such species, full reorganization of their coordination shell needed for a “perfect” sticking to the surface is not a problem. They are thus not expected to stay localized close to the IHP but may undergo a last final jump right inside the crystalline lattice. The immediate result of this ultimate sacrifice is an increase of the spatial extension of the interface by one step, another way of saying that crystalline growth has occurred.

4.3. Surface Charge The next step is now to see how the surface charges may develop. As shown in Figure 6 (top left) metallic cations exposed at the surface are found to be hydroxylated owing to water chimisorption. Consequently, like soluble aquo, hydroxo, or oxo complexes they may acquire or lose protons according to the polarizing power of the metallic cation ⊖ M–O⊖ + H3 O⊕ ⇌ M–O–H + H2 O ⇌ M–OH⊕ 2 + OH

Nanocrystals from Solutions and Gels

568

4.3.2. Point of Zero Charge

Figure 6. A natural model for the oxide/water interface. Top left shows the H-bonded structure of the Stern layer in close contact with the oxide surface. Top right illustrates the Frank and Wen model (scale t0 , one should have   Mt − t0
1/3 r∗ = 1 + r0∗ r0∗
3

⇒


∗ 4 r gt
= gt0
0∗ r

(55)

4.6.4. Size Distribution As the time variation of r ∗ and gt
is known, we may notice that 4Mgt
M dr ∗ dgt
=− = dt 3r ∗
3 dt 3r ∗
2
  M =− ⇒ t r 3r ∗
3

4.6.3. Time Dependence Let us approximate each crystal by a sphere with radius r lying in a spherical diffusion field of solute species. The solubility cr of the small crystals may be computed from (9) with r2 → + (i.e., c2 → cs ) and r1 = r. A similar relationship also applies to the concentration c in the bulk that is in metastable equilibrium with the nuclei of size r ∗ (now with r1 = r ∗ ). Expanding exponential terms up to second order then leads to the following linear growth rate:
 
2v 2v c = cs exp and c = c exp r s kTr ∗ kTr
 2 1 vDc − cr
2v Dcs 1 dr − = ≈ (52) ⇒ dt r kTr r∗ r

2v2 Dcs kT

M=

(56)

In order to get the size dependence h
of nr t
one may insert the growth rate given by (52) into (51) leading, after transformation of variable r =  × r ∗ and some tedious algebra involving relations (56), to the following differential equation:     dh
2 3 dh
+ h
= 3
 − 1
6 h
+  d d ⇒

3 − 62 /
d ln h
= 3 d  / − 3 + 3

(57)

Nanocrystals from Solutions and Gels

572 At this stage, as from (53)  is a number depending on the integral of the yet unknown h function, the solution may seem not obvious. However, we may notice that the denominator in (57) has the simple form x3 = ax + b with a = −b = 3. A possible solution to this cubic equation is thus x = b/2
+ 1/2 1/3 + b/2
− 1/2 1/3 , with  = b/2
2 − a/3
3 (Cardan formula). Consequently, setting  = 9/4 would lead to  = 0 (i.e., to the most simple root x = −3), allowing one to factorize the denominator as ( + 3
 − 3/2
2 . Remembering that with h0
= 1, integration of (57) is straightforward:

D = kT /6a
, the diffusion coefficient D in a solution displaying viscosity  at temperature T is expected to be the highest for species displaying the lowest size a. This means that aggregation, like Ostwald ripening, should be important only at long time. However, if ripening is concerned by the behavior of N r t
when r → 0 and t → , aggregation focuses on the behavior of this same function when both r and t become large.

11/3 7/3
3 3/2 3+ 3/2 − 
  × exp − (58) 3/2 − 

Consequently, we now assume that after a rather long lapse of time during which the function N r t
has assumed an almost constant value hereafter noted N0 , this number may change owing to binary collisions between the crystals. Let VT R
be the potential function covering all possible physical or chemical interactions that may occur during the collision. If CR
is the concentration of crystals at distance R, the flux of particles (number of crystals per unit area and per unit time) jt
is given by the modified Fick law:

=

9 4

⇒

h
=




Figure 7 illustrates the previous considerations for some typical values of the solid phase and solution parameters, assuming a monodispersed and nanosized dispersion of particles (r0∗ = 10 nm) at the beginning of the Ostwald ripening. It is worth noticing the considerable spreading of the size distribution at long time and its typical asymmetric shape. This characteristic shape emerges from the fact that small particles are disappearing from the solution, allowing the bigger crystals to become still bigger. Concerning the time scale of the ripening, it was mainly ruled by the selection of a diffusion-limited growth mechanism for describing the dissolution–reprecipitation events. Obviously, this should hold only for largely ionic crystals, and for other materials, one may expect an interface-limited ripening. In this case, a numerical solution to the ripening equations (51) and (54) may be the best way of handling the problem [41].

5. AGGREGATION It is now time to remove the assumption that nanocrystals may nucleate and grow independently of each other [i.e., that the N r t
function should be more or less constant during the whole precipitation process].

5.1. Position of the Problem As explained, this assumption was crucial for deriving relations (20), (29), (35), (47), or (54) relating sizes to solution conditions and solid phase properties. Accordingly, even if nanocrystals have their diffusion coefficient 2 or 3 orders of magnitude less than solute species they may nevertheless, from time to time, undergo some collisions between each other. If the sticking probability is high during a collision, aggregates may be formed decreasing by two units the value of N r t
. Obviously, if all possible processes influencing the mean size r of nanocrystalline dispersions (nucleation, growth, ripening, and aggregation) were occurring with the same rate, the situation would be hopeless. Fortunately, owing to the physics involved in each kind of phenomenon not all these processes are expected to occur simultaneously. For instance, for any kind of reaction to occur, reactants (either complexes or particles) first have to diffuse toward each other. According to the Stokes–Einstein equation

5.2. Fuchs Integral

dCR
CR
dVT − × dR kT dR 
VT dCR
expVT /kT
 = −Drel exp − kT dR

jt
= −Drel

(59)

In this relationship, the first term arises from the free Brownian motion of the particles. As some external forces FT = −dVT R
/dR may act on the moving particles, the second term takes care of the additional flux CR
× v, proportional to the speed v of the particles. As usual, speeds may be related to forces through a friction factor f v = FT /f
derived from the Einstein relationship D = kT /f . Notice that as we are considering a binary collision between two moving particles, the Fick law uses a relative diffusion coefficient Drel . The link between Drel and D1 or D2 , diffusion coefficients of one single particle, may be easily derived by reference to the fundamental law of Brownian motion: ri2  = 2Di t. Consequently for a collision between two particles at a relative distance ( r1 − r2
we should have  r1 − r2 2  = r12  + r22  − 2r1 · r2  = 2D1 t + 2D2 t = 2Drel t ⇒

Drel = D1 + D2

(60)

Let us now apply (59) to compute the flux of identical particles across a sphere of radius R. From (60) Drel = 2D and considering the spherical symmetry of the problem, we may write J t
= 4R2 × jt
leading after integration to
 
VT J  +

VT dR CR
exp +A =− exp kT 8D R kT R2 
 +

VT dR = 8DC

(61) exp ⇒ Jt kT R2 2a Boundary conditions VT → 0 and CR
→ C ∼ N0 /V when R → + and C2a
= 0 have been applied to get the integration constant A.

Nanocrystals from Solutions and Gels

573

5.3. Hard Spheres Model Let us apply (61) to the most simple case of noninteracting particles characterized by VT ∼ 0 (i.e., by Jt = 16DaC). Now, for a given flux Jt , half particles are expected to move in a direction allowing a close encounter at R = 2a, while the other half are moving in the right opposite direction. As all encounters lead to an irreversible sticking of both partners, the rate of disappearance of the crystals through coagulation should be −

1 dC = Jt C = 8DaC 2 dt 2 C0 ⇒ Ct
= 1 + 8DaC0 t


kf = 8Da =

4kT (62) 3

Here C0 = N0 /V is the total concentration at time t = 0 that governs the characteristic lifetime t1/2 [such that Ct1/2
= C0 /2] of the dispersion. As shown in (62), this time is given by t1/2 = kf C0
−1 = 3/4kT C0
. For water at T = 298 K, we have t1/2 s
= 2 × 1011 /C0 cm−3
, showing that the lifetime of dispersions characterized by VT ∼ 0 is quite short (a few milliseconds when C0 ∼ 1014 cm−3 ).

5.4. Attractive Forces In fact the solution given by (62) is a little bit unrealistic as the situation VT ∼ 0 is never encountered in reality and because the equation applies only to doublets formed by the association of two single particles. For instance, due to the universality of the London dispersion interaction, an attracting potential should always expected at any distance. Accordingly, quantum mechanical considerations have shown that the potential energy of attraction between two atoms A and B, separated by a distance r, is given by VA = −L/r 6 (London force) [45]. The constant L, characterizing the two interacting atoms, has been roughly estimated by London from the atomic polarizabilities  and first ionization energies I as L = 3/2
× A B /40
2  × IA−1 + IB−1
−1 [46].

who first did this analysis [44]. This a characteristic value for any condensed substance (whether solid or liquid) as shown in Table 5 [47]. As detailed previously for similar substances one would expect L ∝ 2 × I [i.e., A ∝ 2 × I
/v2 ]. Materials displaying high Hamaker constants are then those with large polarizability , high first ionization potential I, and high atomic density (1/v). This explains the extreme position of ice and diamond in Table 5. Obviously, Table 5 should be applicable only for vacuum interactions. When two particles of substance A (Hamaker constant A1
and B (Hamaker constant A2
are immersed in substance C (Hamaker constant A3
, one may show [48] that the resulting interaction A123 may be characterized by     A123 =  A1 − A3
 A2 − A3
  if A1 = A2 =  A1 − A3
2

The use of square roots in (63) comes from the fact that A ∝ /v
2 while polarizabilities  are additive quantities. According to this relationship, one may expect for water/oxide interfaces Hamaker constants that are ranging from 0.2 up to 0.5 eV. As far as nanocrystals are concerned the relationship VA = −A/12R2
cannot be very useful as it applies to two infinite planar interfaces. Performing the previous integration with spheres displaying radii a1 and a2 , with a center to center separation S, leads to [44]

2a1 a2 2a1 a2 A VA S
= − + 2 6 S 2 − a1 + a2
2 S − a1 − a2
2  S 2 − a1 + a2
2 (64) + ln 2 S − a1 − a2
2 Table 5. Some Hamaker constants A for condensed matter characterizing the intensity of van der Waals interactions between microscopic objects. Matter

5.4.1. Hamaker Constant A This quantum mechanical expression for the dispersion interaction may readily be used for computing attractive forces between surfaces [42]. For instance, the interaction between an atom and a crown of matter (as always characterized by its molecular volume v
of radius a, width da, and thickness dx, is just d 2 V = −L/v
2adadx
r −6 . If R is the distance separating the atom from the surface, we may write using Pythagoras’s theorem r 2 = R + x
2 + a2 , leading after integration (from zero to infinity) against x and a to VA = −L/6v
/R3 . Considering that the previous atom belongs in fact to a plate of thickness dz situated at a distance (R + x) from the other surface leads to an energy of attraction per unit area dvA = −L/6v2
dz/R + z
3 . A last integration against z from zero to infinity leads to the well-known formula giving the van der Waals interaction between two infinitely large flat plates separated by a distance H VA = −A/12R2
. The parameter A =  2 L/v2
characterizing the macroscopic interaction is called the Hamaker constant after the man

(63)

Hexagonal ice Liquid water H2 O Et2 O, Me2 CO, MeCOOEt MeCOEt Benzene, nitrobenzene Chloroform, dioxan Toluene CCl4 , ethylene glycol CS2 Polyethylene oxide Glycerol Polystyrene CaF2 , polymethylmethacrylate Polyvinyl chloride SiO2 quartz -Fe2 O3 , haematite Silver chloride AgCl Silver bromide AgBr TiO2 , anatase TiO2 , rutile Diamond

A (eV) 0.19 0.23 0.26 0.29 0.36 0.37 0.38 0.39 0.41 0.42 0.46 0.49 0.51 0.62 0.92 1.02 1.07 1.14 1.28 1.41 2.81

574

Nanocrystals from Solutions and Gels

5.4.2. Application

5.5.1. Diffuse Layer Relaxation

In order to see the effect of such a potential on the rate constant kf , we may simplify (64) by writing S = R + a1 + a2 and assuming a very small distance R ≪ a1 + a2
between the two spheres. In such a case the first term of (64) is the leading one and VA R
∼ −A/6R
1/a1 + 1/a2 −1 = −Aa/12R for two spheres of equal sizes (a1 = a2 ). Replacement of VT by VA R
in (61) then leads after integration and expansion of the exponential term up to second order to Jt = 16DaC1 + A/48kT
. As A is at most a few tens of kT, the kinetic constant kf should be at most multiplied by a factor 2, relative to its value at VT ∼ 0. Even if this correction appears to be negligible relative to the 1011 cm−3 term, it nevertheless shows that aggregation is accelerated (particularly at low temperature and for materials displaying high Hamaker constant) relative to pure diffusion. Consequently, if the dispersion has to be stabilized against irreversible aggregation, one must play with experimental factors leading to a VT curve that must display some maximum positive value Vmax at a given distance R > 2a. Accordingly, the previous analysis has shown that the additional destabilization factor coming from the region where the potential displays strongly negative values was at most two. Such a modest contribution is then expected to be negligible even in the presence of a small maximum. This observation simplifies integration of Eq. (61) and allows one to write Jt = Jt /W , where W is the so-called stability ratio W ∼ expVmax /kT
. The higher Vmax , the higher W and the longer the lifetime of the dispersion as kf ∼ 8Da/W and t1/2 = kf C0
−1 ∝ W . For instance, the stabilization for about one year of a dispersion displaying about 1014 particles per cubic centimeter would require a stability ratio of about 10105 . This corresponds to a potential maximum of about 24 kT (∼60 kJ mol−1 or 0.6 eV at T = 298 K).

The first one is the Debye–Hückel relaxation by which counterions located in the diffuse layer move with a diffusion coefficient Di in order to adjust the structure of the double layer to the new conditions. The characteristic relaxation time DH associated with this process is equal to the average time needed for displacement of ions across the double layer: DH = −2 /2Di . For aqueous solutions at room temperature Di ∼ 10−9 m2 s−1 leading to DH ps
∼ 46/Imol l−1
. Consequently, one may safely assume that double layers are always at equilibrium during collision, as even for a = 1 nm we still have B ∼ 4DH .

5.5. Repulsive Electrical Forces The first method widely used to stabilize colloidal dispersion is to work with charged surfaces. For oxide materials, this is done by changing the pH or the ionic strength I. Owing to the rapid diffusion of protons is aqueous solutions, any pH variation instantaneously affects the surface potential 0 as evidenced by Eq. (38). By playing with the ionic strength, the spatial extensions of the double layers around colloidal particles are deeply affected. Consequently, let us evaluate the time duration B of a collision between two charged particles. During this collision, each particle must then diffuse over a length scale of the order of the Debye–Hückel length −1 given by Eq. (39). If Dp is the diffusion coefficient of the colliding partners (fixed by radius a and solution viscosity ), then B = −2 /2Dp = 3a/2 kT
. For water at room temperature (T = 298 K,  ∼ 10−3 Pa s), we should have B (ns) = 02 × anm
/Imol l−1
. For nanosized particles (1 ≤ a ≤ 100 nm) with typical ionic strength (10−3 ≤ I ≤ 1 M), a Brownian collision cannot be shorter than 100 ps (small particles or high ionic strength). On the other hand, for larger size or lower ionic strength it cannot be longer than 0.1 ms. Due to the geometric changes involved by the collision, several relaxation processes have to occur in order to restore complete equilibrium.

5.5.2. Stern Layer Relaxation The second mechanism relies on the adsorption or desorption of all the PDIs involved in the double layer equilibrium. This includes charged species located at the surface as well as those located at the IHP within the Stern layer. Here the rate of charge adjustment is ruled by the value of the exchange current density i0 between the surface and the Stern layer. For a given charge density (0 + 
the characteristic relaxation time may be evaluated as AD = 0 + 
/i0 . If the exact value of i0 is highly dependent on the detailed structure of the interface, 1 A cm−2 is surely a very high value and 10−10 A cm−2 is a very low one [49]. With 1 C cm−2 ≤ 0 + 
≤ 100 C cm−2 , it follows that PDI relaxation should take at least 1 s and may in the worst cases (high surface charge and low mobility of the charges) be as long as several days.

5.5.3. Interactions at Constant Charge or Potential It follows from the last analysis that two limiting cases will be encountered during a Brownian collision between two charged particles: (i) For large nanocrystals displaying a low surface charge with high mobility of the PDI and placed under low ionic strength conditions, one may safely assume that B > AD . In such a case, the interface, as a whole, is completely relaxed during the collision. This means that at all times the potential remains constant. (ii) In all other cases, one may expect that B ≪ AD , and in this case, only the diffuse part of the double layer is completely relaxed. As  = −0 d/dx, this means that at all times the slope at the surface of the  = f x
curve cannot change leading to an increase of the surface potential 0 . A consequence of this fact is that the distance of closest approach should not be S = 2a, but S = 2 × a + 
, where  is thickness of the Stern layer holding some of the PDI ions [49]. Obviously, this nonequilibrium situation holds only during a time B . If particles remain stuck together after the collision, a discharge current will appear allowing a reduction of the potential toward its equilibrium value. This relaxation allows a still closest approach between the two cores of the particles, until S = 2a at equilibrium. In this fully relaxed state particles are irreversibly bonded through the van der Waals interaction and cannot be separated anymore.

Nanocrystals from Solutions and Gels

575

This constant charge mechanism helps to explain the repeptization phenomenon by which a flocculated system may be dispersed again by changing the composition of the medium without stirring [49].

5.5.4. Osmotic Pressure and Repulsive Potential

5.5.5. DLVO Theory

From a physical point of view, the origin of the repulsion between two overlapping double layers comes from the existence of an osmotic pressure pR , which develops due to the accumulation of ions between the two surfaces. At sufficiently long distances, the two interacting particles may be viewed as almost planar interfaces. The actual force per unit area exerted on the plates is given by the difference in the osmotic pressure between the solution in the midplane m and that in the bulk (concentration c0 ). With c+ and c− the concentrations at the middle plane, we may write pR = RT c+ + c− − 2c0 ). Assuming that c± = c0 exp∓zF m /RT
and developing the exponential terms up to second order ( 21 ex + e−x  ∼ 1 + x2 /2 when x is small) allows one to 2 express this osmotic pressure as pR = 21 2 0 m . In the case of small overlap between the two plates, potentials are expected to be additive leading to m = 2x = R/2
∼ 2d exp−R/2
. The resulting repulsion potential is thus obtained after integration over R leading to VR =





R

pR dR =

42 0 2 

d exp−R
dR 2 R

= 20 d2 exp−R


reduce to an expression similar to (65): VR = VR = 20 ad2 exp−R
. Other expressions are available in the literature for situations where the approximations d  < 60 mV and a ≫ 1 are not valid [49, 52–55].

Figure 8 shows the resulting potential curves VT = VA + VR obtained when the Hamaker attraction given by (64) is added to the repulsive contribution VR coming from the overlap of double layers given by (66). As shown, four parameters have a deep influence on the occurrence of a maximum. The curve at the top left part of Figure 8 shows the effect of changing the ionic strength for a constant Hamaker constant, size, and surface potential. At high ionic strength or  there is no maximum and the dispersion should flocculate. This is not true at low ionic strength where the interaction is largely repulsive at all distances R > −1 . It is a well-known experimental fact (Schulze–Hardy rule) that the critical coagulation concentration (c.c.c.) displays a strong dependence on the valency z of the coagulating ion (c.c.c. ∝ 1/z6 ). This c.c.c. should correspond to the point at which the maximum in the total potential energy curve just touches the horizontal axis (VT = dVT /dR = 0). As coagulation implies a low potential and a rather small separation R, we may use VR = VR = 20 ad2 exp−R
and VA R
= −Aa/12R for the repulsive and attractive parts respectively. Applying

(65)

Equation (65) is useful as it shows that a high value of d is to be associated with a strong repulsive potential. It is, however, not very realistic, as it suggests that high ionic strength (i.e., high  values) also favors strong repulsion. Keeping the low potential approximation, but considering spheres of radii a1 and a2 instead of infinite plates, leads to a more satisfying result when d  < 60 mV and a ≫ 1 [50]: VR =

2 2 0 a1 a2 d1 + d2
a1 + a2

 1 + exp−R 2d1 d2 ln × 2 2 1 − exp−R d1 + d2
   + ln 1 + exp−2R

(66)

When a1 = a2 = a and d1 = d2 = d , (66) reduces to a much simpler expression, VR = 20 ad2 ln1 + exp−R
, that does not show the previously noted  dependence. The  superscript in the previous relationships refers to an overlap between double layers occurring at constant potential. For the other case (constant charge), an additional term has to be subtracted [51]:  VR = VR −

2 20 a1 a2 d1

+ a1 + a2


2 d2


ln1 + exp−2R


(67)

Again, when a1 = a2 = a and d1 = d2 = d , (67) reduces to a much simpler expression, VR = −20 ad2 ln1− exp−R
. For large distances (R ≫ 1) both equations

Figure 8. DLVO (Deryaguin, Landau, Verwey, and Overbeek) theory for the stabilization of colloidal particles with radius a against van der Waals attraction (Hamaker constant A). The four curves were computed using a potential fixed by the PZC of the particles: 0 (mV) = 257 × (PZC − pH) = 257pH. These curves are the result of adding an attractive contribution, VA R
= −Aa/12R, to a repulsive one, VR (eV) = 0018 × a (nm) pH2 exp−R
coming from the osmotic pressure induced by the compression of the diffuse layers characterized by their thickness −1 .

576 the conditions VT = VA R
+ VR R
= dVT /dR = 0 to this particular form leads to  240 d2 2z2 F ccc R = 1 ⇒  = = Ae RT0  
4 
RT 0
3 d 288 2 (68) ⇒ ccc = e2 F 2 A2 z2

This interesting formula shows that the sensibility of a given dispersion to an increase in ionic strength is governed by two main factors. The first factor depends mainly on the physicochemical state of the solvent (temperature, dielectric constant ) and on the chemical nature of the dispersed solid phase (Hamaker constant A). Typically a high sensitivity (low c.c.c. value) is expected for materials displaying large polarizability and high density (high Hamaker constant) dispersed in apolar solvents (low dielectric constant) at low temperature. The second factor involves the valency z of the added ions and the electrokinetic potential ∼ d . Here, high sensitivity means low electrokinetic potential and large valency. Recalling that from the Poisson–Boltzmann equation we have d = −0 d with  ∝ z, we may expect that d ∝ z−1 , providing a nice explanation for the empirical Schulze–Hardy rule. The top right curve in Figure 8 shows the effect of changing the surface potential 0 = RT/F ln 10
PZC − pH
at constant Hamaker constant, size, and ionic strength. At the PZC, the attractive term dominates while for pH ≥ 1 a high maximum always exists. The bottom left curve illustrates the effect of changing the Hamaker constant at constant ionic strength, size, and surface potential. It shows that materials such that A > 1 eV are not good candidates for making stable dispersions. A very high surface charge or low ionic strength is mandatory in this case. At last, the bottom right curve shows the effect of the nanocrystal size at constant ionic strength, surface potential, and Hamaker constant. The interesting point is the absence of maximum for small particles. A direct consequence of this fact is that during a precipitation experiment involving aggregation, the smallest crystals should be selectively removed from the solution, while the largest ones would remain unaffected. This means that starting from a highly polydisperse system, a narrowing of the size distribution is to be expected. This explains the possibility of getting, for any kind of material, dispersions displaying very narrow size distributions as exemplified by the beautiful work of Matijevic [25]. Here, through a fine-tuning of experimental conditions it should be possible to heal by aggregation the inescapable polydispersity generated by nucleation and growth or Ostwald ripening processes.

5.6. Entropic Forces We have so far discussed only enthalpic stabilization. Another possible stabilization mechanism would be to play with entropy instead of enthalpy. In fact, steric stabilization through the adsorption of polymeric species is of widespread use. Accordingly, a polymer can adsorb on the surface of a colloidal particle because of various interactions (charge– charge, dipole–dipole, hydrogen bonding, or van der Waals) acting alone or in combination.

Nanocrystals from Solutions and Gels

5.6.1. Depletion Interaction When a surface exerts no net attraction on the polymer, a net attractive force may nevertheless exist between the two colloids coming from the unsymmetrical repartition of the osmotic pressure between the overlapping and nonoverlapping zones. Assuming a perfect gas behavior, this osmotic pressure  = r
kT should be proportional to temperature T and to the local density r
in solute species (here polymers) at distance r from the surface. Let us further assume that the local density r
is close to the bulk density of solute S , and that the distance d is smaller than the sum of the diameters of colloidal C and polymeric species S d < C + S
. Then it is clear that solute species considered as hard spheres should be excluded from the central volume Vc , leading to a nil osmotic pressure in this central zone. To this depletion phenomenon [56] is associated an attractive potential between the two surfaces given by Vdep = −Vc = −kTS Vc . It should be realized that this depletion force is not always attractive. If one looks the interaction at a larger distance (C + S
< d < C + 2S
, then one finds a repulsive potential. Accordingly, as there is now enough room between the two surfaces, a polymer approaching a surface is pushed against it (negative adsorption) by the osmotic pressure unbalance existing between the surface zone (no polymers) and the bulk solution (density S
. Consequently, the local density in polymers in the middle zone should be higher than in the two opposite directions, leading to a neat repulsive force. For a still larger distance (C + 2S
< d < C + 3S
, the potential is again attractive because we have now a system of two coated surfaces displaying again an excluded volume for other polymers in the middle zone. In fact, one may understand that the effective potential for a system of large hard spheres (colloids) in contact with a large amount of smaller hard spheres (polymers) is not a regular one. It always displays a strong attractive component at very small distance (naked surfaces) and displays regular oscillations (period ruled by S
at longer distances. The higher the volume fraction occupied by the small spheres, the more visible the oscillations and the longer the interaction range.

5.6.2. Positive Adsorption The depletion phenomenon (negative adsorption) will always exist when a polymer solution is near an inert surface. However, if the attractive forces are strong enough, the enthalpy gained overcomes the entropy lost, leading to the model at the bottom of Figure 9 [56]. In this model [57], the links in contact with the surface are called trains. These are adsorbed on the surface, by physical forces invoked above. The loops may be defined as parts of the polymer connecting two trains but displaying no contact with the surface. Finally, the tails are all the nonadsorbed chain ends pointing outside the particle. Using this model, one may define the bound fraction as that fraction of chains forming trains. At very low polymer concentrations, a “pancake” conformation having a relatively large bound fraction may be formed. In this conformation, as there is plenty of room at the surface, the chains in contact with the surface tend to spread out. At higher solution concentrations, severe competition for the available space may occur, leading to shorter

Nanocrystals from Solutions and Gels

577 Provided that a loop or a tail does not approach full extension, the probability that it extends randomly from an arbitrary point (x y z
to another point x + dx y + dy z + dz
should be given by a simple Gaussian distribution, leading to

10 9 8 7 6 5 4 3 2 1 0 0.0 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

W =

n

Wi = N0

Figure 9. Colloidal interactions between solids and polymeric chains. For inert interfaces only depletion and negative adsorption may occur (existence of an excluded volume shown in black leading to osmotic pressure unbalance !). Positive adsorption and steric stabilization require some affinity between the surface and the chains. Bridging flocculation is very often observed with small nanocrystals.

trains. In this case, long tails and loops stick out into the solution leading to a “brush” conformation. At last another possibility is that when two particles are brought together it may occur for the loops and tails of one polymer to attach them to bare patches on the other approaching particles (top right drawing in Fig. 9). Obviously, this bridging process is favored if the adsorption density of the polymer is not too high and should be most successful for half-surface coverage and small colloid size.

5.6.3. Relaxation Time Let us now have a closer look at the dynamic aspect of the collision between particles coated with polymeric chains. Relaxation time involved in the adjustment of the conformation of an adsorbed chain or loop has been estimated to be 2 × 10−4 s for polystyrene (M = 50 000) in a liquid with viscosity 0.2 Pa s [49]. On the other hand, adjustment of the loop size distribution is a much slower process requiring several minutes. For these systems, the time involved in a Brownian encounter should be defined as the time needed to travel over a distance equal to the thickness of the adsorbed polymeric layer  B ∼ 2 /2Dp = 32 a/kT. For a viscosity  = 1 Pa s at T = 298 K, B  s
= 23 × anm
× nm
2 . With 1 ≤ a ≤ 100 nm and 1 ≤  ≤ 10 nm, we find that the conformation adjustment can follow the collision process. This is not the case for loop size redistribution.

5.6.4. Steric Stabilization With the help of this model, it is easy to track the entropic origin of the steric stabilization. Let W be the total number of conformations available to the system. Then the corresponding entropy S should be given by the Boltzmann definition S = k lnW
. Let n be the number of loops or tails, let N0 be the number of allowed conformations, and let r 2  be the mean square end-to-end distance for each loop or tail.

Wi

i=1




3 2r 2 

3/2

  3 xi2 + yi2 + z2i exp − (69) 2 r 2 


2 2 In this expression we may replace each xi2 y i , and zi n 2 by the mean-square average for the assembly: i=1 ui = u2  u = x y z
. The resulting conformation entropy SC may then readily be expressed as 3/2
3 SC = k ln W = nk ln N0 2r 2 

−

3nk x2  + y 2  + z2 
(70) 2r 2 

Let us now consider that the loops are deformed along the x direction at constant volume. Relation (70) still holds, but the mean-square averages are now xd = "x x yd = "x y zd = "x z, with "x "y "z = 1 "2y = "2z = 1/"x = 1/". For an isotropic medium all directions are equally probable, so that on the average x2  = y 2  = z2  = r 2 /3 leading to 
nk 2 2 (71) " + −3 S"
= SC − 2 " Consequently, any deformation of the loops or tails occurring during a Brownian collision has an unfavorable entropic cost V = −2T S"
− S" = 1
 = nkT "2 + 2/" − 3
. The curve at the top of Figure 9 shows the steep increase in energy provided by the compression of the polymeric chains occurring when the distance between two coated particles is reduced. Obviously, this repulsive potential could play the same role as the repulsive V R
term of the DLVO theory. When added to the attractive VA R
term, it should also lead to a maximum at some distance R. Let us also notice that when the chains belonging to two particles start to overlap, this amounts to a local increase of the concentration. Consequently, besides the repulsive force coming from the volume restriction, another repulsive contribution coming from the apparition of an osmotic pressure is also present (depletion).

5.7. Kinetics of Aggregation We are now in a position to treat the full problem of irreversible aggregation by looking at the time evolution of the aggregate size distribution.

5.7.1. Von Smoluchowski Equations The kinetic equations that must be used had been derived as early as 1916 by Max Von Smoluchowski trough the use of aggregation kernels Kij associated with the following irreversible reaction: i + j → i + j. Here the notation [i] refers to the ensemble of aggregates containing i particles

Nanocrystals from Solutions and Gels

578 while the Kij carry all the physical and chemical aspects of the collision. The equations may be written by noticing that [k] species may appear in solution as a result of the reaction between [i] and [j] species such that i + j = k. But the same [k] species may also disappear after reaction with any [i] species. Consequently, if ck stands for the number of aggregates of size k per unit volume, the time evolution of this concentration should be given by  dck 1  Kik ci ck = K cc − dt 2 i+j=k ij i j i

allowing one to find an analytical solution. Inserting Kij = K into (72) allows one to perform the following factorizations: C=



k=1

ck

 dck K k−1 c c − Kck C = dt 2 i=1 i k−i

⇒

 dck dC KC 2 = = − KC 2 dt dt 2 k=1

⇒

(72)

=−

KC 2 2

(76)

The 21 factor is there to avoid double counting in the first sum describing the creation of species [k]. As all the physical and chemical aspects are encapsulated in the Kij kinetic constants, all the problems lie in getting a meaningful i j dependence of these kernels and in the resolution of an infinite system of coupled equations. As for the nucleation and growth steps, it may be useful to consider two limiting cases: diffusion-limited and interface-limited aggregation.

If we start from an initially monodispersed system (i.e., at t = 0 we have c1 = c0 and ck = 0 for k > 1), then the variations with time of the total concentration in clusters Ct
or in single particles c1 t
are obtained after integration of (76):

5.7.2. Pure Diffusion Kernel

c1 t
, c2 t
may be obtained from (76) by making k = 2 leading to dc2 /dt = c0 1 + t
−3 − 2c2 t
1 + t
−1 where we have set  = Kc0 /2
. A solution to this equation may be easily found by setting c2 t
= gt
c0 1 + t
−3 with gt
satisfying the differential equation dg/1 + g
=  dt/1 + t
[i.e., gt
= t]. These two particular solutions for k = 1 and k = 2 may be put under the following general form:

If there is no chemistry involved in the sticking of two aggregates, we may use diffusion equations to get a kernel Kij . Here, we are interested by the probability Pij that a cluster with radius Ri shall be hit in the time interval dt by another cluster of radius Rj having the concentration cj . This probability should be equal to the diffusion flux ij into a sphere of radius Rij = Ri + Rj
. From Fick’s first (j = −D × grad c
and second laws dc/dt = D# 2 c
the concentration c t
of species [j] at a distance  from the center of the sphere of radius Rij may be written 
  − Rij Rij 1 − erf √ c t
= cj 1 −  2Dt
 c dc j ⇒ ij = lim = t→ d R ij =Rij

Ct
=

(73)

⇒

Kij = Di + Dj
Ri + Rj
(74)

Now, the Stokes–Einstein equation D = kT/6R and the fact that for compact objects Rk = R1 × k1/3 lead to Kij =

kT 1/3 i + j 1/3
i−1/3 + j −1/3
6

(75)

5.7.3. Getting an Analytical Solution Consequently, even for the simplest situation, the problem has no analytic solution. However, one may notice that there is no i j dependence when i = j as Kii = 4kT/6 = K. This suggests that one look at what the solution will be if Kij = K for all clusters (even those for which i = j). This is obviously a considerable simplification of the problem,

c1 t
=

c0 1 + Kc0 /2
t2 (77)

Kc0 t/2
k−1 1 + Kc0 t/2
k+1
2  k+1
k 1 4 k2 ck t
= 2 K c0 t 1 + 2/Kc0 t


(78)

It is easy to show that (78) is a general solution to (76) leading to dck t
=0 dt

As both clusters are undergoing Brownian motion, their relative diffusion coefficient should be Drel = Di + Dj
. With this diffusion flux of matter, the sticking probability may easily be evaluated as Pij dt = 4R2ij Drel ij dt

⇒

ck t
= c0 ⇒

c0 1 + Kc0 /2
t

k − 1
Kc0

⇒

t=

⇒

ckmax = 4c0

k − 1
k−1
k + 1
k+1


(79)

5.7.4. Discussion Consequently, for a given k > 1 ck goes through a maximum and tends to zero as t −2 for very large times. In this last case (i.e., when t ≫ 2/Kc0 ), the power term in (78) may be developed as 

1 1 + 2/Kc0 t


k+1


≈ 1 − 2/Kc0 t
k = expk ln1 − 2/Kc0 t


2k ≈ exp − Kc0 t

(80)

This shows that for a given time, the size distribution has the shape of a decreasing exponential whose decreasing rate becomes smaller as time increases. It also means that the

Nanocrystals from Solutions and Gels

579

size distribution function may be written under an interesting scaling form
 

kck c0 Kc0 k = k=1 = = 1 + t

Ct
2 k=1 ck
 k ⇒ ck t →
= k−2 exp − k

(81)

The important point in this relation is that the k and t dependence of ck t
is given through an universal function of a single variable k/kt
 ∝ k/t  that does not depend on the initial distribution. For the present case the scaling exponents were  = 2 and  = 1.

5.8. Fractal Geometry Obviously, the case of constant kernel Kij = K is interesting by its analytical solution but not very realistic and one may seek a more general solution. To do that we may notice that according to (75) Kij kernels are invariant under any scaling " as K"i "j
= Ki j
. In fact it may be shown that it is this very particular scaling relation that is responsible for the asymptotic scaling of the solutions ck ∼ k−2 exp−k/k
. Let us recall that (74) and (75) were derived under the assumptions of dense aggregates undergoing Brownian motion. A direct observation of these aggregates by transmission electron microscopy has in reality shown that their structures were highly ramified and tortuous exhibiting a scale invariance [59].

A direct measure of this scale invariance is provided by the associated fractal dimension  [60]. Figure 10 (top right) shows how a bidimensional (d = 2) fractal object may be generated by sticking together identical spherical particles of diameter . First, a seed sphere is centered at the origin. In a second step, four other spheres are added at the left, right, top, and bottom of the seed. In a third step, the ensemble of five spheres is considered a unique object, on which four similar objects may be added using the same rule as before. After a large number of iterations, it is easy to see that the resulting highly ramified object has a diameter L = 3p  and contains N = 5p spheres. Now a fractal object characterized by a fractal dimension  may be defined by the property that the minimal number of spheres N of diameter  needed to cover its matter scales like N ∼ − . In the present case we have L = 3p  ⇒ ⇒

N = 5p ln N lnL/
= p= ln 3 ln 5
 ln 5 L = ≈ 147 N =  ln 3

(82)

The fact that  < d = 2 is here the geometric expression that the object displays holes at any scale. The same model could be used to derive a fractal dimension when d = 3. At each step, we have to add two similar objects above and below the plane. For the same diameter, the number of spheres is just N = 7p−1 + 6 × 7p−1 = 7p , leading to  = ln 7/ ln 3 = 177 < d = 3. Table 6 gives the fractal dimensions observed for some physical processes leading to highly ramified structure. As can be seen the ideal value of  = 177 is found to be very close to that found for Brownian cluster–cluster aggregation. This should not be very surprising, as fractal dimensions are universal exponents that do not characterize uniquely the geometry of ramified objects. They just inform us about the kind of growth mechanism that has been used in order to generate the aggregates. Consequently, all objects grown using a hierarchical cluster– cluster mechanism should share the same fractal dimension close to 1.8, even if their local structure may appear quite different.

〈k〉

k/〈k〉

5.8.1. Fractal Dimension 

Table 6. Some fractal dimensions Df for physical processes leading to ramified structures (compiled from [59]). Structure

Figure 10. Aggregation and fractal aggregates. Top left shows the fractal ( < 1/2) and limited aggregation ( < 0) regimes. Bottom left illustrates the case ( ≥ 1/2) leading to a divergence of the mean cluster size (gelation regime). Top right diagram shows how a fractal object may be generated through iteration of simple rules. Bottom right is a 3D-percolation cluster characterized by the fractal exponents  = 253  = 184 $ = 130 = 187 = 1143 = 389  = 2548 and " = 1374. Black spheres correspond to the backbone ( = 187), large gray spheres to the red contacts ( = 1143), and small white spheres to dangling ends.

Solvated linear polymer Brownian cluster–cluster aggregation Ballistic cluster–cluster aggregation Ideal linear polymer Solvated branched polymer Chemical cluster–cluster aggregation Ideal branched polymer Diffusion limited aggregation Percolation cluster Ballistic limited aggregation Dense particle

Df 166 177 191 20 20 204 216 250 249 2.8–3.0 30

580 A direct consequence of this matter of fact is that fractal dimension gives only information on the total mass MR
∼ R found in a sphere of radius R. In particular, it does not give any details concerning the connectivity properties (the way masses are connected in space). In order to describe these connectivity properties, several other scaling exponents have to be used [59, 60].

5.8.2. Bond Dimension  The bond dimension " (or tortuosity) gives the minimal distance L = R" that must be covered by a walk entirely contained in the object in order to go from two points separated by a Pythagorean distance R. A high " value means that very tortuous circumvolutions are present between one point in space to another. However, since the minimum path in the cluster should not be shorter than the Pythagorean distance d nor longer than a complete random walk, we should have 1 ≤ " ≤ 2. Usually this exponent is evaluated through the use of numerical simulations. For instance, it has been found that diffusion-limited aggregates (" = 102) are much less tortuous than cluster–cluster aggregates (" = 125) [61]. The most tortuous structures are found with 3D-percolation clusters (" = 1374) [62] or branched polymers (" = 136) [63]. One may notice that both  and " are extrinsic dimensions as they link a fractal property of the object (mass M or minimal walk L
to a Pythagorean distance R measured in an Euclidian space.

5.8.3. Topological Dimension  The topological (also graph or chemical) dimension  gives the total mass ML
∼ L visited along a walk of distance L entirely contained in the object. It may be noticed that this last exponent is not independent of the two others  and . Accordingly, as L ∼ R" , M ∼ L ∼ R , it comes that  = ". For determinist fractals one usually have either  =  (e.g., the Sierpinski gasket displaying no tortuosity but only lacunarity) or  = 1 (e.g., the Koch curve that has no lacunarity but is tortuous at all length scales). In contrast, with the fractal or bond dimensions,  is an intrinsic dimension as it links two properties (mass M to the minimal length L
of a given fractal object. This fact is also expressed by the relation  = /" showing that the ratio of two extrinsic dimensions should be another intrinsic one.

5.8.4. Spectral Dimension  The spectral dimension $ affects all properties depending not only on space (static dimensions) but also on time (dynamical dimensions). This exponent is linked to the number S ∼ M ∼ t $/2 of distinct sites visited by a random walk (the de Gennes “ant” [64]) after t-steps, or to the probability P0 ∼ t −$/2 that the ant ends up at time t on its starting point. As $ is clearly an intrinsic property independent of the embedding space, it should also be expressed as the ratio of two other extrinsic dimensions. For example a random walk in ordinary homogeneous space is such that the mean square distance varies proportionally to the time R2  ∼ t, the proportionality factor R2 /t being the diffusion coefficient. Consequently, for a random walk occurring on a fractal structure one may expect that the mean

Nanocrystals from Solutions and Gels

square displacement will scale like R2  ∼ t 2/ , the extrinsic exponent > 2 characterizing the fractal walk. Writing that M ∼ R2 
/2 ∼ t / ∼ t $/2 shows that we have $ = 2/ . The intrinsic exponent $ ratio of two extrinsic dimensions affects all transport properties in a fractal medium. For example, the diffusion coefficient is no more a constant but must depend on the distance R as R2− . A similar relation holds for electrical conductivity that becomes size dependent. Concerning the low-energy behavior of the phonon density of states it becomes nE
= E $/2−1 , leading to a density of states per unit frequency 
= $−1 (fractons) [65]. A consequence is that the specific heat at low temperature T scales like T $ . One of the big advantages of the spectral dimension is that it can be either measured on real objects (mainly through light or neutron scattering) or computed from simulations by at least three independent ways. Strangely enough, very close $ values were found from two very different fractal models (percolation cluster with $ = 130 [66] and diffusion-limited aggregates with $ = 135 [61, 67]). This has led to the conjecture that some fundamental link should exist between static and dynamic exponents. For instance, following conjecture = 3/2 (or $ = 4/3 ∼ 133) [65] may help to explain these data. However, this conjecture does not hold for lattice animals that are characterized by $ = 119 [63] and for screened growth aggregates characterized by $ values ranging from 1.10 to 1.22 [68]. However, it may be demonstrated that for any fractal for which loops are irrelevant one should have $ = 2/ + 1
[68]. This shows that a relation between static and dynamical exponents may occur but only on structures displaying no loops. According to this last relationship, if cluster–cluster aggregation ( = 142) leads to fractals with no loops, their spectral dimension should be $ = 118.

5.8.5. Backbone Dimension  Another exponent has to be introduced for dealing with mechanical properties of fractal aggregates. This is backbone dimension that is always less than the fractal dimension . It allows one to differentiate between domains connected by at least two contacts and dangling ends that are connected to the backbone only once and hence have no effect on mechanical properties. The backbone dimension is thus the fractal dimension of the object generated by removing all dangling ends to a given fractal. Going one step further one may differentiate between red contacts and blobs. Red contacts are those parts of the backbone whose removal cuts the object into two independent pieces (particles with coordination number equal to 2). The isolated clusters remaining after this operation and made of all particles having a coordination number of at least 3 are the blobs. The new object made by all the blobs has its own blob dimension

that should again be less than the backbone dimension. The backbone and blob dimensions are currently known only from numerical simulation (for a 3D-percolation cluster  = 253 > = 187 > = 1143
[69].

5.8.6. Hull Dimension  Another important exponent for fractal interfaces is the hull dimension  [69]. This exponent relates the external perimeter or surface of the aggregates to the Euclidean distance

Nanocrystals from Solutions and Gels

between two points. The hull consists of all cluster sites that are connected to infinity through an uninterrupted chain or plane of empty sites. In other words, it is the negative imprint of the aggregates onto the embedding space. Like the backbone and blob dimensions it is currently known only from numerical simulation (for a 3D-percolation cluster  = 2548).

5.9. General Solution The previous section has shown that the properties of a fractal object cannot be obtained by rewriting formulae valid on 3D-Euclidean space and simply replacing 3 by . In fact, one may rigorously define an 3D-Euclidean object by the fact that  =  = $ = = = 3, =  = 2, and " = 1. This degeneracy no longer holds for a fractal such as a 3D-percolation cluster where  = 253  = 184 $ = 130 = 187 = 1143 = 389  = 2548, and " = 1374 [69]. Obviously, it would be hopeless to find an analytical model able to explain all these values from a given set of kernels Kij . For such situations, numerical simulations are obviously of considerable help. Also, it would have been a very naïve attitude to take the kernel (75) and simply write Kij = kT/6
i1/ + j 1/
i−1/ + j −1/
with the hope that everything will run fine. Even if such expression may be found in a large number of papers or textbooks, it is definitely not correct to use the consequence of a growth process (a fractal object characterized by various exponents   $  ") as the ultimate cause of its appearance. A more correct approach is to guess some general properties for the aggregation kernel Kij from physical principles. Then one may seek either an analytical or a numerical solution to see if the resulting fractal matches some experimental structure.

5.9.1. Realistic and Simple Kernel The really fundamental point in (75) lies in the scale invariance of the aggregation kernels K"i "j
= "0 Ki j
. In this last expression, we have emphasized the null power of the scale parameter " because one may expect that in the more general case we should have K"i "j
= "2 Ki j
. However, we have to restrict the values of  to the range  < 1, since the averaged active sites in an aggregate cannot grow faster than its size i or j [70]. Another physically acceptable assumption is that the largest cluster (say cluster [i]) that has the slowest diffusion rate would be explored for a possible reaction among its i accessible sites by the smallest one [j] that has the largest diffusion coefficient. As far as seeking the simplest model able to handle the largest number of experimental cases, there is no loss of generality to consider the homogeneous kernel: Kij = kT/6
i1 × j 2−1 . The advantage of this quite simple formulation is that all the complex interfacial physics and chemistry are contained in the single -exponent characterizing the most active aggregate. The restriction comes from the unit power affecting the i-cluster. This choice reflects the possibility for species [j] to have full time to explore all exposed sites on cluster [i]. Consequently, we are limiting ourselves to the case of interface-limited aggregation. The case of diffusionlimited aggregation and derived models will thus not be

581 covered. However, as it corresponds to an unphysical mechanism for nanocrystal aggregation in solution, we are safe. Another important physical aspect contained in our kernel is the existence of a critical -value ∗ = 21 for which the kernel becomes independent of j. At this critical point, any [j] species, whatever its size, is able to stick to any i site. This is a very clear signal for gelation to occur and one may understand that two qualitatively different regimes may be anticipated.

5.9.2. Gelation Regime Gelling kernels are characterized by  > 21 (Fig. 10). In this regime it may be shown [71] that there exists a finite time tg such that
 2 − 1 c k ⇒ ck t < tg
= 0   tg = 2c0 k k with k ∝ tg − t
2/1−2


(83)

In this equation  ∝ kT/
is a kinetic constant function of temperature and solution viscosity and  is a universal scaling function such that x
∼ Bx− . The exponent  should be such that  = 2 + 3
/2 > 2 ensuring that the mass flux of finite particles (sol) to the infinite cluster (gel) remains bounded for any time t > tg . As  > 21 (83) shows that the mean cluster size k diverges when t → tg . In the postgel stage (t > tg ) the size distribution is qualitatively different and takes the form ck t
∼ Bt
k− with again  = 2 + 3
/2. For this regime,  > 21 , to occur the key point is that we should have a size selectivity mechanism favoring aggregation of large species over smaller ones. This is well evidenced by the power law ck t
∝ k− (with  > 2) or by the positive contribution in our Kij kernel of the power of [j] (2 − 1 > 0 ⇔  > 21 ). As soon as  < 21 , the power reactivity of [j] species becomes negative explaining the crossover toward a regime where the size selectivity mechanism favors small clusters over larger ones. Therefore, the probability of finding an infinite cluster occupying the whole solution volume becomes zero in which case only precipitates or sizelimited aggregates should be formed (Fig. 10).

5.9.3. Fractal Regime One of the amazing things in this  < 21 regime is that the scaling invariance K"i "j
= "2 Ki j
is sufficient to determine the asymptotic shape ck t
∼ k−2 k/k
of the solutions to the Smoluchowski kinetic equations [70, 71]. In this case, the average cluster size k ∼ t  carries all the time dependence, whereas the universal function  governs the shape of the size distribution. As this function is universal, it does not depend on the complex details of the aggregation kernels and can be determined by just looking at the most probable configuration coming out of a multinomial distribution [70]   knk nk N = Nc = k

k

⇒

nk =


 N − Nc 2 1 − 2
1−2 Nc2  1 − 2
N − Nc kNc
1−2
Nc k × 1− (84) N − Nc

Nanocrystals from Solutions and Gels

582 In this equation, nk = ck × V , where V is the total volume of the solution and  is the gamma function. This expression may be further simplified by introducing the reduced variable x = k/k = Nc k/N and taking the limit Nc → 0 leading to nk =

N x
k2

⇒

x
=

1 − 2
1−2 −2 exp−1 − 2
x x  1 − 2

1 (85) < 2

As explained, the mean cluster size k carries all the time dependence that may be expressed as [71] k =

N ∼ 1 + c0 1 − 2
t1/2−1
∼ t − Nc with  =

1 1 − 2

(86)

Figure 10 shows the behavior of the normalized size distribution x
for several values of the  exponent. It is seen that when 0 ≤  < 21 , the size distribution displays a monotonic exponential decreasing behavior. Interestingly enough, when  = 0, we recover exactly the analytical solution of the Von Smoluchowski equation at constant kernel Kij = K.

5.9.4. Limited Aggregation Regime When  < 0, another qualitative change of the size distribution occurs. Instead of a monotonic decrease, we have now a bell-shaped curve leading to a narrowing of size distribution as  decreases. This crossover between a highly polydisperse size distribution ( > 0) and a more monodispersed limited aggregation ( < 0) is again well modeled by the Kij ∝ i1 × j 2−1  kernel. Accordingly, when  = 0, we get the most symmetric kernel Kij = i/j meaning that no clear distinction exists between the explored cluster and the exploring one. This is no more the case when  > 0 modeling a situation where the most probable events are the sticking of the any [j] species onto the dangling ends of the slowly moving [i] clusters. One may then understand that the result of this site selectivity (dangling ends more reactive than the backbone) would be a polydisperse collection of objects displaying holes at any scale. The situation is also unsymmetrical when  < 0. In this regime, we may say that dangling ends are poisoned becoming inactive toward sticking. By consequence, the largest [j] species, being able to explore only the outer tips of the larger [i] clusters, cannot participate in the growth process anymore. In this case, the better the poisoning, the lower  and the better the selectivity both in size (only the smallest species are allowed) and in site (backbone free of poison becomes more reactive than dangling ends). This explains the crossover from a fractal regime toward a more compact regime characterized by a bell-shaped size distribution (larger clusters just “eat” the smallest ones without being eaten by their congeners). A high compactness may be expected for large negative values of , as only very small aggregates are allowed to explore the whole backbone in

order to fill any hole. The larger ones are still there but they are staying quietly outside waiting their turn to fill the holes. Because of this hierarchical mechanism based on a full osmosis between size and site selectivity, one may also expect a strong narrowing of the size distribution as evidenced in Figure 10.

6. CONCLUSION We are now at the very end of the description of all the physical and chemical processes that may cooperate to make nanocrystals appear from initially homogeneous solutions. We have taken care to cover the whole size range, from molecular solute species displaying sizes less 0.5 nm up to macroscopic crystals or gels having size higher then 1 cm. Besides size, one may notice that we have also covered the whole time range starting from nucleation (t = 0) and ending with ripened crystals or aggregates (t → ). At each step, analytical expressions have been derived, because this is the only way to be able to fully understand the underlying physics or chemistry involved in experimental or simulation results. At this stage, we want to stress that all the derived equations are in fact very new, even if they share the same analytical shape with already published ones. The novelty comes from the fact that they are all clearly interpreted on a molecular basis, leading to deep conceptual modifications in quite old theories. Moreover, as we have for the first time a full coverage of precipitation from solutions, it is worthwhile to emphasize where fundamental changes have occurred. This will also help us to point to the directions where considerable work remains to be done to get a fully quantitative picture. Concerning nucleation theories, the deep change was the explicit introduction of a kinetic barrier G′ linked to the complex underlying chemistry involved in embryo formation. This chemistry has been reviewed and orders of magnitude have been given. The presence of this additional contribution has led to the appearance of a sticking probability gN = exp−G′ /kT
in the pre-exponential factor J0 of the nucleation rate. It was the neglect of this fundamental factor in older theories that explains the differences often observed with experimental measurements [10]. It also allows one to close definitively the controversial discussion relative to homogeneous versus heterogeneous nucleation. Accordingly, for homogeneous nucleation, it was shown that gN carries purely chemical structural information. In all the cases where nucleation is really induced by impurities or defaults, gN carries additional information about the size of the heterogeneous host and about its chemical nature through a contact angle. In fact, with the introduction of this sticking probability, we have reached the ultimate correct formulation of equilibrium nucleation theory resolving most discrepancies with experiments. Going one step beyond would require one to use nonequilibrium thermodynamics based on entropic fluxes avoiding the use of thermodynamic potentials (Gibbs function) that just cannot be defined for irreversible processes such as nucleation. By symmetry, the same conceptual change has been introduced in interface-limited crystalline growth, through another kinetic barrier G′′ and through the associated growth sticking probability gC = exp−G′′ /kT
. Another

Nanocrystals from Solutions and Gels

quite novel aspect was the derivation of Eq. (35) for spiral growth that has never been published before. Here also a deep conceptual change has occurred. In older theories, the accepted paradigm was Solution → Embryo → Nucleus  Diffusion  

 Mononuclear → Interface → Polynuclear    Spiral


This widely accepted view has several conceptual difficulties. First, diffusion should be the rate limiting step only for gC ∼ 1, a very rare case. Second, the most efficient mechanism (spiral growth) plays a minor role in crystalline growth literature and is usually treated separately from diffusionlimited or interface-limited growth. A much more logical scheme emerges by taking into account the existence of a growth sticking probability: 

Diffusion  Spiral → Polynuclear Solution → Embryo → Nucleus →  Mononuclear ↑

Here, just after nucleation, the created interface may act either as a catalyst or as an inhibitor for solute species incorporation. In the first case (gC > gN ), we invoke the most efficient mechanism avoiding the bottleneck of surface nucleation. However, owing to its very high efficiency, it very soon ends up either in the bottleneck of diffusion (gC ≫ gN ) or switching to the polynuclear mechanism if several spirals compete (high sursaturation ratios) for the same limited crystal volume. The essential point is that as the final morphology is always governed by the slowest growth mechanism, the only chance to see well-developed spirals is to use the sursaturation ratio very close to unity. The second case (gC ≪ gN ) means that for some chemical reason, the most reactive growth sites are poisoned. The spiral growth relying on the presence of these active sites is then killed. The only way to proceed is to make somewhere in a flat zone a 2D nucleus that will first grow independently from other nuclei (mononuclear mechanism) and then start to overlap (polynuclear mechanism) at some stage. Future work along these lines would be to reinterpret already published data and design new experimental settings and experiences to validate definitively this simple and logical picture. Few novelties have been brought in the section devoted to the role of the interface on the growth process. This is because the most important conceptual change (existence of a point of zero interfacial energy or PZIE) has been treated elsewhere [41]. Nevertheless, some new features have been added in order to get a deeper coherence. First, we have pointed to a useful link between the Frank and Wen model of solute–water interface and the double layer model (Stern and diffuse layers) for oxide–water interfaces. Then explicit expressions for the PZIE, Eq. (46), and equilibrium sizes, Eq. (47), have been derived. Finally, a more logical derivation from the Cardan formula of the  = 9/4 value allowing one to solve ripening equations has been proposed. Future work should obviously be oriented toward the elaboration of simple models for nonoxide and nonaqueous solid–liquid

583 interfaces. New solutions for the ripening equations covering interface-limited growth also have to be derived. The last section dealing with aggregation processes is surely the most critical one. This is just because, due to their small sizes, individual nanocrystals cannot remain isolated from their congeners. For the same reasons that molecular species may be assembled through weak bonds into supramolecular species, nanocrystals should be used as building blocks for making supracrystalline aggregates. In fact, it may be realized that all major applications involving nanocrystals should handle a more or less ordered array of such objects and not a disordered set. Consequently, if the control of the final size distribution of an assembly of nanocrystals is of the utmost importance, the control of the corresponding mesoscopic or macroscopic texture is yet another scientific challenge. This is the reason we have tried to introduce the very confusing literature devoted to aggregation processes in the most logical and synthetic way. First, we have attempted to make a clear distinction between enthalpy and entropic effects. Furthermore, if we have presented the quite old and criticized DLVO theory, it is just because no other simple theory is yet available. Consequently, if quantum electrodynamics is known to heal some obvious defaults of DLVO theory [72], it is of little practical use, being useful only in some pathological cases. Another highly confusing area concerns the geometric description of fractal objects coming out from aggregation processes. Here most published papers are concerned with the determination or measure of the fractal dimension  of the aggregates. One must realize that reducing such complex objects to a single real number is a considerable loss of valuable information. Moreover, fractal dimension being an extrinsic parameter, it just points to the kind of mechanism that has been used to generate the aggregate in our three-dimensional Euclidian space. In particular, it can say nothing about the internal architecture or detailed topology of the aggregate. To get this kind of crucial information for all practical applications, one has to rely on an intrinsic dimension such as the topological dimension  or the spectral dimension $. Being the ratio of two extrinsic dimensions (one of them being always the fractal dimension ), these intrinsic parameters helps us to understand the chemical or physical properties of the associated fractal object. Unfortunately, accurate determination of these very interesting exponents is rather rare and currently limited to ideal mathematical objects coming from numerical simulations. Future work should then be oriented toward the collection of a wealth of experimental data concerning these intrinsic fractal dimensions. Concerning the kinetics of formation of aggregates, a major conceptual change has been introduced through the Kij = kT/6
i1 × j 2−1  kernel. The simplicity of this kernel relative to other awkward expressions found in the literature is noteworthy. First, it allows one to understand the existence of three qualitatively different aggregation regimes: gelation (apparition of an infinite cluster if  ≥ 21
, fractal growth (exponential distribution when 0 ≤  < 21
, and limited aggregation (bell-shaped distribution when  < 0). Second, it avoids the widespread practice of putting at the origin (kernel Kij
the result (fractal dimension ) of the growth process. Obviously, what is still lacking is an analytical link between the exponent  and the molecular

584 chemistry occurring at the solid–liquid interface. This should be a major challenge for the coming years.

GLOSSARY Aggregate Large particle formed after irreversible sticking of several small colloidal particles. Aggregation Irreversible sticking of particles undergoing Brownian motion. Aggregation kernel Kinetic constant describing the process by which two aggregates containing i and j particles respectively leads to an new aggregate formed of i + j
particles. Aging Change of structure, morphology, or porosity with time. Aquo cations Soluble cationic hydrated species [M(H2 O)N ]z+ displaying low electrical charge z < 3
and stable at low pH. Backbone dimension Fractal dimension of an object generated by removing all dangling ends to a given fractal object. Blob dimension Fractal dimension of an object generated by removing all red contacts to a given fractal object. Bond dimension See tortuosity. Chemical dimension See topological dimension. Chronomal Mathematical integral equation Ix
describing the time evolution t = K×Ix
of a phase separation process in terms of a dimensionless reaction coordinate x and a kinetic constant K, see Eqs. (12), (26), and (33). Classical nucleation theory (CNT) Theory for nucleation based on equilibrium thermodynamics and mean field approximations. Cluster See aggregate. Coagulation Precipitation of a colloidal solution after addition of an electrolyte. Colloidal solution or sol Dispersion of solid particles (diameter 1–100 nm) in a liquid. Critical coagulation concentration (c.c.c.) Minimal electrolyte concentration allowing spontaneous coagulation of a colloidal dispersion. Critical nucleus Unstable concentration fluctuations that either redissolve or undergo further growth. Crystal Solid matter characterized by a well ordered atomic structure allowing X-ray diffraction. Crystal field stabilization energy (CFSE) Stabilization energy associated to a non-spherical charge distribution of electrons around the atomic nucleus of a transition metal element. Debye–Hückel length Thickness of the double layer function of the solution ionic strength, see Eq. (39). Depletion interaction Net attractive or repulsive force between two colloidal particles induces by the presence of a polymer in the dispersion medium. Diffuse layer Layer of counter-ions around a colloidal particle compensating at the OHP the sum of the surface charges and of the charges located at the IHP. The thickness

Nanocrystals from Solutions and Gels

of this layer is mainly function of the ionic strength of the solution. Diffusion controlled growth Growth during which the rate-limiting step is the diffusion of solute species towards the solid/liquid interface. Diffusion-limited aggregation Aggregation process during which the rate-limiting step is the diffusion of colloidal particles in the dispersing medium. Dislocation controlled growth Growth initiated on screw dislocations and bypassing the formation of a surface nucleus. DLVO theory Mathematical law giving the interaction energy of two overlapping diffuse layer as a function of their separation derived by first by Derjaguin, Landau, Verwey and Overbeek, see Eqs. (65–67). Electrokinetic potential In a colloidal dispersion, the difference in potential between the immovable layer attached to the surface of the dispersed phase and the dispersion medium (usually approximated by the potential at the OHP). Embryos Unstable concentration fluctuations that are doomed to redissolve at equilibrium. Extrinsic dimension Scaling exponent linking a property of a given fractal object to a Pythagorean distance measured in an Euclidian space. Fick’s laws Two mathematical expressions relating through the diffusion coefficient (i) the flux of matter to a gradient concentration and (ii) the variation of concentration with time to its laplacian. Fractal Mathematical object displaying holes at any scale. Corresponding physical objects are porous solids displaying porosity over several order of magnitude of scale length. Fractal dimension Scaling exponent  giving for an aggregate the total mass found in a sphere of radius R  MR
∼ R . Frank and Wen model Assumption of the existence of at least three structured domains for a solvent around a given solute (A = solvent in direct contact, C = bulk solvent and B = A/C interface). Frontier energy Energy needed for increasing the length of a given surface perimeter by one length unit. Fuchs integral Total flux of particles towards a given colloidal particle corrected for their possible interaction energy. Gel Dispersion of liquid droplets (diameter 1–100 nm) in a solid. Gibbs equation Relationship linking the decrease in interfacial energy to the concentration of adsorbed species (see Eq. (1)). Glass Solid matter displaying no crystalline order showing only X-ray diffusion. Gouy–Chapman theory Mathematical law linking the diffuse layer charge density to its associated potential at the OHP, see Eq. (40). Graph dimension See topological dimension. Growth constant Dimensionless constant incorporating shape factor, frontier energy, molecular volume, temperature, and ruling the change of the growth thermodynamic barrier with the sursaturation.

Nanocrystals from Solutions and Gels

Growth rate Rate of matter addition to an already existing particle and characterized by the rate of change of a characteristic length with time. Hamaker constant Energy parameter measuring attractive forces between surfaces, see Table 5. Hull dimension Scaling exponent relating the external perimeter or surface of a fractal object to the Euclidian distance between two points. Inner Helmholtz plane (IHP) Mean plane defined by all ionic species adsorbed into the Stern layer and not in direct contact with the surface of the colloidal particle. Interface limited aggregation Aggregation process during which the rate-limiting step is the irreversible sticking of two colloidal particles. Interface limited growth Crystalline growth during which the rate-limiting step is the formation of a surface nucleus. Interfacial energy or surface energy Energy needed for increasing the area of a given interface by one surface unit. Intrinsic dimension Scaling exponent linking two properties of a given fractal object. Isoelectric point (IEP) Solution conditions for which there is an equal number of positive and negative adsorbed species. Kinetic barrier Energetic contribution to the nucleation activation energy associated to the crossing of the solid/liquid interface. Langmuir isotherm Mathematical law describing the adsorption at a given interace of a single layer of ions, see Eq. (42). Lattice animals Connected subsets of the square lattice tiling of the plane used for modeling the theta transition displayed by branched polymers in a solvent. Loops Parts of a polymer connecting two trains. Metal alkoxides Organometallic complexes of general formula M(OR)z R = Cn H2n+1 ) leading after hydrolysis and condensation to metallic oxides MOz/2  M(OR)z + z/2 H2 O → MOz/2  + z ROH. Mononuclear growth Growth process occurring at very low sursaturation and during which a single surface nucleus is able to cover a whole crystalline face. Nucleation Formation of thermodynamically stables particles (solid or liquid) from an initially homogeneous medium (solid, liquid, or gas). It may occur either in the bulk (homogeneous nucleation) or at an interface (heterogeneous nucleation). Nucleation constant Dimensionless constant incorporating shape factor, interfacial energy, molecular volume, temperature, and ruling the change of the nucleation thermodynamic barrier with the sursaturation. Nucleation rate Number of nuclei formed per unit volume and per unit time. Nuclei Stable concentration fluctuations allowed undergoing further growth leading to ultimately to phase separation. Ostwald–Freundlich equation Relationship relating solubility to particle size, see Eq. (9). Ostwald ripening Change upon aging of the size distribution of a collection of particles owing to the occurrence of redissolution/precipitation phenomena.

585 Outer Helmholtz plane (OHP) Slipping plane for solvent molecule defining the thickness of the Stern layer. Oxo anions Soluble anionic species [MON ]2N −z
− displaying high electrical charge z > 4
and stable at high pH. Percolation A simple model in which sites on a lattice are randomly chosen and occupied and where nearest-neighbor particles are then considered to be connected, resulting in clusters of varying sizes and geometries. Percolation cluster Fractal aggregate percolating through an entire lattice network and whose formation is accompanied by the divergence of the mean cluster size and the range of connectivity. Point of zero charge (PZC) Solution conditions for which the surface of a colloidal particle is completely free of ionic species. Point of zero interfacial energy (PZIE) Solution conditions for which full covering of a surface by ionic species occur. Poisson–Boltzmann equation Mathematical law relating the laplacian of the potential to the charge density in volume and to the dielectric constant of the medium. Polyanions Small oligomeric species formed after adding an acid to oxo-anions. Polycations Small oligomeric species formed after adding a base to aquo-cations. Polynuclear growth Growth process during which several surface nuclei compete to cover the same crystalline face. Potential determining ions (PDI) Ions adsorbed on the surface of a colloidal particle or adsorbed into the Stern layer. Red contact Parts of the backbone of a fractal object whose removal cuts this object into two independent pieces. Schulze–Hardy rule Empirical law stating that the c.c.c. of a colloidal dispersion should vary as in the sixth inverse power of the electrolyte valency. Screw dislocation Crystalline defect arising from the occurrence of atomic stacking faults and moving perpendicular to the line joining the two points of an open circuit surrounding the dislocation (Burger’s vector). Shape factor Dimensionless quantity linking the volume or the surface of a particle to the cube or the square of its characteristic length (see Tables 2 and 4). Sol See colloidal solution. Spectral dimension Scaling exponent $ giving for an aggregate the number of distinct vacant sites S visited by a random walk involving t-steps S ∼ t $/2 . Spiral growth Growth process following a screw dislocation. Stability ratio Dimensionless parameter ruling the life time of a colloidal dispersion. Steric stabilization Stabilization of a colloidal dispersion by entropic forces (usually through polymer adsorption). Stern layer Compact shell of solvent molecules moving with a colloidal particle. Sticking probability Probability of incorporation of solute species according to Maxwell–Boltzmann statistics.

Nanocrystals from Solutions and Gels

586 Stokes–Einstein equation Relationship linking diffusion coefficient of a particle to its radius and to medium viscosity. Surface charge Density of adsorbed ionic species in direct contact with the surface of the colloidal particle. Surface energy See interfacial energy. Sursaturation Ratio between the concentration in solution at time t and the concentration at equilibrium (solubility) when t → + . Tails Non-adsorbed chain ends of a polymer pointing towards the solution. Thermodynamic barrier Energetic contribution to the nucleation activation energy associated to concentration fluctuations. Topological dimension Scaling exponent  giving for an aggregate the total mass M visited along a walk of distance L entirely contained in the object: ML
∼ L . Tortuosity Scaling exponenet " giving for an aggregate the minimal distance L that must be covered in order to go from two points separated by a pythagorean distance R  LR
∼ R" . Trains Bonds of a polymer in direct contact with the surface of a colloidal particle. Von Smoluchowsky equations Infinite system of coupled differential equations describing the kinetic of aggregation of a colloidal dispersion.

REFERENCES 1. R. A. Gortner, Trans. Faraday Soc. 26, 678 (1930). 2. R. L. Fullman, Sci. Am. 192, 74 (1955). 3. A. E. Nielsen, in “Crystal Growth” (H. S. Peiser, Ed.), p. 419. Pergamon Press, Oxford, 1967. 4. K. H. Lieser, Angew. Chem. Int. Ed. 8, 188 (1969). 5. A. E. Nielsen, “Kinetics of Precipitation.” Pergamon Press, Oxford, 1964. 6. A. E. Nielsen and O. Söhnel, J. Crystal Growth 11, 233 (1971). 7. O. Söhnel, Coll. Czech. Chem. Commun. 40, 2560 (1974). 8. A. Makrides, M. Turner, and J. Slaughter, J. Colloid Interface Sci. 73, 345 (1980). 9. M. Henry, Solid State Sciences, 5, 1201 (2003). 10. B. J. Mokross, J. Non-Cryst. Solids 284, 91 (2001). 11. D. Turnbull and M. H. Cohen, J. Chem. Phys. 29, 1049 (1958). 12. H. Krüger, Chem. Soc. Rev. 11, 227 (1982). 13. G. W. Neilson and J. E. Enderby, Adv. Inorg. Chem. 34, 195 (1989). 14. M. Henry, J. P. Jolivet, and J. Livage, Struct. Bonding 77, 153 (1992). 15. K. Goto, J. Phys. Chem. 60, 1007 (1956). 16. H. Gamsjäger and R. K. Murmann, in “Advances in Inorganic and Bioinorganic Mechanisms” (A. G. Sykes, Ed.), Vol. 2, p. 317. Academic Press, London, 1983. 17. G. Orcel and L. Hench, J. Non-Cryst. Solids 79, 177 (1986). 18. R. Aelion, A. Loebel, and F. Eirich, J. Am. Chem. Soc. 72, 5705 (1950). 19. C. J. Brinker and G. W. Scherer, in “Sol–Gel Science.” Academic Press, San Diego, 1990. 20. R. A. Assink and B. D. Kay, J. Non Cryst. Solids 99, 359 (1988). 21. D. H. Doughty, R. A. Assink, and B. D. Kay, Adv. Chem. Ser. 224, 241 (1990). 22. J. E. Pouxviel and J. P. Boilot, J. Non-Cryst. Solids 94, 374 (1987). 23. B. J. Ingebrethsen and E. Matijevic, J. Colloid Interface Sci. 100, 1 (1984). 24. V. K. La Mer and R. H. Dinegar, J. Am. Chem. Soc. 72, 4847 (1950). 25. E. Matijevic, Acc. Chem. Res. 14, 22 (1981). 26. T. P. Melia, J. Appl. Chem. 15, 345 (1965).

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70. 71. 72.

G. B. Alexander, J. Phys. Chem. 61, 1563 (1957). E. Matijevic, Annu. Rev. Mater. Sci. 15, 483 (1985). K. L. Cheng, Anal. Chem. 33, 783 (1961). R. W. Ramette, J. Chem. Educ. 49, 271 (1972). L. Gordon and E. D. Salesin, J. Chem. Educ. 38, 16 (1961). P. F. S. Cartwright, E. J. Newman, and D. W. Wilson, Analyst 92, 663 (1967). F. H. Firsching, Talanta 10, 1169 (1963). W. H. Mc Curdy, Anal. Chem. 34, 322R (1962). N. H. Fletcher, J. Chem. Phys. 29, 572 (1958). J. Dousma and P. L. De Bruyn, J. Colloid Interface Sci. 56, 527 (1976). J. Th. G. Overbeek, Adv. Colloid Interface Sci. 15, 251 (1982). W. K. Burton, N. Cabrera, and F. C. Frank, Philos. Trans. Roy. Soc. London Ser. A 243, 299 (1951). H. S. Frank and W. Y. Wen, Discuss. Faraday Soc. 24, 133 (1957). M. Magini, G. Licheri, G. Paschina, and G. Pinna, “X-Ray Diffraction of Ions in Aqueous Solutions.” CRC Press, Boca Raton, 1988. J. P. Jolivet, M. Henry, and J. Livage, “Metal Oxide Chemistry and Synthesis.” Wiley, New York, 2000. R. J. Hunter, “Introduction to Modern Colloid Science.” Oxford Science, Oxford, 1993. R. J. Stol and P. L. DeBruyn, J. Colloid Interface Sci. 75, 185 (1980). W. J. Dunning, in “Particle Growth in Suspensions” (A. L. Smith, Ed.), p. 3. Academic Press, London, 1973. L. Pauling and E. B. Wilson, in “Introduction to Quantum Mechanics,” p. 383. McGraw–Hill, New York, 1935. F. London, Z. Phys. 63, 245 (1930). B. Vincent, J. Colloid Interface Sci. 58, 408 (1973). A. C. Hamaker, Physica 4, 1058 (1937). J. Th. G. Overbeek, J. Colloid Interface Sci. 58, 408 (1977). R. Hogg, T. W. Healy, and D. W. Fuerstenau, Trans. Faraday Soc. 62, 1638 (1966). G. R. Wiese and T. W. Healy, Trans. Faraday Soc. 66, 490 (1970). L. N. Mc Cartney and S. Levine, J. Colloid Interface Sci. 30, 345 (1969). A. G. Muddle, J. S. Higgins, P. G. Cummins, E. J. Staples, and I. G. Lyle, Faraday Discuss. Chem. Soc. 76, 77 (1983). E. Barouch, E. Matijevic, A. Ring, and J. M. Finlan, J. Colloid Interface Sci. 67, 1 (1978). E. Barouch and S. Kulkarni, J. Colloid Interface Sci. 112, 396 (1986). E. Jenkel and B. Rumbach, Z. Elektrochem. 55, 612 (1951). J. F. Joanny, L. Leibler, and P. G. de Gennes, J. Polym. Sci. Polym. Phys. Ed. 17, 1073 (1979). M. Von Smoluchowski, Phys. Z. 17, 585 (1916). D. A. Weitz and M. Oliveria, Phys. Rev. Lett. 52, 1433 (1984). R. Julien and R. Botet, “Aggregation and Fractal Aggregates.” World Scientific, Singapore, 1987. P. Meakin, I. Majid, S. Havlin, and H. E. Stanley, J. Phys. A 17, L975 (1984). S. Havlin and R. Nossal, J. Phys. A 17, L427 (1984). S. Havlin, Z. V. Djordjevic, I. Majid, H. E. Stanley, and G. H. Weiss, Phys. Rev. Lett. 53, 178 (1984). F. Levyraz and H. E. Stanley, Phys. Rev. Lett. 51, 2048 (1983). S. Alexander and R. Orbach, J. Phys. Lett. (Paris) 43, L625 (1982). H. Nakanishi, Physica A 196, 33 (1993). P. Meakin and H. E. Stanley, Phys. Rev. Lett. 51, 1457 (1983). P. Meakin, F. Levyraz, and H. E. Stanley, Phys. Rev. A 31, 1195 (1985). D. Ben-Avraham and S. Havlin, in “Diffusion and Reactions in Fractals and Disordered Systems.” Cambridge Univ. Press, Cambridge, UK, 2000. R. Botet and R. Julien, J. Phys. A 17, 2517 (1984). P. G. J. van Dongen and M. H. Ernst, Phys. Rev. Lett. 54, 1396 (1985). S. Hyde, S. Andersson, K. Larsson, Z. Blum, T. Landh, S. Lidin, and B. W. Ninham, “The Language of Shape.” Elsevier, Amsterdam, 1997.

Encyclopedia of Nanoscience and Nanotechnology

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Nanocrystals in Organic/Inorganic Materials Peter Reiss, Adam Pron CEA Grenoble, Département de Recherche Fondamentale sur la Matière Condensée, Laboratoire Physique des Métaux Synthétiques, UMR 5819–SPrAM, 38054 Grenoble cedex 9, France

CONTENTS 1. Introduction 2. Basic Physical Properties of A(II)B(VI) Semiconductor Nanocrystals 3. Solution Phase Synthesis of A(II)B(VI) Semiconductor Nanocrystals 4. Functionalization of Nanocrystals 5. Conjugated Polymer/ Nanocrystal Composite Systems 6. Hybrid Organic/Inorganic Systems Appendix References

1. INTRODUCTION Since their discovery about two decades ago, the research devoted to colloidal semiconductor nanocrystals grows exponentially as judged from the increasing number of publications and conferences related to the chemistry, physics, and materials science of these nano-objects. This makes any attempt to provide an exhaustive review of the domain difficult and therefore the selection the data presented in this chapter is purely subjective and reflects the research interests of the authors. Special emphasis is put on the aspects of nanocrystal science which are most closely related to their expected technological and industrial applications. The organization of this chapter is as follows: The first part of the chapter reviews progress in the synthesis of monodisperse semiconductor nanocrystals and gives a basic introduction to their specific physical properties. In conformity with the literature, the term “monodisperse” is used here to describe colloidal samples in which the standard deviation of the particle diameter does not ISBN: 1-58883-062-4/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

exceed 5%. Throughout the text we will restrict ourselves to the description of A(II)B(VI) semiconductor nanocrystals with A being an element of the triad zinc, cadmium, mercury and B an element of the chalcogene group. These systems exhibit optical properties which can be varied in the visible part of the spectrum, near ultraviolet (UV) or near infrared (IR), by changing the nanocrystal size. Monodispersity of the samples is of crucial importance for several reasons. First, size induced tuning of the physical properties of nanocrystals is only possible for their fractions with narrow size dispersions. Second, an appropriate functionalization of monodisperse nanocrystals may lead to well-defined individual objects on the molecular scale with specifically designed properties. Third, assembly of monodisperse nano-objects frequently results in close-packed, highly ordered structures such as “colloidal crystals” and superlattices, opening up routes to novel materials with unusual properties. At the center of our interest are A(II)B(VI) systems with A = Cd and B = S, Se, or Te, for which the largest number of gram-scale preparation methods have been developed. In spite of the increasing interest in A(III)B(V) semiconductor nanocrystals (A = Ga, In; B = N, P, As), to date the research concerning their synthesis is still less advanced as compared to that carried out on A(II)B(VI) systems. The second part of the chapter is dedicated to organic/ inorganic materials formed by conjugated polymers and nanocrystals. Their use in optoelectronic devices such as light emitting diodes or photovoltaic cells is—besides biological labelling—the most promising application of nanocrystals which has emerged to date. A number of excellent reviews deal with the synthesis and physical properties of nanocrystals [1–3], whereas less work exists on their organic/inorganic composites [4, 5]. The present chapter gives an overview of the aforementioned research fields with special focus on the latest results and developments including our own work.

Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 6: Pages (587–604)

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2. BASIC PHYSICAL PROPERTIES OF A(II)B(VI) SEMICONDUCTOR NANOCRYSTALS 2.1. Description A(II)B(VI) semiconductor nanocrystals are crystalline particles with diameters ranging typically from 1 to 10 nm, comprising some tens to thousands of metal and chalcogene atoms. In the case of colloidal dispersions of nanocrystals the inorganic core consisting of the semiconductor material is capped by a shell of molecules, which provide sufficient repulsion between the crystals to prevent them from agglomeration. In the nanometer size regime many physical properties of the semiconductor particles change with respect to the bulk material. Examples of this behavior are melting points and charging energies of nanocrystals, which are, to first order, proportional to the reciprocal value of their radii. At the origin of the great interest for nanocrystals was yet another observation, namely the possibility to change the semiconductor bandgap—that, is the energy difference between the electron-filled valence band and the empty conduction band—by varying the particle size. In a bulk semiconductor an electron e− can be excited from the valence to the conduction band by absorption of a photon with an appropriate energy, leaving a hole h+ in the valence band. Feeling each other’s charge, the electron and hole do not move independently of each other because of Coulomb attraction. The formed e− –h+ bound pair is called an exciton and has its lowest energy state slightly below the lower edge of the conduction band. At the same time its wave function is extended over a large region (several lattice spacings); that is, the exciton radius is large, since the effective masses of the charge carriers are small and the dielectric constant is high [6]. To give examples, the Bohr exciton radii in bulk CdS and CdSe are approximately 3 and 5 nm. In Table 1 the bandgaps of A(II)B(VI) semiconductors are listed. Reduction of the particle size to a few nanometers produces the unusual situation that the exciton size can exceed the crystal dimensions. To “fit” into the nanocrystal, the charge carriers have to assume higher kinetic energies leading to an increasing bandgap and quantization of the energy levels to discrete values. This phenomenon is commonly called the “quantum confinement effect” [8], and its theoretical treatment is usually based on the quantum mechanical particle-in-a-box model [9]. With decreasing particle size, the energetic structure of the nanocrystals (often also Table 1. Energy bandgaps at 300 K of A(II)B(VI) semiconductors [7]. Material ZnO ZnS ZnSe ZnTe CdS CdSe CdTe HgS HgSe HgTe

Bandgap (eV) 3
4 3
8 2
82 2
3 2
5 1
76 1
5 2
1 −0
06 −0
3 (at 4 K)

referred to as quantum dots) changes from a bandlike one to discrete levels. Therefore, in some cases a description by means of molecular orbital theory may be more appropriate, applying the terms highest occupied molecular orbital and lowest unoccupied molecular orbital instead of conduction band and valence band. This ambiguity in terminology reflects the fact that the properties of semiconductor nanocrystals lie between those of the corresponding bulk material and molecular compounds. Another class of substances characterized by the quantumconfined state is chalcogene bridged transition metal clusters. Here individual, identical molecules in the nanometer or subnanometer range are assembled periodically in single crystals. Although it has not yet been possible for the majority of A(II)B(VI) semiconductors to isolate clusters in the nanometer size range, the impact of cluster science on nanocrystal research is of great importance. Single crystal X-ray diffraction is a powerful tool to obtain crystal structures from clusters and to elucidate their coordination chemistry [10–12]. In view of the lack of a comparable characterization technique for nanocrystals, this information is very worthy for the understanding of their structural properties, since clusters can be considered as model compounds or building blocks for nanocrystals. Furthermore, it has been observed in a large number of examples that, during nanocrystal growth, stable intermediates, often called “magic-sized clusters,” are formed [13, 14]. Quantum chemical calculations on cluster systems can reveal the structures of such thermodynamically stable species as well as their absorption spectra and thus contribute to a more detailed comprehension of the growth process 15 16. Finally, established preparation methods for cluster compounds are a helpful guideline for the choice of precursors, solvents, and reaction conditions, especially in the case of organometallic and related synthesis routes for nanocrystals (Sections 3.3 and 3.4).

2.2. Optical Properties of A(II)B(VI) Semiconductor Nanocrystals 2.2.1. Absorption As has already been stated (see Section 2.1), absorption of a photon by the nanocrystal occurs if its energy exceeds the bandgap. Due to quantum confinement, decreasing the particle size results in a hypsochromic (blue)shift of the absorption onset 17 18. A relatively sharp absorption feature near the absorption onset corresponds to the excitonic peak, that is, the lowest excited state exhibiting an important oscillator strength (cf. Fig. 1). While its position depends on the bandgap and, consequently, on the particle size, its form and width are strongly influenced by the distribution in size, as well as the form and stoichiometry of the nanocrystals. Therefore polydisperse samples typically exhibit only a shoulder in the absorption spectrum at the position of the excitonic transition. Less pronounced absorption features in the lower wavelength range correspond to excited states of higher energy [19]. As a rule of thumb, it can be asserted that the larger the number of such spectral features and the more distinctly they are resolved in the absorption spectrum, the smaller the size dispersion of

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the sample. In Figure 1 the absorption and photoluminescence spectra of a series of CdSe nanocrystals differing in size are depicted.

2.2.2. Photoluminescence After absorption of photons by nanocrystals, resulting in the formation of excitons, the system may return to the ground state via radiative electron–hole recombination. The emitted photons have an energy corresponding to the bandgap of the nanocrystals and for this reason the emission color can be tuned by changing the particle size 17 18. It should be noted here that efficient room temperature band-edge emission is only observed for nanocrystals with proper surface passivation because otherwise charge carriers are very likely to be trapped in surface states, enhancing nonradiative recombination. Due to spectral diffusion and the size distribution of nanocrystals, the room temperature luminescence linewidths of ensembles lie for the best samples in the range of 20–25 nm [full width at half maximum (FWHM)]. As can be seen in Figure 1, the maxima of the emission peak are redshifted by ca. 10–20 nm as compared to the excitonic peak in the absorption spectra. This phenomenon is usually referred to as Stokes shift and has its origin in the particular structure of the exciton energy levels inside the nanocrystal. Models using the effective mass approximation show that in bulk wurtzite CdSe the exciton state (1S3/2 1Se ) is eightfold degenerate [21]. In CdSe nanocrystals, this degeneracy is partially lifted and the band-edge state is split into five states, due to the influence of the internal crystal field, effects arising from the nonspherical particle shape, and the

Absorbance

4.7 nm

4.3 nm

4.0 nm

Photoluminescence intensity

4.9 nm

3.6 nm

electron–hole exchange interaction (see Fig. 2). The latter term is strongly enhanced by quantum confinement [22]. Two states, one singlet state and one doublet state, are optically inactive for symmetry reasons. The energetic order of the three remaining states depends on the size and form of the nanocrystal. In the case of weak excitation of a given state, absorption depends exclusively on its oscillator strength. As the oscillator strength of the second and third excited (“bright”) states is significantly higher than that of the first (“dark”) one, excitation by photon absorption occurs to the bright states. In contrast, photoluminescence depends on the product of oscillator strength and population of the concerned state. Relaxation via acoustic phonon emission from bright states to the dark band-edge state causes strong population of the latter and enables radiative recombination (see Fig. 2). This model is corroborated by the experimental room temperature values of the Stokes shift, which are consistent with the energy differences between the related bright and dark states.

2.2.3. Emission of Single Nanocrystals, Blinking Phenomenon Spectroscopic investigation of single semiconductor nanocrystals revealed that their emission under continuous excitation turns on and off intermittently. This blinking is a common feature also for other nanostructured materials, involving porous Si [23] and epitaxially grown InP quantum dots [24], as well as chromophores at the single molecule level such as polymer segments [25], organic dye molecules [26], and green fluorescent protein [27]. However, the origin of the intermittence is completely different for nanocrystals and single dye molecules: in the latter resonant excitation into a single absorbing state takes place. Due to spectral shifting events the excitation is no longer in resonance and a dark period begins. Nanocrystals, on the other hand, are excited nonresonantly into a large density of states above the band edge. While their emission statistics and its modelling are the issue of a large number of publications [28–32], a detailed understanding of the blinking phenomenon has not yet been achieved. As a consequence, experimental efforts to overcome it have not been successful so far. Its resolution would be of great benefit in applications associated with the use of nanocrystals as biological labels, in particular on the single molecule level. The sequence of “on” and “off” periods resembles a random telegraph signal on a time scale varying over several orders of magnitude up to minutes and follows a temporal statistics described by an inverse power law [30]. Transition from an “on” to an “off” state of the nanocrystal seems to Degeneracy Energy

2.9 nm

Absorption 350

400

450

500

550

600

650

Figure 1. Absorption and normalized photoluminescence spectra of CdSe nanocrystals (P. Reiss and J. Bleuse, unpublished data). The diameters have been determined on the basis of data published by Mikulec et al. [20].

2nd and 3rd excited state: “bright”

Relaxation Phonons

st

700

Wavelength (nm)

(1) (2)

(2)

1 excited state: “dark”

Luminescence

ground state

Photon

Photon

Figure 2. Schematic representation of the exciton states of CdSe nanocrystals involved in absorption and emission processes.

Nanocrystals in Organic/Inorganic Materials

590 occur by photoionization, which implies the trapping of a charge carrier in the surrounding matrix (dangling bonds on the surface, solvent, etc.). A single delocalized electron or hole rests in the nanocrystal core. Upon further excitation this gives rise to fast (nanosecond order) nonradiative relaxation through Auger processes (i.e., energy transfer from the created exciton to the delocalized charge carrier) [33]. Mechanisms for a return to the “on” state are the recapture of the localized charge carrier into the core or the capture of an opposite charge carrier from traps in the proximity. Both pathways can be accompanied by a reorganization of the charge distribution around the nanocrystals. As a consequence the local electric field changes leading to a Stark shift of the photoluminescence peak 31 32.

2.2.4. Efficiency of the Emission: Fluorescence Quantum Yield The emission efficiency of an ensemble of nanocrystals is expressed in terms of the fluorescence quantum yield (QY), that is, the ratio between the number of absorbed photons and the number of emitted photons. As a consequence of the blinking phenomenon (vide supra) the theoretical value of 1 is not observed because a certain number of nanocrystals are in “off” states. Furthermore the QY may be additionally reduced as a result of quenching caused by surface trap states. As both of these limiting factors are closely related to the quality of the nanocrystal surface, they can be considerably diminished by its improved passivation. This can be achieved by changing the nature of the organic ligands, capping the nanocrystals after their synthesis. To give an example, after substitution of the trioctylphosphine oxide (TOPO) cap on CdSe nanocrystals by hexadecylamine or allylamine, an increase of the QY from about 10% to values of 40–50% has been reported [34]. In this case better surface passivation probably results from an increased capping density of the sterically less hindered amines as compared to TOPO. On the other hand, in view of further nanocrystal functionalization, it is desirable to provide a surface passivation which is less sensitive to subsequent ligand exchanges. A suitable method consists of the growth of an inorganic shell on the (core) nanocrystals, resulting in core/shell systems as depicted schematically in Figure 3. In order to confine both electrons and holes in the core, a wider bandgap semiconductor with an appropriate band alignment (type I or normal configuration; see Fig. 3) is chosen as the shell material. Further attention has to be paid to the lattice mismatch parameter between the core and shell lattices. Significant LUMO

∆E=?

ZnSe 2.82 eV

1 eV

CdSe 1.76 eV ∆Ev

As discussed in Section 2.2, the effects of quantum confinement give rise to a strong size dependence of the optical properties of nanocrystals. However, in such nano-objects essentially all physical properties exhibit size dependence in a more or less pronounced way, including their electronic properties. If one considers a nanocrystal as a spherical capacitor, its capacitance C is a function of its radius r [40], (1)

Cr = 40 r

where 0 and  are the dielectric constants of the vacuum and of the surrounding medium of the nanocrystal, respectively. Adding a simple charge to the nanocrystal requires the charging energy Ec , Ec = e2 /2Cr

(2)

At temperatures where kT < Ec , tunneling of single charges onto nanocrystals can occur, which can be revealed by scanning tunneling microscopy measurements [41–45]. The current–voltage curves obtained in these experiments exhibit a barrier to current flow, arising from Ec , which is called a Coulomb blockade.

Table 2. Shell materials for the overcoating of CdSe nanocrystals: bandgaps (CdSe: 1.76 eV), lattice mismatch parameters a with respect to CdSe, and reported room temperature QYs of the core/shell systems.

0.1 eV

Shell material

∆E=?

HOMO

2.3. Electronic Properties of Nanocrystals

CB ∆Ec

Ligands

constraints at the core/shell interface lead to the creation of new trapping sites for the charge carriers, which quench the fluorescence. This is clearly visible in the case of the most studied system, CdSe nanocrystals. In terms of bandgap and band alignment ZnS is an excellent candidate as a shell material, which has led to its widespread use. However, due to the large lattice mismatch parameter of 10.6% between CdSe and ZnS, the reported values of QY do not exceed 50–60%. Moreover, only relatively thin shells give rise to an increase of the QY. If a certain shell thickness is exceeded, the QY diminishes, clearly pointing out the formation of structural defects. On the other hand, ZnSe is a shell material which provides less efficient charge carrier confinement with respect to ZnS, due to its lower bandgap. This is especially true for the holes as can be seen from the small conduction band offset in Figure 2 [35]. Nevertheless, as a result of the better crystal lattice matching in CdSe/ZnSe as compared to CdSe/ZnS, higher values for the fluorescence QY are reported in the former case. Table 2 summarizes the properties of different core/shell systems with CdSe as the core material.

VB

Figure 3. Scheme of a CdSe/ZnSe core/shell nanocrystal (left) and of its energy levels (right; CB = conduction band, VB = valence band).

CdS ZnS ZnSe

Gap (eV)

a (%)

QY (%)

Ref.

2
5 3
8 2
82

3
8 10
6 6
3

≥50 30–50 60–85

[36] [37, 38] [39]

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3. SOLUTION PHASE SYNTHESIS OF A(II)B(VI) SEMICONDUCTOR NANOCRYSTALS 3.1. Historical Review of the Synthesis Methods Solution phase (or wet chemical) methods for the synthesis A(II)B(VI) semiconductor nanocrystals can be roughly divided into two general categories: 1. room temperature procedures consisting of nanocrystal precipitation in aqueous media, either in the presence of stabilizers (method 1.1) or within inverse micelles (method 1.2) 2. high temperature reactions in nonaqueous media based on temporal separation of nanocrystal nucleation and growth, applying either organometallic precursors (method 2.1) or inorganic precursors, such as oxides or salts (method 2.2) Table 3 gives a nonexhaustive overview of reported applications of the aforementioned preparation methods for the fabrication of A(II)B(VI) nanocrystals. Initially developed procedures comprise nanocrystal formation in homogenous aqueous solutions containing appropriate reagents and surfactant-type or polymer-type stabilizers 53 61. The latter bind to the nanocrystal surface and stabilize the particles by steric hinderance and/or electrostatic repulsion in the case of charged stabilizers. In parallel to this monophase synthesis, a biphase technique has been developed which is based on the arrested precipitation of nanocrystals within inverse micelles [54, 55, 62, 63]. Here nanometer-sized water droplets (dispersed phase) are stabilized in an oil (continuous phase) by an amphiphilic surfactant. They serve as microreactors for the nanocrystal growth and prevent at the same time particle agglomeration. Both methods provide relatively simple experimental approaches using standard reagents as well as room temperature reactions and were of great importance for the development of nanocrystal synthesis. On the other hand, the samples prepared by these synthetic routes usually exhibit size dispersions exceeding 15% and therefore material consuming Table 3. Synthesis methods for A(II)B(VI) nanocrystals. Method 1.1 2.1 1.2 2.1 2.1 2.2 2.2 1.1 1.2 1.2 1.2 1.1 1.2 1.1 1.1

Material

Ref.

ZnS ZnSe ZnSe ZnO CdS, CdSe, CdTe CdS, CdSe, CdTe CdSe CdS CdS CdS CdSe CdTe CdTe HgS HgSe, HgTe

[46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60]

procedures of nanocrystal separation into “sharp” fractions have to be applied in order to obtain monodisperse samples. The introduction of high temperature preparation methods in 1993 [50] constituted an important step toward the fabrication of CdS, CdSe, and CdTe nanocrystals exhibiting much lower size dispersions as compared to samples prepared in aqueous media. As demonstrated in classical studies by La Mer and Dinegar [64], the synthesis of monodisperse colloids requires a temporal separation of nucleation and growth of the seeds. This can be achieved by rapid injection of the reagents into the hot solvent which raises the precursor concentration in the reaction flask above the nucleation threshold. A nucleation burst takes place which lowers immediately the supersaturation and afterward no new seeds are formed. In an ideal case all crystallization nuclei are created at the same time and undergo identical growth until the precursors (sometimes also called “monomers”) in the solution are consumed. At this stage of the reaction it is possible to carry out subsequent injections of precursors in order to increase the mean particle size without deterioration of the narrow size distribution as long as the concentration of the nucleation threshold is not exceeded. Crystal growth from solution is in many cases followed by a second distinct growth process, which is referred to as Ostwald ripening 65 66. It consists of the dissolution of the smallest particles because of their high surface energy and subsequent redeposition of the dissolved matter onto the bigger ones. Thereby the total number of nanocrystals decreases, whereas their mean size increases. If diffusion is assumed to be the rate limiting step, the size dependent growth rate can be expressed by means of the Gibbs–Thomson equation [67]: Sr = Sbulk exp2 Vm /rRT

(3)

Sr and Sbulk are the solubilities of a nanocrystal with radius r and of the bulk solid, respectively. is the specific surface energy, Vm is the molar volume of the solid, R is the gas constant, and T is the temperature. As shown by Reiss [68], Ostwald ripening can lead to smaller size dispersions in the case of micrometer-sized colloids. For nanometer-sized particles, validity of Eq. (3) and focusing of size distributions during the diffusion-controlled nanocrystal growth have been confirmed 69 70. Within the framework of the organometallic preparation method, samples with 8–10% standard deviation from the mean size can typically be obtained. One of the main disadvantages of this preparation method lies in the fact that pyrophoric organometallic precursors such as dimethylcadmium or diethylzinc are applied. Their use requires special experimental precautions and their extremely high reactivity restricts the batches to laboratory scale quantities. As a result, in recent years the development of nanocrystal high temperature synthesis was focused on the replacement of these organometallic precursors by easy to handle standard reagents. To give an example, in the preparation of CdB(VI) nanocrystals, dimethylcadmium can be substituted by cadmium oxide or cadmium salts of weak acids (CdAc2 , CdCO3 ) after complexation with long chain phosphonic or carboxylic acids 51 52. In the subsequent text this and related procedures will be termed “mixed

Nanocrystals in Organic/Inorganic Materials

592 inorganic/organometallic” methods. A further modification of the high temperature methods consists of the appropriate selection of coordinating and noncoordinating solvents, with the goal to determine their influence on the nucleation and growth of the nanocrystals and to reduce their size distributions below 5% [34]. It is very likely that in the near future similar methods for the synthesis of ZnB(VI) and HgB(VI) nanocrystals will be developed. At the end of this brief historical review, it should be pointed out that essentially all discussed preparation methods have one important point in common: slight variations in the experimental conditions can lead to significant differences in the result. The interested reader who desires to reproduce nanocrystal syntheses in his own laboratory should therefore follow exactly the directions given in the original literature.

3.2. Synthesis in Aqueous Media 3.2.1. Precipitation in Presence of Stabilizers Well established preparation methods for CdS and CdTe nanocrystals comprise their precipitation from an aqueous solution containing cadmium ions and appropriate stabilizers such as thioglycerol or thioglycolic acid [71]. If the precipitation is carried out with the use of H2 S or H2 Te the pH value is a crucial parameter in the control of the particle size and its dispersion. Alkaline pH values are necessary to shift the equilibrium of the H2 S (or H2 Te) dissociation enabling the formation of CdS (or CdTe) seeds: H2 S ⇄ 2H+ + S2−

(4)

During the reaction the pH drops to acidic values due to the release of protons and the particles grow either from solution or by Ostwald ripening while no new seeds are formed. The growth can be stopped by increasing the pH to alkaline values once again. An inherent feature of the nanocrystals synthesized by this method is their surface charge, which makes them dispersible in water. Their stabilities as well as their fluorescence efficiencies depend strongly on the nature of the stabilizing agent.

3.2.2. Precipitation in Inverse Micelles Surfactant molecules can be classified into cationic (e.g., amines), anionic (e.g., carboxylic or sulfonic acids), and nonionic (e.g., polyethers) ones. They have an amphiphilic character, which means that they contain both hydrophilic and hydrophobic moieties, and for thermodynamic reasons they self-assemble in aqueous solutions to form aggregates, called micelles. In a biphase system consisting of water and oil (hydrocarbon), the creation of different shaped micelles is possible such as spherical, cylindrical, or lamellar ones, depending on the relative concentrations of the constituents of the ternary system [72]. A high volume fraction of the oil phase leads to the formation of inverse micelles (i.e., water droplets in oil with the hydrophobic parts of the surfactant molecules sticking out of the droplet). These can be used as compartments for the arrested precipitation of nanocrystals. In this case no stabilizers are necessary to prevent from

particle agglomeration (compare Section 3.2.1), because the individual nanocrystals are shielded by the surfactant and the continuous phase. The most popular system in this context comprises sodium bis(2-ethylhexyl)sulfosuccinate, also known as aerosol OT or Na(AOT), as the surfactant in a water/isooctane or water/heptane mixture [54–56]. In this case the diameter d of the inverse micelles can be controlled by the water content w [73]: w = H2 O/AOT

(5)

d nm  0
3 w

(6)

Equation (6) is valid for values of w superior to 15, whereas it underestimates the micellar size for lower values of this parameter. The synthesis of nanocrystals inside inverse micelles can be carried out in two different ways: either by mixing two micellar solutions, one containing metal ions and the other containing chalcogenide ions in the water droplets, or by bubbling the metal ions containing solution with gaseous hydrogen chalcogenide. In addition to the important size distribution, a drawback of the micellar method is the fact that the maximum size, which can be obtained for semiconductor nanocrystals, is limited to ca. 4 nm [72]. On the other hand, it is very versatile synthesis technique that allows the preparation of a large number of different semiconductor, metal, alloy, and oxide nanoparticles (see [72, 74] and references therein).

3.3. Organometallic Synthesis The organometallic nanocrystal synthesis consists of the reaction between an organometallic metal precursor and an appropriate chalcogene precursor carried out in a coordinating solvent at high temperature. The originally reported preparation method [50] typically yields nanocrystals with size dispersions of 8–10% in the case of CdSe and of 10–15% in the case of CdS and CdTe nanocrystals. The procedure can be divided into three steps: (i) Nucleation of the seeds: Nucleation of the seeds is achieved by swift injection of the organometallic precursors into the reaction flask which contains the coordinating solvent vigorously stirred at high temperature (300–350  C). As mentioned in Section 3.1, such quick addition provokes a transient supersaturation necessary for the nucleation process. Besides, the injection of the cold (ca. 25  C) precursors results in a significant temperature drop inside the flask. (ii) Particle growth: During particle growth, which follows the nucleation step, temperature is maintained between 250 and 300  C. The growth process can be monitored by the evolution of the absorption spectra of small aliquots taken periodically from the reaction mixture or in-situ using a fiber optics probe. (iii) Growth termination: When the desired particle size is reached, temperature is dropped below 100  C to stop crystal growth. Nanocrystals are then isolated by precipitation and purified by washing with adequate solvents in order to remove by-products and excess coordinating solvent.

Nanocrystals in Organic/Inorganic Materials

Although originally developed for the CdB(VI) series, a similar approach has been adapted for the synthesis of ZnB(VI) and HgB(VI) semiconductor nanocrystals (see Table 3). Organometallic metal precursors generally comprise metal alkyls or aryls (dimethylcadmium, diethylzinc, dibenzylmercury) whereas S, Se, or Te sources are mostly chosen from trialkylphosphine chalcogenides (R3 PSe, R3 PTe with R = octyl or butyl) or bistrimethylsilylchalcogenides such as (Me3 Si)2 S. The trialkylphosphine chalcogenides can easily be prepared by dissolution of the chalcogenide powder in the phosphine. In the case of sulfur, the silylated compound is preferred over the trialkylphosphine sulfide because the latter exhibits too low reactivity in the temperature range used for the synthesis. The choice of the coordinating solvent is of crucial importance because it influences the reactivity of the precursors as well as the kinetics of the growth process. Furthermore, being the capping agent, it determines the “solubility” of the nanocrystals and the stability of their colloidal dispersions. Usually applied are mixtures of alkylphosphines R3 P, alkylphosphine oxides R3 PO [R = H(CH2 )n with n ≥ 4], long-chain alkylamines, etc. Prerequisites for the selection are that the solvent system does not show any decomposition at the high reaction temperatures and that the boiling points of all components are sufficiently high. Further attention has to be paid to the basic strength of the solvent which has to be adapted according to the type of semiconductor nanocrystal to be synthesized. To give an example, the most widely used coordinating solvent for the preparation of CdB(VI) nanocrystals is a mixture of trioctylphosphine oxide/trioctylphosphine or trioctylphosphine oxide/tributylphosphine. For the synthesis of ZnB(VI) analogs of the CdB(VI) family, the previously described solvent mixtures cannot be applied because the interactions between TOPO and the zinc precursor (ZnEt2 ) are too strong. As a result, the reaction between the metal source and the chalcogenide source is impeded and the nucleation and/or growth process does not occur. This problem can be overcome by the replacement of TOPO with hexadecylamine (HDA) which is a weaker base. The HDA/TOP mixed solvent provides sufficient reactivity between the precursors and enables the growth of ZnB(VI) nanocrystals [47]. A large variety of precursor/coordinating solvent systems, whose mutual interactions can be tuned as to obtain the optimum synthesis conditions for nanocrystals of a given semiconductor, makes the organometallic route a very versatile preparation method. However, the pyrophoric character of organometallic reagents, which implies special experimental precautions, and their high price motivated researchers to develop alternative procedures in recent years. Some of them yield nanocrystals of equal or even superior quality as compared to those prepared by organometallic synthesis (see Section 3.4).

3.4. Mixed Inorganic/Organometallic Synthesis As has been stated, the temporal separation of nucleation and growth is very likely to be of crucial importance for the synthesis of monodisperse nanocrystals. In the framework

593 of the organometallic preparation route this is achieved by the use of highly reactive metal precursors which decompose readily after their injection into the hot solvent. Nevertheless this reaction type is not limited to organometallic, pyrophoric reagents and a number of inorganic compounds such as oxides or salts can be applied in the same way. The first example reported was the use of cadmium oxide, complexed with alkylphosphonic acids, as a Cd source in the synthesis of CdB(VI) nanocrystals [51]. The resulting cadmium phosphonates are sufficiently reactive toward Se or Te solutions in trioctylphosphine and yield nearly monodisperse CdSe and CdTe nanocrystals in the size range of ca. 2.5–5 nm. In the same manner as in the case of the organometallic synthesis route (Section 3.3) [34], the size distribution can be further lowered to values below 5%, if a mixed solvent of TOPO/HDA is used instead of TOPO alone [39]. Larger sized nanocrystals can be prepared by applying cadmium carboxylates as a Cd source, with the crystal growth rate being inversely proportional to the chain length of the carboxylic acid [52]. By proper choice of the cadmium source and solvent, this method allows the synthesis of CdSe nanocrystals with diameters up to 25 nm, while for the organometallic approach maximum values of ca. 11 nm have been reported [50]. Moreover, this scheme can easily be extended to the synthesis of nanocrystals of shapes different from spherical and in particular to the preparation of “nanorods” (i.e., elongated crystals with a high aspect ratio) [75]. In order to promote and control such a one-dimensional (1D) growth, it is desirable to have less reactive cadmium sources than dialkylcadmium compounds, for example certain cadmium phosphonates. The experimental results show that, as in a number of other examples [10, 13, 14, 76], in the early stages of the reaction a relatively stable, “magic-sized” cluster of ca. 10–20 cadmium atoms is formed. Furthermore the same cluster seems to be at the origin of all different shaped nanocrystals (rod-shaped, rice-shaped, or branched). Thus, for a given temperature, the shape can be controlled by the monomer concentration in the solution, which in all cases of anisotropic growth has to be high compared to the growth of spherical particles. The latest studies in the framework of the mixed inorganic/organometallic synthesis reveal a further similarity with cluster chemistry. For a long time the use of coordinating solvents such as TOPO or HDA was believed to be indispensable for a controlled nanocrystal growth. Now, like in cluster synthesis, the use of high boiling noncoordinating solvents (e.g., alkanes such as octadecene), in association with a controlled amount of ligands (phosphine oxides, phosphines, amines, carboxylic or phosphonic acids, etc.), provides a much wider approach to nanocrystal synthesis [77]. The latter allows not only the fine-tuning of nanocrystals sizes, size distributions, and shapes but also the transfer of the synthesis scheme to other types of semiconductors, such as InP, InAs [78], or PbSe 79 80. The listed advantages make the mixed inorganic/organometallic preparation method a very powerful tool for the design of new materials on the nanometer scale.

594 3.5. Synthesis of Core/Shell Systems Among all core/shell systems CdSe/ZnS is the most studied case. The large bandgap of ZnS in combination with a favorable band alignment of CdSe and ZnS (see Section 2.2.4) yields core/shell nanocrystals with a significantly improved fluorescence QY with respect to the “bare” core crystals. The procedure for the shell growth is very similar to the organometallic nanocrystal preparation method (Section 3.3), with the use of diethylzinc and bistrimethylsilyl sulfide 37 38. Important differences are, however, the slow injection of these precursors in combination with relatively low reaction temperatures (150–210  C). These measures are necessary in order to promote an epitaxial-type deposition of the shell material on the core crystals and to prevent nucleation of separate ZnS seeds. Furthermore, at higher temperatures Ostwald ripening of the core particles may occur, deteriorating their size distribution. After the successful introduction of the mixed inorganic/organometallic preparation method to the synthesis of CdB(VI) core nanocrystals, it is a logic step to replace the pyrophoric dialkylzinc precursors, routinely used for the shell preparation, by safer reagents. However, the use of zinc phosphonates, in analogy to the inorganic/organometallic core synthesis, does not result in a successful ZnS shell growth because they exhibit too low reactivity toward the chalcogenide source in the cited temperature range. On the contrary, zinc stearate is an excellent zinc source in this context [39]. This easy to manipulate and commercially available compound reacts readily with both sulfur and selenium precursors to form CdSe/ZnS and CdSe/ZnSe core/shell nanocrystals or CdSe/ZnSe/ZnS core/double shell systems [81].

3.6. Size Sorting Procedures With few exceptions, nanocrystal preparation techniques usually yield samples with a polydispersity significantly exceeding 5% (i.e., the level required for many specific applications of these nano-objects). In such cases postpreparative size-sorting procedures have to be used with the goal to isolate fractions of low polydispersity. The most prominent techniques are based on similar principles as widely applied in polymer technology, size-selective precipitation [50] or size exclusion chromatography [82]. The former method implies the destabilization of the colloidal nanocrystal dispersion by adding a nonsolvent, miscible with the original solvent. Thereby the repulsive force between the nanocrystals due to their capping groups is reduced and the largest ones tend to aggregate because they exhibit the strongest attractive van der Waals interactions. They can be separated by centrifugation or filtration from the smaller-size nanocrystals, which do not agglomerate and remain dispersed in the solvent/nonsolvent medium. Subsequent cycles of redispersion in an adapted solvent and partial flocculation of the largest nanocrystals provide quasi-monodisperse samples. The major disadvantage of this technique is its low yield: less than 30% of nanocrystals with a size dispersion of 5% are obtained from an initial sample with a size dispersion of 10% [3]. In the case of size exclusion chromatography (SEC) [82], the nanocrystal dispersion (mobile phase) flows through a column loaded with porous hydrophobic microgels, such as

Nanocrystals in Organic/Inorganic Materials

cross-linked polystyrene (stationary phase). As the smaller crystals penetrate deeper into the pores than the larger ones, their retention time in the column is longer. More precisely, the elution time te of nanocrystals is in direct relationship with their radius r [83]: te = k1 + k2 lg r

(7)

Additionally, after calibration SEC can be used to determine the mean size and size dispersions of samples containing spherical particles. The technique is limited to nanocrystals, which are well passivated by a cap of nonpolar organic ligands because otherwise they risk being adsorbed permanently inside the column due to strong interactions with the microgel. On the contrary, gel electrophoresis, another size sorting technique which has been used with the goal to lower the polydispersity of nanocrystals [84], requires charged particles and is well adapted for aqueous solutions. The nanocrystals move through a column filled with a polymer gel such as weakly cross-linked acrylamide, driven by an electrical field between both ends of the column. Particles with a high surface charge and small diameter move most quickly through the gel. After sufficient separation, the gel is cut into thin slices and the nanocrystal fractions in each slice are redissolved while gel residues are filtered off.

4. FUNCTIONALIZATION OF NANOCRYSTALS Nanocrystals possess a very high surface/volume ratio, which increases strongly with decreasing radius. Individual crystals are prevented from agglomeration by means of an organic ligand cap on their surface. At the same time, these ligand molecules complete the coordination sphere of the nanocrystal surface atoms and thus reduce the number of dangling bonds, which cause fluorescence quenching. A large number of potential applications of nanocrystals require nonetheless a modification of this organic ligand cap, with the goal to make the colloids dispersible in various solvents and/or to graft them to other molecules of biological or electronic interest, to solid substrates, etc. By consequence, in recent years different approaches have been developed to perform nanocrystal surface chemistry. A widely applied method consists of the exchange of the organic molecules at the surface by bifunctional ligands X–S–Y [85–87]. Such ligands contain, on the one hand, a functional group X, which provides strong interaction with the metal ions on the nanocrystal surface and on the other hand a second chemical moiety Y, which allows the subsequent binding to molecules or substrates. Typical examples for X are thiol or phosphonic acid groups, whereas carboxyl, amine, or alcohol functions are representative for Y, to name a few. The selection of Y is of crucial importance, not only in view of nanocrystals grafting to given objects, but also for their dispersion in polar solvents and in particular in water, indispensable for biological applications. X and Y are usually separated by a spacer, S, of alkyl or aryl type. Bifunctional ligands X–S–Y, in which Y is an ionizable group, can also facilitate the formation of a more or less ordered aggregation of nanocrystals with oppositely charged macromolecules via electrostatic interactions. A typical

Nanocrystals in Organic/Inorganic Materials

example is the electrostatic self-assembly of carboxylic acid coated and thus negatively charged nanocrystals and a synthetically engineered, positively charged protein [88]. Since this protein enables the conjugation of biological molecules such as antibodies, highly stable and specific conjugates for immunoassays can be created using this method. The main problem of the described functionalization methods is the fact that, in the majority of cases, the exchange of the original ligands results in a significant decrease of the fluorescence QY. This problem can be overcome by the use of a so-called “nanocrystal encapsulation method.” Hereby the initial optical properties of the nanocrystals can be essentially maintained, since it does not involve the exchange of the passivating ligands. The procedure will be described here for hydrophobic nanocrystals with TOPO and/or HDA ligands on their surface. The encapsulation is carried out in a three-component system consisting of water, oil, and an appropriate surfactant of amphiphilic nature. The surfactant molecules, being at the interface of the water continuous phase and the droplets of the oil, stabilize the formation of a microemulsion. If hydrophobic nanocrystals are introduced into this microemulsion, micellar-type system, they are placed in the hydrophobic environment (i.e., within the oil microdroplets). After the evaporation of both solvents, alkyl chains of the surfactant molecules “interdigitate” with the alkyl groups of the nanocrystal ligands, encapsulating in such a manner the nanocrystal, while the polar groups of the surfactant are directed on the outside of the encapsulated particle. An example of the successful application of this technique is the nanocrystal encapsulation by phospholipid micelles, enabling in vivo imaging experiments [89].

5. CONJUGATED POLYMER/NANOCRYSTAL COMPOSITE SYSTEMS 5.1. Introduction Conjugated polymers (i.e., polymers with a spatially extended -bonding system), although known for many years, did not draw significant research attention because they were intractable and, in many cases, unstable in ambient conditions. However, in the past two decades extensive and systematic research has been devoted to various aspects of the chemistry and physics of this previously underestimated family of macromolecular systems. It resulted in the preparation of stable, processible conjugated polymers offering unique physical properties which cannot be obtained for conventional polymers [90]. Both in their undoped (semiconducting) and doped (conducting) states, conjugated polymers can be used as components of so-called “plastic electronics.” In 2000 A. J. Heeger, A. G. MacDiarmid, and H. Shirakawa—the founders of “conjugated polymer science”—were granted the Nobel Prize in chemistry (Nobel Lectures, [91–93]). Conjugated polymers in their neutral (undoped) state are materials, which combine electronic properties of intrinsic semiconductors with mechanical properties and solution processibility of macromolecular systems. Moreover they

595 frequently dissolve in the same solvents as the ones that are used to disperse A(II)B(VI) nanocrystals. Thus conjugated polymer/nanocrystal composite films can relatively easily be prepared by casting from a common solvent. Why are such composite materials of technological interest? First, the electronic properties of the two semiconductor constituents can be tuned individually and adapted to each other. In the case of the nanocrystal component of the composite, this can be done by size control (vide supra). The bandgap of the polymeric component can, in turn, controllably be altered by changing the chemical constitution of the conjugated backbone via copolymerization (random or block) and/or by appropriate functionalization with lateral groups exhibiting electron donating or electron withdrawing properties. Second, the interface area between the polymer phase and the nanocrystal one is very large due to the very high surface/volume ratio of the nanocrystals. This enables efficient electronic transport between these two components. Third, the conductivity of the polymeric phase can be varied via oxidative or acid–base doping. For this reason doped conjugated polymers are sometimes used in light emitting diodes as hole or electron transporting layers. They facilitate the charge injection into the emitting layer consisting of an undoped polymer and nanocrystals. Finally, the polymeric phase of the composite assures better mechanical properties of the system as compared to pure inorganic semiconductor materials. For all aforementioned reasons composites of conjugated polymers and nanocrystals have been used in recent years as components of various electronic, optoelectronic, and sensing devices such as light emitting diodes, photovoltaic cells, electrochemical sensors, to name a few 94 95. Although conjugated polymer/nanocrystal composites should exhibit significant advantages over both all-organic materials and inorganic semiconductors, still considerable research efforts have to precede their industrial applications. The main difficulty is caused by the fact that several important properties of the composite, such as charge carrier mobility, electroluminescence, etc., are strongly dependent on even small changes in the polymer supramolecular structure and on the distribution of the nanocrystals within the polymer matrix, which are not easy to control. In the method outlined previously for the preparation of composite materials, both constituents are synthesized individually and then mixed together using a solvent, which easily dissolves the polymer and disperses the colloidal nanocrystals. Alternatively one can synthesize nanocrystals within an already formed polymer matrix, for example by doping the polymer with nanocrystal precursors. However, the control of the nanocrystal size distribution is, in this case, extremely difficult. Thus, this method is used only for those applications in which monodispersity is not crucial, for example in the preparation of polymer supported heterogeneous catalysts.

5.2. Selected Properties of Conjugated Polymer/Nanocrystal Composites Doped conjugated polymers frequently combine metallictype conductivity with film forming properties of macromolecular systems. Some of them, like polyaniline

Nanocrystals in Organic/Inorganic Materials

596 protonated with selected sulfonic acids, are solution processible 96 97. Thus doped polymers can provide simple electrical contacts to nanocrystals, which are easy to fabricate in a large variety of configurations. The same arguments apply to the preparation of composites comprising undoped (semiconducting) conjugated polymers and A(II)B(VI) nanocrystals. It should be, however, noted here that in such composites two semiconductor phases of different properties coexist. At the polymer/ nanocrystal interface the former acts as an electron donor and the latter as an electron acceptor due to its higher electron affinity (see Table 4). Thus in a typical conjugated polymer/A(II)B(VI) nanocrystal composite the polymer phase serves as the hole transporting medium and the nanocrystals as the electron transporting one. This property is very important in view of applications of polymer/nanocrystal composites for the fabrication of solar cells (see Section 5.3). The polymer phase is usually continuous whereas the nanocrystals are dispersed, although some of them may form aggregates of different sizes. Such a picture implies that, if the electron transport is governed by the nanocrystal phase, it must be described in terms of percolation. In the simplest approach the percolation threshold is defined as the lowest volume fraction of the nanocrystal phase which assures an interconnected network of particles and by consequence the transport of the charge carriers on a macroscopic scale. This percolation threshold is strongly dependent on the so-called “aspect ratio” (i.e., the ratio of the longest dimension of the nanoparticle to the dimension perpendicular to it). With an increase of the aspect ratio, the value of the percolation threshold decreases. Thus, it is higher for globular-shaped nanocrystals (aspect ratio = 1) than for rod-shaped nanocrystals (aspect ratio ≫1). Finally, it should be stressed that nanocrystals are incorporated in the polymer matrix not as “bare” objects but together with a layer of (organic) capping ligands on their surface. This ligand layer impedes direct interconnectivity of the nanocrystals and can act as a barrier for the charge carrier transport between adjacent nanocrystals as well as for the charge separation at the polymer/nanocrystal interface. Therefore electrical transport Table 4. Electron affinities and energy gaps of selected conjugated polymers and nanocrystals (see Appendix) [98–100]. Material Indium tin oxide CdS (2 nm) CdS (6 nm) CdSe (2 nm) CdSe (5 nm) MEH-PPV MDMO-PPV PANI-EB PANI-PB PANI-LEB PVK PPV PTPTB PEDOT-EHI-ITN PCBM Al

Electron affinity (eV) −4
7 −3
8 −4
5 −4
0 −4
7 −3
0 −3
0 −4
0 −4
2 −0
5 −2
2 −2
6 −3
5 −4
0 −4
1 −4
3

Gap (eV) 0
0 3
1 2
6 2
6 2
0 2
4 2
3 1
4 2
0 3
8 3
6 2
5 1
8 0
5 0
0 0
0

phenomena in the composite material must involve hopping between individual nanocrystals. In this perspective the chemical nature of the capping ligands is of crucial importance. The exchange of “classical” ligands such as TOPO or HDA, containing aliphatic substituents which act as isolating barriers, for “tailor made” ligands with functional groups facilitating charge transport is a challenging area of nanocrystal and polymer chemistry.

5.3. Conjugated Polymer/Nanocrystal Composites as New Materials for the Fabrication of Organic–Inorganic Solar Cells At the beginning of this section it is instructive to briefly discuss the operation principle of photovoltaic cells and in particular of polymeric solar cells. Photovoltaic cells are devices which transform radiation energy originating from solar light into electricity. A polymeric solar cell, in its simplest version, consists of a layer of a semiconducting conjugated polymer, sandwiched between two electrodes of different work functions. One of them must be transparent and consists usually of ITO (indium tin oxide). Radiation induces the formation of excitons, which then undergo dissociation followed by the migration of the created positive and negative charges to the electrodes. However, in such a simple device the photoinduced charge generation, required for the operation of the cell, is extremely inefficient [101]. Semiconducting conjugated polymers are, in their large majority, good electron donors upon photoexcitation. If an electron-accepting molecule is available in close vicinity, the photoinduced charge generation is facilitated. First electron acceptors used together with conjugated polymers in “plastic” solar cells were fullerene (C60 ) molecules. One can imagine that a fullerene layer is introduced between the anode and the semiconducting polymer layer. This results in an increase of the efficiency of photoinduced charge generation at the polymer layer/fullerene layer interface [102]. Even further improvement of the conversion efficiency is achieved when the previously described bilayered heterostructure is replaced by a single composite layer consisting of C60 dispersed in a conjugated polymer matrix [103]. In this case the large interface area promotes the photoinduced charge generation. The formed charge carriers are then transported to the electrodes via the polymer phase (holes) or the fullerene phase (electrons), which percolates. The same principle applies to solar cells in which, instead of fullerenes, A(II)B(VI) semiconductor nanocrystals are used as composite components, facilitating the dissociation of excitons [104]. This type of solar cell is schematically depicted in Figure 4. As in “pure polymeric” solar cells, ITO is used as a transparent cathode, and aluminum, deposited by vacuum evaporation, as the anode. Additionally a hole transporting layer separates the ITO electrode and the polymer/nanocrystals composite with the goal to facilitate the transport of the charge carriers to the cathode. This additional layer consists of a molecular blend of poly(ethylene dioxythiophene) with poly(styrene sulfonic acid) (abbreviated as PEDOT:PSS), the latter serving as the dopant increasing electrical conductivity of PEDOT.

Nanocrystals in Organic/Inorganic Materials Aluminium Nanocrystal/conjugated polymer blend

hν

PEDOT:PSS ITO Glass substrate

Figure 4. Schematic representation of a polymeric/nanocrystal solar cell.

The composite material used in [104] consists of 90 wt% CdSe nanorods (7 nm by 60 nm) in poly(3-hexylthiophene). The authors claim that (1D) nanorods are preferable to spherical (0D) nanocrystals as they exhibit improved electrical transport due to directed particle stacking as a result of the elevated aspect ratio. Very high mass fractions of nanorods in the composite material are necessary to facilitate the transport of electrons, which at low contents of nanorods occurs via inefficient hopping. As shown in earlier studies [98], the capping ligand TOPO, forming a 1.1 nm thick layer at the surface of CdSe nanocrystals, causes a significant decrease in the device efficiency, as it acts as a charge barrier. This problem can be overcome by using a pyridine/chloroform solvent mixture for the preparation of the polymer/nanocrystal composite [104]. Pyridine is known to easily displace TOPO molecules at the nanocrystal surface, acting itself as a weakly bound ligand subsequently. The extent of photoluminescence quenching in the composite material characterizes the efficiency of the charge separation via exciton dissociation. Many literature examples report a weak remaining photoluminescence of the polymer and/or the nanocrystals, which may originate from a lowering of the polymer/nanocrystal interface area caused by the presence of isolated nanocrystal aggregates and zones significantly enriched in polymer. In this context two types of materials can be distinguished: first, composites in which the conjugated polymer absorbs solar light and excitons can be created in both the nanocrystals and in the polymer matrix; second, composites in which the conjugated polymer does not absorb in the visible spectrum and photoexcitation exclusively takes place in the nanocrystals. In the former, which is the more common case, different photophysical processes are possible [98]: (i) absorption and exciton formation in the polymer, followed by electron transfer onto the nanocrystal (ii) absorption and exciton formation in the polymer, followed by exciton transfer onto the nanocrystal and subsequent hole transfer onto the polymer (iii) absorption and exciton formation in the nanocrystal, followed by hole transfer onto the polymer (iv) absorption and exciton formation in the nanocrystal, followed by exciton transfer onto the polymer and subsequent electron transfer onto the nanocrystal For a given composite material process (ii) excludes process (iv) and vice versa because such Förster-type exciton transfer occurs solely from the larger to the lower bandgap component. Further insight into the photophysical properties of a device can be provided by photoconductivity measurements revealing the spectral response of the photocurrent. Hereby the short-circuit current is measured as a function of the

597 wavelength of the incident light. Obviously the spectral response depends strongly on the absorption spectrum of the composite material. To a first approximation, such a spectrum consists of the sum of the absorption spectra of the conjugated polymer and of the nanocrystals. For the former, the position of the absorption bands depends strongly on the chemical structure, whereas for the latter the absorption threshold depends on size (see Section 2.2.1). Therefore the spectral response can be improved by using CdSe nanocrystals with large diameters, since they absorb the largest part of the visible spectrum. Further improvement toward absorption of solar light in the near infrared region can be achieved by applying either smaller bandgap semiconductor nanocrystals or polymers which absorb in this area. An important parameter is the short-circuit quantum efficiency which represents the numbers of electrons generated per photon. It can be used to determine the optimum content of nanocrystals for a given polymer/nanocrystal couple and solar cell configuration. Although in the majority of cases the charge separation is very efficient, the overall efficiency values may be significantly lower than unity because of problems with charge transport to the electrodes. More precisely, electrons are trapped within the (imperfect) nanocrystal network, in so-called “dead ends,” from which they cannot reach the electrode and recombine instead with holes in the surrounding polymer. This mechanism is consistent with an observed linear intensity dependence of the photocurrent at low intensities. Transmission electron microscopy studies of the composite thin films reveal polymer rich zones separated from nanocrystals 98 104. In general, structural and morphological properties of the composites are strongly influenced by the type of the conjugated polymer, nanocrystal form, size, content, type of surface ligands, solvents used, and last but not least the film preparation conditions. As a consequence, it is very difficult to optimize a system and at present the control of the composite morphology is the most important drawback for conjugated polymer/nanocrystal composite devices. From a technological point of view, conjugated polymer/nanocrystal composite systems offer rather facile processing steps for the fabrication of solar cells, which are in addition not very energy consuming. However, the values of the energy conversion efficiency of these devices are still significantly lower, not only with respect to those reported for crystalline silicon based solar cells, but also in comparison to cells fabricated from amorphous silicon [105]. Given the large number of different parameters which characterize the performance of photovoltaic cells, it is sometimes difficult to compare literature values. To eliminate this problem, all data given in the following represent energy conversion efficiencies under air mass (AM) 1.5 conditions (typical solar spectrum, 100 mW/cm2 ) according to the relationships [4] energy conversion efficiency fill factor

= ISC UOC FF/P

FF = IM UM /ISC UOC 

(8) (9)

where ISC is the short circuit current and UOC the open circuit voltage of the cell. IM , UM are the current and voltage, which provide maximum power output of the cell and P stands for the integral radiation power per device surface area.

Nanocrystals in Organic/Inorganic Materials

598 In Table 5 the energy conversion efficiencies of devices based on conjugated polymer/nanocrystal composites are compared to a number of “all-inorganic” and “all-organic” solar cells. This list is nonexhaustive and serves rather as an illustration of technological trends in solar cell technology. Thermodynamic calculations show that, if one assumes an ideal behavior, there exist a “limit” energy conversion efficiency of ca. 30% and an optimum value for the energy gap of the light absorbing material. The latter accounts for ca. 1.5 eV, a value for which the maximum of energy can be transferred from the incident sunlight to excitons [106]. As can be clearly seen from the data in Table 5, “classical” silicon based devices possess the highest performances approaching the limit value. Furthermore they exhibit an excellent long-term stability versus aging processes such as photocorrosion. The latter parameter is of crucial importance for large-scale terrestrial applications. Nevertheless the high production costs of large-size crystalline silicon devices makes research on substitute materials indispensable. Recent progress on photovoltaic devices based on conjugated polymer/nanocrystal composites [104] resulted in the fabrication of solar cells with conversion efficiencies reaching the same range as reported for “plastic” solar cells with fullerene admixtures, such as MEH-PPV/C60 [103]. Taking into account the relatively short time since their discovery and their easy fabrication as compared to crystalline silicon based devices, this research direction seems very promising. Still significant effort must be put into improving their efficiency and long term stability.

5.4. Light Emitting Diodes Made of Conjugated Polymers and Nanocrystals A light emitting diode (LED) is an electronic device which exploits the phenomenon of electroluminescence. In an elementary manner, electroluminescence can be defined as light generation caused by electrical excitation. In this Table 5. Energy conversion efficiencies reported for photovoltaic devices of various types. Material Crystalline silicon Polycrystalline silicon Amorphous silicon Dye-sensitized mesoporous TiO2 /redox couple in liquid electrolyte Dye-sensitized mesoporous TiO2 /OMeTAD (solid state) MEH-PPV/C60 MDMO-PPV/PCBM MEH-PPV/CdSe nanocrystals P3HT/CdSe nanorods

(AM 1.5)

Ref.

24.4% (12–16%) 18% (9–12%) 13% (4–8%) 10–11%

[107]

2.6%

[110]

1.4% 2.5% 0.2% 1.7%

[103] [111] [98] [104]

[108] [105] [109]

Note: In addition to the highest reported value, the numbers in brackets indicate typical values observed for the corresponding device type (see the Appendix).

respect LEDs can be considered as inverse to photovoltaic cells. The simplest version of a LED consists of a single layer of a semiconducting electroluminescent material, sandwiched between two electrodes. Similar to the case of photovoltaic cells, one of the electrodes must be transparent to transmit the light created through electroluminescence. Such a one-layer/two-electrode device is called an electroluminescent diode because it shows I–V characteristics typical of diodes. This means that up to a given voltage no current flows and, above this onset voltage, the current quickly increases with increasing voltage. If the quantum efficiency for electroluminescence is constant, the luminance–voltage characteristics follow the current–voltage characteristics. The operation of a single-layer device can be described as follows. Opposite charge carriers (holes and electrons) are injected into the semiconductor layer from the anode and cathode, respectively. The injected charges may form either singlet or triplet excitons, while only the former decay radiatively to give out light. In more advanced structures, additional layers, which lower the barriers for hole and electron injection are used, the so-called “hole transporting layer” and “electron transporting layer.” In the past 12 years impressive progress has been achieved in the fabrication of conjugated polymer LEDs, with lifetimes exceeding several thousands of hours and external efficiencies ext as high as 20% 112 113. An alternative way to fabricate LEDs is the use of an emissive layer made of nanocrystals. However, to date the reported efficiencies of such devices are far below those of presently developed polymeric LEDs, with the highest value being ext = 0
52% [114]. So why is it still interesting to perform research on conjugated polymer/nanocrystal LEDs? The principal reason is that semiconductor nanocrystals of low polydispersity show emissive properties unmatched by any class of polymeric chromophores. Typical electroluminescence linewidths of nanocrystals are as low as ca. 30 nm (FWHM) whereas emissive lines of conjugated polymers are much broader and frequently perturbed by the vibrational structure [113]. One may expect that conjugated polymer/nanocrystal composites may combine the efficiences of polymeric LEDs with the color purity of semiconductor nanocrystals. In reality this is only possible when an efficient energy transfer from the polymer host to the nanocrystal occurs, resulting in electroluminescence essentially from the nanocrystals. However, the optimization of a LED with an emissive layer consisting of a conjugated polymer/nanocrystal composite is a difficult task. First, an appropriate core/shell system has to be selected, which efficiently shields the created excitons localized in the core from nonradiative relaxation induced by interactions with the polymer host. Simultaneously the energy transfer from the polymer host to the nanocrystals must be possible either through charge transfer or through neutral-excitation energy transfer via Förster or Dexter mechanisms [115]. An advantage of conjugated polymer/nanocrystal LEDs is the precise tunability of their emission color. This can be done throughout the whole visible range of the spectrum in the case of CdSe core nanocrystals. By using a semiconductor with a different bandgap, the flexibility can even be further extended to other spectral regions, for which no appropriate polymeric emitters exist. To give an example, when

Nanocrystals in Organic/Inorganic Materials

InAs/ZnSe core/shell nanocrystals are applied, a conjugated polymer/nanocrystal LED emitting in the near infrared can be realized [116]. Moreover, by mixing polymers with fractions of nanocrystals differing in size one can produce LEDs emitting white light. Similar to the case of photovoltaic cells 102 103, two device architectures are possible: (i) The nanocrystals and the conjugated polymer form a bilayer structure. (ii) The nanocrystals are dispersed in the conjugated polymer. The latter facilitates energy transfer between the polymer and the nanocrystals; however, it also increases the possibility of different nonradiative relaxation pathways (vide supra). Composites of semiconductor nanocrystals with conventional polymers, which do not show semiconducting properties, have been used in the fabrication of tuneable “nanocrystal–polymer down-conversion LEDs” [117]. The principle of these devices, based on CdSe/ZnS core/shell nanocrystals, can be outlined as follows. Due to their absorption threshold in the visible part of the spectrum, different sized nanocrystals can be excited simultaneously by a single, shorter wavelength light source. Therefore, if the light of a blue emitting diode passes through a nanocrystal–transparent polymer composite, it is absorbed and re-emitted in a color depending on the size of the nanocrystals (see Fig. 5). By controlling the ratio of different sized nanocrystals one can precisely tune the color of the re-emission. Of course, the polymer matrix must fulfill several conditions. First, nanocrystals dispersed in the polymer should retain their original emission efficiency to the largest possible extent. Second, the matrix must be amorphous to assure optical transparency. Third, nanocrystals should be homogeneously dispersed in the matrix since their aggregation not only lowers the transparency of the composite but also results in some luminescence quenching. Poly(alkyl methacrylates) with long and branched alkyl substituents, for example poly(lauryl methacrylates), respond to these requirements. The composite can be obtained by radical polymerization of the corresponding monomer (lauryl methacrylate) in the presence of ethyleneglycol dimethacrylate as the cross-linking agent and CdSe/ZnS core/shell nanocrystals [117]. Thereby composites exhibiting good optical quality and low luminescence quenching can be fabricated.

Blue LED Nanocrystal/polymer composite

Figure 5. Scheme of a nanocrystal/polymer down-conversion LED.

599

6. HYBRID ORGANIC/INORGANIC SYSTEMS The composite materials described in Section 5 are sometimes referred to as “hybrid systems” in the literature, despite the fact that they are simple physical mixtures of conjugated polymers and nanocrystals of different degrees of dispersion. Thus, from a chemist’s standpoint this is not totally correct since the term “hybrid system” or “hybrid molecule” is reserved to a chemical species consisting of at least two entities of different origin (for example, inorganic and organic), which are linked together by chemical bonds. One can easily imagine several types of true polyconjugated molecules/nanocrystal hybrid systems. This is an emerging area of research and to the best of our knowledge the only true hybrid system reported to date is penta(alkylthiophene) phosphonic acid, grafted on CdSe nanocrystals [118]. The synthesis of this hybrid material, consisting of conjugated oligomer/nanocrystal adducts, is very promising, since phase separation phenomena are less pronounced in this case as compared to the physical mixture of both constituents. Moreover, even relatively short conjugated oligomers usually well mimic the majority of physical properties of their corresponding polymers. If for the grafting reaction linear oligomers with two reactive functional groups were used, a three-dimensional network of nanocrystals linked by conjugated spacers could be created. Among other potential approaches leading to conjugated macromolecule/nanocrystal hybrid compounds of different topology, one seems especially interesting. It involves the synthesis of comb-shaped polymers in which the pending groups, attached to the conjugated backbone, bind to nanocrystals. This idea is closely related to the fabrication of so-called “double-cable polymers,” which has recently been developed in connection with the fabrication of polymeric photovoltaic cells of the newest generation [111]. In a double-cable system side groups being good electron acceptors are attached to a conjugated polymer, which is in turn a good electron donor. This can be exemplified by grafting functionalized fullerenes such as PCBM to conjugated polymers [111]. The term “double cable” points out the ability of this true hybrid system to transport simultaneously electrons and holes to the corresponding electrodes. In principle, double-cable polymers containing nanocrystals as pending groups are very promising candidates for the fabrication of photovoltaic cells, especially in view of the fact that even simple physical mixtures of nanocrystals and conjugated polymers yield devices with remarkable efficiencies (see Section 5.3). Although the research on true conjugated polymer/nanocrystal hybrids is just in the beginning stages, several advantages of these systems with respect to the corresponding composite materials can already be pointed out. First, the separation of charge is facilitated in this case, since both the electron donor and the electron acceptor are inherent parts of the same chemical entity and for this reason no interface, in the classical sense of the term, exists between them. Furthermore, the chemical bonding between the organic and inorganic components eliminates or

Nanocrystals in Organic/Inorganic Materials

600 at least strongly impedes phase segregation in solid films of hybrid materials. The latter is the principal problem of polymer/nanocrystal composites, showing frequently the coexistence of polymer rich and nanocrystal rich zones. As a result, in true hybrid materials, electron transport to the electrode can occur in a more efficient way, as “dead ends” in the nanocrystal network are suppressed. Generally conjugated polymer/nanocrystal hybrids provide better control of the

material morphology with the possibility to build up really interpenetrating organic/inorganic networks. Finally, from a synthetic point of view, hybrid systems facilitate the preparation of high-quality thin films by casting from solution. This is an advantage over composite materials because for the latter it is sometimes difficult to find a cosolvent, which enables the simultaneous dissolution of the polymer and the colloidal dispersion of the nanocrystals.

APPENDIX: CHEMICAL STRUCTURES O

O

Na(AOT)

+

SO3 - Na

Bis(2-ethylhexyl)sulfosuccinate O

TOPO

Trioctylphosphine oxide

TOP

Trioctylphosphine

HDA

Hexadecylamine

PPV

Poly((p-phenylene)vinylene)

O

O

P

P

H H

N

(CH2 )15

CH3

* n

MDMO-PPV

Poly-((2-methyloxy-5-(3,7-dimethyloctyloxy)-p-phenylene)vinylene)

*

O * n

*

O

MEH-PPV

O

Poly((2-methoxy-5-(2′ -ethylhexyloxy)-p-phenylene)vinylene) *

n

*

O

continued

Nanocrystals in Organic/Inorganic Materials

601

Appendix. Continued

CN-PPV

O

Cyano-PPV

CN * n

*

O

PCBM

{6,6}-Phenyl C61 butyric acid methyl ester

Polyanilines PANI-LEB

Leucoemeraldine base

NH n

PANI-EB

Emeraldine base

NH

NH

N

N n

PANI-PB

Pernigraniline base

N

N n

PVK

Poly-N -vinylcarbazole

N * n

* N S

C12H25

PTPTB

Poly(N -dodecyl-2,5-bis(2 -thienyl)pyrrole-2,1,3-benzothiadiazole) ′

N *

S

N

S n

O

PEDOT

O

Poly(ethylene dioxythiophene) *

n

S

* n

PSS

*

*

*

Polystyrene sulfonic acid SO3 H

PEDOT-EHI-ITN

Poly(benzo[c]thiophene-N -2′ -ethylhexyl-4,5-dicarboxylic imide)

O

*

N

O

S

n

*

continued

Nanocrystals in Organic/Inorganic Materials

602 Appendix. Continued

OMeTAD

2,2′ ,7,7′ -Tetrakis(N ,N -di-p-methoxyphenyl-amine)9,9′ -spirobifluorene

P3HT

Poly(3-hexylthiophene)

ACKNOWLEDGMENTS The authors thank Joël Bleuse and Bernard Metz for critical review of the manuscript.

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Encyclopedia of Nanoscience and Nanotechnology

www.aspbs.com/enn

Nanodeposition of Soft Materials Seunghun Hong, Ling Huang Florida State University, Tallahassee, Florida, USA

CONTENTS 1. Introduction 2. Dip-Pen Nanolithography 3. Microcontact Printing 4. Conclusions Glossary References

1. INTRODUCTION 1.1. History of Writing Direct deposition is one of the oldest methods to create patterns on solid surfaces. The early Egyptians, Romans, Greeks, and Hebrews utilized pens to write on papyrus and parchment paper. One of the oldest pieces of writing on papyrus known to us today is the Egyptian “Prisse Papyrus” which dates back to 2000 B.C. The Romans used reed pens to write documents on paper [1]. Then quill pens appeared at about 700 A.D., and it became the main writing tool until 1800 A.D. Quill pens are made of birds’ feathers. When the ink-coated pen is in contact with paper, liquid ink flow is driven onto paper via capillary flow. After the development of advanced metallurgy during the industrial revolution, feathers were replaced by metallic nibs. However, the basic strategy of utilizing capillary flow has not changed. One important event in the history of pens may be the invention of fountain pens. Working fountain pens were first invented by Lewis Edson Waterman in 1884 [2]. Before the invention of fountain pens, one had to dip the pen in the ink well frequently to write long documents. Waterman attached a small ink well as a part of the pen and modified the shape of the nib to achieve stable ink flow. It should be noted that the fountain pen was realized only after proper scientific understanding about liquid flow and technological advances to build small capillary tubes and ink wells. The development of electronics and mechanics has automated modern pen writing. Current ink jet printers, with the help of microelectromechanical system technology, can now ISBN: 1-58883-062-4/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

deposit a picoliter volume of liquid ink with ∼20
m spatial resolution. However, modern automated pens still share remarkable similarities with their predecessors: liquid ink and capillary flow. In all conventional pen writing, solid ink materials are first mixed with solvent to prepare liquid ink, then liquid ink is deposited onto the surface via capillary flow or small driving pressure on it. After writing, the solvent molecules are vaporized leaving only solid ink patterns on the surface. Another direct deposition strategy is the stamping method in which solid templates with built-in structures are utilized to deposit ink onto the substrate via direct contact. Stamping also has very long history. The “Phaistos disk” found on the island of Crete was produced by pressing relief-carved symbols into the soft clay in 1500 B.C. In 450 A.D., seals were printed with true ink, which was the first instance of actual printing with an incised stamp upon paper. The basic mechanism of the stamping method is quite different from that of pen writing. Unlike pen writing that relies on the capillary flow of liquid ink for deposition, the stamping is based on direct contact between ink and paper. Since the stamping method patterns the entire surface simultaneously in a parallel manner, it is inherently a faster method than pen writing. However, once the template is made, it is very difficult to change its pattern shape. For these reasons, stamping is suitable for producing multiple copies of identical patterns, while pen writing has been extensively utilized to generate a small amount of arbitrary shape patterns very quickly.

1.2. Microfabrication One of the key technologies that enable modern microelectronics and information technology is the micrometer scale photographic patterning method, photolithography. Figure 1 shows the basic steps of the photolithography technique. In this process, solid surfaces are first coated with a polymer resist layer, and then a specific region on the resist layer is exposed to the ultraviolet light through a photographic mask. The exposure of light breaks (or strengthens) the molecular bonding in the polymer resist layer. The exposed (or unexposed) resist layer is specifically removed by immersing the substrate into certain solvents, and the

Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 6: Pages (605–622)

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that depends on the photoresist. It is usually believed that resolution of the photolithography is approximately /2. Extensive efforts have been given to use shorter wavelength light to improve the resolution. Ultraviolet light with a wavelength of ∼160 nm has been employed to fabricate ∼90 nm commercial chips. However, it is increasingly difficult to find a proper optics component for shorter wavelength light. On the other hand, the minimum feature size is also affected by the thickness of the resist layer. It is due to the unpredictable slope at the edge of the photoresist patterns as shown in Figure 1. High-resolution lithography resist layers are usually thinner than 100 nm. Considering these two parameters, the resolution limit of the photolithography technique is believed to be around ∼100 nm. Extensive efforts have been given to develop a next generation lithographic technique that can overcome the resolution limit of photolithography and continue to decrease the size of electronic chips. Possible candidates include X-ray lithography, e-beam projectors, scanning probe-based lithography, and soft lithography [4]. These methods demonstrated lithography resolution down to 10 nm. However, it is not yet clear which method will eventually replace the photolithography technique. Modern nanodeposition methods such as dip-pen nanolithography or microcontact printing also have been extensively developed as a possible candidate to replace photolithography. Since the direct deposition strategy does not rely on light, the resolution is not limited by the wavelength of the light.

1.3. Hybrid Devices Figure 1. Schematic diagram depicting the basic steps of photolithography.

polymer resist patterns were left on the specific area of the substrate. The polymer resist pattern can be used as a resist of subsequent etching or other processing steps. By repeating these processes, many complicated microelectronic components can be created on a single substrate, which enables integrated computer chips and, eventually, modern information technology. During the last four decades, the semiconductor industry has been extensively working on improving the resolution of photolithography method so that more components can be integrated in a single chip. This size reduction and higher degree of integration are crucial to improve the performance and power efficiency of the integrated circuits, which can effectively reduce the manufacturing cost. Currently, microelectronic chips with feature sizes as small as 90 nm are commercially available. There are two major parameters determining the ultimate resolution of the photolithography method: (1) wavelength of light and (2) thickness of the resist layer. The resolution of the photolithography method is subject to the limitation set by optical diffraction according to the Rayleigh equation [3],

On the other hand, we can find another important motivation for the development of nanodeposition methods in soft material-patterning applications. Recent dramatic development of nanotechnology and biological science provide us new nanometer scale building blocks for functional devices (Fig. 2). By combining these new materials with conventional solid-state devices, one should be able to build

R = k1 /NA where  is the wavelength of the light used, NA is the numerical aperture of the lens system, and k1 is a constant

Figure 2. New nanostructures and their possible applications.

Nanodeposition of Soft Materials

a generation of new functional devices. These include biological sensors [85–89] to detect harmful viruses and protein motor-based nanomechanical systems [90]. These new generation devices can be termed as hybrid devices because they are comprised of organic materials as well as solid-state nanostructures. These hybrid devices are expected to flourish for the next few decades because there is a huge demand for new functional devices, especially for medical and biological applications. One significant difference between hybrid devices and conventional solid-state electronics is the mode of fabrication. Since with hybrid devices most of the molecular functional units are first synthesized under solution or vapor conditions, additional nanometer scale assembly steps are required to fabricate such structures. In contrast, the functional components (e.g., transistors, resist) of conventional solid-state devices are directly fabricated by modifying the solid substrate. Conventional microfabrication techniques such as photolithography cannot be used for fabricating molecule-based structures because of the complex chemical reactivity of most of the molecular units. The nanoscale direct deposition strategy seems to be an ideal method because it can deposit general organic materials directly onto solid surfaces without any complicated processing steps. Nanodeposition methods have been extensively utilized to pattern chemical and biological molecules on solid substrates in a nanometer scale resolution.

1.4. Modern Nanodeposition As a possible solution to solve the resolution problem in the semiconductor industry and the compatibility issue in soft materials-based applications, two new direct deposition methods have been drawing attention: (1) dip-pen nanolithography (DPN) and (2) microcontact printing. DPN utilizes an atomic force microscopy (AFM) tip as a nanoscale pen to deposit organic molecular substances onto solid substrates, and its basic idea is similar to that of its macroscale counterpart—the quill pen. The microcontact printing method utilizes micro- and submicrometer scale stamps to print general organic molecules on solid surfaces. Despite their similarities with conventional direct deposition methods, these state-of-the-art nano-deposition methods differentiate themselves from macroscale deposition methods in several aspects: (1) nanoscale resolution and (2) generality in chemical and biological molecular ink. In the following sections, we will provide a comparative overview of these two nanoscale direct deposition methods. Furthermore, we will try to answer several in-depth questions regarding nanodeposition processes: (1) What are the key scientific aspects which enable the nanoscale resolution deposition of general organic molecules? (2) What are the possible future impacts of this new lithographic technology in everyday human life?

607 pen, molecular substances as ink, and solid substrates as paper. Figure 3(a) shows the basic mechanism of DPN as well as approximate dimensions of commonly used pen and ink molecules. When the molecule-coated tip is in contact with the substrate, molecules diffuse out onto the substrate, chemically anchor to the surface, and form well-ordered selfassembled monolayer (SAM) patterns. Under ambient conditions, water condenses at the AFM tip/substrate junction and affects the molecular diffusion. Like macroscale quill pens, the molecular ink coating on the tip surface works as an ink reservoir. A number of variables including relative humidity, temperature, and the tip movement speed can be adjusted to control the ink transport rate, feature size, and linewidth. Figure 3(b) shows an example patterns generated via DPN. With the help of automated lithography software, one can directly print out organic molecular patterns from the PC onto solid substrates like ink-jet printers print graphics on paper. Even though the DPN technique shares remarkable similarities with ancient quill pens, they also have significant qualitative and quantitative differences. First of all, the dimensions involved in the DPN process including the size of the pen and the thickness of the generated patterns are in the nanometer scale regime (Figure 3a), which is crucial in achieving nanoscale patterning resolution. In this case, one can say, “size does matter.” Even with its short history, the DPN method demonstrated unprecedented ∼10 nm patterning resolution [6]. Considering the resolution of current commercial ink-jet printers, ∼20
m,

2. DIP-PEN NANOLITHOGRAPHY 2.1. Key Strategy The DPN process is a new direct deposition technique that was first developed in Mirkin’s lab at Northwestern University in 1998 [6–10]. It utilizes an (AFM) tip as a nanoscale

Figure 3. (a) Schematic diagram depicting dip-pen nanolithography. (b) Nanoscale “greetings” written via dip-pen nanolithography. The letters are written with 16-mercaptohexadecanoic acid on amorphous Au surface.

Nanodeposition of Soft Materials

608 the resolution of DPN is revolutionary. This revolutionary resolution can be attributed to several core scientific developments in nanotechnology including the nanofabrication technique for AFM tip preparation, the self-assembled monolayer for a new type of molecular ink, and nanoscale precision control system for nanoscale AFM tip movements. Second, unlike conventional pens, bulk ink coating on the pen (the AFM tip) usually remains solid throughout the DPN process because DPN writing is usually performed below the melting temperature of molecular ink. [However, readers should be cautioned. At this stage, the exact phase at the tip/substrate junction is not yet clearly understood. Because of the water meniscus and nanoscale dimension of the junction, the phase of molecules at the junction might be quite different from that on the tip surface (Fig. 3a).] Thus, the behavior of molecular ink in the DPN process can be described by individual molecular diffusion rather than capillary flow of liquid ink. In case of a macroscale pen that is based on the capillary flow of liquid ink, the ultimate resolution of pen writing is determined by the properties of ink solvent. It is often very difficult to control the liquid flow in nanoscale resolution due to several unpredictable behaviors of liquid such as viscosity change, ink meniscus, etc. However, in most DPN processes, ink molecules behave like a noninteracting two-dimensional gas whose behavior can be described by the Fickian diffusion model [11]. Molecular diffusion based on random walk is usually easier to predict and control than the capillary flow of liquid. The nanometer scale precision of DPN can be partly attributed to this different phase of molecular ink and writing mechanism. It is also worth mentioning several other important characteristics of DPN. One aspect of practical importance is a stable ink deposition rate. When the DPN process is stabilized, the deposition rate of molecules from the tip to the substrate remains almost constant. The stable writing speed can be attributed to the small contact point between the AFM tip and the substrate. As a result, the amount of ink molecules deposited through the contact point is relatively small compared with the amount of molecular ink (ink reservoir) on the AFM tip surface. This is the same reason macroscale quill pens and fountain pens have a stable ink deposition rate. Second, unlike other scanning probe-based nanolithography methods, DPN is relying on molecular diffusion for writing, and it usually does not require external forces. With the same environmental conditions, the amount of deposited molecules simply depends on the contact time between the tip and the substrate. However, additional forces such as the electric field can be utilized to achieve better control of the process. Third, since DPN is based on diffusion of individual molecules, its behavior depends on several environmental conditions including temperature and humidity. For example, the temperature change can change the diffusion constant of molecules on the surface. The change of humidity should alter the amount of water condensation at the tip/substrate junction as well as that on the surface, and it will change the behavior of diffusing molecules. However, it should be noted that DPN is now able to deposit quite a broad range of molecular species with quite different chemical and physical properties [12–20]. Thus, one should be cautious when

understanding this dependence because the results for each molecular ink may be different depending on the properties of individual molecular species such as hydrophobicity and melting temperature.

2.2. Experimental Procedure 2.2.1. Molecular Ink Various types of organic molecules have been used for DPN experiments. Most commonly used organic molecules form SAMs on substrates (Fig. 4A). These molecules are comprised of three different parts: (1) a chemisorbing group, (2) an end group, and (3) a spacer (inert part). When these molecules are deposited onto a proper substrate, they chemically anchor to the substrate and form a well-ordered stable crystalline monolayer film with a thickness ranging from 1 to 10 nm. Molecules that form SAMs on various substrates are listed in Table 1. Specific binding groups can be chosen depending on the substrate. By depositing these molecules, one can completely change the chemical properties of the surface to that of end groups. Various end groups can be used for specific applications. For example, one can even use specific sequence DNA or proteins as end groups. The best characterized systems of SAMs are alkanethiols R(CH2 n SH adsorbed on a gold surface (Fig. 4B). Alkanethiols are chemisorbed spontaneously on a gold surface and form alkanethiolates. This process is assumed to occur with the loss of dihydrogen by the cleavage of the S–H bond. Sulfur atoms bonded to the gold surface bring the alkyl chains into close contact: these contacts freeze out configurational entropy and lead to an ordered structure. For alkyl chains of up to approximately 20 carbon atoms, the

Figure 4. (A) Self-assembled monolayer molecules. (B) Alkanetiols on Au(111).

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Table 1. Self-assembled monolayer molecules on different substrates. Molecular species

Substrate

Example molecules

Ref.

RSH, ArSH

Au Ag Cu GaAs InP

C12 H25 SH, C6 H5 SH, 4-PySH C18 H37 SH, C6 H5 SH C6 F5 SH, C10 H21 SH, C8 H17 SH C18 H37 SH C18 H37 SH, C6 H13 SH

[21–23] [24, 25] [26–28] [29] [30, 31]

RSSR′ (disulfides)

Au

(C22 H45 2 S2 (C19 H39 2 S2 [CH3 (CH2 15 S]2

[32, 33]

RSR′ (sulfides)

Au

[CH3 (CH2 9 ]2 S CH3 (CH2 11 S(CH2 10 CO2 H

[34, 35]

RSO2 H

Au

C6 H5 –SO2 H

[36]

R3 P

Au

(C6 H11 3 P

[37]

RNC

Pt

(C5 H6 Fe(C5 H5 –(CH2 12 –NC

[38]

RSiCl3 , RSi(OR′ )3

SiO2 , glass

C10 SiCl3 , C12 SiCl3 , C16 SiCl3 CH2 = CHCH2 SiCl3 C12 H25 SiCl3

[39–41]

(RCOO)2

Si/Si–H

[CH3 (CH2 10 COO]2 [CH3 (CH2 16 COO]2

[42]

RCH = CH2

Si/Si–H

[43]

RLi, RMgX

Si/Si–Cl

CH3 (CH2 15 CH = CH2 CH3 (CH2 8 CH = CH2

RCOOH

metal oxides

C4 H9 Li, C18 H37 Li C4 H9 MgX, C12 H25 MgX, X = Br, Cl

C15 H31 COOH, H2 C = CH(CH2 19 COOH

CH3 (CH2 m OC10 H6 COOH, m = 9, [15–19]

[44]

[45, 46]

Significantly, when these molecules are deposited via DPN, they also form high quality crystalline SAMs like those SAMs resulting from bulk solution immersion or vapor deposition methods. For example, when 1-octadecanethiol molecules are deposited onto the atomically flat Au (111) surface via DPN, the molecular patterns show hexagonal crystalline structures (Fig. 5). This implies that DPN is based on a natural molecular diffusion and self-assembly process, and the molecule-coated AFM tip simply directs the formation of the self-assembled monolayers in the desired regions. Thin self-assembled monolayer formation is an important factor that enables patterning of very large substrate areas via DPN. DPN relies on thin molecular coating on the AFM tip as an ink reservoir. Considering the total size of commercial AFM tips (∼5
m), the volume of molecular coating on the AFM tip is ∼1
m3 (Fig. 6), which is very small. However, the thickness of DPN-generated patterns is just a single molecular layer, ∼2 nm, implying that a single molecular coating on the AFM tip is enough to cover a surface area as large as 500
m2 . Even though a self-assembled monolayer with chemical surface binding helps reliable DPN writing, the covalent surface binding of molecules to the substrate is not a necessary condition for DPN writing. There are several reports utilizing molecules without covalent binding on the surface. Usually, it is possible to deposit molecules via DPN if the molecules have a large diffusion constant and the affinity to substrate. Various molecular species that have been utilized in the DPN process are listed in Table 2.

2.2.2. Nanoscale Pen

RCONHOH

metal oxides

CH3 (CH2 16 CONHOH HO(CH2 15 CONHOH,

[47]

RPO3 H2

ZrO2

Zr(O3 PCH2 CH2 COOH)2

[48]

In2 O3 /SnO2 (ITO)

RPO3 H2

(C5 H6 Fe(C5 H5 (CH2 6 –PO3 H2

[49]

degree of interaction in a SAM increases with the density of molecules on the surface and the length of the alkyl backbones. This assembly is a very quick process that may occur in a couple of seconds. This ability to form ordered structures rapidly might be one of the factors that ultimately determine the success of nanodeposition techniques. The structures and properties of SAMs of alkanethiolate binding on a gold surface have been extensively investigated using a number of techniques such as contact angle measurement [50], ellipsometry [51], infrared [52], Raman [53], electrochemistry [54], X-ray photoelectron spectroscopy [55], scanning tunneling microscopy (STM) [56], and AFM [57]. As a result, it is generally accepted that sulfur atoms form an overlayer in SAMs. Recent STM studies show that these systems are heterogeneous and structurally complex: The alkyl chains may form a “superlattice” at the surface of the monolayer, that is, a lattice with a symmetry and dimension different from that of the underlying hexagonal lattice formed by sulfur atoms [58].

AFM tips with various shapes and chemical surfaces have been utilized as nanopens for the DPN process. Figure 6 shows the scanning electron microscope (SEM) image of a typical AFM tip made of Si3 N4 . The shape of the AFM tip is determined by the fabrication step. Most common materials for the AFM tips are Si3 N4 and Si. Si3 N4 tips usually have a pyramid shape, while Si tips are conical [62]. The heights of usual AFM tips are about 3–10
m. The diameter of the

Figure 5. Lattice resolved lateral force image of a 1-octadecanetiol selfassembled monolayer deposited onto Au(111) by DPN. The image has been filtered with a fast Fourier filter, and the fast Fourier transform of the raw data is shown in the lower right insert. Adapted with permission from [7], R. D. Piner et al., Science 283, 661 (1999). © 1999, American Association for the Advancement of Science.

Nanodeposition of Soft Materials

610 Table 2. Organic molecular ink tested via DPN. Substrate

Molecules

Binding

Examples

Ref.

Au

alkanethiols

RS–Au

CH3 (CH2 17 SH, HS(CH2 15 COOH

[6–10]

Au

thiol modified DNA

RS–Au

5 –HS–(CH2 6 –CAC GAC GTT GTA AAA CGA CGG CCA G-3′

[55b]

Au

thiol modified proteins

RS–Au

thiol modified collagen

[20]

SiO2

DNA

covalent bond

5′ –HS–(CH2 18 –CAC AAA ACG GGG GCG G-3′

[59]

Si, SiO2

inorganic precursor

Si–O–metal bonding

SnCl4 and P-23, AlCl3 and P-123

[19]

Glass

dye molecules

van der Waals

rhodamine 6G (R6G)

[18]

Glass

protein

chemical bond

cysaxonin-1 on silane modified surfaces

[18]

Glass

polymer

hydrogen bond or electrostatic interaction

PAA and PAM PAA, PAH, and SPS

[18]

Si

metal

electric field induced chemical reactions

H2 PtCl6

[13]

Mica

water

capillary force

H2 O

[60]

SiO2

conducting polymer

electrostatic interaction

DETA

[61]

tip can be as small as ∼10 nm. The sharpness of the tip is one of the major factors determining the resolution of the DPN process. Utilizing commercial silicon nitride AFM tips, Hong et al. demonstrated patterning of ∼10 nm size molecular nanostructures via DPN [10]. Further improvement of the resolution can be expected if special tips are utilized. Possible higher resolution tips are carbon nanotube tips [63] and electrodeposited carbon tips [64]. Since DPN relies on molecular ink coating on the tip surface as an ink supply, ink loading on the AFM tip surface is critical for reliable DPN writing. For reliable ink loading, one should consider the surface chemistry of AFM tips. When the AFM tip is coated from the solution of molecular ink, the amount of loaded ink is determined by the adhesion properties of solvent molecules. Even though clean Si3 N4 and Si surfaces are hydrophilic, the AFM surfaces become hydrophobic after a couple of days of air exposure because of carbon contamination. In the case of nonpolar solvent, one can use commercial AFM tips without special treatment. However, many biomolecules can be dissolved only in polar

′

solvent like water. For stable ink loading of those molecules, surface treatment is required. One common method for the surface treatment is cleaning AFM tips with the oxygen plasma cleaner. Oxygen plasma treatment creates –OH group on the AFM tip surface and makes the surface hydrophilic. However, the effect lasts only for a short time period ranging from a few minutes to a few hours because of the contamination from the air. To achieve the desired functionality on the AFM tip for a relatively long time period, a self-assembled monolayer (e.g., Cl3 SiR-X) can be formed on the plasma treated AFM tip surface [65]. An alternative method is thin solid film coating. For example, evaporation of an ∼10 nm thin titanium coating can make the AFM tip more hydrophilic. However, one should be careful when depositing a metallic film on the AFM tip because solid coating may deform the AFM cantilever significantly. Usually, a solid coating with thickness less than ∼10 nm can change the surface properties without significant deformation of AFM cantilevers. One trick that can be utilized for general molecular species is coating the tip surface with the same solid materials as substrates and then coating the tip surface with ink molecules. For example, if one wants to deposit certain thiol molecules on an Au substrate, the AFM tip can be coated with Au followed by the thiol molecules. Thiol molecules can form a monolayer easily on the Au coating on the AFM tip and thus make the tip compatible with solvent molecules which will be utilized to prepare molecular solution.

2.2.3. Molecular Coating Figure 6. Atomic force microscope tip (nanopen for DPN) made of Si3 N4 .

Molecular coating can be achieved via solution or vapor coating methods. Solution coating is similar to dipping macroscale pens in ink solution. In this method, the solution of a desired molecular species is first prepared utilizing

Nanodeposition of Soft Materials

proper solvents. Then, the AFM tip is dipped into the solution for a short time period (e.g., ∼30 sec), and excess molecular ink is blown dry by clean nitrogen gas. This process leaves a thin solid molecular coating on the AFM tip. In case of 16-mercaptohexadecanoic acid, the AFM tip is usually dipped in the 1 mM solution in acetonitrile for ∼30 seconds. Reliable coating of organic molecules on the AFM tip is one of the keys for successful DPN writing. Molecules with a high vapor pressure can be coated via the vapor coating method. In this method, the AFM tip and molecules are placed together in a small closed reaction vessel and the vessel is heated to vaporize the molecular species. When the vessel is cooled down, the vaporized molecules are adsorbed on the AFM tip surface and a thin molecular layer is formed. In case of 1-octadecanethiol (ODT), 200 mg ODT and AFM tips are placed in a small closed tin can (∼15 ml) and the tin can is heated up to 60  C for 20 min. When the tin can is cooled down to room temperature, the vaporized molecules are adsorbed on the AFM tip surface and leave a thin molecular coating. However, the vapor coating method is usually limited for volatile molecular species. Even though both coating methods leave a solid molecular coating on the AFM tip, the properties of the coatings on the AFM tip via two different methods may be quite different. A vapor coated molecular coating is usually pure and contains less impurities. In case of the solution coating method, the molecular coating on an AFM tip contains a significant amount of solvent molecules for a time period as long as a couple of hours. During the time period, solvent molecules significantly enhance the diffusion of organic molecules and thus enhance the DPN writing speed. For example, 16-mercaptohexadecanoic acid (MHA) molecules coated from 1 mM acetonitrile solution will contain a significant amount of solvent and will have a fast writing speed for a couple of hours. Also, the residual solvent molecules may alter the behavior of DPN writing under different temperature and humidity conditions.

611 that the interaction between the AFM tip and the substrate is much weaker than that in contact mode. DPN writing via noncontact mode may be more suitable for extremely soft nanostructures such as weakly bound proteins [66]. The patterned surface can be imaged and tested with the moleculecoated AFM tip. Since the molecular coating on the AFM tip is very thin, one can still image surface patterns with the molecule-coated AFM tip. The most common method for imaging thin organic molecular patterns is lateral force microscopy (LFM) in contact mode or phase imaging in noncontact mode. Lateral force microscopy measures the tip bending due to the frictional force, while phase imaging measures phase shift of the tip oscillation caused by the attractive force between the AFM tip and the molecular patterns. Since the frictional force also originates from the attractive force, both techniques are, in fact, utilizing the attractive force map to characterize the molecular patterns. In the air, the attractive force is usually determined by capillary force due to water meniscus at the tip/substrate junction. The capillary force is larger than any other attractive forces at least by an order of magnitude. Since the magnitude of the capillary force depends on the hydrophobicity of the tip and the surface, LFM or phase images under ambient conditions simply measure the hydrophobicity of the molecular patterns. In the DPN process, complicated patterns can be generated by the combination of two basic patterns: (1) dots and (2) lines. A dot pattern can be generated by holding the molecule-coated AFM tip at a fixed position on the substrate so that molecules diffuse out in a radial direction to form a circular “dot” pattern (Fig. 7A). The size of the dot pattern is determined by the contact time between the AFM tip and the substrates. Line patterns can be generated by

2.2.4. DPN Writing Once the tip coating is completed, one can create complicated soft nanostructure patterns on the solid surfaces by putting the AFM tip in direct contact with the substrate. Since DPN writing is driven by natural thermal diffusion of molecules, and it does not rely on the contact force, the contact force does not affect the deposition rate of molecular inks much. In this case, a smaller contact force is preferred to avoid any accidental damage on the substrate due to excessive force. In actual DPN writing, the AFM tip is operated in a contact mode with a contact force ∼1 nN and the tip is moved along the substrate to direct the deposition of molecular species onto the desired region. However, some researchers have demonstrated DPN writing in tapping mode. In tapping mode, the AFM tip oscillates and gently taps the substrate. As a result, the AFM tip periodically makes contact with the substrate only in a short time period. In this case, the deposition rate (amount of deposited molecules in a unit time) depends on the AFM set point because the effective contact time changes depending on the set point. The advantage of tapping mode writing is

Figure 7. (A) Typical DPN-generated “dot” patterns. Each dot is generated by holding the AFM tip coated with 16-mercaptohexadecanoic acid at a fixed point on the Au substrate. If the deposition rate is constant, R ∼ t 05 . (B) R vs t graph showing a constant deposition rate of the DPN writing.

Nanodeposition of Soft Materials

612 moving the AFM tip with a constant speed while in contact with the substrate. Here, the linewidth is determined by the moving speed of the AFM tip. To apply the DPN process for practical lithography applications, one should be able to predict the final shapes of molecular patterns. It is especially crucial to precisely predict the sizes of two basic patterns, “dots” and “lines.” If deposited molecules form SAMs with a uniform density, the total number of deposited molecules is proportional to the area of the molecular patterns. Utilizing the assumption of “constant deposition rate” which has been experimentally proved in many cases, a simple empirical equation can be utilized to characterize the DPN generated patterns, Area = C × Contact time where C is the deposition rate. From a practical point of view, this equation implies that if the deposition constant C is measured once, one can precisely predict the pattern size with known contact time. For example, for dot patterns, Area = R2 = Ct, which results in the equation for the radius,
R = Ct/

For line patterns, Area = WL = Ct where W and L are the width and length of the line, respectively. W = C/L/t = C/speed

C can be easily measured by a simple test experiment before actual DPN patterning. Once C is measured, one can generate desired size “dot” and “line” patterns by controlling the contact time and tip sweeping speed. Eventually, one can get more complicated patterns with a high precision. In the scanning probe-based lithography processes which rely on a contact force or electric current as a mean of writing, it is very difficult to precisely predict the shape and size of final patterns. However, in the DPN process, once one finds out the diffusion constant C by a simple test experiment, one can precisely control the pattern size for the rest of the experiments. This predictability is one of the most critical advantages of the DPN process as a practical lithographic method.

2.3. Lithographic Capability 2.3.1. Resolution Limit Hong et al. demonstrated ∼10 nm resolution of DPN writing [6]. The ultimate resolution of DPN should depend on various parameters such as the tip diameter, substrate roughness, and the properties of molecules. Figure 8 shows example patterns of MHA on Au (111) and amorphous gold surfaces. On the atomically flat Au (111) surface, molecular dots as small as 25 nm show isotropic circular shape (Fig. 8A), while the larger dots on the amorphous Au surface are distorted significantly due to the surface roughness (Fig. 8B). These pictures show a routine resolution which can be easily achieved via DPN under ambient conditions without any special preparation. It should be noted that considering the lattice structures of SAMs, a single 25 nm diameter dot is comprised of only 4500 molecules.

Figure 8. (A) Sub-50 nm dot patterns on atomically flat Au (111). Each dot is comprised of 16-mercaptohexadecanoic acid molecules. (B) Molecular dots on an amorphous Au surface showing the effect of surface roughness.

Since DPN relies on direct deposition of molecules utilizing the AFM tip as a pen, its resolution is not limited by the wavelength of light. Sharper tips can be used to achieve better resolution. Current resolution of DPN could be improved if special tips such as carbon nanotube tips are used for DPN writing. The high resolution of DPN can be attributed partly to the properties of ink molecules. Unlike conventional direct deposition methods, DPN utilizes solid ink in most cases, and it relies on molecular diffusion. In case of conventional pens, the ultimate resolution is limited by the ink properties such as capillary size of liquid ink at the pen/surface junction. Since DPN utilizes solid ink, individual molecules diffuse by a random walk, and it is easier to control the molecular flow in the nanometer scale precision. The formation of high quality self-assembled monolayers is another important factor for the high resolution of DPN. It allows one to generate uniform nanoscale patterns reliably via the DPN method. Moreover, DPN has two major advantages over traditional nanolithographic techniques: ultrahigh registration and multiple-ink patterning [6]. Because DPN allows one to image nanostructures with the same tool used to form them, one can use DPN to generate and align nanostructures with preexisting patterns on the substrate with ultrahigh registration (Fig. 9). With the help of the dip-pen nanolithogaphy software, one can generate multicomponent patterns using alignment marks, a strategy analogous to that used to register e-beam lithography patterns. A distinct advantage of this approach over e-beam methods is that it utilizes the scanning probe for generating and locating alignment marks. This is very important because it is less destructive than e-beam methodology for finding alignment marks (i.e., it is compatible with soft materials), and it is an inherently higher resolution imaging technique than optical or electron beam methods.

2.3.2. Multiple Pen Writing DPN writing is based on the thermal diffusion process and does not rely on the contact force. As a result, slight variation of the contact force does not affect the deposition rate in the DPN process.

Nanodeposition of Soft Materials

613 the force between the tip and surface may be different, it still results in the same deposition rate. Hong and Mirkin demonstrated that DPN writing with eight pens and a single feedback gives identical nanoscale patterns (Fig. 11) [8]. The possible maximum force variation on the contact point depends on the mechanical strength of SAMs and substrates. Under ambient conditions, there is a report of applying up to 100 nN contact forces on alkanethiol SAMs without significant structural damage [58]. Extensive efforts are currently given to increase the density of tips. Zhang et al. demonstrated high density 32-pen parallel writing (Fig. 12) [67].

2.4. Applications Figure 9. Left: Diagram depicting the method for generating aligned soft nanostructures. Right: SAMs in the shapes of polygons drawn by DPN with 16-mercaptohexadecanoic acid on an Au surface. An ODT SAM has been overwritten around the polygons. Adapted with permission from [6], S. Hong et al., Science 286, 523 (1999). © 1999, American Association for the Advancement of Science.

One major problem in serial writing processes is patterning speed. Since one has to generate complicated patterns with a single pen, it usually takes much longer time than parallel patterning methods such as photolithography. One strategy to overcome this limitation is writing with multiple pens simultaneously. In most other scanning probe lithography methods, the writing speed depends on the contact force or applied electric field between the AFM tip and substrate. Since these parameters depend on the surface conditions, complicated feedback circuits are required to precisely maintain identical contact forces or electric field on each tip. In this case, to achieve the identical pattern size, one has to build a separate feedback circuit for each AFM tip, which dramatically increases the instrumentation cost. In the case of DPN with multiple pens, even with different contact forces on each AFM tip, each tip should generate the same patterns. Figure 10 shows a schematic diagram depicting the multiple-pen writing strategy. In this scheme, the laser feedback is applied on the AFM tip with the largest separation from the surface to ensure that all other AFM tips are in contact with the substrate. Although

Figure 10. Schematic diagram depicting multiple dip-pen writing utilizing a single force feedback system.

The soft materials patterning capabilities of DPN opens up new possibilities in many practical applications.

2.4.1. Etching Self-assembled monolayer patterns generated via DPN have been utilized to fabricate solid nanostructures (Fig. 13). In this process, the monolayer patterns are used as an etching resist layer. Weinberger et al. demonstrated etching of Au utilizing 1-octadecanethiol as an etching resist layer [9]. Then, the etched Au patterns are used as an etching resist for the silicon etching process (Fig. 14).

Figure 11. Lateral force microscope images of eight identical patterns generated with one imaging tip and eight writing tips coated with 1-octadecanethiol molecules. Adapted with permision [8], S. Hong and C. A. Mirkin, Science 288, 1808 (2000). © 2000, American Association for the Advancement of Science.

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614

Significantly, since the thickness of the SAM is ∼2 nm, it can be an ideal etching resist layer. Also, the resolution of DPN is not limited by optical wavelength. One disadvantage for practical applications might be its speed because DPN is a serial process. Zhang et al. demonstrated fabrication of multiple solid nanostructures via a multiple pen writing strategy [67]. Considering recent active works in multiple pen systems such as Millipede from IBM, further improvement of its speed can be expected. Table 3 shows possible SAM resist layers with corresponding etchants.

2.4.2. Surface-Templated Assembly Figure 12. SEM micrograph of a 32 DPN probe array. The insert shows an enlarged view of a single tip at the end of a beam. Adapted with permission from [67], M. Zhang et al., Nanotechnology 13, 212 (2002). © 2002, Institute of Physics Publishing.

Figure 13. Schematic diagram depicting solid nanostructure fabrication via DPN

Nature uses molecular recognition between complex macromolecules to form sophisticated meso- and macroscopic architectures. Proteins, DNA, and other biomolecular structures all have been programmed to form specific structures based upon relatively simple precursor molecules such as nucleotides or peptides. Recently, significant efforts have been given to construct functional materials utilizing the molecular recognition mechanism. Specific assembly steps inspired by DPN-generated molecular patterns can be utilized to place nanoscale functional elements at the specific position. In the process as depicted in Figure 15, the desired nanometer scale region on the surface is first functionalized with specific organic molecules via dip-pen nanolithography. The molecules contain specific functional groups which have a strong affinity to desired nanostructures. For example, MHA binds on the Au surface with thiol group and exposes carboxylic acid group on the SAM surface. The Fe3 O4 magnetic nanoparticles have a specific affinity to the carboxylic acid groups. After surface functionalization the remaining surface area should be passivated via the SAM with inert functional groups to avoid nonspecific binding of nanostructures. Methyl (−CH3 ) terminated molecules such as 1-octadecanethiol are often used for passivation. Then, the sample is placed in the solution containing desired nanostructures so that nanostructures can assemble onto the desired area via molecular recognition mechanism. Figure 15 shows magnetic nanoparticle patterns assembled onto the SAM surface covered with carboxylic acid groups (−COOH). In this process, nanoscale dot patterns comprised of 16-mercaptohexadecanoic acid are prepared via DPN and the remaining surface is passivated via methyl terminated ODT molecules. Various interactions can be utilized to specifically assemble nanostructures onto a desired surface area. These include covalent bonding, electrostatic interactions, and Table 3. Possible combination of SAMs and etchants.

Figure 14. Nanoscale silicon structures utilizing DPN-generated SAM patterns as an etching resist layer. Adapted with permission from [9], D. A. Weinberger et al., Adv. Mater. 12, 1601 (2000). © 2000, Wiley–VCH.

SAM

Surface

Etchant

Example molecules

Thiol

Au

KCN/O2

Ag Cu GaAs

KCN/O2 FeCl3 /HCl HCl/HNO3

RPO2− 3

Al

HCl/HNO3

C18 PO(OH)2

[74]

RSiO3/2

Si/SiO2

HF/NH4 F

HSC15 H30 COOH

[78]

RSiO3/2

Glass

HF/NH4 F

HSC15 H30 COOH

[78]

HS(CH2 15 SH, HS(CH2 18 SH CH3 (CH2 15 SH CH3 (CH2 15 SH CH3 (CH2 15 SH

Ref. [9, 68–70] [71, 76] [69, 72] [69, 77]

Nanodeposition of Soft Materials

Figure 15. Surface-templated assembly process for nanoparticles. An array of iron oxide dots prepared by the surface-templated assembly process. Adapted with permission from [91], X. Liu et al., Adv. Mater. 14, 231 (2002). © 2002, Wiley-VCH.

biomolecular interactions. Biomolecular interaction is especially intriguing because of its variety and specificity. Unlike most other molecular recognition mechanisms where possible choices are limited (e.g., thiol to Au, carboxylic acid to aluminum, etc.), biomolecular recognition provides a virtually infinite number of combinations. For example, Demers et al. demonstrated surface functionalization with single strand DNA (ssDNA) molecules [16]. When the functionalized substrate is immersed in the solution of DNA-functionalized nanoparticles, only nanoparticles with a specific complementary sequence of ssDNAs can assemble to the desired surface area. Suppose one uses ssDNA with n base pairs. Since each base pair of ssDNA can have 4 different sequences (A, T, G, or C), 4n different combinations are possible.

2.4.3. Patterning of Biomolecules Biomolecular patterning via DPN is of huge practical importance. DPN allows one to directly deposit general biological molecules onto solid surfaces with a nanometer scale resolution. This new capability allows one to envision new biomolecular functional devices such as ultrahigh density gene chips or nanoscale biosensors. Usually, additional consideration is usually required for DPN patterning of biomolecules. First of all, most biomolecules are relatively large compared with other selfassembled monolayer molecules. As a result, the interaction between AFM tip and biomolecules can be very large. Contact mode writing with a small contact force or tapping mode writing is often necessary for stable DPN patterning of large biomolecules [6]. Second, most biomolecules prefer water as solvent. So the AFM tip should be treated to make it hydrophilic. Finally, some biological molecules lose their functionality and are destroyed when dried. Those sensitive molecules could be patterned via a surface-templated assembly process instead of a direct deposition method. In

615 this method, the surface is first coated with specific functional groups and the assembly of biomolecules is directed via specific assembly. Wilson et al. demonstrated direct patterning of ∼100 nm size thiol-modified collagen molecules on a Au surface [20]. In this experiment, thiol groups bind to the Au surface and form stable structures. However, they also observed that the contact mode writing is not suitable for patterning large biomolecules because direct contact of the AFM tip to the molecules can destroy the biomolecular structures on the surface. Tapping mode patterning is first applied to generate the organic molecular patterns on the surface. In the tapping mode, the AFM tip gently taps the surface without a direct contact, which can minimize the interaction between AFM tip and the surface nanostructures. It allows one to create stable biomolecular structures with less damage. By this method, Wilson et al. created a collagen patterns with 30 nm linewidth [20]. Demers et al. demonstrated direct deposition of thiolmodified DNA molecules (Fig. 16) [93]. To enhance the ink loading on the AFM tip, the surface of the AFM tip is first modified by 3′ -aminopropyltrimethoxysilane, which promotes reliable adhesion of the DNA ink to the tip surface. Demers et al. also demonstrated the direct deposition of DNA onto the SiO2 surface. Before the DPN writing, the surface of the thermally oxidized Si wafer was activated with 3′ -mercaptopropyltrimethoxysilane. Then, DNA molecules with acrylamide groups are deposited via DPN, and they form stable nanostructures on the surface. The final patterns are characterized by nanoparticle assembly and optical methods. On the other hand, some proteins lose their functionality when dried for DPN experiments. One example might be motor proteins such as actomyosin. In this case, the surface is first patterned via other chemical molecules and the assembly of proteins in the protein buffer solution is directed via electrostatic interaction. This method allows one to pattern sensitive biological molecules while maintaining their functionality. Demers and Mirkin demonstrated patterning of DNA molecules via indirect surface-templated assembly process [16].

Figure 16. Direct patterning of multiple-DNA inks by DPN. (A) Combined red–green epifluorescence image of two different flourophorelabeled sequences (Oregon Green 488-X and Texas Red-X) simultaneously hybridized to a two-sequence array deposited on a SiO2 substrate by DPN. (B) Tapping mode AFM image of 5 and 13 nm diameter gold nanoparticles assembled on the same pattern after dehybridization of the fluorophore-labeled DNA. Adapted with permission from [93], L. Demers et al., Science 296, 1836 (2002). © 2002, American Association for the Advancement of Science.

Nanodeposition of Soft Materials

616 2.5. DPN Theory 2.5.1. Diffusion Model Jang et al. presented a theoretical model explaining DPN as a three-step process (Fig. 17) [11]: (1) constant rate molecular deposition, (2) lateral diffusion on a monolayer of molecules, and (3) termination of diffusion by chemical binding to a substrate. In many previous experimental results, DPN writing demonstrated almost constant deposition rate (Fig. 7). It is mainly because the amount of deposited molecules is much smaller than the volume of organic molecules on the AFM tip. On the substrate, molecules can diffuse via random walk until they meet the bare Au surface. Whenever the molecules meet the bare substrate, molecules are irreversibly bound onto the surface. For a tip fixed in a position, the ink diffusion is isotropic, giving (filled) circles on the surfaces. Assuming cylindrical symmetry of diffusion and treating the position of ink molecules as continuous variable, a simple analytical theory for the growth of circles can be derived based on diffusion equations and boundary conditions   1  C C = rD t r r r In this picture, molecules cannot move on the bare surface but can diffuse through the region already covered by other molecules. However, the boundary of a circle with radius Rt varying in time has been known as a moving boundary problem, specifically, for a given boundary, Rt the diffusion equation for the number density within (r < R) and outside the boundary with different diffusion constant D (finite) and D′ − > 0, respectively. At the boundary, r = R, the number density is taken to be the monolayer density , and the density flux must be continuous, CR t = C ′ R t = D

C C ′ = D′ r r

where Cr t and C r t are the densities within and outside the boundary, respectively. This kind of boundary growth has been solved for various geometries of boundary including spheres, cylinders, and ellipsoids. The derivation of solution is well described in [79]. ′

In order for the first boundary condition to be met for all t Rt must take the form Rt2 = 2 4Dt The number densities inside and outside the boundary are given by   2  n −r Cr t = − Ei − Ei−2  4D 4Dt C ′ r t = 0 where 2 satisfies the equation 2

e− =

4D 2 n/ 

This analytical result assumed perfectly circular patterns. This assumption can be tested via random walk simulation. In case of random walk simulation, the results do not have perfect cylindrical symmetry assumed in the analytical theory. Thus the boundary of the circular patterns may fluctuate from a perfect circle. This fuzziness of the circle boundary pertains to the quality of circles generated via DPN and thus is of practical importance. The first step quantifying the noncircular deviation is calculating circularity. Moreover, for an N -side polygon whose peripheral points are uniformly distributed, it has been found that N  13869
R / R 04721 where
and are the average and standard deviation of the distance of the peripheral points. The random walk simulation shows that the circularity is independent of the deposition rate and increases as the pattern size increases. This implies that even the very large patterns should have a smooth edge, which is also a very good indication for future DPN patterning applications.

2.5.2. Deposition Jang et al. successfully explained the pattern formation on substrate [11]. However, the theory simply assumed a constant deposition rate and does not provide any explanation about the deposition step. Several researchers presented different models. Sheehan and Whitman adapted a different assumption to describe the DPN process based on the diffusion model [80]. Instead of the constant deposition rate, the density of molecules below the contact point is assumed to be identical to that on the AFM tip and remains constant through the DPN process. This assumption provides a solution different from that of Jang et al. The analytical approximation is Cr t = C0

Figure 17. DPN process with strong surface binding.

Ei r 2 /4Dt ln4Dt/a2 e2 

where Ei is the exponential integral and  is Euler’s gamma (0.577). However, this solution provides only a decreasing flux (deposition rate), and it cannot explain the DPN writing cases with a constant or slightly increasing flux. Considering the complicated geometry of the tip/surface junction

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617

and possible water condensation under ambient conditions, the constant density assumption might be too much simplification. This contradiction implies that it is necessary to consider more complicated aspects of tip/substrate junction such as water meniscus to provide the proper description of the DPN process. Weeks et al. showed a model including the water meniscus at the junction between the AFM tip and substrate [81], where the deposition of organic molecules is explained by dissolution kinetics of organic molecules in the water meniscus at the tip/substrate junction. In the model, the total number of molecules N transferred to the substrate will be given by the integral of the transfer rate dN /dt over the total tip– surface contact time . Two terms contribute to dN /dt: First molecules dissolve from the tip through thermally activated detachment at a rate 

dN dt



+

=

A A

+ = e−ED /kT 2 a a2

where A is the contact area between the tip and the meniscus, a2 is the average area per thiol ink molecule, ED is the activation energy of ink detachment, k is Boltzmann’s constant, T is the temperature, and  is an attempt frequency. Second, molecules return to the tip simply due to improvement and attachment at a rate given by 

dN dt



−

= A − C0 ≈ A



kT 2m

1/2

e−ED /kT C0

where m is the mass of a thiol, E is the activation energy for attachment, and C0 is the concentration of thiols in solution adjacent to the tip. The dot radius is related to N through R2 = Na2 . Combining these relationships gives   r 2 R = A + − a − C0 r dt 2

0

The results show transition to the diffusive regime with a slow diffusion rate after a long time. In the model, the density of molecules on the substrate below the AFM tip is assumed to depend on the dissolution kinetics of thiol molecules and surface diffusion. As described in Section 2.5, the DPN process is based on nanoscale molecular diffusion on solid substrates. Since DPN allows one to deposit organic molecules in a nanometer scale resolution and image the result directly without complication, it can be an ideal tool to study the nanoscale surface diffusion process. In addition to practical applications, the development of DPN brought up many scientific questions: What is the phase of diffusion molecules in nanoscale direct deposition processes? What is the effect of environmental conditions? Is there any interaction between diffusing molecules? These are the questions we have to answer in the future.

2.6. Variation from Conventional DPN The conventional DPN process is based on thermal diffusion of organic molecules and it usually utilizes self-assembled monolayer molecules which chemically anchor to the substrate. However, one can also apply additional driving forces to provide the better control of the deposition process. Also, it is possible to deposit molecules without covalent bond to the substrate.

2.6.1. Electrochemical DPN Li et al. utilized an electric current to induce electrochemical reactions during the DPN writing process. In the electrochemical DPN, precursor molecules are utilized to create metallic structures on solid surface. For example Li et al. coated the AFM tip surface with H2 PtCl6 and applied a current inducing chemical reaction [13] − PtCl2− 6 + 4e → Pt + 6Cl

Here, the water meniscus between the AFM tip and surface works as a small reaction vessel. The writing leaves Pt nanostructures on the silicon surface. Li et al. successfully demonstrated the deposition of Au, Ge, Ag, Cu, and Pd via this strategy [13, 82]. These results demonstrate that DPN can be utilized to generate metallic nanostructures on solid surfaces. Metallic nanostructures are of particular interest in the semiconductor industry because they allow one to modify electronic circuits in nanometer scale resolution without any complicated processing steps.

2.6.2. Nanodeposition via Electrostatic Interaction Conducting polymers are of great interest these days due to their possible applications in organic display and flexible electronic circuits. They form well-ordered crystalline structures on insulating surfaces such as on SiO2 . However, conducting polymers usually do not have strong chemical bindings to the substrate. Since their electronic properties are determined by the crystalline structures, any chemical modification can significantly change their electronic structures. Lim and Mirkin utilized electrostatic interaction between conducting polymers and substrate to create polymer nanostructures on the surface [61]. In the experiment, self-doped sulfonated polyaniline (SPAN) and doped polypyrrole (PPY) conducting polymers dissolved in water are used for writing. SPAN and PPY have negatively or positively charged backbones, respectively. The SiO2 surface is positively charged by coating the surface with trimethoxysilylpropyldiethylenetriamine (DETA) and negatively by piranha solution. Negatively charged SPAN can be deposited only onto the positively charged DETA coated surface, while positively charged PPY molecules can be assembled onto the piranha solution cleaned surface. This experiment first proves that it is possible to generate stable nanostructures utilizing electrostatic interactions. The constant deposition rate is also confirmed in the conducting polymer writing process.

618 2.6.3. Nanografting In most DPN method, molecules are directly deposited onto bare surface. If molecules are deposited on top of other molecular layers, the exchange reaction may occur depending on their binding energies and detailed kinetics. The exchange can be enhanced by a strong contact force during the DPN writing. Xu et al. coated the AFM tip with molecules and wrote patterns on top of other molecular layers [83]. The strong contact force induced the exchange reaction and the molecules from the AFM tip can replace the molecular layer on the surface.

3. MICROCONTACT PRINTING 3.1. Key Strategy The microcontact printing method was first developed by Kumar and Whitesides at Harvard University in 1993 [68]. In this method, soft micrometer scale stamps made of poly(dimethylsiloxane) (PDMS) are utilized to deposit organic molecules onto solid substrates via direct contact like macroscale printing techniques (Fig. 18A). Since microcontact stamping is a parallel printing method, it can pattern a large surface area very quickly (Fig. 18B). Stamping methods have demonstrated ∼35 nm resolution with thiol molecules on a Au surface [69]. However, since the stamps are made of soft polymer materials, the bending of stamps due to swelling of solvent molecules or external pressure is one of the major factors limiting its resolution. In typical applications, the microcontact printing method has been utilized to pattern large surface areas very quickly with a micro- or submicrometer scale resolution. Dip-pen nanolithography and microcontact printing can be good complimentary methods for general organic materials patterning. Microcontact stamping is a parallel printing

Figure 18. (A) Stamping procedure. (B) 1-Octadecanethiol patterns on Au surface generated via microcontact printing.

Nanodeposition of Soft Materials

method which is inherently faster than dip-pen nanolithography utilizing a single pen. However, once stamps are made, it is difficult to modify the design, while DPN allows one to modify and directly print out new patterns from the computer without any intermediate steps. Since the stamping method relies on direct contact for molecular deposition, it can be used to deposit quite large molecules or nanostructures such as a few micrometer long carbon nanotubes. The maximum size of molecules that can be deposited via DPN is usually limited by the size of the AFM tips. On the other hand, the DPN process can have additional driving forces for deposition of various materials including metals. By applying electric current at the AFM tip during the DPN process, Li et al. could deposit metallic nanowires onto solid surfaces, while it is extremely difficult, if not impossible, to apply current during the stamping experiment. Overall, microcontact printing is suitable for patterning large surface areas with submicrometer resolution, while DPN is suitable for rapid prototyping of various nanoscale organic structures. A more comprehensive review about the microcontact printing technique can be found in [4]. Here, we will describe the basic concepts of the microcontact printing method and compare it with the dip-pen nanolithography method.

3.2. Procedures to Make Stamp Figure 19 shows the basic procedure for stamp fabrication. The first step is preparation of a template. The template can be virtually anything with structures. These include TEM grids and photoresist patterns on SiO2 surfaces. Then, PDMS elastomer mixed with a curing agent is poured onto the template and is heated up to 60  C until the PDMS becomes solid. Once the PDMS is cured, it is separated and can be utilized to deposit organic molecules onto substrates. One key condition to make a good stamp is that the template should not have undercut structures. If there are undercut structures as depicted in Figure 19B, it is difficult to separate stamps from the template after the curing process. For example, developed photoresist layer patterns can be a good template because they do not have undercut structures, while etched SiO2 substrates are not a good template because wet etching often results in significant undercut structures.

Figure 19. Stamp fabrication procedure with (A) a good template and (B) a bad template.

Nanodeposition of Soft Materials

A fabricated stamp surface can be coated with molecules from the solution. For reliable stamping, good adhesion of ink molecules on the surface is very important. In the air, the stamp surface usually remains hydrophobic making it suitable for molecular ink based on nonpolar solvent. Additional treatment is required for stamping of water-based molecular solution. A common method for stamp surface modification is plasma cleaning followed by SAM assembly. Plasma cleaning created hydroxyl (−OH) group on the surface, and desired functionality can be achieved by attaching molecules with silyl chloride group. Once the good molecular coating is achieved, one can generate submicrometer scale patterns simply by applying the coated stamp to the solid surface (Fig. 18).

3.3. Mechanism The detailed mechanism is well described in [84]. The major deposition mechanism for microcontact printing is direct contact [(a) in Fig. 20]. However, other deposition routes were also observed: (b) diffusion and (c) vaporization. Direct contact is the major deposition mechanism in the stamping process. The key for successful direct contact is uniform coating of molecules on the stamp surface. In most cases, molecular ink is coated from solution. It is desirable to make the stamp surface favorable to the “solvent.” Another key parameter of stamping is the fast reaction of organic molecules with the surface. The reaction speed of self-assembled monolayer varies depending on molecules and environment. For air sensitive molecules, it is required to do the stamping under a controlled environment such as a nitrogen-filled glove box. Another deposition path is the diffusion of molecules on the substrate. Unlike DPN experiments where the diffusion is the major deposition mechanism, the surface diffusion is not a favorable phenomenon in the stamping method because it increases the pattern size and often results in unpredictable pattern shapes. The equation to describe the diffusion results in the stamping method is also quite different from the DPN experiment. For lines with a fixed length L, the linewidth W of the stamped patterns is proportional to log t, where t is the contact time. This implies that the deposition rate of molecules in the stamping is proportional to 1/t. In the DPN method, the linewidth is proportional to the total contact time t since the deposition rate of molecules remains almost constant. This difference comes from different boundary conditions, especially the different shapes of the deposition region in each process. DPN is relying on a point contact between the AFM tip and the substrate as a deposition region of molecules. As a result, the amount of deposited molecules is much smaller than the molecules on the AFM tip (ink reservoir) and it does not

Figure 20. Deposition routes of stamps: (a) direct contact, (b) diffusion, and (c) vaporization.

619 affect the deposition rate in time. However, the deposition region of the stamping method is the long linear edge of the stamp and the amount of deposited molecules via the diffusion process is comparable to the total amount of ink in the ink reservoir. Another deposition path is vapor deposition. Some volatile molecules can be vaporized and directly deposited onto the substrate. This is another undesirable phenomenon in both stamping and DPN writing. A small amount of vapor deposited molecules usually forms submonolayer films on substrates. To avoid unwanted vapor deposition, molecular ink with low vapor pressure is preferred in both stamping and DPN methods.

3.4. Applications Since the development of microcontact printing [68], the stamping method has been extensively utilized in many applications. There are three major strategies in stampbased applications. First of all, various materials have been directly deposited on the surface in a parallel manner. These include most of the SAM molecules in Table 1, various biomolecules, and very large nanostructures such as nanoparticles or carbon nanotubes. Second, the molecular patterns can be utilized as an etching resist for semiconductor fabrication. Various devices have been demonstrated via the stamping method including silicon transistors and GaAs devices (Fig. 21). Table 3 shows possible etchants for various SAM molecules. Third, the patterned surface can be utilized for the surface-templated assembly process to capture additional materials. In this process, the substrates are first patterned with a self-assembled monolayer and then the substrate is

Figure 21. Micrographs of FETs with various gate lengths L and gate widths Z fabricated by soft lithography. (a) L = 26
m and Z = 16
m; (b) L = 34
m and Z = 30
m; (c) L = 44
m and Z = 32
m; (d) L = 52
m and Z = 47
m. Adapted with permission from [92], J. Hu et al., Appl. Phys. Lett. 71, 2020 (1997). © 1997, American Institute of Physics.

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620

GLOSSARY

Figure 22. Actin proteins assembled onto stamp-generated imidazole SAM patterns.

immersed in the solution which contains desired nanostructures. The desired nanostructures are captured onto the surface via a molecular recognition mechanism. Figure 22 shows actin motor proteins assembled onto stamp-generated imidazole molecular patterns.

4. CONCLUSIONS DPN and microcontact printing are two complementary methods which allow one to pattern general soft nanostructures on solid substrates. DPN is suitable for nanoscale high resolution patterning with a precision alignment. Since DPN can directly print out nanoscale soft material patterns without intermediate processing steps, the time required from pattern design to realization can be extremely short. It is an ideal tool for rapid prototyping of nanoscale devices. On the other hand, the preparation of microcontact stamps takes a long time. However, once stamps are made, they can be utilized to pattern very large surface areas in a parallel fashion quickly. Microcontact printing is an ideal choice to pattern large surface areas with a sub-microscale resolution. The development of nanodeposition methods can be a historic triggering event that opens up the door to new generation devices. Since one can now combine chemical or biological molecules with conventional solid state devices, it is possible to envision new hybrid devices. These include nanoscale biological sensors which can detect a single biomolecular unit [85–89]. Many researchers are now working on new nanoscale mechanical systems driven by the power of biological motor proteins [90]. As predicted by many pioneering researchers, now is the dawn of the new age when people first begin to understand and manipulate individual molecular functionalities. It is the time when mankind first touches the secret of life at the molecular level. For the next few decades, new functional devices assembled by the newly developed nanodeposition methods could flourish and eventually change the face of everyday human life.

Atomic force microscopy (AFM) One of the most common scanning probe microscopy modes. It operates by measuring attractive or repulsive forces between the tip and the sample and provides information on the topography of the surface. AFM probes the surfaces of the sample with a sharp tip a couple of micrometers long and often less than 100 Å in diameter. Depending on the interaction between the AFM tip and surface, there exist various AFM modes such as contact AFM, noncontact AFM, intermittent contact AFM etc. Dip-pen nanolithography (DPN) A recently developed technique which is very useful in the field of nanofabrication and nanometer sized surface modification. It uses the SPM tip as a pen and the target chemical compound as ink to “write” on the sample surface just like a pen writing on paper. This method can produce nanometer sized patterns, which is critical for the nanofabrication of molecular devices and complicated nanostructures. Hybrid nanodevices A generation of new nanometer sized functional devices that are built by combining soft materials with conventional solid-state devices. These include biological/chemical sensors to detect harmful viruses/environments and protein motor-based nanomechanical systems. Microcontact printing A recently developed high resolution printing method which utilizes micro- or submicrometer scale polymer stamps to “print” general organic molecules onto solid surfaces. It has a principle similar to conventional printing techniques, but unlike conventional printing, it utilizes solid substrates (e.g., gold, silicon, etc.) such as paper and soft materials such as ink. The printed feature size is usually in the micrometer scale, but it can be as small as a few tens of nanometers some considerations. Molecular recognition The ability of molecular components to “recognize” other molecular components based on specific interaction forces (e.g., chemical bond, biomolecular interaction, electrostatic interaction, etc.). Nanofabrication Nanometer-scale precision fabrication technology appeared with the development of nanotechnology. This technique can be used to design and produce nanometer sized devices that have distinct advantages such as ultrasmall size, multifunctionalities, and high sensitivity compared to conventional devices. Scanning probe microscopy A widely used instrument in the field of surface/interface research which can provide atomic scale and real-time/real space topography information of the scanned surface. It works by scanning the nanometer sized tip on the substrate surface (or sample surface scanning under the tip) and measuring various interactions (e.g., attractive or repulsive forces, tunneling current, frictional force, etc.) between the tip and the substrate surface, providing the topographic information of the substrate surface. It includes STM, AFM, magnetic force microscopy, LFM, etc. Self-assembled monolayer (SAM) When certain molecules are in contact with a certain solid surface, the molecules will form a highly packed, naturally uniform monolayer on the solid surface via chemical reactions between the function groups of the molecules and the active atoms of the solid surface. It is now widely used

Nanodeposition of Soft Materials

in the field of corrosion inhibition, surface modification, nanofabrication, etc. Soft materials Materials like classifical fluids, liquid crystals, polymers, colloids, and emulsions are representative of what are now identified as “soft” as opposed to “hard” materials. They are materials that flow or distort easily in response to shear and other external forces. When deposited or put on the solid surface, some soft materials can form a chemically stable and highly oriented thin film or even monolayers, which can be used in the fields of nanofabrication and surface modification. Surface-templated assembly A new assembly method based on the interaction force existing between the molecules on the solid surface and the target molecules. In this method, the desired region on the solid substrate is first coated with organic molecules with specific chemical functional groups, and then the substrate is placed in the solution of target molecules (or nanostructures). Due to the specific attractive force between the chemical functional groups on the surface and molecules in the solution, the assembly of molecules (or nanostructures) from the solution is directed only onto the functionalized region of the surface. Especially useful in mass production of some nanometer sized devices.

ACKNOWLEDGMENTS We acknowledge the AFOSR for support of our DPN works and the DARPA for supporting our protein motor research. We also thank P. Bryant Chase at Florida State University for supplying protein motors. Pradeep Manandhar is acknowledged for his help in preparing some figures.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.

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Encyclopedia of Nanoscience and Nanotechnology

www.aspbs.com/enn

Nanodielectrophoresis: Electronic Nanotweezers P. J. Burke University of California, Irvine, California, USA

CONTENTS

1.1. Other Reviews

1. Introduction 2. Overview of Dielectrophoresis 3. Electronic versus Optical Tweezers 4. Trapping and Manipulation of Micron-Sized Objects 5. Trapping and Manipulation of Nano-Sized Objects 6. Applications 7. Unanswered Questions 8. Conclusions Glossary References

The main reference for the fundamentals of dielectrophoresis is Pohl’s 1978 book [2]. The physics of the dielectric properties of biological molecules in solution are covered in a 1979 book by Pethig [3] and a 1978 book by Grant et al. [4]. Pethig [5, 6] has a good review of applications of dielectrophoresis in biotechnology. Another review article covering the manipulation of cells with electric fields is in Führ’s 1996 book chapter [7, 8]. The topic of dielectrophoresis is covered in Madou’s textbook on microfabrication [9]. A review by Hughes [10] discusses some applications of dielectrophoresis in nanotechnology. This review will also be concerned primarily with the applications of dielectrophoresis in nanotechnology: “nanodielectrophoresis.”

1. INTRODUCTION At neutral pH, DNA is a charged molecule. As such, it responds directly to an electric field, the phenomenon of electrophoresis. In contrast, the phenomenon of dielectrophoresis occurs when there is a dc or an ac electric field gradient. In that case, the development of nonuniform electric fields causes a force on any polarizable object, charged or neutral. The term dielectrophoresis was coined by Pohl in 1951 [1], and the general principles are outlined in his 1978 book of the same title [2]. Since then, the use of microfabricated electrodes has been employed for separating micron-sized objects such as cells, and this technology is currently being integrated with lab-on-a-chip systems. This review article discusses recent progress at extending the practice of dielectrophoresis to the nanoscale, for applications in nanomanufacturing, nanobiotechnology, and molecular electronics. Compared to the use of dielectrophoresis for the manipulation of cells, the use of electric fields at the nanoscale to assemble nanocircuits is still in its infancy. ISBN: 1-58883-062-4/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

2. OVERVIEW OF DIELECTROPHORESIS The discovery of dielectrophoresis (DEP) goes all the way back to at least 600 B.C., when Thales of Miletus in Turkey observed that rubbed amber attracted small particles of fluff [2]. In retrospect the amber, being charged up from the rubbing, generated an electric field which polarized the fluff particles. The induced dipole in the fluff particles was acted on by the (nonuniform) electric fields, attracting it to the charged amber. Today we would call this effect (dc) positive dielectrophoresis. In Figure 1, the principle is illustrated schematically. If a polarizable object is placed in an electric field, there will be an induced positive charge on one side of the object and an induced negative charge (of the same magnitude as the induced positive charge) on the other side of the object. The positive charge will experience a pulling force; the negative charge will experience a pushing force. In a uniform field, as depicted in Figure 1A, the pulling force will cancel the pushing force, and the net force will be zero. However, in a nonuniform field, as depicted in Figure 1B, the electric field will be stronger on one side of the object and weaker on the other side of the object. Hence, the pulling and pushing

Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 6: Pages (623–641)

Nanodielectrophoresis: Electronic Nanotweezers

624

where v is the volume of the particle, E
RMS is the RMS value of the electric field (assuming a sinusoidal time dependence), and r is the real part of what is called the Clausius– Mosotti factor, which is related to the particle dielectric constant p and medium dielectric constant m by

Non-uniform field Net force ≠ 0

Uniform field Net force = 0

r ≡ Re




∗ p∗ − m ∗ p∗ + 2m



(4)

Here the star (*) denotes that the dielectric constant is a complex quantity, and it can be related to the conductivity  and the angular frequency  through the standard formula A

B

∗ =  − i

Figure 1. Schematic depiction of dielectrophoresis. The direction of the arrows represents the direction of the electric field; the length of the arrows represents the magnitude of the electric field.

forces will not cancel, and there will be a net force on the object. In this simple overview we have neglected the polarizability of the surrounding medium. If both the medium and the polarizable particle are considered, then one comes to the conclusion that there are two classes of DEP: positive and negative. If the suspended particle has a polarizability higher than that of the surrounding medium, then the DEP force pushes the particle toward the higher electric field region. This is called positive dielectrophoresis. If the suspended particle has a polarizability less than the surrounding medium, the particle is pushed toward the region of weaker electric field, and this is called negative dielectrophoresis.

2.1. Quantitative Force Predictions
a dielectric particle behaves as an In an electric field E, effective dipole with (induced) dipole moment p
proportional to the electric field, that is, p
∝ E


(1)

The constant of proportionality depends in general on the geometry of the dielectric particle. In the presence of an electric field gradient, the force on a dipole is given by F
=
p
· 
E


(2)

Combining the two equations, and using known results for the relationship between p
and E
for a spherical particle of radius r and dielectric constant p , and taking into account the medium dielectric constant m , it can be shown that the force acting on a spherical particle (the dielectrophoresis force) is given by [2, 11] 2  F
DEP = 2vm r 

E
RMS

(3)

 

(5)

Equation (5) also takes into account surface conductances [12–14] of the particles. We must make several comments now about Eq. (3). First of all, the Clausius–Mosotti factor can vary between −0 5 and +1 0. When it is positive, particles move toward higher electric field regions, and this is termed positive dielectrophoresis. When it is negative, the particles move toward smaller electric field regions, and this is termed negative dielectrophoresis. Second, the force grows smaller as the particle volume. This has important implications for the manipulation of nano-sized particles, as we will discuss below. Of course this is a bulk, classical calculation. Surface charges and quantum effects will no doubt be important at the molecular level, and these need to be dealt with. Therefore, the application of Eq. (3) to single molecules may not be quantitatively valid. Third, the dielectric constants of the medium and particle can be highly frequency dependent. This gives rise to a force that can be different at different frequencies, and this fact can be exploited for practical micro- and nanomanipulations based on dielectrophoresis. For example, at one frequency positive dielectrophoresis may prevail, while at another frequency negative dielectrophoresis may prevail. These effects are all buried in the physics of the dielectric response function . Fourth, the derivation of Eq. (3) assumes that the electric field does not vary too strongly; this will have implications when we compare to optical tweezers below. Finally, Eq. (3) is true for both dc and ac electric fields. While there are practical advantages to using ac electric fields to be discussed below, the mathematics of the dielectrophoresis force does not differentiate between dc and ac. Furthermore, it should be noted that the direction of the electric field does not matter. That is to say, in the dc case, for (e.g.) positive dielectrophoresis, the particle moves from the region of weaker field to the region of stronger field magnitude, regardless of the direction in which the field is pointing. For an ac field, the particle experiences a time-varying force, but the time-averaged direction of that time-varying force is always the same, even though the direction of the electric field vector is changing in time. In most cases, the ac component of the dielectrophoretic force can be neglected and we need only concern ourselves with the dc (i.e., time-averaged) component, which is the one given by Eq. (3).

Nanodielectrophoresis: Electronic Nanotweezers

2.2. Generation of Electric Field Gradients

(a) Simple gap

electrode

electrode

electrode

electrode

Historically [2], the use and study of dielectrophoresis was between a sharp pin and a flat surface, because that is the easiest geometry in which one can create a strong field gradient, hence a strong dielectrophoretic force. This has been used to manipulate cells in solution [5, 6], since a cell is polarizable. It has also been used to deflect individual molecules in molecular beams [15]. This application can be considered the first application of nanodielectrophoresis, although the molecular beams were in a high-vacuum system. Since the advent of optical and then electron-beam lithography, the use of micro- and nanofabricated planar metal electrodes on insulating substrates has achieved much more attention, since it allows many different flexible geometries to be designed, tested, and used. Moreover, by using small gaps between electrodes, large electric field strengths can be achieved, thus further increasing (in general) the achievable dielectrophoretic force. Although any arbitrary geometry for planar electrodes can be easily designed and fabricated with modern lithography, the three most commonly used geometries are shown in Figure 2. (The DEP force from these and other geometries can be calculated numerically [16, 17].) Part A shows the simplest geometry, a gap between two electrodes. Because the electrodes are planar, there will be fringing fields out of the plane which are very nonuniform. This design is useful for positive dielectrophoresis, in which case particles are attracted to the edges of the electrodes, or negative dielectrophoresis, in which case particles are pushed away from the plane of the electrodes. In order to achieve a higher electric field gradient, geometry B is sometimes used. The castellations can be square (as shown), triangular, or circular. For both geometries A and B, interdigitated fingers are often used. Geometry C is used normally for negative dielectrophoresis. Huang and Pethig showed that particles experiencing negative dielectrophoresis that are in the plane of the electrodes will get trapped in the center of the

(b) Castellated electrodes

625 electrode geometry [18]. Another design which has received some attention is a spiral electrode design [19]. Modern interest in nanodielectrophoresis, in contrast to that applied to molecular beams in high-vacuum environments, is concerned with the manipulation of molecules in solution, especially for applications in nanobiotechnology, where wet environments are necessary for life itself, but also as methods of nanomanufacturing molecular electronic circuits, integrated with micro- and nanofabricated electrodes. After the dielectrophoresis-assisted nanofabrication occurs, the sample can be dried and the remaining molecules that were placed in position while dissolved now can form the basis of some tailor-designed circuit which in principle was fabricated one molecule at a time. This vision is currently under development but in principle there is no reason it cannot be achieved, as we discuss in the remainder of this article.

2.3. Traps for Negative Dielectrophoresis For negative dielectrophoresis, the polarizable objects feel a force pushing them away from the high field region. Therefore, for most planar geometries, the particles are pushed away from the substrate where the electrodes reside. In 1991, Huang and Pethig calculated [18] the necessary geometry that electrodes need to have in order to trap particles using negative dielectrophoresis at specific locations on the plane of the substrate. The geometry they found which traps a particle at a specific point in the plane of the electrodes is a quadrupole-like geometry. This trap is only in two dimensions, and in the third dimension (perpendicular to the plane of the electrodes), the particle is still not trapped. Gravity or some other force must be exerted to bring the particle close enough to the plane of the electrodes to feel the dielectrophoretic force of the electrodes. Later, work of Schnelle and co-workers [20] and Fuhr and co-workers [21] considered geometries necessary for trapping of particles in all three dimensions. They name these traps “cages.” The most straightforward geometry realized and tested consisted of two quadrupole traps fabricated on two microscope slides which were mounted facing each other with a small gap (of about 0.1 mm). In that work, they trapped 10- m latex particles and cells in three dimensions, with applied ac voltages up to 1 GHz in frequency. We show in Figure 3 an example realization of a quadrupole trap: four gold electrodes surrounding a central

10 µm

3 beads (d=500 nm) in “trap”

(c) Quadrupole 500 nm beads. V = 8 Volts. Figure 2. The most commonly used geometries for the study of dielectrophoresis. The electrodes are usually thin metal films (1–100 nm) fabricated lithographically on an insulating substrate.

Figure 3. Electrodes to trap small particles. Three 500-nm beads can be seen fluorescing but not resolved. We have also been able to trap a single 500-nm bead (not shown).

Nanodielectrophoresis: Electronic Nanotweezers

626 region with 10- m gaps are used to trap a 500-nm latex bead [22]. The frequency used for these studies was 1 MHz, with a voltage of 8 V. With smaller gaps it should be possible to trap much smaller particles, as we discuss below.

2.4. Scaling with Particle and Electrode Size In order to calculate the force acting on any given polarizable particle, one can use Eq. (3) as long as the electric field intensity and (more importantly) its spatial gradient are known. For arbitrary electrode geometries it is possible to numerically calculate this force. However, some simple electrode geometries can be calculated analytically in order to give some general insight into what can be expected for a more complicated geometry. The case of two concentric spheres in this regard can be very enlightening, as the radius of curvature can be used as a rough estimate for the smallest feature size of a given electrode. The electric field between two concentric spheres is straightforward to calculate, and based on this one can calculate the gradient of the electric field intensity. One finds [2] 2r 2 r 2 V 2 2 rˆ 

E
RMS =− 5 1 2 r
r2 − r1 2

(6)

where rˆ is a unit vector in the radial direction, r1 is the radius of the inner electrode, r2 is the radius of the outer electrode, r is the distance from the origin, and V is the applied voltage, as shown in Figure 4. In the case where the inner electrode is very sharp compared to the distance to the outer electrode (i.e., r1 /r2 ≪ 1), this becomes 2r 2 V 2 2 

E
RMS  ≈ − 1 5 rˆ r

(7)

In this case the force exerted on a particle is given by F
DEP =

r 2V 2 −4vm r 1 5 rˆ r

Fthermal ≈ kB T /2rparticle

(8)

r2

(9)

where kB is the Boltzmann constant, T is the temperature, and rparticle is the particle radius. For DEP to be of use, the DEP force must overcome the randomizing thermal motion acting on the particle. In 1978, Pohl used 500 m for the radius of the inner electrode, 5000 V for the applied voltage, and 1 mm for the particle distance from the electrode, and concluded that particles smaller than 500 nm would not respond very well to the DEP force [2]. These numbers were pessimistic, and it should be possible to trap 1-nm and smaller particles, as we now show. First, as our experiments [22], as well as other experiments [23–31] show, it is possible to use optical or electron-beam lithography to fabricate electrodes with much smaller radius of curvature than 500 m (as Pohl originally assumed), and hence to trap submicron particles (see Fig. 3). For example, in our experiments, we trapped 500-nm beads with less than 10 V applied to the electrodes. Second, it is possible in principle to use carbon nanotubes or other nanowires as the electrodes themselves [22], which would have radius of curvatures of less than 1 nm. In this case, for a 1-nm particle that was a distance 100 nm away from the nanotube electrode, our calculations [32] indicate that the DEP force would exceed the thermal force at an applied voltage of only 50 mV. Experiments to test this scaling prediction with carbon nanotube electrodes are currently underway in the author’s lab [22].

2.5. Electrorotation Another effect of an ac electric field on a polarizable object is to orient that object with respect to an electric field. Specifically, the induced dipole moment of an object interacts with the electric field to produce a torque given by T
= p
× E


Now, if the particle were in a vacuum with no other forces acting upon it, then it would respond only to the DEP force. However, in solution, the particle is undergoing Brownian motion, and is continually being bombarded with other molecules of the solution. This thermal motion exerts

r1

an effective random force on the particle, whose maximum value is given roughly by [2]

(10)

where p
is the induced dipole. This effect can be used to orient DNA and nanotubes in solution, and also nanotubes during growth in gas or vacuum, as we will discuss below. It also can be used to orient cells and other micron-sized objects. The term electrorotation is usually applied to a situation where the direction of the electric field is rotating as a function of time. This can be achieved by using four electrodes surrounding a central region, where the ac voltage on each electrode is properly phased. Under the rotating electric field direction, the torque also rotates, and hence the particle rotates. This effect is reviewed in [8, 33].

2.6. Traveling Wave Dielectrophoresis

r

Figure 4. Spherical geometry electrodes for analytical calculation of dielectrophoretic force in the text.

The electrode geometries shown in Figure 2 are useful for trapping particles with either positive or negative dielectrophoresis. However, more sophisticated geometries are possible that allow a particle to be moved. Figure 5 shows schematically a set of electrodes with ac voltages adjusted in such a way as to generate a traveling wave electric field. This traveling wave can act on a polarizable particle and cause

Nanodielectrophoresis: Electronic Nanotweezers 90º

electrode

180º

electrode

270º

electrode

electrode

0º

traveling wave

electrode

electrode

180º

electrode

electrode

effective force

90º

0º

270º

Figure 5. Schematic electrode geometry for traveling wave dielectrophoresis.

a net force in the direction of the traveling wave. In [34], Hagedorn et al. analyze geometries optimum for traveling wave dielectrophoresis. Fuhr in 1994 was able to design and demonstrate a particle manipulator that could apply force in two orthogonal directions [35].

2.7. Summary The combined effects of dielectrophoresis, electrorotation, and traveling wave dielectrophoresis (TWD) have all gone under the same name: “pondermotive force,” as they have the same underlying physical origin. The relationship among these effects is explored in more detail in [8, 36–40]. With the combined use of dielectrophoretic traps, traveling wave dielectrophoresis, and electrorotation, it is possible to electronically control (via microfabricated electrodes) the threedimensional position and orientation of a small micro- or nanoparticle that is suspended in liquid.

3. ELECTRONIC VERSUS OPTICAL TWEEZERS From Eq. (3), we calculate that a typical dielectrophoretic force for a particle of size 100 nm will be roughly 1 fN; the force on a 1- m particle would be roughly 1 pN. In comparison, the force exerted by optical tweezers [41–46] is also the same order of magnitude. In fact both optical tweezers and dielectrophoresis are the same physical phenomena, only different frequencies. For example, our Eq. (3) is equivalent to Eq. (2) in [44]. (There is a factor of 4m difference due to the units, and an incorrect sign in the denominator of [44].) The equations look a little bit different, because optical engineers like to use the index of refraction, and electrical engineers like to use the√dielectric constant; they are of course related through n = . A difference between optical tweezers and electronic tweezers is that optical tweezers also affect particles whose size is comparable to the (optical) wavelength, of order m, the so-called Mie limit. The analogy with electronic tweezers is more appropriate in the limit where the particle size is

627 smaller than the optical wavelength , the so-called Rayleigh limit. For optical tweezers in the Rayleigh limit (particle size ≪ ), the force is proportional to the volume of the particle, as in DEP Eq. (3). For optical tweezers in the Mie limit (particle size ≫ ), the force is independent of the particle size. Furthermore, optical scattering of light in optical tweezers is an important force, whose analog in electronic tweezers is not clear-cut. One main similarity between optical and electronic tweezers is that, when applied to particles in solution, both must strive to overcome the random forces due to Brownian motion. Hence, it makes sense that the induced forces for both optical and electronic tweezers exert comparable forces. To date, both electronic and optical tweezers have not trapped particles with size below 10 nm. However, with nanowire or nanotube electrodes we predict that electronic tweezers can trap particles down to 1 nm in size, which may be useful for nanoassembly. An advantage that electronic tweezers have over optical tweezers is scalability: millions or even billions of electronic tweezers could be easily, economically integrated onto a silicon chip for low-cost “lab-on-a-chip” systems. Additionally, the electronic trap can in principle hold a particle indefinitely, while the optical tweezers in some cases only last for a few seconds due to laser-induced damage. Third, the use of optical tweezers is not possible in optically opaque systems; in contrast, the use of electronic tweezers is difficult in conducting solutions [47], a severe restriction for in vivo operation. Thus, as with everything, both types of tweezers have their own advantages and disadvantages; the choice of which to use will depend upon the application. In fact, in some applications, both types of tweezers have been used in the same experiment [48].

4. TRAPPING AND MANIPULATION OF MICRON-SIZED OBJECTS 4.1. Steel Balls In a pioneering patent [49] granted in 1983, Batchelder proposed the use of lithographically patterned microelectrodes to manipulate and position chemical species, potentially with the ability to manipulate a single molecule, for electronic control of manufacturing. As such, this patent covers the lab-on-a-chip concepts as well as single molecule dielectrophoresis very well, much ahead of its time. Batchelder further described his techniques in a 1983 article [50], where he described one of the first instances of “traveling wave dielectrophoresis.” That was also one of the first instances of photolithographically patterned electrodes for applications in dielectrophoresis. Batchelder’s realization experimental apparatus was capable of manipulating 600- m steel balls and 1-mm water droplets in heptane. In 1987, Washizu and co-workers used this effect to manipulate 15- m solid particles in solution, and also proposed to use it for moving cells [51]. A year later they reported moving blood cells (sheep erythrocytes) using this effect [52]. Those initial experiments were on traditionally machined electrodes.

Nanodielectrophoresis: Electronic Nanotweezers

628 4.2. Cells Interestingly, in two papers appearing in 1989 and 1990 [53, 54], Masuda and co-workers used photolithography for fabricating microelectrodes in order to use DEP to control the position of living cells. They also developed what they coined “fluidic integrated circuit,” which currently would go by the term “lab-on-a-chip.” They used photolithography and a molding process with silicone to make microfluidic channels capable of handling individual cells, and they made a cell-sorter based on dielectrophoresis: cells entering through one microfabricated inlet could be deflected electronically into one of two microfabricated outlets. We show in Figure 6 an example of using negative dielectrophoresis to trap human breast cancer cells in a planar quadrupole trap [55]. As this review is meant to cover mainly nanodielectrophoresis, we will only briefly highlight some of the applications of dielectrophoresis in cell manipulation. The polarizability of a cell is a complicated function of its membranes and inner workings generally, and generally depends on frequency. By exploiting the difference in the frequencydependent dielectric properties of different cells, it is possible to separate out many different kinds of cells from one another and from other microorganisms in solution. The first separation of viable and nonviable (yeast) cells by dielectrophoresis was in 1966 [56]. Chloroplasts were manipulated in 1971 [57]. Cells can undergo both positive and negative dielectrophoresis as was shown in [58, 59]. The separation of viable versus nonviable yeast cells was studied carefully with microfabricated electrodes in [60–62]. Different species of bacteria were separated in [63, 64]. Electrorotation was used to separate leukemia cells from blood in [65]. Electrorotation was used to separate human breast cancer cells from blood in [66]. Concentration of CD34+ from peripheral-stem-cell harvests was achieved in [67]. TWD linear motion of cells was shown in [34, 68]. Viable and nonviable yeast cells were separated with TWD in [69]. TWD was used to separate white blood cells from erythrocytes in [70]. Continuous separation is also possible (viable vs. nonviable yeast cells) [71]. Separation of trophoblast cells from peripheral blood mononuclear cells was achieved in [72]. Separation of breast cancer cells from normal T-lymphocytes (among other things) was achieved using DEP FFF (see next section) in [73]. The manipulation of E. coli and other bacteria with photolithography-fabricated electrodes was reported in 1988 in [74]. The E. coli Cells clumped in “trap”

50 µm

A. Cells. V = 0.

D. Cells. V ≠ 0.

Figure 6. Dielectrophoretic trapping of human breast cancer cells (cell line HCC1806 from ATCC).

were attracted to the high fringing field regions of interdigitated castellated electrodes. Cervical carcinoma cells were separated from peripheral blood cells in [75]. Living (Eremosphaera Viridis) cells were trapped in quadrupole and octopole traps in [20]. An extruded-quadrupole geometry (where the electrodes are metallic posts) was used for cell manipulation in [76]. The effect on cells of the large electric field strengths necessary for DEP (typically 106 V/m) was investigated by Archer et al. [77], who found a 20–30% increase in the expression of fos protein, as well as upregulation of unidentified genes. While the large electric fields are not fatal to cells studied, and their long-term effect on cells manipulated with DEP seems to be minimal, at this stage there is insufficient evidence to draw more quantitative conclusions about the effects of exposure to high electric fields. We note that, once the electrodes are in place for the dielectrophoretic manipulation of cells, it is straightforward and economical to integrate further optical and electronic measurements that are complementary to DEP techniques into the same measurement platform. These can include optical and electronic methods of genetic expression profiling using microarrays, with applications in point-of-care clinical diagnostics, biological warfare detection, and many other applications. For example, Cheng and co-workers separated E. coli bacteria from a mixture containing human blood cells and integrated this with cell lysing and DNA hybridization analysis on a single chip [78]. The integration of electrophoresis and dielectrophoresis using the same electrodes for manipulating E. coli cells with DEP and antibodies with electrophoresis was developed in [79]. DEP was used to separate certain cell types from complex cell populations, which significantly improved the accuracy of gene expression profiling in [80]. In the spirit of integration mentioned above, an integrated system using DEP, DNA amplification, and electronic DNA hybridization for the detection of E. coli and other biological agents was recently developed [81].

4.3. Field Flow Fractionation (FFF) Field flow fractionation (FFF) is a very general chromatographic separation technique in chemistry and biology [82]. The use of dielectrophoresis as the force in field flow fractionation was proposed and analyzed by Davis and Giddings in 1986 [83]. The principle of dielectrophoretic field flow fractionation (DEP FFF) is shown schematically in Figure 7. Part A shows interdigitated finger electrodes, and parts B and C depict the levitation of latex beads when an ac voltage is applied to the electrodes. The levitation height is a function of the dielectric properties of the particle being levitated. If these electrodes are introduced into a laminar flow chamber (typically 100 m thick), the flow velocity parallel to the chamber walls is also a function of height, as indicated schematically in part D. Thus, the speed at which a particle is swept through the chamber depends on the height at which it is levitated, which in turn is a function of its dielectric properties. Since different types of particles (or cells) generally have different dielectric properties, each takes a different time to traverse the chamber. This dependence can be used to separate different particles or cells, and is termed dielectrophoretic field flow fractionation (DEP FFF).

Nanodielectrophoresis: Electronic Nanotweezers

(b) V=0. Beads settle to bottom.

Fluid velocity profile

(a) Image of electrodes. Gaps = 10 µm.

(c) V ≠ 0. Beads “levitate”. Levitation height depends on particle’s dielectric property.

(d) Beads levitating higher are swept through chamber faster than beads near substrate.

629 England achieved trapping of single 93-nm latex beads in 1998 [25, 26]. Green and Morgan used planar microelectrode arrays to separate a mixture of 93-nm and 216-nm latex beads into their constituent components [27]. In 1999, Hughes and Morgan separated unlabeled and protein-labeled 216-nm latex beads [28]. The dielectrophoretic properties of these beads were carefully modeled in [29, 30]. A detailed study of the DEP response of latex beads as a function of electrolyte composition and conductivity, electric field frequency, and particle size for 93-, 216-, and 282-nm latex beads was presented in [31]. The use of latex beads has been and continues to be a good testbed for the use of DEP in manipulating micro- and nanoparticles.

5.2. Molecular Dielectrophoresis Figure 7. Schematic depiction of dielectrophoretic field flow fractionation (DEP FFF).

In 1994, Washizu and co-workers constructed a DEP FFF apparatus and used it to trap DNA of various sizes (9–48 kbp) and the protein avidin [84]. They were able to trap each macromolecule with some efficiency, but separation experiments were not reported. Initial experimental demonstration of DEP FFF separation was reported in 1997, where viable and nonviable yeast cells were separated [85], and human leukemia cells were separated from peripheral blood mononuclear cells [86]. In the same year, demonstration experiments on latex beads were performed [87]. Later experiments have demonstrated the separation of erythrocytes from latex beads [88], separation of mixtures of polystyrene beads [89], and the separation of human breast cancer cells from CD34+ stem cells [73, 90]. Thus, DEP FFF has been successfully demonstrated as a viable technique to separate many micron-sized objects such as cells and latex beads. However, the principles should also be applicable at the nanoscale, and it should in principle be possible to separate objects such as DNA, proteins, viruses, nanoparticles, nanowires, nanotubes, quantum dots, and possibly even small molecules.

5. TRAPPING AND MANIPULATION OF NANO-SIZED OBJECTS In principle, all of the above techniques that have so far proved useful for micron-sized objects such as cells could be useful for nano-sized objects, especially if the nanowires or nanotubes could be used as the electrodes themselves.

5.1. Latex Beads Latex beads have been used extensively in order to test various aspects of dielectrophoresis because they are robust and can be fluorescently labeled, and hence imaged. Furthermore, they are readily available in a variety of sizes from 10 m to 10 nm. The Fuhr group in Germany has been able to trap aggregates of 14-nm latex beads, aggregates of viruses of diameter around 100 nm, as well as single latex beads down to 650 nm in size [23, 24]. Subsequently the Morgan group in

One of the most promising applications of dielectrophoresis in nanotechnology is the possible electronic manipulation of individual molecules. Later in this chapter we discuss the applications such an achievement would enable, such as massively parallel nanomanufacturing of new materials, one molecule at a time, with tailor-designed electronic, optical, magnetic, and mechanical properties. However, to date the clear demonstration of the manipulation by dielectrophoresis of a single molecule has not been achieved for any molecule less than 100 nm in size. A large reason, as discussed in Section 2.4, is that (to date) the thermal Brownian force dominates the dielectrophoretic force for such small objects. While such an achievement may be possible in the future, it is still true that the nonuniform ac and dc electric fields establish some force, which, even though less than the thermal Brownian motion, will still cause a tendency for molecules to move in a certain direction, depending on the geometry of the electrodes. The quantitative study of these effects has been termed “molecular dielectrophoresis” [2]. To date all studies of molecular dielectrophoresis have used positive dielectrophoresis: the DEP force tends to push the molecules toward regions of higher electric fields. The geometry which has been studied almost exclusively is that of two concentric cylinders with the molecules dissolved in a solution in between the cylinders. If the density of the molecules as a function of the radial distance changes, this changes the dielectric constant as a function of the radius, and hence the capacitance from the inner to the outer cylindrical electrode. In 1954, Debye and co-workers used dc dielectrophoresis of polystyrene (molecular weight 600,000) in cyclohexane [91, 92]. They used a dc non uniform electric field in a cylindrical geometry and monitored the capacitance change by measuring the shift in the resonant frequency of an LC circuit; similar studies were carried out by Prock and McConkey in 1960 [93]. In 1955, Lösche and Hultschig [94] used ac dielectrophoresis to study nitrobenzene in carbon tetrachloride, and poly(vinyl acetate) in nitrobenzene; however, both have permanent (instead of induced) dipoles. In 1973 Eisenstadt and Scheinberg [95, 96] studied dielectrophoresis and measured the diffusion constant of the biopolymers poly -benzyl-L-glutamate (PBLG, M.W. ≈ 120 000 and polyn-butyl isocyanate dissolved in ethylene dichloride (EDC);

Nanodielectrophoresis: Electronic Nanotweezers

630 both have permanent dipoles. By measuring the time dependence of the concentration change of the PBLG concentration due to the dielectrophoretic force, Eisenstadt and Scheinberg were able to determine its diffusion constant. Thus, while the manipulation of a single nanomolecule is still not yet achieved, the ability to affect the concentration of large numbers of nanoscale molecules in solution with dielectrophoresis has been demonstrated over 30 years ago, giving hope to the use of nanodielectrophoresis at the single molecule level.

5.3. Conducting Nanoparticles 5.3.1. DC Dielectrophoretic Trapping The basic principle of dielectrophoresis applies regardless of whether the field is dc or ac. (For example, the first recorded instance of dielectrophoresis was dc dielectrophoresis in 600 B.C., as discussed in Section 2.) Furthermore, Pohl calculated that metal balls in water would have the largest dielectrophoretic force of many different possible particle/solvent combinations [2]. In 1997, Bezryadin and Dekker combined these two ideas and used (positive) dc dielectrophoresis to trap 20-nm Pd nanoparticles between lithographically fabricated electrode gaps of about the same distance, that is, 20 nm [97, 98]. The Pd nanoparticles were dissolved in water. Bezryadin applied 4.5 V dc between the gaps, and then investigated the samples with a scanning electron microscope (SEM) after drying. The SEM images showed clearly the presence of one or a few nanoparticles bridging the gap between the electrodes, and this was confirmed by measuring the electrical resistance between the electrodes.

5.3.2. Pearl Chains Particles undergoing dielectrophoresis often exhibit mutual attraction. This is due to the fact that dielectrophoresis involves an induced dipole moment in each particle, and dipoles interact and form what are called “pearl chains.” The tendency of a group of particles in a field to form lines has been known for over two hundred years [2, 99]. This is, for example, responsible for the behavior of electrorheological fluids [100]. Pohl also studied this effect extensively in his experiments in cells [2]. In 1999, Bezryadin et al. observed this pearl-chaining phenomenon in conducting graphite nanoparticles (d = 30 nm), and named it self-assembled chains [101]. They used dc dielectrophoresis with the nanoparticles dissolved in toluene, and applied 40 V across a gap of 1 m between Cr and Pt electrodes. They were able to pass current through this pearl chain of nanoparticles, and furthermore observed Coulomb gap (single electron transistor) behavior at temperatures all the way up to 77 K, because the capacitive charging energy of the nanoparticles was still comparable to the physical temperature even at 77 K.

5.3.3. AC Dielectrophoresis In 2002, Amlani and co-workers used positive ac dielectrophoresis to trap 40- to 100-nm gold nanoparticles between a lithographically fabricated 60-nm gap between two gold electrodes [102]. The gold nanoparticles were dissolved in

water, and a 2.5-V p-p ac voltage between 1 and 10 MHz is found to provide a yield of 100%, much higher than the yield if a dc dielectrophoresis is used. These structures were found to conduct electrically when a single gold nanoparticle was trapped, with a resistance of 3 k. In a second experiment, prior to the dielectrophoretic trapping, the gold electrodes were coated with a self-assembled monolayer of 1-nitro-2,5di(phenylethynyyl-4*-thioacetyl)benzene, a compound similar to one previously studied using a nanopore configuration and found to exhibit negative differential resistance [103]. In the dielectrophoresis experiment of Amlani, the current flow was presumably electrode-molecule-nanoparticle-moleculeelectrode. Amlani and co-workers also observed negative differential resistance at room temperature, presumably due to the intrinsic electronic properties of the molecules in the self-assembled monolayer.

5.3.4. From Nanoparticles to Nanowires In 1999, Velev and co-workers developed a biosensor which is chemically selective based on gold nanoparticles and latex micron-sized beads. The latex beads (suitably chemically functionalized) were assembled into a “pearl chain” wire between two electrodes with positive dielectrophoresis. The target molecules would then bind with immunoactive sites on the latex particles, and then a further set of chemically functionalized gold nanoparticles would bind to the target molecules. Then a silver enhancer is introduced to complete the circuit. The net result is a large change in conductance if and only if the target molecule is present above some minimum threshold in the test solution. Later work by the same group used dielectrophoresis to directly assemble microwires from gold nanoparticles [104]. They found that 10- to 15-nm gold nanoparticles in solution, when subjected to 50- to 200-Hz electric fields by electrodes spaced apart by a few millimeters, grew wires of micron size and conducted electricity. This is analogous to the pearlchain formation discussed earlier.

5.4. DNA 5.4.1. Washizu and Co-Workers Starting in 1990, Washizu and Kurosawa began studies on DNA which showed that it is indeed possible to use dielectrophoresis to manipulate DNA [105]. They used the electric field produced between two parallel, thin-film aluminum electrodes (thickness 1 m, spacing 60 m) to “stretch” DNA molecules. When large concentrations of DNA molecules are used, they form bands due to the complicated and poorly understood DNA–DNA interactions. When low concentrations of DNA are used, one can see individual DNA molecules through fluorescence, and it is clear that the electric fields “stretch” each individual molecule out. The field strength used is approximately 106 V/m, and the frequency is varied from 40 kHz to 2 MHz, with only slight frequency dependence of the effect. Washizu and co-workers studied  phage DNA (48.5 k base pairs, kbp), so that fully stretched they were about 17 m long. It is not clear from that data whether the ac electric field needs to be nonuniform for the stretching. It would be an interesting experiment to determine whether DNA is

Nanodielectrophoresis: Electronic Nanotweezers

stretched in uniform electric fields. Finally, they showed that it is possible to attach DNA to electrodes, which they interpret as being due to positive DEP: Near the edges of the thin electrodes, the electric field gradients are large, hence the DNA is attracted there. Once attached to the Al electrode (in this experiment, only one end is attached), it is bound chemically and remains, even after the electric field is switched off. In Figure 8, the results found by Washizu and co-workers are indicated schematically. In 1995, Washizu and co-workers described several possible applications of this technique [106]. First, they described an optical/DEP technique to size-sort long DNA (with length greater than 10 kb pairs), which is difficult for conventional gel electrophoresis. This was demonstrated with  phage DNA (size 48.5 kbp). Second, they measured the activity rate of exonuclease digestion of DNA, by measuring the double strand length as a function of time during digestion. DNA lengths of order 10 m can be measured because DEP caused the DNA to be stretched out. (They found that single strands of DNA are not stretched by DEP.) A further method was developed to stretch DNA molecules and position them at two different electrodes, using a combination of a floating electrode geometry and also chemically treated (biotin and avidin) electrodes. For unknown reasons, without the floating electrode geometry it was possible to attach one end of a DNA molecule to one electrode, but not the other end to the other electrode. Apparently, the high electric fields near the electrode induced currents away from the electrode, preventing the second end of the DNA molecule from binding, but not the first end. The DNA so immobilized is shown to still be biochemically active. In 1993, Banata and co-workers used the DEP technique to attach one end of DNA to an aluminum electrode; the other end was free but stretched out with DEP. Just after turning off the electric field, and before the DNA had a chance to re-coil, they imaged single fluorescently labeled RNA polymerase molecules sliding along the DNA [107]. The technique was used to study the DNA– protein interaction with other proteins (Pseudomonas putida CamR) in 1999 [108]. Future applications of this technique

631 may lend insight into DNA–protein interactions in general, and the regulation and control of genetic expression in particular. In 1999 Ueda and co-workers studied the DEP stretched DNA molecules with AFM, after drying the solvent (water). They concluded that the DEP stretched and trapped molecules do not aggregate but in contrast are trapped individually [109]. In 2000, the Washizu group used dielectrophoresis and floating electrodes to attach both ends of  phage DNA molecules to aluminum electrodes [48, 110], using the floating electrode technique described above. In this work, they etched the glass slide below the gap between the electrodes so that the DNA was freely suspended. (Although it has gone largely unnoticed by the MEMs community, this technique to assemble freely suspended DNA should have many applications in nanomechanical systems made of DNA.) Since the DNA was freely suspended in solution there is no issue of steric hindrance of biochemical activity. Then, in a further set of experiments [48], they used optical tweezers to manipulate 1- m latex spheres labeled chemically with the digestive enzymes DNaseI (which has no base pair selectivity) and HindIII (a restriction enzyme which cuts DNA at only specific base sequences). They were able to bring the bead up to the DNA. In the case of DNaseI, the DNA was immediately cut. In the case of HindIII, the bead was moved up and down the DNA until it matched the correct sequence, at which point it was cut. In 1998, the Washizu group studied the polarization of the fluorescent emission from dielectrophoretically stretched DNA [111]. The polarization of the emitted light was quantitatively measured and correlated with the applied electric field intensity, as well as the pH of the solution. Several interesting results were obtained, indicating that the counterion cloud surrounding the DNA molecules has a large influence on the stretching of DNA by electric fields. The details of this influence are still not fully understood. Many of these results from Washizu and co-workers are reviewed in two book chapters [112, 113].

5.4.2. Asbury and Co-Workers E

(a) DNA coiled

(b) DNA stretched by 1 MHz, 106V/m field

E

(c) DNA anchored to electrode by positive DEP

or

electrode

electrode

E=0 electrode

electrode

electrode

electrode

DNA

electrode

electrode

E=0

(d) DNA stays anchored after field removed (recoil depends on local surface properties.)

Figure 8. Schematic representation of the findings of Washizu and co-workers.

In 1998, Asbury and van den Engh were able to use dielectrophoresis to trap DNA with a floating electrode geometry: The electric field was applied from external electrodes; floating gold electrodes spaced by 30- m gaps concentrated the electric field, which served to trap the DNA [114]. They also studied  phage DNA in de-ionized (D.I.) water, but used gold electrodes (thickness 40 nm), and audio frequency (30 Hz) fields. As in the Washizu experiments, the DNA underwent positive dielectrophoresis: it was attracted to regions of high electric field intensity, which occurs near the edges of the electrodes. Asbury used much lower frequency voltages (typically 30 Hz) than Washizu, and found no stretching of the DNA at these frequencies. Furthermore, Asbury found that the DNA did not become stuck to the gold electrodes, in contrast to Washizu’s experiments where the DNA did become stuck to aluminum electrodes. Regarding the frequency, at dc no more than roughly 1 V can be applied across an electrode/water interface; otherwise electrolysis followed by bubbling can occur. Washizu found

632

Nanodielectrophoresis: Electronic Nanotweezers

that much larger voltages could be applied as the frequency was increased from 1 kHz to 1 MHz (they did not study frequencies below 1 kHz). In Asbury’s experiments, the gold electrodes were floating, but there was still less than 0.5 V between each (floating) electrode pair, so that electrolysis did not occur. Asbury’s experiments found that DNA could be trapped in deionized water, but not in isotonic saline. They estimate that the force on the DNA was in the femtonewton range. Since the DNA molecules were not stuck to the gold electrodes, Asbury was able to simultaneously apply a dc field and move the stretched DNA molecules with electrophoresis. In 2002, Asbury and co-workers continued this work by integrating it with a simple microfluidic device, fabricating a 15- m-wide PDMS channel on top of gold electrodes which, in contrast to their earlier work, were electrically contacted (not floating) [115]. With the gold electrodes and 30-Hz voltages of roughly 3 V p-p, they were able to trap DNA and then release it using positive dielectrophoresis. Their estimates show that 50% of the DNA introduced into the microfluidic channel was trapped. Asbury found the trapping “efficiency” to decrease with increasing frequency between 5 Hz and 2 kHz, with an effective time constant of 3 ms. The origin of this frequency dependence is attributed to the distortion of the counterion clouds that surround the DNA molecules in solution, although the details of this effect are currently poorly understood.

high field regions near the edges of the electrodes) for frequencies between 1 kHz and 500 kHz, and negative dielectrophoresis between 500 kHz and 1 MHz, in contrast with the findings of previous work. This is to date the only reported observation of negative dielectrophoresis of DNA; the discrepancy may be related to the different solvents used, although at this point it is still an open question. Furthermore, Tsukahara and co-workers used electric fields that were roughly a factor of 10 smaller than previous workers, and still were able to observe the dielectrophoretic forces on a single DNA molecule. This may again be due to the solvent used, or the fact that Tsukahara used a quadrupole electrode geometry, which is different than previous works. Additionally, Tsukahara did not observe any stretching of the DNA with the application of an ac electric field.

5.4.3. Ueda and Co-Workers

The detailed mechanisms for the frequency dependence, electric field dependence, concentration dependence, pH and ionic dependence of the dielectrophoretic manipulation of DNA are still not explained in a systematic, quantitative way, and many of these dependences have yet to be quantitatively measured. However, it is clear now that it is possible to use dielectrophoresis to manipulate DNA under a variety of conditions and frequencies. This knowledge could be used in a variety of contexts, including lab-on-a-chip diagnoses and genetic expression profiling, as well as electronic methods of controlling DNA chemistry. This latter possibility has the potential to provide a new nanomanufacturing technology based on both chemical self-assembly techniques and integrated, massively parallel, economical electronic control of the same.

In 1997 Ueda et al. used much-lower-frequency ac electric fields, and studied the electronic dielectrophoretic stretching of DNA in polymer laden solutions. They found the polymer (polyacrylamide) assisted the stretching of DNA for applied electric fields in the frequency range of 0.1 to 100 Hz [116]. They found this stretching to occur at field strengths as low as 104 V/m; no net motion of the DNA was reported.

5.4.4. Chou and Co-Workers In another work with floating electrodes, Chou and co-workers used insulating posts fabricated with micromachining techniques, and electrodes external to the device [117]. The slightly conductive solution served to enhance the electric field near the gaps between the posts, and DNA was found to be trapped there for voltages on the electrodes of roughly 1000 V and frequencies between 50 Hz and 1 kHz. The corresponding electric field strength was 105 V/m. In this work, the DNA was apparently not stretched at all, presumably because of the constricted geometry used. In contrast to the work of Asbury, Chou found that the trapping force increased with increasing frequency, and also calculated that the trapping force was roughly 1 fN.

5.4.5. Tsukahara and Co-Workers In recent work [118], Tsukahara and co-workers studied dielectrophoresis of single DNA molecules using frequencies between 1 kHz and 1 MHz and field strengths around 104 V/m, using quadrupole electrode patterns similar to those shown in Figure 3. They found that the DNA underwent positive dielectrophoresis (i.e., it was attracted to the

5.4.6. Porath and Co-Workers In 2000, Porath and co-workers used positive dc dielectrophoresis to putatively trap 10-nm-long poly(G)-poly(C) double strands of DNA between Pt electrodes with 8-nm spacing [119]. Through a series of control experiments, Porath concluded that the trapped object was indeed DNA, and that its electrical properties were semiconducting. Many other researchers up to and since then have considered the electronic properties of DNA as a molecular wire. The issue is still under investigation [120].

5.4.7. Summary

5.5. Viruses 5.5.1. Influenza To date two different research groups have succeeded in trapping at least four different species of virus with dielectrophoresis. The first group to trap viruses was that of Fuhr and co-workers in 1996 [121]. They used quadrupole, threedimensional traps to trap fluorescently labeled influenza viruses (d ≈ 100 nm) using negative dielectrophoresis traps, and 1-MHz electric fields with field strength around 105 V/m. (The gap between electrodes was approximately 5 m with 11-V p-p voltage.) They also trapped 14-nm latex beads. In these experiments, the viruses formed aggregates in the centers of the traps. In later work with similar geometries, fields, and frequencies, the same group was also able to trap Sendai viruses into aggregates as well [122].

Nanodielectrophoresis: Electronic Nanotweezers

5.5.2. Tobacco Mosaic In later work, Morgan and co-workers used interdigitated electrode fingers spaced by 4 m with saw-tooth shapes to manipulate tobacco mosaic viruses [123, 124]. The tobacco virus is rod-shaped, with length of 280 nm, and width of 18 nm. Morgan used field strengths of roughly 106 V/m, and varied the frequency between 1 kHz and 2 MHz. Although they were not able to observe individual virions, they could see a faint haze as the density increased or decreased in response to the applied electric field. They found both positive and negative dielectrophoresis, depending on the frequency used. Positive dielectrophoresis was observed for frequencies below about 1 MHz, and negative dielectrophoresis for higher frequencies. The crossover frequency was very dependent on medium conductivity, which was varied between 2 × 10−3 and 10−1 S/m by varying the potassium phosphate buffer concentration.

5.5.3. Herpes In 1998, Hughes and co-workers used planar quadrupole traps such as the one shown in Figure 3 with 6- m gaps to trap Herpes simplex viruses, which are spherical with diameter of about 250 nm [125]. They studied dielectrophoresis of the virus with frequencies from 10 kHz to 20 MHz, and observed negative dielectrophoresis for frequencies above about 5 MHz. The field strengths required for the trapping were about 106 V/m. Later work by the same group found that the crossover frequency between positive and negative dielectrophoresis for the herpes virus was very dependent on the medium conductivity in the range between 10−4 and 10−1 S/m, and this dependence was strongly affected by the presence or absence of manitol [126, 127].

5.5.4. Virus Separation Using the results from their previous studies, Morgan and co-workers studied both tobacco and herpes virus in the same solution, using quadrupole electrode geometry [124, 128]. At 5 MHz, the herpes virus experiences negative dielectrophoresis and is collected in the center of the quadrupole. In contrast, at 5 MHz the tobacco virus experiences positive dielectrophoresis and is collected at the edges of the quadrupole geometry. Thus, two different virus species were physically separated due to their different frequency response to dielectrophoresis.

5.6. Proteins A protein consists of a long chain of subunits (amino acids) which are folded into very complicated three-dimensional structures; the structure is closely related to the function. Most proteins of biological significance are around 1–10 nm in physical size. All species of life are based on only 20 common amino acids [129]. The modern field of proteomics seeks to understand, categorize, and tabulate all proteins useful for life [130]. There have been several studies of the effects of moderate electric fields and strong pulsed fields on the conformational state of proteins such as the helix-coil transition [131]. Reviews of the dielectric properties of biopolymers, dealing predominantly with linear response, low field behavior,

633 are given in [3, 4, 132–134]. However, given the importance of protein chemistry in modern molecular biology, it is surprising how little work to date has been performed on the interaction between strong electric fields and proteins.

5.6.1. Protein Trapping In 1994, Washizu and co-workers studied the effect of dielectrophoresis on the following proteins: avidin (M.W. 68 kDa), concanavalin A (M.W. 52 kDa), chymotripsinogen A (M.W. 25 kDa), and ribonuclease A (M.W. 13.7 kDa) [84]. These proteins have diameters ranging from 1 to 5 nm. In this series of experiments, they used aluminum (thickness 1 m) electrodes in an interdigitated, castellated geometry with gaps ranging from 4 to 55 m. The solvent was D.I. water. They used fluorescence to observe the positions of the proteins. They observed excess fluorescence near the electrodes (i.e., near the high field regions), so that they observed positive dielectrophoresis. They knew it was DEP because they found a dependence on the field strength, not the voltage, by using different gaps between the electrodes. According to rough estimates of the DEP force for their electrodes (a quantitative calculation was not performed), the thermal Brownian motion should overwhelm the DEP force so that nothing should be observed. And yet they observed increased fluorescence in the high field regions. This can be interpreted one of two ways: first, that we do not understand why DEP works so well on proteins; second, that the proteins are accumulating and the agglomerate acts as an effectively large polarizable particle that is less susceptible to Brownian motion and can be trapped. Washizu argues that the second explanation (agglomeration) is not occurring because when they change the initial concentration by a factor of 10, the time to form the “aggregation” does not vary much, and this is inconsistent with a simple aggregation model of dipole–dipole attraction. Dipole–dipole attraction goes as d −4 , so that the time to form the agglomeration should vary as the density n4 . If an optical setup with enough sensitivity to image a single fluorescing protein [135] could be achieved, this issue could be resolved. Washizu was able to demonstrate that trapping of various sized proteins depends on their molecular weight, so that separation of chemical species of various sizes could in principle be observed for applications in nanobiotechnology. Thus a “single molecule fluorescence” experiment, if it could be performed, would be definitive proof the DEP can be used with 106 V/m to manipulate 1- to 5-nm proteins. In more recent work, Kawabata and Washizu [136] developed a biosensor for the protein AFP (alpha-fetoprotein, 70 kDa), an important diagnostic protein, which is detected in the serum of a liver-cancer patient. There, they used the DEP properties of proteins (antigens and antibodies) as well as 150-nm latex beads with antibodies immobilized on the surface. This is an example of an important point: even though we have organized this review according to the types of nano-objects that can be manipulated with DEP, the application of DEP to a heterogeneous population of objects could provide even more applications than just manipulating one type of object at a time.

Nanodielectrophoresis: Electronic Nanotweezers

5.6.2. Protein Folding

E=0

5.7. Carbon Nanotubes 5.7.1. Nanotubes in Solution Several research groups have successfully used dielectrophoresis to manipulate carbon nanotubes in solution. The general procedure is similar to that of Washizu’s manipulation of DNA, with the exception that nanotubes are known to be good conductors. Most experiments demonstrating manipulation of carbon nanotubes in solution are a variation of the general process depicted schematically in Figure 9. Nanotubes are not known to be soluble in any solvent, but can be dispersed by sonication. Once dispersed, a drop of the solution can be placed onto microfabricated electrodes as shown in Figure 9A. Next, either a dc or an ac voltage is applied. This serves two purposes. First, it induces a dipole moment in the carbon nanotube, and this dipole

CNT

electrode

electrode

electrode

CNT

E

(a) Nanotube free in solution

(b) Nanotube stretched, attached to electrodes by DC or AC field

CNT

electrode

electrode

CNT

electrode

E=0 electrode

The previous section discussed primarily controlling the location of proteins with dielectrophoresis. However, given that the conformational state of a protein is related to its function, it is natural to consider whether an applied electric field can change a protein’s conformational state, and possibly even unfold the entire chain of amino acids into a straight line, as Washizu was able to do with DNA. While the latter is still unproven experimentally, Washizu and coworkers have shown that it is indeed possible to use electric fields to change the conformational state of a certain protein, the flagellum of a bacteria. The flagellum of certain types of bacteria consists of a single, spiral shaped protein about 20 nm wide and 10 m long. When it is rotated it acts as a corkscrew, propelling the bacteria forward. However, other conformational states of the amino-acid chain are possible; three in particular are called “straight,” “curly,” and “coiled.” Because the flagellum is a long protein, its conformational state can be directly observed under a microscope, if fluorescently labeled. Washizu and co-workers found that ac electric fields of roughly 106 V/m could transform flagella from one conformation state to another [112, 113, 137]. Furthermore, they found this process to be reproducible and reversible, observing no permanent damage to the flagella after application of the electric field. Similar work on the electric field-induced conformation changes in other proteins (e.g., poly-(L-lysine) and poly-(Lglutamic acid)) has been reviewed in [134]. There, the work described involves measurements of optical dichroism as a function of applied electric field pulses. The optical dichroism is also strongly affected by electric field-induced orientation, making it difficult to conclusively demonstrate electric field-induced conformational changes in protein structure. This relatively unexplored area has great potential for the future. By electronically controlling the conformational state of proteins, it may be possible to electronically control their biological function, or even to engineer new functionality into existing or tailor-designed proteins. This future molecular nanotechnology could have broad applications, which will be discussed toward the end of the review, and could also allow for further scientific studies of the process of protein folding.

electrode

634

(c) solution dries Resistance meter (d) electrical measurement Figure 9. Schematic representation of the manipulation of carbon nanotubes in solution.

experiences a torque, given by Eq. (10). This torque tends to align the nanotube with the axis of the electric field. The electric field need not be nonuniform for this alignment, but to date experiments have not tested the dependence of the alignment on the uniformity of the field in any quantitative fashion. Simultaneously, the induced dipole [138] in the nanotube experiences a force given by Eq. (2). (Equation (3) is not directly applicable as it assumes a spherical particle.) To date all measurements on carbon nanotubes have found that they undergo positive dielectrophoresis; that is, they are attracted to regions of high electric field strength. This can be exploited to electrically contact nanotubes: the electrodes which generate the electric field gradient can also be used as electrical contacts to the nanotube. This is indicated schematically in Figure 9D. When water is used as the solvent (which is desirable for biologically interesting measurements), as discussed above, the applied voltage to the electrodes should be less than 1 V to avoid hydrolysis (and hence bubbling). By using ac voltages, as Washizu et al. found in 1990 [54], the applied voltage (hence electric field strength) required for hydrolysis increases with increasing frequency. If one is willing to use an insulating solvent, then the applied voltage (hence electric field) can be much larger, even at dc. Pohl, for example, used commonly used applied (ac) voltages of thousands of volts with insulating solvents such as organic solvents and CCl4 [2].

5.7.2. DC Dielectrophoresis and Electrophoresis The first dielectrophoretic manipulation of nanotube ropes was done using dc dielectrophoresis in 1997 by Bezryadin and Dekker [97]. Bezryadin used cyclohexane as the solvent, and a dc voltage of 4.5 V between AuPd electrodes spaced by 150 nm. He simultaneously measured the dc current flowing between the electrodes, and was able to see an electric current flow as soon as a nanotube rope was trapped.

Nanodielectrophoresis: Electronic Nanotweezers

Bezryadin found that the trapping was effective, but the nanotube ropes were not aligned parallel to the electric field. This is possibly due to the fact that the length of the trapped ropes was much larger than the gap between the electrodes. When a dc electric field is used, if the object is charged it will respond to the electric field via conventional electrophoresis. A simple way to test whether the nanotubes are charged and experiencing electrophoresis or neutral and experiencing dielectrophoresis is to observe whether they preferentially move toward the cathode or anode or neither. If the nanotubes do not preferentially conglomerate at one polarity, then the effect is dielectrophoresis. Apparently in Bezryadin’s experiments, the nanotubes behaved as neutral objects, and underwent dielectrophoresis. However, in two other experiments, multiwalled nanotubes (MWNTs) are found to behave as positively charged, conglomerating at the cathode [139], and negatively charged, conglomerating at the anode [140]. (Chen et al. found that singlewalled nanotubes (SWNTs) also conglomerated at the anode under a dc electric field [141].) These discrepancies may indicate that the electrical properties of nanotubes are sensitive to the chemistry of the solvent. This effect, if it can be further characterized and explained, could prove very useful in nanomanipulation of nanotubes with electric fields in solutions.

5.7.3. AC Dielectrophoresis of MWNTs In 1998, Yamamoto and co-workers studied the effects of ac electric fields on MWNTs of lengths between 1 and 5 m, and diameter 5–20 nm, using Al electrodes with 400- m gaps and field strength of 2 × 105 V/m [142]. The MWNTs were dispersed in isopropyl alcohol. They found that the nanotubes were both aligned and attracted to the electrodes (i.e., underwent positive dielectrophoresis) for ac frequencies between 10 Hz and 10 MHz. Yamamoto and co-workers found that the degree of orientation of the nanotubes increased with increasing frequency, and with increasing nanotube length. Furthermore, they found that graphite impurities had a different frequency-dependent response to the ac electric field, which may be important technologically in separating nanotubes from impurities. Yamamoto also found that the alignment was more effective with ac dielectrophoresis than with dc dielectrophoresis [139], consistent with the findings of Bezryadin. A complementary technique of optical polarization measurements showed that ac electric fields could align nanotubes dispersed in ethanol [143].

5.7.4. AC Dielectrophoresis of SWNTs In 2001, Chen and co-workers carried out a similar study of the effects of ac electric fields on SWNTs dispersed in ethanol [141]. They applied fields of 5 × 106 V/m in the frequency range from 500 Hz to 5 MHz. They found the SWNTs to be oriented more strongly at higher frequencies, and they found the SWNTs experienced positive DEP for all frequencies studied. They also found no alignment effect from a dc electric field. Thus SWNTs and MWNTs appear to behave similarly under intense ac electric fields. The first application of ac dielectrophoresis to attach two ends of SWNTs was reported in an e-print in early 2002 [144]. The authors used Ag and Au electrodes spaced

635 by 100 nm to trap ropes (bundles) of SWNTs dispersed in N,N-dimethylformamide (DMF). They found the nanotubes formed electrical contact with the Ag electrodes, but not the Au electrodes. The trapping was effective for frequencies between 1 kHz and 1 MHz, at applied fields of 107 V/m. Krupke was also able to simultaneously measure the ac resistance between two electrodes for the 1-kHz trapping experiments, allowing real-time monitoring of the trapping. Nagahara et al. found similar results [145], trapping SWNT bundles with gold electrodes spaced by either 20–80 nm or 20 m, and applying 1 MHz and dc electric fields of strength 107 V/m. They found that the dc fields trapped bundles of SWNTs and graphite impurities, whereas the ac fields trapped only nanotube bundles. They were also able to electrically measure the current through the nanotubes after drying the Triton solvent. Diehl and co-workers have taken this process one step further, and fabricated cross-bar structures by first aligning and immobilizing SWNT ropes in one direction and then, aligning and immobilizing nanotube ropes in a perpendicular direction [146]. The distance from one rope to the next was not determined by the lithography, but rather the chemical control of the coulombic interactions between the tubes and between the ropes. Diehl’s experiments used frequencies between 104 and 106 Hz, with very little frequency dependence. The solvent consisted of a mixture of ortho-chlorobenzene and CHCl3 . (The field strength was not reported.) This represents an initial step toward one of the ultimate goals of self-assembled systems and nanotechnology in general: nonlithographic, economical, massively parallel manufacturing of electronic circuits on the nanoscale. While to date there has been no reported trapping of an individual SWNT between two electrodes (as opposed to a bundle), such an achievement does not seem unreasonable to expect in the near future.

5.7.5. Controlling Nanotube Growth Chemical vapor deposition (CVD) of carbon nanotubes is a promising new technique for the growth of high-quality single- and multiwalled carbon nanotubes [147]. The nanotubes grow from catalyst sites that can be lithographically defined on a chip [148]. However, the direction of the nanotube growth from these lithographically patterned catalyst sites is generally random, an issue that needs to be solved before massively parallel integrated nanotube circuits can be realized. One possible technique to control the direction of nanotube growth is to apply an electric field (dc or ac) during the growth. The electric field will induce a dipole moment in the (growing) nanotube, which will experience a torque (see Eq. (10)), hence becoming aligned with the electric field. This technique was first applied to the growth of vertically aligned MWNTs in 2001 by Avigal and co-workers [149]. Later work by Zhang and co-workers [150] used both dc and ac (5 MHz) electric fields to direct the growth of SWNTs parallel to the substrate. The field strengths used were 5 × 105 V/m, and freely suspended SWNTs up to 40 m in length were grown. The fields were generated between thin-film electrodes which were electrically contacted during growth. Later work by the same group achieved aligned

636 nanotube growth where the end result was a SWNT immobilized on the surface of the substrate [151].

5.7.6. Nanotubes as the Electrodes Ultimately, for nano-DEP, one wants the smallest gap possible, and the smallest electrode radius of curvature possible. We would like to suggest that one way to achieve this would be to use nanotubes themselves as the electrodes. Very high electric field gradients should be possible [32].

5.8. Nanowires 5.8.1. Metallic Nanowires In 1999, van der Zande and co-workers studied the orientation effects of uniform electric fields on 15-nm-diameter gold rods of lengths 39–259 nm in water using optical polarization techniques [152]. They found that, for an applied field strength of 105 V/m and an applied frequency of 10 kHz, significant orientation of the gold nanorods could be achieved. Later work by Smith and co-workers studied gold nanowires down to 35 nm in diameter, although most work was performed in 350-nm-diameter wires of several microns in length [153]. Smith and co-workers used a combination of floating and electrically contacted electrodes, field strengths of up to 107 V/m, and frequencies from 20 Hz to 20 kHz. They found strong orientation effects and positive dielectrophoretic trapping of the nanowires to the floating electrodes for frequencies above 200 Hz; higher frequencies were most effective. Due to the floating electrode geometry used, the process was self-limiting: as soon as one wire bridged a particular pair of floating electrodes, it would short out the capacitively induced voltage on that pair of floating electrodes, preventing further trapping across that pair. Post manipulation lithographic contact to the floating electrodes showed the nanowires to be in good electrical contact with the trapping electrodes.

5.8.2. Semiconducting Nanowires In 2001, Duan and co-workers used dc dielectrophoresis to align and electrically contact InP nanowires (d = 30 nm) [154]. There, electric field strengths of 107 V/m were applied from electrodes spaced by 25- m gaps. The solvent used was chlorobenzene, so that electrolysis was not an issue. (DC voltages of 100 V were used.) By selectively energizing different pairs of electrodes, Duan was able to align InP nanowires into a cross-bar topology using layer-by-layer application of dielectrophoresis.

6. APPLICATIONS

Nanodielectrophoresis: Electronic Nanotweezers

One possible application of nanodielectrophoresis is the controlled placement of individual molecules for molecular electronics. If nanotubes and nanowires can be used themselves as the electrodes (and then as the interconnects), our calculations [32] show that it should be possible (based on the scaling consideration presented in Section 2.4) to trap individual molecules as small as 1 nm. In Figure 10, we show one possible application of our proposed nanotube trapping scheme. An electrically contacted nanotube is cut with an AFM, then a large ac voltage is applied. By the method of images, the electric field gradients are the same as a geometry where a nanotube is in close proximity to a large conducting plane; the field gradients of a reasonable voltage (1 V) on the nanoscale should be quite large, allowing us to trap very small objects, possibly even single molecules. Trapping of DNA at the ends of nanotubes does not seem to be out of the question, nor is it impossible to trap any other number of molecules for nanotubeelectrode molecular electronics. This electronically assisted chemical self-assembly contains the ingredients for molecular transistors wired up with nanotube interconnects in a possibly massively parallel process for large-scale integrated molecular electronics (“LIME,” if you will). In Figure 11, we illustrate one possible application of this nano-trapping. 2′ -amino-4-ethynylphenyl-4′ ethynylphenyl-5′ -nitro-1-benzenethiolate (AEENBT) is used as a model [155]. Note that the hydrogen atom at the end bonded to sulfur can be replaced by other functional groups, for example, -COCH3 . Likewise, the protruding hydrogen atom farthest away from the sulfur atom can also be replaced by another group. By chemically selecting and optimizing the bridging molecule, in particular, the end functional groups, can one achieve ideal contact between the bridging molecule and carbon nanotubes? Using Au as electrical contact, the Reed group [155] has made a molecular random access memory cell [156]. Multiple read write cycles were realized in a self-assembled monolayer film of AEENBT. The bit retention time was found to be of the order of 15 minutes. However, it is very difficult to combine lithography with 2-nm molecules. Nanodielectrophoresis uses the natural nanometer size of carbon nanotubes. With a defined carbon nanotube gap (2 nm) and diameter (1–2 nm), one will have a chance to electrically contact a single AEENBT. Another potential advantage of trapping molecules with carbon nanotubes is the potentially better contact quality between carbon and other nonmetal atoms. Most molecule– metal junctions are poor circuit elements. The resistance Dielectrophoretic trapping of a nanoparticle or single molecule? ~ 1 nm

6.1. Molecular Electronics Recent work of Chen, Reed, and co-workers [103, 155, 156] has investigated the conducting properties of layers of molecules. The investigation of electronic properties of molecular conductors has been termed molecular electronics. The use of lithography alone will not allow for the controlled, rational design and fabrication of single molecule conductors.

nanotube

nanotube

Figure 10. Schematic representation of an idea of how to trap 1-nmsized particles or molecules.

Nanodielectrophoresis: Electronic Nanotweezers

1 nm

O N S H

NH2 S H

H O2N

?

637

?

Figure 11. An overly simplistic schematic view of potential molecular electronics with carbon nanotubes assembled with nanodielectrophoresis. This technique could allow rapid investigation of many such schemes in a massively parallel fashion.

is usually of the order of 1 M [157], which is far away from the ideal contact. One of the reasons is the different electronegativity between metals and nonmetals. For example, in a S–Au(Ag) junction, an interfacial dipole leads to a Schottky barrier in that sulfur is more electronegative than gold and silver. Carbon, which is also a nonmetal element, may prove better to contact molecules.1 One can ultimately investigate more complicated geometries and architectures for integrated molecular electronic devices with nanotube interconnects.

6.2. Nanomanufacturing Future applications of nano-DEP do not need to be limited to the manipulation of individual or small numbers of nanoparticles. Rather, it should be possible to scale up these nanomanipulation methods for massively parallel processing at the single molecule level. Even macroscopic quantities of materials could be fabricated one molecule at a time. New materials with tailor-designed electronic, optical, magnetic, and mechanical properties could go from nano-CAD design to reality in a matter of hours or minutes at very low cost. This integration would be a true synthesis of the top-down and bottom-up approaches to nanotechnology.

by external electrodes. Such a nanomachine would be a step toward Drexler’s vision of molecular nanotechnology [160], proving Feynman’s statement that “there’s plenty of room at the bottom” [161].

6.4. Nanobiotechnology The applications in nanobiotechnology are practically limitless. For example, Washizu has taken the first step toward DEP FFF of proteins [84], on one protein. It is natural to speculate that in the future, DEP FFF may find application in the ability to separate all proteins from the human proteome, uniquely based on their dielectric spectral properties. If enough sensitivity could be achieved, one could measure genetic expression of the entire human genome in a single cell. This could have numerous applications in drug screening and discovery. One does not need to consider only passive, scientific or diagnostic-based measurement of biochemical activity. Nano-DEP has already proved capable of manipulating viruses. This leads one naturally to ask the question: Based in part on nano-DEP, can one design an active, electronically controlled artificial immune system? A nano-liver or a nano-kidney? The answer to this question is not yet known, but would have significant impact on humanity in general if it turns out to be “yes.”

6.5. Nanochemistry The force required to break a single chemical bond is roughly 1 nN [162]. Our calculations show that this can be the same order of magnitude that is generated by DEP on a micro- or nanoparticle, if nanotubes are used as the electrodes [32]. While to date AFM and SPM have been used for studying single molecule chemistry, it is also natural to speculate that nano-DEP experiments can be designed to electronically study and control the breaking of a single chemical bond.

6.3. Nanomachines Through rotating electric fields generated by microfabricated electrodes, it has been possible to rotate 5- m latex beads and also cells in solution [8]. One could call such an apparatus a dielectric micromotor, where the electrodes are the stator and the rotating latex bead the rotor. Hagedorn et al. took this concept one step further and microfabricated a large variety of micro “rotors” out of Al and polyimide, which had dimensions of approximately 100 m [158]. They were able to demonstrate rotor speeds of up to 3000 RPM. Recently Hughes has presented a theoretical evaluation of the ultimate limits of rotor performance, using nano-DEP to drive rotors down to 1 nm across [159]. He concluded that a 1- m-long by 100-nm-wide rotor should be able to generate a torque of 10−15 N/m, equivalent to that of a bacterial flagellar motor. Although he does not discuss how one might realize such a rotor, we suggest that using carbon nanotubes as both the rotor and stator is one feasible technique to realize this, since it is known that nanotubes can be contacted 1

We thank Shengdong Li for pointing this issue out to us.

7. UNANSWERED QUESTIONS Although DEPs application in nanotechnology is still in its infancy, it can be considered a proven technique to electronically manipulate micro- and nanosized objects. However, the studies performed to date have left some key questions unanswered: • • • •

What is the effect of Joule heating? What is the smallest molecule that can be trapped? What field strengths are needed for this? Since the forces depend on the field gradient only, is it possible to design different electrode geometries to achieve stronger trapping forces for a given applied voltage? • Can trapping of individual macromolecules occur in biologically relevant solutions, fraught with conduction ions? • What is the effect of molecule–molecule interactions on traps that hold more than one molecule? • What is the role of electrohydrodynamics?

638 Joule heating occurs due to current flow through the solution. This is especially a question in solutions of biological significance with ionic concentrations that can also carry current. The heating may cause connective fluidic currents which will overcome the dielectrophoretic forces. The amount of Joule heating is difficult to predict, since the conductive properties of the solution at MHz frequencies may not be known. Macromolecules may not behave as bulk dielectrics, but have deviations from simple bulk behavior. These issues are difficult to address theoretically and more experiments need to be done to push DEP to the single molecule limit. At the very high electric fields necessary for DEP to overcome Brownian motion of nanoparticles, the electric field may also interact directly with the fluid itself. The study of the interactions between electric fields and fluids is called electrohydrodynamics. Serious, concerted effort to understand electrohydrodynamics at the nanometer scale has only recently begun [163–169]. Understanding these effects will obviously have important implications for the applications and ultimate limits of nano-DEP. The importance of these effects was made clear by Washizu et al. [106], who found that, while it was possible to stretch and attach DNA to one electrode, electrohydrodynamical effects prevented attaching the other end of the DNA molecule to a second electrode. Instead, a floating electrode geometry was needed to avoid the electrohydrodynamical effects. The electrohydrodynamic effects of high electric fields at the nanoscale is a difficult problem to investigate both experimentally and theoretically, and will require considerably more effort to quantify, understand, and eventually control.

8. CONCLUSIONS The use of dielectrophoresis has already found numerous applications in biotechnology, nanotechnology, and nanobiotechnology. Using conducting metal and carbon electrodes fabricated with either optical or electron beam lithography, coupled with modern microfluidic integrated circuits, it has been possible to manipulate, trap, separate, and transport DNA, proteins, viruses, cells of various types from many different species, including both plant and animal, metal nanoparticles, latex beads, carbon nanotubes, semiconducting and metallic nanowires, semiconducting nanoparticles, and quantum dots. In order to bring this vast body of knowledge to fruition, several steps remain to be taken. First, the power and economy of massively parallel fabrication and manufacturing methods, as well as massively parallel operations on a single chip, have not yet been exploited. While the techniques described here are compatible with the processing techniques of modern semiconductor integrated circuits which achieve routinely millions of transistors on a chip at the cost of only a few dollars, to date most studies and demonstrations of nanodielectrophoresis have only been on a few or at most a dozen operations at a given time, such as the separation of viable and nonviable cells. These processes need to be integrated with each other, with microfluidics, and with

Nanodielectrophoresis: Electronic Nanotweezers

existing silicon microelectronics technology for many (millions) of operations for a true, integrated lab-on-a-chip. Second, new applications must be found for this massively parallel processing, manipulation, and manufacturing capability. To date the manipulation of nano-sized objects has traditionally been painstaking, expensive, and slow. If massively parallel techniques of nanomanipulation can be manufactured and made readily available, many new opportunities which harness this economy of scale will need to be imagined, designed, and realized, such as new materials and devices with tailor-designed electronic, optical, magnetic, and mechanical properties. By integrating these with biological and chemical functions, artificial cell, immune systems, tissues, and even organs may someday be designed, fabricated, and made readily and cheaply available to every human being on the planet, for medical applications such as point-of-care diagnostics, drug discovery, artificial immune systems, and ultimately the treatment and prevention of disease. Third, and finally, the next step in size reduction must be taken in order to create a true nanomanufacturing technology. The origins of dielectrophoresis allowed the use of traditionally machined electrodes to manipulate micron-sized objects such as cells. With the advent of photolithography and electron beam lithography, the trapping of objects as small as 10 nm has been enabled. The next step will be to use the electrically contacted nanowires and nanotubes themselves as the electrodes in the next generation of nanodielectrophoresis. These nanoelectrodes, perhaps themselves manipulated and interconnected with microelectrodes, will have even larger electric field gradients and will be able to manipulate 1-nm-sized objects. This is one possible route to molecular electronics. Furthermore, this will provide a new, economical, easy to handle, and direct link to the nanometer world, which could lead to many new discoveries and a truly new technology: nanotechnology.

GLOSSARY Carbon nanotube A nanometer-scale tube of carbon atoms, which can be either metallic or semiconducting, depending on the chirality. DEP field flow fractionation The separation of objects according to their dielectric properties. Dielectrophoresis The force acting on a polarizable object (neutral or charged) due to an ac or dc electric field gradient. Nanobiotechnology The control of biological processes at the nanometer length scale. Nanowires Narrow-diameter metallic or semiconducting wires whose dimensions (typically less than 10 nm) cannot be realized by lithography alone. Traveling wave dielectrophoresis The transport through space in three dimensions of polarizable objects due to a traveling wave electric field.

Nanodielectrophoresis: Electronic Nanotweezers

ACKNOWLEDGMENTS Some of the experimental work presented here was performed by Sunan Liu and Lifeng Zheng. We thank J. Brody and Noo Lee Jeon for experimental assistance with the work, and Marc Madou and Shengdong Li for interesting discussions. This work was supported in part by the Army Research Office and the Office of Naval Research.

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Encyclopedia of Nanoscience and Nanotechnology

www.aspbs.com/enn

Nanoelectromechanical Systems Josep Samitier, Abdelhamid Errachid, Gabriel Gomila University of Barcelona, Barcelona, Spain

CONTENTS 1. Introduction: From Micro- to Nanoelectromechanical Systems (NEMS) 2. NEMS Fabrication Technologies 3. NEMS Based on Solid-State Suspended Nanostructures 4. NEMS Based on Nanofluidic Structures 5. Molecular NEMS: The Ultimate Miniaturization Limit 6. Concluding Remarks Glossary References

1. INTRODUCTION: FROM MICRO- TO NANOELECTROMECHANICAL SYSTEMS (NEMS) The laws of physics do not forbid the possibility to develop devices and machines at very small scales, even of a few atoms or molecules [1]. Nature is full of examples of such small scale “machines,” which are able to manufacture various substances, to move, and to store information, with everything at very small molecular scale. There are many obvious advantages of making machines and devices as small as possible. Smaller devices are more compact, lighter, faster, and cheaper and they require less power than larger scale devices [2]. Moreover, they offer new capabilities (e.g., access to single molecule properties) not available in larger scale devices.

dimensions in the micrometer range. By “electromechanical” we refer to devices that contain mechanical elements in combination with some electronics that control and read out the mechanical motion or perform some additional functions, as schematically illustrated in Figure 1. In this definition we include microfluidics based MEMS [4–9], which consist of microsystems of channels, pumps, valves, mixers, filters, or separators most often externally controlled by means of electric fields. MEMS have found many and important commercial applications. Among others we cite arrays of micromechanical mirrors for optical crossbar switches used in the optical communication industry, ink-jet printers using control of fluid jets, accelerometers used as sensors for deploying automobile air bags, microcantilevers for scanning probe microscopes, computer disk read heads, radio switches and filters, and lab-on-a-chip or micro total analytical (
TAS) systems. The latter have found many applications ranging from the life sciences industries for pharmaceuticals and biomedicine (drug design, delivery and detection, diagnostic devices) to industrial applications of combinatorial synthesis (such as chemical analysis and high throughput screening) [6]. Most of the MEMS in practical use today were made with silicon-based technologies [10], because of the well-known methods developed by the microelectronics industry. To this respect, the importance of MEMS technology is not so much the size of the devices, but rather the use of planar processing technologies, related to those used in the fabrication of electronic integrated circuits, that allows simultaneously “machining” of large numbers of relatively simple mechanical devices in an integrated fashion (for a recent example of large-scale integration in microfluidic systems see [11]).

1.1. Microelectromechanical Systems: The First Generation of Small-Scale Mechanical Devices

1.2. Nanoelectromechanical Systems: The Second Generation of Small Scale Mechanical Devices

The first generation of small scale machines and devices appeared in the mid 1980s when the technology of microelectromechanical systems (MEMS) was firmly established [3]. This technology allowed the design and fabrication of electromechanical devices with at least some of their

With the advent of new nanolithographic techniques (electron and ion beam lithography, nanoimprint lithography, reactive ion etching, etc.), further miniaturization became possible. These techniques allowed scaling down of MEMS into the submicrometer domain thus opening the door to

ISBN: 1-58883-062-4/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 6: Pages (643–663)

Nanoelectromechanical Systems

644 Electrical Input Signal

Input Mechanical Transducer Stimulus

Electrical Output Signal

Mechanical System

Mechanical Response

Output Transducer

Mechanical Perturbation

advances. Techniques such as scanning probe and tunnelling microscopy or the use of optical tweezers have allowed the characterization of the mechanical and electrical properties of many single molecules, thus making closer to reality the possibility of developing molecular NEMS (i.e., electromechanical devices whose active parts consists of a single molecule or atom). Some preliminary demonstrations based on carbon nanotubes, single proteins, or molecular biomotorson indicate that molecular NEMS can enter into play earlier than expected.

Control Transducer

1.4. Scope of the Chapter Electrical Control Signal

Figure 1. Schematic of an electromechanical device [12].

a new generation of electromechanical devices: nanoelectromechanical systems (NEMS) [12–14]. NEMS can be characterized by critical feature sizes in the range from hundred to a few nanometers, and contrary to the case of MEMS, their small dimensions are relevant for the function of the devices. In NEMS applications physical properties resulting from the small dimensions may dominate the operation of the devices, and new fabrication approaches may be required, including the use of materials others than Si or the use of fabrication processes with spatial resolution higher than the ones used in the silicon microelectronics industry. In this sense, both top-down (from large to small) and bottom-up (from small to large) fabrication approaches are expected to be necessary in the manufacturing of NEMS. At present, NEMS are still in a very early stage of development and only elemental devices based on suspended solid-state nanostructures or on nanofluidic systems have been developed. Even though elemental, these developments have shown that NEMS can provide a revolution in applications such as sensors, medical diagnostics, displays, and data storage. In particular, NEMS may enable experiments on the structure and function of individual biomolecules, opening unforeseen biomedical applications. Furthermore, NEMS may offer access to fundamental frequencies in the microwave range, mechanical quality factors in the tens of thousands, active masses in the femtogram range, force sensitivities at the attonewton, mass sensitivity at the level of individual molecules, or heat capacities far below a “yoctocalorie” [12].

1.3. Molecular NEMS: The Next Generation The ultimate limit in the miniaturization of devices and machines will be reached when devices approach molecular or atomistic scales or, more precisely, when the active parts of the devices consist of single molecules or atoms. Fabrication at these scales will generally require a bottomup approach by using naturally occurring molecules that self-assemble into useful devices or machines. In recent years, the ability to measure and manipulate matter at the level of single molecules has experienced spectacular

This chapter will provide an overview of the most relevant advances achieved so far in the emergent field of NEMS. For the purpose of the present chapter we will group NEMS into three main classes: NEMS based on suspended solidstate nanostructures (Section 3), NEMS based on nanofluidic systems (Section 4), and molecular NEMS (Section 5). Fabrication nanotechnologies will be reviewed in Section 1. We end the chapter with some concluding remarks in Section 6.

2. NEMS FABRICATION TECHNOLOGIES The introduction of nonoptical lithography has been announced several times during the last 20 years, but optical methods like projection lithography have always been extended beyond predicted limits. However, a further “simple” downscaling of the optical wavelength beyond 193 nm is not feasible because of the lack of refractive lenses and the problems involved in the fabrication of pure reflective systems with high enough numerical apertures. Hence the need for new lithographic techniques is one of the big challenges for further progress in semiconductor technology. At the moment, several approaches toward sub-100 nm lithography are under discussion that can contribute to nanotechnological development, especially for provision of NEMS. The present section summarizes the principles of operations of some of them.

2.1. Electron Beam Nanolithography Electron beam lithography [15, 16] is at present the essential basis of nanostructure fabrication. Electron beams can be used to write directly onto a substrate using high energy electrons (100 to 200 keV) and a small electron probe size (1 to 10 nm). With electron beams the creation of lines typically 30 nm wide can be satisfactorily produced (widths up to 7 nm have been reported). The resolution limiting factors in electron beam lithography strongly depend on the resist properties. The disadvantages of this technique are the large writing times, causing a low throughput that makes electron beam lithography prohibitively expensive for mass production. However, the approach is certainly useful for making masters for nanoimprinting lithography, which are in turn used multiple times.

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2.2. Ion Beam Nanolithography

2.4. Microcontact Printing

This technique is similar to electron beam nanolithography in terms of application but uses a beam of ions instead of electrons [17]. A fundamental difference is that ions are charged atomic matter that can interact physically and chemically with, and settle into, the exposed material and are many orders of magnitude more massive than electrons. Deep ion beam lithography is a new technique that can be used to produce three-dimensional nanostructures and is particularly good at creating side walls with almost 90-degree angles and slopes.

The principle of microcontact printing [23, 24] is shown in Figure 3. A stamp consisting of an elastometer is covered by an ink, for example an alkanethiol. Upon contact a selfassembling monolayer is formed within a few seconds which protects the substrate so that a selective wet etch can be performed. The main advantages of this technique result from the conformal contact to nonflat surfaces, which is due to the elasticity of the stamp. As a consequence flatness of the surface over large areas is not a problem, and even threedimensional surfaces can be printed.

2.3. Nanoimprint Lithography Nanoimprinting [18, 19] can produce patterns with (sub)micro- and nanometer scales in nanometer thin films in a relatively simple and reliable manner. It makes use of the mechanical deformation of a polymer under pressure and elevated temperature. The master, with its patterned surface, and a sample prepared with a layer of polymer are heated up to the printing temperature, which is above the glass temperature of the polymer to be molded. Then the stamp is pressed against the sample. Stamp and substrate are brought into physical contact and pressure is applied, followed by a down-cooling. After removal from the sample, the resulting polymer relief can be used as a mask for dry etching if the imprinted polymer is resistant enough or as a step in a lift-off process. Figure 2 shows a scheme of this parallel processing technique. The main advantage of this technique in comparison to electron beam writing is the parallel nature of the process, the high throughput, and the low system costs, because no energetic particle beam generator is needed [20, 21]. In addition, nanoimprinting eliminates a number of adverse effects of conventional lithography techniques [21, 22] like wave diffraction, scattering and interference in the resist, electron backscattering from the substrate, and chemical issues.

2.5. Scanning Probe Since their invention, scanning tunnelling microscopy (STM) [25] and atomic force microscopy (AFM) [26] have been promising tools for a wide range of applications: imagining nanostructures, manipulating individual molecules or atoms [27], and more recently for lithography process [28, 29] to build nanostructures. In the technique of STM, a sharp metal tip is brought extremely close to a conducting sample surface. When a bias voltage is placed across the tip–sample junction, electrons tunnel quantum mechanically across the gap between them thus giving rise to measurable tunnelling current (from 10 pA to 10 nA). During image acquisition, the tip is scanned across the sample using x–y piezoelectric elements, and a feedback circuit typically adjusts the tip height (z piezo) in order to maintain a constant current. On the contrary, in contact AFM mode, the tip and sample are brought into tip–sample force during scanning, usually by maintaining a constant cantilever deflection. In most commercial AFM, this is achieved by focusing a laser onto the back of the cantilever and measuring its reflected intensity using a photodiode. During scanning, the

Mold Monomolecular layer

Mold Polymer

Substrate

Mold

Substrate

Nanoimprint

Nanoimprint

Release

Release Figure 2. Schematic of the nanoimprint lithography process.

Figure 3. Process for the production of a microcontact stamp and the formation of self-assembled monolayers on a substrate.

Nanoelectromechanical Systems

646 cantilever motion is then detected via the photodiode signal and a feedback circuit is used to maintain a constant tip–sample force. In spite of being very young, lithography techniques employing STM/AFM represent a promising way toward the fabrication of new nanodevices for electronic applications with good reproducibility and positioning accuracy. Unfortunately, the serial nature of the writing process makes it time consuming and not economical for commercial applications. One solution to this problem has been the introduction of multiple tip arrays. Techniques such as dip-pen lithography are adaptable to such an array geometry and may eventually yield viable nanodevices applications.

2.6. Fabrication Issues for Nanofluidic Applications Fabrication of nanofluidic structures requires the improvement of two challenges: reduction of size and creation of sealed fluidic channels [8]. The first challenge can be overcome by the use of electron beam, ion beam, or nanoimprint lithographies described previously. Very recently, the fabrication of 10 nm enclosed nanofluidic channels using nanoimprint lithography has been reported [30]. Techniques based on the use of sacrificial materials to create sealed small hollow fluidic structures have gained popularity in recent years [31]. However, steps needed in removing the sacrificial materials such as heating the substrate up to 200–400
C or wet etching might not be compatible with downstream fabrication process or may limit the use of certain materials. Concerning sealing techniques, methods such as wafer bonding or elastomeric sealing are suitable for relatively large planar surfaces and provide an effective seal. Wafer bonding consists of creating a bond between a glass slide and a silicon substrate by gentle heating while applying an electric field across the silicon/glass structure to ensure good contact via the associated electrostatic force. Wafer bonding, also called anodic bonding, requires an absolutely defectfree and flat surface. In addition to silicon and glass materials, elastomeric materials have also been considered for the fabrication of micro/nanofluidic structures [32]. These materials provide good sealing properties, fast design times, low cost, the ability to fabricate nanoscale features, and the possibility of deformable shapes.

3. NEMS BASED ON SOLID-STATE SUSPENDED NANOSTRUCTURES A great part of the research developed so far in NEMS has focused on devices consisting of a freestanding or suspended solid-state nanostructure able to freely move in at least one direction and that can be actuated and sensed by means of electromechanical transducers. Nanostructures such as single clamped nanobeams (also known as nanocantilevers) [33–38], doubly clamped nanobeams [39–46], and nanopaddles [47–51] have been fabricated and electromechanically actuated and sensed. A schematic representation of these nanostructures is shown in Figure 4. These nanostructures present at least one dimension in the tens of nanometer range and can be fabricated out of single crystals

w

t L

(b)

(a)

(c) Figure 4. Schematic representation of some basic nanostructures for solid-state freestanding NEMS. (a) Single clamped nanobeam, (b) doubly clamped nanobeam, (c) nanopaddle.

or from noncrystalline materials by means of the nanolithographic techniques described in Section 2. Among the materials used in their fabrication we cite Si [39–41], GaAs [47], GaAs/AlGaAs [34, 43, 46], SiC [44], AlN [45], InAs [38], SiN [51], and piezoresistive materials [35]. Very often, the nanostructures are covered with a thin metallic layer for an easier actuation and sensing. The more relevant physical properties of this class of NEMS, as well as the techniques developed to actuate and sense them, will be described.

3.1. Physics of Solid-State Suspended Nanostructures Solid-state freestanding NEMS are designed basically for two types of applications: very low force measurement and high frequency resonators for communication and sensing applications. For the former application low equivalent elastic spring constants are required. For the latter one, high natural frequencies of oscillation and high quality factors become necessary. The values of these physical properties can vary over a broad range depending on the geometry of the nanostructure, the material used in its fabrication, and the conditions of operation (air, liquid, ultrahigh vacuum). One can estimate these dependencies in the framework of classical elasticity theory [52, 53], which assumes a continuous description of matter, the absence of relevant finite size effects (bulk properties are assumed to hold), and the absence of quantum mechanical effects. Later we will discuss the limitations of this type of description.

3.1.1. Equivalent Elastic Spring Constant The equivalent elastic spring constant, k, determines the sensitivity of the nanostructure to external applied forces. It is defined as the force constant a spring would have in order to display an elongation equal to the maximum displacement of the nanostructure in response to a given external force [53] k=

F 

(1)

where F is the applied force and  is the maximum displacement of the nanostructure. This definition is mainly used for structures of the cantilever type (Fig. 4a). For this type of

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647

nanostructure classical elasticity theory predicts an equivalent elastic spring given by [52] k=

3EI L3

(2)

where L is the length of the beam, E is the Young elasticity modulus of the material, and I is the momentum of inertia of the nanobeam cross-section. For the case of a rectangular beam the momentum of inertia is I = 1/12wt 3 , where w and t are the width and thickness of the beam, respectively. The spring constant then reads k=

1 Et 3 w 4 L3

(3)

Similar expressions can be obtained for other geometries. The validity of Eq. (3) in the nanorange has been proved for SiC nanorods [54]. By inspection it is clear that structures with large aspect ratios (i.e., large values of the ratio L/w or L/t) will present the smallest spring constants and hence the highest force sensitivity (i.e., they will deform in an appreciable way in response to very small forces). Furthermore, for a given geometry, materials with the lowest values of the Young modulus are expected to give the lowest spring constants. Table 1 presents the values of the equivalent spring constant for different Si nanocantilevers as calculated from Eq. (3). Suspended solid-state nanostructures are also able to display torsions in response to the action of lateral forces. Torsional phenomena can be described in very much the same way as deflection phenomena. In particular, one can define an equivalent torsional spring constant to characterize the torque sensitivity of the nanostructure as =

M 

(4)

where  is the maximum angle of twist and M is the torque producing such a twist. As in the case of deflections, the value of the equivalent spring constant, , depends on the properties of the material and on the geometry of the nanostructure. For the simplest case of a single clamped rod classical elasticity theory gives [53] =

GIp r 4 = G L 2L

(5)

where G is the shear modulus of the material, Ip is the polar momentum of inertia of the rod cross-section, and L is the length of the nanostructure [in the second equality in Eq. (5) we used that the polar momentum of inertia of a rod is Ip = 1/2r 4 ]. Similarly, for the case of a single clamped rectangular beam one obtains [52]  = w/t

t3w G L

(6)

where w and t are the width and thickness of the beam, respectively, and w/t is a dimensionless numerical function of the ratio w/t. Again, in order to reach high torque sensitivity small aspect ratios values are required. The validity of Eq. (6) in the nanorange has been demonstrated with Si nanopaddles [50].

3.1.2. Natural Frequencies of Oscillations The values of the natural frequencies of oscillation of suspended nanostructures determine many of the potential applications of resonant NEMS (e.g., in mass sensors [55–57] or for communication purposes [58, 59]). A very important feature of resonant NEMS is their potential capability to reach the GHz domain (at present, values as high as 380 MHz have been already reported [60]). The natural frequencies of oscillation of a suspended nanostructure depend basically on the geometry of the nanostructure, on the material used in its fabrication, and on the way the nanostructure is fixed to the supports. Indeed, for the case of transversal oscillations the natural frequencies of oscillation are given by [52]
Cn2 1 EI fn = (7) 2 L2 A where is the density of the material, A is the crosssectional area, and I is the momentum of inertia of the cross-sectional area. Moreover, Cn is a numerical factor that depends on the way the nanostructure is fixed to the supports and on the harmonic considered. For example, for the fundamental mode of oscillation of a rod clamped at one end one has C0 = 1 875, while for a rod clamped at both ends one has C0 = 4 730. Finally, for a rod clamped at one end and with an external force applied to the free end one has C0 = 1 316. For the particular case of a rectangular beam, for which I = 1/12wt 3 , the natural frequencies of oscillation read
E t Cn2 fn = (8) 2 12 L2 According to this relationship, the highest frequencies are obtained with nanostructures with the shortest aspect ratios L/t and the highest E/ ratios. Moreover, doubly clamped structures give frequencies more than one order of magnitude higher than single clamped beams, due to the higher value of the numerical factor Cn . The validity of Eq. (8) in the nanorange has been tested with SiC [44], AlN [45], and SiN [51] nanobeams. After corrections due to the effects of the thin metallic layer, nonuniform geometries, and tensile stress, good agreement between theory and experiments has been observed.

Table 1. Equivalent spring constant for Si nanocantilevers of different geometries as calculated from Eq. (3). L × w × t (
m ×
m ×
m) Spring constant, k (N/m)

10 × 0 2 × 0 1 9 × 10−3

Note: The bulk Si Young modulus is used in the calculations.

1 × 0 2 × 0 1 9

1 × 0 05 × 0 05 0.3

Nanoelectromechanical Systems

648 Table 2 presents the calculated values of the fundamental frequency of oscillation for Si nanocantilevers of different geometry. We note that high frequencies of oscillation imply in general high force constants. In the MEMS domain this fact has sometimes prevented the possibility of reaching very high frequencies. However, in the NEMS domain very high frequencies seem to be compatible with low force constant [12], as can be seen by comparing Tables 1 and 2. One of the more relevant applications of resonant solidstate freestanding NEMS is as mass sensors [55–57]. Why these resonators display a so high mass sensitivity can be understood by approximating the nanoresonator by a simple harmonic oscillator. In this case, the fundamental frequency of oscillation is given by  k 1 (9) f = 2 m where k is the force constant and m is the mass. According to this relationship, if a small variation in the mass of a suspended nanostructure, m, occurs then a frequency shift, f , on the natural frequency of oscillation, f , should take place, which is related to the mass increment through the simple relationship   1 1 k (10) − m = 4 2 f 2 f + f 2 where we have assumed that the value of k is independent of the mass of the structure. According to Eq. (10), the higher the resonant frequency, the higher the mass sensitivity. With the high frequencies reachable with nanostructures mass variations of the order of single molecules are potentially measurable [55–57]. Suspended nanostructures can also display torsional oscillations. Frequencies up to 18 MHz have been reported for these oscillations [51]. As for the case of transversal oscillations, the values of the frequencies depend on the geometry of the nanostructure and on material properties. A simple method to estimate them is from the relation   1 (11) f = 2 Im where Im is the polar mass momentum of inertia of the system and  is the torsional spring constant defined previously (this expression is correct except for a numerical factor that can be calculated by using the methods of classical elasticity theory). It is worth noting that the precise dependence of the torsional frequencies of oscillation on the nanostructure properties is completely different from the one corresponding to transversal oscillations. This fact can be illustrated with a nanopaddle (see Fig. 5), a nanostructure able to display

Figure 5. Scanning electron micrograph of a nanopaddle. Reprinted with permission from [50], S. Evoy et al., J. Appl. Phys. 86, 6072 (1999). © 1999, American Institute of Physics.

both types of oscillations and which has received some attention in the scientific literature [50, 51, 61]. The equivalent torsional spring constant of the two beams subjected to the central rectangular part can be calculated from Eq. (6); that is,  = 2a/b

b3 a G L

where the factor 2 affords for the fact that there are two beams subjected to the central structure. Moreover, the mass momentum of inertia of the central part of the paddle (we neglect here the contribution of the beams) is Im = 1/12md 2 . Therefore, according to Eq. (12) the fundamental torsional frequency of oscillation of the nanopaddle can be approximated by
 G b3 1 (13) f = 2 Lwd 3 On the other hand, by using Eq. (9) the fundamental frequency of transversal oscillations can be taken to be
k 1 (14) f = 2 awd with k being the equivalent spring constant for deflections and which depends only on the properties of the nanobeams but not on the ones of the nanopaddle. As can be seen the frequencies of the torsional and transversal oscillations depend on the width of the nanopaddle as d −3/2 and d −1/2 ,

Table 2. Fundamental frequency of oscillation for a single clamped Si nanocantilever for different geometries as calculated from Eq. (8). L × w × t (
m ×
m ×
m) Fundamental frequency (MHz)

(12)

10 × 0 2 × 0 1 0.76

1 × 0 2 × 0 1 75.7

1 × 0 05 × 0 05 37.8

Note: The bulk Si Young modulus is used in the calculations. The frequencies corresponding to double clamped structures can be obtained by simply multiplying by 12.

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649

respectively. These dependencies have been experimentally verified for Si [50] and SiN [51] nanopaddles.

3.1.3. Quality Factor Real resonant structures lose their mechanical energy due to the action of different energy loss mechanisms, generically known as damping mechanisms. This means that in order to keep the nanostructure in motion, energy must be pumped to the resonant structure. The same energy loss mechanisms also induce a broadening of the response of the nanostructure at the resonant frequency, thus reducing considerably the sensitivity for many applications. The effects of damping on a resonant nanostructure can be understood in a simple way by approximating it by a simple harmonic oscillator subject to friction (proportional to the velocity) and a sinusoidal external driving force with frequency f and amplitude F0 . Under these conditions the structure oscillates with frequency equal to the external forcing frequency and with amplitude given by A = 

F0 m

2 − 20 2 +

(15)

2 20 Q2

where 0 = 2f0 and  = 2f , with f0 and f being the natural and forcing frequencies, respectively, m the mass of the nanostructure, and Q a dimensionless parameter known as quality factor whose value is determined by the damping mechanisms. In the absence of any damping effects, the quality factor is infinity and the amplitude diverges at the natural frequencies of oscillation. When damping is present the resonant frequency remains almost unchanged (in the usual case that Q ≫ 1, but the height and width of the resonance are significantly modified, as illustrated in Figure 6. The height and width of the resonance in the presence of damping can be approximated by Amax ∼

F0 Q m0

and

f ∼

f0 Q

(16)

respectively. A physical interpretation of the quality factor is that Q−1 gives the fraction of energy loss by the resonator in one oscillation or conversely Q gives the number of oscillations the oscillator performs before losing completely its energy.

response [a.u]

Q = 104 3

Q = 10 2

Q = 10

f0 frequency [a. u.] Figure 6. Response of a resonator for different levels of damping as a function of frequency.

In resonant nanostructures the values of Q depend on both intrinsic and extrinsic damping mechanisms [12]. The extrinsic mechanisms include air damping, clamping losses at supports, or coupling losses mediated through the transducers. In particular, viscous damping in ambient conditions is known to be the greatest source of dissipation in MEMS and NEMS structures at atmospheric pressures. Intrinsic damping mechanisms include defects in the bulk or interfaces, fabrication-induced surface damage, adsorbates on the surfaces, or viscoelastic loss mechanisms [62–65] (e.g., thermoelastic damping). Some of these anelastic loss mechanisms can be minimized by a careful choice of the materials, processes, and handling. However, some of them are inherent (e.g., thermoelastic damping), thus imposing an ultimate upper bound to the attainable Q’s. Intrinsic loss mechanisms related to surface effects have been suggested to play a relevant role in resonant nanostructures due to the high surface to volume ratios [60]. Also the presence of a metallic layer covering the nanostructure has been demonstrated to decrease the quality factor [51, 66]. The relevance of the extrinsic versus intrinsic damping mechanism depends very much on the operation conditions [67]. For pressures in low vacuum extrinsic damping is negligible and only intrinsic damping affects the resonator (internal friction). Experimentally this region happens roughly below 10–100 Pa for microresonators. The highest values of Q have been obtained under these conditions. For intermediate pressures momentum transfer between the resonator and individual ambient molecules dominates the damping. By neglecting the interaction between the molecules in the ambient the quality factor can be shown to depend inversely on the pressure. This region typically ends around 103 Pa. Finally for high enough pressures for which the interaction between ambient molecules is relevant, viscous damping dominates. In this regime the quality factor is inversely proportional to the fluid viscosity and takes very low values [68]. In this case, methods of quality factor control can be envisaged to keep functionality of NEMS [68–70]. Experimental results have reported values of Q in the range from 102 to 104 for resonating NEMS [the higher values have been obtained in ultrahigh vacuum (UHV) conditions]. Some of these values greatly exceed those typically available from electrical resonators, although they are orders of magnitude smaller than the values expected from fundamental loss mechanisms. In fact, the maximum attainable value of Q seems to scale downward with the linear dimension of the resonator when going from the macroscopic to the nanoscale domain [12] (the linear dimension of the resonator is roughly estimated as V 1/3 , where V is the volume of the nanostructure). Currently, there is no clear understanding of the underlying physics determining this unexpected phenomenon. Damping phenomena always carry with them other phenomena like fluctuations. For instance, a simple harmonic oscillator in the presence of damping experiences random forces whose mean is zero and whose spectral density is given by [12] SF f  =

4kB T k 2f0 Q

(17)

Nanoelectromechanical Systems

650 where k is the equivalent elastic spring constant of the resonator and f0 is the fundamental frequency of oscillation. The presence of these fluctuations is unavoidable and limits, among other things, the minimum measurable forces. Finally, through the quality factor and natural frequencies of oscillation one can estimate the minimum pump energy rate necessary to keep the nanostructure in motion to be [12] Pmin ∼

kB T f Q 0

(18)

where kB T is the thermal energy and f0 /Q is the rate at which the resonator exchanges energy. The high Q values attainable in NEMS imply that a very small amount of power is required to drive the devices, which constitutes one of the big advantages of these systems for communication applications with respect to high frequency microelectrics.

3.1.4. Other Factors Determining the Performance of Suspended Solid-State NEMS In solid-state freestanding NEMS there are other factors, in addition to the ones considered previously, that can alter its performance. These factors should be taken into account when analyzing or designing suspended solid-state NEMS. Weight of the Nanostructures In the estimations performed previously of the equivalent elastic spring constant the effect of the mass of the nanostructure has been neglected. This approximation holds as long as the forces applied to the nanostructure are much larger than the weight of the nanostructure. To give an order of magnitude we note that a 10 × 0 2 × 0 1
m3 Si cantilever weights W = mg = Lwt g = 4 66 × 10−15 N while a 1 × 0 05 × 0 05
m3 does W = 5 8 × 10−17 N (we have taken for the density of Si = 2330 kg/m3 . Therefore, this effect is not expected to be relevant for most of the applications. Phase Noise The extremely high mass sensitivity of the resonators is predicted to induce a high level of phase noise (i.e., fluctuations in the value of the resonating frequency), the reason being that when operated in air or liquids adsorbates are expected to adsorb and desorb from the surfaces in a random way, thus changing the mass of the resonator and hence the natural resonant frequency. Another source of phase noise can be temperature fluctuations or similar phenomena affecting the resonant frequency [71, 72]. Nonlinearities Nolinear effects are easily observable in suspended solid state nanostructures [42, 44, 60, 73]. The onset of nonlinear effects can occur for small applied forces (and hence lower input power) in large aspect ratio structures. In nanostructures nonlinear effects have been observed for displacements as small as 10–15 nm. A signature of the nonlinear behavior is the presence of an asymmetric resonant response. The nonlinear behavior can be harnessed to create parametric oscillators and possibly could be used to create highly sensitive resonant charge [73], force, and mass sensors [12].

Strain Effects In many electromechanical systems bi- or multilayered structures are very often used. In these structures the presence of internal strain or stress is almost unavoidable. Moreover, even for homogeneous mechanical devices (e.g., those patterned from doped semiconductors materials), surface nonidealities may impart significant modifications to the free strain picture. Strain is well known to induce modifications in the values of the equivalent spring constant and resonant frequencies in addition to additional losses. This property has been used to develop state of the art nanomechanical chemical [74] and biological sensors [75]. In the former case use has been made of the fact that analyte molecules chemisorbing or physisorbing on a coated nanocantilever and chemical reactions produce interfacial stress between analyte molecules and the cantilever. In the latter case, the surface strain is induced by a self-assembled monolayer grown on top of one side of a cantilever when it interacts with specific molecules [75]. The induced strain comes from the changes in the configurational entropy and intermolecular energetics of the selfassembled monolayer [76]. Finite Size Effects In most of the experiments reported in the literature the values of the Young modulus obtained differ from the value corresponding to bulk materials (usually lower values are observed [37]). It has been suggested that effects due to the finite nature of the structures (finite size effects) could be responsible for such deviations. A theoretical understanding of this phenomenon is still lacking. Atomistic Behavior When going down to smaller scales, one can ask at what scale continuum mechanics breaks down and corrections from atomistic behavior emerge. Molecular dynamics simulations [77] for ideal nanostructures appear to indicate that this becomes manifest only at the truly molecular scale, of the order of tens of lattice constants in crosssection. Hence, for most of the suspended nanostructures the continuum approximation will be adequate. Heating Effects Due to the presence of losses the materials can heat up and as a result the frequency and the spring constant can vary due to changes in dimensions, density, strain, etc. Although it was forecast that these small structures should dissipate heat very efficiently [1], investigations are still on the way to establish the appropriate heat transport laws for nanostructures [47, 78, 79]. Quantum Effects The ultimate limit for suspended nanostructures is to operate at, or even beyond, the quantum limit [12, 80]. This regime can be defined by the condition that a mechanical quantum, hf0 , where h is the Planck constant and f0 is the resonant frequency, is of the order of, or greater than, the thermal energy kB T . In the quantum regime jumps between discrete quantum mechanical states should be observable. As a rule, very high frequencies and very small temperatures are required (for instance 1 GHz corresponds to 50 mK in temperature). In order to reach the quantum limit a number of challenges have to be overcome, among others, the experimental definition of the resonator discrete quantum states, the development of transducers able to resolve an individual quantum jump, or the cooling of the resonator to very low temperatures in the presence of loss mechanisms [12]. The quantum limit for mechanical

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nanoresonators opens fascinating possibilities in the measurement sciences at the molecular level, in the development of new device possibilities for phase coherent measurements and quantum computation or in the control of thermal transport involving the exchange of individual phonons. Furthermore, in this limit the wave nature of matter will become manifest and the division between quantum optics and solid state physics is expected to become increasingly blurred.

3.2. Actuating and Sensing Solid State Suspended Nanostructures Up to now we have focused on the physical properties of suspended solid-state nanostructures for NEMS applications. In addition to the mechanical part, essential components of any NEMS are the transducers in charge of actuating and sensing the mechanical part of the device. For NEMS applications the transducers must be able to detect minute displacements, induce minute forces, detect very high frequencies, or detect very small frequency shifts. Most of these actions are very challenging in the NEMS domain. Below we report the techniques currently available to actuate and sense solid-state suspended nanostructures.

(a)

3.2.1. Electrostatic Actuation Electrostatic transduction is the method most widely employed in MEMS and can also be applied to NEMS [33, 56, 57]. The principle of actuation of this technique is very simple. It consists of charging electrically the nanostructure and then actuating on it by means of the electrostatic interaction with an external charged element (e.g., a charged substrate), often referred to as the driver. To apply this technique the mechanical element has to be a good conductor or have been recovered by a good conductor. Two examples of driver-free standing nanostructures are shown in Figure 7. This method of actuation allows both static and dynamic actuation depending on whether a constant or variable potential is applied between the nanostructure and the driver. In the latter case, the system can eventually be driven into resonance. Several factors determine the actual motion induced to the nanostructure by the driver. Among others we cite the geometry of the nanostructure, the geometry of the driver, the coupling between both elements, the environment (air, liquid, UHV), the way the nanostructure is fixed, the damping mechanisms, or even the relevance of the Casimir effect [81, 82].

(b) Figure 7. Scanning electron micrograph of (a) a double clamped nanobeam and (b) a single clamped nanocantilever including the driver for electrostatic actuation. Reprinted with permission from (a) [41], L. Pescini et al., Nanotechnology 10, 418 (1999) and (b) [57], G. Abadal et al., Nanotechnology 12, 100 (2001). © 1999/2001, Institute of Physics Publishing.

3.2.3. Secondary and Local Actuation The secondary actuation method consists of using a piezoelectric or another actuator to oscillate the supports where the resonant nanostructure is suspended (Fig. 9a). In scanning probe microscopes this is sometimes the method used to set into resonance the tip. Local actuation [84] consists of using a nanoelement whose dimensions are smaller than the nanostructure (e.g., an STM or AFM tip) to locally induce a motion in the nanostructure (Fig. 9b). This method works better the larger the nanostructure. Both methods

3.2.2. Magnetomotive Actuation Magnetomotive actuation [42, 83] makes use of the Lorenz force (i.e., the force exerted by a magnetic field on an electric current). It uses a setup like the one schematically shown in Figure 8, which consists of a closed conducting circuit, which includes the moving mechanical element, located in a strong magnetic field perpendicular to the nanostructure. When a dc current passes through the circuit a force perpendicular to the electric current appears that eventually can bend the suspended nanostructure. For electric current varying with time a dynamic motion can be induced to the nanostructure. This method of actuation also requires electrically conducting nanostructures.

V I

B Figure 8. Schematic drawing of a freestanding nanostructure magnetomotively actuated.

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652

Nanostructure

Actuator

Actuator Nanostructure

Support (a)

(b)

Figure 9. Schematic drawing of a nanostructure actuated by (a) secondary actuation and (b) local actuation.

have the advantage of not requiring electrically conducting nanostructures.

3.2.4. Actuation by Means of Internal or Superficial Strain As mentioned before internal or superficial strain can produce the bending of freestanding nanostructures and hence offers a method to actuate them. One way to implement this method has been to use bi- or multilayered structures, with layers having different thermal expansion and light absortion coefficients [85]. When such a nanostructure is irradiated with a continuous wave laser and a standing wave is formed between the freestanding structure and the support, then the more absorbing layer absorbs more energy, and heats up more, than the lower absorbing layer (Fig. 10). Due to the different thermal expansion coefficients of the two layers a strong strain is induced in the nanostructure that eventually can bend it. If the amplitude of the laser light is appropriately modulated a resonant behavior can be induced by this method. A similar technique can be implemented in a monolayered nanostructure by irradiating only one part of it [86–88]. In this way a temperature gradient can be induced in it that produces the modulation of the elastic constant and hence the bending of the nanostructure.

3.2.5. Electrostatic Sensing Electrostatic sensing of a free suspended nanostructure can be accomplished by measuring the changes in the capacitance of the capacitor formed by the suspended nanostructure and the driver (see Fig. 7). In the case of a resonant structure the equivalent circuit of the system is more complicated than a simple capacitance, but this method can be equally well applied to measure the motion frequencies [56, 57]. Electrostatic sensing, initially developed for MEMS, does not scale well into the domain of NEMS [12]. Very small

Laser light

electrode capacitances are to be expected for electrodes at the nanoscale, thus making parasitic capacitances dominate the dynamical capacitance of interest. One possible solution would be to eliminate the large embedding and parasitic impedances by locating a subsequent amplification stage directly at the capacitive transducer. This would make the NEMS electrode serve a dual purpose, as both the motion sensor for the NEMS and as the gate electrode of a field effect transistor (FET) readout.

3.2.6. Optical Sensing Very small displacements can be detected by optical methods like simple beam deflection methods or more sophisticated optical and fiber-optic interferometry methods. In the simple beam deflection scheme [89] a laser beam is focused on top of the nanostructure and its reflection is measured on a photodiode (Fig. 11). This method can be applied to both static deflections as well as dynamic ones. In the latter case a spectrum analyzer is usually used to analyze the frequency components of the electrical signal provided by the photodiode. Scaling down this technique to the NEMS regime can be very challenging since the nanostructure cross-section can become smaller than the size of the focused laser spot. Interferometry methods [36, 40, 90], on the other hand, use the fact that the motion of the nanostructure modulates the reflected signal as a result of interference phenomena, thus allowing one to detect the amplitude and phase of the nanostructure motion. For very small size NEMS applications, nonconventional optical methods, like integrated and near-field optical displacement sensors, may become a valid alternative to the above-mentioned methods [12].

3.2.7. Magnetomotive Sensing Magnetomotive sensing is based on Faraday’s law (i.e., on the induction of an electromotive force in a closed circuit when the magnetic flux through it changes with time). There are different ways to implement this technique. One of them consists of using the same setup as the one used for magnetomotive actuation [39] (see Fig. 8). In this case, when the nanostructure is set into motion an electromotive force is induced in the closed circuit, whose measurement provides information on the dynamical response of the device. More elaborate versions of this method, which makes use of a balanced electronic detection [91], have been developed for some especially demanding applications.

Laser

Bi- layered Nanostructure

Photodiode

Standing wave Support

Figure 10. Schematic drawing of a nanostructure actuated by means of the induction of internal strain.

Support

Nanostructure

Figure 11. Schematic drawing of a nanostructure sensed by a simple beam deflection scheme.

Nanoelectromechanical Systems

An alternative implementation of this technique could be done in the case that the moving element behaves like a nanomagnet [12]. In this case, a closed conducting loop located close to the nanostructure can be used to induce an electromotive force in it due to the nanostructure motion. This implementation can be used with nonconducting and both single and doubly clamped nanostructures.

3.2.8. Piezoelectric Sensing In the case that the nanomechanical element displays piezoelectric phenomena sensing of the displacements can be achieved by measuring the voltages generated due to the piezoelectric properties. This method has been implemented with nanostructures fabricated with a piezoelectric material [35] and with GaAs/AlGaAs nanostructures [34, 46]. One advantage of piezoelectric sensing with respect to other methods is that it provides a high degree of integration.

3.2.9. Sensing by Means of Electron Tunnelling Electron tunnelling currents between two conducting materials depend exponentially on the separation between them. This property is used in scanning tunnelling microscopes to image material surfaces up to atomic resolution. This same property can be used to sense small displacements in freestanding nanostructures [33], as illustrated in Figure 12. The same restrictions concerning operation conditions and material properties as for STM will apply by using this method.

3.2.10. Sensing by in-situ SEM or TEM Finally, one can also use in-situ scanning electron microscopy or transmission electron microscopy to sense directly the bending or the motion of the nanostructures [84]. In this case, the usual requirements of these microscopic techniques should be satisfied by the samples.

653 3.3. Applications of NEMS Based on Solid-State Suspended Nanostructures There is no doubt that NEMS based on solid-state suspended nanostructures will find a broad range of applications. A number of NEMS applications are being pursued, which might hold immense technological promise for fields such signal processing in very high frequency, ultrahigh frequency, and microwave bands [58, 59], ultrahigh sensitive magnetic resonance force microscopy [12], noninvasive medical diagnostics devices, BioNEMS for single molecule analysis [12], or ultra-high-density data storage systems. At present, however, most of the research efforts are centered on basic studies of fabrication approaches and on the understanding of the science of nanoscale systems. Functional NEMS devices have been demonstrated only for charge detection [49, 73] and thermal transport studies [47, 78] with relevance for metrology and fundamental science. Moreover, significant advances toward functional NEMS for ultraprecise mass sensors [55, 56] and biomolecular recognition [75, 76] have been recently reported. Based on the present developments, one can anticipate that in a decade or so, one may be seeing a prevalence of solid-state NEMS devices at the level one now finds equivalent MEMS systems [13].

4. NEMS BASED ON NANOFLUIDIC STRUCTURES Many potential applications of NEMS, like those involving chemical, biological, and biophysical processes, require the presence of a fluid environment and hence the use of nanofluidic structures. Nanofluidic NEMS may have dimensions in the order of hundreds to a few nanometers, thus displaying characteristic dimensions of the order of the diffusion length of molecules, the molecular sizes, or the electrostatic screening lengths of ionic conducting fluids. At these scales fluids are expected to display qualitatively new behaviors that will allow one to perform techniques and experiments not possible on the microscale. Although transport phenomena in nanoscopic structures are not well understood yet, some relevant advances have been achieved in recent years. In the present section we review the more relevant developments achieved so far in this field.

4.1. Physics of Nanofluidic Structures

Figure 12. Scanning electron micrograph of a nanobell ring sensed by means of electron tunnelling. The inset displays an equivalent circuit representation of the nanoelectromechanical system. Reprinted with permission from [33], A. Erbe et al., Appl. Phys. Lett. 73, 3751 (1998). © 1998, American Institute of Physics.

Fluids confined in nanometric spaces (with at least one dimension in the tens to hundred of nanometers regime) have been observed experimentally and theoretically to exhibit unique structural, dynamical, mechanical, and rheological properties [92]. These properties have been shown to depend on the degree of confinement (e.g., load), operational conditions (e.g., shear rate and temperature), nature of the fluid (e.g., molecular shape, molecular size and molecular complexity), and interactions with the boundaries (e.g., chemical or physical binding) [93, 94]. The understanding of the structure and mechanical properties of fluids at these scales is then of fundamental scientific and practical interest for nanofluidics (as well as for other fields of research such as lubrication, adhesion, or wetting). Experimentally, this problem has been addressed essentially by

Nanoelectromechanical Systems

654 the use of three techniques, namely open fluid geometries in which two extremely flat surfaces are immersed to come nearly in contact, optical methods able to probe flow properties near a surface in a macroscopic container, and flow experiments in ultrasmall nanofluidic channels. Extensive molecular dynamic simulations have been developed to complement experimental findings. In nanofluidic structures whose characteristic dimensions exceed some tens of the molecule fluid diameter, simple fluids behave like a continuum. Otherwise, for smaller structures, the molecular graininess of the fluids becomes important and a discrete molecular description must be adopted. In the continuum regime the main difference between macro- and nano/microflows (both can described through the Navier–Stokes equation) comes from the relevance of viscous forces. Viscosity represents the tendency of a fluid to undergo deformation when subject to a shear stress. In the case of a pure liquid consisting of simple molecules, viscosity is an intrinsic property and its value is dependent on the temperature of the fluid alone. For complex fluids, such as solutions of macromolecules, viscosity shows a complex dependence on an additional number of parameters, such as the type of solvent and concentration or molecular weight of the solute. In macroflows, the inertia of fluid mass is usually much larger than the viscous force, while in nano/microflows the opposite condition is found. The relevance of inertial versus viscous forces can be quantified through the Reynolds number, defined as the ratio between these two types of forces Re =

vl


(19)

where is the fluid density, v is the characteristic velocity of the fluid,
is the fluid viscosity, and l is a characteristic length. In nano/microfluids the Reynolds number takes low enough values as to allow neglect of the nonlinear terms in the Navier–Stokes equation, thus giving rise to laminar flows (as opposed to turbulent flows present in macrofluidics). For instance, the Reynolds number corresponding to water flow [ = 1 g/cm3 ,
= 0 01 g/(cm s), v = 1 cm/s] through a micropipe of 50
m in diameter with smooth walls is Re = 0 5, largely satisfying the experimental condition Re < 2300 for laminar flow in a pipe. The linear nature of low Reynolds fluid flows, labeled Stokes flows, can be broken in some cases due to the presence of special boundary conditions, as has been shown recently in a T-shaped microfluidic structure [95]. The laminar nature of the fluid flow in nano/microfluidic applications may have important consequences for mixing, sample concentration, and separation of species [4–9]. Although micro- and nanoflows are both laminar, there is an important difference between both, namely that in nanofluidic flows the condition of zero tangential velocity at the walls (i.e., no-slip boundary condition) does not accurately describe the flow properties. It has been recently shown that in any flow the velocity of the fluid at the walls is nonzero. This effect is characterized by means of a phenomenological slip length, , which corresponds to the distance outside the channel at which the liquid velocity extrapolates to zero. The experimental values reported

for this length range in the tens to hundred of nanometers, thus being only relevant for nanofluidic flows. The value of the slip length has been shown to depend strongly on the molecular size of the fluid and on the nature and roughness of the surface. One consequence of the presence of slip at the fluid–solid interface is that flows do not satisfy the standard Poiseuille law. The Poiseuille law describes the pressure driven flow of a fluid through a channel and states that the flow rate, Q, is proportional to the pressure drop across the channel Q=

P R

(20)

where R is the channel resistance. For a circular geometry one has R=

8
L r 4

(21)

where L is the channel length,
is the fluid viscosity, and r is the channel radius. For the case of a rectangular channel whose width, w, and length, L, are much greater than the height, h (an appropriate geometry for nanochannels), one has R=

12
L h3 w

(22)

Recent experiments have reported significant differences between Eq. (22) and the values measured in fluid flows through nanochannels with heights ranging from 2.7
m to 40 nm [96]. The discrepancies between standard theory and experiments have been accounted for by the introduction of slip. The values determined for the slip length are ∼ 25–30 nm for hexadecane, ∼ 14 nm for decane,

∼ 9 nm for hexane, and ∼ 0 nm for water (note that the larger the molecular size, the larger the slip length). At present, it is not clear how to calculate the magnitude of the slip length from fundamental theoretical principles or how it depends on factors such the molecular size, surface properties, or flow nature [97–104]. Other phenomena related to the physicochemical interaction between fluid molecules and wall molecules include “wall depletion” in dilute polymer solutions [105]. Note that, at these scales, and provided the appropriate boundary conditions are used, the nanofluid can be still treated with the Navier–Stokes flow equations in the framework of lowReynolds hydrodynamics or “microhydrodynamics” [106]. The presence of slip in nanoflows is not the unique effect due to the confinement of fluids in nanometric structures. For very small structures, of the order of ten times the molecule diameter, effects due to the discrete molecular nature of the fluid start appearing, thus breaking down the continuum description of the fluids. A well known example is the ordering of molecules in layers when the liquid is confined by surfaces [93, 94, 107]. These density variations lead to an oscillatory solvation force which decays exponentially [104] and to a high value of the “apparent” viscosity of the fluid as high as 105 times the regular viscosity [108]. At these scales, then, the fluid loses its liquidlike behavior and assumes solidlike characteristics [107]. In this regime

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the description of the system can be carried out by means of molecular dynamic simulations. At smaller scales, below one or two molecule fluid diameters one should resort to a quantum-mechanical description, in which the distinction between solids and fluids loses its meaning. Nanofluidic applications involve in most of the cases the presence of “particles” embedded in the fluid. The term “particles” is used here in a broad sense and includes [7] organic molecules (a few angstroms in size), protein molecules (typical sizes from 2 to 5 nm), large biopolymers such as DNA, and suspended solid particles or cells (typically 100 nm–10
m). At these scales, due to the large surface to volume ratios, the motion of the “particles” can be largely influenced by surface forces, thus leading to the appearance of finite size effects, not very well understood yet [7]. Moreover, the presence of even small amounts of particles in suspension can modify the rheological properties of the bulk flow resulting in non-Newtonian fluid properties. In some instances, non-Newtonian fluids at low Reynolds number have been shown to display turbulent-like instabilities (elastic turbulence) that could be advantageous for efficient mixing [109]. The special problems involving particles coming into close proximity can be analyzed using the “Stokesian dynamics” approach, where hydrodynamic effects are split into “far field” and “near field” components [110]. A particular case is the analysis of Brownian effects in the so-called “Brownian dynamics.” Stokesian and Brownian dynamics can be regarded as large-scale versions of the molecular dynamics. The interaction of macromolecules with a surrounding fluid phase and, in general, solvent–solute systems at these scales can be simulated by using multispecies molecular dynamics. Figure 13 summarizes the different transport regimes encountered in nanofluidics. The vertical axis represents the solid fraction of the fluid (the value 0 corresponds to simple fluids and the value 1 to solids. Intermediate values represent solutions with different degrees of solvent). The horizontal axis, ranging from 0.1 nm to 1
m, represents the scale of the problem or the level of description.

4.2. Driving Forces in Nanofluidic Structures Driving fluids and “particles” through nanofluidic structures constitute an essential issue in the development of nanofluidic applications. We review the properties of the basic forces used for this purpose. For the sake of clarity, we distinguish between forces used to drive fluids and forces used to drive the particles with respect to the fluids.

4.2.1. Driving Forces for Fluid Flows Hydrodynamic Pressure Hydrodynamic pressure is the primary force driving fluids in macroflows, but it may be impractical in nanopassages, since the resistance to fluid flow increases with the inverse of the fourth power of the transversal channel dimensions [see Eq. (22)]. This means that in order to reach practical fluid flows very high pressures may be required that in turn may require specific fabrication processes. Furthermore, the sensitivity of the resistance to channel geometry imperfections becomes very high, thus not enabling accurate control of the fluid flow. Finally, actuators inducing the pressures necessary are not easily integrated in lab-on-a-chip systems. For these reasons, and because they also allow selective driving of the embeded “particles,” electrokinetic forces have been preferred by many researchers in micro/nanofluidics. Electroosmosis Electroosmotic flow [111] is related to the motion of an ionic fluid induced by a dc potential applied along the stream. The electroosmotic flow arises from the fact that the surfaces of a flow channel are generally charged or can be made so with a suitable coating, thus inducing a layer of charged ions next to them. The ionic layer consists of a space charge region composed by a rigid sheet of solvated ions bound to the charged surface (known as Helmholtz layer) followed by a region of mobile ions beyond the Helmholtz layer, with a characteristic dimension given by the Debye screening length (whose value can range from nanometers for high ionic concentrations to
m for deionized water). This charged mobile layer can be made to move by the application of an electric potential, dragging the neutral fluid along with it. The resulting velocity profile is constant across the channel and its value can be estimated from v=

1 Macroscopic multibody problems

Solid Fraction

Molecular Mechanics

Quantum Mechanics

Muti-species Molecular Dynamics

Stokesian Dynamics Brownian Dynamics

Molecular Dynamics

Stokes flow+slip

0 0.1 nm

1 nm

10nm

100nm

1000nm

10000 nm

Figure 13. Phase diagram of the different transport regimes as a function of the solid fraction and the characteristic spatial scale of the problem [92].

E


(23)

where E is the tangential electric field,  is the permitivity of the medium, and
its viscosity. Moreover,  is the zeta potential (i.e., the potential difference across the mobile part of the double layer). External electrical control of the zeta potential by the application of a transversal electric field has been recently demonstrated [112], thus offering enhanced performance of electroosmotic control of fluid flows. Note that the fact that the velocity profile is flat (as opposed to the parabolic profile of a Poiseulle flow) is advantageous for nanofluidic applications since it introduces less dispersion in the sample. More complicated, nonuniaxial fluid motion can be generated with electroosmotic forces by creating charged patterns along the walls of the channels [113]. Recently, it has been suggested that an ac electric field can induce a more complicated, and sometimes useful, electroosmotic force [114, 115]. The existing theory is nowadays

Nanoelectromechanical Systems

656 still far from exactly matching the experimental data for high voltages and medium conductivities, even in its enhanced version [116], and it is still under controversy with other theories developed [117]. Despite all these drawbacks, this theory still seems able to capture the fundamental features of the frequency behavior of low frequency fluid movement experimentally measured in structures with microelectrodes. Electrocapillarity Capillary forces constitute a valid alternative since they can generate large forces in small channels. They require a discontinuity such as an air/liquid interface or immiscible liquids and seem appropriate for filling devices or single-use applications [6]. In recent years, external electrical control of capillary forces (electrocapillarity) has been demonstrated in micro/nanofluidic structures. Electrocapillary fluid motion refers to the motion induced by electrostatic control of the solid/fluid interfacial tension in a micro/nanochannel [118]. The principle of electrocapillarity actuation is based on the fact that the capillary pressure on a fluid/fluid meniscus inside a micro/nanochannel can be controlled by the charge density accumulated at the solid/fluid interface. Based on this phenomenon, and by inserting electrodes inside the walls, control of the fluid motion can be achieved, in some cases in a more efficient way than with electroosmosis [118].

Dielectrophoretic Force For neutral particles one has to resort to dielectrophoretic forces to drive the particles with respect to fluids [119]. The origin of this force is found on the electric dipole induced on a neutral particle when an external electric field is applied. The magnitude of the force can be evaluated as follows. Let us represent the electric properties of a dielectric spherical particle of radius a by means of a complex permittivity of the form ∗p = p − j

Viscous Drag As is well known any particle moving with respect to a fluid experiences a drag force due to viscous forces. In the case of a rigid particle the drag force can be approximated by (we assume a spherical particle of radius a) Fdrag = 6
av

(24)

where v is the velocity of the particle relative to the fluid and
is the fluid viscosity. For nonrigid particles (e.g., large polymers and macromolecules) the equivalent of the drag force is more complicated to evaluate. The drag force can be approximated by Eq. (24) as long as the size of the “particle” is much larger than the fluid molecule size. Electrophoretic Force The electrophoretic force refers to the electrostatic force acting on a charged particle embedded in a neutral medium in response to an external applied field. The magnitude of the force is easily calculated as F = QE

(25)

where Q is the charge of the particle and E is the electric field. Moderate voltages applied to short distances, such as the ones characteristic of nanofluidics, give rise to high enough electrophoretic forces to impart significant velocities to the embedded particles. Electrophoretic forces are very often used to separate different species having different sizes. In ionic or polar fluids the presence of other forces can perturb the simple picture presented.

(26)

where p is the dielectric constant of the particle, p is its conductivity, and  is the frequency of the applied field. Let us suppose that the particle is immersed in a dielectric fluid medium of permittivity ∗m = m − j

m 

(27)

and subjected to an uniform z-directed ac electric field of magnitude E0 and radian frequency . Under these conditions the particle presents an effective dipolar momentum given by peff = 4m a3

4.2.2. Driving Forces for “Particles” in Fluids

p 



∗p − ∗m ∗p + 2∗m

 E0

(28)

Due to this effective dipolar momentum, a net force, called dielectrophoretic force, acts on the particle [119] FDEP  = 2m a3 Re



∗p − ∗m ∗p + 2∗m

  Erms 2

(29)

where Erms is the root mean square value of the electric field. As can be seen this force, due to its dipolar origin, only appears when spatially nonhomogeneous electric fields are present. One of the most interesting features of the dielectrophoretic force is its frequency-dependent behavior. Depending on the electric field frequency and the particle properties, the dielectrophoretic force can attract or repel the particle to the electrical field minima or maxima. When the particle is attracted to the electric field maxima it is said to have a positive dielectrophoretic behavior (p-DEP). In the opposite case, one refers to a negative dielectrophoretic behavior (n-DEP). The two behaviors are illustrated in Figure 14 where we display the simulated frequency dependence of the dielectrophoretic force for a 297 nm latex sphere within a medium of conductivity 17 uS/cm at three different voltages. As can be seen, at low frequencies a p-DEP region appears due to the greater conductivity of latex particles in front of that of the medium. At higher frequencies an n-DEP region is observed due to the fact that the medium has a greater permittivity than the particle for these frequencies. Dielectrophoretic forces have been shown to be able to manipulate or collect tobacco mosaic virus (about 300 nm × 18 nm) [120], macromolecules [121], or bacteria [122, 123] without significant disturbance from Brownian motion.

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657 4.3. Applications of NEMS Based on Nanofluidic Structures

Figure 14. Simulated dielectrophoretic force acting on submicrometric latex sphere as a function of the frequency of the applied electric field. Both positive and negative dieletrophoretic behaviors are observed.

Nanofluidic structures provide powerful tools for the field of biotechnology. They have been used for the direct manipulation and analysis of single biomolecules such as stretching genomic DNA in extremely small nanochannels, in scanning for bound transcription factors [125], or to sort DNA molecules [126, 127]. The techniques developed so far make use of the particular properties displayed by long biopolymers in confined fluids, in which the structure dimensions are comparable to the diffusion length or the gyration radius of single biomolecules. Present nanofluidics structures used are still simple and very far from the complexity reached with microfluidics [11]. However, they offer fascinating possibilities not available in microfluidics. We describe the more relevant nanofluidic applications developed so far for biotechnology.

4.3.1. Sorting Biomolecules by Rectification of the Brownian Motion

Electrothermal and Other Forces Other forces exist which are also likely to cause movement in the particles or in the fluid. In addition to gravity (which causes sedimentation) and the van der Waals forces responsible for adhesion, there are electrothermal forces [124], which can cause movement of fluid due to gradients in permittivity and conductivity induced by the temperature gradient in the points where the electrical fields have their strongest nonhomogeneities. Although these forces can become significant at high voltages, it seems not to be relevant compared to the other forces at the typical scales. Nevertheless, as not all the experimental effects are yet fully understood, none of them can be absolutely disregarded in advance. Accordingly, each particular micro/nanoelectrofluidic system must accurately analyzed.

This technique consists of using the fact that an asymmetric disposition of obstacles in a nanofluidic structure is able to rectify the Brownian motion of molecules in structures with characteristic dimensions of the order of the diffusion length of the molecules. Based on this principle, and due to the relationship between diffusion coefficient and molecular size, a technique to separate macromolecules with different sizes can be developed. This technique has been demonstrated in [126], where a sieve consisting of a twodimensional lattice of microobstacles disposed in an asymmetric way was used to sort DNA molecules according to size. In the system the DNA molecules were driven through the device by electrophoretic forces [128]. A similar principle has been also used to sort phospholipids in a twodimensional fluid bilayer [129].

Brownian Motion Brownian motion is a stochastic process consisting of the irregular motion of a particle embedded in a fluid due to the random forces imparted by the fluid molecules. On average the forces, and hence the displacement, are zero, but the mean square displacement is not. In a simple one-dimensional picture the mean displacement is given by

4.3.2. Scanning the Local Structure of Single Macromolecules

 x2 = 2Dt

(30)

where t is the time variable and D is the diffusion coefficient of the particle whose value is related to the fluid viscosity. For the case of a spherical particle of radius a this relation is given by D=

kB T 6
a

(31)

Most often, the Brownian motion is seen as a nuisance that induces dispersion of the particles in a fluid. However, in recent years a positive role to this movement has been identified in nanofluidic applications, as will be discussed.

The fact that long macromolecules stretch when passing through nanochannels makes it possible to locally probe the structure of the molecules as they move through the device. In order to implement this technique two basic requirements have to be satisfied, namely a good stretching of the macromolecules in the channel (this requires channel dimensions smaller than the persistence length of the macromolecule) and a high local sensing resolution. This technique has been implemented recently for analysis of double stranded DNA molecules [128, 130]. The device consists of a flow geometry in which molecules are driven by an external applied bias through a microchannel with narrow slits on it (see Fig. 15). Based on near-field optical effects the molecule can be probed when passing over the slit regions. Initial resolution was limited to 200 nm. Recent progress in the fabrication of smaller channels (fabrication of arrays of millions of nanochannels (10 nm × 50 nm) over a 100 mm wafer using nanoimprinting lithography to stretch, align, and analyze long genomic DNA in a highly parallel fashion has been recently reported [30, 131]) is expected to increase significantly this initial resolution level [125].

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A similar technique has been implemented in the separation of DNA molecules in a device that presented an abrupt interface between regions of vastly different configuration entropy [133, 136]. Based on the same physical principles a separation method based on the motion of macromolecules within a two-dimensional array of interconnected spherical nanocavities has been suggested recently [137].

5. MOLECULAR NEMS: THE ULTIMATE MINIATURIZATION LIMIT

Figure 15. Scanning electron micrograph of a nano/microfluidic system to scan the local structure of double stranded DNA. Reprinted with permission from [122], R. H. Austin et al., IEEE Trans. Nanotech. 1, 12 2002. © 2002, IEEE.

4.3.3. Sizing Macromolecules With present fabrication technologies it is possible to build nanofluidic structures small enough as to facilitate single molecule detection and minimize events of simultaneous passage of more than one molecule through the region of measurement. This opens the possibility to develop devices able to determine the distribution and relative proportions of fragments of individual macromolecules, as well as to determine the overall concentration from a single experiment. This technique has been recently implemented for DNA fragment sizing [132]. The device consisted of a T structure in which the smaller regions presented submicrometric dimensions. The DNA molecules were passed through the device by means of an external applied field (electrophoretic force) and were detected by means of fluorescence based optical methods. Speeds as high as 5 mm/s were reached corresponding to a few milliseconds of analysis time per molecule.

As mentioned in Section 1 the ultimate limit in NEMS miniaturization will be reached when the active parts of the devices consist of single molecules or atoms. In this section, and in order to illustrate the great potentialities of molecular NEMS, we review some of the advances performed in this field in recent years. Most of the cases are based on carbon nanotubes but some of them also refer to other molecules and biomolecules, including nanomechanical structures powered by molecular biomotors.

5.1. Molecular NEMS Based on Carbon Nanotubes

4.3.4. Separation of Macromolecules by Means of Entropic Traps

Carbon nanotubes constitute ideal molecular nanostructures for the fabrication of NEMS devices due to their exceptional mechanical and electrical properties. Carbon nanotubes present a cross-sectional area in the range from a few nanometers up to tens of nanometers and a molecular length in the range from tens of nanometers to micrometers. Furthermore, they display a very high Young modulus (in the TPa regime) and can be both semiconducting and metallic. The simplest NEMS based on a carbon nanotube consists of a freestanding nanotube, for instance a single clamped nanotube. Due to its exceptionally high Young modulus very high natural frequencies of oscillation are expected for these structures. A rough estimation of these natural frequencies of oscillation can be obtained from the classical expression of a single clamped empty cylinder,
 Cn2 1 E 2 fn = (32) D2 + Di 8 L2

Linear polymers tend to form a compact random coil in free solution. For them, it is thermodynamically unfavorable to spontaneously elongate since large free energies to reduce entropy would be required. In confined nanostructures a different behavior has been observed in recent years, and new insights for understanding the confinementmediated entropic behavior of biopolymers in ultrasmall nanoscale fluidics have started to emerge [127, 133]. In particular, it has been demonstrated that in channels comprising narrow constrictions and wider regions size dependent trapping of DNA molecules occurs at the onset of the constriction. This process determines elctrophoretic mobility differences among different macromolecules (surprisingly enough, longer macromolecules move faster than shorter ones) thus enabling efficient separation methods. A demonstration of this method has already been implemented [134] and developed up to a parallel performance [127, 135].

where D and Di are the outer and inner diameter, E is the elastic modulus (which can be identified with the Young modulus of the material if the beam bends by elongation of the outer arc and compression of the inner arc), is the density, Cn is a constant for the n harmonic (C0 = 1 875 for the first harmonic), and L is the length of the nanotube. By substituting characteristic values for a nanotube, frequencies in the GHz domain are naturally obtained. Up to now experiments have been performed with long carbon nanotubes and thus lower frequencies (in the MHz domain) have been measured [138, 139]. In addition to its use in freestanding NEMS, carbon nanotubes offers many other possibilities for NEMS applications. One of these applications is in the development of very low friction nanoscale linear bearings [140]. This device uses the retraction force induced by the van der Waals interaction when different shells of a multiwalled carbon nanotube are

Nanoelectromechanical Systems

pulled apart. The absence of frictional forces (dissipation) in the process opens the possibility to develop high frequency– high Q resonators [141]. Other applications of carbon nanotubes to NEMS are based on the possibility to actuate electrically these molecules. Among them we find nanotweezers and nanoelectromechanic memories. The nanotube based nanotweezers [142] consist of two metal arms with a carbon nanotube attached on each of them (see Fig. 16). By applying a bias between the two metallic arms the nanotubes become electrically charged, and then interact with each other. By an appropriate choice of the value of the applied bias the nanotube separation can be adapted at will. The nanotweezers can be used to grasp nanometric objects or to measure the conducting properties of nanoscale objects (by using the nanotubes tweezers as alligator clips). The nanoelectromechanic memory concept [143] is based on the same principles as the nanotweezers. It consists of a carbon nanotube suspended on top of another nanotube (or a nanowire) in a crossbar configuration (see Fig. 17). By playing with the elastic energy, the van der Waals energy, and the electrostatic energy, one can create a bistable system in which the nanotubes are either in noncontact (OFF state) or in contact (ON state). In order to sense the state of the system the current flowing between the two nanotubes can be used. Indeed, when the applied bias between the nanotubes is small and the system is in the OFF state (not in contact) the electric current between the nanotubes takes place only by tunnelling and is very small. In contrast, when the applied bias reaches a critical value and the system moves to the ON state (in contact) the electric current between the nanotubes increases significantly, thus allowing one to distinguish between the ON and OFF states. Finally, carbon nanotubes [144] offer great potential for nanofluidic applications [145, 146]. Carbon nanotubes provide cylindrical nanochannels similar to pipes used in macrofluidics, with inner diameters of less than 10 nm and wall thicknesses that may exceed the inner diameter. At present, a lot of effort is devoted to understanding the nanofluidic properties of carbon nanotubes. On the one hand it is believed that the interaction of fluid molecules with the nanotube walls could be conceivably so strong as to prevent through-flow. On the other hand, capillary forces can facilitate filling of thin channels in case of good wettability of the solid wall surface by the fluid [147]. Wetting of nanotubes by liquid metals, salts, oxides, and HNO3 has been studied [148] and it has been shown that some liquids could be sucked into nanotubes due to capillary forces [149,

659

Figure 17. Crossbar configuration for a nanomechanical random access memory.

150]. Studies of the wetting and capillarity of carbon nanotubes demonstrate that only relatively low-surface-tension materials can be drawn inside nanotubes [151]. The reported cutoff value of surface tension of 100–200 mN/m is sufficiently high to allow water and organic solvents to wet and fill the interior of carbon nanotubes. Simple experiments of placing a water droplet (surface tension 73 mN/m) on the surface of a carbon nanotube bundle showed the water to be readily sucked into the capillary channels, eventually leaving a dry surface [152]. The behavior of fluids in nanotubes may differ fundamentally from that in macroscopic pipes or even microcapillaries [153, 154]. The major obstacle to insitu experimental studies of fluid behavior in nanotubes has been the rarity of such systems filled, at least partially, with fluids [155]. A recently suggested hydrothermal method of nanotube synthesis has produced nanotubes with an encapsulated aqueous fluid, which includes segregated liquid and gas, and well-defined interfaces [156].

5.2. Molecular NEMS Based on Other Molecules In principle, any molecule or biomolecule is suitable to be characterized electrically and mechanically. This opens the possibility to develop molecular NEMS based on practically any single molecule or biomolecule. We illustrate this possibility with two examples that have already been realized in practice. The first example refers to an electromechanical transistor based on a C60 molecule [157, 158]. It consists of a C60 molecule adsorbed onto a conducting substrate which is actuated on the other side by a scanning tunnelling microscope tip (Fig. 18). The conductance of the system can be seen to depend on the compression applied to the molecule. Indeed, when compression is applied to the molecule the molecular orbitals change due to the modification of the interatomic distances. As a result, the highest occupied molecular orbital and the lowest unoccupied molecular orbital broaden and shift, thus increasing the weight of the tails of these levels at the electrode’s Fermi

STM tip

C60

Substrate

Figure 16. Nanotwezeers based on carbon nanotubes.

C60

Substrate

Figure 18. Schematic drawing of the operation of a single molecular electromechanical transistor.

Nanoelectromechanical Systems

660 Ligand

Optical tweezers

Protein

RNA

Redox e Centre

DNA

Functionalisation layer Microsphere

RNA Polymerase Substrate

Conducting Substrate Figure 19. Schematic drawing of the operation of a single protein nanobiosensor.

energy, and hence the conductance of the system (in the tunnel regime the conductance depends strongly on the occupancy of the energy band at the Fermi energy). Similar behaviors have been found for other molecules [159]. The second example consists of a single protein based nanobiosensor. This nanobiosensor takes advantage of a structural change occurring at the level of a single protein when it binds a ligand [160]. Essentially, the nanobiosensor consists of some proteins anchored onto a conducting surface (previously functionalized) with one “end” free to move and at which a redox center is inserted (Fig. 19). The redox center can exchange electrons with the conducting substrate, with a rate of exchange depending strongly on the distance of the redox center to the substrate. When the protein binds a ligand it suffers a conformational change that modifies the distance between the redox center and the substrate thus inducing a change in the rate of exchange of electrons that can be detected. In addition to these examples, it is worth noting that naturally occurring molecular structures, such as lipid membrane pores [161] or lipid nanotubes [162], show promising potential for applications in nanofluidics. In particular, the formation of geometrically complex lipid nanotube–vesicle networks has been reported recently [162].

5.3. NEMS Powered by Molecular Biomotors A fascinating possibility of molecular NEMS is to power them by means of molecular biomotors. Molecular biomotors convert chemical energy into mechanical energy and are able to generate forces compatible with currently available nanostructures (the forces generated by molecular biomotors can range from a few pN to tens of pN [163], thus being large enough to actuate on some engineered nanostructures). Examples of molecular biomotors include stepwise motion of single kinesin molecules along a microtubule track, displacement of an actin filament by single myosin molecule, forces and transcriptional pauses associated with RNA polymerase activity, nonlinear elasticity of single polymers, reversible unfolding of single protein domains by

Nanopropeller

Molecular Biomotor Substrate

Figure 20. Schematic drawing of a nanopropeller powered by a molecular biomotor.

Linear motion of a microsphere powered by RNAP Figure 21. Schematic drawing of the linear motion of a trapped microsphere powered by RNA polymerase [166].

applied force, and discrete rotations of a single F1 subunit of the F0 F1 -adenosine triphosphate (ATP) synthase [164]. The properties of these molecular biomotors open the possibility to integrate the power supply in NEMS applications at a molecular level. To illustrate this fact we present below some examples of primitive hybrid nanomechanical systems in which molecular biomotors drive the motion of inorganic nanostructures. The first example refers to a nanopropeller driven by the F1 -ATAase biomolecular motor [165]. The device consists basically of three components: an engineered substrate, an F1 -ATAase biomolecular motor, and a fabricated nanopropeller (Fig. 20). It was demonstrated that rotation of the nanopropeller can be initiated with the addition of adenosine triphosphate to the system and stopped by the addition of sodium azide. Two other examples refer to RNA polymerase (RNAP). RNAP carries out an essential step of gene expression, the synthesis of an RNA copy out of the template DNA. Each RNA molecule is synthesized in its entirety by a single molecule of RNAP moving progressively along the template. During transcript elongation, RNAP progresses along the DNA at speeds higher than 10 nucleotides per second and generates considerable force, higher than 10 pN. Moreover, rotation at a velocity greater than 100 revolutions per second and torques greater than 5 pN/nm are induced. In the experiments, RNAP was fixed onto a substrate and the forces and torques developed during transcription were used to move [166] and rotate [167] a microsphere trapped in optical tweezers (see Fig. 21) and suspended below a magnet, respectively.

6. CONCLUDING REMARKS Nanoelectromechanical systems offer unique properties for advanced applications in nanoelectronics, biomedicine, and sensor technologies. Among others, NEMS structures may be applied as oscillators for wireless communications, very sensitive mass and magnetic field sensors, devices for single molecule separation, and devices for detection and analysis in lab–on-a-chip systems. The enormous relevance of these applications has made NEMS investigations one of the more active fields of research at present. NEMS systems exist today at the laboratory level and NEMS production and applications show still many technical obstacles. By comparison with the previous evolution of the MEMS technology, which has taken about 20 years to

Nanoelectromechanical Systems

become mainstream, the NEMS commercialization opportunities must be considered in a medium term, although in some cases a faster commercial implementation is expected. If NEMS potential is fully realized, there is no doubt that NEMS technology will become a key technology for the 21st century, even surpassing solid-state or biotechnologies.

GLOSSARY Biomotors Molecular biological motors that convert chemical energy into mechanical energy and are able to generate forces and torques compatible with engineered nanostructures. Microelectromechanical system (MEMS) Device combining mechanical elements with optoelectronic elements, with the mechanical part having at least one dimension in the range from hundred to a few micrometers. Nanocantilever Single clamped freestanding solid-state structure with at least one dimension in the range from a hundred to a few nanometers. Nanofluidics Study of the mechanical and structural properties of fluids confined in structures with at least one dimension in the range from a hundred to a few nanometers. Nanoelectromechanical system (NEMS) Device combining mechanical elements with optoelectronic elements, with the mechanical part having at least one dimension in the range from hundred to a few nanometers. Nanoimprint lithography (NIL) Lithographic technique able to produce patterns with submicro- and nanometer scales based on the mechanical deformation of a polymer under pressure and elevated temperatures. Nanoresonator Electromechanical device whose active part consists of a mechanical nanostructure able to freely oscillate.

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Encyclopedia of Nanoscience and Nanotechnology

www.aspbs.com/enn

Nanoelectronics with Single Molecules Karl Sohlberg Drexel University, Philadelphia, Pennsylvania, USA

Nikita Matsunaga Long Island University, Brooklyn, New York, USA

Also shown in Figure 1 is an extrapolation based on Moore’s Law, from which one unavoidable conclusion is that in order to maintain the historical progression, in the near future it will be necessary to fabricate devices with feature sizes on the scale of individual molecules. Herein we discuss both experimental and theoretical efforts to “do electronics” with single molecules [1]. Some of the questions that will be addressed are as follows:

CONTENTS 1. Introduction 2. Measurement Techniques 3. Theoretical Techniques 4. Proposed Architectures 5. The Mechanism of Electron Transport 6. Technological Roadblocks Glossary References

1. INTRODUCTION Over the past 40 years, computer hardware performance has improved with such regularity that predictable advances in computer performance have come to be an expectation of the computer hardware industry. This phenomena is captured in the well known Moore’s Law, which holds that typical measures of performance, such as processor speed and memory capacity, double about every 18 months. Mathematically this is written n


future performance = 2 15 ×
current performance

(1)

where n is time in years. So predictable has been the rate of advance in hardware performance that corporate budgeting decisions actually factor in projected advances. For example, given that computers become unmanageably incompatible when they differ in performance by a factor of ten, it follows that hardware must be replaced at intervals no greater than every five years. As captured in Figure 1, Moore’s Law advances have at their root the fact that the typical feature size in electronic device elements has decreased geometrically with time over the past four decades. There has been a contemporaneous “shrinking” of virtually all consumer electronic equipment. ISBN: 1-58883-062-4/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

• How are the electrical properties of an individual molecule measured? • What theoretical techniques may be used to predict the electrical characteristics of an individual molecule? • What properties of molecules might be exploited to design a functional electronic device? • What is the mechanism of electron transport in molecular devices? • What are the current technological roadblocks to molecular electronics? Since the term “molecular electronics” is applied to a wide range of phenomena, it is important to delineate some of the closely related areas that are sometimes placed under the umbrella of molecular electronics, but will not be addressed here. The first of these categories is “quantum computing.” Quantum computing is a nascent technology whereby one capitalizes on the properties of quantum mechanical systems to carry out computations, a completely different paradigm from the digital computing of today. While it is conceivable that molecular quantum states might form the basis for data representation in a quantum computer, this is at best only tangentially related to doing electronics with individual molecules as circuit components. The interested reader may begin study of this area with Ref. [2]. Second, we will not cover the areas of “conducting ploymers” or “organic electronics.” These are very real current technologies employing polymeric and organic materials with useful electrical properties in the construction of electronic devices, where their material properties give them

Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 6: Pages (665–682)

Nanoelectronics with Single Molecules

666 Year

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feature size (microns)

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Figure 1. Historical progress in microelectronics. Data from [91].

an advantage over traditional metals and semiconductors. While there is considerable effort underway to reduce the physical dimension of electronic device elements that are composed of organic or polymeric materials (as has been true for traditional electronic circuitry over the past halfcentury), these advances are far from reaching the molecular scale. To begin study of these materials, the reader may wish to start with Ref. [3].

2. MEASUREMENT TECHNIQUES Manipulating a single molecule is a daunting task. While there are millions of known stable molecules, covering an enormous range of sizes, in general the molecular domain is characterized by nanometer and subnanometer length scales. This is nine orders of magnitude smaller than the characteristic dimension of a human (about 2 meters). Manipulating an object smaller in dimension than ourselves by a factor of 10 or 100 is relatively straightforward and requires no special technology. A softball (characteristic length ≈ 01 m) or a paperclip (characteristic length ≈ 001 m) can be manipulated manually. At about 1000 times smaller, some sort of technology is required. A poppy seed (characteristic length ≈ 0001 m) is difficult to handle without tweezers. At 10,000 times smaller, objects become essentially invisible to the naked eye. Their manipulation requires technology to aid in their observation as well as manipulation. Imagine attempting to manipulate a leg severed from a flea. Certainly this would require a magnifying device just to see it. In addition, it would be nearly impossible to hold ones hand steadily enough for precise manipulation, assuming it could be grabbed with tiny tweezers. A flea’s leg is only 104 times smaller than a human. To manipulate a single molecule requires precise control on a length scale 105 times smaller yet. Said another way, a molecule looks much smaller to a flea than a flea does to a human! It is not even possible to “see” a molecule in the traditional sense. The wavelength of visible light is 400–700 nm, hundreds of times longer than the characteristic length of a molecule. This is but one challenge in use of individual molecules for electronic device elements. A key challenge of measuring the electrical properties of a molecule involves connecting the single molecule into a closed circuit. Conceptually, one would like to affix a nanometer-scale “alligator clip” onto one end of the

molecule and a second nanometer-scale “alligator clip” onto the other end of the molecule. These alligator clips would be attached to micron-scale wires that would in turn be connected to a macroscopic circuit, including a power source and measuring device as shown schematically in Figure 2. Today’s computer chips employ two stages of size reduction. As described previously, a molecular device would require at least three [4]. The problem is discussed in some detail in Ref. [5]. There are no bantam alligator clips, but the concept of capturing a molecule between two classical conductors that are part of a macroscopic circuit has been realized in several ways. We will refer to the generic situation of a molecule in contact with two electrodes as a “molecular junction.” A key challenge in measuring the electrical properties of a single molecule is therefore the problem of creating a molecular junction. One conceptually simple technique is to use a break junction. In this method, a thin wire of some ductile material is immersed in a solution containing the molecular species whose conductivity properties one desires to measure. The wire, while in solution, is then drawn or bent to failure to form opposing tips. The opposing tips then become coated with a self-assembled monolayer (SAM) of the molecular species of interest. The coated tips are then withdrawn from the solution (or more conveniently, the solution is allowed to evaporate). Finally, a potential difference is established between the two tips, and the tips are brought together until current flows [6]. There are several disadvantages to the break junction method. First of all, it is only suitable if the molecular species of interest adheres to form a SAM on the material of the wire. Benzene-1,4-dithiol has proven to be an excellent test species for exactly this reason: the dual thiols serve as alligator clips to attach the ring to the electrodes [7]. It is sometimes necessary to employ protecting groups on the thiolate functions until just prior to the self assembly step, owing to the tendency of thiolates to oligomerize [8]. Thiol linkages have become a de facto standard for attaching molecules to metal electrodes. (Selenium (-Se-) linkages have been tried as well but appear to introduce a large potential barrier to electron transport [7].) Second, the break junction technique assumes that a solution can be prepared that contains the species of interest in sufficient concentration. Synthetic chemistry can be employed to address both limitations. Functional groups may be added to the molecule that increase its solubility and/or facilitate

molecule Figure 2. Schematic of circuit for measurements on a single molecule. One great difficulty is creating “probes” that are small enough to contact the molecule, but large enough connect into the macroscopic circuit.

Nanoelectronics with Single Molecules

its adhesion to the wire material. Nevertheless, these limitations still exist, and functionalization of the molecule almost certainly alters its electrical characteristics. Another disadvantage of the break junction is that it is not possible to guarantee that the tip-molecule-tip geometry is the same upon repeat experiments, or even that a single (and the same) molecule is subjected to measurement. Despite these limitations, replicate measurements of molecular conductance that employ the break junction method have yielded good reproducibility [6], suggesting that the chemistry of the system dictates the formation of similar junctions each time the junction contact is made. A second, more robust technique involves the construction of a molecular junction within a nanopore by employing a combination of techniques from traditional device manufacture and materials chemistry. This technique starts with a 50 nm thick insulating membrane of Si3 N4 , supported on its edges by silicon. A bowl-shaped 30 nm cavity (nanopore) is made in the nitride membrane with reactive ion etching so that the bottom of the “bowl” just barely breaks through the membrane. The bowl-shaped nanopore is then filled with Au by vapor deposition. This leaves gold exposed in a nanometer-scale window through the nitride membrane. The molecular species of interest is then coated onto this tiny area of exposed Au by a SAM technique. Finally, the SAM side of the device is coated with Au by vapor deposition. A device is thereby created where a SAM of the species of interest is sandwiched between Au contacts in a nanometer-scale region. The junction is then incorporated into a measuring circuit. Exact details of the preparation may be found in [9]. A distinct advantage of the nanopore technique is that it creates a structure that is less fragile than a break junction and therefore more akin to a traditional solid state device. The nanopore technique may be suitable for practical devices, not simply as a measurement technique. The nanopore technique probably results in a molecular junction with several (possibly up to 1000) molecules per junction, although some reduction of scale is conceivable [10]. Another technique that employs some features from conventional semiconductor fabrication and others from synthetic chemistry has been presented by Rinaldi et al. [11]. To form a molecular junction, two triangular shaped metal electrodes are fabricated on a SiO2 substrate with electron beam lithography and lift-off processing. The two electrodes are oriented so that they point toward each other, that is, they have adjacent vertices separated by 30–120 nm. A microliter drop of solution containing the molecular species of interest is then deposited between the two electrodes and vacuum evaporated. At sufficiently low evaporation rates, an ordered structure self assembles between the two electrodes. I/V characteristics are then measured by placing an applied potential across the junction. Such devices have been demonstrated to have good reproducibility over a period of months. As a disadvantage, these measurements have been carried out in a vacuum, and it is not clear whether devices can be fabricated that are useful in atmospheric conditions. As reported [11], these devices are nanoscale, but have not been scaled to the single-molecule level.

667 Other techniques employ the instruments of ultramicroscopy. It was first demonstrated by Becker et al. [12] that a scanning tunneling microscope (STM) may be used to measure the conductance properties (I/V curves) of a surface with a spatial resolution on the order of 0.1 nm. This high spatial resolution provides the opportunity to investigate the local electronic structure features of surfaces, such as those associated with point defects [13]. The molecularscale spatial resolution of the STM has been applied to the problem of measurement of the electrical characteristics of molecules. For example, the electrical properties of singlewalled nanotubes [14], self-assembled alkanethiol monolayers [15], and even single C60 molecules [16] have been measured by capturing them between the tip of a scanning tunneling microscope and a conducting substrate. Denoting the tip-to-substrate distance as s, I
s measurements (current as a function of tip-to-substrate distance) on C60 exhibit three distinct regimes. At large s, the current is very low and shows distance dependence characteristic of a vacuum gap. As the tip is brought closer to the substrate, at a critical separation (corresponding to the inner root of the interaction potential between the tip and the C60 molecule) there is a shift in the slope of I
s, indicating opening of new tunneling channels. Finally, true “electrical contact” is made when the C60 molecule begins to be deformed or crushed under the force of the tip [16]. An extension of the STM technique allows for its application to a wider class of molecules. To do so, a conducting substrate (typically Au) is coated with a SAM of the molecular species of interest. Nanoparticles of gold are then dispersed onto the SAM. If the tip of an STM is positioned above one of these nanoparticles, the I/V characteristics of the molecules, caught between the nanoparticle and the conducting surface, may be measured by tracking current flow as a function of the potential difference applied between the tip and conducting surface [17]. Like the nanopore technique, this method incorporates several molecules into the junction. It is estimated that about 60 molecules are active [18]. Scaling to the few-molecule level seems possible. Another microscopy based measurement technique employs a conducting tip atomic force microscope (AFM) probe [19]. First, a SAM of molecules is formed on a Au (111) surface. A fraction of the molecules is then functionalized with a thiol substituent on the top end (farthest from the surface). This thiol functionality allows for chemical bonding to gold nanoparticles that are subsequently dispersed onto the surface. Contact is made between the AFM tip and one of the gold nanoparticles. The AFM tip and conducting surface are then wired into a circuit containing a power supply and measuring device. This allows for the measurement of the I/V characteristics of the probed molecules that are bonded to both the Au (111) surface and the gold nanoparticle [20]. This measurement technique has the distinct advantage that I/V curves are found to be integer multiples of a fundamental I/V curve, allowing for the identification of single molecule junctions. The final microscopy-based technique that we will discuss here was employed by Frank et al. [21] to demonstrate quantum resistance in carbon nanotubes. Arc-produced carbon nanotubes are sometimes found to be embedded in larger fibers composed of graphitic particles and nanotubes. First,

Nanoelectronics with Single Molecules

668

3. THEORETICAL TECHNIQUES The theoretical description of electron transport across a molecule is fundamentally a problem in scattering theory. In principle, the entire arsenal of weapons for solving traditional gas-phase scattering problems may be brought to bear on the problem of electron transport in molecular junctions. Theoretical treatments of scattering problems may be divided into two broad categories, time independent approaches (that is, those that solve the time-independent Schrödinger equation) and time dependent ones (those that solve the time-dependent Schrödinger equation). To date, the majority of theoretical treatments of electron transport in molecular junctions have been of the time-independent variety.

3.1. Scattering In a very primitive picture, the junction molecule presents a potential barrier to electron flow between the source and sink of electrons. (Such a picture is closely related to the contact in a scanning tunneling microscope and many aspects of the theory of STM [22] may be applied.) A schematic molecular junction is shown in Figure 3. (Here we treat the junction molecule as presenting a potential barrier to electron flow, although the shape of the potential varies with the details of the nature of the system.) The quantum

I

Energy

fibers with a single carbon nanotube protruding from the end are selected. One such fiber is affixed in place of the tip of a scanning probe microscope (SPM). The z-axis (height) control of the SPM probe is then used to lower the carbon nanotube that protrudes from the fiber tip into a pool of liquid mercury. By connecting an electrical lead to the fiber tip and another to the mercury pool, a single carbon nanotube may be incorporated into a macroscopic circuit. The carbon-fiber/mercury-pool scheme is very elegant and appears to have the best repeatability of all the measurement schemes reviewed here. The major drawback is that it is specific to nanotubes. It is conceivable that it might be possible to functionalize the nanotube tip by employing some clever chemistry. This would open the application of this scheme to use with any molecular system that can be bonded to a nanotube tip, although this remains a future achievement. In 1991, Joachim discussed the issues associated with measuring the electrical properties of a molecule [5]. At that time the idea was largely hypothetical (although there had been some successful efforts to create circuits with elements at or near the nanometer scale). As reviewed above, in the ensuing decade, several techniques were developed and successfully employed so that the problem of measuring the electrical properties of a molecule is now effectively solved. This is not to suggest that no problems remain. One of the most important is that the molecule must be affixed in some way to two contacts. This inevitably involves functionalizing the molecule to facilitate chemical bonding to the contacts. Such functionalization alters the electrical characteristics of the molecule. We will return to the issue of the influence of contacts later, when we discuss technical roadblocks to molecular electronics.

II

III

incident electrons e

e transmitted electrons

Figure 3. Primitive model of electron transport across a molecular junction. The molecule presents a potential barrier along the electron transport coordinate.

mechanical treatment of transmission across a potential barrier (or well) is discussed in many quantum mechanics texts [23]. In the asymptotic regions on either side of the barrier, the potential is constant so we may write down the wavefunction 
x directly, 
x = A exp
ikx + B exp
−ikx 
x = C exp
ikx + D exp
−ikx


I

(2)


III

(3)

where A, B, C, and D are the amplitudes of the left and right propagating waves and k =
1
2me E
1/2 , E being the total energy, and me the rest mass of the electron. Based on the form of the wavefunction in the region of the barrier (II), we may find a matrix M that relates the wave amplitudes in the asymptotic regions.


 A C M1 1 M1 2 = (4) B M2 1 M2 2 D The matrix M is called a transfer matrix and is closely related to the scattering matrix S, which relates the amplitudes of the incoming and outgoing waves, 


A B S1 1 S1 2 (5) = S2 1 S2 2 D C The inverse of the transfer matrix M −1 is a transfer matrix as well, relating wave amplitudes in the opposite direction. Independent of the formalism used, the quantity  2 C  T =   (6) A

is termed the transmissivity of the barrier and gives the probability that an electron incident from the left (i.e., D = 0) will pass through the barrier and emerge on the right. It follows that T = S1 2 2 . In general, T has energy dependence. If one knows the incident flux of electrons, the product of this flux with T yields the current. The barrier shown in Figure 3 is a constant potential, one for which the transmissivity may be determined exactly, and is given in many quantum mechanics texts [23]. Generalization to nonsquare potential barriers is possible. In such a case, an approximate WKB formula is useful for thick barriers of slowly varying potential. In this case,
b  T ≈ exp 2 k
x dx (7) a

Nanoelectronics with Single Molecules

669

where k =
1
2me
V
x − E
1/2 , and a and b are the left and right classical turning points of the potential barrier for a particle of energy E [23]. The above conveys the basic physics of electron transport across a molecular junction, but it is a very primitive model. First of all, it assumes that the electron transport takes place along a hypothetical one-dimensional coordinate. It completely neglects the space-filling three-dimensional nature of a real junction molecule. Second, in a real junction, the incident electrons are unlikely to be monochromatic, so it may be necessary to integrate over a distribution of incident electron energies (typically a Fermi distribution). Perhaps most importantly, the molecule where the scattering takes place interacts with both the source and sink of electrons (electrodes), and the form and strength of these interactions depend on the contacts. The theoretical treatment of electron transport in molecular junctions, therefore, includes several complications that typically do not appear in a traditional gas-phase scattering problem.

3.2. The Role of the Fermi Distribution In a molecular junction, the molecule is typically connected to two metallic electrodes. Within these electrodes, the population of orbitals is dictated by a Fermi distribution. This means that the source of electrons is, generally speaking, not monoenergetic. Given that the transmissivity T
E of the molecule is known, the current I is given by e  T
Ef
E − a   − f
E − b   dE (8) I= 
− where f is the Fermi function, E is energy, is temperature,
is the Planck constant divided by 2, e is the unit of charge, and a and b are the electrochemical potentials within the two electrodes so that b − a = eV (V being the applied voltage). The difference of Fermi functions is interesting. At low E, both f
E − a  and f
E − b  are equal to one, so their difference is zero. Similarly, at high E, both are equal to zero and their difference is also zero. The difference in Fermi functions only has appreciable magnitude when E falls above the lower of a and b but below the higher. In this region, the orbitals in the high energy electrode are full, and those in the low energy electrode are empty. This is the only energy region in which there can be appreciable current. Below this region, there are no empty orbitals on the acceptor electrode to accept the transferred electrons. Above this region, there are no full orbitals in the high energy electrode from which the electrons may be transferred. For very low temperatures and small applied voltages, the function f
E − a   − f
E − b   is adequately approximated by a delta function. This “finite-voltage finitetemperature” approximation can be seen quite elegantly in the formalism of Bagwell and Orlando [24]. The difference of Fermi functions is written as a difference of two Heaviside step functions (h
) convoluted with a thermal smearing function f
E − a   − f
E − b   
f
E  = h
E − a  − h
E − b  ⊗ − E

(9)

Here ⊗ denotes convolution. From this formalism, it is clear that if the applied potential is small and the temperature broadening is minimal, the expression for current reduces to [25]

I=

e2 TV 


(10)


e2 T

(11)

It follows that R=

which shows that the quantum of conductance [21] is

G0 =

e2 


(12)

Eq. (11) assumes that the molecule is in contact with a perfect conductor [25] and is valid for T → 0. More complete analysis [26, 27] yields

R=



1 − T  e2 T

(13)

from which it is clear that T → 0 ⇒ R →  and T → 1 ⇒ R → 0. Eqs. (11) and (13) agree for T ≪ 1, as in high resistance junctions. In the WKB approximation, we may write
b  G = G0 exp 2 k
x dx

(14)

a

For a constant potential, 

b a

k
x dx = c1 L

(15)

where c1 is a constant and L is the width of the barrier. If we describe a molecule of width L as a one-dimensional tunnel barrier we may then write G = G0 exp
2c1 L = G0 exp
L

(16)

This is the “exponential law,” which is widely used to characterize molecular conductance [28]. The finite-voltage finite-temperature approximation is very common in the theoretical description of electron transport across molecular junctions. As discussed by Bagwell and Orlando [24], this approximation is valid if the applied voltage and thermal broadening are less than any of the features in T
E. For the theoretical description of practical devices, where applied voltages are presumably as high as several eV, it is desirable to go beyond this approximation.

Nanoelectronics with Single Molecules

670 3.3. Multiple Transmission Channels At the next level of sophistication, we recognize that there exists a plethora of possible initial states i (chemists may think of these roughly as electrons in orbitals of the electron donor electrode) and a plethora of final states as well f  (which chemists may think of as electrons in orbitals of the electron acceptor electrode). The transition matrix t has elements f ti that reflect the coupling of i to f  and is related to the scattering matrix by [29] S = I − it

(17)

The transmission coefficient for a wave incident in i to emerge in f  is given by ti f 2 . The structure of the t matrix is determined by the electronic structure of the junction molecule and its coupling to the electrodes, and can be found with any of numerous electronic structure techniques. (Several approaches are reviewed next.) The overall energydependent transmission coefficient is then given by T
E =

  f i f =i

i

tif
E2

(18)



where the velocity ratio f accounts for differences in flux i due to differences in velocity. In this formalism, it is easy to see that there are multiple scattering channels and that the overall transmissivity depends on the sum over all channels [30]. The current is then given by [30] I=

2e  f
Ei 1 − f
Ef + eV  tfi 2 
Ei − Ef 
i f

(19)

where f
E is the Fermi function (for the donor i and acceptor f electrodes), V is the applied potential, and 
Ei − Ef  is a Dirac delta function that ensures contributions only from states in energy resonance. Note in particular that for the donor electrode the Fermi function is employed since the electron must be donated from an occupied state, but for the acceptor electrode 1 − f
E is used since the electron must be accepted into an empty state. Eq. (19) is quite general. One common simplification is to assume that t is independent of any applied potential. This is a reasonable approximation if one is considering small applied potentials, and may be used effectively in conjunction with the small-voltage low-temperature approximation just described.

3.4. Fermi Level Alignment One important problem in developing a theoretical model of electron transport in a molecular junction is that of “Fermi level alignment,” placing the Fermi level of the electrodes relative to that of the molecular orbitals of the junction molecule [31]. The issue is particularly critical because the electrode/molecule interface directly impacts the electron transport properties of the junction [32]. In the simplest approximation, one might start by relating both the electrode Fermi level and the highest occupied molecular orbital (HOMO) of the junction molecule to some common zero of potential. For example, the

energy cost of removing an electron from a relaxed neutral molecule to infinite separation is simply the ionization energy (IE). Using Koopmans’ theorem, IE is approximated by the negative of the energy of the HOMO of the neutral molecule. Similarly, pulling an electron from a metal electrode out to infinity requires paying the work function Ew . If one defines the zero of potential as that of an electron removed to infinite separation (as is customary in molecular electronic structure calculations), Fermi level alignment can be achieved by placing the Fermi level at −Ew and the HOMO at −IE. There are two problems with this approach. The first is that the HOMO energy is only an approximation to −IE, and sometimes a poor one. The second is that in a molecular junction, the molecule is in direct contact with the electrode. This close contact both alters the electronic structure of the molecule and obviates the need to remove the electron from the metal to infinity before placing it on the molecule. It is widely accepted that in the case of zero-applied potential, the Fermi level lies somewhere between the HOMO and the lowest unoccupied molecular orbital (LUMO) of the junction molecule. If the electrode Fermi level were below the HOMO, electron charge would flow from the molecule to the electrodes, completely depleting the HOMO. Likewise, if the Fermi level of the electrodes were to fall above the LUMO of the junction molecule, electron charge would flow onto the molecule to fill the LUMO. With the Fermi level between the HOMO and LUMO, the degree of charge transfer between the molecule and the metallic electrodes depends on the exact position of the Fermi level, and it has been shown that charge transfer can, in some instances, be appreciable [33]. Fermi level alignment and charge transfer are therefore intimately tied together. It is correspondingly unsurprising that the most rigorous approaches to Fermi level alignment require iteration of charge transfer and the molecular energy levels to self-consistency. Closely related to the issue of Fermi level alignment is describing the distribution of an applied potential across the molecular junction. The most common approach has been to introduce an empirical parameter into the formalism to distribute the applied potential, as described quite elegantly by Datta et al. [34]. Given an applied potential Vap , in the zero-order approximation one may assume that the potential Vmol is constant within the junction molecule, with the potential drop between the electron-donor and electron-acceptor electrodes partitioned at the interfaces such that the chemical potentials within the left and right electrodes (L and R ) are given by L = Ef − eVmol = Ef − eVap

(20)

R = Ef + eVap − eVmol = Ef +
1 − eVap

(21)

and where =

Vmol Vap

(22)

Ef is the equilibrium Fermi level and  is an empirical parameter, commonly taken to be  ≈ 05 [35]. These expressions show that with zero applied potential, the chemical potentials of the electrodes are set to the equilibrium

Nanoelectronics with Single Molecules

Fermi level. This formalism implicitly assumes that in the case of zero applied potential, the zero of potential in the molecule (as defined by whatever molecular electronic structure calculation technique is employed) lines up with the equilibrium Fermi level. Traditional quantum chemistry techniques may be employed to determine the Fermi level alignment in a nonempirical way, at least in the case of zero applied potential. An ab initio molecular electronic structure calculation is carried out on the junction molecule, including part of each electrode into the molecular structure. Effectively one is placing a metal cluster on each end of the molecule. The size of these clusters is then increased and the calculation repeated until a common Fermi level is reached that is not significantly displaced in energy from the Fermi level of the pure metal [31, 36, 37]. This method has been applied to the case of a single C60 molecule bound to two Al electrodes of size similar to the C60 itself [36]. An interesting “natural doping” of the junction molecule is found. Electron charge flow occurs from the Al electrodes to the junction molecule until the LUMO (which is threefold degenerate) is half filled. Qualitatively, this is the most “metallic” distribution of electrons in C60 , presumably leading to enhanced conductance. As discussed later, an added benefit of including a portion of each electrode into the electronic structure description of the junction is that this allows exact atomistic specification of the electrode/molecule contact geometry, which affords investigation of the influence of variations in contact geometry on electron transport [38].

3.5. Examples of Theoretical Studies We now turn to specific examples of theoretical treatments of electron conduction through molecular junctions and similar systems. Sautet and Joachim studied the closely related problem of the influence of a single impurity on current flow along an otherwise homogeneous repeating chain [39]. The energydependent transmission coefficient is written in terms of the diagonal elements of a transfer matrix, which relates wave amplitudes across the defect as in Eq. (6). The transfer matrix is in turn constructed from the elementary site-to-site propagators through the defect. The construction of these site-to-site propagators requires knowledge of the electronic structure of the system. The electronic structure of the chain polymer is described with a tight-binding Hamiltonian. There are five parameters: 1) e the coupling of two sites away from the defect, 2) h the energy of a nondefect basis function, 3)  the energy of the defect site basis function, 4)  the coupling of the defect site to the site immediately adjacent on the left, and 5)  the coupling of the defect site to the site immediately adjacent on the right. The elementary site-to-site propagators P are constructed in terms of these Coulomb and resonance parameters to connect the coefficient vectors across a site 

Cn Cn+1 =
P (23) Cn Cn−1 In overview, the electronic structure of the system determines the elementary site-to-site propagators P. The siteto-site propagators determine the transfer matrix t. The

671 transfer matrix determines the ratio of wave amplitudes across the defect and therefore the transmission function T . A multichannel transfer matrix technique for the theoretical description of electron transport in a molecular wire with a lateral (transverse to the direction of conduction) confining potential has been described by Sheng and Xia [40]. For a wire aligned along the x axis with a confining potential U
x y between 0 ≤ x ≤ L , the wavefunction in the asymptotic regions x < 0 and x > L may be written L
x y =

N  

n=1

and R
x y =

N  

n=1

 aLn eikn x + bnL e−ikn x n
y

(24)

 aRn eikn x + bnR e−ikn x n
y

(25)

in the regions x < 0 and x > L , respectively. Here kn may be extracted from
2 kn2 = E − En 2m

(26)

where E is the total energy of the system, m is the effective electron mass, and En is the energy of the nth transverse mode. The amplitudes in the left and right asymptotic regions are then related by a transfer matrix M



 aL aR M1 M3 aR =
M = (27) bL bR M2 M4 bR where aL  aR  bL  bR are vectors of incident and reflected wave amplitudes, and M is partitioned into submatrices M1  M2  M3  M4 for convenience. The transfer matrix is related to the transmission (t) and reflectance (r) matrices in the usual way. Typically, one considers the case where bR = 0, that is, there is no incident flux from the right. Within the scattering region where the potential is described by U
x y, the wavefunction is expanded as 
x y −

N 

fn
xn
y

(28)

n=1

where n
y describes the transverse modes and fn
x may be thought of as an x-dependent expansion coefficient. Substituting Eq. (28) into the Schrödinger equation, multiplying by an arbitrary m
y, and integrating over all y yields 

N  −
2 2 + U
xfn
x 2m x2 n=1 mn 
−
2 − E fm
x = 0 + 2m

(29)

where Umn
x is the matrix element of U
x y between transverse states n and m, n U
x ym . Integrating these coupled equations from R to L for a linearly independent set of initial conditions and matching the asymptotic boundary conditions for fn
x = 0 and fn′
x = 0 yields the transfer matrix. The method is particularly useful for investigating the influence of the lateral confining potential on electron transmission.

Nanoelectronics with Single Molecules

672 Perhaps the most widely used theoretical description of electron conduction across a molecule is that presented by Mujica et al. [30]. The method begins with Eq. (19). The system is partitioned into two metallic reservoirs A and B and the molecule M. The Hamiltonian for the system is then partitioned H = H0 + V

(30)

where H 0 is assumed to have orthonormal eigenstates: i corresponding to states of A, f  corresponding to states of B, and  corresponding to states of M. V is the interaction potential connecting M to A and B. It is assumed that there is no direct coupling of A and B. Physically, this corresponds to the approximation that thorough space coupling of the two reservoirs is negligible, quite reasonable for all but the smallest molecules M, where the separation of the electrodes would be correspondingly small. It is then possible to define a transition matrix t connecting the states i of the donor reservoir to the states f  of the acceptor reservoir in terms of the coupling matrices Vi  and V f and the eigenstates of H 0 . The current follows directly from Eq. (19). In this formalism, the current factors into a contribution from the electronic structure of the wire (coupled to the reservoirs through its end sites) and the density of initial and final states. In the original presentation of Ref. [30], a tightbinding Hamiltonian is used and the matrix t is assumed to be independent of any applied potential. The latter assumption limits the valid range to low voltages, but the formal expression of the current is quite general, and these assumptions may in principle be relaxed. The basic scheme of Ref. [30] has been generalized to employ a nonorthogonal basis [41, 42], to include vibrational broadening [35], and to include multiple orbital interactions of the molecule with the electrode [42]. A floquet theory approach to the case where the wire is driven by a monochromatic radiation field has also been reported [43]. Lang has presented an approach for calculating the current flow across a few-atom wire connecting two metals that is essentially fully first principles [44]. Fermi level alignment and charge transfer are handled in an entirely selfconsistent manner. Density-functional theory calculations are employed to produce an initial electronic wavefunction. The electrostatic potential distribution across the junction is computed self-consistently. That is, the charge density distribution resulting from the electronic wavefunction is used in the Poisson equation, which in turn produces the applied electrostatic potential. The electronic structure and applied potential are iterated to self-consistency. Current is calculated from the final self-consistent wavefunction. Electrostatic self-consistency is key to moving beyond the small-voltage low-temperature approximation. The method of Lang and colleagues is therefore one of only a few to be formally applicable to cases of large bias voltage. The technique has been generalized for molecular junctions [32], applied to a hypothetical multiterminal molecular electronic device [45], and used to study temperature effects on electron transport properties of molecules [46]. A different scattering-theory approach has been taken by Emberly and Kirczenow [47, 48]. They start by dividing

the electrode-molecule-electrode system into five conceptual components. The electrodes on the left and right are labeled L and R, respectively. Each electrode terminates in a gold cluster, each denoted C. The molecule m is trapped between the two clusters so that the overall system may be written symbolically LCmCR. For the purposes of the theoretical description, three components are identified: the left “lead” L, the CmC central supermolecule (shorthand M), and the right lead R. The wavefunction    is expanded in a basis of orbitals {n j} where n denotes the site (A “site” is a unit cell in L and R, and is n = 0 for M.), and j denotes the orbital index on the specific site. The overall wavefunction is then a sum over expansions for all three components (31)

   = L  + M  + R 

where the superscript  is a mode index. To find the scattering t matrix,  a  is written as as a right-propagating wave and a sum over reflected waves whose amplitudes are specified by the reflection matrix r  −1 
       = r  cj eink n j cj eink + (32) n=− j



Here kq is the unitless signed wavenumber for mode q, and q cj are the expansion coefficients. The index j sums over molecular orbitals of a unit cell in the lead. The unit cells are indexed n, (n < 0 for L, n = 0 for M, and n > 0 for R). M  is written as a sum over the orbitals in M   aj 0 j (33) M  = j

where the site label is denoted 0 for convenience. R  is written as a sum over transmitted waves whose amplitudes are specified by the transmission matrix t R  =

  

n=1 j



t  dj eink n j

(34)



Eq. (31), expanded in {n j}, is then substituted into the Schrödinger equation (35)

H    = E  

and closed with the bra n i. This produces a system of equations whose unknowns are the elements of the r and t matrices   i j  imk  i j  An 0 aj An m cj e r  + j

m j

∈L

+



∈R i j

t 



m j

 Ainjm dj eimk

=−



Ainjm cj eimk



(36)

m j

where An m = n iHm j − E n im j [47]. The current is then related to the t matrix in the finite-voltage finitetemperature approximation. The Hamiltonian H is expanded as H = H 0 + W , where H 0 is the Hamiltonian for L, M, and R, and W is the coupling of L to M and of M to R. In the implementation of Emberly and Kirczenow [47], H 0 is based on a tight-binding Hamiltonian. The coupling W is composed of Hückel (tight binding) matrix elements between the

Nanoelectronics with Single Molecules

673

orbitals of the cluster-molecule-cluster system and the adjacent orbitals in the leads. More sophisticated electronic structure descriptions could in principle be employed within the same formalism. One of the benefits of this method is that the explicit treatment of atoms in the contacts allows for direct investigation of different contact geometries. A chemically intuitive method of directly relating the electronic structure of a molecule to its resistivity has been discussed by González and Morales [27]. The technique is again based on the inverse relationship between the transmission probability through the molecule and its resistance, Eq. (13). As the transmission nears unit probability, the resistance approaches zero. As the transmission probability approaches zero, the resistance increases without bound. The transmission probability is approximated by the normalized charge-transfer across the molecule from an electrondonor functional group to an electron-acceptor functional group, upon electronic excitation. A long “wire” molecule is functionalized with a donor CH3 ) and an acceptor subsubstituent on one end (D = CHO). The charge distribution stituent on the other (A = is analyzed in the molecular ground state and again in the charge-transfer photoexcited state. During photoexcitation, charge is transferred from the Donor D to the acceptor A. In the presentation of González and Morales [27], the wire is taken to be n ethene units ( HC CH )n . A hypothetical charge transfer for a zero-length molecule Q0 may be extrapolated by plotting charge transfer Qn versus n. The hypothetical zero-length molecule is assumed to have unit transmissivity T = 1. It follows that for the transmissivity for n . In principle any a wire of n units one may write, Tn ≈ Q Q0 molecular wire could be treated within this formalism. The qualitative variation in transmissivity with molecule length predicted by the method of González and Morales [27] is completely consistent with that given by much more sophisticated multichannel scattering calculations [28]. A unique feature of this technique is that it yields information about the resistance intrinsic to the molecule, with no contribution from contacts. One shortcoming of this method is that it does not allow the prediction of the I
V  characteristics of the molecule. Nonlinear effects may be investigated to first order by taking advantage of the fact that the charge transferred differs for different donor and acceptor groups. If calculations are carried out for several pairs of donor and acceptor groups, the resulting molecular resistance R versus molecule length l data may be fit to R
l = L l + NL l2

(37)

where L and NL are the linear and nonlinear resistance coefficients, respectively. Other groups have taken the approach of concentrating on the electronic structure of the junction molecule or wire instead of explicit calculation of the current. Molecular orbital studies can provide considerable insight into the electrical behavior. Seminario et al. [49, 50] have used first principles methods to investigate the influence of torsional distortions on the electronic structure of conjugated oligo(phenylene ethynylene) systems, such as 1,4-(ethynylphenyl)phenylene. (See Fig. 4.) Knowledge of the energy barrier to torsional

Figure 4. 1,4-(ethynylphenyl)phenylene.

distortion (which is typically quite low, on the order of a few kcal/mole), and of the changes in molecular electronic structure with torsional distorsion, allow for a qualitative prediction of the effects of temperature on the electrical transport properties of the system. In an extension of this work, Derosa and Seminario [51] have combined the DFT electronic structure description of the molecule plus a number of Au atoms from each adjacent electrode with a modification of the formalism for transport properties presented by Samanta et al. [41] to describe electron transport through single-molecule junctions. In related work [52, 53], semiempirical methods were employed to investigate the effect of interspersing valencesaturated “spacer” atoms along the otherwise conjugated wire. In particular, the formation of resonances due to changes in the energetic alignment of the molecular orbitals with applied static electric field is discussed.

4. PROPOSED ARCHITECTURES Today, molecules with extended  conjugation are most often identified as candidates for molecular electronic devices [28, 54, 55]. The property of conjugation allows for effective electron delocalization over great distances, presumably facilitating low resistance electron transport [56, 57]. This is most easily visualized with Lewis structure diagrams. Consider a long conjugated chain as depicted in Figure 5. If a charge is introduced at one end (here by removing H− to form a primary carbocation), it is easy to

C

C C

C

(a)

+

C

C

(c)

C

C

C

C

C

C +

C C

(b)

C C

C

C

C

C C

C C

C

Figure 5. Schematic of electron transfer across linear polyene. (a) A linear polyene. (b) H− is removed from the left-most carbon atom inducing a formal charge of +1. The electrons in the double bonds may then shift as shown by the arrows to transfer the positive charge to the right-most carbon atom. (c) Right-most carbon carries formal charge of +1.

Nanoelectronics with Single Molecules

674 see how the charge can be transported across the molecule by successively shifting the double bonds. In unconjugated systems, such transport can only occur by migration of atoms, or by violating the rules of valence. Since even the lightest atom, hydrogen, is 1836 times heavier than an electron, atom migration is a much less facile method of charge transport. If the system is unconjugated, charge transport by electron transfer requires violating the rules of valence. Such processes are therefore energetically unfavorable. From the perspective of molecular orbital theory, a conjugated  system can be described through the construction of the molecular  orbitals as linear combinations of atomic p-orbitals. The atoms forming the conjugated domain must all lie in a plane (or nearly so), here taken to be the yz plane. To describe the conjugated  system, one may take as a basis a single atomic px -orbital on each atom in this domain. In the construction of molecular orbitals from this basis, there will always be one molecular orbital that consists of a positive contribution from each atomic orbital, that is, a nodeless molecular orbital delocalized over the entire conjugated domain. (See Fig. 6.) Such a structure is widely believed to be favorable for low-resistance electron transport. Conjugated organic molecules are a particularly attractive choice for molecular electronics, not only because of their electronic structure properties, but also because the chemistry community has more than a century of experience in their synthesis and handling, which should facilitate the fabrication of devices composed of conjugated organic components. The use of individual molecules as device elements has another potentially revolutionary advantage. In a chemical synthesis, a large number of molecules is produced (on the order of Avogadro’s number 6 × 1023 ), and they are all absolutely identical (notwithstanding isotopomers, whose chemical properties are essentially indistinguishable). There is the potential, therefore, for the inexpensive fabrication of a staggering number of individual units with near perfect uniformity [54]. Numerous examples may be found in [55].

x

C

4.1. Wires Perhaps the most fundamental component of any circuit is the wire. Molecular electronic circuits will require wires also, and numerous species have been proposed to fill the need. Samanta et al. [41] have proposed molecules consisting of multiple paralinked benzene rings as molecular wires. The generic formula is HS (C6 H4 )n SH, where the thiol terminators are the molecular equivalent of alligator clips, which are used to attach the wire to electrodes. Their calculations predict an exponential dependence of resistance on molecular length. This has been observed experimentally for similar molecular species [57, 58] and is a consequence of tunneling-dominated electron transport. This feature of molecular wires is qualitatively different from conventional macroscopic wires. Conventional metal wires exhibit a linear dependence of resistance on length. (A wire of length l and resistance R when clipped into two halves, produces two wires of length l/2 each with resistance R/2.) A commonly used descriptor for molecular wires is the  factor. One writes the electron transfer rate constant kET as [57] kET = k0 exp
−rda 

(38)

where k0 is a kinetic prefactor, rda is the distance between the electron donor and the electron acceptor (basically the wire length), and  is the characteristic parameter. Davis et al. [57] have carried out measurements of the (C6 H4 electron transfer rate in molecules of the form CHCH)n (C6 H2 (OR)2 ) (CHCH C6 H4 )n . For these systems, they find  ≈ 004 Å−1 . Sikes et al. [58] have reported similar studies for ferrocene oligophenylenevinylene methyl thiols and report  ≈ 006 Å−1 . This class of molecules is shown in Figure 7. These low  values indicate remarkably weak length dependence in these systems, a desirable characteristic for molecular wires. By contrast, typical  values for unsaturated and saturated electron transfer bridges are 0.5 Å−1 and 1.0 Å−1 , respectively [58]. As discussed previously, Gonzáles and Morales [27] have considered polyenic molecules of the form D (CH CH)n A as molecular wires. Rather than employing the  parameter, they use Eq. (37) to describe the length dependence of resistance.

z

C C

C C

C

(a)

C

C O

C

C

Fe C

C C

(b)

C

SH C

C O

Figure 6. A linear polyene with the px   orbital structure shown. (a) Highly antibonding linear combination of px orbitals; (b) fully bonding linear combination of px orbitals leads to nodeless  orbital extending across the entire molecule.

n

Figure 7. Ferrocene oligophenylenevinylene methyl thiols. One possible repeat unit is enclosed in brackets.

Nanoelectronics with Single Molecules

675

4.2. Devices The electronic devices themselves can be broadly classified into two categories: i) those with nonlinear I/V characteristics, and ii) those whose I/V characteristics can be influenced by an external stimulus. An example of the first type is a diode. Under positive bias, (forward current flow) the device presents a constant (typically small) resistance to current flow so that the current flow is linearly dependent on the applied potential. Under negative bias, however, the device presents a large resistance to current flow. There is a significant nonlinearity in the I/V characteristics, near zero applied potential. An example of the second class of devices is a switch. In the closed position, the device presents an essentially infinite (or at least very large) resistance to current flow of either bias, but after the action of some external stimulus (depressing a button for example), a new state is accessed where the device presents little resistance to current flow. Architectures have been proposed for molecular devices of both types. The idea of creating molecule-sized electronic components has almost certainly been around in science fiction literature for many years. The first serious attempt to identify molecular properties on which one might capitalize to create real molecular devices is widely attributed to Aviram et al. [59]. Much early work focused extensively on the potential use of hydrogen bonds for information storage [60]. In some systems, the hydrogen atom, caught between two highly electronegative atoms in a hydrogen bond, is governed by a double well potential. The system has a local minimum in potential energy when the hydrogen is more closely associated with either one or the other of the two highly electronegative atoms, and these two local minima are separated by a potential barrier. This situation is known as asymmetric hydrogen bonding. Such a situation has two physically distinct states. If the system can be induced to switch from one state to the other by some external stimulus, a binary information storage device has been created. This idea is motivated in part by the observation that DNA accomplishes information storage with hydrogen bonds [59]. While conceptually appealing, experimental studies of 9-hydroxyphenalenones [61] and theoretical and experimental studies of hemiquinones [59] show that in these systems the proton tunneling rate is too high for enduring information storage. This problem might be resolved with massive redundancy or a heavier switching group. A switching scheme based on enol-keto isomerization in N-salicylidenaniline was studied by Sautet and Joachim [62]. The molecule exhibits qualitatively different transmission properties T
E in the enol versus keto tautomers. It is proposed that if this system is embedded into a polyene chain by replacing one of the C C linkages in the chain with one of the C C edges of the C6 ring in N-salicylidenaniline, then switching between the keto and enol tautomers will change the resistance of the polyene molecular wire. The enol form is shown in Figure 8. One particularly intriguing idea is to capitalize on the the conductivity change that accompanies changes in the relative alignment of phenyl rings along a polyphenyl chain, in a spirit similar to the “conformational switching” concept of

N H

C

H O

Figure 8. N-salicylidenaniline inserted into a polyene chain. The enol tautomer is shown.

Joachim and Launay [63]. Theoretical work has predicted that the conductivity of such a conjugated chain may be varied by 104 simply by varying the torsional alignment of two adjacent phenyl rings along a polyphenyl chain [41]. More recent studies by Olson et al. [64] have expanded upon this concept, exploring the influence on conduction of molecular vibrations in general along normal mode coordinates. It was reported that for the p-benzene-dithiol molecule, none of the vibrations lead to appreciable changes in current, owing to the rigidity of the molecule. By contrast, DiVentra et al. [46] note that when the molecule is modified with a NO2 substituent (2-nitro-1,4-benzene-dithiol), twisting of the NO2 substituent can lead to appreciable changes in the molecular orbital energies and potentially observable changes in the I/V characteristics. Theoretical studies of atomic-scale aluminum wires have shown that atomic disorder in general alters the electron transport properties, and the effect is stronger for “thin” wires [37, 65]. Clearly there will be some cases where molecular vibrations will have appreciable impact on electron transport. Molecules that exhibit vibronic coupling (coupling of intramolecular vibration to electronic structure) are especially strong candidates. In fact, the Jahn–Teller effect has been implicated as the origin of key features in the tunneling spectroscopy of C60 [66]. If the electron transport properties depend sensitively on a vibrational mode (or modes) with sufficiently low characteristic vibrational frequency, any molecular device incorporating such a component will display temperature-dependent electrical characteristics. Conceivably one might capitalize on such temperature sensitivity to fabricate an extremely sensitive temperature sensor. When a molecule exhibits changes in its electrical characteristics with vibrational excitation, it results from differences in the electronic structure when vibrationally distorted. Such distorted structures may, in principle, also be sampled mechanically by applying a force to the molecule. This suggests a novel way to control conductivity in a molecular junction, with an applied force. A theoretical formalism to investigate the effect of stretching molecular wires on their electronic properties has been presented by Mikrajuddin et al. [67] and used to demonstrate mechanical/electronic coupling.

Nanoelectronics with Single Molecules

676 A beautiful example of the influence of vibrational motion on electron transport has been demonstrated in C60 transistors [68]. The fabrication of these devices starts with a thin insulating SiO2 layer on a conducting (doped) Si substrate. A pair of connected nanometer-scale gold electrodes are then fabricated on top of the SiO2 by electron-beam lithography. A toluene solution of C60 is deposited on the electrodes, and the connection is broken to form a break junction. The conducting Si substrate then serves as the gate and the gold electrodes as the source and drain. The I/V characteristics between the source and drain are observed to be highly dependent on the gate potential. In addition, the differential conductance of the device exhibits peaks with an energy spacing characteristic of the frequency of the oscillation of the C60 relative to the gold surface, about 1.2 THz. Fabrication of a molecular transistor is, of course, a key step in the advance of molecular electronics. The “transistor effect” in C60 has been the subject to detailed theoretical investigation as well [69, 70]. More recently, a new paradigm for molecular scale electronics capitalizing on changes in the electrostatic potential for information storage and transport has been presented by Tour et al. [54, 71]. The electrostatic potential within a molecule is influenced by the presence of charge. Such changes in the electrostatic potential extend sufficiently far from the molecule that they could, in principle, be used to transfer information to an adjacent molecule. Based on this concept, Tour et al. [54] have proposed architectures for molecular logic gates. Of the many potential molecular electronics applications, data storage is one of the most advanced, and the first practical implementations of molecular electronics technology quite possibly will evolve in this area. Several actual demonstrations of binary data storage near the single molecule threshold have been reported by a team from the Beijing Laboratory of Vacuum Physics [72–75]. High resistivity polycrystalline thin films of a conjugated organic compound (or binary mixture of compounds) are prepared by vacuum evaporation onto room temperature substrates at a rate ≤5 nm/min to a thickness of 20 nm on freshly cleaved, highly oriented pyrolytic graphite (HOPG). Local conductance transitions are then induced in the film with a scanning tunneling microscope (STM). A potential pulse (square waveform ≈ 4 V × 10 s) is applied between the STM tip and the conducting graphitic substrate. This pulse induces local changes into the electrical characteristics of the thin film so that an area comparable in size to the crystal unit cell increases conductivity by about ×104 . These tiny regions of high conductivity can be thought of as binary data storage units. Bit densities of 1014 cm−1 have been reported [72]. The technique has been demonstrated for several materials, including N-(3-nitrobenzylidene)-pphenylenediamine [73] (NBPDA), 3-phenyl-1-ureidonitrile [72] (PUN), and a 50:50 mixture of 3-nitrobenzal malononitrile (NBMN) and 1,4-phenylenediamine [74, 75] (pDA). (See Fig. 9.) The reverse transition in individual marks may be achieved in the latter material by applying a reversepolarity voltage pulse of −45 V for 50 s [76, 77]. Another molecular-scale switching technology has been demonstrated by Collier et al. [78–80]. This technology is based on topologically interesting assemblies of molecules

NBPDA CH NH 2

N NO2 O

N

C PUN

NBMN

C

N

N

H

H

CH

C

N

C

N

C

NO2 pDA

H2N

NH 2

Figure 9. Several systems used to form thin polycrystalline films with switchable electrical properties on the nano scale. The boxed pair are used in a 50:50 mixture. N-(3-nitrobenzylidene)-p-phenylenediamine [73] (NBPDA), 3-phenyl-1-ureidonitrile [72] (PUN), 3-nitrobenzal malononitrile (NBMN), and 1,4-phenylenediamine [74, 75] (pDA).

known as catenanes and rotaxanes. These are nanosystems that are composed of two or more molecular components, wherein the components are linked mechanically but not chemically. For example, a (CH2 )n ring may be “threaded” with an alkane chain when n ≥ 18 [81]. Two such rings, when interlocked, form a catenane. When a single ring is threaded by a linear chain molecule, a rotaxane results. (Note that in a rotaxane, the linear chain component is terminated on each end by a bulky substituent, which prevents the unthreading of the ring. In contrast, a pseudo-rotaxane lacks one or both of these bulky end-groups and thus can be unthreaded.) A catenane, rotaxane, and pseudorotaxane are shown schematically in Figure 10. As shown in Figure 11,

catenane rotaxane

pseudorotaxane

Figure 10. Schematic diagrams of a catenane, rotaxane, and pseudorotaxane.

Nanoelectronics with Single Molecules

O

677

O

O O O

N+

N+ S

S

S

S

N+

O

N+ O

O O

O

Figure 11. A switchable catenane [80].

Collier et al. [79] have selected a catenane in which one of the rings has charged centers. In this way, the relative orientation of the rings may be influenced by the presence of an applied electric field. The applied bias may then be used to switch the system between two co-conformations. A solid state device is created by sandwiching a monolayer of these catenanes between an n-type silicon electrode and a metallic electrode. The device exhibits negligible deterioration after numerous cycles. Collier et al. [78] have employed a similar fabrication to create molecular logic gates. The device is created by sandwiching a monolayer of redox-active rotaxanes between two metal electrodes. By wiring several such devices together, they were able to demonstrate AND and OR logic gates. A different approach to molecular scale data storage has been presented by Rueckes et al. [82]. The device architecture starts with a conducting substrate topped with a thin layer of SiO2 . Single-walled carbon nanotubes (SWNT) of diameter d are then placed on the surface and aligned in parallel. Separating the nanotubes is an array of insulating organic blocks of thickness s arrayed on the surface. This array of blocks is used to support a second set of parallel nanotubes that is perpendicular to the first set. The insulating blocks are sufficiently thick that the upper nanotubes do not contact the lower nanotubes at the crossing points (s > d), but are still sufficiently close for electrostatic interaction. Each crossing point will therefore have two locally stable minimum energy configurations. In the state described above, elastic forces hold the two nanotubes separated by s − d. There is also a minimum dictated by van der Waals interactions between the two tubes. By charging two tubes, attractive forces can be generated that will deflect the upper tube down toward the lower tube near the crossing point and bring their separation at the crossing point into this van der Waals minimum. Oppositely charging the tubes can produce repulsive forces to return the junction to the s − d separation. It has been shown that the resistance between one nanotube and a perpendicular one varies by many orders of magnitude between these two states [82]. Such a device, therefore, represents a rewritable random access memory array on the molecular scale. An array

of 2N nanotubes arranged with N tubes in the lower layer perpendicular to N tubes in the upper layer has N 2 addressable junctions. Given the dimensions of carbon nanotubes, data density near 1012 bits/cm2 is possible. The nanotube-based memory device has two advantages over the thin-film architecture of Ma et al. already described. First, the switching time for the nanotube-based memory is reported to be 10−11 s, much faster than 80 × 10−9 s as reported for the thin film case. Secondly, the nanotubebased memory, being based on the intersections of parallel nanotubes, solves the problem of addressing a multitude of spatially separated physical memory locations efficiently. The thin film technology has only been demonstrated with an STM tip for read/write operations and would require some technological innovation to incorporate into a solidstate device with multiple addressable bits. Carbon nanotubes have also been used to construct logic gates, specifically NOT gates [83]. The construction capitalizes on a fortuitous property of semiconducting SWNTs; they may be made n-type (electron carriers) or p-type (hole carriers) with proper doping and/or annealing. The logic gates consist of two complementary carbon-nanotube fieldeffect transistors (CNTFETs). To fabricate the device, gold electrodes are patterned on an oxidized silicon substrate. The unoxidized reverse side of the Si wafer forms the gate. Semiconducting SWNTs are the dispersed onto the surface. One of a pair of SWNTs positioned over Au electrodes is then protected with the common resist material PMMA. Vacuum annealing then converts both SWCT into n-CNTFETs. Finally, exposing the system to 10−3 Torr of oxygen converts the unprotected n-CNTFET to a p-type CNTFET, yielding a complementary n-type/p-type pair. The devices are unstable in air, but air-stable devices can be produced by employing a 10 nm SiO2 capping layer. While not strictly single-molecule devices, nanoscale logic storage devices have been fabricated from molecule-gated nanowires [84]. In these devices, nanowires of p-type silicon, n-type InP, or n-type GaN are coated with a layer of cobalt phthalocyanine (CoPc), a redox active species. These nanowires lie on a SiO2 layer on silicon, the back silicon layer serving as the gate. An applied gate voltage, or sourcedrain voltage pulse, injects charge into the molecular layer. The nanowire is then switchable between a high and low conductance state, depending on the charge state of the CoPc coating. Assigning each conductance state to a logic “on” or “off” state, yields a logic storage device. Storage times of >20 min have been reported.

5. THE MECHANISM OF ELECTRON TRANSPORT As noted in the preceeding section, a considerable array of device architectures has been proposed, and some realized. The mechanism by which electrons are transported in these systems is of great interest, since knowledge of this mechanism would facilitate a priori design of molecular electronic devices. Studies of potential molecular wires have revealed an interesting difference between conventional wires and molecular wires. In a conventional wire, the resistance of the wire to current flow is linearly dependent on its length.

Nanoelectronics with Single Molecules

678 For a given material and cross section, a wire of length l has twice the resistance (half the conductance) of a wire of length 2l . Molecular wires, by contrast, exhibit an exponential dependence of current flow on molecular length [27, 56, 57]. If current flow were to take place by a classical transport mechanism, resistance would depend linearly on length, and such current versus length measurements would be expected to show a linear dependence. This is an indication that the actual mechanism of electron transport in molecular wires differs from that in conventional wires, and is probably dominated by tunneling, as supported by the derivation of Eq. (16). One likely clue to the transport mechanism is the fact that certain molecules, when employed as molecular junctions, exhibit negative differential resistance (NDR) behavior. NDR describes the situation where the current (I) passing through a device decreases as the potential difference (V ) applied across the device is increased. Since I/V typically has a positive slope, NDR gives rise to peaks in the I/V curve. The measured I/V characteristics of these molecular junctions show highly nonlinear characteristics, with current peaking sharply at a critical applied voltage. It has been postulated that as the applied potential (Vap ) is increased, the junction molecule becomes charged. It is assumed that the uncharged junction molecule is insulating, the singly charged (−1) anion is conducting, and the doubly charged (−2) anion is again insulating. In the presence of a critical applied potential, the junction molecule would be reduced to its (−1) anion and become conducting. Higher applied potentials would further reduce the junction molecule to its (−2) anionic state, shutting down the conduction. A simple time-scale analysis, however, suggests that this picture is incomplete. Transit times for transfer of an electron through a molecular junction are estimated at 10−16 –10−15 s [64, 70]. On the other hand, device currents are typically less than 1 nA. This converts to less than 1010 electrons per second, or one electron every 10−10 seconds [5]. With five orders of magnitude between the transit time and the time delay between electrons, the electrons are unlikely to interact. In fact, based on theoretical calculations on p-benzene-dithiol as a resonant tunneling transistor, it has been suggested that the electrons do not spend enough time on the junction molecule to charge it [45]. Another proposed mechanism [4] identifies the changes in conductivity that accompany changes in the torsional alignment of adjacent phenyl rings in a conjugated chain as critical to controlling current flow [41]. For example, in 2′ -amino-4-ethynylphenyl-4′ -ethynylphenyl-5′ -nitro-1benzenethiolate, (hereafter referred to as AEENB; see Fig. 12) while the system is conjugated, there is little rigidity in the relative alignment of the rings.

NO2 SH NH2 Figure 12. 2′ -amino-4-ethynylphenyl-4′ -ethynylphenyl-5′ -nitro-1-benzenethiolate.

The presence of a large dipole moment due to the amino and nitro substituents affords relatively easy twisting of the central ring through the application of an external electric field [4]. In the natural coplanar arrangement, current flows with relative ease compared to the situation where the rings are in a twisted configuration. This mechanism is consistent with attenuating the conductivity with increasing applied potential. As the applied potential is increased, the torsional misalignment is forced to increase, and conductivity drops. It is more difficult to rationalize, based on this mechanism, why current flow remains negligible up to a critical applied potential, then increases by many orders of magnitude as reported for molecular junctions of AEENB [9]. One intriguing question that remains open is whether charge is carried in molecular junctions by electrons or holes. Both possibilities have been considered by Karzazi et al. [52]. This question is not simply a matter of semantics in the case of conduction in molecular junctions. If the current is carried by electrons, then applied potentials that bring the LUMO of the junction molecule into resonance with the electrode Fermi level may lead to resonance effects, while if the charge is transported by holes, applied potentials that bring the HOMO of the junction molecule into energetic alignment with the electrode Fermi level are key to resonance effects. Since the energy cost to make an ion from a neutral (negative of electron affinity) is generally different than the ionization potential of the molecule, the nature of the charge carrier will play a role in determining the energetics of electron transfer across the junction. Quantum resonance effects could logically give rise to large increases in conductivity near a critical applied potential as alluded to in [52]. A mechanism based in part on this concept has been given considerable theoretical scrutiny by the present authors [85]. The mechanism is shown schematically in Figure 13. Consider a molecular junction in the case of no applied potential. Here the two electrodes line up in energy. In the absence of tunneling, for an electron extracted from the left electrode to jump to the molecule forming the junction, it must have sufficient energy to access the ground state of the corresponding molecular anion, at the minimum energy geometry of the neutral molecule. This is the vertical attachment energy Ev of the junction molecule. Once the anion is formed, it naturally relaxes into its own minimum energy conformation. The difference between this energy and the energy of the relaxed neutral molecule is denoted Ea , the adiabatic attachment energy of the junction molecule. For the electron to jump from the junction molecule to the right electrode, it must have sufficient energy to reach the ground electronic state of the neutral junction molecule, at the geometry of the relaxed anion. This is denoted En , the vertical detachment energy or vertical reneutralization energy of the anion. In the case {Ev > Ea and En > 0}, there is a potential well between the electron-attachment and electron-detachment barriers, which contains resonances. Resonances are solutions of the one-dimensional Schrödinger equation that have a finite lifetime (energy width) owing to the fact that an electron, confined by the two barriers into a resonant state, may escape by tunneling.

Nanoelectronics with Single Molecules

679 I(V)

(a)

(d) Ev

En V

(b) Ev En V

(c) Ev En

V

Figure 13. Energy variation along the electron transfer coordinate for three representative applied potentials (a)–(c). (d) Schematic I/V characteristic of a resonant tunneling junction. There will be a dramatic increase in current due to resonant tunneling in the case where the applied potential brings the relaxed anion into resonance with the incident electron energy.

Figure 13 depicts three different cases of an applied potential (V ). When a potential difference is applied between the two electrodes, the individual electrodes are separated in energy by this difference (shown as V in Fig. 13). The minimum energy of the potential well between the electron-attachment and electron-detachment barriers will thereby be lowered with respect to the electron-donor (hole acceptor) electrode by some fraction of the applied potential [34]. (Note that since we are considering electron energy, “lowered” here means that the molecule is actually at a higher electrostatic potential.) At some applied potential, a resonant state of the potential well between the barriers will match the incident electron energy. At this point, a large increase in current due to quantum mechanical tunneling through the barrier is expected [86]. This is depicted in Figure 13b. As the applied potential is increased further, the resonant state of the molecular junction will move out of alignment with the incident electron energy and correspondingly, the tunneling current will drop. This is shown in Figure 13c. Clearly, such resonant tunneling will give rise to peaks in the I/V curve, as shown schematically in Figure 13d. The peak in the I/V curve will have a finite width due to lifetime broadening. This mechanism has been tested by computing the values of Ev  Ea , and En for several molecules for which the molecular junctions’ electronic behavior has been reported. In all cases, a highly stable anion, as indicated by a large value of En , correlates with the observation of NDR in the corresponding molecular junction. The origin of this correlation is clear. If the molecular junction molecule exhibits a negative vertical detachment energy, reneutralization is spontaneous and barrier free. In this case, therefore, the junction will not

give rise to a double barrier along the electron transport coordinate, and there is no resonance-enhanced tunneling. It is interesting to consider the difference between a molecular device and traditional semiconductor band device. To the first approximation, in a molecular device the conducting electron comes from one of the valence atomic orbitals of a gold atom with which the junction molecule is in direct contact. In the case of a thiol-gold contact, for example, the S atom bonds in an fcc site [87], giving three adjacent Au atoms. The local density of states for the contact, set by just a few Au atoms, is more molecular in nature than metallic, and therefore sharply peaked. This feature, whereby the density of states is sharply peaked for the species on either side of an interface (electrode and junction molecule here), is key to a molecular device that manifests NDR [88, 89]. Much remains to be developed for this model. First of all, the partitioning of the applied potential drop across the junction molecule and associated contacts is implemented empirically, following Datta et al. [34]. A complete treatment would determine the variations in potential with first-principles theory. Secondly, the model considers a one-dimensional electron transport coordinate. A complete model would incorporate the full three spatial dimensions of the molecular junction. Finally, the model treats only the electronic properties that are intrinsic to the junction molecule. Ideally, one would like to include effects due to the molecule/electrode interfaces, which are known to be important [32]. Despite these shortcomings, however, the model gives important insight into the mechanism by which substituents on the junction molecule influence the presence of NDR characteristics in its I/V performance.

6. TECHNOLOGICAL ROADBLOCKS Just over a decade ago, the principal challenge to molecular electronics appeared to be the problem of manipulation of matter on the nanometer scale. In the ensuing decade, this barrier was breached. This is not to suggest that it is now possible to construct any imaginable molecular device, but several techniques have been demonstrated for measuring and manipulating the electrical properties of individual molecules and molecular-scale domains of bulk material. New techniques and novel modifications of these existing techniques are being reported frequently. Today, molecular-scale binary data storage appears to be the nearest-term application of molecular electronics technology. Data storage densities well in excess of 10 terabit · cm−2 have been shown to be possible. Such high data capacities bring a new challenge. How can one read and/or write such enormous amounts of information? Even at the blazing pace of one gigabit per second (1 ns write time), it would take 20 min to write a terabit of information. High-speed massively parallel data I/O technology will be required to take advantage of the data densities possible with molecular electronics technology. A second major challenge to molecular-scale data storage is data integrity. Molecular-scale data storage techniques have been demonstrated with retention times of a period of days [76, 82]. This duration of data integrity is suitable for random access memory where frequent refreshes may be

Nanoelectronics with Single Molecules

680 employed, but is not suitable for semipermanent storage as with today’s hard disk and CD technology. It seems likely that practical molecular electronic circuits will be realized in the more distant future. The promise of creating circuits by chemical synthesis is great. Even laboratory-scale synthesis produces near-molar quantities (≈1023 units) of product. Moreover, all units are identical [4]. This level of reproducibility is unheard of in conventional manufacturing. The technical challenge lies in incorporating each of these units into a practical device. The units must be connected in some predetermined (or at least well known) manner, and the network of interacting units must be connected to a conventional macroscopic system that controls the circuitry and utilizes its interconnectivity. To date, no commercially practical analogue of the threeterminal solid state transistor has been demonstrated at the single-molecule level, although several devices with interesting nonlinear I/V characteristics have been reported (some of which have been reviewed herein) including some devices with transistor-like functionality. The development of molecular electronics technology will certainly be guided and accelerated by parallel theoretical work. As reviewed here, the theoretical techniques for describing electron transport in molecular junctions are reasonably mature. Certainly there is great room for further development, but existing techniques are already valuable for yielding physical insight into the nature of electron transport, investigating the influence of different contact geometries on device performance, identifying the effects of changing substituent functional groups on the junction molecule, etc. Beyond the technical challenges, however, are two other important considerations. First of all, it is possible, likely in fact, that quantum effects will be so important at the molecular level that the laws of conventional electronic circuitry simply will not apply. If Ohm’s law, Kirchovs’s laws, etc. can not be employed, an entirely new paradigm will be required for molecular electronic circuitry, with new devices, new design equations, etc. Quantum mechanics will serve as the starting point for the development of design equations, of course. Perhaps the computing circuitry will take advantage of the quantum mechanical nature of molecules, but this is in the realm of “quantum computing” and beyond the scope of this chapter. The second consideration is fiscal. Even if molecular scale electronics can be demonstrated, manufacturing costs may dictate the breadth of their applications. When digital computers were first available, they were so costly that they were purchased and used only by governments. Later, the price-to-performance ratio dropped to the point where their acquisition was cost-effective for large corporations, then mid-size institutions, then individuals. Today, digital computers are so inexpensive that they are used even in inexpensive consumer products. It is plausible that computing based on molecular electronics may follow a similar life cycle. A detailed discussion of cost considerations may be found in Ref. [90]. In brief, it is now possible to make a great variety of molecules with interesting electronic properties, and even to measure their electrical characteristics directly, but wiring them together into a circuit, then wiring the circuit to a robust macroscopic system, are outstanding challenges.

Beyond these technical challenges, cost considerations will play a large role in the future of molecular electronics.

GLOSSARY Break junction A junction formed by breaking a thin conductor, then closing the gap between the two ends until current flows under an applied potential difference. Catenane An assembly of two or more ring molecules that are chemically independent, but mechanically linked, i.e., interlocked rings. Chain polymer Linear molecule with a repeating fundamental unit. Conformational switching A scheme for altering the electrical properties of a molecule by altering its geometric conformation. Functional group A group of atoms that act collectively in forming molecules (Ex: CH3 , OH, NO2 , NH2    ). Molecular junction A single molecule captured between two metal electrodes. Molecular wire A molecule with physical and electrical properties suitable for charge transport: high aspect ratio and high conductance. Moore’s Law A formal statement of the empirical observation that quantitative measures of computer performance (such as processor speed or memory capacity) double every 18–24 months. Nanoparticle A particle of matter with characteristic dimensions in the nanometer range. Nanoparticles are characterized by a high fraction of atoms on the surface, and by electronic properties that are dependent on the size of the particle. Nanopore A cavity in a soil material with characteristic dimensions in the nanometer range. Nanotube Cylindrical arrangement of atoms with a diameter in the nanometer range. Most nanotubes are pure carbon and may be described as sheets of graphite rolled up and joined along opposite edges. Negative differential resistance (NDR) Voltage increase is accompanied by a decrease in current, dI/dV < 0. Pseudorotaxane A rotaxane that lacks one or both bulky terminal groups and therefore may spontaneously unthread. Quantum of conductance The fundamental unit of conductance, G0 = e2 /

. Rotaxane As assembly of two or more chemically independent molecules in which a long chain molecule is encircled by one or more rings. The chain component is terminated on both ends with bulky functional groups to prevent unthreading of the ring(s). Self-assembled monolayer (SAM) A single molecular layer that spontaneously forms on a surface, typically in a regular arrangement of molecules. Thin film A thin (typically 1–100 nm) layer of material. Thiol A molecule containing the SH group.

Nanoelectronics with Single Molecules

ACKNOWLEDGMENTS K. S. acknowledges support from the National Science Foundation Nanoscale Exploratory Research program, Drexel University in the form of generous startup support, and Dupont Corp. for a Dupont Young Professor Award. Computations were partially supported by the National Center for Supercomputing Applications (NCSA) under grant CHE010012N to N.M. and utilized the SGI Origin2000 at NCSA, University of Illinois at Urbana-Champaign.

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Nanoembossing Techniques Yong Chen CNRS, Marcoussis, France and Ecole Normale Supérieare, Paris, France

CONTENTS 1. Introduction 2. Mold Fabrication 3. Nanoembossing at Elevated Temperatures 4. Nanoimprint Lithography 5. Nanoembossing of Photocurable Polymers 6. Applications 7. Conclusion Glossary References

1. INTRODUCTION The ability to fabricate well defined large area nanostructures has important implications for both fundamental research and industrial applications [1–3]. In fact, the state of the art microelectronic circuits are made of semiconductor features of a critical dimension close to 100 nm which can only be produced cost-effectively by using high performance optical lithography tools. To extend the current CMOS (complementary metal oxide semiconductor field effect transistor) technology with a critical dimension down to 20 nm, new manufacturing tools will be required because of the diffraction limit of the conventional optical methods. For this reason, the semiconductor industry has developed the so-called next generation lithography by considering new irradiation sources such as extreme ultraviolet (UV) light, X-rays, as well as projection electron or ion beams. Not only the microelectronic industry but also many research and other industry branches need more and more nanofabrication tools. For example, patterned nanostructures such as photonic crystals are becoming attractive for the development of new optical and optoelectronic devices [4]. Patterned magnetic nanostructures are now studied for ultrahigh density storage and for the fabrication of the emerging spin–electronic devices [5]. In the domain of biology and biomedical research, microarray chips and microfluidic devices are in rapid progress toward a high degree of functionality and integration [6]. In all these areas, ISBN: 1-58883-062-4/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

flexible and lost-cost manufacturing techniques are required for research, prototyping, and low volume production. A broad range of conventional and nonconventional nanofabrication methods is under investigation [7]. The challenge is to develop straightforward fabrication tools and processes that allow one to produce patterns with a minimum feature size down to a few nanometers and to integrate various functionalities over large areas. Here, the requirement of the nanometer scale is important for both current research and future development. For example, the fabrication of molecular electronic circuits will be based on molecular self-assembly with high density nanoelectrodes [8]. Nanoembossing is one of the most studied nanofabrication methods during the last few years [9–16]. Unlike conventional lithography methods which use photons or charged particles to expose a resist layer in a way similar to photography [17, 18], nanoembossing relies on pattern replication by physical deformation of a thin polymer layer with a rigid mold. Although the classic embossing techniques have been widely used for many years, only quite recently attention has been paid to the replication ability of ultrasmall features. Compared to the sophisticated optical lithography methods, nanoembossing is more flexible and much less expensive. Compared to electron beam (e-beam) lithography and scanning probe lithography, nanoembossing is well suited for large scale and high throughput production. Due to these advantages, nanoembossing techniques are now considered a new strategy for future nanotechnology development [16]. Nanoembossing technologies include mold fabrication, polymer design, pattern replication, and subsequential pattern transfer. Molds are generally obtained by e-beam lithography which defines pattern in a thin layer of resist and reactive ion etching (RIE) or electroplating for the pattern transfer. Either thermoplastic or thermosetting polymers can be embossed at elevated temperatures but embossing can also be performed at room temperature with photocurable polymers and UV irradiation. In general, the embossed nanostructures can be used directly in plastic device making or as masks for a subsequent pattern transfer. This latter technique, namely nanoimprint lithography, consists of embossing first a thin layer of polymer spin coated on a substrate and then removing the recessed area by reactive

Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 6: Pages (683–702)

Nanoembossing Techniques

684 ion etching (Fig. 1). Thus, the resulting resist profiles are comparable to those obtained by optical or e-beam lithography so that a large number of applications can be developed. In this chapter, several nanoembossing techniques are described, including discussions of their fabrication performances and application examples.

2. MOLD FABRICATION All embossing techniques rely on the fabrication of molds which defines the original patterns to be replicated. For nanoscale features, molds are produced by advanced nanofabrication methods. A silicon wafer, with or without a covering of a thin film of dielectric or metal material such as silicon dioxide (SiO2
, silicon nitride (Si3 N4
, or tungsten (W), can be used as substrate. E-beam lithography is commonly used to expose a resist layer on the substrate [18]. Then, reactive ion etching or electroplating is used for the pattern transfer. Finally, an antisticking film is coated on the mold surface to promote the mold–sample separation. Commercial e-beam systems working at 50 keV electron energy provide a routine resolution of 50 nm or smaller [19]. Features of higher resolution can be obtained by using the state of the art e-beam systems at high beam energy (100–200 keV) [20, 21]. Under optimal conditions, 10-nm [22] and sub-10-nm features [23–25] can be obtained but particular attention has to be paid to the resist development and the pattern transfer processes. Poly(methylmethacrylate) (PMMA) is commonly used as e-beams resist but the recent development showed that other polymers such as hydrogen silsesquioxane (HSQ) are also suitable for very high resolution patterning [20, 26, 27]. The resist pattern defined by e-beam lithography can then be transferred by reactive ion etching into the underlayer material or by electroplating [28, 29]. If reactive ion etching is used, an etching mask, commonly obtained by a thin metal film deposition and lift-off, is required for high resolution pattern transfer [18]. The quality of the lift-off is mainly affected by the resist profile and the thickness of the deposited metal film is typically three times less than the resist thickness. The reactive ion etching is based on simultaneous exposure of the sample to chemical reaction species and fluxes of energetic particles. The etched materials are then pumped away as volatile gaseous species. For polymers, silicon, silicon-based dielectric materials, and some 1. Imprinting Mold PMMA Substrate

2. Separation

3. Etching

Figure 1. Schematic representation of nanoimprint lithography.

metals, SF6 , CHF3 , and O2 gas mixtures are commonly used to obtain vertically etched sidewalls with an accurate control of the etch depth. If electroplating is used, as a thin layer of metal is first evaporated on the embossed surface, followed by electroplating until a desired thickness is obtained. Then, the electroplated sheet is separated from the resist sample and can then be used as metal mold for embossing. Patterning can also be done with a focused ion beam directly but this method is time consuming and suited only for particular applications. As mentioned, high resolution patterns can be obtained by high energy e-beam lithography. It is, however, difficult to obtain high density features over large areas. A spatial frequency doubling technique has been tested for the fabrication of gratings of 100-nm period [30]. This technique consists of exposing a grating of 200-nm period by interferometric lithography and then processing a sequence of standard microfabrication steps to double the grating’s spatial frequency. Other techniques such as edge defining [31] and photoelectrochemical etching [32] can be used to obtain some specific sub-10-nm features. To emboss photocurable polymers, transparent molds are generally required which can be obtained by patterning a quartz plate either with or without an indium tin oxide (ITO) thin film coating. More sophisticated mold configurations such as a SiO2 /ITO double layer on a substrate have also been tested, showing several advantages in terms of e-beam writing performance (no charging), electron microscope inspection, and pattern transfer because of the high selectivity of dioxide to ITO during a dry etching process [33]. Silicon molds of large etch depth can be obtained by deep RIE [34]. Conventional RIE with SU-8 resist as etch mask has also been used to achieve an etch depth of more than 10 m and silicon molds containing both shallow and deep features could be obtained using mix and match techniques [12]. Finally, three-dimensional (3D) structures can be obtained by anisotropic wet etching of a silicon substrate [35] or two-step RIE [36, 37]. More complex 3D structures can be obtained by e-beam lithography with a modulated dosage distribution [38]. For example, Ni molds with curved cross-sectional structures could be obtained and tested for the fabrication of diffractive optical elements [39]. Once a master mold has been made, it can be reproduced by nanoimprint lithography, followed by either RIE or electroplating for the hard material pattern transfer. With a well controlled fabrication process, the quality of the copied molds can be comparable to the original ones. Finally, full plastic molds can be obtained by casting-and-molding a thermosetting polymer, which can then be used as conventional molds [40]. In general, a surface treatment of the mold is necessary to avoid the sticking problem. It is known that the sticking or adhesion strength between a mold and a polymer coated sample depends on the physical and chemical properties of the surfaces of the two materials in contact. Physical adhesion is related to the van der Waals force and hydrogen bonds, while chemical adhesion is due to ionic, atomic, or metal bonds between surfaces. The larger the contact area, the stronger the adhesion. An antistick layer deposited on

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685

the mold is generally necessary to promote the mold separation. A number of layers have been tested including a deposition of metal thin films [41], Teflon-like molecules [42], or fluorinated silanes [43]. Commercial release agents such as manufactured by Dow Corning (DC20) can also be used and a detailed analysis of the antisticking methods can be found in [14]. In practice, the choice of the antisticking treatment depends on the type of the mold and the polymer in use as well as the embossing conditions. For nanoembossing of photocurable polymers for example, specific polymer mixtures and fabrication sequences are required because of the chemical reaction involved during photopolymerization [14].

1. Placing Si wafer PMMA pellets Si mold

2. Hot embossing

3. Separation

3. NANOEMBOSSING AT ELEVATED TEMPERATURES Both thermoplastic and thermosetting polymers can be embossed at elevated temperatures. Commercial embossing systems [44, 45] as well as a cheap hydraulic press equipped with a pair of hot plates [46] have been used for nanoembossing with a wide range of working temperatures and pressures. In this section, we focus on “hot embossing” of high resolution polymer features. In the next two sections, we will discuss nanoimprint lithography and nanoembossing of photocurable polymers.

where A is a constant and Tg 

is the value of large molecular weight. For example, Tg is 113  C for 50 kg/mol PMMA and 120  C for 950 kg/mol PMMA. The deformation rate of a perfect viscous liquid is proportional to the shear stress, 1  =  t 

3.1. Nanoembossing of Thermoplastic Polymers Thermoplastic polymers such as PMMA, polycarbonate (PC), polyvinylchloride, and poly(ethylene terephthalate glycol) can be used for the fabrication of miniaturized plastic pieces [29]. They soften and eventually liquefy when heated and harden when cooled. Nanoembossing of thermoplastic polymers can be performed in different ways: (a) imprinting a commercial plastic plate, (b) imprinting a thin polymer film spin coated on a substrate, and (c) compressing polymer pellets. The first technique is the simplest one. A rigid mold is pressed into a heat-softened polymer plate at temperatures slightly above Tg under moderate pressure or below Tg under elevated pressure [47, 48] The second technique, imprinting a thin polymer film spin coated on a substrate, will be discussed in detail in the next section. The third technique is based on thermal compression of cheap polymer pellets, which takes advantage of both injection molding and imprinting techniques [12, 49] (Fig. 2). Here, polymer pellets are placed on a silicon mold and covered by a flat silicon wafer. They are then inserted between two hot plates of a hydraulic press and the temperature is raised to a value well above the polymer’s Tg . At the embossing temperature, a pressure is applied and maintained during cooling down. Below Tg , the pressure is released and the patterned plastic sheet is removed from the mold. Let us first consider some general properties of thermoplastic polymers. Thermoplastic polymers are formed from monomers via chemical bonding. When an amorphous thermoplastic polymer is heated above its glass transition temperature, Tg , it behaves like a viscous liquid. Tg depends on the molecule weight of the polymer [50], Tg MW
= Tg 

−

Figure 2. Schematic representation of the fabrication method involving hot embossing of thermoplastic polymer pellets.

A MW

(1)

(2)

where  is the viscosity parameter of the liquid which also depends on the molecule weight of the polymer. For small shear, ∝M ∝M

34

M < Mc
M > Mc


(3a) (3b)

where Mc is the critical value of the molecular weight for the given polymer type. For PMMA, Mc = 30 kg/mol [50]. The viscosity parameter of a polymers decreases rapidly with temperature. For the temperature range well above Tg , the Arrhénius law can be applied, 
E (4)  = 0 exp RT where R is the universal gas constant (8.3 J/mol K) and E is the activation energy of the viscous flow which is of the order of 104 J/mol and depends on the specificity of the polymer. Typically, nanoembossing can be done at a temperature of about Tg + 60  C and the applied pressure must be maintained during cooling so that the embossed articles will retain their sharp sidewall. We have embossed PMMA pellets (Oroglas V825T, Tg = 108  C from Atofina) at 180  C with a pressure of 100 bar for a few minutes. For thick PMMA plates, a metallic frame for lateral confinement is added. Typically, 4 to 5 pellets of roughly 3 × 3 × 3 mm3 are needed to produce a 3 × 4 cm2 PMMA sheet of thickness of several hundred micrometers, while roughly 40 pellets are needed for millimeter-thick plates [12]. The fabricated structures showed well-defined shapes and excellent surface quality, exhibiting a roughness less than 5 nm, as on the mold. Figure 3a displays a scanning

Nanoembossing Techniques

686 a

b

Figure 3. Scanning electron micrograph of micro- and nanostructures simultaneously embossed on a PMMA plate: (a) the intersection of two 11-m-deep and 50-m-wide microchannels with an excellent surface roughness and (b) a portion of a 300-nm-period triangular array of 150-nm-diameter nanopillars of 200-nm thickness. Reprinted with permission from [12], V. Studer et al., Appl. Phys. Lett. 80, 3641 (2002), © 2002, American Institute of Physics.

electron microscopy (SEM) image of the intersection of two 10-m-deep and 50-m-wide microfluidic channels. These channels reproduce the high surface quality and vertical sidewalls of the Si master. Figure 3b shows a SEM image of a 300-nm-period triangular array of 150-nm-diameter nanopillars of 200-nm height, created inside a channel of 200-nm depth and 50-m width, extended over a total length of 7 mm. This structure was initially designed as an artificial gel for DNA molecule separation [51]. The embossed features show extremely good uniformity and can be covered by another PMMA sheet via thermal bonding. Our experiences showed that complex features can be obtained without carefully adjusting process parameters, indicating the simplicity of the process and the ability to produce high resolution plastic devices. Thermoplastic polymers other than PMMA such as cyclo-olefin copolymers have also been used, showing also the ability to replicate nanostructures. Compared to injection molding which is the common manufacturing technique of plastic articles [52], nanoembossing is more suitable for prototyping and the replication of high aspect ratio features. In practice, all injection machines are designed for high volume production and the fabrication of injection molds requires high accuracy machining and careful mold adaptation. Besides, the large sizes of the injection molding machines are not compatible to the laboratory scale experimentation. Nevertheless, the production rate of injection molding is substantially high which should also enable one to produce nanometer features [53, 54].

3.2. Nanoembossing of Thermosetting Polymers Thermosetting polymers become permanently hard once cured by a chemical reaction at elevated temperatures. Embossing of a thermosetting polymer consists of first filling a mold cavity with a liquid prepolymer (linear polymer with a low molecular weight) and then converting it into hard product with the desired shape. During curing, chemical and structural changes occur by cross-linking which makes the final product dimensionally stable. Compared to

thermoplastic polymers, thermosetting polymers are generally inert and difficult to remove chemically [55]. A number of thermosetting polymers, including epoxies, phenolies, and polyester, can be useful for the embossing experiments [55, 56]. In particular, poly(dimethylsiloxane) (PDMS), which consists of repeated units of -OSi(CH3
2 O-, is now widely used for the fabrication of microfluidic devices and stamps for microcontact printing [57–64]. PDMS is attractive because it is mechanically deformable (elastomer), nontoxic, chemically inert, and optically transparent. High resolution PDMS structures can be obtained by casting a liquid prepolymer mixed with a cross-linking catalyzer. After curing at 80  C for one hour, the solidified PDMS is separated from the mold which can then be used for various applications. To obtain PDMS thin films, the mold is coated with PDMS prepolymer solution and then covered with a plastic film. After curing under a desired pressure and cooling down, the plastic film is removed. By placing a thicker PDMS carrier on the top of the embossed thin film and thermal bonding, a bilayer PDMS structure is obtained. Repeating this process several times, a multilayer PDMS device can be made [60, 61]. The bilayer PDMS structure can be used for example as a stamp for high resolution microcontact printing [58, 62]. Here, the stamp is first inked with thiol molecules [hexadecanethiol (C16 H33 SH) in ethanol] and then placed on a gold coated substrate for a few seconds. This results in a self-assembled monolayer of the thiol molecules in certain portions which can then be used as a mask for chemical etching. In order to make the microcontact printing fully compatible to other pattern transfer techniques, a resist film can be introduced before depositing the gold layer. After chemical etching of the gold, the pattern can then be transferred into the resist [63, 64]. The advantage of using a bilayer PDMS stamp relies on its enhanced bulk stiffness so that a large area stamp cavity is allowed. By spin coating PDMS prepolymer liquid on both mold and substrate surfaces and then bonding them together thermally, high quality features can be obtained after removal of the mold [65]. For very thin PDMS structures, the embossed features can be used for pattern transfer via RIE or liftoff [66].

3.3. Nanoembossing of Other Types of Materials Nanoembossing can also be applied to other types of materials. One of the examples is direct embossing of silicon nanostructures with a high power laser irradiation [13]. In the first experience, an excimer laser of 308 nm wavelength and 20 ns pulse duration is used which passes through a quartz mold and melts the silicon surface to a depth of a few hundreds of nanometers. Under pressure, the melt silicon is deformed and then solidified rapidly, resulting in a perfect replication of the mold surface structures. The total processing time including heating, embossing, and cooling is short (250 ns). To illustrate the high resolution ability, replication of a grating of 300-nm period and 110-nm depth has been demonstrated. Under a scanning electron microscope, one can observe a reproduction of 10-nm edge features. The same process has been used to emboss large mesa areas as

Nanoembossing Techniques

well as a polysilicon layer deposited on a silicon wafer separated by a 200-nm silicon dioxide. These results have largely enhanced the interest of nanoembossing techniques because of the direct embossing strategy and fast processing. This technique could be extendable to other materials and fabrication processes [67]. More generally, materials including functional polymers [68–70], photoresists [71], block copolymers [72], liquids [73], metals [74], as well as sol–gels [75] and piezoelectric materials [76] can be directly embossed. In the case of photoresist embossing, for example, a small amount of solvent ( 80
(i.e., the glancing angle regime). This effect is shown clearly in Figure 2, where both a plot of a vs
(Figure 2b) and a titanium film deposited at progressively more oblique angles are illustrated: both
and the columnar separation, a, are observed to correspondingly increase significantly for
> 80
. This property of increased separation of columns can be used to subsequently control the film growth and its resulting microstructure. Films deposited at
< 80
may be viewed as relatively dense by comparison.

2.1.3. Substrate Rotation In 1959, Young and Kowal observed optical activity and circular Bragg reflection in fluorite films deposited with active rotation of the substrate about an axis normal to its center [26]. This axis will be subsequently referred to as . “The possibility of evaporating in vacuum an optically active film of an otherwise isotropic material, by oblique deposition on to a flat glass substrate revolving about its normal as an axis, is confirmed. The helically deposited fluorite films ranged up to about 18 m thick and turned the plane of polarization of a normally incident beam by as much as 2.25
at  = 0 546 m” ([26], quoted from [27]). At the time, scanning electron microscopy (SEM) was not available to directly observe the films fabricated by Young and Kowal, although the relatively conservative incidence angle (
< 70
 of their deposition indicates that the structures would have been reasonably dense. However, this work represents one of the first attempts to “sculpture” film microstructures to enhance or change the resulting material properties. Unfortunately, their work went relatively unnoticed until recently. In 1989, Motohiro and Taga [28] deposited columns at an oblique incidence angle of
= 70
and showed that these films undergo an abrupt transition when the substrate is rotated through 180
. For the initial portion of the film evolution, the column grows at a set angle  toward the flux source. At the point the substrate is rotated by 180
, the column abruptly changes direction so that the column inclination again points toward the incoming flux. Essentially, the column forms a chevron structure (i.e., a “V” lying on its side) where the interface between the two distinct column directions is referred to as the Motohiro–Taga interface [29]. A stacked series of Motohiro–Taga interfaces thus forms a zigzag structure. By significantly increasing the flux incidence angle, these zigzag/chevron structures can be grown isolated from each other as a highly porous medium [30]. Initially, it was assumed that either the tangent rule (
< 60
 or Tait’s rule (
> 60
 were valid for all types of columnar thin films grown at oblique incidence, including those with chevron microstructure. This assumption incorrectly assumed that errors introduced by differences between the

Nanofabrication by Glancing Angle Deposition

surface normal and the substrate normal were insignificant for oblique growth. Although for many types of microstructures this assumption is valid, in chevrons the growth plane changes significantly with each subsequent turn in the flux direction: the growth surface is no longer the substrate but the previous chevron “arm.” From the perspective of the new surface normal, flux appears to be arriving at a less oblique angle. A recursive algorithm has been developed to take into account the changes in surface normal with each additional arm grown in the chevron. This algorithm is captured in Eq. (4), which calculates the theoretical  for the nth arm given  for the previous arm.    tan
+ n−1 − 90
−1 − n−1 + 90
(4) n = tan 2 n approaches an asymptotic limit as n → , which is typically greater than that described by Tait’s rule [31]. At low incidence angles, the correction factor introduced by Eq. (4) is not significant (i.e., the change in  is not observed in the earlier Motohiro–Taga films), although its effect becomes more apparent as the flux begins to arrive at glancing incidence. For example, if
= 85
, a swing in  of nearly 8
is observed between the initial arms of the chevron. Theoretical work by Azzam [32], later expanded on by Lahktakia and Weiglhofer [33], continued the work of Motohiro and Taga by suggesting that a chiral response suitable for unique optical applications may be fabricated by coupling substrate rotation with oblique incidence. After experimental development of highly porous film structures [30] the term “sculptured thin film” (STF) [34] was coined to describe films where the microstructure is actively adjusted during deposition to manipulate its properties. This term is rapidly gaining some acceptance in the literature and is often used to describe relatively dense films fabricated using oblique incidence (
< 75
 and substrate rotation [24, 35–37]. Earlier films such as the Young and Kowal experiments mentioned previously are considered to be among the first STFs fabricated.

2.1.4. Simple GLAD Structures Earlier, we showed a figure of an obliquely deposited film to demonstrate the inclination of columns with respect to flux incidence (see Fig. 1). The growth of a structured thin film can be described succinctly by noting that columnar growth occurs in the plane parallel to that defined by the trajectory of the incoming vapor and the substrate normal and is henceforth referred to as the deposition plane. If this plane is moved (either by rotating the substrate and keeping the source fixed, or rotating the source and keeping the substrate fixed) the columnar growth direction can be controlled. The first porous chiral structures were fabricated by utilizing highly oblique or specifically glancing angle flux incidence to separate the chiral structures and more actively control their resulting porosity and morphology [38]. From Figure 2, it is clear that the difference ( =
− ) in columnar angle and flux incidence angle increases with increasing
. More highly separated columns, and the resulting increase in film porosity, are a direct consequence of this

Nanofabrication by Glancing Angle Deposition

707

observation. If, for example,
= , columns would be inclined toward the source, yielding no separation. By choosing a point on the  vs
plot, the porosity of the film can be easily tailored due to the increasing effect of shadowing on the substrate surface. This technique, referred to here as glancing angle deposition [39], has since been used to fabricate a range of porous thin film morphologies with isolated microstructures, many of which have been built upon the four simple structures shown in Figure 3 and described below. For these and subsequent examples, the deposition rate, r, refers to the amount of film deposited at the position of the substrate, but on a plane that is held normal to the arriving flux. This definition is used because it describes the standard geometry for film growth measurements by a crystal thickness monitor. • Oblique columns: Formed when substrate rotation about  is zero. Porosity is introduced by glancing incidence flux • Chevron or zig-zags [30]: Stacked Motohiro–Taga interfaces deposited at glancing incidence whereby a rotation about  of 180
occurs for each arm of the chevron. • Helices [38]: Formed when the substrate is rotated slowly and continuously relative to the deposition rate, r. Typically, / t ∼ 0 1 RPM for r ∼ 10 Å/sec. Each complete turn of the substrate results in a single turn of the helical structure. The speed of rotation determines the pitch length (i.e., slow rotation = longer pitch; fast rotation = smaller pitch). • Pillars or posts [40]: A special case of helical growth, though usually treated as its own film morphology. If rotation is sufficiently fast (e.g., / t > 1 RPM for r = 10 Å/sec), the pitch of the helix is so small that it 1 µm

1 µm

(a)

(b) 1 µm

cannot be distinguished. The structure thus appears as a vertical column. The structural details for all the above film types inherently depend on the source material being used, the substrate, crystallography, and other factors. Low melting point materials, for example, tend to have higher surface diffusion which blurs the distinctiveness of the helical pitch and thus require less rotational speed to form a structure resembling vertical columns. High melting point materials tend to have lower surface diffusion and so take higher rotational speeds to form posts. By utilizing glancing incidence, the user can control both the film porosity and structure, opening up a wide range of applications including, for example, sensing technologies, catalysts, optical devices, and biochip devices. Some STF papers define the flux incidence and columnar angles relative to the substrate plane, using the symbols v for the flux incidence and c for the columnar angle. To avoid confusion, in this chapter we will consistently use
and  defined relative to the substrate normal. This nomenclature is consistent with the majority of GLAD literature (i.e.,
≡ 90
− v and  ≡ 90
− c , and the original paper defining the tangent rule [17]. Using these definitions, the flux angles used with the GLAD technique are typically in the regime of 75
or higher: GLAD films can be classified as “dense” for 75
<
< 80
, “porous” for 80
<
< 85
, and “superporous” for
> 85
[41].

2.2. Advanced GLAD Structures 2.2.1. Advanced Control System The power of the GLAD technique does not arise from simply rotating the substrate at oblique incidence, but rather through the dynamic changing of the substrate through
and/or  during deposition at glancing incidence [42]. The external control apparatus for growth of GLAD films has evolved considerably since the early “proof-of-concept” experiments. Individual stepper motors, each controlled externally by software running on a single computer, allow the user to adjust both
and  independently while the film is being grown. Hence, a variety of microstructure forms can be programmed into the computer and subsequently grown. In addition, the control system can adapt to changing conditions within the deposition chamber through feedback provided by in-situ measurement of film growth by a crystal thickness monitor. This growth is reported back to the computer software which adjusts
and  accordingly. Figure 4 shows a schematic of the current GLAD setup without the feedback control blocks shown.

2.2.2. Pause–Spin Growth

(c) Figure 3. Examples of the basic GLAD morphologies: (a) Zigzags or chevron structures fabricated from yttria stabilized zirconia (ZrO2 ) at
= 85
; (b) helices of SiO deposited at
= 85
, and (c) vertical SiO2 posts at
= 87
.

Using this advanced control system, more specialized microstructures can be designed and fabricated in a one-step deposition process. For example, the standard morphological trend suggests that if
is low, films are dense and the columnar structure is more vertical. If
is high, films are porous and columns are inclined. The fabrication of separated vertical columns (see Fig. 3c) suggests that while the porosity may be intimately related to the deposition angle, the angle of inclination () may be more dependent on the speed of substrate rotation.

708

Nanofabrication by Glancing Angle Deposition

cross-section where the column thickness along the axis connecting 0 and 180
is significantly greater than that along the axis connecting 90
and 270
[41]. This process can be thought of as adding an artificial anisotropic component to the film growth. Obliquely grown columns also have a natural anisotropic component which can be observed by their tendency to “fan out” perpendicular to the deposition plane [16, 18, 43, 44]. This growth mechanism may be observed from the lower panel in Figure 2 and is probably a manifestation of the shadowing effect. Hence, the observed columnar cross-section is more a measure of whether the deposition rate factor or shadowing factor was dominant during film growth.

2.2.4. Other Advanced GLAD Structures Figure 4. The GLAD system schematic. Stepper motors are used to control both the tlit (polar) angle
and the rotation (azimuthal) angle  of the substrate holder. Reprinted with permission from [45], S. R. Kennedy et al., Nanoletters 2, 59 (2002). © 2002, American Chemical Society.

From the perspective of the film, pillars are grown when flux arrives isotropically from all azimuthal angles. Porosity is imposed by
, but  is forced to zero because of the high rotational speed. Inclined columns of a desired porosity or separation can be fabricated at any  between zero and Tait by using a “spin–pause” approach. In this methodology, pure “paused” growth represents oblique columns (i.e., substrate is stationary), while pure “spin” growth represents vertical columns (i.e., substrate rotates at “infinite” speed). By alternating the phases of spun and paused growth, stacked layers of inclined and vertical columns can be formed. If the stacked layers are made sufficiently small, the individual “pitches” between layers become indistinguishable, and the structure appears as a smooth column. The angle of the resulting column can be set by adjusting the proportion of spun and paused phases of growth, while maintaining a desired porosity set by
. Helical growth can also be controlled to some extent. The angle at which a helical arm leaves the substrate is determined by Tait; in other words, it is fixed by
. Using the pause–spin methodology, the radius and pitch of a helix can be manipulated without adjusting the porosity of the film.

2.2.3. Control of Columnar Cross-Sections The cross-section of columns can also be controlled in a similar fashion. Ideally, posts are formed when the helical pitch (p) equals zero; however, in reality this transition typically occurs when the pitch is less than 15 nm. If the column is cut perpendicular to its direction of growth, a circular crosssection occurs because the film sees flux coming from all directions at the same rate. If this rate were to become more anisotropic, the cross-section similarly becomes anisotropic (i.e., more ellipsoidal). Pausing or slowing down the rotation rate at positions along  can bias the columnar cross-section at points. For example, if the substrate rotation is slowed (or stopped) at  = 0 and 180
, the result is a flattened

A number of film microstructures can be developed utilizing the advanced GLAD control system, including square spiral staircases (where each arm of the spiral is grown at 90
from the preceding arm) [45], superhelices (where a helical film is modulated by helical growth of higher pitch) [46], twisted ribbons (arguably pillars with a highly ellipsoidal cross section and relatively large pitch) [41], or microstructures with a capping layer [47]. Capping layers provide encapsulation and protection to the porous films beneath them and also allow for multilayer structures [48, 49], while square spirals, particularly when arranged as components in a lattice, have possible application as three-dimensional photonic bandgap filters [50]. Some of these structures will be revisited later in this chapter, while for the others we refer the interested reader to the appropriate references.

2.2.5. Periodic Structures Typically, microstructures fabricated by GLAD are randomly distributed on the substrate. This feature is not detrimental for such applications as sensors, thermal barrier coatings, and catalytic devices. However, some optical (e.g., photonics crystals) [51–53] and magnetic applications [54] require a periodic lattice of structures in order to operate effectively. In addition, some of the fundamental properties of GLAD films are more easily acquired when the exact density of structures per unit area can be calculated [55]. The formation of randomly distributed GLAD structures on the substrate surface is inherently due to the nucleation stage of film growth, when energetically stable clusters of atoms seed randomly on the substrate and subsequently shadow the surrounding area. Recently, it was shown that near identical structures can be formed by enforcing this shadowing effect at the initial stages of film deposition through the use of substrates with a prefabricated seed layer [56]. In this case, the seed structures were created using electron beam lithography, while more recent efforts by other groups have shown that periodic pillars and oblique columns can be grown on plastic embossed substrates [57], and square spirals can be grown on seeds produced using standard photolithography [45]. It is expected that any process that creates small, regular mounds out of an appropriate material may serve as seed layers for a subsequent GLAD deposition to form periodic microstructures. If the seed morphology is optimized with regard to material parameters (e.g., melting point), substrate temperature,

Nanofabrication by Glancing Angle Deposition

709

and the flux incidence angle, growth initially occurs predominantly at the seed sites. The highly oblique incidence of the flux and the subsequent competition effects at the surface force subsequent growth to also occur at these sites. These microstructures grow regularly for some time, the extent of which will be explored later in this chapter. For most materials deposited by GLAD, surface shadowing is the dominant growth mechanism, allowing the optimal seed separation to be approximated by

= t tan


100 nm

1 µm

(5)

and t are the seed separation and height, respectively. Figure 5 illustrates the geometry of this expression, while examples of periodic GLAD structures are shown in Figure 6. The growth of periodic structures, particularly those of helical microstructures, is found to be quite robust. Defects introduced into the lattice in the form of missing seeds or lines of seeds have little effect on the growth of structures surrounding the defect [56]. Defects transfer to the film (the extreme flux incidence angle ensures that there is no flux coverage of the seedless defect area), while the uniformity of the film is preserved outside of the defect area. Structures along the edge of defects tend to increase in density or thicken slightly to take up the flux that would otherwise have gone into the growth of their neighbors. This effect is marginal if the number of missing lattice points is limited to the distance enclosed by one or two seed periods. The demonstration of low defect periodic GLAD arrays is of particular significance, as it may be applied to the introduction of light-guiding structures for use in photonic bandgap devices (see Section 5.5.4).

(a)

(b) 1 nm

(c) Figure 6. Examples of periodic GLAD morphologies grown at
= 85
are shown above: (a) nickel oblique columns with a lattice period of 2 m; (b) SiO2 helices with a lattice period of 600 nm; and (c) SiO2 posts with a lattice period of 900 nm. Figure 6a reprinted with permission from [55], M. Seto et al., Micromech. Microeng. 11, 582 (2001). © 2001, Materials Research Society.

For the remaining part of this chapter, we will describe some of the fundamental growth properties of both randomly situated and periodic GLAD films. In addition to the flux incidence angle (
) and substrate rotation about , which clearly have significant effects on the overall film structure, a number of other parameters affecting growth will be discussed. We will close this chapter with a few application directions and our current understanding of how GLAD films are either demonstrated or expected to function within these fields.

3. GLAD FUNDAMENTALS The isolated structures of GLAD films allow for the study of fundamental thin film growth behavior, particularly in regard to self-shadowing and surface energies. For example, by observing that the diameter of a helix arm gradually increases during deposition, one might assume a number of processes to be at work including [58]:

Figure 5. The geometry of film growth for a randomly situated film (a) and periodic film (b) are compared. If the seed separation ( ) is optimized relative to the height of the seed (t) and the angle of flux incidence (
), film growth occurs primarily at the seed sites. This seed separation is loosely based on Eq. (5). If ≫ optimized , or no seeds are present on the substrate, self-shadowing initializes film growth.

1. An increase in adatom diffusion length due to an increase in substrate temperature during growth. 2. An increase in the amount of material deposited on a given helix due to the suppression of neighboring structure growth (i.e., columnar competition). 3. Increase in scatter of incident flux between helices. 4. Bifurcation within a helix arm. 5. Preferential growth of fast growing crystal planes.

710 6. Recrystallization and growth of crystallites within a growing helix. These processes show that not only is the geometry of the deposition system a factor during growth (due to its imposed effect on the shadowing mechanism at the substrate surface), but material properties such as crystallography, vapor pressure, etc. and the deposition technique itself (either sputtering or evaporation) all have strong roles to play in the form of the resulting film microstructure. In the section that follows, we will explore a number of these factors.

3.1. Competition, Scaling, and Growth Evolution In common with solid thin films, GLAD microstructures exhibit self-affine or self-similar behavior [58, 59]. To illustrate this concept and give some insight into how a GLAD film evolves during its deposition, a SiO2 post film (deposited at
= 85
with normal pitch set to 10 nm) is shown in Figure 7. The left side of the image shows the complete growth evolution as a side view, while on the right, slices of the film taken at various thickness intervals are displayed. First we note that the separation of columns occurs early in the growth evolution, as the extreme shadowing at the substrate surface inhibits adatoms from filling in the voids between columns. This behavior is an extreme example of what is classically referred to as Zone 1 behavior: selfshadowing is the dominant growth mechanism, and adatom diffusion is limited [11]. A simple analogy, often referred to as the “grassy lawn” model, is often used to capture the essential concepts of these growth conditions [60]. Blades of grass (representing the columns) grow in proportion to the amount of light they receive (i.e., flux density). This circumstance introduces positive feedback into the growth; if a blade overgrows its neighbor, it receives more light flux and has a higher potential of shadowing its neighbors, thus suppressing their rate of growth. Similarly, adatom diffusion tends to smooth out the surface in the length scale over

Figure 7. The left side of the image shows an edge view of a SiO2 post film. Plan views of the same film taken at various stages of growth are shown at the right. The representative film thickness of each slice is shown by a line. Reprinted with permission from [129], D. Vick et al., Res. Signpost, in press. © 2002, Research Signpost.

Nanofabrication by Glancing Angle Deposition

which it operates, while shadowing tends to magnify surface roughness [61]. In the SiO2 film shown here (Fig. 7), column competition, extinction, and broadening can be seen as the film evolves. Transmission electron microscopy (TEM) images have suggested that column broadening correlates on the nanometer scale with bifurcation of the fibers that constitute the columns [62]. The similarity in column morphology suggests that the growth may obey a scaling law. Scanning probe microscopy can be used to quantify the interface width of the tops of films with topography hx y. This interface width is defined as 2


1 N w= hi − h¯ (6) N i Experiments on fixed and rotated substrates have shown that these films obey a scaling law in the form ¯ ∼ h¯ wh

(7)

where is a growth exponent [63, 64].

3.2. Relationship between Flux Incidence and Film Density The effect of columnar competition and thickening may pose a fundamental limitation on engineering microstructures. In addition, these effects may be detrimental for those applications that require a constant microstructure form throughout the film thickness. Through the use of periodic films and understanding how the film density is affected by flux incidence angle, the onset of competition and columnar thickening effects may be controlled. Both simulated and experimental studies suggest that the film density () is primarily a function of flux incidence angle [18, 65–68]. Measured densities reported between different laboratories can vary widely due to differences in the respective deposition processes and source materials. In addition, some laboratories report film density as a normalized value (i.e., [0 − 
= 0
/
= 0
, while others report densities relative to the bulk density (bulk  of the source material. In the latter case, it is more critical that the system geometry be clearly represented. Generally, film density is observed to fall with increasing flux incidence angle. Decreases of up to 50% are commonly reported in 0 for films deposited between
= 50
and
= 85
. From Figure 2b it is clear that film density is most affected by the flux incidence angle when
> 75
(i.e., in the extremely oblique to glancing angle regime). In this regime, evaporated manganese has shown a reported change in 0 from 0.71 at
= 75
to 0.40 at
= 87
[68] while sputtered tungsten has shown a change in 0 of over 40% between a film deposited at
= 75
and a film deposited at
= 85
[18, 69]. All these studies, particularly those involving simulation, showed that neither seed period nor, in most cases, substrate rotation rates (see Section 3.4) has an effect on these characteristics. To maintain a constant density at a given flux incidence angle, increases in the surviving pillar diameter (s) are compensated by a corresponding increase in pillar separation

Nanofabrication by Glancing Angle Deposition

(p). The ratio of these two parameters is thought to be thickness invariant and dependent on the flux incidence angle (
); that is, s/p = 
 [64]. This property arises through the competitive effects linked to the constancy of flux density striking a given region on the substrate surface. Films grown on prepatterned substrates may provide an opportunity to minimize columnar competition by optimizing the seed topography to the observed s/p ratio in randomly situated structures. Although a clearly defined diameter and period do not exist in these latter films, a measure of their values can be obtained. The “average” separation, d, of randomly situated columns can be determined by scanning probe measurements of GLAD film topography. This separation (governed loosely by Tait’s equation) can be found experimentally by explicitly measuring the distances between surviving columns and averaging the results. These measurements result in values on the order of a few hundred nanometers for film thicknesses of up to a one or two micrometers and with
∼ 85
. In a similar fashion, the “average” diameter of columns can also be calculated, although the results are not as definitive. Promising results have indicated that the competitive effects in periodic films can be delayed compared to the randomly situated structures [65]. If periodic pillars deposited under the same deposition conditions and seed geometry are compared based on the spacing of individual seed elements, the following observations can be made: 1. Initial seed separations much larger than d (i.e., approaching one micrometer), result in larger pillar diameters and a corresponding decrease in intercolumnar competition. 2. Films grown on relatively dense seed arrays (i.e., seed periods less than 100 nm) show highly competitive growth. 3. At a given film thickness, the crossover between increased competitive behavior and increased pillar diameter appears to occur at d. Column diameters and separations are based on the interplay of both self-shadowing and the adatom diffusion length of incoming flux. Based on the above observations, it is thought that the averages observed in a randomly growing film represent the optimized geometry for a given set of conditions (i.e., s/d is the optimized s/p for a given
). Let us consider a seed topography consisting of dots with 50 nm diameter, 80 nm height, and 600 nm separation. The flux incidence angle is set to 85
. Initially, a pillar film grown on this substrate will have a low s/p factor (i.e., s/p = 0 08) compared to a typical value of (s/prandom = 0 4 to 0.8 for a randomly situated film grown under the same conditions. To compensate for this discrepancy, the pillar diameter increases, effectively delaying the onset of columnar competition within the growth evolution. Competition effects are observed to occur more readily when the pillar diameter reaches a value determined by (s/prandom (i.e., in this case s ∼ 240 to 480 nm). It should be noted that competition effects are observed to be significantly diminished in randomly situated and periodic helices, specifically in relation to pillars grown on the same substrate topography. It is believed that this effect may be due to the self-correcting nature of helical growth and its

711 ability to adjust its pitch arm diameter to counter additional competitive pressures during growth.

3.3. Relationship between Flux Angular Distribution and Film Growth In addition to the flux incidence angle, the angular flux distribution (
) of the incoming flux is also important to GLAD microstructure growth. To control film growth most effectively at glancing incidence, a narrow angular distribution of vapor flux centered at a known oblique incidence angle is required. Indeed, some research has suggested that for incidence angles greater than
= 80
, small variations in the flux incidence angle result in large changes in film densities [18]. The resulting film density tends to be most greatly influenced by that fraction of flux which is least oblique and, therefore, least subject to the shadowing mechanism. For most of the applications and films shown in this chapter, electron beam evaporation has been used for film depositions. This process typically yields a flux beam geometry suitable for controlling microstructure growth at glancing angles. Unfortunately, high melting point materials (e.g., tungsten and molybdenum) are not easily deposited in this fashion, and a sputtering process may be required for growing GLAD films from these materials. Standard sputtered PVD generally deposits films with greater flux incidence distribution at the substrate due to the larger target size used and flux scattering off of the working gas. Techniques such as collimated sputtering [70, 71], ionized PVD [72], and lowpressure, long-throw (LPLT) sputtering [73] have been suggested to narrow 
. Although still not yielding as tight a flux beam geometry as present in typical evaporation processes, the last of these techniques, LPLT, has been used successfully to fabricate randomly situated chevrons [74], and both randomly distributed and periodic structures of helices and pillars [74, 75]. Periodic structures deposited by LPLT sputtering more easily identify the effect of increasing 
on GLAD film growth. Recent work has shown [75] the following film characteristics: 1. Quasi-helical microstructures are formed when the seed period (p) is less than d. 2. Pillar microstructures are formed when p > d. Hence, as the seed period increases, helical structures degenerate into posts. Why does this effect occur? Let us first consider what is meant when incident flux has a given angular flux distribution; for example, if
= 85
and 
= 4
, the majority of flux arrives between
min = 83
< x <
max = 87
. Recall that a pillar is simply a helical microstructure within which the pitch is indistinguishable. Hence for large seed separations (i.e., on the order of 1 m), although a helical structure may form at
= 85
, incoming flux arriving at the lower portion of the incidence range tends to “fill in” the helical pitch, smoothing out the resulting microstructure. At lower seed periods, shadowing by neighboring structures diminishes this “filling” effect, albeit at the expense of increased competition. As a result, when the seed period is less than d, quasi-helices are formed. When p > d, helices degenerate into posts, while a transitional region between pillars and quasi-helical behavior is observed to exist about p = d.

712

Nanofabrication by Glancing Angle Deposition

3.4. Relationship between Substrate Rotation and Film Growth Substrate rotation is one of the primary means of manipulating the film morphology at glancing angles. As mentioned previously, the film density is not observed to be dependent on the speed of rotation about the  axis for most materials. Generally, substrate rotation affects GLAD morphology in the following fashion: Isolated posts are fabricated when flux arrives isotropically from all azimuthal angles (i.e.,

/ t is “infinite”); helices form at various pitch lengths when / t is decreased; and, finally, oblique columns are formed when / t = 0. This general relation between morphology and / t has been presented previously in Section 2.1.4 and is shown in Figure 8. Recent research suggests that this morphological trend may not be applicable to all materials. Liu et al., studying under the Center for Materials for Information Technology (MINT) at the University of Alabama, found that the growth rate for cobalt increased [76], while iron films display leaflike columnar growth [77] at high rotational speeds ( / t ∼ 30 RPM,
= 75
. Their results were recently quantified by comparing aluminum, silicon, and silicon dioxide films grown at glancing angles with increasing rotational speeds [78]. This work relied on a gearbox which allowed for simultaneous deposition of six separate films over two orders of magnitude of rotation by stepping up or down the rotation about n relative to the central driving axis, c . Silicon dioxide and silicon films were found to follow the general trend observed for most materials, while the structure of aluminum was found to be highly dependent on

/ t. The trend for aluminum is shown in Figure 9. At low rotational speeds, aluminum films have “mushroomlike” growth, whereby with increasing thickness the film

Figure 8. Films of SiO2 grown with a deposition angle of
= 85
, and at various rotational speeds (shown below each image). Pillar growth occurs when / t > 1 RPM (at a deposition rate of 10 Å/sec), while helical growth occurs more dearly for / t < 0 1 RPM.

Figure 9. Aluminum films deposited at
= 85
at different / t. The films deposited at / t = 3 0 RPM show a flattened out structure while the film deposited at / t = 42 RPM shows peaked structures. Faceting is clearly visible in all the films, and TEM analysis that shows the film consists of a simple cubic, monocrystalline structure.

spreads out from a thin base. The tops of these structures are both flat and consistent in height with their neighbors. As / t is increased, the number density of structures with a pyramidal faceted peak increases. Also observed is a corresponding increase in the average thickness of the film. Hence, at / t = 42 RPM (for most materials, a pillar structure will typically form at 1 RPM, while a helix forms at 0.1 RPM using
= 85
as a reference), the peaked structures are in the majority, and the film thickness is almost twice that at / t = 3 0 RPM. This result, coupled with the previous study by Liu, suggests that the morphological structure is highly dependent on the propensity of the structures to form solid crystals. TEM analysis of the aluminum films showed them to have a simple cubic, monocrystalline structure. A similar analysis of silicon and silicon dioxide films shows both have amorphous structures, consistent with the statement that fiber bundling is thought to contribute to columnar competition in GLAD films [62]. One possible explanation for this behavior is the effective rate of adatom burial at increasing rates of substrate rotation at constant
[78]. At glancing angles, the effective shadowing mechanism is enhanced. Because all films in a given rotation set were deposited simultaneously, it is not believed that differential temperatures across the individual samples are a factor. The burial rate seems to be dependent on the number of times the flux “visits” a particular spot on the substrate (i.e., at fast rotation, the burial rate increases relative to the slow rotation rate because a particular site is “visited” more often). Hence, different crystal planes are thought to be preferred as the diffusion length of adatoms decreases with / t. Simulations indicate that the diffusion length of adatoms on structures with strongly preferred crystal planes changes with / t [78], while experimental results on chromium films deposited at a relatively conservative
= 65
show a similar result. Figure 10 shows that at high rotational speeds, the film surface shows a number of peaks typical of sputtered chrome surfaces. At low rotation speeds, the surface shows a smaller number of peaks with long channels linking film regions, seemingly indicating a longer effective diffusion length. It is noted that if this result is confirmed, a similar effect should be apparent on the same materials deposited at lower rotational speeds with an increased deposition rate.

Nanofabrication by Glancing Angle Deposition

Figure 10. The potential effect of substrate rotational speed on adatom diffusion length is apparent from these images of chromium films deposited at
= 65
. At low rotational speeds, the surface of the film is smooth, while at faster speeds, the surface roughness increases.

3.5. Simulation Software Simulations have been used as tools to describe obliquely deposited films at least since the pioneering work by Dirks and Leamy [20]. Although a number of simulation paradigms exist including continuum models [20], conservation of parallel momentum (primarily supported by a group of Japanese researchers starting with [79] and summarized in [80]), and angular dependent growth [81–83], ballistic deposition simulations have proven the most successful in describing the growth of thin films deposited with limited adatom diffusion and high mean free-path (the typical conditions in a GLAD chamber). In these simulations, particles are serially launched from just above the growing film. Each particle is allowed to follow straight-line trajectories until it strikes the substrate or the film. The subsequent surface diffusion is described by an equilibrium model whereby each particle is allowed to aggregate into the film after diffusing a distance determined by an algorithm which minimizes the surface curvature-dependent chemical potential. Throughout most of the history of thin film simulation, insufficient computing power has limited software to simple two-dimensional [19, 27] and three-dimensional models [84, 85] which tended to exclude the effects of surface diffusion of adatoms over large scales. This exclusion is important as it is universally accepted that surface diffusion is very important to the growth of obliquely deposited films, as it is for all thin film growth processes. Over the last decade, however, this limitation has been lifted significantly, allowing for the creation of three-dimensional (3D) simulation programs to more properly model both adatom diffusion and the resulting porous thin film structures created at glancing incidence [67, 86]. Typically, for example, even films evaporated obliquely onto stationary substrates grow anisotropically, with flakelike morphology and significant growth fanning in the direction perpendicular to the incident flux and parallel to the substrate plane [16, 18, 43, 44].

713 Although a number of software packages have recently been developed, one simulator that has proven quite successful in the modeling of films deposited at glancing angles is the Monte Carlo ballistic simulator program, 3D-FILMS [67]. This progeny of the two-dimensional simulation package SIMBAD [87] was developed in part to model several aspects of porous thin films. In its simulations, 3D-FILMS models a film as a large number of identical units. Each unit has cubical geometry and represents the statistically averaged behavior of a large number of atoms (typically 1000). Nucleation, self-shadowing, adatom mobility, and a variety of other physical effects are all incorporated into this model, and simulated films can be displayed graphically as threedimensional images. Temporal dependence of the incident flux [
t t] can be introduced to reproduce most of the GLAD film morphologies observed experimentally including simple helices, post, and chevron structures, as well as multilayered and capped structures. Periodic arrays of films can be grown by setting the initial substrate topography to match the desired predefined seed layer geometry. See Figure 11. A second 3D simulator, the Virtual Film Growth System (VFIGS), has also been recently reported [86]. This simulator, also built around the basic SIMBAD system and following a similar development framework as 3D-FILMS, was primarily created to understand the surface area of STFs (referred to in their work as dynamically obliquely deposited films). By simulating the growth of various film

Figure 11. 3D-FILMS simulations of different film morphologies deposited at the same flux incidence angle. These morphologies include: (a) helices; (b) a single helix from the simulation of (a); (c), (d) posts; (e) chevrons. A plot of the differential density as a function of height for the simulations at the left is shown in (f). Note that the simulation predicts that the resulting average film density is not dependent on microstructure form. Reprinted with permission from [67], T. Smy et al., J. Vac. Sci. Technol. A 18, 2507 (2000). © 2000, AVS—The Science & Technology Society.

714

Nanofabrication by Glancing Angle Deposition

morphologies from
= 0
through
= 82
, VFIGS found no significant dependency of either packing density or effective surface area on . These properties were found to be primarily a function of
, and, although the packing density diminished in the expected fashion, the effective surface area was observed to increase sharply to a maximum at
= 70
. Ballistic simulations of GLAD films have confirmed that only collimated flux and low diffusion length are needed to explain most aspects of these films including column morphology, column extinction and broadening, and bifurcation. In other words, self-shadowing is the primary growth mechanism. See Figure 12.

4. FABRICATION PROCESSES FOR SPECIALIZED APPLICATIONS One of the strengths of the GLAD process is that it can form a variety of microstructures using a one-step process. However, for some applications (i.e., the periodic films mentioned earlier), either pre- or postprocessing steps are required. In this section we describe a few tools that have been developed for application to GLAD films.

4.1. Perforated Thin Films There has been a great deal of research into the production of thin films perforated by an organized array of pores. Photoanodic etching has been used to produce 2 m diameter pores, 400 m deep into a silicon wafer [88], while phosphoric acid can be used to anodically etch high purity aluminum foils to produce regular patterns 100 m deep over a limited area [89]. As a final example, Chelnokov used an optical drill to produce triangular lattices of deep pores in photoresist [90]. In all these cases, the perforated films were limited to a regular geometric cross-section (either circular or rectangular) extending perpendicularly into the substrate. GLAD films, however, can be used to provide a template for etching a wider range of geometries into the substrate in a few, simple steps (see Fig. 13) [91]. In the first step, the inverse form of the desired substrate geometry is fabricated using the GLAD process. For the example shown, SiO2 helices were deposited at
= 85
with a pitch of 300 nm. The second step requires the filling in of the GLAD template using photoresist, spin-on glass or another similar material to provide not only protection to the underlying substrate but a medium in which the pores can be etched. For our example,

Figure 13. The stages involved in the fabrication of a perforated film: (a) template formation; (b) filling; (c) partial etch-back; and, finally, (d) template removal. Reprinted with permission from [91], K. D. Harris et al., Electrochem. Solid-State Lett. 4, C39 (2001). © 2001, Electrochemical Society.

HPR504 photoresist was used as the filler medium. To help aid the etching process, in the third step the filler medium is partially removed to reveal the tips of the GLAD structures. Timed immersion in a developer solution was used to remove the photoresist to partially expose the SiO2 helices. In the final step, the GLAD film is etched away using a suitable process (here, a 7:1 buffered oxide etch solution was used), to leave behind a mold of the film in the filler medium. This process has been used successfully to not only create the helical pores shown in Figure 13 but also randomly oriented chevron pores and periodic helical pores. Subsequent research has taken this process further by showing that it provides a clever means of fabricating GLAD-type microstructures from materials that are not easily deposited using that process. These materials, such as copper, have a low melting point and corresponding high adatom mobility when deposited on uncooled substrates. The high mobility of adatoms smoothes out the microstructure and diminishes the predominance of self-shadowing at the surface. In contrast, finely structured copper helices can be formed by electroplating copper back through a mold prepared by the above process. If the filler material is photoresist, for example, it can be easily etched away by acetone leaving an exact replica of the original template structure in copper [92].

4.2. Raised Topography

Figure 12. Pseudo-SEM images were obtained using a plan perspective of 3D-FILMS simulations. The images are displayed as insets over SEM images of real films. Reprinted with permission from [64], D. Vick et al., Mater. Res. Soc. Symp. Proc, 648, (2001). © 2001, Materials Research Society.

In Section 2.2.5 we discussed the fabrication of periodic structures where a single microstructure (i.e., helix, oblique column etc.) made up each element of a larger array. If this seed element is much larger than a, the columnar separation described by Eq. (4), multiple structures will form on individual seed elements [93]. For most of the envisioned applications mentioned thus far, such multiplicity is an undesirable property, and seed arrays typically are optimized to avoid this circumstance.

Nanofabrication by Glancing Angle Deposition

715

However, if the standard GLAD process is applied to seed elements with dimensions several orders of magnitude larger than a, a wall of dense film is built up at the seed edges [94]. This effect is illustrated in the SEM images shown in Figure 14. In these images, a helical GLAD film has been deposited on substrates containing arrays of 14 m tall mesas. Over the majority of the mesa tops, a porous, helical film is grown. At the edge, flux is accumulated as vapor hits at a less oblique angle (more normal). This effect results in a thick solid wall surrounding the porous region, and essentially a deposition in this fashion can be thought to fabricate a highly porous, self-sealing structure. If a complete seal is desired, a capping layer (see [47]) can be easily applied after the required film thickness is deposited. Seto et al. [94] found that walls form naturally around any raised pattern that exhibits sharp edges, and hence a variety of topographies such as T-junctions or via-connected chambers can also be formed. They suggest that such a structure may be suitable for microfluidics chromatography, nano-assay, lab-ona-chip, biochemical, and other related applications.

4.3. Sharpening GLAD Microstructures Using Ion Milling As a final example of some of the micro- and nanofabrication techniques that can be applied to the GLAD process, we mention the possibility of ion milling microstructures to sharpen their features. The sputter yield of an ion beam is angularly dependent, with the maximum yield lying typically between 30
and 60
. When columns are milled uniformly across the tip surface 10 µm

(a)

1 µm

(b) 1 µm

(c) Figure 14. SiO2 GLAD helices deposited onto etched silicon mesa substrates (a) fabricate a porous helical film with a wall of film built up at the seed edges (b, c). Reprinted with permission from [94], M. Seto et al., J. Mater. Chem. 12, 2348 (2002). © 2002, Royal Society of Chemistry.

by a beam incident parallel to the substrate normal, the tips not only become slightly shorter (a perhaps undesirable consequence) but also significantly sharper. A recent article [95] showed that the radii of curvature for vertical columns of silicon and carbon could be decreased to less than 20 nm with a 1 kV (18 mA) ion beam treatment of just 10 minutes in a vacuum. This ion milling treatment produces films that exhibit superior field emission properties when compared to unmilled films. These structures may be applied as field emitters, which provide electron sources in flat panel displays, plasma generators, analytical instrumentation, and power/high frequency devices. However, these films need not be useful for only field emission, for indeed their potential application could easily be limited by the growing and considerable interest in the possible field emission properties of nanotubes [96, 97]. The sharp features presented by the ends of the columns could find a use as SPM probe tip characterization surfaces, an area of growing importance as these tools become more common in industrial fabrication processes [98]. It has also been suggested that sharpened tips may be suitable for the more esoteric application of providing propulsion for microsatellites.

5. SOME PROPERTIES AND APPLICATIONS 5.1. Mechanical Properties Nanoindentation measurements have been done on several films of varying pitch lengths to answer questions on whether GLAD films show resonance properties [55, 99]. Theoretical work indicates that a GLAD film fabricated from a suitable piezoelectric material may form a tunable chiral thin film laser [100], while experimental research has shown that the films undergo elastic deformation when small forces are applied to the surface, corresponding to a stiffness as low as 1/1000th that of a similarly deposited solid film. Force displacement curves for one, two, and three turn SiO films have been obtained using a nanoindentation tip as a probe. This probe applied low force indentation measurements on the films over areas much larger than individual columns. To decrease the number of free variables, the thickness was left constant, resulting in pitches of 1900, 850, and 600 nm respectively. Using this technique, displacement at the maximum applied force amounted to less than 15% of the total film thickness. Indentations at the same site showed an overlapping displacement curve, indicating that the deflection is nondestructive or elastic for small deformations. The force–displacement curves for these films are shown in Figure 15. Somewhat surprisingly, the dependence of film stiffness on spring geometry scales in a manner similar to a bed of macroscopic springs and is on the order of −1  3+ 3s 2 Gs 4 2 (8) + tan 
 1 − k= 64R3 n 64R2 21 + 

where G is the Shear modulus, s is the column diameter, R is the coil radius, n is the number of turns,  is Poisson’s ratio, and
is the rise angle [55]. Although measurements of helical parameters (e.g., coil diameter etc.) could

Nanofabrication by Glancing Angle Deposition

716

microstructure with well-defined boundaries. Unfortunately, these films have less porosity than plasma sprayed coatings and, consequently, have diminished thermal protection.

Figure 15. Force–displacement curves for single, double, and triple turn helical SiO thin films of comparable thickness. To contrast, an indentation curve for a dense SiO film is also shown. Reprinted with permission from [99], M. Seto et al., J. Vac. Sci. Technol. B 17, 2172 (1999). © 1999, Materials Research Society.

not be precisely obtained, the areal stiffnesses of experimental and theoretical films were comparable. These values were on the order of 10 to 18 N/m-m2 for one to three turn SiO helices, as opposed to the 18,500 N/m-m2 value for a similarly deposited dense SiO film. From Eq. (8), it is expected that helical films will exhibit a resonant frequency between 10 and 50 MHz and suggests that it may be feasible to engineer beds of microsprings with well-defined stiffness and mechanical response. Periodic slanted posts can be used to aid in deflection measurements, by diminishing the error inherent within dimension values. These structures resemble cantilevers with rectangular cross-sections, of which an example was shown previously in Figure 6a. The theoretical expression for the displacement of this film is given by x =

F L3 cos2 
 3EI

(9)

F is the applied force, L is the cantilever length,
is the rise angle, E is Young’s modulus, and I is the moment of inertia (where for a rectangular cross-section, I = wt 3 /12, where w is the width and t is the thickness) [55]. These structures deflected 80 nm under 27 N of applied force, while Eq. (9) predicted a deflection of 90 nm under the same conditions.

TBCs deposited by oblique deposition may provide solutions to these problems, and, in particular, it has been suggested that a suitable GLAD structure may provide diminished stress induced deterioration while retaining the film’s porosity. A film was grown with alternating porous and dense layers of YSZ, as shown in Figure 16 [102]. YSZ is used because of its low thermal diffusivity. The inclusion of porosity into the film matrix would be expected to further lower the bulk thermal conductivity. The thermal properties of these multilayer films were directly measured at the National Institute of Standards and Technology using two techniques. The first, referred to as the 3 technique, introduces heat into the coating by an ac current of frequency  flowing through an evaporated resistor [103]. A fit of resistor voltage as a function of frequency yields the thermal conductivity. The second technique is called the Mirage technique. Here, an oscillating temperature was induced immediately above the film using a pulsed laser [104, 105]. A second probe laser aligned parallel to the surface underwent deflection in the boundary layer above the film surface, and the thermal diffusivity was then found by fitting amplitude and phase shift data to the solution of a three-dimensional diffusion equation. The Mirage method was applied to a dense film of 1 m thickness, and yielded a room temperature thermal diffusivity of 0 0053 ± 0 0007 cm2 /s. This value is comparable to those previously reported for YSZ TBCs [106]. Measurements on the GLAD film using both methods led to thermal diffusivity estimates of approximately 9% that of solid YSZ films. It is possible that this result may be improved by further optimizing this YSZ TBC fabrication process.

5.2. Thermal Properties Capping and multilayer structures were introduced briefly in Section 2.2.4. It has been suggested that if multilayer GLAD film were constructed out of suitable materials, a thermal barrier coating (TBC) may result. Two types of TBCs are described in the literature: 1. A layer of yttria-stabilized zirconia (YSZ) is applied to a critical surface by plasma spraying, resulting in a highly porous microstructure [101]. Its thermal barrier properties, however, can be significantly reduced by repeated heating cycles that may induce stress, causing cracking due to differing thermal expansion coefficients. 2. Electron beam evaporation is used to deposit the film. The stress-induced deterioration is reduced by the presence of a laterally compliant columnar

Figure 16. YSZ film structures grown from alternating porous and dense layers display a low thermal diffusivity. These films can be grown by dynamic alteration of the deposition angle,
. Reprinted with permission from [102], K. D. Harris et al., Surf. Coat. Technol. 138, 185 (2001). © 2001, Elsevier.

Nanofabrication by Glancing Angle Deposition

The high thermal resistance of these films offers an alternative use for these film structures. Possibly, the resistance can be exploited as a heating source to increase the operating temperature and/or efficiency of devices created using it as a base.

5.3. Enhanced Surface Area Devices Perhaps the easiest and most directly applicable products for GLAD films are enhanced surface area devices. These films inherently have an extremely high surface area relative to their bulk counterparts [68], which may make them ideal media for a number of applications including humidity sensors, catalysis media, chemical sensors, and lab-on-a-chip devices.

5.3.1. Supercapacitors High surface area (>1000 m2 /g) carbon-based capacitors are commercially available exhibiting specific capacitances of 100–200 F/g. These devices rely on the formation of an electrical double layer between the carbon surface and electrolyte to provide their capacitance [68]. Recently, efforts have been made to develop metal oxides as capacitor materials. These materials utilize a reversible redox reaction as the basis for their pseudo-capacitive behavior. These efforts have primarily focused on rubidium oxides, which have been shown to have specific capacitances of up to 770 F/g [107]. The problem with this material is that rubidium is expensive, leading to the exploration of less expensive alternatives such as MnO2 , NiO, and Co3 O4 as faradaic capacitors. Sol–gel [108], colloidal suspensions [109], and electrochemical deposition [110, 111] have all been used to create capacitor media out of one or all of these materials. As examples, Chin et al. [109] observed a specific capacitance of 720 F/g using MnO2 via a colloidal solution. Hu et al. used anodic deposition of NiO/CoO mixtures to obtained 720 F/g [110], while a similar process on MnO2 resulted in a specific capacitance of 300 F/g [111]. The film microstructures described in this chapter may provide an alternative path for electrochemical capacitor development, based on their high surface area and the notion that vacuum deposition of thin metal films onto flexible substrates is both highly scalable and a well known manufacturing process [68]. Chevron structures have been used for most of the capacitance experiments to date due to its resemblance to the type of structure that would be expected from an obliquely angled multipass coating deposition process. For a 500 nm thick, four-turn chevron structure, the maximum specific capacitance obtained was 225 ± 25 F/g at
= 82
[68]. Further work may be undertaken to improve the surface area of the films which they believe is the detrimental step in their process.

5.3.2. Humidity and Chemical Sensors Capacitance measurements on GLAD films are not new, and certainly other applications can arise by applying this property elsewhere. Two of these other applications are relative humidity detection [112, 113] and chemical sensing, where humidity or chemical concentrations are sensed as a

717 change in capacitance between two parallel plates. A humidity device of this style is typically termed a capacitive relative humidity (RH) sensor. For these films, the interactions between sensing material, water moisture, and the applied field become strong, making the conventional equivalent circuit model insufficient to explain the observed results [112, 114–117]. Crucial microstructure related parameters are also important, including the diameter of pores and pore size distribution. Shimizu et al. [115] introduced a computation program demonstrating the importance of these parameters to the sensing characteristics and were subsequently followed by Li [116] who used a similar approach to explain their porous Sr1−x Lax TiO3 sensors. Khanna and Nahar incorporated the interactions between sensing materials, water moisture, and applied field using Sillars’ medium theory [118] to successfully explain the sensing behavior of their porous Al2 O3 sensors fabricated by anodization [117]. Typically, though, these models assume a solid structure within which pores are etched. GLAD films present the opposite approach— essentially, a “void” within which solid structures are grown. Reasonable capacitive RH characteristics can be obtained by sandwiching a GLAD SiO pillar film between two electrodes [113]. A model, based upon a modification of Sillars’ medium theory and incorporating the influence of net heat adsorption of water molecules, the change in conductance on the surface of SiO film after water adsorption, water condensation in the pores of the sensors due to the capillary effect, changes in conductivity of the condensed water with RH, and the pore size distribution on the sensing characteristics of these devices, was developed and is applicable through an RH range from dry to saturation. This model shows that pore size distribution and porosity have critical effects on the sensing characteristics. Early RH studies on GLAD films showed that a rapid response time of a few seconds could be obtained, with a capacitive range over five orders of magnitude. This range corresponded to relative humidities of 10% to 90%. Further work on these structures was conducted by Harris et al. at the University of Alberta, who decreased the response time to 25 ms by further optimizing some of the film deposition parameters and measurement techniques [119]. These results are several orders of magnitude quicker than capacitive RH sensors currently on the market. It is thought that the natural pore size in the upper capping layer tends to be near the optimal size for allowing moisture to either adsorb or escape depending on the humidity differential between the film structure and the surrounding air. Work on humidity sensors opens up the possibility that by modifying the evaporant or using surface treatments, rapid detection of different gases using a similar process design may be obtainable. Engineering a device that incorporates a number of films grown from different materials, it may be possible to differentiate between different gas-borne species.

5.3.3. Catalytic Media Platinum films have been used as electrodes or catalysts in sensors [120, 121], direct methanol fuel cells [122, 123], and electrochemical deposition systems [124]. The first category

718 of these applications includes rapid detection of hydrocarbons at low concentrations and is of considerable interest to the automotive industry. Ford Research Laboratory, in conjunction with the University of Alberta, is studying the catalytic behavior of porous GLAD films for microcalorimetric HC sensors [125]. This method compares the resistance changes between a membrane coated with a catalytic material (in their case platinum, or Pt) and a reference material, when both are subjected to hydrocarbons. Because of the high surface area of GLAD films, a magnification of the detection limit for these particles was expected. It was found, however, that although the performance of the tested films was superior to sputtered Pt films, they were not competitive with commercially available automotive honeycomb monoliths. Although these results may be improved by optimizing the film thickness, the critical problem remaining is the significant degradation of both the GLAD and sputtered films after repeated use. This problem must be understood and addressed before GLAD films can seriously compete in this particular market. Titania is a second catalytic material of interest. The columnar morphology in sputtered TiO2 has been shown to enhance both photocatalytic and photovoltaic efficiency [126, 127]. The Toyota Central Research and Development Laboratories assessed the photocatalytic activity of obliquely deposited TiO2 films on glass substrates [128]. Several film morphologies including chevrons, posts, and helices were fabricated. These films were evaluated by immersing the films in methylene blue solution, irradiating the samples with 350 nm wavelength light, and recording time dependent absorption spectra within the range 200 <  < 800 nm. Several films were tested with angles of incidence between 0
and 82
. All the obliquely deposited films performed slightly better than solid films, although the specific column morphology (i.e., chevron, post, and helical geometry) was not found to be as important as the deposition angle, which had an optimal value at
= 70
. This optimal value was confirmed by VFIGS simulations, which found
= 70
to yield a maximum in effective surface area regardless of the specific film morphology [86]. To explain how an optimal value may result from these films, a simplified argument is presented [129]. For many materials, structures of the film separate beyond
= 70
. If the porous film is treated as an arrangement of identical, isolated cylinders of height h, radius r, and occupying an area A, the resulting number density of columns is given by N = 1/A. The corresponding surface area of a single column thus scales as s ∼ r2h + r, while the fractional density of the film scales as  ∼ r 2 /A. Hence, the surface area of the film per unit area of substrate scales as Ns ∼ 2h/r + 1. Thus, for high surface areas, higher densities with long, narrow, isolated columns are preferred. As density is increased (i.e.,
is decreased), the passages between film columns narrow and eventually close. The characteristic diffusion times for gaseous or liquid-borne species to enter or leave film must therefore increase. As a result, there is a trade-off between the response time and the surface area for obliquely deposited films. In addition, the role of optical scattering of UV light on photocatalysis in porous films has yet to be assessed.

Nanofabrication by Glancing Angle Deposition

5.3.4. Lab-on-a-Chip As a final example of enhanced surface area applications, we look at the current research activities taking place in molecular biology, particularly in the separation and identification of genetic materials and proteins. Presently, primarily capillary tubes with inner diameters of 100 m or more are used for this application [130]. These tubes do not lend themselves well to integration and require equipment which is large, expensive, and monofunctional. Microfluidic structures fabricated by photolithographic processes have been proposed as an alternative means by which genetic materials and proteins can be measured [131]. These structures have demonstrated performance which is similar to capillary tubes but have a compact size, promising increased speed and reduced cost while allowing far greater levels of integration. These areas of research have been termed the “labon-a-chip” concept [132]. A common feature to existing and conceived lab-on-achip analytical systems is the existence of microchannels. These channels not only provide passageways between different regions on the chip for fluid flow but typically incorporate filtering, separation, or high density reaction sites [133]. It has been shown that a porous SiO2 film can be grown in an etched microchannel (see Fig. 17) [134]. Precise alignment of the trench and source is required such that the flux arrives parallel to the trench direction, thus restricting the film morphology to either chevrons or oblique columns. Using this method, a surface area enhancement of two orders of magnitude was obtained. The limitation in film morphology for this type of device may be removed through the use of raised topography, which was described in the previous section. If the channels are constructed as raised topography, a standard GLAD process can be used to form a variety of microstructure morphologies over the channel surface. This structure would be

Figure 17. SiO2 films are shown grown within an etched microchannel. Precise alignment of the flux and channel are required for proper microstructure growth. Reprinted with permission from [134], K. D. Harris et al., J. Electrochem. Soc. 147, 2002 (2000). © 2000, Electrochemical Society.

Nanofabrication by Glancing Angle Deposition

self-sealing at the edges and can be sealed on the top by depositing the appropriate capping layer.

5.4. Magnetic Properties It would not be unfair to say that the properties of magnetic microstructures are poorly understood. Although in recent years this understanding has grown immensely with the advent of better and faster computer simulations, much research still focuses on film characterization studies. What is well known, however, is that the microstructure of a magnetic thin film significantly affects its magnetic properties [54]. The ability to control the size, shape, orientation, and composition of the magnetic structure on a nanometer (or subdomain) scale offers a greater range in magnetic properties that can be controlled. This level of control can be applied not only to magnetic recording media (i.e., to increase storage densities) but also leads to the ability to test micromagnetic theories/modeling, and the fabrication of more innovative magnetic materials and devices. Originally, it was thought that periodic GLAD pillars might serve as a suitable medium for high-density storage media. TEM and X-ray diffraction measurements of cobalt pillars grown on a chromium underlayer (to promote epitaxial growth in subsequent layers [135]) show the films to be monocrystalline, hexagonal close-packed structures with a strong crystal axis alignment perpendicular to the substrate. Reasonably defined periodic structures were shown to exhibit the equivalent of approximately 3 Gigabits/in2 , assuming each particle consisted of a single bit [93]. Subsequent research using a TEM to etch a small sample indicated that nickel films might be grown with periods of less than 10 nm [58]. However, magnetic force microscopy imaging of the domain structure for these and previous films was inconclusive, and subsequent developments in this field (namely demonstrated storage density of over 25.7 Gigabits/in2 in a commercial device by IBM, and potential research focusing on 1 Terabit/in2 [136]) rapidly outpaced potential GLAD development. Certainly, the possibility of growing unique microstructures for magnetic studies remains, and a few researchers have analyzed the hysteresis curves from several GLAD morphologies including columnar structures, helices, and posts [77, 93].

719 a density gradient across the film thickness (i.e., adjusting the flux incidence angle during deposition). By varying
between 50
and 80
, filters have been fabricated which exhibit 82% reflection peaks and bandwidths of 50 nm centered at 460 nm [138]. The second example, diffraction gratings, results from the sinusoidal morphology at the cleaved edge of a helical film. This morphology acts like a diffraction grating oriented vertically. These examples are not particular to the GLAD technique, however, and have been reported for less obliquely deposited films by other researchers (see, for instance, an example of a STF rugate in [139] and a Sol˘c filter in [140]). It is hoped, however, that these references help introduce the reader to the power of simply rotating the substrate at oblique incidence to manipulate the optical properties of a thin film.

5.5.1. Chirality in GLAD Structures One of the unique properties of some GLAD film structures is their chirality, which is to say that their geometry is nonsymmetric [141]. A necessary and sufficient condition for chirality is that a chiral object cannot be superimposed by rotation and translation onto its mirror image. Some examples of chiral objects include Möbius strips, many types of complex molecules (generally organic substances), and, of course, one’s hands. And, just like hands, chiral structures have a both a left- and right-handed version. Helical GLAD films (and their derivatives) are primary examples of chiral structures: their handedness depends on the direction of substrate rotation during deposition (i.e.,  is clockwise or counterclockwise). An example of a left-handed GLAD helical film is shown in Figure 18. The chiral nature of these GLAD structures becomes important when we consider the effect on their optical properties. Chiral crystals or molecular structures are known to exhibit optical activity, which is the rotation of the plane

5.5. Optical Properties Optical properties of films deposited at both oblique and glancing angles have been a study of research for some time. Indeed, the initial experiments into sculptured thin films were borne through the possibility that the optical properties of a thin film could be manipulated by changing its structure [22, 26]. The application of the advanced GLAD technique to a deposition process can give the user considerable latitude in both planning and optimizing the optical properties of a thin film. Two simple examples are used here to introduce these concepts: rugate filters and diffraction gratings [137]. Rugate filters are fabricated when thin films exhibit a spatially modulated index of refraction. The GLAD technique can easily introduce this modulation by introducing

Figure 18. An example of a chiral GLAD film. Here, a left-handed SiO2 helical film with a pitch length of 410 nm and 8.4 turns is shown. Reprinted with permission from [129], D. Vick et al., Glancing angle deposition of thin films, Res. Signpost, in press. © 2002, Research Signpost.

720 of polarization of linearly polarized light [142]. The fundamentals of chiral optical activity were discovered in the mid-19th century, and were mostly studied by chemists who concentrated on natural optical activity (see [141] for a good review). This work led to Louis Pasteur’s postulate stating that optical activity may arise due to the chirality of its molecules ([143], from [141]). The chirality in a GLAD film, however, does not arise through the material but rather through the columnar shape (i.e., a form of artificial chiral media). Research on artificial chiral media initially occurred in the 1920s with experiments on wire spirals and microwave propagation [144, 145]. These results were later confirmed by Tinoco et al. [146, 147] who investigated electromagnetic activity with microwave radiation incident on copper wire helices in a box. The pitch length of these early studies was on the order of 1 centimeter, yielding electromagnetic (EM) activity in the microwave regime. In contrast, thin films (e.g., GLAD helices) can be fabricated with pitch lengths on the order of a few hundred nanometers, yielding EM activity in the visual spectrum ( = 400 to 700 nm).

5.5.2. Optical Activity Earlier we mentioned work by Young and Kowal (1959) [26], who investigated optical activity by depositing films at oblique incidence (
∼ 70
 onto rotating substrates. These films exhibited rotatory powers of around 155
/mm (as measured by the amount of angular rotation per thickness of film). In this and all examples that follow, the standard sign convention for optical rotation is used. If we define nA as being the index of refraction of the structured material, while nB is the index of refraction of the medium surrounding the material, a left-handed film with nA > nB produces a positive (clockwise, looking back at the light source) rotation in the plane of polarization for transmitted light. Its enantiomeric counterpart, a right-handed film produces a negative rotation. In the case where the structure is film material and the surrounding medium is air, nA = nfilm and nB = nair . Young and Kowal’s results were the first known work where artificial media showed an optical rotatory response. However, although advancement in the production and characterization of nonchiral, obliquely deposited films continued (primarily by groups in New Zealand [148] and Japan [28]), it was not until Robbie et al. [38] fabricated porous helical thin films using the GLAD technique that further spectroscopic measurements of optical activity in a chiral thin film were reported [149–151]. Leading up to Robbie’s work, an extensive and growing body of work modeling the interaction of EM waves with chiral media had been reported (see for example, [152–154], and many other works by Lakhtakia). This theoretical modeling indicated that highly porous structures are not suitable for maximizing rotatory power. Experimental results have shown that GLAD films display an average rotatory power ranging from 0.16
/m for MgF2 to 1 05
/m for Al2 O3 [155], significantly less than that obtainable by denser films which have demonstrated rotation up to 5
/m for titanium oxide films [156]. Perforated GLAD films, however, being the inverse of the GLAD template (described previously in Section 4.1), show a diminished porosity, while

Nanofabrication by Glancing Angle Deposition

maintaining the same geometric form. Analysis of optical rotation in right- and left-handed perforated films has found an improvement of up to three times over their GLAD templates. For example, right-handed perforated films had a measured rotation of 3 93
/m compared to −1 53
/m for its template, and the left-handed perforated film had a measured rotation of −1 48
/m and 0 49
/m for its template [92]. The measured power of the perforated film is the reversal of rotation displayed by their respective templates, since the refractive index gradient has been inverted with an air helix n = 1 surrounded by a photoresist matrix n ∼ 1 6. The enhanced rotation in the right-handed film is not clear at this time, and both it and the generally stronger optical activity of the perforated films over their GLAD templates bear further study.

5.5.3. Liquid Crystal Hybrid Optics Although the porous nature of GLAD films may not be the most optimal morphology for enhancing the rotatory power of thin films, it does allow for hybrid devices when combined with liquid crystals. These devices are not possible with dense films. Optimizing the optical properties for liquid crystal (LC) devices requires control over the long-range orientation of the LC molecules. Two techniques serve as common examples of how this orientation is controlled. In the first, thin coatings of polyimides are applied to the substrate surface, which is subsequently rubbed to produce planar alignment of LCs [157]. In the second, obliquely deposited thin films are used as alignment layers to generate a certain “tilt” of LC molecules at the substrate [158, 159]. In both these examples, the influence on LC orientation is felt near the substrate surface only. Controlling the LC orientation in thicker switching cells (particularly with chiral or cholesteric LCs) becomes problematic and can lead to difficulties such as irreversible switching [160]. Techniques that are used to control the orientation of LC molecules through the film media make use of polymerdispersed liquid crystals or photopolymerization. GLAD helical films can provide an alignment structure or “backbone” for the LC, inducing a chiral nematiclike ordering in nonchiral LC materials. GLAD films filled with birefringent materials such as nematic LCs, for example, show an enhanced transmission difference between left- and rightcircularly polarized (LCP and RCP respectively) light [161]. This difference was removed when the films were filled with an isotropic liquid such as water or some polymer materials which had indices of refraction approximately matching the film material. Switching cells were demonstrated using a SiO2 LC/GLAD hybrid [162, 163] fabricated by depositing the GLAD film on glass substrates with an indium tin-oxide (ITO) electrode. A counterelectrode was provided by another ITO coated glass substrate. When brought together, these two pieces form a “sandwich” which can subsequently be filled with LCs (see Fig. 19). Switching can then be accomplished by exploiting the dielectric anisotropy of the LCs. In the unaddressed state (no voltage applied), the LC orientation is controlled by the presence of the GLAD chiral films. Hence, an enhanced transmission is observed. In the

Nanofabrication by Glancing Angle Deposition

Figure 19. Electro-optic switching cells for GLAD/LC composites are constructed from two ITO coated glass substrates containing a LC filled GLAD thin film. The fill port is present to add the LCs after the GLAD film “sandwich” is fabricated. This port is plugged before use. Reprinted with permission from [162], J. C. Sit et al., Liq. Cryst. 27, 387 (2000). © 2000, International Society for Optical Engineering (SPIE).

addressed state (a 200 Vpp , 1 kHz signal applied), the LCs align parallel to the applied field, and no transmission difference between LCP and RCP occurs. In this latter case, light transmitted through the cell along the helical axis (which is now parallel to the LCs) “sees” the ordinary refraction index n0 of the LC. If the n0 index matches with the index of refraction of the film, the cell appears to be a homogenous medium (n = n0 = nfilm . Thus the chiral optical response vanished in the addressed mode. An illustration of both the addressed and unaddressed states in shown in Figure 20. The lower panel of this diagram shows the transmission difference observed between these two states. Increasing the porosity of the films allows for a greater degree of LC filling, at the cost of a lower deposition rate (which is dependent on the cosine of
). Additionally, when the film microstructures become further separated, the order of LC molecules can become more randomized, resulting in a degradation of the film’s optical properties. These effects must be balanced in an optimal structure. This point has been found to occur at
= 85
for a similar film to the hybrid example described above [155]. Filling GLAD films with LCs has two beneficial sideeffects: The matrix of LCs more closely matches the index of refraction of the film materials, resulting in less light scatter in the film/LC hybrid devices, and the risk of contamination by ambient humidity (which would degrade the effectiveness of the devices) is reduced [164].

721

Figure 20. Electro-optical switching in GLAD/LC composites consists of two steps: in the unaddressed state (top left), the LC is aligned by the chiral GLAD medium and exhibits a transmission difference between right and left circularly polarized light; when an electric field is applied (top right), the LC molecules align and the transmission difference disappears. Lower panel reprinted with permission from [162], J. C. Sit et al., Liq. Cryst. 27, 387 (2000). © 2000, International Society for Optical Engineering (SPIE). Upper panels reprinted with permission from [41], J. C. Sit, Thin Film/Liquid Crystal Composite Optical Materials and Devices, Ph.D. Thesis, University of Alberta, Edmonton, 2002.

5.5.4. Photonic Bandgap Optics A second optical application for GLAD films has been closely investigated. Photonic bandgap (PBG) crystals are artificial, periodic structures which exhibit the characteristics of a bandgap for light. In other words, the propagation of electromagnetic waves within the frequency range of the bandgap is restricted [51, 52, 165]. Hence, a photonic bandgap crystal is the light analogy to the bandgap in a semiconductor material which restricts electron movement based on their energies. This “stop-band” must lie in all directions in the lattice, requiring a three-dimensional structure. Three-dimensional photonic bandgap crystals with a periodicity which exhibit a stop-band falling in or near the visible spectrum are of particular interest. Recently, it was proposed that a square spiral microstructure should exhibit a large 3D photonic bandgap [50, 166]. This structure consisted of a tetragonal lattice of square spiral posts and was based on the distortion of nonstandard diamond helices. It was suggested that the GLAD process might be ideally adapted to form this morphology. Soon after this “challenge” was issued, the structures were fabricated using prepattered substrates and advanced GLAD control [45]. These structures are shown in Figure 21. Here, photolithography was used to design substrate topography with lattice seed diameters of 500 nm and separations of 1 m. Further optimization of the process

Nanofabrication by Glancing Angle Deposition

722

(e.g., porous membranes). The successful demonstration of low defect periodic GLAD arrays is of particular significance and could lead to a method for the manufacture of photonic bandgap devices. It will also be evident from this chapter that much work will be required on both fundamental and applied fronts before this technology fully matures. We may expect a rapid expansion of the field in the coming years as more researchers incorporate GLAD films into their processes and devices.

LIST OF SYMBOLS

a Figure 21. A tetragonal square spiral GLAD film which has been suggested as a potential three-dimensional, photonic bandgap material. A side view of this film is shown in the inset. Reprinted with permission from [45], S. Kennedy et al., Nanoletters 2, 59 (2002). © 2002, American Chemical Society.

 c v

should yield a structure even closer to what the theory originally envisioned. Photonic bandgap materials manipulate light through the introduction of lattice defects. These defects allow for the confinement and guiding of light, requirements for the application of these media in photonics and integrated optics. As mentioned in Section 2.2.5, these defects can be introduced into a periodic GLAD film without degradation to the microstructure growth [56]. Defects in the seed topography transfer to the film, as the extreme flux incidence angle ensures that there is little or no flux coverage over the nonseeded region. Provided that this defect area is not on the order of the shadowing distance cast by individual seeds, the uniformity of the periodic film is preserved. A subsequent series of processing steps can be applied to the square spiral films to yield a structure that exhibits an even larger PBG. An inverse square spiral film, which can be fabricated using the perforated film recipe described in Section 4.1, is expected to have a PBG approximately twice the size of the standard structure (∼24% of the central band frequency, compared with ∼16% [166] of the central band frequency exhibited by the standard structure). At the time of this publication, this structure has not yet been presented.

6. CONCLUSION This review has introduced a promising and versatile tool for materials engineering at the submicrometer scale. GLAD films can be fabricated with relative ease from a variety of materials and are readily incorporated onto lithographically prepared and micromachined surfaces. Examples of such surfaces include interdigitated electrodes, microcantilevers, mesa arrays, and microfluidic channels. In some proposed applications, such as sensors, the films would play an active role in a device. Alternatively, the films may serve as supporting matrix for the active component (e.g., embedded liquid crystals), or as a template in a manufacturing stage



d  p pc

 s T t

Tm

The angle of incident flux at the substrate measured relative to the substrate normal. A measure of the angular distribution in flux incident at the substrate. The normalized column separation as determined by Tait’s rule. Columnar angle measured relative to the substrate normal. Columnar angle measured relative to the substrate plane. The angle of incident flux measured relative to the substrate plane. The optimized period of seed elements used to grow periodic GLAD structures. At this period, film growth occurs only at the locations of seed elements. In other words, ≡ poptimized . The “average” separation of randomly grown GLAD columns. Rotation angle about an axis located at the substrate center, and parallel to its normal. The period of seed elements used to grow periodic GLAD structures. Ambient chamber pressure. For evaporation, pc is less than 10−5 Torr (10−3 Pa) and typically on the order of 10−6 Torr (10−4 Pa) for refractory metals. For sputtering, pc is on the order of 10−3 to 10−2 Torr (0.1 to 1.0 Pa). Thin film density. The diameter of columns grown using the GLAD technique. Substrate or film surface temperature. The thickness (i.e., height) of individual seed elements used to grow periodic GLAD structures. This parameter, coupled with the flux incidence angle, helps determine the optimal seed period. Melting temperature of source material.

GLOSSARY 3D-films A 3D, Monte Carlo ballistic simulator, based on the SIMBAD program, which models the creation and dynamic evolution of 3D microstructures in PVD thin films. Adatoms Incident atoms which have transferred their kinetic energy to the substrate lattice and become loosely bound to the surface. Ballistic deposition (BD) Modeling which treats flux as arriving colinearly at the substrate surface. Adatom diffusion and surface shadowing are the primary growth mechanisms.

Nanofabrication by Glancing Angle Deposition

Bulk diffusion Movement of atoms within the film. This process is characteristic of Zone 3 films as described by the Movchan and Demchishin structure zone model. Chirality Material property describing its nonsymmetric geometry. A chiral object cannot be superimposed by rotation and translation onto its mirror image. Collimated sputtering The process by which sputtered atoms outside a desirable incidence angle range are mechanically inhibited from striking the substrate. A honeycomb sheet-metal array is placed perpendicular to and between the target and substrate plane. Although 
is minimized, the deposition rate at the substrate surface is significantly reduced. Column competition The process by which thin film columns extinguish their neighbors due to shadowing at extremely oblique flux incidence angles. The resulting decrease in column number density is compensated by an increase in individual column diameters, leaving the overall film density constant. Columnar growth The tendency of PVD thin films to grow columnar microstructures. These columns are oriented in the direction of the flux source. Chemical vapor deposition (CVD) A volatile material compound reacts chemically with other gases to produce a nonvolatile solid that deposits onto a substrate as a film. Electron beam lithography (EBL) Technique for creating extremely high resolution patterns. EBL consists of scanning an electron beam across a resist sensitive to electron irradiation, while controlling the beam to create any desired two-dimensional pattern. The technology is capable of creating an infinite number of patterns in a variety of materials at sub-50 nm resolution. However, although very versatile, EBL is more expensive and considerably slower than photolithography. Evaporation The controlled transfer of gaseous atoms from a heated source to a substrate where film forms. Porosity A solidity measurement for a thin film. This parameter is inversely proportional to the density of the thin film compared to its bulk counterpart and is sometimes used as a expression of surface area. Film porosity tends to increase with increasing flux incidence angle and, most significantly, within the glancing incidence regime 
> 80
. Glancing angle deposition (GLAD) The use of substrate rotation and flux incidence angle variation to fabricate a range of thin film morphologies with controlled structure and porosity. This technique requires columnar vapor flux to be deposited at extremely oblique incidence angles 
> 80
. Incident flux Term used to describe source vapor arriving at the substrate. Usually implies a directional component. Lab-on-a-chip Chemical analyses wherein processing, transport, etc., occur in microchannel structures located on-chip. Liquid crystals (LC) Term used for a type of organic molecule having inherent optical anisotropy. Strongly birefringent media are produced when the molecules are purposefully aligned. Low-pressure, long-throw (LPLT) sputtering Technique by which the sputtering target and substrate are separated by a

723 relatively large distance (typically greater than 15 cm), and the plasma is ignited under low chamber pressures [pc < 1 m Torr (0.1 Pa)]. This process attempts to minimize 
by increasing the mean-free path of particles in the chamber. Flux arrives at the substrate with a linear trajectory, though not necessarily with an origin at the source due to collisions with the working gas atoms. Microfluidics The study of microliter quantities of flowing fluids usually confined to microchannels. Movchan and Demchishin SZM One of the first structure zone models to classify continuous film structure according to substrate temperature during deposition. Three “zones” of film texture are identified: Zone 1, where atomic shadowing effects predominate T /Tm < 0 3; Zone 2, where surface diffusion effects predominate 0 3 < T /Tm < 0 5; and Zone 3, where bulk diffusion effects predominate T /Tm > 0 5. Motohiro–Taga interface The transition region occurring when the column angle is abruptly altered through a change of flux incidence angle. The resulting microstructure is similar in form to a chevron, with the apex being the Motohiro– Taga interface. Nanoindentation A process by which a small probe compresses a thin film surface to obtain force versus displacement curves under a variety of loading conditions. Normal incidence A condition for deposition where the substrate is held perpendicular to the incident flux. This substrate configuration typically maximizes the film deposition rate while minimizing surface shadowing effects. Oblique deposition A condition for deposition where the substrate is inclined relative to the incident flux. Columnar growth is inclined toward the flux source. Optical activity Rotation of the plane of polarization for light transmitted through a material. Photonic bandgap (PBG) crystals Artificial, periodic structures.

ACKNOWLEDGMENTS The authors thank our colleagues in the Nanotechnology and Microdevices Research Group in Electrical and Computer Engineering at the University of Alberta for their suggestions during the writing of this review. The contributions of Michael Colgan, Martin O. Jensen, Ken Harris, and Douglas Vick are particularly acknowledged for their assistance in editing the final manuscript. We also make special note of George D. Braybrook for his excellent SEM imaging of many of the structures presented in this chapter. This work has been supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC), Alberta Informatics Circle of Research Excellence (iCORE), and Micralyne, Inc.

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Encyclopedia of Nanoscience and Nanotechnology

www.aspbs.com/enn

Nanofibers Jason Lyons, Frank K. Ko Drexel University, Philadelphia, Pennsylvania, USA

CONTENTS 1. 2. 3. 4. 5. 6. 7. 8.

Introduction Formation of Nanofibers Solution Electrospinning Melt Electrospinning Structure and Properties Modeling of the Electrospinning Process Applications of Nanofibers Summary Glossary References

1. INTRODUCTION Nanofibers are solid-state linear nanomaterials characterized by flexibility and an aspect ratio greater than 1000:1. According to the National Science Foundation (NSF), nanomaterials are matters that have at least one dimension equal to or less than 100 nanometers. Therefore, nanofibers are fibers that have diameter equal to or less than 100 nm. Materials in fiber form are of great practical and fundamental importance. The combination of high specific surface area, flexibility, and superior directional strength makes fiber a preferred material form for many applications ranging from clothing to reinforcements for aerospace structures. Fibrous materials in nanometer scale are the fundamental building blocks of living systems. From the 1.5-nm double helix strand of DNA molecules, including cytoskeleton filaments with diameters around 30 nm, to sensory cells such as hair cells and rod cells of the eyes, nanoscale fibers form the extracellular matrices or the multifunctional structural backbone for tissues and organs. Specific junctions between these cells conduct electrical and chemical signals that result from various kinds of stimulation. The signals direct normal functions of the cells such as energy storage, information storage and retrieval, tissue regeneration, and sensing. Analogous to nature’s design, nanofibers of electronic polymers and their composites can provide fundamental ISBN: 1-58883-062-4/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

building blocks for the construction of devices and structures that perform unique new functions that serve the needs of mankind. Other areas expected to be impacted by the nanofiber based technology include drug delivery systems and scaffolds for tissue engineering, wires, capacitors, transistors and diodes for information technology, systems for energy transport, conversion and storage, such as batteries and fuel cells, and structural composites for aerospace structures. Considering the potential opportunities provided by nanofibers, there is an increasing interest in nanofiber technology. Amongst the technologies including the template method [1, 48], vapor grown [2], phase separation [3], and electrospinning [4–20], electrospinning has attracted the most recent interest. Using the electrospinning process, Reneker and Chun [4] demonstrated the ability to fabricate nanofibers of organic polymers with diameters as small as 3 nm. These molecular bundles, self-assembled by electrospinning, have only six or seven molecules across the diameter of the fiber! Half of the 40 or so parallel molecules in the fiber are on the surface. Collaborative research in MacDiarmid and Ko’s laboratory [5] demonstrated that blends of nonconductive polymers with conductive polyaniline polymers and nanofibers of pure conductive polymers can be electrospun. Additionally, in-situ methods can be used to deposit 25-nm-thick films of other conducting polymers, such as polypyrrole or polyaniline, on preformed insulating nanofibers. Carbon nanotubes, nanoplatelets, and ceramic nanoparticles may also be dispersed in polymer solutions, which are then electrospun to form composites in the form of continuous nanofibers and nanofibrous assemblies [6]. Specifically, the significance of fiber size effect has been recognized.

1.1. Effect of Fiber Size on Surface Area One of the most significant characteristics of nanofibers is the enormous availability of surface area per unit mass. For fibers having diameters from 5 to 500 nm, as shown in Figure 1, the surface area per unit mass is around 10,000 to 1,000,000 m2 /kg. In nanofibers that are 3 nm in diameter, and which contain about 40 molecules, about half of the molecules are on the surface. As seen in Figure 1, the high surface area of nanofibers provides a remarkable capacity

Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 6: Pages (727–738)

Nanofibers

728

Silica gel Carbon black

Figure 1. Effect of fiber diameter on surface area. Reprinted with permission from D. H. Reneker.

for the attachment or release of functional groups, absorbed molecules, ions, catalytic moieties, and nanometer-scale particles of many kinds.

1.2. Effect of Fiber Size on Bioactivity Considering the importance of surfaces for cell adhesion and migration, experiments were carried out in the Fibrous Materials Laboratory at Drexel University using osteoblasts isolated from neonatal rat calvaria and grown to confluence in Ham’s F-12 medium (GIBCO), supplemented with 12% Sigma fetal bovine on PLAGA sintered spheres, 3D braided filament bundles, and nanofibrils [7]. Four matrices were fabricated for the cell culture experiments. These matrices include, (1) 150- to 300-
m PLAGA sintered spheres, (2) unidirectional bundles of 20-
m filaments, (3) 3D braided structure consisting of 20 bundles of 20-
m filaments, (4) nonwoven matrices consisting of nanofibrils. The most proliferate cell growth was observed for the nanofibrils scaffold as shown in the thymadine–time relationship illustrated in Figure 2.

1.3. Effect of Fiber Size on Electroactivity The size of conductive fiber has an important effect on system response time to electronic stimuli and the current carrying capability of the fiber over metal contacts.

In a doping-de-doping experiment, Norris et al. [8] found that polyaniline/PEO submicron fibrils had response time an order of magnitude faster than that of bulk polyaniline/PEO. There are three types of contact to a nano polymeric wire: ohmic, rectifying, and tunneling. Each is modified due to nano effects. There exist critical diameters for wires below which metal contact produces much higher barrier heights, thus showing much better rectification properties. According to Nabet (unpublished report), by reducing the size of a wire we can expect to simultaneously achieve better rectification properties as well as better transport in a nano wire. In a preliminary study [64], as shown in Figure 3, it was demonstrated, using submicron PEDT conductive fiber mat, that significant increase in conductivity occurs as the fiber diameter decreases. This could be due to intrinsic fiber conductivity effect or the geometric surface and packing density effect or both as a result of the reduction in fiber diameter.

1.4. Effect of Fiber Size on Strength Materials in fiber form are unique in that they are stronger than bulk materials. As fiber diameter decreases, it has been well established in glass fiber science that the strength of the fiber increases exponentially due to the reduction of the probability of including flaws. As the diameter of matter gets even smaller as in the case of nanotubes, the strain energy per atom increases exponentially, contributing to the enormous strength of over 30 GPa for carbon nanotube. Although the effect of fiber diameter has long been recognized, the practical generation of fibers down to the nanometer scale was not realized until the rediscovery and popularization of the electrospinning technology by Professor Darrell Reneker almost a decade ago [9]. The ability to create nanoscale fibers from a broad range of polymeric materials in a relatively simple manner using the electrospinning process coupled with the rapid growth of nanotechnology in recent years have greatly accelerated the growth of nanofiber technology. Although there are several alternate methods for generating fibers in a nanometer scale, none matches the popularity of the electrospinning technology due largely to the great simplicity of the electrospinning process. Accordingly, our review will be focused 450 140

400 350 300 250 200 150 100

205

50 260

0 2.1

Figure 2. Effect of size on cell growth. Reprinted with permission from [47], F. Ko and C. Laurencin, “Society of Biomaterials Proceedings,” 1998. © 1998, Society of Biomaterials.

2.15

2.2

2.25

2.3

2.35

2.4

Log of fiber diameter (nm)

Figure 3. Conductivity vs. fiber diameters of a PEDT polymer.

2.45

Nanofibers

on the electrospinning technology. We will begin with a general overview of the electrospinning technology. The significance of the various processing parameters in solution electrospinning is discussed, followed by a review of the limited work on melt electrospinning. The structure and properties of the fibers produced by the electrospinning process are then examined with particular attention to the mechanical and chemical properties. There is a gradual recognition that the deceivingly simple process requires a deeper scientific understanding and engineering development in order to capitalize on the benefits promised by the attainment of nanoscale and to translate the technology from a laboratory curiosity to a robust manufacturing process. Some of the initial efforts in modeling of electrospinning process are reviewed in Section 6. This chapter is closed with a review of the potential applications of nanofibers and a conclusion and projection of the future direction of nanofiber technology.

2. FORMATION OF NANOFIBERS Perhaps the history of this subject begins in 1745 when Bose created an aerosol spray by applying a high potential to a liquid at the end of a glass capillary tube. The ideology behind what is now known as electrospinning was furthered when Lord Rayleigh calculated the maximum amount of charge which a drop of liquid can hold before the electrical force overcomes the surface tension of the drop [10]. On October 2, 1934, Anton Formhals [11] was issued a patent for a process capable of producing monofilament fibers on a micron size scale using the electrostatic forces generated in an electrical field on a variety of solutions. The patent describes how the solutions are passed through an electrical field formed between electrodes in a thin stream or in the form of droplets in order to separate them into groups of filaments. This process, later to become known as a variant of electrospinning, allows the threads, which are repelling each other when placed in the electrical field, to pile up parallel to each other on the filament collector in such a way that they can be unwound continuously in skeins or ropes of any desired length. In December, 1969, Sir Geoffrey Taylor published a paper titled “Electrically driven jets” describing the shape of the droplet at the end of a tube filled with a viscous fluid when applied to an electrical field. Taylor first introduced the formation of a cone and the resulting jet that forms on the apex known nowadays as the “Taylor cone” [12]. Taylor’s contribution was actually the measurement of the potential required to form the Taylor cone for a variety of viscous liquids and then the comparison of these measurements with mathematical calculations. In his paper the derivation began with the expression for the equilibrium state of a droplet at the end of a pressurized tube. The coefficients for the electrostatic potential were then generated by observing the deflection of charged solutions at the end of an inverted capillary:
 2L 3 H2 Vc2 = 4 2 ln − 0117R (1) L R 2 where Vc is the critical voltage, H is the separation between the capillary and the ground, L is the length of the capillary,

729 R is the radius of the capillary, and  is the surface tension of the liquid. A similar relationship was developed [13] for the potential required for the electrostatic spraying from hemispherical drop pendant from a capillary tube:  (2) V = 300 20r

where r is radius of the pendant drop. In each case, the conducting drop was assumed to be surrounded by air, and suspended at a stable distance from the capillary tube. These equations are the appropriate physical models for the formation of a droplet of slightly conducting, monomeric fluids. By examining a small range of fluids, Taylor determined that a 493
equilibrium angle balanced the surface tension with the electrostatic forces, and used this value in his derivation. However, it was later shown that the conductivity and the viscosity of the fluid both play vital roles in the electrostatic atomization process and can greatly influence the equilibrium angle as well as other aspects of the process [4]. This dependence on conductivity and viscosity was missing from the previous two equations; however, this relationship between surface tension and applied voltage still serves as a useful guide for slightly conducting, medium-tolow viscosity solutions. Baumgarten advanced the field by being amongst the first to take the existing atomization techniques and apply them to a polymer solution [14]. He was able to determine the voltage required in order to be capable of electrospinning a PAN/DMF solution, and he also observed a dependence of the fiber diameter on the solution viscosity described through the following equation: d = 05

(3)

where d is fiber diameter, and  is solution viscosity (in poise). Baumgarten also showed that the diameter of the jet reached a minimum after an initial increase in field strength and then became much larger with increasing fields. This effect was caused by the feed rate of the polymer solution being pulled through the capillary and illustrates one of the many complexities of the electrospinning process. That is, increasing the field does increase the electrostatic stresses, therefore creating smaller diameter fibers, but it also reduces the size of the Taylor cone and draws more material out of the syringe. Larrondo and Manley observed that the fiber diameter decreased with increasing melt temperature as a result of the decreasing value of the viscosity due to the free movement of the molecular chains. They were able to draw a qualitative correlation between diameter and viscosity [15]. They also determined that doubling the applied electric field decreased the fiber diameters by roughly half. Larrondo and Manley also showed that the strain rate in the spinning jet is an important parameter for orienting the polymer molecules along the fiber axis. In 1986, another paper was published by Hayati et al. [16] studying the effect of the electric field and the surrounding environment on pendant drops and the factors affecting the formation of stable jets. In this paper it was concluded that

Nanofibers

the liquids conductivity is a major factor in the electrostatic disruption of the surface. For example, with conducting liquids such as water, very unstable streams were produced. With insulating liquids such as paraffin oil, no disruption occurred due to lack of sufficient free ions in the bulk liquid. Stable jets having a conical base were only produced with semiconducting liquids (nonpolar liquids with dissolved ionic materials). They also concluded that the cone angle at the base of the jet increased, whereas its length decreased, with an increase in applied voltage. This was in agreement with the experimental results that Baumgarten was observing. At higher voltages, there have been reports of secondary jets splaying from the primary jet. The number of these splays increases with an increase in the applied field. As the electric field is increased further, the shape of the droplet deforms and in some cases a phase is present in which the droplet simply drips onto the collection plate. Continuing to increase the applied electric field, a potential is reached that is slightly larger than that needed to cause instability of the liquid meniscus. At this critical potential, the liquid ejects either a small droplet or a long filament as was observed by Baumgarten and Lorrondo and Manley. In case of an insulating liquid, the surface charge is small and hence no appreciable electrostatic force can build up at the interface. The liquid behaves as a dielectric in a nonuniform field which will seek the region of highest field intensity; in this case, the tip of the capillary. In the case of a highly conducting liquid such as water, when the voltage was increased, the pulsating and dripping modes could be observed. However, by further increasing the potential, very unstable streams were produced from the drop which whipped around in different directions. In case of semiconducting liquid such as Isopan M + butanol (conductivity = 33 × 10−7 S/m1 ), the stable jets could be produced, using an applied voltage of 10–12.5 kV. With an increase in voltage, the conical base of the jet, near the capillary, expands as its cone angle widens, and the cone height becomes shorter. By measuring the critical voltage for stable jet formation using these capillaries at a constant flow rate [12], it become clear that the small capillaries were most suitable for the formation of stable jets of highly conductive liquids. However, with low conductivity liquids, wide capillaries were needed in order to form a stable jet. For a conductivity in the intermediate range (714 × 10−9 to 222 × 10−6 −1 m−1 ), the effect of capillary diameter, at constant flow rate, altered the velocity of the liquid issuing from the capillary, the velocity being measured as the ratio of the mass flow rate to the cross-sectional area of the tube [16, 17]. The description of electrospinning phenomenon, as seen in Figure 4, was introduced by Smith in 1994 [18]. In his paper he derived the relationship between the capillary radius, capillary plane distance, and the applied voltage:
   2Tr cos 0c 05 4h V0 = A1 ln (4)

0 rc where T is surface tension, 0 is cone half angle, and 0 is permittivity of free space. Finally he reached the following three conclusions: 1. As capillary radius increases, the onset potential should increase.

Ex t Sc rud re ing w

730

10 cm

45 deg. 10 cm 10 cm

Copper Plate

High Voltage

Figure 4. Schematic of an electrospinning station.

2. As the plane distance increases, the onset potential should increase. 3. As the surface tension increases, the onset potential should increase. In 1995, Doshi and Reneker [9] started using electrospinning as a technique to produce small diameter fibers. In their paper they used poly(p-phenylene terephthalamide) to produce Kevlar fibers with superior physical properties using a dry-jet-wet spinning technique assisted by electrostatic charges. Monofilament Kevlar fibers ranging from 13 to 18
m were produced with an applied voltage of 12 to 18 kV at a distance of 3 cm in a vertical arrangement. Doshi and Reneker [9] then shortly described the electrospinning process, processing conditions, fiber morphology, and some of the possible uses of electrospun fibers made from polyethylene oxide (PEO) of (molecular weight) Mw = 145,000 g/mol. They found that for viscosities below 800 centipoise, the polymer solution was too dilute to form a stable jet, and at viscosities higher than 4000 centipoise it was difficult to form fibers due to a lack of sufficient solvent in the solution. Doshi and Reneker [9] used concentrations varying from 1% to 7%, by weight, and concluded that as the concentration increases, the required voltage to successfully spin is increased. For example, for concentrations of 2.5% and 5%, by weight, the required voltages to electrospin were 9 kV and 12 kV, respectively. This paper also observed that the diameter of the jet increased as the distance between the spinneret and the target decreased due to the shorter time period the stream had to elongate. More than 20 polymers including PEO, nylon, imides, DNA, aramids, and polyaniline have been electrospun by Reneker’s group [4]. Buchko et al. [13] proved that polymeric solutions behave differently compared to monomeric liquids during electrostatic atomization in that they persist as elongated jets over a much grater distance. A wide variety of synthetic and natural polymers were electrospun from solution and several polymers including poly(propylene) and poly(ethylene) were

Nanofibers

electrospun from the melt. One major difference in the production of fibers from different mediums is the final size. When electrospinning from solution, fibers on the nanometer scale have been successfully produced. On the other hand, melt spun fibers were considerably larger, ranging from tens to hundreds of microns [15]. Nanofibers of aromatic heterocyclic polybenzimidazole (PBI), with a diameter of 300 nm, were later produced by Kim and Reneker [10]. They produced sheets of nonwoven fabric about 8 cm wide and 50 cm long with a compressed thickness of a few microns. The mass per unit area of these sheets was a couple of g/m2 . The electro-spun PBI fibers were also found to be birefringent, which indicated that the molecules were to some degree aligned. Although a vast majority of the research devoted to the production of nanofibers has concentrated on electrospinning, it is important to mention the other experiments that have been and continue to be utilized. It was shown that nanofibers can be made using a radiation polymerization of vinyl monomers trapped in clathrate crystals. This process does not yet allow for the formation of continuous nanofibers but allows for the formation of fibers several microns in length [1]. The architecture of the clathrates is quite similar to that of a tunnel. Multiple tunnels can be placed next to one another and it is possible to have highly oriented nanofibers once the polymerization has occurred. Other research has mimicked the process to make carbon nanotubes to produce carbon nanofibers using a chemical vapor deposition (CVD) process. In a horizontal tubular reactor, benzene can be used for the carbon source, hydrogen as a carrying gas, and thiophene as the growth promoter. The tube is heated to 1373 K at a speed of 25
C per minute allowing hydrogen gas to flow into the benzene solution containing thiophene and then into the reaction tube. The ratios of the above can be changed to affect the final diameter of the vapor grown carbon nanofibers [19]. Researchers have been able to successfully produce nanofibers in bulk ranging from 50 to 200 grams per experiment. Using this technology, fibers ranging from 50 nm to several hundred nanometers have been produced [2]. Again, the limiting aspect of this technology is the capability of producing continuous nanofibers. One final method that has been used to produce nanofibers recently is a method called “islands in the sea” [3]. This method is a combination of two polymers, one implanted inside the other. Islands in the sea uses a special spinneret that allows two polymers to be extruded at once. One polymer acts as the core and another polymer acts as the sheath. Once the fiber(s) has been extruded from the melt, the sheath layer is dissolved using some known solvent, leaving behind several smaller core fibers. It is obvious that the more islands that can be packed into the sea, the smaller the end diameter will be. Hills Inc., in collaboration with North Carolina State University, has produced fibers with up to 3000 islands in the sea, resulting in fibers as small as 500 nm [20]. This may be the best and most efficient way to produce continuous and highly aligned nanofibers, but where this process suffers is the extreme cost that is experienced with such high-tech machinery.

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3. SOLUTION ELECTROSPINNING 3.1. Introduction Over the years, many papers have been published observing the effects of a single parameter on the electrospinning process. Researchers have developed a relationship between the molecular weight and the concentration to describe the spin-ability of PEO in an aqueous solution [9]. The observation was made that the jet will break up more readily when a lower viscosity solution is being used. Thus, the solution or melt viscosity was shown to affect both the processing window for electrospinning and the diameter of the fibers that were being produced. Numerous polymers have been electrospun by several groups across the country as shown in Table 1. With solvents of varying pH, polymers with molecular weights ranging from 10,000 to 300,000 and above have been electrospun. An accurate statement can be, “If it has been made, someone has tried to electrospin it.”

3.2. Processing Parameters 3.2.1. Voltage One of the most important and recent studies made by Deitzel et al. [21, 53, 59] on the effect of processing variables on the morphology of electrospun nanofibers concluded that the morphology of the nanofibers produced from PEO is influenced strongly by parameters such as feed rate of the polymer solution, electrospinning voltage, and other properties of the solution such as concentration, viscosity, and surface tension. They also concurred that an increase in the voltage changed the shape of the surface from which the electrospinning jet originated. This shape change was correlated with an increase in the number of beaded defects forming amongst the electrospun fibers as seen in Figure 5.

Table 1. List of various polymers that have been electrospun. Polymer Rayon Acrylic resin PE, PPE PEO PPTA (Kevlar) Polyester DNA PAN Styrene-butadienestyrene triblock PVA/nylon 6,6 PAN and Pitch PANi/PEO PEO Silk CNT/PAN Polyurethane Nylon-6 Poly(ethylene-co-vinyl alcohol)

Solvent dimethyl formamide melted water 98% sulfuric acid 1:1 dichloromethane: trifluoroacetic acid 70:30 water:ethanol dimethyl formamide 75:25 tetrahydrofuran/ dimethylformamide n/a dimethyl formamide chloroform water HFA-hydrate DMF DMF 95:5 HFIP/DMF 2-propanol/water

Ref. [11] [14] [15] [4] [42] [49] [27] [5] [45] [44, 61] [43, 63] [8] [21] [51, 54, 62] [25] [58] [60] [57]

Nanofibers

732

DMF-MEK 25–75

DMF-MEK 50–50

DMF-MEK 75–25

DMF-MEK 100

17 wt%

20 wt%

23 wt%

Figure 5. Effect of viscosity on fiber morphology.

3.2.2. Concentration/Viscosity Deitzel [53, 59] also noticed that the diameter of the electrospun PEO fibers increased with solution concentration according to the power law relationship while other noticed, as in Figure 6, that it followed the function of x2 . This observation was in agreement with others that observed that the polymer’s ability to be electrospun was directly dependent on its viscosity. Also, general properties such as surface area of the electrospun fiber mats were evaluated. The textiles were found to have specific surface area in the range of 10– 20 m2 /g. It was also stated that the analysis of the produced fibers by WAXD and DSC showed poor development of any crystalline order.

3.2.3. Berry Number In his study of intrinsic viscosity, Berry developed a number called the Berry Number (Be). Be was used as a measure of molecular conformation [22–24]. This number was the product of the intrinsic viscosity and concentration. Han [50] utilized the work of Berry in an attempt to further understand electrospinning. It has been well documented that the concentration has a major role on the electrospinning process. Han discovered, with PAN, that if the Be was lower than 1, beads would be formed because the viscosity of the solution would not be sufficient to hold together during the electrospinning process. In the other cases (a Be from 1 to 4), the fiber diameters steadily increased as seen in the below chart. Han’s study was the first to use Be for electrospinning. It was

later shown by Ali that the Be is a function of the polymer being spun and the numbers are not contained between 1 and 4, but this remains an effective way to classify the polymer solution [25].

3.2.4. Alternative Fields In another study, Deitzel et al. [26] tried to control the deposition area of the electrospun PEO fibers by using multiple field electrospinning apparatus that applied a secondary external field of the same polarity as the surface charge on the jet. This mechanism allowed for a greater control over the deposition of the electrospun fiber on a surface and permitted collection of the electrospun fibers in alternative forms to nonwoven mats. After analysis, the yarns produced using this new electrospinning technique indicated the presence of a slight molecular orientation and a poorly developed crystalline microstructure within the fibers. In addition to what is listed above, there are many factors that can be altered in order to achieve different nanofibrous mats. Deitzel stated that increasing the voltage increased the number of beads that are observed on the created fibers. Other researchers have noted that increasing the voltage will also decrease the fiber size up to a critical value, after which the fiber size will begin to increase as a result of the diminishing Taylor cone.

3.2.5. Spinning Distance/Spinning Angle Two other common parameters that are frequently changed are the spinning distance and the spinning angle. It is commonly noted that the further the increase between the anode and cathode, the finer the fiber diameter will be as a result of having more time and distance to elongate itself. Many angles have been experimented with, 0
 45
, and 90
being the most common. Although little evidence was seen to affect fiber diameter, fiber uniformity was often increased at 45
because the flow rate was often decreased and gravity was not allowed to form as many beads.

3.2.6. Spinneret Diameter As touched upon earlier, the spinneret diameter has a major effect on the size of the nanofibers produced. The smaller the spinneret, the smaller the fibers tended to be, but the smaller diameter also presented itself to be a problem when higher viscosity fluids were used. It is a constant trade-off between which type of material is being worked with and what size diameter is hoped to be obtained. In addition to the size of the spinneret used, shape has also been recorded to play a major role in electrospun samples. Whether the tip of the spinneret is flat like an extruder or sharp like a syringe, many interesting morphological features were discovered.

3.2.7. Annealing

Figure 6. Effect of concentration on fiber diameter.

One tactic that is used in the industrial production of fibers that is often overlooked in the realm of electrospinning is annealing. Annealing is a form of post-treatment that heats the polymer while stretched in order to allow the chains to align themselves, giving the fiber far superior mechanical properties. What little work that has been done in this area

Nanofibers

has shown promising results, but the problem resides in the capability of isolating single samples to be annealed.

4. MELT ELECTROSPINNING There has been little work published in the area of melt electrospinning. The first work was published by Lorrondo and Manley in 1981 [15] and nothing has been published since. There are many papers that include solution or melt in their titles, but the work that was done has concentrated exclusively on solution spun fibers. There are several groups throughout the world trying to break through with new results, including, but not limited to, Drexel University and the University of Akron. Traditionally melt spun polymers such as polyester [49], polyethylene, and polypropylene have been attempted to be spun by several groups. These polymers have been spun using different temperatures, different voltages, and in different atmospheres. The main reason that there has been nothing published in the last 20 years is that it has been proven to be very difficult to produce fibers in the nano range. In solution spinning, it is believed that one major contributor to the decrease in diameter is the evaporation of the solvent. Solution spun fibers contain as much as 90% solvent and 10% polymer. Simply by understanding that polymer melts contain 0% solvent, an order of magnitude increase in fiber diameter is realized. In addition to the lack of solvent that helps loosen up the molecular entanglements, melt spinning suffers other drawbacks. One of these hindrances is the effect of the temperature gradient between the polymer and the surrounding temperature. If the surrounding temperature is too cool, the ejected polymer will quench upon exiting the spinneret, preventing any decrease in diameter and orientation of molecular chains leading to improved mechanical properties. If the surrounding temperature is too hot, then the ejected polymer will fuse to itself upon collecting on the target. Temperature of the melt is another key issue when melt electrospinning polymers. In solution, it has been readily shown that the electrospinning process is highly dependent on viscosity. Polymeric melts are inherently much more viscous than polymer solutions that are being electrospun. Therefore, in order to get the polymer melt to a viscosity that is capable of being electrospun, the melt temperature is often raised well above the melting temperature. If the polymer being used has a degradation temperature that is relatively close to the melting temperature, it will likely not be electrospun. Analyzing the results that have been seen at conferences around the world, the same processing parameters that apply for solution spun nanofibers apply to melt spun nanofibers. Melt spinning continues to be a hot topic and would be the ideal way to make nanofibers by electrospinning because of the incredibly high yield as compared to solution electrospinning. As referenced before, the islands in the sea method is a form of melt spinning but may not be the most feasible of methods due to the extremely high cost of the machinery.

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5. STRUCTURE AND PROPERTIES Table 2 represents the spectrum of instruments used to test nanofibers. As shown, instruments are capable of analyzing everything from a few angstroms in diameter to several meters. As more and more machines are used to study the characteristics of electrospun fibers, a better understanding of the process is being developed. In the future, more sophisticated machines will be developed to draw a more accurate portrait of the process, but until that time, researchers will have to be satisfied with what is at hand, such as the following. The scanning electron microscope (SEM) is one of the most popular and powerful tools that has been used in the literature [4, 9, 15, 27] to measure the diameter of electrospun fibers as well as the general morphology. Kim and Reneker [10] showed that SEM could also be used to examine the fibers’ cross section. They stated that the electrospun fibers are mostly circular in cross section but other shapes such as ribbons and coils could be produced. This method is extremely easy to use and more importantly, the sample size required to get useful data is extremely small, less than 1 mm2 . One drawback of this equipment is that a gold coating is usually needed to enable viewing the fibers and this coating slightly alters the accuracy of the actual diameter. The gold sputtering process typically adds a 04-nm layer to the fibers. This can be ignored with larger diameter fibers but with a 4-nm fiber, it becomes more of a concern. Using an environmental scanning electron microscope (ESEM), the gold coating process can be skipped if the micrographs are taken in a low vacuum. However, if the general shape and size of the fibers are needed, SEM and ESEM are fast and easy ways to derive the information that is needed. Another methodology that has been utilized to measure the diameter of smaller diameter samples is transmission electron microscopy (TEM). Fang and Reneker [27] analyzed the electrospun DNA by using TEM and reported diameters as low as 62 nm. Ko et al. [28] used the TEM to study the morphology and order versus disorder for the electrospun PAN fiber, PAN/CNT, and PAN/GNP nanocomposites. Also, Ye et al. [29] used TEM technique to study the alignment of singlewalled carbon nanotubes (SWNT) in two different electrospun polymers (PLA and PAN), as seen in Figure 7, as well as to study the effect of the heat treatment of electrospun PAN/CNT composites on the alignment of the CNT. Other researchers have utilized equipment such as X-ray diffraction (XRD) and differential scanning calorimetry (DSC) to observe whether there is any degree of crystallinity in the electrospun samples. To this day, the argument persists, with some parties arguing that the samples lack crystallinity while others say that the intense strains to which Table 2. Instrumentation available at various size scales. FIBER FORM: PROCESS:

Scale (m):

CVD –10

SWNT MWNT ESNF Whiskers Fibers Wire Electrospinning Spinning Drawing Extrusion

10 10 atomic

–9

–8

10 nano

10

–7

–6

–5

10 10 micro

–4

10 10 meso

–3

–2

10 10 macro

AES XPS EDX µ-Raman µ-FTIR µCOMPOSITION : EELS TESTBEDS: STRUCTURE : TEM STM AFM XRD SEM Light microscopy PHYSICAL : AFM Nanoindentation MEMS Test Devices Conventional

–1

Nanofibers

734 10 nm

direction to one day being capable of producing woven and knitted fabric out of nanofibers.

5.1. Mechanical Properties

200 nm

5 nm

Figure 7. Carbon nanotubes inside of PLA (top) and PAN (bottom).

the samples are subjected are sure to produce highly crystalline samples. When spinning from solution, there have been some reports by Deitzel [21] that limited crystallization occurs but not to a high degree using PEO. On the other hand, when spinning from the melt, Lyons [65] demonstrated that a crystallization peak was observed in PET. This peak is consistent in what is seen in quenched polymer systems lacking crystallinity. An important note to mention is the misnomer that is often associated with fibers on this scale. Researchers will often say that a 500-nm fiber was produced when in reality this is the same as a 0.5-
m fiber. There are several groups that have been doing this with a variety of polymers, yet there are many other polymers that have been unable to break the 100-nm barrier. There have been reports from Reneker of producing fibers as small as 4 nm, yet while dealing with melt electrospinning, many of the fibers are on the micron scale. Although most of the fibers that are produced though electrospinning are in the form of cylinders, there are occasions when tubes, ribbons, coils, and beaded structures can be produced. Tubes have been discovered by several groups and it was shown by Ali [25] that there was a high likelihood of forming tubes when electrospinning into water. In a similar fashion, ribbons are more than likely the result of collapsed tubes. Polymeric nanotubes elude reproducibility. Today, researchers are focusing on this problem and they are developing more advanced techniques that will allow for continuously produced nanotubes that can be used for drug delivery or hydrogen storage. The most common way of collecting the nanofibers is in the form of 2D fibrous nonwoven mats. Mats such as these are well suited for filtration and tissue culturing but are not sufficient if single fibers or yarns are desired. It has been shown by Ko [30] that nanofibrous yarns can be directly produced from the electrospinning process under the precise processing parameters with certain polymers. These yarns tended to be on the micron scale but were composed of numerous fibers that were on the nano scale that were naturally twisted together throughout the process to form the yarn. This was the first step in a positive

180 E c (AFM Experiments.) = 15.734Wt% + 66.237

160

Modulus (GPa)

500 nm

Measurement of elastic properties of electrospun fibers is very limited in the literature and only a few papers have worked with advanced techniques to determine the elastic properties of the material. The atomic force microscope (AFM), invented by Binning, Quate, and Gerber in 1986, was developed to exploit contact and noncontact forces for imaging surface topology and to study new physical phenomena at microscopic dimensions. The heart of the AFM is the cantilever and tip assembly, which is scanned with respect to the surface. For contact imaging the sample is scanned beneath the atomically sharp tip mounted on the cantilever providing a repulsive force. Atomic resolution can be obtained by very light contact and measuring the deflection of the cantilever due to the repulsion of contacting atomic shells of the tip and the sample [29]. Silicon device technology has introduced microfabrication techniques to produce silicon, silicon oxide, or silicon nitride micro-cantilevers of extremely small dimensions, on the scale of 100
m × 100
m × 1
m thick. Micro-cantilevers exhibit force constants around 0.1 N/m. In contact imaging, the measurement of cantilever deflection is performed directly (quasi-statically) as the tip is being scanned over the surface [29]. Ko et al. [30] used this AFM technique to measure the elastic modulus of a single fiber produced from an electrospun PAN polymer solution. The atomic force microscope is one of the most powerful and useful techniques that has been used to measure the elastic properties of the electrospun fibers in addition to being able to determine diameter. Kracke and Damaschke [31] used the AFM to measure the nanoelasticity of thin gold films. Later, Ali [25] showed in Figure 8 similar results obtained using AFM. They based the calculation of the modulus on the following relationships: 
2 dF (5) = E ∗ A05 d h  05     1 − 12 1 − 22 1 = + (6) E∗ E1 E2

E c (Rule of Mixture) = 3.4783Wt% + 66.237

140 120

Rule of Mixture

100 80 60 40 20 0

1

2

3

CNTs in Wt%

Figure 8. Effect of carbon nanotubes in composites.

4

5

Nanofibers

735

where E1  E2  1 , and 2 are the elastic moduli and Poisson numbers of the sample and the tip, respectively, A = r 2

(7)

F = 2rE h

(8)

∗

where r is tip radius, and h is deformation between tip and sample. Sundararajan et al. [32] used the AFM technique to evaluate the elastic modulus of nanobeams as well as their bending strength. By using this technique, the measured values were comparable to those measured in bulk. Mechanical properties and the deformation behavior of materials having ultrafine microstructures can also be illustrated by using a nanoindentation machine following the same guidelines. Finally, micro-Raman spectroscopy (MRS) has been used to measure the load transfer in short-fiber, high-modulus/epoxy composites as a function of angle to loading direction [33] as well as to monitor the strain in short fiber composites as a result of fiber to fiber interactions.

5.2. Chemical Properties Raman spectroscopy is one of the more powerful techniques used to detect the presented elements especially on the nano scale. It is also extremely useful in investigating the state of carbon in detail due to its sensitivity to changes in translational symmetry. Duchet et al. [34] used Raman spectroscopy to correlate the molecular structure of the nanoscopic tubules with their conducting properties. Raman spectroscopy has been used for the characterization of carbon nanotubes (CNT) by many researchers [35]. Rao et al. [36] reported that there are two frequencies or bands of the single-walled carbon nanotubes (SWCNT) that can be detected by Raman spectroscopy. One is known as the radial band at 160 cm−1 and the other is called the tangential band at 1590 cm−1 . They showed that the first band could be detected at higher Raman shift values (10 cm−1 higher) when it was dispersed in a solution. The ratio (I (D-band)/I (G-band)) has been crosscorrelated to crystallite size using X-ray diffraction data. This correlation is given by the following equation:
−1 I (9) La = 44 D IG where La is the crystallite size in (nm). Also, Huang and Young [37] showed a linear relationship between the ID /IG band and the 1/La for commercialized carbon fibers produced from both PAN and PITCH. In the same paper they showed that there is a variation of the Raman spectra between the skin and core regions. These spectra show that ID /IG decreases from core to skin, which indicates smaller crystallite values in the fiber core more so than on the skin. Laser Raman spectra have been used by Matsumoto et al. [38] to examine the carbon nanofibers and films produced by hot filament-assisted sputtering and it was found that the films showed three Raman bands at 1581, 1368, and 1979 cm−1 . In this paper they explained the Raman peaks as follows: the first two peaks belong to polycrystalline

graphite and the last peak corresponds to carbine, one of the allotropes of carbon.

6. MODELING OF THE ELECTROSPINNING PROCESS It is crucial that there exists a theoretical understanding of the electrospinning process. With this knowledge, specific parameters can be fine-tuned in order to maximize the efficiency of the process. To date, there have only been a handful of attempts made to theoretically quantify the electrospinning process. In 1971, the first was perhaps Baumgarten who attempted to identify the electric field maps to determine the jet radius. This approach was crude and met only limited success. Ten years later Larrondo and Manley continued to define the velocity gradients and electric fields and also began the first work of molten bead deformation in an electric field. An analytical modeling of a steady-state jet flow in the electrospinning process made by Spivak et al. [39, 47, 52] showed the applicability of using the power law asymptotic to a wide class of fluid described by the nonlinear Oswald– deWaele law. This group used a one-dimensional differential equation to represent their jet radius and, when compared against experimental results, fared quite well. In 1999, Reneker et al. [40] submitted the first attempt at a mathematical model that predicted the path of an electrospun fiber from solution. What was unique about this submission is that the group incorporated the instability region and plotted its results in three dimensions. Although capable of predicting the path for the fiber to traverse to a relatively accurate degree, this model was not capable of determining the fiber’s diameter upon hitting the target. Shin et al. [41] continued work on this challenging puzzle by describing the jet behavior in terms of known fluid properties and operating conditions. One of the main differences between this group and the Reneker group is the incorporation of current. Shin et al. described the behavior of two competing instabilities and summarized their results that closely mimic experiment in terms of operating diagrams and delineating regimes of operation in electrospinning. The evolution of the model has become more and more accurate, but there is still no exact model to predict what the ending fiber diameter will be. All of the models that have attempted to predict the fiber diameter focus on solution spinning; melt spinning has only recently been modeled by Lyons et al. [65]. Many questions, such as what happens to the charge on the fiber while in transit, remain unanswered and a totally accurate model may never be developed. When a conducting liquid is supplied to a capillary nozzle at a low flow rate and when the interface between air and the liquid is charged to a sufficiently high electrical potential, the liquid meniscus takes the form of a stable cone, whose apex emits a microscopic jet. Farouk et al. (unpublished report) described an axisymmetric formulation of the flow and electric fields of the electrostatically driven meniscus through a capillary nozzle. Based on the governing equations, a numerical model has been developed to calculate the shape of the liquid cone and the resulting jet, the electric fields, and the surface charge density along the liquid surface. The liquid

Nanofibers

736 properties, liquid flow rate, and electrode configuration are needed as input parameters. Two-dimensional axisymmetric equations of continuity, momentum, and Gauss’ law are solved numerically.

7. APPLICATIONS OF NANOFIBERS Today’s researchers are trying to find as many uses as they can for electrospun fibers. To date, filtration is the primary market for these fibrous mats as researched by Gibson [46, 56]. There is an extremely small pore size that is capable of blocking most particles and hence is quite useful in the filtration industry. Today’s society is also directing research toward making protective clothing for military personnel to protect against chemical agents. Nanofibrous mats also have an incredible amount of surface area and industries such as the composite and biomedical industries are taking advantage through usage as wound dressings, tissue scaffolds, and practically any form of reinforcement agent for composites. Ko and Ali [28] have looked into forming carbon/carbon composites directly from the electrospinning line. PAN was electrospun and carbonized with nanotubes on the inside to form this triple carbon composite. If this fiber, or yarn in Ali’s case, is placed in a carbon resin, triple carbon composites can be made and used in ballistic proof plates and helmets of the future. The ideas are endless as to where an electrospun fiber or mat may be used in the future. The aerospace industry is currently working on developing space antennae, solar sails, light reflectors, and a variety of other devices used in the voids of space. In addition, MacDiarmid and Lec [5] have focused their efforts to the production of electronic systems and many forms of sensors. Biosensors have been an important element of the information revolution of the 20th century, and their role as an enabling factor of the incoming 21st century biotechnology and medical revolution will be essential. Modern biosensors developed with advanced microfabrication and signal processing techniques are becoming inexpensive, accurate, and reliable. Increasing miniaturization of biosensors leads to realization of complex analytical systems such as BioChemLab-on-a-Chip. This rapid progress in miniature devices and instrumentation development will significantly impact the practice of medical care as well as future advances in the chemical, pharmaceutical, and environmental industries. Important sensor parameters such as sensitivity, selectivity, response time, reproducibility, and aging depend directly on the properties of the sensing film [42, 43]. Sensitivity is of particular interest, because there is a strong need for detection of gases and biological substances and organisms at low concentration. A lower sensor detection limit allows direct measurement of the vapor from explosives and drugs or the presence of a few bacteria and viruses. It is a well-known fact that the sensitivity of a film is proportional to the surface area of the film per unit mass. Therefore new technologies capable of producing thin films with large surface area are of particular interest. In reality, these mats are simply a form of nonwoven fabrics. With that in mind, these electrospun fabrics have the potential to be used in any application that nonwovens are currently being used, such as brake pads, postal envelopes, and insulation, to name a few.

8. SUMMARY Electrospinning is a unique process that produces polymeric fibers having diameters ranging over several orders of magnitude, from the micrometer range typical of conventional fibers down to the nanometer range. Until now, the shape and pattern of produced fibers in all electrospun polymer solutions have taken an in-plane random pattern and are determined by the shape of the collector. A notable phenomenon has been recognized under certain spinning conditions for PAN solution, which enable the production of continuous yarn containing partially oriented nanofibers. This phenomenon opened the door to achieve many objectives such as the production of carbon-carbon nanocomposites by dispersing CNT’s of superior physical properties inside the PAN polymer solution and producing continuous carbon nanotube reinforced PAN based carbon nanocomposite fibrils. The present study is an attempt to optimize the electrospinning process for truly nanoscale fibers ( wa ). (C) Experimental setup. Reservoirs are made at both ends of the channel, and filled with DNA solution. Reprinted with permission from [62], J. Han and H. G. Craighead, Science 288, 1026 (2001). © 2000, American Association for the Advancement of Science.

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15 V

(a)

(b)

(c)

(d)

(e)

(f)

10 µm

Figure 12. The image presents a picture taken with an intensified CCD camera of the single molecule sizing device. The outline of the capillary has been added for clarity. Time series of the motion of single molecules of DNA under the influence of an electric field can be downloaded at http://www.hgc.cornell.edu/Microfluidics/Movies.html. Reprinted with permission from [65], M. Foquet et al., Anal Chem. 74, 1415 (2002). © 2002, American Chemical Society.

with the sacrificial layer technology, using material optically transparent and with low fluorescence background. The small channel dimensions facilitate single molecule detection, and minimize events of the simultaneous passage of more than one molecule through the measurement volume. The size of the fluorescent-labeled DNA molecules was determined from the number of photons per photon burst, each burst coinciding with the passage of a single DNA molecule. Interesting fabrication techniques for the confinement of biological molecules in ultra small spaces were shown by Cao and colleagues [66]. High-density arrays of nanofluidic channels (Fig. 13) were fabricated using nanoimprint lithography (NIL), reactive ion etching, and nonuniform deposition to both reduce the cross section of the nanochannels and, if desired, seal the channels. The resulting sealed channels had a cross section as small as 10 nm × 50 nm. Kameoka et al. [67] presented a refractive index sensor based on photon tunneling in a nanofluidic channel. A nanochannel was etched into a glass wafer, and enclosed by bonding of a second glass wafer to the first. The channel height is less than or comparable to the wavelength of the laser light used, allowing light transmission by photon tunneling if the angle of incidence of the laser light is larger than the critical angle. The photon tunneling probability depends strongly on the refractive index of the material in the nanofluidic channel, and can therefore be used to measure chemical composition changes of the fluid in the test volume. Nanofluidic pumps and flow sensors can be used in applications where accurate dosing of a chemical substance is required. Wu et al. [49] reported the fabrication and

Figure 13. (a), (b) Nanofluidic pillar array structures before and after sealing by the sputtering process. (c), (d) Top view images of half-sealed pillar array structures with 200 nm of SiO2 deposited and a completely sealed structure after 400 nm of SiO2 was deposited. The scale bars are all 500 nm. Reprinted with permission from [66], H. Cao et al., Appl. Phys. Lett. 81, 174 (2002). © 2002, American Institute of Physics.

successful testing of a thermal flow sensor fabricated on top of a surface micromachined channel. The sensor uses borondoped polysilicon thin-film resistors embedded in the silicon nitride wall of a microchannel as the sensing and heating elements. The sensors have demonstrated a flow rate resolution of 0.4 nL/min, as well as the capability to detect microbubbles in the liquid. Chmela et al. presented an on-chip hydrodynamic chromatography (HDC) system consisting of a shallow, large aspect ratio separation channel (1 m deep and 1000 m wide) fabricated using silicon and glass microtechnology [68]. The basic principle is that, in narrow conduits with a laminar flow, large molecules or particles (size 0.002–0.2 of the conduit size) are transported faster than smaller ones as they cannot fully access slow-flow regions near the conduit walls. Ramsey and co-workers investigated the electrokinetic (EK) transport of fluids and macromolecules through nanometer-confined channels fabricated using standard photolithography and wet chemical etching techniques [69, 70]. Experimental measurements of electroosmotic mobilities under electrical double-layer overlap conditions showed that the mobilities are reduced, in qualitative agreement with the theory [71]. The authors reported the use of EK transport under double-layer overlap conditions to generate hydraulic pressure, and to separate 100 and 1000 base pair fragments of dsDNA in solution. This could be achieved because of the flow profile in the nanochannel and the hydrodynamic radius of the two sizes of dsDNA molecules (Fig. 14). Unlike the case at microscale, the EK-induced flow profile for the submicron deep channel the authors used

Nanofluidics

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response

9.5 µm

320 nm

0

5

10

time (s) Figure 14. Electrokinetic migration of 100 and 1000 base pair dsDNA at two different channel depths (9.5 m and 320 nm). Reprinted with permission from [70], J. M. Ramsey et al., “Proceedings of Micro Total Analysis Systems 2002,” 2002, pp. 314–316. © 2002, Kluwer Academic.

nanotubes can be wet and filled by substances with low surface tension, the upper limit of the surface tension being less than 200 mN/m. The wetting cutoff value of the surface tension is still sufficiently high to allow wetting by water ( ∼ 72 nN/m) and most organic solvents ( < 72 nN/m). Ugarte and co-workers [75] filled open carbon nanotubes with molten silver nitrate by capillary forces. They concluded that there is a size constraint on the capillary filling of nanotubes, the capillarity being reduced for narrow tubes and the wetting depending on the cavity size. They explained this as a result of the increase of the nanotube–salt interface energy with decreasing curvature of the nanotube walls. The authors continued, demonstrating the formation of chains of silver nanobeads separated by high-pressure gas pockets as a result of the silver nitrate decomposition in-situ in an electron microscope Gogotsi et al. and Megaridis et al. [76–78] observed the complex behavior of the gas–liquid interface of aqueous liquid inclusions in carbon nanotubes, upon heating by an electron beam in the transmission electron microscope (TEM). The carbon nanotubes used were produced by hydrothermal synthesis, and had a wall thickness in the 10–25 nm range and an outer diameter of about 100 nm (Fig. 15). Sun and Crooks employed a 100 m long single carbon nanochannel with 150 nm diameter embedded in an epoxy matrix as a Coulter counter [79]. Polystyrene particles of ∼60 nm diameter were used as probes to study the hydrodynamic, electrophoretic, and diffusive transport properties of the nanochannel. The inner surface of the nanotube was found to be essentially charge neutral, so that electroosmotic effects could be neglected. The authors pointed out the advantage of using a single straight nanochannel to obtain information about fundamental modes of transport.

(320 nm) is expected to have a parabolic character. The smaller molecules can, therefore, approach the channel walls more closely, and experience lower flow velocity than the larger molecules. Kitamori and colleagues [72] studied the behavior of aqueous solutions of rhodamine 6G, sulforhodamine 101, and rhodamine B in nanometer-sized fused silica channels. By using time-resolved spectroscopy, the spectra of the solutions were determined in the nanochannels, and compared to those obtained in microchannels. From the analysis of the fluorescent decays, it was suggested that the solutions had lower dielectric constants and higher viscosities in the nanometer-sized channels. The channels were fabricated on fused silica substrates by a fast atom beam (FAB) etching method and hydrofluoric bonding of cover plates.

5.1.2. Bottom-Up Approach The inner hollow cavity of carbon nanotubes offers the possibility for intriguing nanoscale experiments if it could be filled with other materials in a systematic way [73]. Interesting experiments concerning the capillarity of carbon nanotubes have been caried out. Ajayan et al. [74], Dujardin et al. [73], and Ugarte et al. [75] reported capillarity-induced filling of carbon nanotubes by molten materials (liquid metals, salts, or oxides). Dujardin and colleagues [73] proved that

Figure 15. TEM micrograph sequence of a typical carbon nanotube portion showing the reversible volume contraction/expansion of a liquid entrapment upon heating/cooling achieved by manipulating the illuminating electron beam. (a) Initial shape of liquid at temperature Ta . (b) Inclusion gets thinner upon heating at Tb > Ta . (c) Liquid returns to its initial size upon cooling at Tc < Tb . (d) Heating is repeated (Td > Tc ), resulting in a renewed contraction of the liquid volume. Reprinted with permission from [76], Y. Gogotsi et al., Appl. Phys. Lett. 79, 1021 (2001). © 2001, American Institute of Physics.

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5.2. Ensembles of Nanofluidic Channels as Selective Interconnects The discussion presented here is limited to ensembles of onedimensional channels with sub-200 nm radial dimensions. One of the pioneering works on fluid transport through nanochannels was performed by Martin and co-workers [80, 81]. The internal pore walls of PCTE membranes were coated with a gold layer using the electroless deposition technique, which yielded straight metallic nanotubules with channel diameters of 0.8–10 nm. They placed a membrane between two KF electrolyte solutions of different concentrations, and varied the electrical potential of the membrane relative to the reference potential in the solution with the higher electrolyte concentration. Depending on the sign of the membrane potential relative to the reference electrode, the membrane exhibited complete anion- or cation-permselective behavior. This effect was attributed to double-layer overlap inside the nanotubules, by which means ions of the same sign as the membrane are rejected. The extent of membrane permselectivity can be expressed quantitatively by the transference numbers for cations (t+  and anions (t− . For a 1:1 salt such as KF, the potential Em over the membrane is given by   a k T Em = B
t+ − t−  ln h e al where ah and al are the activities of the salt at high and low concentration, respectively [82]. The equation indicates that Em is positive when the tubules are predominantly cation permselective (t+ > t− , and negative when they are anion permselective (t+ < t− . Figure 16 illustrates a series of Em values measured at different applied potentials, which proves that Au nanotubules can function as electronically 70

t+ = 1 50

Em (mV)

30 10 –10 –30 –50 –70 –0.6

t– = 1 –0.4

–0.2

0

0.2

0.4

0.6

switchable ion-exchange membranes. Studies on the permeabilities of complex cationic and anionic species of ∼1 nm diameter showed high tunability of the fluxes with variation of potential [83]. Some selected data are listed in Table 3. It was shown that the permeability in 1.5 nm channels was mainly due to electrostatic rather than to steric effects. Another external handle to effect molecular transport in nanosized channels is pH. Bluhm et al. studied the diffusion of mono-, di-, and trivalent cations across anodic alumina membranes with pore diameters of 20 and 100 nm as a function of ionic strength and pH [84, 85]. It was concluded that the cation diffusion coefficients decreased with cation valency, which was attributed to the larger electrostatic interactions between the cations and the positively charged alumina surface at pH below 9. The diffusion rates could be enhanced by increasing the pH of the electrolyte solution from 5 to 8, as this leads to a decrease of the positive surface charge density on the alumina pore walls, and thus to a decreased electrostatic repulsion between cations and the channel wall [84]. Bohn and co-workers also studied the influence of electrolyte strength and pH on the permeability of cationic, anionic, and neutral species in aqueous buffer solution [21, 86]. Further control over the pH dependence of the surface-charge density can be obtained by employing self-assembled monolayers (SAMs) on the pore walls [83, 84]. Stroeve and co-workers modified the surface chemistry of Au-coated 8 nm nanotubular PCTE membranes with a covalently bonded monolayer of acid-functional thiols HS–(CH2 10 –COOH [87]. The diffusion of benzene sulfonate anions was shown to be highly dependent on the external pH of the solution, in contrast to anion diffusion through bare or Au-coated PCTE membranes. This effect is illustrated in Figure 17, and was attributed to the pHdependent ionization of the surface carboxylic groups in the SAMs and electrostatic interactions between the anions and the surface charge. Cysteine, a thiol-functional amino acid with an isoelectric point around 6.0, was also employed as a surface-modifying agent [83, 88, 89]. Here, the permeating cationic species showed high fluxes at pH 12, where cysteine is negatively charged, and low flux at pH 2, where cysteine is positively charged. The opposite trend with pH was observed for anionic species [88]. The concept of sizebased separation was elaborated in a study on size-based protein separation by gold nanotubule membranes [90]. Table 3. Flux data of complex ionic species through 1.5 nm gold nanotubular membranes versus potential E applied to the membrane. Background electrolyte 0.5 mM KF. Concentration of permeation ion ′ + 2.5 mM. Ru(bpy)2+ 3 = ruthenium tris–(2,2 –bipyridine) cation; BTA = benzyl tributyl–ammonium cation; NDS2− = 2,6–naphtalene disulfonate anion; PTS− = p–toluene sulfonate anion.

Potential applied to membrane (V vs. Ag/AgCl)

Flux (10−9 mol · cm−2 · s−1  Permeate ion

Figure 16. Variation of Em with potential applied to a gold-nanotubule membrane (1 mM KF on the low concentration side; 10 mM on the high side of the membrane; tubule radius ∼1.1 nm). The dashed lines indicate the expected Em values for ideal cation- and anion-permselective behavior. Reprinted with permission from [80], M. Nishizawa et al., Science 268, 700 (1995). © 1995, American Association for the Advancement of Science.

Ru(bpy) BTA+ NDS2− PTS−

2+ 3

E = −400 mV

E=0

E = +400 mV

030 034 0002 004

009 019 001 013

008 011 003 020

Source: Data excerpted with permission from [83], M.-S. Kang and C. R. Martin, Langmuir 17, 2753 (2001). © 2001, American Chemical Society.

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Flux (mol/cm2s)

a

10–8

b

10–9

c

10–10 2

4

6

8

10

12

pH Figure 17. Flux of benzene sulfonate anions as a function of external pH obtained with (a) PCTE/Au/HS(CH2 10 COOH, (b) bare PCTE, and (c) PCTE/Au membranes. Tubule radii 8–10 nm. Debye length ∼7 nm. Reprinted with permission from [87], Z. Hou et al., Langmuir 16, 2401 (2000). © 2000, American Chemical Society.

The Au nanotubule inner diameter was controlled by variation of deposition time of the gold layer inside the PCTE nanochannels. It was shown that the low-molecular-weight protein lysine (Mw = 14 kg/mol) was transported preferentially over high-molecular-weight bovine serum albumin (Mw = 67 kg/mol) through nanochannels of 23 nm diameter. The transport of nonhydrophilic molecules can be enhanced by the covalent attachment of a hydrophobic SAM on the internal channel walls [80, 81, 91, 92]. This allows the preferential separation of neutral molecules based on their degree of hydrophobicity/hydrophilicity. Derivatization of gold nanotubules using the hydrophobic thiol HS–C16 H33 showed an enhanced transport rate of hydrophobic solvents [91]. Flux and selectivity data for hydrophobic toluene and hydrophilic pyridine through nanotubules modified with hydrophobic and hydrophilic SAMs are listed in Table 4. A similar approach can be utilized to selectively separate chiral neutral molecules, as was demonstrated recently [93]. In view of the fact that chiral enantiomers exhibit chemically and physically identical behavior, and are therefore very difficult to separate by simple means, the proposed concept appears very promising. Silica nanotubes were chemically Table 4. Flux and selectivity data for toluene and pyridine through Au nanotubule membranes modified with hydrophobic (–C16 H33  and hydrophilic (–C2 H4 OH) SAMs. Thiol HS–C2 H4 –OH HS–C16 H33 HS–C2 H4 –OH HS–C16 H33

Channel diameter (nm) 30 30 20 20

Flux (10−9 mol · cm−2 · min−1  Pyridine Toluene 70 046 56 01

26 28 061 20

Source: Data excerpted with permission from [92], S. B. Lee and C. R. Martin, Chem. Mater. 13, 3236 (2001). © 2001, American Chemical Society.

synthesized within the 20–35 nm diameter channels of an anodic alumina membrane. An antibody that selectively binds to only one of the enantiomers of a mixture of a clinical drug was chemically bonded to the channel walls of the silica nanotubes, after which the membrane became selectively permeable to the enantiomer that can attach to the antibody. Dynamic control over the channel diameter was demonstrated by Ito et al. [94]. Ionizable thiolfunctionalized poly–(L–glutamic) acid polypeptides were covalently bonded to the internal channel walls of a goldcoated PCTE membrane. The polypeptides respond to changes of pH and ionic strength by a conformational change: at low pH, they become positively charged, and fold to form a relatively short (∼1.5 nm) -helical coil. Upon deprotonation at high pH, the polypeptide chains form a relatively extended (∼16 nm) random structure. The water permeation rate through the channels can thus be reversibly regulated by pH since the channel diameter can be made larger or smaller. The effect becomes less pronounced at high ionic strength, as illustrated in Figure 18. The application of carbon nanotubes as nanofluidic channels has been limited so far [79, 95, 96]. Ensembles of straight parallel carbon nanotubes can be formed by the thermal decomposition of ethylene or propylene in an anodic alumina film [97, 98]. EOF studies were performed on ∼60 m long carbon nanotubes with an inner diameter of 120–200 nm [95, 96], which is too large for complete double-layer overlap to occur. The direction of the EOF indicated that the as-synthesized tubes have a negative surface charge between pH 3 and 7.2, and the EOF velocity was found to vary linearly with applied current density [95]. An electrochemical derivatization method was used to covalently attach acidic (negative) carboxylate groups to the channel walls, thus increasing the negative surface-charge density and potential. In this way, the EOF rate could be increased in comparison with the as-synthesized tubes [96]. 5.00

Water permeation rate (g/min)

10–7

4.00

3.00

2.00

1.00 1

2

3

4

5

6

7

8

pH Figure 18. pH-dependent permeation of water with different ionic strengths through a PCTE membrane with an internal polypeptide SAM. Ionic strengths were 0 M (circles), 0.1 M (diamonds), and 1.0 M (triangles). Reprinted with permission from [94], Y. Ito et al., Langmuir 16, 5376 (2000). © 2000, American Chemical Society.

Nanofluidics

GLOSSARY Carbon nanotube (CNT) Carbon nanotubes are graphene sheets rolled-up into cylinders with diameters as small as one nanometer. A single-wall carbon nanotube (SWCNT) is a graphene sheet rolled-over into a cylinder with typical diameter on the order of 1.4 nm. A multi-wall carbon nanotube (MWCNT) consists of concentric cylinders with an interlayer spacing of 3.4 Å and a diameter typically on the order of 10–20 nm. The lengths of the two types of tubes can be up to hundreds of microns or even centimeters. The intriguing electrical and mechanical properties of carbon nanotubes have led to an explosion of research efforts worldwide. Double layer, electric double layer (EDL) The region near a charged surface where counter-ions and co-ions in a polar medium are preferentially distributed, such that the net charge density is not zero. According to the Stern model, a plane (Stern plane) splits the EDL into an inner, compact layer considered to be immobile, and an outer, diffuse layer in which the ions are mobile. Electroosmosis (EO) The movement of ionic conducting fluids through a capillary or a channel under the influence of an applied electric field applied. An electric field applied along the capillary/channel generates the movement of a thin layer of fluid at the channel walls where a small separation of charges occurs due to the equilibrium adsorption and desorption of ions. As the layer of fluid moves, it drags the fluid bulk resulting in an essentially flat velocity profile across the channel. Electrophoresis (EP) The movement of charged particles suspended in a liquid under the influence of an applied electric field. Particles can be separated by electrophoresis on the basis of their relative electrical charges. Microelectromechanical systems (MEMS) Electromechanical systems fabricated using materials and techniques developed in the integrated circuit (IC) industry. MEMS contain both electronic circuits and mechanical parts with dimensions in the micron range such as transducers, valves, and motors. Microsystem technology (MST) Similar to MEMS with or without the electronic circuitry (e.g. optical, mechanical or fluidic structures). Reynolds number (Re) Dimensionless number that represents the ratio of inertia forces to viscous forces. The Reynolds number of a fluid flow characterizes the regime of the flow as laminar or turbulent. Scanning electron microscopy (SEM) A scanning electron microscope is a type of electron microscope capable of producing high resolution images of a sample. In electron microscopes (EMs) a focused beam of electrons is used to image the specimen and gain information as to its structure and composition. EMs were developed to achieve resolutions higher than those of light microscopes. SEM usually monitors secondary electrons which are emitted from the surface due to excitation by the primary electron beam. The first scanning electron microscope (SEM) was developed in 1942 and it was commercially available around 1965. See also TEM. Self-assembled monolayer (SAMs) SAMs are monomolecular layers of a compound bound to a surface in a highly

753 organized fashion and with a bond whose strength typically varies between ionic and covalent. The process of self assembly is thermodynamically driven and capable of self repairing: if the layer immersed in the solution of the same compound is damaged, new molecules can replace the empty spaces on the surface. Examples are thiolates, sulfides and dithiols self assembling on gold. The monolayers formed by trialkoxysilanes on glass are erroneously defined as self assembling layers. In fact the coupling to the surface is covalent and not reversible. The concept of monolayer was introduced in 1917 when Langmuir studied film formed by amphiphiles spreading on water. He realized the film had the thickness of one molecule. Surface tension The energy stored at the surface of liquids. The surface tension of a material is the energy needed to increase the surface of a unit area. It arises because of the difference in the intermolecular forces between molecules in the bulk of the liquid and molecules at the surface of the liquid. As the molecules in the bulk of the liquids are in favorable energy configuration, surface tension tries to minimize the surface area, resulting in liquids forming spherical droplets. Surface tension is measured in newtons per meter (Nm−1 ) which are equivalent to joules per square metre (Jm−2 ). Transmission electron microscopy (TEM) It is an imaging technique whereby an image of a specimen is produced on a fluorescent screen or layer of photographic film by electrons focused on the specimen and travelling through the specimen. The transmission electron microscope (TEM) was developed by Max Knoll and Ernst Ruska in Germany in 1931. It was the first type of electron microscope to be developed. As its name suggests, the TEM is patterned on the Light Transmission Microscope: the image is produced by detecting electrons that are transmitted through the sample. Zeta potential (
) The electric potential at the shear plane in the electric double layer. The zeta potential is defined with respect to the potential of the bulk of the solution.

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Encyclopedia of Nanoscience and Nanotechnology

www.aspbs.com/enn

Nanofluids Stephen U. S. Choi Argonne National Laboratory, Argonne, Illinois, USA

Z. George Zhang The Valvoline Company, Lexington, Kentucky, USA

Pawel Keblinski Rensselaer Polytechnic Institute, Troy, New York, USA

CONTENTS 1. Introduction 2. Background of Nanofluids 3. Making of Nanoparticles 4. Making of Nanofluids 5. Measurements in Nanofluids 6. Models and Mechanisms 7. Future Directions 8. Concluding Remarks Glossary References

1. INTRODUCTION Nanofluids are a new kind of heat transfer fluid containing a very small quantity of nanoparticles that are uniformly and stably suspended in a liquid. The dispersion of a tiny amount, yet tremendous number, of solid nanoparticles in traditional fluids dramatically changes their thermal conductivities. The average size of particles used in nanofluids may vary from 1 to 100 nm. The goal of thermal nanofluids is to achieve the highest possible thermal conductivities at the smallest possible concentrations of the smallest possible nanoparticles (preferably K11 for the high molecular weight carbonaceous mesophases, which would make the radial (toroidal) structure unlikely, and indeed this structure has not to our knowledge been reported in mesocarbon microbeads. Structure B in Figure 19 apparently represents weak anchoring, although it is easy to imagine this simple structure arising in the early stages of growth to bipolar spheres, perhaps as a metastable intermediate. One of the reports of the laminar structure is for very small (