Encyclopedia of Nanoscience and Nanotechnology 9781588830630, 1588830632

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Encyclopedia of Nanoscience and Nanotechnology Volume 7 Number 1 2004 Nanomechanical Properties by Nanoindentation

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Carlos M. Lepienski; Carlos E. Foerster Nanomechanics of Nanoscale Materials

21

Robert Geer Nanomembranes

47

Cees J. M. van Rijn; Wietze Nijdam Nanomotor F1-ATPase

83

Pia D. Vogel Nanoparticle Drug Delivery to the Brain

91

K. Ringe; C. M. Walz; B. A. Sabel Nanoparticle Layers in Multilayers

105

Diana Nesheva Nanoparticle Reinforced Thermoplastic Composites

125

Ming Qiu Zhang; Min Zhi Rong; Klaus Friedrich Nanoparticles as Drug Delivery Systems

161

Jörg Kreuter Nanoparticles for Live-Cell Dynamics

181

Xiao-Hong Nancy Xu; Rudrax N. Patel Nanoparticles in Nanostructured Polymers

193

Lyudmila M. Bronstein Nanopinning in High-Temperature Superconductors

207

J. Horvat Nanopipes in Transition Metal Nitrides

219

Daniel Gall Nanopore Analysis of DNA

229

David W. Deamer; Stephen Winters-Hilt Nanoporous Carbons

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Yoshio Yamada; Jun-ichi Ozaki Nanoporous Materials

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Dongyuan Zhao; Chengzhong Yu; Haifeng Yang

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Nanopowders Produced Using Microreactors

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Rainer Schenk; Volker Hessel; Nathalie Jongen; Vincenzo Buscaglia; Sophie Guillemet-Fritsch; Alan G. Jones Nanoprecipitates and Nanocavities in Functional Materials

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J. Th. M. De Hosson; A. van Veen Nanorobotics and Nanomanipulation

351

Wen J. Li; Ning Xi; Wai-Keung Fung; Tak Sing Wong Nanorecognition

367

P. Tarakeshwar; Kwang S. Kim Nanoscale Characterization of Biomaterials

405

E. Jallot Nanoscale Dilute Magnetic Semiconductors

417

S. J. Pearton; C. R. Abernathy; Y. D. Park Nanoscale Heat Transfer

429

G. Chen; D. Borca-Tasciuc; R. G. Yang Nanoscale Magnetic Random Access Memory Elements

461

S. J. Pearton; J. R. Childress Nanoscopic Optical Tracers

477

Wolfgang Schaertl; Sabine Schaertl Nano-spintronics for Data Storage

493

Yihong Wu Nanostorage

545

Jooho Kim Nanostructured Carbide-Derived Carbon

553

A. Nikitin; Y. Gogotsi Nanostructured Barium Strontium Titanate Thin Films

575

Bonnie D. Riehl; Guru Subramanyam; Rand R. Biggers; Angela Campbell Nanostructured Biomaterials

595

R. Murugan; S. Ramakrishna Nanostructured Bipolar Organic Polymers

615

Antonio Cravino; Helmut Neugebauer; N. Serdar Sariciftci Nanostructured Chalcogenide Glasses

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Keiji Tanaka Nanostructured Extracellular Matrix

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Zuwei Ma; S. Ramakrishna

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Nanostructured Hybrids from Layered Double Hydroxides

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Toshiyuki Hibino Nanostructured Metals and Alloys

669

Dmitri Valentinovich Louzguine; Akihisa Inoue Nanostructured Metals in Surface Enhanced Raman Spectroscopy

699

Helena I. S. Nogueira; José J. C. Teixeira-Dias; Tito Trindade Nanostructured Organic Light-Emitting Diodes

717

Thien-Phap Nguyen; Gilles Horowitz Nanostructured Surface Modifications for Biomedical Implants

741

Shane A. Catledge; Marc Fries; Yogesh K. Vohra Nanostructured Zeolite Films

763

Yushan Yan; Huanting Wang Nanostructures Created by Lasers

783

E. G. Gamaly; A. V. Rode Nanostructures Within Porous Materials

811

Y. Kumzerov; S. Vakhrushev Nanostructuring at Surfaces Using Proteins

851

Michael Niederweis; Stefan H. Bossmann Nanotribology

869

T. Coffey; J. Krim Nanotribology: Friction Force Microscopy

879

Enrico Gnecco Nanotribology of Carbon Films

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F. L. Freire Jr.; R. Prioli Nanotubes for Nanoelectronics

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Zhi Chen Copyright © 2004 American Scientific Publishers

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Encyclopedia of Nanoscience and Nanotechnology

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Nanomechanical Properties by Nanoindentation Carlos M. Lepienski Universidade Federal do Paraná, Curitiba-PR, Brazil

Carlos E. Foerster Universidade Estadual de Ponta Grossa, Ponta Grossa-PR, Brazil

CONTENTS 1. Introduction 2. Fundamentals of Nanoindentation 3. Applications 4. Theoretical Analysis of Depth-Sensing Indentation 5. Conclusion Glossary References

1. INTRODUCTION Load and depth-sensing indentation, also known as the nanoindentation technique, started to be developed in the 1980s, and nowadays is being continuously improved. The experimental device is based on recording load, depth, and time during the indentation process. The physical models and experimental systems are based on contact mechanics adapted to conditions of very low applied loads and indenter displacements. This means sensitivity of the applied load and tip penetration on the order of micronewtons and nanometers, respectively. The determination of the mechanical properties of nanostructured materials is a new and very interesting area. Nanostructured materials are characterized by nanoscale structures with a significant volume comprised of surfaces, interfaces, and grain boundaries, giving properties vastly different and often greatly superior to their bulk-metallic, ceramic, and polymeric counterparts. They can be produced by different techniques to form a myriad of engineered structures. These advances will provide better sensors, medical diagnostics, displays, data storage technologies, and surface protection coverings. However, the determination of

ISBN: 1-58883-063-2/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

their mechanical properties and how these properties are measured in nanostructured materials are in constant revision. As a result, an intense effort has been made in recent years to adapt and develop methods in order to measure deformation and fracture properties at the nanoscale. At the same time, experimental and theoretical work is being done to determine and understand the properties and processes influencing the mechanical behavior and fracture in small volumes. Advanced and novel characterization and testing methods, as well as analytical, continuum, and atomistic simulations, are being continuously developed. Of particular interest are those studies that extend over length scales from atomistic to nanometer or from nanometer to submicron, and thus provide insight regarding length-scale effects. The characterization of mechanical properties at nanoscale includes: structure–property relationships at the nanoscale in nanostructured materials, composites, films, multilayers, and functionally graded materials; mechanical properties of bulk materials at the nanoscale; deformation and fracture processes at the submicron scale; dislocation emission at probes and crack tips at the nanoscale; effects of intrinsic stresses on properties and fracture; creep measurement and mechanism determination; tribological properties of nanostructured material; comparative results for the modeling of submicron-scale indentation, scratch, and wear response; and development of standards tests to measure mechanical properties at the submicron scale. The purpose of this review is to show the reader the basic concepts of nanoindentation, and how it can be used to determine mechanical surface properties in the nanoscale regime. These concepts include the basic equations, a brief discussion about theoretical models, the equipment calibrations, and the correct choice of an appropriate indenter. In the following, focus will be given to a series of application results for modified surfaces and thin films (coatings),

Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 7: Pages (1–20)

2 tailoring the use of this technique. The further tendencies about using load and depth-sensing indentation are also shown. This chapter consists of four parts. First, a definition of nanoindentation and some comments with respect to how this technique can be useful for nanoscience and nanotechnology are given. Historical aspects, fundamental equations, and experimental methodology follow. A third part concerns the most important applications and principal results that can be found in the literature. Finally, some discussions about new applications, recent developments in the technique and in the theoretical approach, as well as future perspectives are also taken into consideration. Nanoindentation is a term used to designate indentation experiments where very low loads are used to press a hard indenter into a surface in a controlled way at submicronmeter penetration depths. As an important feature of the process, the applied load, the indenter displacement, and the time are continuously recorded during the experiment. Due to its versatility, nanoindentation is one of the most important methods to obtain the mechanical properties in the near-surface regions, and it can be applied to practically all types of solid materials. The Vickers and Brinnel conventional tests use the indentation image to measure the contact area which is necessary to calculate hardness. Unlike this, in nanoindentation, the contact area is obtained from the load and displacement data recorded in a complete load–unload cycle, without the necessity of imaging methods. If more elaborate analyses are performed, other mechanical properties, such as elastic modulus, residual stresses at the surface, strain rate sensitivity, toughness of brittle materials, and adhesion quality of thin films, can be determined by applying the nanoindentation technique. The determination of nanomechanical properties is a new field, as well as practically all areas in nanoscience and nanotechnology. For this reason, there is a considerable gap to link the mechanical properties from a continuum mechanics approach to an atomistic point of view. This atomistic approach takes into account the forces and movements of individual atoms or groups of atoms that are not considered in continuous mechanics. Atomic force microscopy (AFM) gives us a better understanding of the weak mechanical forces that govern the behavior of atoms in the surface of the materials. However, AFM is not well suited to determine the behavior of the material in a region deeper than a few atomic layers under the surface. Nanoindentation that presents high depth and load resolution is very useful to correlate the nanoscale mechanical behavior with the material structure. In the near future, an improved modeling and interpretation of load versus displacement data is expected since a considerable effort is being developed in the nanoindentation area. The new incoming equipment will probably become better. For these reasons, nanoindentation will continue to play an important role in nanotechnology development. Surface mechanical properties of several different materials, like metal nanocomposites, polymer films, metal surfaces, coatings, and microelectromechanical systems (MEMS), are being determined by applying the nanoindentation technique. Tailoring modified surfaces to

Nanomechanical Properties by Nanoindentation

improve mechanical and tribological applications requires a good knowledge of the mechanical properties at the material surface. Knowledge of the hardness, elastic modulus, and wear resistance is very important to specify the correct application for newly developed materials used in the electronic, automotive, or aerospace industry. Then, nanoindentation has an important role in the analysis of nanoscale mechanical properties of materials, and its application is continuously increasing. Finally, despite the fact that results will be more consistent, a great effort must yet be made to adequately interpret the depth and load-sensing indentation data because the deformation process under the indenter is very complex.

2. FUNDAMENTALS OF NANOINDENTATION In this section, the basic principles of nanoindentation are presented. Historical aspects are described, and it is shown how this technique is used to obtain the surface mechanical properties of materials. Far from being a complete treatise about the theme, the present section can be considered more like a straight guide to understand how nanoindentation can be applied to the study of nanoscale mechanical properties of surfaces and thin films. More advanced works and extended reviews about this theme are indicated in the text.

2.1. Historical Indentation experiments have been extensively used since the middle of the last century to measure the hardness of materials [1]. However, techniques for probing the mechanical properties of materials at nanoscale were developed only in the early 1980s. This mechanical probing consists of a load and depth-sensing indentation, which gives information about the surface mechanical properties of materials at depths lower than 1
m. Pioneer works of Pethica et al. [2, 3] showed the first results of indentation at nanoscale that were obtained with an instrumental device that is known now as nanoindentation equipment. They developed an electromechanical apparatus that was used to obtain the hardness at nanoscale. A few years after that, a sequence of other articles were published, showing a great instrumental development, and a new research area on mechanical surface properties was established. The original equipment’s purpose was to measure hardness at nanoscale. However, nanoindentation is now used in a wide spectrum, and the recorded data obtained from the indentation are applied to determine different mechanical properties. Other independent works were done in the same period [4, 5], and equipment of different designs, but for the same purpose, were constructed. All of these works were important for developing this new research area. In conventional indentation methods such as Vickers and Brinnel tests, the hardness is obtained from the ratio of the applied load to the area of the residual impression, which is determined by image methods. However, for indentation at

Nanomechanical Properties by Nanoindentation

nanoscale, imaging methods demand a long time, and very special techniques are necessary to obtain the actual area. Sometimes it is very difficult, if not impossible, to make good images from indentations when very low loads are used. Now, with the depth-sensing indentation, it is possible to measure the hardness without imaging the indentation impression. Pethica et al. [2, 3] reported the use of an area function to calculate the indentation area for a determined indenter penetration depth. The method is based on the knowledge of the shape of the indenter, and on the fact that the material normally conforms to the shape of the hard indenter. The contact area was obtained from final depth after the unloading. However, this first method was not correct as it did not consider the elastic recovery of the sample. Doerner and Nix [6] later elaborated a method to determine the hardness, and additionally the elastic modulus, from load versus displacement data. In their method, the unloading curve is considered to be governed by the elastic properties only. In addition, the elastic recovery is considered similar to that obtained from a flat cylindrical punch, where the contact area remains constant during the unloading process. Since the elastic recovery from unloading a flat punch is linear [7], they extrapolated the initial part of the unloading curve by a linear fit to obtain the contact depth, which gives better results than at maximum depth or at the residual depth that was previously used in the area function. As an improvement, with this new method, the elastic modulus of materials surface could then be obtained from the loading and unloading data. However, this approach does not give accurate results since the areas measured by imaging methods give different values when compared to the ones obtained by the Doerner and Nix [6] method. Oliver and Pharr [8], in 1992, described the necessary approach to make nanoindentation a widely acceptable probing method to obtain hardness and the elastic modulus in practically every kind of surface. Their article is the most cited in the nanoindentation area at the present moment. The principle, called the Oliver and Pharr method, is practically a standard when it is necessary to obtain hardness and the elastic modulus from load–unloading curves using load and depth-sensing indentation. After that, a great number of papers were presented showing new improvements on how to obtain new properties of materials from nanoindentation data, and they are described in the following as each aspect is being discussed. In what follows, the basic principles are presented, and some recent improvements in analysis and data interpretation are discussed.

3

Figure 1. Schematic of a nanoindenter showing the various equipment parts.

or piezoelectric actuators are also used in different equipment designs. The force actuator normally is capable of applying forces as lower as 1
N, and the displacement gauge sensor can give a depth resolution better then 0.1 nm. However, for measurements at depths lower than 20 nm, additional rigor and care are needed to obtain useful results. The maximum load used in this kind of equipment is normally about 500 mN. On the other hand, if better displacement and load resolutions are necessary, the maximum load is normally lower, and the depth resolution is increased for shallow penetration. An extensive description with details of different equipments used in nanoindentation, as well as their calibration processes, is presented by Bhushan [9]. Some nanoindentation machines allow the user to build an indentation pattern in a two-dimensional array by using a previous programming. These arrays can consist of a combination of a linear x and y pattern in order to form different two-dimensional geometrical figures like a square, a rectangular, or also triangular shapes. A typical example of an indentation shape produced by a Nanoindenter XPTM is shown in Figure 2. The distance between each indentation can also be programmed, and in the most general case, it is about 50
m in order to avoid residual deformation

2.2. Basic Principles 2.2.1. Depth and Load-Sensing Equipment A schematic diagram of equipment that is often used in depth-sensing indentation is shown in Figure 1. It consists of a system of a vertical axis supported by springs to a cell. The indenter is at the end of the axis, as shown in Figure 1. The system is composed of a force actuator, normally an electromagnetic shaker actuator, and a sensor of depth that is generally a capacitance displacement gauge. Other systems that use electrical force applied by capacitance plates

Figure 2. Typical two-dimensional indentation pattern obtained by a Nanoindenter XPTM machine. The distance between the indents is 50
m.

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Nanomechanical Properties by Nanoindentation

generated by indentations. This resource permits an easy method to map the mechanical properties in a composite surface, for example. At low loads, the nanoindentation area is small. Then one indentation can be made inside a single grain. In this case, it is also possible to make several indentations, and after that, to make some chemical attack to reveal the grain boundaries. Finally, the indentation position inside or at the grain boundary of grain may be verified, and the different behavior analyzed.

2.2.2. Load x Displacement curve A typical load versus displacement curve, obtained from the recorded data, is shown in Figure 3. The loading curve presents a typical parabolic behavior which is associated with elastic–plastic deformations during the loading. The maximum tip penetration hmax , the contact depth hc , the residual penetration after unloading hf , and the measured stiffness S are indicated in Figure 3. The elastic recovery after the unloading corresponds to the difference hmax − hf . The form of these curves, including small changes in the increasing depth rate or in the elastic recovery under unloading, can give information about the surface response to the applied load, and consequently about the mechanical properties at the surface.

2.2.3. Basic Equations During the indentation process, indenter–sample contact presents elastic and plastic components. Figure 4 shows a schematic view of the indentation contact during loading and after unloading. It was verified by Oliver and Pharr [8] that the unload curve behaves as a power law function P = h − hf m

Figure 4. Schematic view of sample surface during and after the indentation, showing the parameters definition used in the equations.

of Sneddon [7] and Doerner and Nix [6], they proposed a method that considers the unload curve as being due only to elastic recovering. The proposed equation, which is the basis for hardness and elastic modulus measurements, is hc = hmax −

(2)

with S being the unload stiffness,

(1)

where hf is the final depth after complete unload and P is the load. Oliver and Pharr [8] showed that the tip contact depth into the sample material hc at maximum load Pmax can be obtained by analyzing the unload curve. Based on the work

Pmax S

dP dh

S=

(3)

determined in the initial part of unloading curve. In Eq. (2),

is a parameter that depends on the tip shape, and is equal to 0.75 for a triangular-based pyramidal Berkovich tip normally used in nanoindentation. According to the method, the reduced elastic modulus is related to the measured values by the relation Er =

√

 S √ 2 A

(4)

and

 1 − 2 1 − i2 1 = + Er E Ei

Figure 3. Typical load versus displacement curve showing the loading and unloading parts, the maximum tip penetration (hmax ), the contact depth (hc ), the final depth hf , the system stiffness (S), and the elastic recovery.

(5)

where the i index indicates the values for the indenter material, and values not indexed correspond to the indented sample material. The projected contact area is calculated from the contact depth. For a perfect Berkovich indenter, the expression is A = 245h2c where hc is the contact depth from Eq. (1). The hardness is then obtained from the usual expression: H=

P A

(6)

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Nanomechanical Properties by Nanoindentation

2.2.4. Calibration, Errors, and Limitations The correct evaluation of mechanical properties from load and depth-sensing indentation depends on the minimization of errors [10] and the comprehension of the method’s limitation. However, even in the case of a well-calibrated machine, good results are not obtained if the sample presents a high surface roughness. Another problem appears when the material presents pile up at indentation. Pile up increases the contact area that is not correctly determined when the Oliver and Pharr method is used. Then the calculated values of hardness and elastic modulus are lower than the actual values [11]. The errors and limitations in load and depth-sensing indentation can be separated into three major different groups: calibration of the equipment and determination of contact surface, calibration of the area function for the indenter, and sample effects, such as roughness and pile up. In the following, the calibration processes and how these errors affect the results are detailed. A correct calibration of the indentation system is very important. Force and displacement calibrations are performed only at installation, and when the system is modified. The following calibration step is to obtain the compliance of the machine. The compliance of an ideal machine for a nanoindentation test must be very low. In this case, the frame machine presents only a small deformation when the load is applied to the sample. However, every machine suffers some deformation during the test. Then, the machine compliance must be deducted from the total compliance obtained from load versus displacement in order to calculate the elastic behavior of the sample. This is done by indenting a sample with high loads, as proposed by Oliver and Pharr [8]. Samples of well-known mechanical properties (like Al and fused silica) are indented at high loads, and the stiffness from the unload is obtained accurately. Considering that the machine is not perfectly rigid, the unload stiffness (dP /dh) has contributions from the elastic responses of both the sample under test and the instrument. The compliance of the instrument Cf = 1/Sf is then incorporated as 1 1 1 + = S Ss Sf

(7)

with Ss being the sample contribution and Sf the machine frame stiffness.   1 1 1 dh = = + (8) dP S 2E ∗ A Sf Then, for a Berkovich indenter where A = 245h2c , we have  dh 1 1  1 1 = = + (9) dP S 245 2E ∗ hc Sf Frame compliance is obtained from the data of indentations made at high loads. Values of 1/S are plotted versus 1/A1/2 or 1/hc . The data are then extrapolated to an infinite depth or h−1 c = 0, and then Sf is calculated. The obtained value is known as the frame compliance of the machine. A common value for load and depth-sensing indentation

machine compliance is about 0.1 nm/mN, which corresponds to a frame stiffness of 107 N/m. Environmental effects such as thermal variations and vibrations are another source of errors. Nanoindentation tests have a high sensitivity to temperature changes due to the different values for the thermal expansion coefficients of different materials in the structure frame. Consequently, it is necessary to minimize the thermal fluctuations in the room where the machine is installed. The effect of mechanical vibrations is normally avoided by using a nonvibrating table, and enclosing the machine in an acoustic-damped cabinet. Thermal drift rates lower than 0.1 nm/s are necessary when small-scale indentations are being performed. Nanoindentation is normally performed at room temperature since the effect of thermal drift is higher when it is necessary to maintain a constant high temperature. However, there are machines suited to operate at temperatures of about 100  C. In this case, the entire structure composed of the frame, motors, and measurement head are maintained at the same high temperature inside an oven at a constant temperature. This maximum temperature operation is limited by the electrical and electronic components that are inside the oven. Some other high-temperature systems perform nanoindentation at high temperatures, but nanoindentation at high temperatures is still a very complex process. Another routine calibration is to determine the tip’s area as a function of indentation depth. In practical situations, the indenter is not completely sharp, but it shows some roundness at the end, and some errors can be observed because of this fact. Mencik and Swain [10] described a series of errors that are present in the nanoindentation data, which can be due to several factors like tip blunt effects and surface roughness. The correct determination of the projected contact area as a function of the contact depth is very important to obtain the values for hardness and elastic modulus. Pyramidal indenters present a round end, while spherical indenters are never perfectly spherical. Then, it is necessary to compensate these effects. Scanning electron microscopy and atomic force microscopy performed in real Berkovich indenters showed that indenters with a radius of about 20 nm can be considered relatively good, “sharp” indenters. Berkovich tips extensively utilized have an indenter radius larger than 20 nm. To take into account the blunting of the tip, Oliver and Pharr [8] proposed a relation of the projected contact area to the contact depth that can be described by the equation 1/4 A hc  = 245h2c + C1 hc + C2 h1/2 c + C 3 hc

+ · · · + C8 h1/128 c

(10)

where C1 –C8 are constant, and determined by fitting the hardness versus penetration data of materials supposed to have a constant hardness at different depths, such as fused silica. Indentations at different loads are performed, and then the area function coefficients are fitted to obtain a constant hardness versus depth profile. This procedure is the most used method to correct the Berkovich rounding tip. In a recent work, Thurn and Cook [12] presented an analysis of the area function for nanoindentation. A twoparameter area function, obtained from the harmonic average of a spherical tip profile and a perfect conical profile,

6

Nanomechanical Properties by Nanoindentation

was proposed. According to the authors, the two-parameter area function adequately describes the Berkovich indenter tip contact area over the entire load range used in the indentation tests. The calculated projected contact areas for indentations were compared with values obtained from scanning electron microscopy (SEM) observation. Values of the modulus and hardness determined using the two-parameter area function are very similar to the ones obtained using the eight-parameter area function of Oliver and Pharr [8]. The calibrations of spherical indenters are normally made by performing indentations in fused silica in the elastic limit. Then the Hertz elastic model P=

4 E R1/2 h3/2 e 3 r

(11)

is used to obtain the actual radius of the indenter. However, normally, the radius is not constant, and then some area function is needed to correct the hardness and elastic modulus obtained. A good review of these corrections was presented by Fischer-Cripps [13]. Another calibration process was suggested by Swadener and Pharr [14]. An important factor that limits the determination of the actual surface mechanical properties by nanoindentation is related to the sample surface finishing quality [15–16]. The samples should be flat to have good results under nanoindentation tests. A perfect orthogonal approximation of the tip relative to the surface is more difficult in rough surfaces. In almost all cases of a present roughness, the measured mechanical properties change from point to point in the sample surface, making it difficult to obtain a correct interpretation of the results. Bobji and Biswas [15–16] analyzed the effect of roughness on hardness values measured by nanoindentation. They established a relation between the penetration depth normalized with respect to a roughness scale parameter. The practical usefulness of their model was verified by the numerical simulation of nanoindentation on a fractal surface. They found that an increase in surface roughness also causes an increased deviation in hardness measured values. They presented a method to deconvolute the effect of roughness in arriving at real hardness characteristics of the near-surface region of a material. The major conclusion they obtained is that, knowing the indenter geometry and given the roughness and penetration depth, it is possible to deconvolute the effect of roughness on measured hardness using a simple algebraic equation, to determine the actual mechanical property profile of the surface region. However, a problem emerges, which is the lack of good knowledge of the indenter geometry. Other methods to overcome the surface roughness can also be used in order to minimize its influence on the hardness and elastic modulus values: (1) to estimate a correct zero depth surface contact point by analyzing the stiffness of the sample at the contact, and comparing it with similar results in a flat surface [17]; or (2) to determine the hardness based on the stiffness at maximum loading [18], where the contact area is calculated from the loading stiffness at the loading and unloading curves. Using this method and an analysis of the extrapolated contact depth from the loading curve, it is possible to obtain the hardness [19]. In this case, the hardness calculation does not depend on the

knowledge of surface contact, and consequently, it may be independent of the knowledge of surface roughness. The usefulness of these two methods, with respect to the direct Oliver and Pharr method, can be observed by comparing the data in Figure 5. The hardness profiles correspond to a Ti nitride surface created by glow discharge at high temperature. A high surface roughness is present. Drastic differences in hardness profiles are observed when the results from the two methods are compared to the one obtained by the Oliver and Pharr method. Both correcting methods agree very well, and the reported values are according to the literature data on titanium nitride hardness. In a purely elastic contact regime, all materials always sink in during indentation, while for elastic–plastic contact, the material may either sink in or pile up. In some cases, material flowing up from the indentation cavity may occur, as shown in Figure 6. The indenter still maintains contact with the surface, but in this case, the real contact depth becomes larger than the penetration depth obtained from the Oliver and Pharr method. In materials that show pile up, the actual hardness is lower than measured by the Oliver and Pharr method. Bolshakov and Pharr [20] performed a finiteelement analysis of the pile-up effect on the measurement of the contact area, hardness, and elastic modulus by load and depth-sensing indentation methods. They found that the parameter hf /hmax , which can be measured experimentally, can be used as an indication of when the pile-up effect is an important factor. According to the authors, pile up is significant only when hf /hmax > 07 for materials that do not appreciably work harden. For these materials, if pile up is not considered, the contact area may be underestimated by as much as 60%, and as a consequence, an overestimation of the hardness and elastic modulus occurs. For materials that moderately work harden or in the case of hf /hmax < 07, pile up is not a significant factor, and the Oliver and Pharr data analysis procedure can be expected to give reasonable results. The same metal may present different behavior with respect to pile up, depending on the presence of an annealed or cold-worked state. Well-annealed samples present much less pile up than cold-worked samples of the same metal. Measurements of pile up and sink in of material around Vickers and spherical indentations in metals and ceramics

Figure 5. Hardness profile for a high rough Ti-modified surface obtained by using the Oliver and Pharr method [8], contact stiffness analysis [17], and Odo–Lepienski method [19].

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Nanomechanical Properties by Nanoindentation

3.1. Determination of Mechanical Properties of Coatings

Figure 6. Pile-up phenomena during indentation.

were made by Alcalá and coworkers [21]. They found that surface displacement at the contact boundary under applied load and in the unloaded state is correlated with the uniaxial strain hardening exponent n. Sinking in predominates in materials where n > 02. A state of nonuniform deformation is detected around Vickers indents, in contrast to the case of spherical indentation, where the deformation state is more uniform as a result of the axisymmetry of the contact conditions. The average (mean) surface deformation state around the contact perimeter in Vickers indents follows a similar correlation with n as that found for spherical indentation. The study of pile up and sink in is very important to the analysis of instrumented indentation experiments.

3. APPLICATIONS Load and depth-sensing indentation are applied to practically every kind of solid material. This wide field of applications can be attributed to the facility of use since it does not require more than a relatively flat and not rough surface. Comparative results are straight forwardly obtained, being very useful to determine the effect of some parameter variation in the production or treatment of a specimen. In this section, the application and some results of load and depthsensing indentation in different kinds of materials are presented. The objective is to show the major applications and to discuss the principal results in order to give the reader a direct way to analyze some of the most important fields of nanoindentation application. In addition, some nonconventional and very specific applications are described to show the technique capabilities and new ways to determine the mechanical properties of materials. Some of the major applications of the nanoindentation technique, as indicated by the number of published articles in the last ten years, are listed: (1) determination of the hardness and elastic modulus of deposited thin films and coatings, principally metallic thin films and diamond-like carbon films; (2) determination of mechanical properties of irradiated materials including ionic irradiated surfaces and plasma-based ion implantation; and (3) study of mechanical properties of brittle materials, such as hardness, elastic modulus, toughness, and adhesion properties. Some new and not totally well-developed areas where the depth and load-sensing indentation is being applied are: plasticity at low dimensions, mechanical properties of nanostructured materials, stress–strain simulation and residual stress determination, viscoelastic properties of polymers, and the creep and strain rate effect on the deformation of materials at low temperature. In these cases, non-Berkovich indenters may also be used to access mechanical properties other than hardness and elastic modulus.

In one of the first attempts to obtain the hardness of modified surfaces and coatings using depth and load-sensing indentation, Jonsson and Hogmark [22] developed a useful method for high applied loads based on the tip area function. Some progresses were described by Burnett and Rickerby [23] and Burnett and Page [24]. But independent of all efforts, hardness measurements based on these models are only completely successful for thick layers (on the order of several micrometers) because substrate effects are present, and it is not so clear yet how they can be excluded from the hardness profiles [25–28]. Nowadays, technological advances to produce surface coatings (thin films) and new materials at nanometer scale play an important role in technological applications. The thickness in these situations is reduced to the order of a tenth of a micrometer or less, and consequently, nanoindentation practically is the unique technique indicated to obtain mechanical properties in these regions. In the following, the principal results of the mechanical characterization of deposited coatings by nanoindentation methods are pointed out.

3.1.1. Variation of Mechanical Properties According to Deposition Process Coatings are predominantly produced by physical vapor deposition (PVD) and chemical vapor deposition (CVD) processes, which are being continuously developed and improved, with their indication depending on the end product [29–31]. The surface properties are strongly dependent on the bonding nature of the film structure and the substrate [32]. Coatings with an intense covalent bond nature have a tendency to present the highest hardness values, while metals are the lowest, and ionic coatings have intermediate values. Typical applications of coatings are scheduled below simultaneously with their basic composition [33–34]: • magnetic and electronic films (Nd–Fe–B; Sm–Fe–N; Al–Co; Fe–Co; Cu; Au) • optical films (SiO2 ; TiO2 ; Al2 O3 ; Ta2 O5 ; ITO) • decorative, hard, and wear-resistant films (Ti–Al–N; Ti–O–N; B–Ti–Nb–N; DLC; Ti–Al–O–N; h–BN; c–BN; Zr–Cu–N; SiC; VC; VN; TiC; WC; AlN; CrAlY) • corrosion barriers (Nb–Cr; Fe–Cr alloys; Ti–Al–Cr– N–C) • solid lubricants (MoS2 ; C60, V2 O5 , W3 O) Figure 7 shows the range of hardness and elastic modulus values that can be obtained by using the nanoindentation technique for different material compositions and at different deposition processes as found in the literature. The values present a great dispersion associated not only with the different tailoring processes, but also with different methodologies to obtain the mechanical properties. Despite the substrate influence on the hardness or film modulus values, typical load/unloading curves can be used to obtain global information about the film-tailoring process. In a comparative study of different coatings, it was recommended to extract these values at a depth on the order of 10% of the coating thickness or, as in some situations, obtain

8

Nanomechanical Properties by Nanoindentation

Figure 8. Schematic drawing of the elastic and plastic zone in film substrate.

Figure 7. Hardness and elastic modulus of coatings for different deposition processes.

the ones at depths that were reached at the same applied load [25, 28, 36]. Detailed studies of hardness, elastic modulus, and elastic recovery for metal nanocomposite coatings were performed by Musil et al. [36] and Kourtoukova et al. [37]. They showed the relation between hardness to elastic modulus (E/H ), hardness to elastic recovery E 2 /H 3 , and elastic modulus to elastic recovery (E/We and H/We ) that can be used to tailor the best ensemble of mechanical properties, depending on the end application of the coating. Literature data are very extensive on the subject of mechanical and tribological properties of coatings using the nanoindentation technique. These properties, referred to before, are strongly dependent on the deposition process used, and the following references are indicated to the reader to be consulted: • • • •

carbides and nitride-based coatings [38–53] DLC coatings [54–86] metal and oxide coatings [87–92] polymeric coatings [93–95]

3.1.2. Effect of Substrate on Coating Characterization A very large number of articles were written to describe the effect of the substrate in the determination of mechanical properties of thin films [22, 25, 96–105]. Several models were developed to describe the nanoindentation hardness and elastic modulus variation as a function of penetration to film thickness ratio [20, 23, 27, 106–109]. However, this problem continues without a satisfactory solution, and new models are expected to appear in the future. The major difficult factor for modeling the film–substrate behavior under indentation is the complex triaxial stress state in the region constituted by the film, the indenter, and the substrate. The effect of the substrate in the determination of the hardness of thin films is schematically shown in Figure 8. The elastic zone during indentation is not restricted to the film, but also reaches the substrate. Substrate plastic deformation also occurs for deeper penetrations. Tsui and Pharr [11] analyzed the effect of hard substrates on the nanoindentation mechanical property measurement

of soft films. In their work, substrate effects on the measurement of mechanical properties of thin film of aluminum on glass have been studied experimentally by nanoindentation methods. The hardness and elastic modulus of aluminum films with thicknesses of 240, 650, and 1700 nm sputter deposited on glass were systematically characterized as a function of indenter penetration depth using standard nanoindentation methods. They performed scanning electron microscopy and atomic force microscopy of the hardness impressions that revealed that indentation pile up in the aluminum is significantly enhanced by the substrate. It was found the substrate also affects the form of the unloading curve in a manner that has important implications for nanoindentation data analysis procedures. According to the referred article, nanoindentation measurement techniques can overestimate the film hardness and elastic modulus by as much as 100%, depending on the indentation depth, with the largest errors occurring at depths approximately equal to the film thickness. They also verified that indentation pile up in soft aluminum films is significantly enhanced when the films are deposited on hard substrates. In the case where the indentation depth is be about one tenth of the film thickness, the substrate-induced enhancement of pile up is negligible. Saha and Nix [26] recently performed a study on the effects of the substrate on the hardness and film modulus using the nanoindentation technique. Different films of Al and W were deposited over substrates like Al, Si, glass, and sapphire. The intrinsic hardness and elastic modulus of the films were analyzed using the relation P H = S2 4 2 E ∗2

(12)

where P is the applied load, S is the contact stiffness, H is a is the hardness, E ∗ is the reduced modulus, and tip geometrical constant. According to referred authors, for homogeneous materials, P /S 2 is constant with depth. Then, plotting P /S 2 versus depth may provide useful information about the substrate effect for different combinations of hard film/soft substrate and soft film/hard substrate. The substrate influence is small for soft film over hard substrate. On the other hand, for hard film over soft substrate, the film hardness can be obtained only for total indenter penetrations lower than 10% of the film thickness. Of course, correction of the contact area is needed because pile up will be necessary if the traditional Oliver and Pharr method is used. Considering elastic modulus measurements, the strong effect of

Nanomechanical Properties by Nanoindentation

9

the substrate exists because the elastic field presents a longrange character, and special care must be taken in order to extract the actual elastic modulus value for the film material. For a large mismatch between the film and substrate modulus, King’s analysis to estimate the film modulus is indicated [27].

3.2. Surface Modification by Ion Irradiation Ion implantation (II) and plasma-based ion implantation (PBII) processes are also well established to offer wide possibilities for the surface modification of materials. The application potential of these modified surfaces is very high in the different fields of the modern technology, like the microelectronic, metallurgical, and biological industries. However, these processes are different with respect to coating deposition processes. Atomic species are introduced in the nearsurface region by a nonequilibrium process which depends on the parameters used, like ion energy, ion current, chamber vacuum, and temperature conditions. The modified surface region can then be constituted of embedded phases, buried layers, and also, under some conditions, to form a coating layer. In the general case, a graded region is produced from the near-surface to deeper regions. The modified region is, in almost all cases, localized at depths on the order of ten nanometers to thousands of nanometers. Because of this, the nanoindentation technique is the most indicated to obtain mechanical properties such as hardness, elastic modulus, as well as elastic recovery and surface toughness. Nitrogen is the most used atomic species that has been irradiated to improve surface hardness in metals by II or PBII processes because of its ability to form nitride compounds. However, other atomic species like C, B, Cr, Ti, and O can also be used to prevent wear and corrosion [110]. Notwithstanding, there exist a great number of commercially available metal alloys; the number of reported works in the literature about mechanical properties obtained by the nanoindentation technique for metal surfaces modified by II or PBII is small. Equally as performed for coatings, the influences of the substrate (matrix) and very near-surface region need to be excluded, or at least minimized, in order to obtain the actual hardness and elastic modulus values for the ionic modified surfaces. Surface modifier processes typically produce graded regions. These regions may be formed by a natural oxide layer, the presence of a solid solution of implanted ions, and some stoichiometric phases. The description of a unique hardness value for the material surface is then almost impossible. Consequently, it is recommended to analyze the ionic effect on surface hardening by using the hardness-to-depth profile to compare the different physical parameters of the irradiation process used to modify the surface. A typical hardness profile for the pure iron surface submitted to N ion implantation is shown in Figure 9. The N peak position is around 70 nm in depth for both substrates. High hardness occurs in the near-surface region, and slowly decreases until it reaches the substrate value. The high surface hardness is attributed to the formation of iron nitrides. The distribution range of the N ions is not sharply defined (it is a Gaussian-like distribution). Then N atoms in solid solution are also present before and after the ion peak

Figure 9. Hardness values as a function of depth for N irradiated iron.

position. Because of the influence of high hardness in this graded region, substrate hardness values are only reached at very deep depths. Table 1 summarizes the hardness values obtained using the nanoindentation technique (low applied loads ≤100 mN), in different commercial metals and metals alloys submitted to different ion irradiation processes (II and PBII). Additional mechanical property information can also be extracted from the load/unloading curves in the surfaces modified by II or PBII processes. It is well known that II or PBII processes introduce surface damage. The damage profile is basically a function of the ion species and its energy. In this region, atomic displacements, vacancies, Frankel pairs, and extended defects are observed. These defects may alter the elastic field in the region around the tip contact, delaying the plastic deformation by increasing the tip ending pressure, and finally reaching the necessary energy to emit dislocations and form microcracks. This specific phenomenon can be observed in a load/unloading cycle, and it is characterized by a typical tip incursion (pop in) [111]. The extension of the tip incursion at an applied load and time can be then used to estimate the energy to create dislocations. The pattern of the tip incursion allied to electronic microscopy was then used to confirm these hypotheses. At this point, it is important to distinguish this phenomenon from pop in that occurs in dislocation-free materials. Polymers are also widely used in most industrial applications due to their excellent chemical and physical properties, easy working processes, and low operational costs. On the other hand, when polymers are submitted to loadbearing and abrasive conditions, the mechanical and tribological properties need to be enhanced. The use of II and PBII processes has shown to be a very efficient technique to modify polymer surfaces because there is a large energy transference in II and PBII processes when compared to other more traditional processes like X-ray, !-ray, ultraviolet rays (UV light), and electron beams. The polymers present a lower bond strength compared to metals, ceramics, or semiconductors; then the transferred energy to the electrons and atoms by the incoming ions stimulates chemical reactions and chain scissions that, at the final stage of the process, produce hardening and stiffening of the polymer surface by a cross-linking mechanism of the chains or

10

Nanomechanical Properties by Nanoindentation

Table 1. Relative hardness (RH) for different metal alloys submitted to different ion implantation processes. Material

Ion process

Ion type

RH

Ref.

Fe

II II

AISI D2

II

AISI M2

II

AISI P20 AISI M3:2

II II

AISI 420 A286

II II

AISI 316L SS 316L AISI 304 AISI 440C

II II II II

3 3 3 3 3 1.4 1.8 1.48 1.02 1.43 1.56 1.51 1.26 1.42 1.55 1.87 1.13 1.09 8.0 1.6 2.72 1.3 1.15 1.15 2.5 2.5 1.5 1.2 1.3 1.4 1.8 1.23 1.53 2.0 2.0 4.0 5.0 5.0 3.0–5.0 10.0 2.0 2.5 1.1 5

[111]

AISI 1020

N Ar N Ar N + Ar N C N Cr N + Cr C N C Cr + C N N Y Y+N N + Ar N N C C TI N O B N C B+N B+C N N Ti + C Ti + C N N N N N C C N N

AISI 304 Al 7075 CoCrMo alloy

PBII PBII II

304L AISI S7 Ni Ni80 Fe20 Zr Al Al-6061 Ti6Al4V Ti6Al4V Ti6Al4V Si

II II II II II II II II PBII II PBII

Al

II

[112]

[113] [114] [115]

[116] [117] [118]

[119] [120] [121] [122] [123] [17] [124] [125] [126]

also by the formation of a three-dimensional microstructure which restrains the chain movements. Literature data about mechanical and tribological properties, using the nanoindentation technique, of polymers, like polyisoquinoline (PIQ), poly-2-vinylpiridine (PVP), polyacrylonitrile (PAN), polyethylene (PE), polycarbonate (PC), polyetherimide (PEI), polystyrene (PS), Kapton polypropylene (PP), polypropylene (PP), polystyrene (PS), polyethersulfone (PES), polyethylene terephthalate (PET), polyhedral oligomeric silsesquioxane (POSS), poly(ether ether ketone) (PEEK), polystyrene (PS), fotoresist AZ 1350, C60 films, and plasma-formed polymers, in a bulk or coating form, submitted or not to surface-modifying processes, can be obtained by consulting the references [68, 127–141].

3.3. Hardness at Nanoscale: Anisotropy, Grain Size Effect, and Indentation Size Effect The study of very small-scale indentation has increased in the last few years. A considerable effort has been made in theoretical and practical aspects of this problem. At very low loads, nanoindentation is being used to understand the strain gradient plasticity and dislocation emission from the plastic region under the indenter. At larger scales of indentation, a number of models exist for plastic flow, but as experimental scales shrink, properties change; then these models may not be applicable. A detailed understanding of the atomic-level processes that contribute to the initial nucleation of dislocations, their motion, and multiplication will greatly facilitate the design of tailored materials with specific mechanical properties. Nanoindentation tests performed at very small penetrations increase the probability that some indentations occur only inside one grain in the material, and then anisotropy effects are very important. At high loads, hardness is obtained from a mean value from several grains. At low loads in nanoindentation tests, the hardness value may correspond to one grain only. For polycrystalline materials, the crystalline orientation of the indented grain relative to the tip geometry is not well known. In addition, for wellannealed metals, the typical dislocation separation is about 1
m, and the region under the tip should behave close to that of a perfect single crystal, that is, a dislocation-free specimen. Consequently, the understanding of the contact mechanics of small volumes becomes increasingly important. Corcoran et al. [142] developed a study of the anomalous plastic deformation of single-crystal Au(111), Au(110), and Au(100) surfaces under nanoindentation, and observed a yield behavior composed of a series of discrete yielding events separated by elastic deformation. The onset of this behavior is in agreement with calculations for the theoretical shear strength of gold. Good quantitative agreement is found between the experimental results and a model developed for the nucleation and multiplication of dislocations by a simple Frank–Read source under the indenter tip. In another paper, Fougere et al. [143] used nanoindentation to measure the Young’s modulus for nanocrystalline Fe samples produced by inert-gas condensation and warm consolidation. The samples had grain sizes of 4–20 nm and a residual porosity of 2–30% calculated relative to conventional Fe. Values of the Young’s modulus for the nanocrystalline Fe are reduced relative to values for conventional, fully dense Fe. According to the above authors, the observed reductions in the Young’s modulus for both the nanocrystalline and the conventional porous Fe can be described adequately by several theories utilizing spheroidal porosity. It is well known that hardness is observed to increase in metals with decreasing indentation size, especially in the submicrometer depth regime [144, 145]. Conventional theories of plasticity do not include material length scales. In these theories, the flow stress at any particular point in a solid is only related to the strain at that point. Some new theories have appeared where the deformation is influenced by the strain gradient present at that point, and related to the concept of geometrically necessary dislocations [146].

11

Nanomechanical Properties by Nanoindentation

In their article, Nix and Gao [146] proposed that the indentation size effect for crystalline materials can be modeled using the concept of geometrically necessary dislocations. Their model describes the variation of hardness with penetration depth as given by  h∗ H = 1+ (13) H0 h where H is the hardness for a given depth of indentation h, H0 is the hardness in the limit of infinite depth, and h∗ is a characteristic length that depends on the shape of the indenter, the shear modulus, and H0 . They observed, from indentation experiments on annealed (111) copper single crystals, cold-worked polycrystalline copper, and single crystals of silver, that this relation is well obeyed. One interesting scale aspect is that indentation hardness can drop by more than a factor of 2 with increasing depth, and this depth dependence appears to be more accentuated in single crystals than polycrystals. Whether this is strictly due to the difference in the initial dislocation density and/or number of sources is still under investigation. Tymiak et al. [147] studied the plastic strain and strain gradient with nanoindentation at very low penetration depths. Plastic strains and their respective strain gradients produced by nanoindentation have been theoretically interpreted and experimentally measured at shallow indentation depths for spherical and wedge indenters. For a sharp wedge, both experimental continuum-based and theoretical geometrical approaches suggest the strain gradient decreasing with increasing indentation depth. For spherical indentation, theoretical geometrical analysis yields a depth-independent strain gradient proportional to 1/R. Tungsten and aluminum single crystals exhibit about a factor of 2 decrease in hardness with increasing depth, irrespective of either increasing or decreasing average strain gradients. Kiely and collaborators [148] performed nanoindentations on Au single-crystal surfaces. They observed two distinct regimes of plastic deformation, which are distinguished by the magnitude of discontinuities in load relaxation. At lower stresses, relaxation occurs in small deviations from elastic behavior, while at the higher stresses, they take the form of large load drops, often resulting in complete relaxation of the applied load. These major events create a relatively wide plastic zone that subsequently deepens more rapidly than it widens. They proposed two regions of plastic relaxation result from two distinctly different processes. In the first region, deformation likely occurs through the nucleation, glide, and locking of several dislocations, resulting in deformation several atomic layers deep. At higher stress levels, dislocation multiplication occurs, and produces mobile dislocations.

3.4. Applications Using Different Indenter Geometries Several indenter geometries are used in nanoindentation tests. The most common is the Berkovich indenter, which is a three-sided pyramid, with the face angle to normal equal to 653 . This indenter has the advantage of being well suited to obtain mechanical properties at a small depth since it is

possible to obtain indenters with a relatively sharp end, and at the same time, a good relation contact area to depth. Other indenters commonly used are Vickers, conical, spherical, cube-corner, and the flat-end shape. Each one of these indenters has some advantages and disadvantages. Indenters with different shapes are normally used to obtain mechanical properties diverse from hardness and elastic modulus, although these properties can also be obtained using indenters with a geometry other than Berkovich.

3.4.1. Berkovich The great majority of results obtained by nanoindentation tests are performed by using Berkovich indenters. A Berkovich indenter has a three-sided pyramidal shape, with angles of 653 between the normal and the median of each face, and 769 between the normal and each corner line. For a perfectly sharp indenter, the projected contact area is A = 245h2 , where h is the contact penetration depth. A Vickers four-sided pyramidal indenter has the same area function with respect to the depth penetration relation as a Berkovich indenter. Berkovich indenters are the most used in nanoindentation tests. Although real indenters are never perfectly sharp, three-sided pyramidal indenters such as Berkovich are normally less blunt than four-sided indenters like Vickers.

3.4.2. Vickers Vickers indenters are also used in load and depth-sensing indentation machines. However, since it is more difficult to obtain sharp Vickers indenters at small depths, its use is more common for some hard materials and higher loads [149]. Some theoretical work also has been performed, comparing Vickers and conical indenters [150, 151].

3.4.3. Spherical Indenters Spherical indentation was one of the first tests to determine the hardness of material. The Brinnel test is one of the most used to determine the hardness in a macroscale [1]. Francis [152] describes the deformation mechanisms of plastic spherical indentation, in an attempt to correlate the deformation mechanism to the pressure distribution under the indenter as a function of depth penetration. Spherical indentation has an interesting, and at the same time challenging, aspect: the contact between the indenter and surface is not self-similar, that is, the contact angle increases continuously with penetration. This characteristic permits us to determine properties such as the elastic-toplastic transition. However, analysis of loading–unloading curves is more complex because the contact angle is varying continuously. Spherical indenters are widely used, not only to obtain the hardness of the material. A number of papers were published about the application of spherical indentation to determine the hardness and other mechanical properties of materials [153–156]. Depth and load-sensing indentation with spherical indenters is also used to simulate a relationship between the stress and strain, in a similar way as in an uniaxial applied stress, and then to try to obtain the yield strength from appropriate models and nanoindentation load–unload tests. Herbert

12 and coworkers [157] performed uniaxial tests and nanoindentation tests with spherical indentation in order to explore the accuracy to predict the uniaxial stress–strain behavior of aluminum alloys from nanoindentation tests. They related that spherical indentation can be successfully used to establish an engineering estimate of the elastic modulus and yield strength of Al alloys. However, nanoindentation tests could not reproduce the physical shape of the uniaxial stress–strain curve. The use of spherical indentations to obtain good results is a more challenging matter. Since spherical indenters are not perfect in the majority of cases, presenting a profile that is not a perfect spherical surface, they are very sensitive to calibration. In most cases, the area and the frame compliance calibrations cannot be obtained from indentations in a unique sample as proposed by Oliver and Pharr for pyramidal indenters. Spherical indenters sometimes show a more acute surface, in others a more blunt surface, and also irregular, not spherical shapes. These effects are not easily incorporated to the area calculus as in the case of the blunt effect of pyramidal indenters. Then each case must be analyzed very carefully. Swadener and Pharr [158] presented a calibration method for nanoindentation with spherical indentation. They proposed to perform indentation on two ceramic materials to the same contact depth. The results are then used to determine the radius of the spherical indenter and the machine compliance. Another analysis of the basic equations and methods to use spherical indenters with load and depth-sensing indentation machines was presented by Fischer-Cripps [13]. Residual stress determination is another application of spherical indentation. Several studies have been performed to determine the residual stress at the surface from indentation techniques. Carlsson and Larsson [159] performed pyramidal indentation in materials with residual stress using pyramidal indenters, and they found that the effect of residual stress on load–unload curves with pyramidal indenters and on measured hardness is small. However, as the contact angle in spherical indentation increases with penetration, the sensitivity to residual stress is higher for spherical indentation than for pyramidal indentation. For these reasons, spherical indentation may be useful to obtain the residual stress at surfaces of metallic materials. A new experimental technique for making measurements of biaxial stress using load and depth-sensing indentation using spherical indenters was presented by Swadener et al. [160]. The residual stress at the surface is obtained from analysis of the mean pressure pm as a function of the ratio a/R, a being the contact radius and R the indenter radius. The presence of residual stress causes an increases in the values of mean pressure during indentation for the same contact area.

3.4.4. Cube-Corner and Other Sharper Indenters The indentation of ceramic and other fragile materials can generate cracks, such as radial cracks at the indentation corners and conical cracks. The presence of cracks can be useful to determine the toughness of fragile materials [161, 162]. Then, by measuring the extension of a radial crack at indenter corners, it is possible to determine the toughness of the fragile material. However, radial cracks are not normally

Nanomechanical Properties by Nanoindentation

observed in indentations with a Berkovich indenter if the applied loads are in the range commonly used in nanoindentation because fragile materials have a critical load for crack initiation. Consequently, cracks are not formed for loads lower than the critical load. It was observed that this critical load is a function of the contact angle between the indenter face with respect to the sample’s surface [161]. Increasing the contact angle, the critical load decreases. Loads of about 400 mN are necessary to generate radial cracks at the indentation’s corner for Berkovich or Vickers indentation in soda lime glass. On the other hand, a load as low as 20 mN can cause radial cracks when cube-corner indentation is performed in the same material [163, 164]. Because of their low critical load, cube-corner indenters are used in toughness measurements with load and depth-sensing indentation. Indentation fractures at low loads with a cube-corner indenter are used to study the toughness and adhesion characteristics of thin films [28, 165, 167]. The maximum loads that can be applied by nanoindenters are normally not high enough to induce surface cracks if Berkovich pyramidal indenters are used. However, with sharp indenters, the toughness can be obtained from determination of the radial crack length with different loads and a model proposed by Anstis and Lawn [161, 162]. Some additional difficulties appear when it is necessary to determine the length of cracks because, as loads, the lengths are also very small. The validation of toughness values for thin films cannot be completely established since it can be verified by other methods in the same way as in the case of a bulk material. In thin films, there are also the effects due to the presence of the substrate and the interface region. The characterization of thin-film fragile behavior is a challenging matter since, in nanoindentation tests, it is very difficult to eliminate the effect of the substrate. In addition, it is possible to perform analysis of the adhesion, by qualitatively determining the delamination and interfacial behaviors, with cube-corner indentation. However, the models used to obtain adhesion energy and toughness values need further development. The use of indenters sharper than the Berkovich indenter has become more frequent recently. The most used of this sharper indenter is the cube-corner geometry, where the angles of the corners are 90 . Cube-corner indenters are normally used in order to evaluate the material’s resistance to microcrack initiation and propagation [168] and residual stresses in ceramic materials [169]. In addition, analyses comparing the unload curves obtained with cube-corner, Berkovich, and spherical indentation are also being performed [170]. Nanoindentation results made using indenters with different triangular pyramidal geometries are described by Ikezawa and Maruyama [171]. Malzbender et al. [28], in a review article, described the practical use of nanoindentation and scratch tests in determining the mechanical properties of thin coatings. They presented the major methods to determine the mechanical properties of coatings, with emphasis on brittle coatings.

3.4.5. Flat-End Indenters and Viscoelastic Behavior The determination of mechanical properties of polymers from nanoindentation tests needs special care due to their viscoelastic behavior. The penetration and load are now

13

Nanomechanical Properties by Nanoindentation

dependent on the strain rate. The indenter penetration depends on the loading time being higher if the test is performed at lower rates. Even at constant load, the penetration depth continues to grow. The values of the hardness and elastic modulus measured by nanoindentation are then dependent on the time and strain rates used in the experiment. For this reason, it does not make sense to define a unique value hardness for a polymer since it depends on the strain rates and interval times used in the experimental procedure. The elastic modulus is also not well defined, the values being obtained from nanoindentation tests higher than those measured from uniaxial tension tests in bulk materials. Much work, however, has been done to determine the mechanical properties in polymers despite this additional difficulty caused by their viscoelastic behavior [172–174]. An additional capability of nanoindentation is to measure the viscoelastic properties of polymers. In order to do so, flat-end cylindrical indenters are normally used. The contact area being constant during penetration, the pressure distribution for a determined depth under the indenter can be considered almost constant if low loads are used. Basic equations of flat punch nanoindentation on polymers are presented by Cheng et al. [175]. The standard three-element viscoelastic material indented by an axisymmetric flat-ended indenter was investigated theoretically. The solutions of the equations of viscoelastic deformation were derived for the standard viscoelastic material for compressible as well as incompressible solids. They analyzed both the flat-punch creep test and the load-relaxation test, providing a fundamental basis for probing the elastic and viscous properties of coatings with nanoindentation tests.

3.5. Scratch Test A scratch test consists of drawing a surface with a tip applying a normal load (P ). Since the nanoindentation system permits very good control in the applied force and penetration depth, it is only necessary to add a tangential movement actuator to obtain a very well-controlled scratch test at nanoscale. The used tip can be conical, spherical, or pyramidal. Theoretical studies have been developed in order to understanding the contact mechanical at nanoscale. Buldan and coworkers [176] presented a very interesting study on the contact at atomic scale of an indenter, and subsequent pulling and dry sliding of a sharp and blunt metal tip on a metal surface. They used molecular dynamics methods and empirical potential on an embedded-atom model to determine the atomic structure evolution and the variation of the normal and lateral forces. The results are very different for each of the diverse tips used in the study. Finite-element analysis of the deformation during indentation and scratch tests on elastic–perfectly plastic materials was performed by Bucaille and Felder [177]. The understanding and quantification of elastic and plastic deformation during a scratch test was presented by Jardret and coworkers [178]. Basically, in a scratch test, the load can be applied in two different ways: (1) a constant load during the entire scratch, or (2) an increasing load (ramp loading) from an initial to a maximum value at the end of the scratch. Lateral force transducers, adapted to a DSI device, are used to measure the lateral force (F ) that acts on the scratch tip. If

the applied load P tends to zero, and if ploughing is absent, it is possible to estimate the friction coefficient by using F =
a +
p P

(14)

where
a is the adhesion friction coefficient and
p is the ploughing friction [179, 180]. Additional mechanical properties, like elastic modulus, hardness, and fracture toughness, may also be obtained qualitatively by using a scratching test [180–186]. To calculate the hardness, it is necessary to include two components: the scratch hardness Hs and the ploughing hardness Hp [179–185]. For a perfect plastic surface, Hs is obtained by using P A∗

(15)

w 2 8

(16)

Hs = where A∗ =

is the load-bearing area and w is the local width of the scratch. On the other hand, Hp is defined by Hp =
p

P Ap

(17)

where Ap is the projected contact area in the normal direction to the tip movement, and is obtained by 2

Ap = R sin

−1



w 2R



  w w 2 1/2 2 − R − 2 4

(18)

with R the tip radius and
1/2 w = 2 2Rh − h2

(19)

where h is the tip penetration depth. Particularly for coatings, the load/displacement curve and its characteristics provide a simple method to obtain the critical load that produces a coating detachment if the scratch device is used in the linear ramp loading mode. The loaddisplacement curve can show an abrupt discontinuity. Using additional imaging analysis, it is observed that this region corresponds to the onset of the detachment. The critical load to produce cracks is defined by these observations. This process permits us to obtain a measure of the coating/substrate adhesion quality. Of course, the failure modes (cohesive and interfacial) and the load that produces the detachment will depend on the substrate properties, the coating thickness, the tip shape, the loading rate, the friction coefficient, and the surface quality [187–192]. The models to describe the adhesion quality by using the scratch test basically employ the fact that the detachment occurs due to a chipping process on the front side of the tip, with the elastic strain energy realized by an interfacial fracture at the critical load. According to Bull and coworkers [192], detachment occurs when the in-plane compressive

14

Nanomechanical Properties by Nanoindentation

stresses in front of the tip create conditions to induce a critical stress normal to the interface by a Poisson effect. The interfacial fracture energy &i is then obtained by &i =

1 t 2 Ec



 f
c Pc Ac

2

(20)

where Ac is the cross-section area at critical load Pc , Ec is the coating elastic modulus, t is the coating thickness, f is the Poisson ratio, and
c is the friction coefficient. A modified model of Attar and Johannesson [190] shows that a tangential force is required to remove the coat; on the other hand, Burnett and Rickerby [193] concluded that the elastic–plastic indentation stress is dominant for low friction and thick coats. Some recent literature reporting scratch tests on the surfaces of different materials, including coatings and bulk, are: for PET films by using a spherical tip at constant load, Beake and Leggett [194]; for fullerene films at constant and ramped load, Lopes [195]; for Cr and CrN films, Hones and coworkers also use constant and ramped loads [196]; a discussion about DLC interface tribology by Menon [197]; Li et al. for metal-particle magnetic tapes [198]; Qi and coworkers for nitrogenated diamond-libe carbon films (CNx ) [199]; Hones and coworkers on hard chromium tungsten nitride coatings [200]; for TiN/SiNx multilayer coatings, Chen and coworkers [201]; Nelea and coworkers on hydroxyapatite thin films [202]; Charitidis and coworkers, a comparative study of the nanoscratching behavior of amorphous carbon films [203]; investigations of nano- and macrowear of magnetic tape head materials by Tan et al. [204]; in Shen and coworkers, a study of tribological properties of coating/substrate systems in micrometer and nanometer scales [205]; nanotribology studies by Wei and coworkers of Cr, Cr2 N, and CrN thin films using constant and ramped load nanoscratch techniques [206]; evaluation of the adhesion of TiN films using nanoindentation and scratch testing by Toparli and Sasaki [207]; a review of the mechanical properties and tribology of thin sol–gel MTMS coatings by Malzbender and coworkers [28]; indentation depth recovery in a poly(methyl methacrylate) sheet on the microlength scale by Adams and coworkers [208]; nanotribology and surface chemistry of reactively Ti–B–N hard coatings by Ott and coworkers [209]; and hard coating adhesion on ionimplanted polymer using nanoscratch tests by Guzman and coworkers [210].

films deposited over very soft materials [220], and in the case of surface cracking in brittle materials during loading [139]. Pop in also occurs during the indentation of lamellar materials like graphite and mica. Figure 10 shows load versus displacement curves for four different lamellar materials: graphite, mica, GaSe, and NbS2 . Lamellar materials are characterized by highly perfect cleavage, so they readily may be separated into very thin leaves. Indentation tests in these materials present, as a special feature, a deformation process that is practically elastic for pyramidal indenters, even at high loads [221–224]. If the elastic energy is high enough, a sudden plastic deformation occurs and, in most cases, the subsequent deformation may also continue to be elastic. The mechanical properties of lamellar InSe and GaSe single crystals have been studied by means of nanoindentation tests by Mosca and collaborators [222]. The course of plastic deformation induced in the crystals by application of a definite shear stress through the penetration of a Berkovich tip indicates that the deformation occurs predominantly by pop-in events along easy slip directions, having a fairly elastic character between displacements. Hardness anisotropy along the crystal axes is clearly seen, and the measured elastic modulus presents a discrepancy smaller than 5% in comparison with theoretical calculations performed using previous experimental values of the elastic constants. Some authors [142] attribute the pop-in excursion to dislocation creation and multiplication by Frank–Read sources. However, in lamellar crystals, which present very different bonding energies at perpendicular directions, the dislocation multiplication by this kind of source does not appear to be the major mechanism to accommodate the plastic deformation during pop-in events. Alternatively, another mechanism that considers the disruption (breaking) of crystal layers and their slip into the existing ones in a layer intercalation process is proposed by Veiga and Lepienski [221].

3.6. Pop-In in Loading Curves Load-displacement indentation curves in some materials show sudden discontinuities on depth penetration. These discontinuities are called pop ins. A pop-in event may be associated with different aspects, depending on the kind of tested material and its mechanical properties. A series of articles reporting the applications of nanoindentation to measure the mechanical properties of materials was published, showing the sudden penetration of the indenter, which is followed by elastic or elastic–plastic deformation. Pop ins may occur in very small load indentations made in well-annealed single-crystal materials [211–219]. Other types of pop ins occur during the indentation of hard

Figure 10. Pop-in events in load versus displacement curves for four different lamellar materials. (a) Mica. (b) Graphite. (c) NbS2 . (d) GaSe.

15

Nanomechanical Properties by Nanoindentation

Gouldstone et al. [211–212] reported nanoindentation experiments followed by TEM and AFM observations on single-crystal and polycrystal Al thin films and polycrystal Cu thin films on Si substrates. They concluded that both single-crystal and polycrystal thin films exhibit periodic displacement pop ins at essentially constant loads during loadcontrolled nanoindentation. The first displacement pop in appears to occur when the maximum shear stress at the indenter tip is on the order of the theoretical shear strength of the material. The nanoindentation response of the film in between the displacement bursts was found to be purely elastic, and representative of the behavior under a “sharp” Berkovich indenter. The study of pop-in events can be very helpful to understand the deformation mechanisms that occur under the indenter as the load is applied.

4. THEORETICAL ANALYSIS OF DEPTH-SENSING INDENTATION Considerable efforts have been undertaken to develop comprehensive theoretical and computational models, in an attempt to elucidate the mechanics and mechanisms of indentation, and to characterize the mechanical properties [225–229]. These models normally are developed based on elastic–plastic models. Advances in modeling are being obtained by interactive studies, where simulations are verified by experiments and vice versa. The computational simulation of indentation by finite-element methods has been extensively used since the 1970s [230–236]. The first theoretical analysis of indentation was made by Hertz, who examined the elastic contact between two spherical solids [237]. In the context of P –h measurements, for the case of a flat surface (with infinite radius of curvature) which is indented by an elastic sphere of radius R, Hertz showed that P=

4 E R1/2 h3/2 3 r

(21)

where P is the load, h is the displacement, Er is the reduced elastic modulus, and R is the indenter radius. Analyzing the plastic deformation of a spherical indentation, Meyer [1] proposed an empirical relation P=

Kam

2Rm−2

(22)

where m is the hardening factor, a is the contact radius, R is the indenter radius, and K is a material constant. Considering a stress–strain relationship given by ) = )0 n

(23)

where ) is the stress, is the strain, and n is the strain hardening, Tabor [1] correlated the strain hardening n to the m hardening factor of Meyer by m=n+2

(24)

Johnson [238] suggested that the outcome of a sharp indentation test on elastic–plastic materials will fall into one of three levels, depending on the parameter & &=

E tan

1 −  2 )y

(25)

where E is the elastic modulus,  is the Poisson coefficient, )y is the flow stress at first yield, and is the angle between the sharp indenter and the nondeformed surface of the material. According to Johnson, for & < 3, considered level I, very little plastic deformation occurs during the indentation, and the properties can be derived from an elastic analysis. In level II, for 3 < & < 40, an increasing effect of plasticity is observed. In this region, both the plastic and elastic properties of the material must be taken into account. Based on the solution of the expansion of a spherical cavity from Hill, and considering the fact that the pressure in the region beneath the indenter is mostly hydrostatic, Johnson suggested that the mean pressure, and consequently the hardness, could be expressed by   E tan 2 (26) H = )y 1 + ln 3 3 1 −  2 )y For & > 40, the plastic deformation is present all over the contact area, and the elasticity no longer influences the hardness value of the material. In this region, the hardness can be given by relation H = C)y

(27)

where C is a constant that only depends on the geometry of the sharp indenter. Sometimes )y is substituted by )r , which corresponds to the flow stress at a plastic strain r . The observed value of C varies from 2.5 to 3 for metals. Hainsworth et al. [239] observed that the loading curve obtained by depth-sensing indentation experiments can be described by P = Kh2

(28)

where K is a constant. This relationship was tested by finite-element calculation by Zeng and Rowcliffe [240]. The dimensional analysis of Cheng and Cheng [241] supports this assumption. According to Hainsworth et al. [239]    −2 E H K=E * (29) ++ H E where E is the elastic modulus, H is the hardness, and * and + are empirical constants. The values obtained from Hainsworth were * = 0194 and + = 0903. Malzbender et al. [242] derived an analytical expression for the indentation load–depth relation during loading, given by     −2 1 Er  H P = Er √

h + ,2 (30) + 4 Er 245 H where Er is the reduced modulus, is the geometrical constant which take a value of 0.72 for a conical indenter and 0.75 for a paraboloid, and , is a correction for blunt tips.

16 Larsson [243] developed an investigation of the contact of a sharp indenter under rigid-plastic conditions using theoretical and numerical approaches. He found that, in a general situation, where stress–strain relations are not idealized, there is no single representative value of the uniaxial stress–strain curve that can be used in order to evaluate the global parameters at contact. There is an important effort underway in the theoretical analysis of nanoindentation. However, analytical models are not available due to the complexity of the problem. Then, finite-element methods are the most promising ways to analyze the contact of a hard indenter with a solid material.

5. CONCLUSION Nanoindentation is a powerful technique to determine the surface mechanical properties in the nanoscale regime in practically all kinds of solid materials. This technique is especially important for new materials developed by nanoscience and nanotechnology applications. The method is based on the analysis of the load–unload curve, which allows us to obtain information about the elastic–plastic surface behavior in a well-controlled way. Hardness and elastic modulus values are measured using known analysis methods which are widely accepted nowadays. However, certain additional care is necessary in measurements performed under extreme conditions, such as when the elastic–plastic behavior is strongly dependent on the ratio H /E, or when soft surfaces show pile up around the indenter and very hard surfaces present a sink-in effect. In these situations, the measured values of the hardness and elastic modulus may show deviations from the actual values. Additional care is also recommended for measurements on thin films where the substrate influence is an important factor. The more common indenters used in nanoindentation are the Berkovich and Vickers tips, but additional information about the mechanical surface properties may be accessed by other kinds of indenters: • Surface fracture toughness for brittle materials can be studied by using a cube-corner indenter. • Viscoelastic properties, typical for polymer materials, can be obtained by using cylindrical or flat punch indenters. • Surface adhesion quality between the coating substrate and residual stress at the surface can be studied by using spherical indenters. A scratch test performed by using a modified nanoindentation machine can also give extra information about the mechanical surface properties, especially for coatings. However, it is not very clear because of their complexity, and mainly due to the frictional force. The obtained results are qualitatively correct, but more theoretical work is needed in order to compare the different results. Despite the great number of published papers relating mechanical surface properties acquired by using nanoindentation, supplementary efforts still need to be performed on the theoretical approach in order to quantify and better understand the results in the nanoscale regime.

Nanomechanical Properties by Nanoindentation

As a future challenge, it is necessary to develop nanoindentation devices that permit us to perform indentations at higher temperatures. In some materials, temperature dependence on their ductile-brittle behavior occurs, and it may be better investigated if high-temperature nanoindentation is available in the future.

GLOSSARY Chemical vapor deposition (CVD) process used to product coatings or thin films by using chemical route. Diamond-like carbon (DLC) a hard noncrystalline carbon film grown by CVD or related techniques, and that contains predominantly sp2 carbon–carbon bonds. Friction coefficient In tribology, denotes the dimensionless ratio between the tangential friction force and the normal applied force in a two-body interaction. Hardness Relative resistance of a metal or other material to denting, scratching, or bending. Denotes, for a solid material, the resistance to penetration by other bodies. The equation used to calculate the hardness is the ratio between the applied load and the residual area produced by the penetration (H = F /A). Value depends on the method used for measurement. Ion implantation Process where atomic species are introduced in the near-surface region by a nonequilibrium process which depends on the parameters used, like ion energy, ion current, chamber vacuum, and temperature conditions. The modified surface region can then be constituted of embedded phases, burried layers, and also, under some conditions, to form a coating layer. In the general case, a graded region is produced from the near-surface to deeper regions. Nanohardness Denotes, for a solid material, the resistance to penetration by other bodies for depths at nanometerscale. Nanohardness test Hardness measurement based on analysis of loading–unloading load versus depth curve in nanoscale regime. The indenter used can be Berkovich, Vickers, cube corner, flat end, and cylindrical. Nanoindentation Process of indenting a solid surface by a pointed hard material at very low load using a load and depth-sensing device to obtain the surface hardness. Nanoindenter Device constructed to perform nanoindentation and capable of measuring hardness and elastic modulus of material surfaces in the nanoscale regime. Physical vapor deposition (PVD) process used to produce coatings or thin films by using a physical route. Plasma-based ion implantation Surface modifier process based on two approaches one for conventional ion implantation, and the other to give thermally enhanced diffusion. The plasma sheath around the target expands dynamically, and permits the target surface to be uniformly treated, forming a modified layer.

ACKNOWLEDGMENTS The authors thank CNPq-Brazil, Capes-Brazil, and Fundação Araucária-PR-Brazil for the financial support, and Maria Fabíola Vasconcelos Lopes for helping in the final revision.

Nanomechanical Properties by Nanoindentation

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Encyclopedia of Nanoscience and Nanotechnology

www.aspbs.com/enn

Nanomechanics of Nanoscale Materials Robert Geer University at Albany, State University of New York, Albany, New York, USA

CONTENTS 1. Introduction 2. Nanomechanical Imaging 3. Nanotube Materials 4. Nanotube Composites 5. Nanomechanics of Nanoporous Materials for Dielectric Applications 6. Concluding Remarks Glossary References

1. INTRODUCTION 1.1. Nanotechnology The fields of nanotechnology and nanoscience represent an intersection of multiple, sometimes diverse, fields of science with a single commonality: manipulation and functionalization of matter at the nanometer-length scale. As defined by the National Nanotechnology Initiative (NNI), a document crafted by the Interagency Working Group on Nanoscience, Engineering and Technology, nanotechnology “


is concerned with materials and systems whose structures and components exhibit novel and significantly improved physical, chemical, and biological properties, phenomena, and processes due to their nanoscale size” [1]. The essence of this statement revolves around so-called emergent properties or processes that are a sole result of the nanoscale engineering of matter. The NNI goes on to state, “Reducing the dimensions of structures leads to entities, such as carbon nanotubes, quantum wires and dots, thin films, DNA-based structures, and laser emitters, which have unique properties. Such new forms of materials and devices herald a revolutionary age for science and technology, provided we can discover and fully utilize the underlying principles.” The fundamental capability to manipulate the nanoscale organization of matter and control its mechanical, electrical, optical, chemical, and/or biological functionality is not a completely novel idea. For example, R. P. Feynman predated

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the realization of a nanotechnology solution to integrated circuit fabrication by more than four decades. In the late 1950s, Feynman gave his now famous “Plenty of Room at the Bottom” talk, where he presented the idea of a nanometer scale or molecular scale logic device [2]. Such devices are attractive for a variety of reasons. Molecules comprise structures with characteristic length from subnanometer to hundreds of nanometers. Hence, they bridge the dimensional regime between current lithographic structures and atomic sizes. Moreover, the tremendous flexibility in the design and chemical synthesis of molecular structures provides a broad adaptability with respect to potential device functionality, device implementation, and device operation. Virtually every other field of technology development possesses parallel potential with respect to the device miniaturization and integration conceivable via nanotechnology. The emergent functionality of nanoscale structures and devices has its origins in the unique aspects of quantum mechanics and molecular self-assembly. The quantummechanical or wave nature of matter can be exploited to tailor electronic, optical, and chemical properties of a given material system, while the penchant for matter to spontaneously organize at the molecular-length scale provides novel structural templates with which to manipulate the quantum-mechanical boundary conditions that are so critical to controlling quantum phenomena. This is not to say that quantum-mechanical effects are not present in macroscale systems, or that molecular-level self-assembly guarantees new material functionality. Rather, it is the exploitation of the two in concert that opens vast new areas of technological promise. Current examples of nanotechnological breakthroughs are continuously emerging. The discovery of molecularscale graphene tubes, dubbed carbon nanotubes, typifies the potential impacts of nanotechnology [3]. By virtue of the propensity of carbon atoms to form threefold coordinated 2-D atomic sheets and the structural perfection of such sheets when rolled into a tubular geometry, entirely new mechanical, chemical, and electrical functionalities have been demonstrated. Such sheets exhibit mechanical properties superior to virtually all macroscopic materials with respect to the combination of strength, flexibility, and light

Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 7: Pages (21–46)

22 weight. Likewise, the perfection of the carbon atomic configuration in such nanotubes has led to the confirmation of the ballistic transport of electrons along the direction of the tube axis. Interestingly enough, the structural details of the “rolling” of the graphene sheet can be exploited to program metallic or semiconducting electronic properties of the nanotube. There is certainly no analogous macroscopic system which possesses such a rich variety of functionality. Hence, this electrical programmability certainly qualifies as an emergent property. Other examples of emergent functionality associated with the nanoscale control of materials include quantum well and quantum dot phenomena exploited for optoelectronic applications of semiconductors, and the rich fields of macromolecular self-assembly that have led to entirely new paradigms for chemical and biological sensor development.

1.2. Mechanics Versus Nanomechanics As noted previously, the advances promised by the nanoscale material manipulation of matter “


herald a revolutionary age for science and technology, provided we can discover and fully utilize the underlying principles.” The “underlying principles” referred to in this statement are those that govern the modification of the conventional understanding of a system as nanoscale effects or phenomena emerge. Consider the case for nanomechanics. The conventional theories for mechanics and the mechanical properties of materials are perhaps the oldest and best studied of all the classical physical sciences. Although it was recognized early on that the microscopic aspects of materials governed their mechanical properties (e.g., the nature of chemical bonding and the microscopic aspects of surface and interface morphology), the validity of so-called continuum elastic mechanics to correctly describe the mechanical properties of materials (even down to micrometer-length scales) has been self-evident for small deformations. However, as the relevant length scale for mechanical deformation of a material system decreases to that of the interatomic or intermolecular spacing, the theories of continuum mechanics are expected to break down. At such length scales, realistic modeling of the mechanical response of a material or structure must take into account the quantum nature of the material. For example, in crystalline materials, the presence of lattice defects, impurities, and grain boundaries must be included to correctly describe the evolution of internal strains resulting from internal and externally applied stresses. This constitutes classical dislocation theory [4]. (The term “classical” is applied to this theory since it treats the crystal imperfection itself as a mathematical singularity, while assuming that the atomic or molecular displacements in the near vicinity of the imperfection are small and sufficiently well described by continuum elastic mechanics.) Of course, there exist entire classes of inelastic mechanical phenomena that are successfully described by empirical or semiempirical classical continuum theories. Simply enumerating them is beyond the scope of this chapter. In light of the success of such classical continuum theories, it is natural for one unfamiliar with the field to ask whether or not emergent mechanical phenomena at the nanometer-length scale are to be expected at all. Yes and

Nanomechanics of Nanoscale Materials

no are both correct answers to this question. The equations of classical elasticity are based on linear response theory; a stress applied to a solid will produce a deformation (strain) linearly proportional to that stress. This linear relationship is a direct result of the electrostatic potential energy of an atom, ion, or molecule as a function of its relative displacement in virtually all bulk materials. For small atomic displacements from an equilibrium position, this potential energy varies quadratically, leading to a linear restoring force (similar to a spring force). As long as this constraint is satisfied, elastic response may be expected, even if the spatial extent of the object is only a few nanometers [5]. However, by tailoring the atomic or molecular interaction forces within a material, as well as its physical-length scale, dramatic departures from elastic behavior may be observed and exploited. In contrast, it has also been shown that certain nanoscale systems can possess linear response behavior at strains well beyond the limits of conventional elastic materials [6]. Thus, there is no question that nanoscale-manipulated materials may “


exhibit novel and significantly improved


” mechanical properties or phenomena. The challenges in this field of “nanomechanics” encompass the discovery process by which the underlying principles behind such manipulation are investigated and understood.

1.3. Overview of Present Work The goal of this work is to review critical areas of research in the fields of nanomechanics of nanoscale materials and structures that represent vital efforts in the development of nanotechnology. This document is not a monograph on the theory of mechanics nor is it a compendium of experimental approaches in the study of mechanics. Rather, it focuses on recent experimental and theoretical investigations of emergent mechanical behavior at the nanoscale. Detailed overviews are presented regarding nanomechanical material systems, as well as the development of new instrumentation that will enable the underlying principles of nanomechanics to be more fully elucidated. To optimize the accessibility of this work to the widest possible audience, broader narrative descriptions of the phenomena under consideration are combined with more formal theoretical and experimental summaries. The necessary mathematical definitions of material mechanical properties or summaries of relevant experimental or computational methodologies will be introduced as required. A background in theoretical or experimental materials science or engineering is not required, although a familiarity with the physical principles of mechanics and elasticity will be helpful. The work is separated into four major sections. The first section comprises a review of newly developed characterization and metrology instrumentation that is enabling the direct measurement of material mechanical properties on the nanometer-length scale. The successful introduction of direct “nanomechanical imaging” is absolutely essential for the degree of fundamental understanding of the mechanics of nanoscale materials necessary for technological exploitation. The second section reviews perhaps the most important nanoscale system with respect to emergent nanomechanical functionality, nanotubes. The third section

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Nanomechanics of Nanoscale Materials

reviews the most recent work regarding nanotube composites, and the fourth section details extremely recent work regarding the mechanics of nanoporous materials for applications in nanoelectronics. To this point, no significant mention is made considering the field of microelectrical mechanical systems (MEMS) or its more recent incarnation, nanoelectrical mechanical systems (NEMS). Traditionally, MEMS has focused on micromachining 3-D structures utilizing the materials of the integrated-circuit (IC) industry. As MEMS has matured, it has provided entirely new experimental platforms from which to test and evaluate the dependence of material and structural mechanical properties as a function of reduced length scale. However, the vast majority of MEMS experimental and theoretical work will not be discussed as conventional elastic continuum models provide an excellent framework for characterizing relevant mechanical properties of MEMS structures.

2. NANOMECHANICAL IMAGING Macromechanical characterization is an extremely mature field. The basic theory of mechanics was founded on empirical observations that solid bodies exhibit a deformation of some sort (i.e., shape or volume) under the action of applied forces [4]. Standard continuum mechanical theory describes the change in distance between any two points in a solid under the application of an external stress. Assuming linear response, this treatment results in the conventional definitions of elastic constants (bulk modulus, shear modulus, Poisson’s ratio, etc.) and the generalized form of Hooke’s law. Mechanical characterization beyond elastic behavior is primarily concerned with the onset of inelastic (plastic) deformations and the investigation of material hardness, fracture toughness, and yield (tensile/compressive) strength. Consequently, the study of mechanics is, in large part, the study of deformation. The study of nanomechanics is no different from the previous discussion of nanomaterials illustrated. Recall that the elastic response of an ideal ordered material is directly determined by the local electrostatic atomic, ionic, or molecular potential energy well, the minimum of which is approximately parabolic. If the local atomic, ionic, or molecular mechanical response is preserved in nanoscale structures, it is reasonable to assume that some analogy to “classical” mechanics will exist, and that analogs to classical mechanical measurements will exist. This assumption is the foundation for the fields of nanoindentation, nanotribology, and nanomechanical imaging. These techniques, generally, utilize some type of point contact probe with a nanometer characteristic length scale. Classical mechanics has, for the most part, been used to interpret the results of such experiments, providing empirical confirmation of the propriety of such models. Acoustic, optical, and ultrasonic microscopy techniques have long been the choice for the micrometer-scale characterization of certain surface and subsurface mechanical properties of solids; however, the inherent resolution limitations in farfield lenses and/or coupling media have limited their application at the nanoscale [7]. Nanotribology is an exciting vibrant field and, although intimately related to nanomechanics, is beyond the scope of this review [8]. Nanoindentation is the

culmination of decades of empirical research, and is now on the verge of a truly nanoscale characterization technique, although it is typically implemented as a destructive methodology better suited to planar surfaces than nanoscale structures [9]. Since the rising fields of nanoscience and nanotechnology focus on emergent functionality, it is appropriate to restrict detailed discussions to those methodologies that provide not only nanoscale resolution, but that are appropriate for the characterization of nanoscale structures and devices. Consequently, this section will focus on nanomechanical imaging, defined as the cadre of techniques capable of spatially resolving the variation of mechanical properties of nanomaterials, structures, and devices on the nanometer-length scale. Since the mechanics of these techniques use models developed, in part, for nanoindentation, it will be referenced throughout this discussion. The remainder of this section is organized as follows. First, a brief overview is presented of the simple mechanics of a point-probe contact with a surface. This is followed by a brief description of the experimental apparatus used to control such contacts with nanoscale precision, and to exploit them for the extraction of nanomechanical image data. Third, the development and application of a variety of these techniques will be reviewed with respect to the current literature. Lastly, a review of recent results will be presented to demonstrate the potential of nanomechanical imaging and its coming role in the development of nanotechnology. If an object is of insufficient size or disposition to measure its deformation upon application of an external stress to determine elastic moduli, it is often necessary to apply a point probe to characterize mechanical properties. Hertz was the first to treat such a situation to determine the deformation of two objects in direct contact under an external load [10–11]. (The original problem treated two hemispherical surfaces. A sphere/plane system was recovered by letting one radius diverge to infinity.) The situation and the necessary parameters are outlined in Figure 1. Assuming only elastic deformation (short-range forces) and no interfacial adhesion between the tip probe and sample surfaces, the relation between the contact radius a of the tip/sample contact and the load F is a3 =

3F R  4Er


   −1 Er ≡ ET−1 1 − T2 + ES−1 1 − S2 (1)

where the S and T subscripts denote the sample and tip, respectively. Er is defined as the reduced Young’s modulus.

R h a Figure 1. Idealized representation of the elastic deformation of a sphere/plane contact. Note that the radius R of the sphere is defined predeformation.

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Nanomechanics of Nanoscale Materials

At the apex of the tip, this relation can be rephrased:  F = Er2 Rh3

(3)

The classical derivation of this indentation raises questions regarding its applicability in realistic situations due to the presence of long-range attractive forces (van der Waals), electrostatic forces (surface charging), capillary forces, or general adhesive forces, and not least of all, the quantummechanical limit if the mechanical contact is reduced to the atomic-length scale. Several models discussed below include the former effects. And although a number of authors have considered atomic-scale models for tip interaction with respect to the relatively small forces used in topographical imaging, no solely quantum models have addressed mechanical response [12–16]. Although no formal criterion has been universally adopted, it is assumed here (and consistently shown in the vast majority of the experimental literature) that the mechanical response for a surface with a contact radius on the order of 5 nm or larger can be described by elastic mechanics. If an adhesion energy is associated with the contact area, the local profile of the tip/sample deformation is changed. Johnson, Kendall, Roberts, and Sperling (JKRS) included an adhesion energy w in the Hertzian problem [17–18]. The solid–solid contact deformed locally into a connective neck due to adhesion, resulting in a modified contact area radius:  6Er F 3 Er 3/2 =a −a Rw R2 w R2 w (4) hEr2/3 a2 Er2/3 2 6aEr1/3 = − 2 2 1/3 2 2/3 2 1/3  w R wR  3 wR  w ≡ T + S − T S Here, T S refers to the tip (sample) surface energy, and T S is the interfacial energy. Although typically applied to soft materials with large radii, this model has been shown to be applicable over a wide range of materials and nanoprobe tips [19]. An alternate model which reduces artifacts in JKRS theory related to stress variation at the edge of the connective neck was developed by Derjaguin, Muller, and Toporov (DMT), wherein the surface forces are assumed to act only in an annular region just outside the contact radius [20]. Er F = a3 −2 Rw R2 w hEr2/3 a2 Er2/3 = 2 2 1/3  w R wR2 1/3

(5)

In all cases, the force–displacement relation depends upon the elastic (or elastic/adhesive) property of the solid. These relationships have been applied to describe the interactions

of scanning probe microscope tips and sample surfaces to relate contrast in the scanned image to sample mechanical properties. However, to understand their application, it is necessary to first review the operation of scanning probe microscopes. The scanning probe microscopy (SPM) platform consists of a nanoscale probe tip placed on or near (∼nm) a surface, and scanned across that surface using a high-resolution piezoceramic crystal scanner (Fig. 2). The probe tip interacts with the surface, and transduces some type of surfacerelated signal into a digital intensity which is collected into a spatially resolved image with an appropriate raster. The positional control of the piezoscanner is subangstrom, and enables tremendous spatial resolution of the signal transduced by the probe tip. In most cases, the scans are carried out in a feedback mode, where the tip signal is kept constant as the tip is scanned across the sample surface. An early example of such an approach was the so-called scanning tunneling microscope (STM) [21–23]. In an STM, the tip consists of an ultrasharp metal probe which is kept at a reference voltage with respect to a conductive surface. When the tip is brought sufficiently close to the conducting surface (by a piezoscanner), it is possible to measure a current associated with electrons tunneling from the tip to the sample (for separations less than a few nanometers). In this manner, scanning the tip at a constant height permits the measurement of the local density of electronic states (LDOS) at the surface. If the LDOS is constant, the tunneling current between the tip and sample primarily depends on the tip–sample separation, and a feedback circuit can be applied during the scan to keep this current constant by adjusting the tip height during the scan using a vertical piezoceramic scanner. This results in a nanometer-scale image of the surface topography. A separate SPM implementation is the so-called atomic force microscope (AFM) [24] or scanning force microscope (SFM). In the SFM, the nanoprobe typically consists of a pyramidal tip on the end of a micromachined Si cantilever (Fig. 3) [25]. The tip is brought close to the sample. As the tip–sample separation decreases, a long-range attractive van der Waals force deflects the cantilever toward the sample. This is measured via a laser reflected from the backside of the cantilever into a differential photodiode where the deflection of the laser

Sp ph litot dio od d ec e tec to r

Taking the origin at the center of the contact area and defining r as the radial distance in the plane of the sample, the elastic indentation h as a function of r is given by   r2 3P r ≤a (2) 2− 2  h= 8aEr a

Sample

Laser diode

Cantilever substrate

XYZ single tube piezo scanner Figure 2. Schematic of conventional SPM configuration. The laser diode beam is focused onto the back of the cantilever at the sample. Deflection of the laser beam due to tip motion is recorded by the split photodetector. This intensity variation is incorporated into a feedback loop incorporating the z axis of the piezoscanner. The x–y axes of the scanner are used to raster the tip across the sample surface.

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Nanomechanics of Nanoscale Materials

kc, βc d (t) z (t)

ki, βi

Figure 4. Schematic of tip–sample model used by Burnham et al. The time-dependent vertical position of the sample is denoted by zt. The resulting deflection of the tip is denoted by dt. kci and ci denote the spring stiffness and damping constants of the tip and sample, respectively.

The effective mass of the oscillator is defined in terms of the resonant frequency of the cantilever: o = kc /m∗ 1/2 . This is the classic damped-coupled oscillator problem. Solving the equation of motion yields the frequency dependence of the relative displacement ratio d1 /z1 and the phase :

Figure 3. Electron micrograph of pyramidal tip of an Si cantilever.

is calibrated to the change in tip height. If the tip is brought into contact with the sample and scanned across the sample surface, the deflection of the tip can be used to determine the sample topography. Usually, a feedback mode is established wherein the deflection of the cantilever is kept constant by adjusting the relative z position of the tip or sample using a vertical piezoceramic scanner. From this point of view, the end of the pyramidal tip is a nanomechanical probe when a load is placed on the tip in contact with a surface. Although the AFM has been used in a wide range of configurations, we will only focus on those relevant to nanomechanical characterization. An SFM can be used as a nondestructive nanoindentor. However, due to the low spring constant required to provide a high surface topography sensitivity, the tip can only “indent” relatively soft materials. Still, by oscillating the tip below the fundamental resonance of the cantilever against a surface, and measuring the resultant oscillation amplitude as the tip is scanned across that surface, it is possible to record an image for which the intensity is proportional to the mechanical response. This mode is conventionally referred to as force-modulation microscopy (FMM) since the tip–sample force is modulated as the sample is scanned [26–30]. A simple theoretical treatment of this mode was treated by Burnham and co-workers to investigate not only the low-frequency (FMM) mechanical response, but also the high (superresonant) frequency response supplied to the sample by a piezooscillator fixed to the sample [31]. That model is detailed in Figure 4. The sample elastic properties are modeled as a simple spring of spring constant ki with damping i . Assuming that ET ≫ ES , the quantity ki is linearly related to the sample Young’s modulus, and is referred to as the contact stiffness. The details of this relationship are dependent upon the choice of model used. The time dependences of the tip and sample along with the equation of motion are [31–32] z = zo + z1 cost;

d = do + d1 cost − 

˙ + kc z − d m d¨ + 2m c d˙ + kc d = 2m∗ c z˙ − d ∗

∗

(6)

ki 1 + 2m∗ i /ki 2 d1 =

z1 ki + kc − m∗ 2 2 + 4m∗2 2 i + c 2

2m∗  i m∗ 2 − kc  + c ki ! tan  = ki ki + kc − m∗ 2  + 4m∗2 2 i i + c 

(7)

These results yield two important limiting cases with respect to SFM mechanical imaging modes. Consider the lowfrequency ( ≪ o ) and high-frequency ( ≫ o ) limits of this motion: ki d1 ≈  z1 ki + kc k 2 d1 ≈ i o2  z1 kc 

for  ≫ o (8) for  ≫ o

The low-frequency limit is indicative of the conventional FMM mode. Here, the ratio of the tip deflection (experimentally measured quantity) to the sample oscillation amplitude is only sensitive to the surface mechanical properties if the contact stiffness is on the order of the cantilever spring constant. Hence, if the cantilever is “soft” enough to measure nanoscale topography, it will only be capable of qualifying the spatial dependence of the surface modulus for soft materials. Consequently, FMM is primarily a tool used for polymeric or soft materials. The high-frequency limit is more intriguing from the viewpoint of nanomechanics. At high frequencies, the cantilever cannot follow the driving frequency (superresonant motion), and the driven tip oscillation amplitude decreases as a square of the driving frequency. However, the prefactor of this amplitude depends linearly on the ratio of the surface contact stiffness to the cantilever spring constant. In other words, large deflection implies large, local contact stiffness. Imaging in this mode can provide a signal directly proportional to the surface Young’s modulus. Since the contact area of the tip is still on the order of the radius of curvature of the pyramidal tip (∼5–20 nm), this mode (christened SLAM by Burnham for scanning local acceleration microscopy) is truly capable of imaging the mechanical properties of a wide range of

26 materials. Care is required in this technique as the superresonant frequency must fall within the bandwidth of the photodiode detector of the SFM. Also, the expression [Eq. (7)] is valid only in the limit of amplitude-independent contact stiffness, that is, a linear force–displacement response. This is not strictly true in the case of the aforementioned JKRS or DMT models due to the force-dependent area of the contact (even in the case of a flat-end punch) [17, 18, 20]. Consequently, the calibration of SLAM images requires detailed knowledge of the true contact stiffness so that a region of model validity can be determined. However, the simplicity of the model is a major advantage in data interpretation and image artifact identification. A variation of this approach was investigated several years earlier by Yamanaka et al. [33–34]. Similar to SLAM, an out-of-plane surface vibration was applied to the sample. This approach considered ultrasonic frequencies beyond the response of the photodiode, so the direct oscillation of the cantilever was not observed. However, at high oscillation amplitudes (typically >0
4 nm), a nonzero dc tip deflection was observed. This observation implied that the nonlinear force–displacement curve was being probed, as expected from the models presented above. Moreover, the use of such frequencies reduced the tip oscillation amplitude dramatically, rendering it effectively immobile. As such, the tip constituted (on the high-frequency time scale) an infinitely stiff surface against which the sample periodically is indented [34]. Ideally, then, the force–displacement curve for the tip–sample indentation should precisely correspond to the models presented above. The appearance of a nonzero dc displacement of the tip implies that a nonlinear region of the force–displacement curve is being probed. The oscillation amplitude at which this nonlinearity appears is then related to the slope of the linear portion of the F versus h curve, that is, the contact stiffness. This imaging mode has been referred to as ultrasonic force microscopy or UFM. The critical concept for mechanical imaging via UFM is the inherently nonlinear interaction of a scanning-probe cantilevered tip in contact with a surface that is undergoing outof-plane ultrasonic vibrations at a frequency far exceeding the resonant frequency of the cantilever [33]. In such a case, the cantilever is inertially damped and, on the ultrasonic time scale, effectively rigid [34]. Hence, the surface rigidity of materials with contact stiffness orders of magnitude higher than the cantilever spring constant can be quantitatively measured. To illustrate how surface nanomechanical rigidity can be extracted via UFM, Figure 5 shows a schematic of a prototypical force–displacement curve for a rigid nanoprobe tip in contact with a surface. Negative displacement (indentation) of the sample by the tip results in a strong repulsive force. For positive displacement, an attractive force exists between the tip and sample until the sample is pulled away from the tip. This attractive force may result from van der Waals forces, adsorbed fluid layers, or other types of adhesive interactions. For a scanning probe tip in static contact with a surface, the relative tip–sample distance is ho and the tip–sample contact force is Fo . Apply an ultrasonic out-of-plane oscillation #ht = ho + A cost). If A is small, the average of the force excursion #F is approximately equal to Fo , that is,

Nanomechanics of Nanoscale Materials

Force F(h)

Fo

∆F

ho

Indentation (h)

Pull-off ∆h=ho+Acos(ωt)

h

Figure 5. Schematic force–displacement curve for nanoprobe tip and a sample surface. F h is the applied force. h is the relative displacement between the tip and the undeflected sample surface.

the tip undergoes no average displacement. If the oscillation amplitude is increased, the nonlinear region of the curve must be included to correctly calculate the average force on the cantilever tip [35]:   2/ F ho − A cost dt (9)

F ho  A = 2 0 kc zc = F ho  A

(10)

where kc and zc are the cantilever spring constant and tip deflection, respectively. A simulation of this #F as a function of oscillation amplitude A is shown in Figure 6 using the JKRS model [17–18]. The inset in Figure 6 highlights a critical feature of this average force. There is a “kink” or slope discontinuity in the averaged force, which appears for oscillation amplitudes exceeding a certain threshold value Ath , for which the tip approaches pull off. This slope discontinuity in F ho  A translates into a sudden increase in steady-state tip deflection [19]. The threshold amplitude is directly related to the slope of the force–response curve, defined as the contact stiffness between the sample surface and tip Sh ≡

%F %h

(11)

Figure 6. Simulated average tip–sample force–displacement curves for increasing values of A using Eq. (9) and the JKRS model (normalized units). Inset details the discontinuous slope resulting from oscillation amplitudes approaching or exceeding tip pull off.

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Nanomechanics of Nanoscale Materials

aluminum 0.3 0.0 -0.3 0.0

0.6 0.3 0.0

Figure 7. Simulated deflection response of a cantilevered tip (bottom) to a modulated ultrasonic vibration (top). Note that the onset of tip deflection requires a threshold amplitude.

1.4 1.2 1.0 0.8 10

20

30

TipForce(nN)

-0.3 0

Time

-4

4.0x10

resolved. To translate these tip-deflection curves into pixilated mechanical image maps, lock-in amplification is used to translate the area under each curve into a raster-scan pixel intensity. Determination of the sample modulus from these data can be carried out by mapping the amplitude response of the tip deflection to extract the functional dependence of the threshold amplitude versus Fo [33, 35, 39]. Extracting the amplitude variation of the “kink” (Fig. 7) provides the necessary information to determine the static or zero-amplitude contact stiffness from which the Young’s modulus can be calculated. Figure 9 displays the ultrasonic tip-deflection response as a function of applied tip force Fo for a spin-on polymer film. The inset in Figure 9 plots the variation of threshold amplitude against increasing force. Assuming a Hertzian response for the contact stiffness, the reduced Young’s modulus was directly calculated to be 4.8 GPa using a known tip radius and the absolute vibration amplitude (determined from an optical vibrometer). Using this methodology, Young’s modulus measurements have been undertaken for materials ranging from nanoporous silicates (Er ∼ 2 GPa) to Si3 N4 (Er ∼ 300 GPa). Application of this technique by Dinelli et al. reported relatively large sample-to-sample variations of modulus measured using this method [35]. This variation is significantly reduced for measurements carried out in vacuum following a low-temperature bake to remove surface-adsorbed water

Tip Deflection (a.u.)

Amplitude

‘Force jumps’

-4

2.0x10 Time (sec)

Figure 8. Experimental ultrasonic tip-deflection curves obtained from aluminum (upper curve) and polymer (lower curve) surfaces. Arrows denote the onset of tip deflection, estimating threshold amplitudes. The ramped modulation envelope for the ultrasonic sample vibration is shown at the bottom of the figure.

Modulated Ultrasonic Waveform

Threshold amplitude Nanoprobe Tip Deflection (simulated)

polymer

Amplitude (a.u.)

F is the average force, and R is the scanning probe tip radius. For a more realistic approach, such as the JKRS model, the relationship is more complex, and can be extracted using a forward modeling approach based on curves similar to those in Figure 6. As noted above, it is critical for the oscillation frequency to significantly exceed the fundamental cantilever resonance frequency (typically hundreds of kilohertz). In this frequency domain, the cantilever is inertially damped, not responding quickly enough to the oscillation to be deflected. For cantilever probes designed for use with conventional SPMs, this superresonant frequency typically exceeds 1 MHz [33]. The indentation of such tips at the forces of interest are totally elastic, and do not damage the sample. Frequencies as high as 80 MHz have been used, although higher order cantilever flexural resonance effects must be considered or instabilities may arise [36–37]. Since Ath depends monotonically upon the sample contact stiffness, its spatial variation will provide a map of the surface elastic response. Periodic ramping of the vibration amplitude beyond Ath as the tip is scanned across the sample provides elastic maps in the same fashion as topographic images. Figure 7 shows a simulated average tip deflection resulting from the application of a triangular-modulated vibration amplitude to the tip–sample displacement [36]. In the half cycle containing the ramp, note the discontinuity at Ath . Experimentally, this periodic tip deflection is extracted for modulation frequencies that are large compared to the tip–displacement feedback frequency in a normal topography mode, but small compared to the response frequency of the SPM photodiode detector used to measure tip deflection (typically, a few kilohertz). Experimental results are shown in Figure 8 for UFM tip deflection responses from aluminum and polymer substrates [38]. The differentiation of threshold voltages between the two materials is clearly

0.6 Tip Deflection (a.u.)

In the repulsive regime of the force–displacement curve, S is related to the reduced Young’s modulus of the tip and the sample. The details of this relationship depend on the complexity of the model used to describe the tip–surface interaction. For a simple Hertzian contact [10–11]  3 SHertz = 6FREr2 (12)

-4

2x10

-4

4x10

Time(s) Figure 9. Variation of ultrasonic tip deflection as a function of applied tip force Fo for a polymeric film. The variation of threshold amplitude is apparent. Inset plots this variation as a function of applied force.

28 films. For silicon oxide films, recent work has demonstrated an absolute error for modulus determination of 1 micrometer!) between

Figure 18. SEM micrograph of a microsieve with a membrane and a support structure. Courtesy of Aquamarijn Research.

Nanomembranes

57

Figure 19. SEM micrograph of a microsieve with circular and slitshaped pores. Courtesy of Aquamarijn Research.

the mask and the photolacquer layer may blur the pattern transfer. The amount of blurring is of course directly related to the ratio of the wavelength of the used light and the smallest feature size. Defect-free processing of wafer sized microsieves with small perforations is therefore virtually impossible even in high class clean room environments. A particle with a size of 10–20 micrometer between the

UV-light exposure Mask

Figure 21. SEM micrograph of the surface of a microsieve where the silicon is etched and removed via the perforations in the membrane. Courtesy of Aquamarijn Research.

contact mask (e.g., patterned chromium layer on a glass plate with thickness 2 mm) and the lacquer layer is able to blur or destroy the pattern transfer over an wafer area larger than 1–100 mm2 . For wafer sized microsieves or for microsieves with a pore size smaller than 1 micrometer one often makes use of other more modern lithographic techniques, such as wafer steppers, to produce microsieves.

2.1.2. Wafer Stepper Lithography

Development and CHF3 /O2 etching

KOH-etching from both sides

KOH-etching finished W

d

Figure 20. Fabrication process of a microsieve with contact mask lithography.

In light projection lithography [49–51] an optical lens system is used to project the pattern of the mask onto the photolacquer layer (contact-free technique). The blurring of the pattern is now only restricted to the size of the particles present on the photolacquer layer. The projection system often reduces the pattern of the mask between 1 and 10 times with respect to the projected pattern in the lacquer layer. The typical lacquer area that can be projected in one step is about 1–2 cm2 . More steps (of the wafer stepper) are therefore needed to project the full wafer (3–12 inch diameter). A typical single step time is 1–2 seconds. This time cannot easily be reduced because of the mechanical repetition step time and the minimum exposure time per light shot. Although wafer steppers are very expensive (new generation >5 M euro) they are very economical in mass production applications. Also it is relatively more easy to get smaller pattern dimension (e.g., 0.12 micrometer linewidths) than contact mask applications due to the use of high resolution lenses with a large numerical aperture. See Figure 22. Additional advantages are that the mask pattern is relatively large and can be made with relatively cheap laser writers. Lithographic reduction has historically been accomplished by optimizing the parameters in the Rayleigh model for image resolution: In this model [53, 54], image resolution = k1 /NA, and depth of focus = k2 /NA2 , where  = exposure wavelength and NA = numerical aperture (k1 , k2 are constants for a specific lithographic process). To pattern devices with decreasing feature sizes, photolacquer exposure wavelengths were reduced and numerical apertures were increased [55, 56]. See Table 3.

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58

1

2

3

4

5

12

6

7 11 8 10 9

Figure 22. Wafer stepper. (1) Optical adjustment system, (2) reticule, (3) telecentric lens, (4) alignment optic, (5) laser interference meter, (6) mirror, (7) wafer, (8) wafer chuck, x–y table, (9, 10) projected and unprojected pattern fields, (12) objective. Reprinted with permission from [52], D. Widmann et al., “Technologie hochintegrierter Schaltungen (2. Auflage).” Springer-Verlag, Berlin/Heidelberg/New York, 1996. © 1996, Springer-Verlag.

2.1.3. E-beam and Future Semiconductor Lithography Electron beam lithography (EBL) is a specialized technique [57, 58] for creating the extremely fine patterns required by the modern electronics industry for integrated circuits. Derived from the early scanning electron microscopes, the technique in brief consists of scanning a beam of electrons across a surface covered with a resist film sensitive to those electrons, thus depositing energy in the desired pattern in the resist film. The process of forming the beam of electrons and scanning it across a surface is very similar to what happens inside the everyday television or cathode ray tube display, but EBL typically has three orders of magnitude better resolution (typical spot size for EBL is 18 nm). The main attributes of the technology are (1) it is capable of very high resolution, almost reaching the atomic level; (2) it is a flexible technique that can work with a variety of materials and an almost infinite number of patterns; (3) it is slow, Table 3. Deep UV and extreme UV monochromatic laser light sources. Wavelength (nm) 248 193 157

Laser type KrF ArF F2

being one or more orders of magnitude slower than optical lithography; and (4) it is expensive and complicated— electron beam lithography tools can cost many millions of dollars and require frequent service to stay properly maintained. The first electron beam lithography machines, based on the SEM, were developed in the late 1960s. Shortly thereafter came the discovery [59] that the common polymer PMMA (polymethyl methacrylate) made an excellent electron beam resist. It is remarkable that even today, despite sweeping technological advances, extensive development of commercial EBL, and a myriad of positive and negative tone resists, much work continues to be done with PMMA resist on converted SEMs. Currently, electron beam lithography is used principally in support of the integrated circuit industry, where it has two niche markets. The first is in mask making, typically the chrome-on-glass masks used by optical lithography tools. It is the preferred technique for masks because of its flexibility in providing rapid turnaround of a finished part described only by a computer-aided design file. The ability to meet stringent linewidth control and pattern placement specifications, on the order of 20 nm each, is a remarkable achievement. See Table 4. Second, EBL is used for research into the scaling limits of integrated circuits and studies of quantum effects and other novel physics phenomena at very small dimensions. Here the resolution of EBL makes it the tool of choice. A typical application is the study of the Aharanov–Bohm effect [60, 61], where electrons travelling along two different paths about a micrometer in length can interfere constructively or destructively, depending on the strength of an applied magnetic field. Other applications include devices to study ballistic electron effects, quantization of electron energy levels in very small structures, and single electron transistors [62, 63]. To see these effects typically requires minimum feature sizes of 100 nm or less as well as operation at cryogenic temperatures. Alternative Techniques It is prudent to consider possible alternatives before committing to EBL technology. For chrome-on-glass optical mask fabrication, there are optical mask writers available that are based either on optical reduction of rectangular shapes formed by framing blades Table 4. New predictions (year node potential solutions) for the ever decreasing linewidths from the 1999 ITRS Lithography Roadmap. Year 1999 2002 2005 2008 2011 2014 >2014

Linewidth 180 130 100 70 50 35

nm nm nm nm nm nm

Lithographic tool KrF KrF + RET, ArF ArF + RET, F2, EPL, PXL, IPL F2 + RET, EPL, EUV, IPL, CBDW EUV, EPL, IPL, EBDW EUV, IPL, EPL, EBDW innovative technology

Note: KrF, ArF, and F2 are laser types. RET is resolution enhancement technology, including phase-shift-mask technology for enhanced resolution. EPL is electron projection lithography. EUV is extreme ultraviolet. IPL is ion projection lithography. PXL is proximity X-ray lithography. EBDW stands for electron-beam direct-write techniques.

Nanomembranes

or by multiple individually controlled round laser beams. Although at present EBL is technologically ahead of optical mask writers, this may not continue in the future. However, EBL will continue to provide a resolution advantage over the optical mask writers which may be important for advanced masks using phase shift or optical proximity correction. For 1:1 mask fabrication (i.e., X-ray), EBL will continue to be the most attractive option. Optical lithography using lenses that reduce a mask image onto a target (much like an enlarger in photography) is the technique used almost exclusively for all semiconductor integrated circuit manufacturing. Currently, the minimum feature sizes that are printed in production are a few tenths of a micrometer. For volume production, optical lithography is much cheaper than EBL, primarily because of the high throughput of the optical tools. However, if just a few samples are being made, the mask cost (a few thousand dollars) becomes excessive, and the use of EBL is justified. Today optical tools can print 0.12
m features in development laboratories, and 0.08
m should be possible within a few years. By using tricks, optical lithography can be extended to 0.1
m or even smaller. Some possible tricks include overexposing/overdeveloping, phase shift and phase edge masks, and edge shadowing [64]. The problem with these tricks is that they may not be capable of exposing arbitrary patterns, although they may be useful for making isolated transistor gates or other simple sparse patterns. Another specialized optical technique can be used to fabricate gratings with periods as small as 0.2
m by interfering two laser beams at the surface of the sample. Again, the pattern choice is very restricted, although imaginative use of blockout and trim masks may allow for the fabrication of simple devices [65]. X-ray proximity printing may be a useful lithographic technique for sub-0.25
m features [66]. Again, it requires a mask made by EBL, and since the mask is 1:1 this can be a formidable challenge. Especially if the throughput required exceeds the limited capabilities of EBL, this may be an attractive option. The disadvantage is that X-ray lithography is currently an extremely expensive proposition and the availability of good masks is limited. It also requires either a custom built X-ray source and stepper or access to a synchrotron storage ring to do the exposures. With care, X-ray lithography can also be extended to the sub-0.1
m regime [67]. Another technique to be discussed is ion beam lithography. The resolution, throughput, cost, and complexity of ion beam systems is on par with EBL. There are a couple of disadvantages, namely, limits on the thickness of resist that can be exposed and possible damage to the sample from ion bombardment. One advantage of ion beam lithography is the lack of a proximity effect, which causes problems with linewidth control in EBL. Another advantage is the possibility of in-situ doping if the proper ion species are available and in-situ material removal by ion beam assisted etching. The main reason that ion beam lithography is not currently widely practiced is simply that the tools have not reached the same advanced stage of development as those of EBL.

59 2.1.4. Laser Interference Lithography In 1995 van Rijn [3] proposed for the first time the use of laser interference lithography for the production of microand nanoengineered membranes (micro- and nanosieves). Because of the relatively simple periodic structures (orifices and slits) that are needed for the production of nanosieves and the fact that laser interference is potentially a very nonexpensive patterning technique [68–72] that is also applicable on nonplanar surfaces (very large focus depth) this method will be discussed more in detail, also because there is little published material on this subject so far [73]. In 1996 in a collaboration of van Rijn [74] with G. J. Veldhuis [127], A. Driessen, P. Lambeck, and Professor C. Lodder of the University of Twente an existing laser apparatus was modified to obtain photolithographic patterns for the development of nanosieves and isolated magnetic domains [76]. Double Laser Interference Exposure Technique When two planar waves of coherent light interfere, a pattern of parallel fringes will appear. These fringes can be used for the exposure of a photosensitive layer. See Figure 23. The depth of focus of this method is dependent on the coherence length of the light and can be on the order of meters or more, compared to (sub)micrometers for conventional optical lithography systems. As a result the demands on substrate flatness and wafer positioning are less critical. After the first exposure the substrate is rotated over 90
and exposed to laser interference lines again. Now the gratings cross each other and after development a square array of lacquer pores (Fig. 24, left) remains. The exposure time of the photolacquer layer is a critical factor. In case the exposure time is chosen larger the middle pattern of Figure 24 will be obtained. Upon further increasing this time isolated photolacquer dots (right) remain. Device Fabrication with Relatively Short Exposure Time Part of an incoming plane wave is reflected by the mirror and interferes with the undisturbed part of the wave to form an interference pattern (grating) on the substrate surface. To produce the plane wave, TE polarized light of an argon laser with a wavelength uv = 3511 nm is spatially filtered and expanded by focusing it onto a pinhole. See Figure 25. If the light intensity of each beam is I0 , the radiance on the surface is given by I = 4I0 sin2

θ




x x



θ

Figure 23. Left: first exposure of the substrate with the photolacquer layer. Middle: rotation of the substrate 90
. Right: second exposure of the substrate.

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60

Figure 24. SEM micrograph of photolacquer layer that remains after a double exposure in the laser interference setup. Left: short exposure time, middle: intermediate exposure time. Left and middle: Courtesy of J. Micromech. Microeng. Right: long exposure time. Courtesy of Aquamarijn Research.

with x the fringe period in the x-direction planar to the photolacquer layer: x =

between the beams inside the resist. We used = 20
and with n = 17 at   = 3511 nm we find  = 510 nm and ⊥ = 105 nm. Therefore the thickness of the photoresist layer is chosen smaller than 105 nm. The area that can be patterned using our mirror of 25 × 25 cm2 equals approximately 9 × 9 mm2 for  = 510 nm. In Figure 26, the backside of a support (1), a single crystalline 3′′ 100-silicon wafer with a thickness of 380
m, is pre-etched to a thickness of 15
m using optical lithography and conventional KOH etching (25%, 70
C). On the front side of the pre-etched support (1) a layer (2) of amorphous low stress [78] silicon rich silicon nitride with thickness 0.1
m is deposited by means of LPCVD by reaction of dichloresilane (SiH2 Cl2 ) and ammonia (NH3  at a temperature of 850
C. Except at the area where the microsieve pattern will be formed an etch mask layer (3) of sputtered chromium with a thickness of 30 nm is deposited. On top of this chromium layer (3) a layer (4) of positive resist was spun and patterned using interference lithography. A 100 nm thick layer (4) of positive photoresist (Shipley S1800 series) was spun, followed by a 5 min prebake at 90
C to evaporate the solvent. The resist was exposed to the

4

a

UV 2 sin

3 2

Here uv is the wavelength of the laser light in the medium that surrounds the substrate (usually air) and is the halfangle between the two beams. The smallest period that can theoretically be obtained occurs for = 90
and is equal to uv /2. The smallest period that can theoretically be obtained with our configuration is  = uv /2 = 175 nm. The corresponding minimum pore size (with a porosity >30%) will be approximately 175/2 = 88 nm. At low porosity of course smaller pore sizesa can be made. Since the beam is only split for a short path length near the substrate, this setup is very insensitive to mechanical instabilities and no feedback loop [77] is required to stabilize the interference pattern. The thickness of the photosensitive layer needs to be chosen with care to avoid problems with the periodic pattern normal to the substrate surface due to interference between the incoming beam and the one reflected on the substrate surface. Its period is given by ⊥ =   /2n cos n where n is the refractive index of the photoresist and 2 n is the angle Mirror

1

4

b

3 2

1

c

3 2

1

d

2

Pinhole

UV-laser

2θ 1

Lens Substrate Substrate holder

Figure 25. Setup for laser interference lithography. Courtesy of J. Micromech. Microeng.

Figure 26. Schematic representation of the fabrication process of a microsieve. The numbers indicate the silicon support (1), the silicon nitride membrane (2), the chromium etch mask (3), and the photoresist layer (4).

Nanomembranes

interference line pattern for 45 s. The intensity of the incoming light in the exposed area was measured to be 2 mW/cm2 for normal incidence ( = 0
). After rotating the substrate over 90
the exposure was repeated. The resist was developed for 15 s in a 1:7 mixture of Shipley–Microposit 351 developer and deionized water and dried by spinning. The exposure time was chosen such that only at the crossings of the grid lines (after first and second exposure) does the resist receive enough energy to be removed completely after development. Therefore a two-dimensional pattern of pores is created in the resist. A SEM picture of the exposed (2 × 45 s) and developed resist is given at the left in Figure 26. The diameter of the pores in the photoresist depends on the duration of exposure, herewith giving a possible tool to vary the pore size at a constant pore to pore distance. However, when the exposure time is chosen too long (2 × 75 s) the pores in the resist pattern may become too large and will overlap (Fig. 26, middle). Next the interference pattern is transferred into the silicon nitride membrane layer (2) by means of CHF3 /O2 reactive ion etching at 10 mTorr and 75 W for 2 minutes forming the required perforations. Subsequently the silicon underneath the membrane layer (2) is anisotropically etched with an SF6 O2 plasma at 100 mTorr and 100 W for 10 minutes with an etch rate of 2
m/min in order to form the macroscopic openings in the support (1). Figure 27 shows a SEM photograph of the resulting perforated membrane layer (2) showing a very regular pore pattern, the pore size being 260 nm with a pore to pore spacing of 510 nm. The pore size was very uniform over the whole 9×9 mm2 area. Microsieves with pore sizesa down to 65 nm have been fabricated using double-exposure laser interference lithography. The pores are obtained with an inverse process, as the direct process of pore formation in photolacquer has a narrow process latitude. An array of posts is transferred into an array of pores by evaporating chromium onto the posts, followed by a lift-off in acetone. The resulting patterned chromium layer is used as an etch mask for plasma etching of the silicon nitride membrane. See Figures 28 and 29.

Figure 27. SEM micrograph of the microsieve membrane showing pores with a diameter of 260 nm in a 100 nm thick silicon nitride layer. Courtesy of Nanotechnology.

61

Figure 28. Left: SEM micrograph of 80 nm wide posts with rippled sidewalls caused by the vertical interference pattern. Right: SEM micrograph of a membrane after plasma etching through the pores in a chromium layer. Courtesy of Aquamarijn Research.

2.1.5. Nanocontact Printing and Etching with Phase Separated Membranes Aloys Senefelder used in 1796 a porous stone (in Greek, lithos) as a tool for printing by patterning the stone with ink attracting (hydrophobic) and ink repelling (hydrophilic) regions. Lithography for semiconductor mass fabrication and other microsystem and nanotechnology applications has nowadays regained interest in inexpensive microprinting methods as an alternative or complement on current high tech optical wafer stepper technology. A need exists therefore in the art for a convenient, inexpensive, and reproducible method of plating or etching a surface according to a predetermined pattern. The method would ideally find use on planar or nonplanar surfaces and would result in patterns having features in the micrometer and submicrometer domain. Additionally, the method would ideally provide for convenient reproduction of existing patterns. Additionally, the need exists for the fabrication of surfaces that can pattern portions (e.g., SAMs) amenable to attachment of biological species, such as antibodies, antigens, proteins, cells, etc., on the (sub)micrometer scale. The study of self-assembled monolayers (SAMs) is an area of significant scientific research. Such monolayers are typically formed of molecules each having a functional group that selectively attaches to a particular surface, the remainder of each molecule interacting with neighboring molecules in the monolayer to form a relatively ordered array. Such SAMs have been formed on a variety of products including metals, silicon dioxide, and gallium arsenide using relief printing with a molded stamp made from polydimethylsiloxane (PDMS) [79]. The upper relief part of the stamp provided with a suitable SAM coating is then being contacted

Figure 29. SEM micrograph of a high-porosity microsieve made with the lift-off method. Courtesy of Applied Optics Group, University of Twente.

Nanomembranes

62 with a product with a high affinity for the SAM species and a conformal SAM pattern is formed on the product (e.g., alkanethiol pattern on a gold coated product).PDMS is a rather elastic and relatively strong material very well suited for reproducible contacting purposes on nonplanar surfaces; however, it lacks a microporous microstructure for enabling functional fluid (ink) transport to the product domains or to enable other functional properties as will be described. In Figure 30 three basically different printing techniques are represented. Microporous stamps 21 (Fig. 30) with (alternating) regions with a dense skin layer and adjacent regions with a (porous) layer without the skin layer have easily been made with a phase separation process by locally removing the skin layer by, for example, oxygen plasma etching with the aid of a perforated mask shielding the remaining dense skin layer regions. The stamps are made with a phase separation process with the aid of a mold having patterned regions with sharp protrusions penetrating the microporous layers and 5

6

3

16

2

25 22

26

15 12 11

1

21 23

13 7 1

17 15 12

27 25 22 21

11 2

5

14

4 7

17

24 27

Figure 30. Left: the art of relief printing. The upper relief part 2 of the stamp 1 provided with a suitable ink coating 3 is contacted with a substrate 7 with a high affinity for the ink species and a conformal pattern 4 is formed on the substrate 7. The lower relief part 5 may be made ink repelling with a suitable coating (e.g., PVA, PVP) in order to avoid smearing of the pattern 4 of ink originating from sections 5. The upper relief part of the stamp 1 is provided with a macro- or nanoporous structure to contain ink or to transport ink from an injection point 6 for reproduction or continuous printing of the pattern 4 on the substrate 7. Middle: the art of gravure printing. The engraved part 12 of the stamp 11 provided with a suitable ink coating 13 is then contacted with a substrate 17 with a high affinity for the ink species and a conformal pattern 14 is formed on the substrate 17. The nonengraved part 15 may be made ink repelling with a suitable coating (e.g., PVA, PVP) in order to avoid smearing of the pattern 14 of ink from sections 15. The engraved part of the stamp 11 is provided with a macro- or nanoporous structure (cf. SEM picture below: engraved part is microporous, nonengraved part has a dense skin layer) to contain ink or to transport ink from an injection point 16 for reproduction or continous printing of the pattern 14 on the substrate 17. Right: the art of planographic printing (i.e., art lithography). The ink delivering part 22 and the nonink delivering part 25 of the stamp 21 are not determined by a difference in height but are made by the provision of suitable ink repelling and ink attracting coating s. The stamp 22 with a suitable ink coating 23 on part 22 is then contacted with a substrate 27 with a high affinity for the ink species and a conformal pattern 24 is formed on the substrate 27. Part 25 may be made ink repelling with a suitable coating (e.g., PVA, PVP) in order to avoid smearing of the pattern 24 of ink to sections 25. Part 22 is provided with a macro- or nanoporous structure to contain ink or to transport ink from an injection point 26 for reproduction or continuous printing of the pattern 24 on the substrate 27. Also in another embodiment part 25 may be microporous and filled with an ink repelling medium (e.g., water; Senefelder 1796).

patterned regions without such sharp protrusions where a dense skin layer is formed. In case the skin layer is not dense but nanoporous the skin layer can of course first be hermetically sealed without sealing the microporous part of the stamp with, for example, a hydrophilic coating (e.g., aliphatic and cyclic olefin-based polymers, or fluoropolymers or silicon based polymers). The stamps may also be subpatterned through use of photosensitive precursors in the casting solution of the product. In one embodiment a (coplanar) stamp 11 with alternating nanoporous hydrophilic and dense hydrophilic surface regions is locally filled with an aqueous chromium etch solvent and brought into contact with a substrate having a chromium layer with a thickness of 20 nm. Whereas the dense regions 13 locally protect the chromium layer, in the nanoporous regions 12 an exchange between the chromium layer and the etch solvent may result in a locally dissolved and patterned chromium layer. Instead of chromium, many other materials or combinations of materials are applicable (e.g., aluminum, metal oxides and nitrides, metals, semiconductors, polymeric lacquer layers, etc.). The chromium layer may be replaced by a one phase lacquer layer and the solvent may be replaced by a second phase vulcanizing agent for the one phase lacquer layer. Instead of solvents also reactive gases can be used to etch patterns (e.g., SF6 to etch and pattern silicon products). The microporous stamp can also be used to dab or adsorb locally a liquid or viscous layer that has been casted on a product. Dabbing may be improved by locally compressing the microporous regions during the contact of the stamp with the product. See Figure 31.

Figure 31. Left: Microporous stamp 1 produced with a phase separation process on a suitable mold. At left is a cross-section of a polyimide microporous microprinting tool with a smooth skin layer as obtained with a phase separation process. Courtesy of Aquamarijn Research/Membrane Technology Group, University of Twente.

Nanomembranes

2.2. Fabrication of Micro/nanosieves with Silicon Wafers Most of the processed silicon wafers today have a 100 orientation. The 111 planes etch approximately 200–1000 times slower than other oriented planes. This means that the 111 planes practically function as an etch stop. In order to obtain a silicon microsieve with a high degree of perforation, KOH etching must be carried out from the back side as well as through the pores on the front side. The etch rate on the front side decreases for smaller pores. For 1
m pores it is roughly one order of magnitude smaller than the etch rate on the back side. If the wafer thickness is d, the width w√of the openings on the back side must be approximately d 2 (depending on the etch rate underneath the membrane) to etch through the wafer, due to the 54.74
angle between the 111 planes and the wafer surface. For a 3-inch wafer with a 375
m thickness this would result in membrane fields of approximately 530
m width. Scaling up to 4-inch or 6-inch wafers with a thickness of 525 and 675
m would give fields of 740 respectively 950
m. As large fields are weaker than smaller fields, usually small additional support bars are etched underneath the membrane to reduce l (cf. Fig. 32).

opening to back side I

top view

W

In order to facilitate mask alignment of different mask stamping steps and to reduce thermal expansion differences between the stamps and the product, stamp regions parts are provided on a transparent (e.g., Pyrex, borosilicate glass) support material with the same thermal expansion coefficient as the substrate. Preferentially the microporous parts leading to the injection point have a high inner porosity to reduce flow resistance and a relatively small total dead volume in order to reduce the amount of adsorbed species. In some cases it has proven to be useful to first print an ink pattern with the stamp on an intermediate dense or microporous transfer foil that transfers the ink pattern subsequently to the substrate, especially foils which have a well defined wetting contact angle with the selected ink medium. The substrate may also first be provided with a suitable adsorbive nonsplattering or nanoporous (sacrificial) coating for more adsorption of the ink (e.g., obtained with a phase separation method). In another embodiment this nanoporous coating is made by deposition of an aluminum layer with a thickness of 200 nm on a silicon wafer and transforming this aluminum layer to a nanoporous (porosity 60–90%) honeycomb structure with thin vertical walls (pore spacings 10–50 nm) by anodic oxidation techniques well known in the art. Silicon and many other materials with different layer thicknesses can be transformed as well with anisotropic etching techniques for similar purpose. After the local deposition of the ink or an etch resistant lacquer in and/or on this layer, and preferentially dissolving the remaining uncovered layer, the substrate is ready for further processing steps. Of course stamps may also be used for the formation of microstructures or microtransfer molding on planar and nonplanar surfaces of polymeric, ceramic, or metallic articles.

63

h

silicon support bar

Figure 32. Top view of a membrane field that has been split up by small silicon support bars. The dashed line indicates the channel to the back side of the wafer.

2.2.1. Wet Etching through the Pores However, for pore diameters below about 1
m problems occur due to pressure buildup of the hydrogen gas that is created during KOH etching. Figure 32 shows that the silicon is etched through the pores. The gas can only escape through the pores in the hydrophilic membrane if its pressure exceeds the bubble-point pressure Pb , given by [80], pb =

4 cos d

where  is the surface tension of the KOH solution, is the liquid–solid contact angle, and d is the diameter of the pores. After the hydrogen gas has pushed the liquid out of a pore it will form a bubble on top of this pore. When the contact angle of the bubble with the pore wall becomes 0
, the gas pressure reaches a maximum value. For our KOH solution with an estimated value [81] for  of 0.075 N/m, this reduces to 030 pb = d The bubble-point pressure increases for smaller pores. If the pore size is below a certain value, the gas can break the membrane. The maximum pressure pmax that an unperforated rectangular membrane can stand has been calculated by van Rijn et al. [115]: pmax = 069

3/2 h yield

lE 1/2

This equation shows that a decrease in size of the membrane field leads to a stronger membrane. A critical step in microsieve manufacturing is the release of the perforated membrane from the silicon support. Hydrogen gas that is created during KOH etching of the silicon builds up a pressure that might damage the membrane. Especially for submicrometer perforated membranes rupture is

Nanomembranes

64 likely to occur. Two different approaches were investigated to avoid the pressure problem. The first approach is based on plasma etching instead of KOH etching. Since no liquids are involved, the gaseous reaction products do not have to exceed a bubble-point pressure to escape through the pores. Using an SF6 /O2 plasma and cryogenic substrate cooling, submicrometer perforated membranes were successfully released. A second approach is the formation of gas-escape channels to the back side of the wafer. This was achieved by using wafers with a 110 orientation, which allows for the possibility to etch channels with vertical sidewalls. With this second method also membranes with submicrometer pores were successfully released. The advantage over plasma etching is the possibility to process large batches. Furthermore, thanks to the vertical sidewalls thick (and thus strong) wafers can be used, while small (and thus strong) membrane fields are obtained. See Figure 33.

Small Support Bar Large Support Bar

2.2.2.
100 Silicon Wafers The base material of a microsieve is a 100 oriented silicon wafer. The wafer is coated with a silicon-rich nitride layer (intrinsic stress 108 Pa) by means of LPCVD. This layer is perforated using photolithography and reactive-ion etching with a CHF3 /O2 plasma. Finally the silicon underneath the perforated layer is partially removed by anisotropic KOH etching to form a support. This last step is crucial for the production of microsieves. If the silicon is etched from the back side with a KOH solution, a substantial part of the membrane will not be released due to the oblique 111 crystal planes in the 100 wafer. A much better result is obtained when etching takes place from the back side as well as through the pores on the front side. An additional advantage of this method is the possibility to etch extra support bars underneath the membrane (see Fig. 34). The hydrogen bubbles that arise from KOH etching (25%, 70
C) cause a pressure buildup underneath the membrane. This pressure may cause rupture of the membrane. An investigation was made of under what conditions KOH etching through the pores is still applicable and of the possibilities of dry etching to release the membrane. UV-laser interference

Mask

UV-light

Silicon Nitride Photo resist

Chromium Etch Mask

Chromium lift off Silicon Nitride

Photo mask lithography for support definition

Figure 34. Releaseof the perforated membrane by anisotropic KOH etching from both sides of the wafer.

Dry Etching through the Pores In order to overcome the problems of wet etching, another possibility is releasing the membrane with the use of dry etching through the pores. The basic idea is given in Figure 35. A patterned etch mask (photolacquer or chromium) is used to perforate the silicon nitride layer by CHF3 /O2 etching. The mask is not removed from the nitride layer, as it will serve again as a mask for the silicon dry etching. The use of an isotropic etch gas is not satisfactory, because the small support bars would be etched away. Therefore an anisotropic-etch recipe is required, with just enough undercut to remove all the silicon between the pores. Plasma etching gives such an anisotropy that the ions can be accelerated Etch Mask

Silicon Nitride

Plasma etching (front side)

Plasma etching (front side)

KOH-etching (back side) Photo resist posts

Development

20 µm 100 µm

Pattering and KOHetching of back side

Small Support Bar 380 µm Large Support Bar 1 mm

Figure 33. Fabrication process of a microsieve using laser interference lithography.

Small Support Bar Large Support Bar

Figure 35. Process scheme for the release of perforated membranes by plasma etching.

Nanomembranes

into a vertical direction by an electric field. SF6 /O2 mixtures are normally used, as SF6 etches silicon isotropically while O2 gives an anisotropic profile by passivating the silicon sidewalls of the trenches via LPCVD [83]. In order to obtain a higher etch selectivity between the silicon support and the silicon nitride membrane, the etch step was performed in an apparatus with cryogenic substrate cooling (Plasmalab 100, Oxford Plasma Technology [84–86]). In contrast to KOH etching the depth of the channel underneath the membrane does not seem to be influenced by the pore size. The porosity will play a much more important role in the silicon etch rate, as it determines the amount of plasma that can enter the channel. See Figure 36.

2.2.3.
110 Silicon Wafers The possibility of creating vertical channels in 110 silicon by KOH etching allows for the formation of small and therefore strong membrane fields. Buildup of a hydrogen pressure no longer occurs, as the gas can escape through the channels (see also Fig. 39). Furthermore the vertical anisotropy makes it possible to construct very thick and thus strong microsieves. For the new fabrication process a chromium etch mask is used instead of photolacquer. This chromium mask has an additional advantage of giving better defined pores, herewith improving the filter performance.

(a)

65 KOH etching on 110 wafers gives vertical walls but unfortunately two oblique 111 planes disturb the possibility to make small channels. However, as the shortest width of the fields determines the membrane strength, long but thin slit-shaped channels would still give strong membranes (see Fig. 37). For 110 wafers the walls of such channels have mutual angles of 70.53
and 109.47
. The walls are vertical, but in the sharpest corners (70.53
) the oblique planes arise with an angle of 35.26
relative to the horizontal 110 plane. A schematic view of such a channel is given in Figure 38. In this figure the silicon nitride on the front side has not been patterned yet, in order to etch the silicon only from the back side. The channel length l has been chosen such that the two oblique planes intercept at the membrane layer on the top of the wafer before crossing each other. The front view in Figure 38 shows that the angle between the oblique planes and the wafer surface is 30
in the direction parallel to the long vertical walls. This means that in order to etch through the entire √ wafer the length of the channel has to be larger than 2d 3. For the channel width w the only restriction that applies is given by flow-resistance requirements. The width should be chosen such that the channel resistance becomes much smaller than the resistance of the attached membrane field. It can be calculated that—even for extremely porous membranes—a width of 100
m is sufficiently large. Using the new 110 method the microsieves can be made much thicker—and thus stronger—than with the conventional 100 method, as the vertical anisotropy makes the membrane width independent of wafer thickness. Since the aspect ratio of the trenches can be as much as 600 it can be expected that etching of deeper grooves will not cause any problems for the KOH solution (25%, 70
C) we used [87]. For concentrations above 30% the formation of 311 planes has been reported, which disturbs the possibility to etch deep trenches [88]. The maximum etch rate of the 110 planes occurs for a KOH concentration of 25% and is nearly twice the etch rate of the 100 planes [89]. As the slit-shaped channels can be made very small, they can be placed close together, thus creating membrane fields with small widths. Figure 39 gives a schematic illustration of the fabrication process of a microsieve on 110 silicon.

(b)

Figure 36. Shown are (a) 45 min, −130
C, 400 nm pores and (b) 45 min, −130
C, 70 nm pores, SF6 /O2 etching through very small pores. Courtesy of Aquamarijn Research.

Figure 37. SEM micrograph of a microsieve with slit-shaped pores. Courtesy of Aquamarijn Research.

Nanomembranes

66 Silicon Nitride

Vertical Walls

l

w

Silicon

109.53° 70.47°

30° Microsieve Membrane Layer

Figure 38. Schematic view of a slit-shaped pore after KOH etching of a 110 wafer. The shaded walls inside the channel on the right are 111 planes. Two planes are oblique and four planes are partly vertical.

Instead of a photolacquer mask a patterned chromium layer was used as a mask for plasma etching. This layer is obtained either by a lift-off process on photolacquer dots or by wet etching of the chromium through pores in a photolacquer layer. Before plasma etching of the membrane, vertical escape channels are etched in a KOH solution. Subsequently the membrane is patterned by plasma etching, using the chromium as the etch mask. Expected differences in etch rate due to variation in heat conduction between the released and unreleased parts of the membrane were not observed: the pores are uniform over the entire surface. For very small pores or very thin membranes it may be necessary to do an isotropic HF/HNO3 etch to release the membrane and make a small space underneath it (third step in Fig. 39).

Anisotropic KOH Etching

Pore Etching

If the HF/HNO3 solution is chosen in the right composition (less then 1 part 50% HF on 100 parts 69% HNO3 ), no hydrogen gas will be formed during this release process. The function of the small space underneath the membrane is to give the gas an escape route to the vertical channels. In the discussion we will calculate the required depth for this space. Using the new method a microsieve was fabricated with slit-shaped perforations and a porosity of 75%. SEM micrographs of this sieve are shown in Figure 40. The shortest walls underneath the membrane should be partly vertical, but instead they are somewhat oblique with a rough surface. This is probably caused by the presence of the perforated membrane, as the back side of the wafer does show the vertical walls.

2.3. Research and Applications with Nanosieves 2.3.1. Patterning of Nanostructures With laser interference lithography it is easily possible to reduce pore sizesa in microsieves to the nanometer regime, herewith giving birth to “nanosieves” [74]. A known technique to pattern surfaces on a substrate is to evaporate a material through a thin membrane (shadow mask) with welldefined openings [90] (see Figs. 42 and 43). It is also well known to use such shadow masks as a poor man’s technique to make patterns on a substrate if photolacquer patterned layers are too elaborate or not wanted. Shadow masks with nanosized perforations may therefore be used in applications such as ion beam etching [91], electron beam patterning, near field optics, etc. Reactive ion etching through a shadow mask can be used for direct etching [3] of a (nano)pattern in a substrate (for example metal or polymeric foils). Self-assembly (Nano)mask Preparation The micro/ nanopattern may for instance be formed by using particles with a uniform size, for example a silica dispersion or a latex suspension, with particle sizes ranging from 5 nm to 5
m.

Isotropic Etching via Pores

Anisotropic KOH Etching

Figure 39. Schematic view of the microsieve fabrication on a 110 wafer. First vertical wall KOH etching in 110 silicon, then silicon nitride etching of the pores followed by release of the membrane with isotropic etching of silicon, and finally KOH etching to make the distance between the perforated membrane and the wafer larger.

Figure 40. High-porosity microsieve fabricated on a 110 silicon wafer. Through the slit-shaped pores some typical etch angles can be recognized. Courtesy of Aquamarijn Research.

Nanomembranes

This suspensions may directly be formed on a substrate with use of a spin coating or evaporation technique. A more or less ordered distribution of particles will then be found in the pattern forming layer on the support. After the evaporation of the solvent of the suspension a very thin metal layer (e.g., a 10 nm chromium layer) may be deposited (e.g., by means of vapor deposition, i.e., sputtering or evaporation) on the substrate and on top of the particles, for example silica particles with a diameter of 30 nm. The silica particles are then solved in a buffered HF solution and a perforated chromium layer remains with perforations of approximately 20–30 nm in diameter depending on the chromium deposition conditions (correction for shadow effect of deposition). The chromium layer may be used as a membrane layer or alternatively as a mask layer for the (dry) etching of a membrane layer underneath the chromium layer (see Fig. 41).

2.3.2. Nanosieves for Photonic Structures Recently, there has been growing interest in photonic bandgap materials, which have a spatially periodic refractive index with a lattice constant on the order of the wavelength of light, because of potential scientific and technological applications based on their unique light propagation properties [94]. However, experimental surveys of the optical properties of photonic bandgap materials have been limited due to the difficulty in preparing well-constructed samples except in the long wavelength region [95, 96]. Photonic crystals are novel materials with unique optical properties [97]. The crystals have a periodic modulation of the refractive index. As a result, the dispersion of light will be described by a band structure analogous to those of electron wave atomic crystals. Under the right conditions a photonic crystal can exhibit a photonic bandgap: light in a certain range of optical frequencies is forbidden in the crystal [98]. The existence of a photonic bandgap enables an unprecedented control of spontaneous emission and propagation. By locally disturbing the periodicity, a defect-associated photon state is created which can be used to guide light. A photonic crystal slab is a thin film with a twodimensionally periodic refractive index modulation in the

Figure 41. Photographs of a membrane made with a self-assembled mask. Left: arrays of nanosized particles on a silicon nitride membrane layer. Right: after chromium deposition over the particles and removal of the particles, the pores in the membrane have been etched. Reprinted with permission from [3], C. J. M. van Rijn, membrane Filter as well as a Method of Manufacturing the Same, PCT Application 95/1386206.

67

Figure 42. A nanosieve may be used as a shadow mask (nanostencil) for evaporation of material (e.g. gold) through the pores of the nanosieve. Reprinted with permission from [92], J. Brugger et al., Microelectron. Eng. 53, 403 (2000). © 2000, Elsevier Science.

plane [100, 101]. In a photonic crystal slab the light is confined to the crystal plane by a classical slab waveguide construction. For in-plane wave vectors a bandgap can be created. Thus, the slab has applications in light guiding without the need for a full bandgap in all three dimensions. Optimal performance of the photonic crystal slab is expected when the slab is mirror symmetric in the vertical direction (i.e., when the material on both sides of the slab has equal refractive index at least in the region of the near-field tail of the in-plane propagating light) [102]. Photonic crystals are fabricated by periodically arranging materials with highly dissimilar refractive index. To obtain a bandgap in the visible the periodicity of the index modulation has to be in the submicrometer range, 40 pN·nm. By comparison, the sliding force that linear motors like myosin and kinesin (that were mentioned in the Introduction) generate is much smaller. Myosin produces a sliding force of 3–6 pN [41, 42] and kinesin a force of 5 pN [43]. The energy required to generate the torque in F1 is about 8 × 10−20 J for a 120 rotation step. The free energy that is provided by the hydrolysis of one ATP (one ATP is hydrolyzed for a 120 rotation) is about 9 × 10−20 J. In other words, Nature has designed here a nanomotor, the ATP synthase, which runs at more than 90% efficiency. The efficiency may even be higher if the viscoelastic mechanics of the ATPase–actin construct are considered. In two “head-to-head” papers [44, 45], Junge and coworkers studied the effects of slow viscoelastic relaxation of the actin filament on the torque generated by the F0 F1 holoenzyme. The construct they used is depicted in Figure 6.

Figure 6. Diagram of an experiment to determine the torque generated by the ATPase (for more details see [44]). The basis of the experiments to determine the torque generated by the F0 F1 -ATP synthase is as described in the legend to Figure 3. The F1 part is fixed to glass slides using oligo-histidine tags and a Ni–NTA-coated surface. The ring of c subunits carries Strep-tags that allow the actin filament to bind. The analysis of the viscoelasticity of the actin filament was performed using video microscopy in an inverted fluorescence microscope.

The results of these experiments and theoretical analysis suggest that indeed the torque that is generated by the synthase (here being powered by the electrochemical proton gradient) exceeds 40 pN · nm and was estimated to be more in the range of 50 ± 6 pN · nm. There were only very small variations in the torque output of the motor, implying a soft, elastic power transmission between the two parts of the motor, F0 and F1 . This elastic transmission seems to be an essential feature to allow this biomotor to perform under such high turnover rates. The higher torque value that was calculated also shows that indeed this nanomotor works with almost perfect energy efficiency.

5. POWERING NANOELECTROMECHANICAL SYSTEMS Very soon after details of the rotary mechanism became known, researchers started to investigate the nanomechanical world. Montemagno and his co-workers pioneered in this work and reported the “powering [of] an inorganic nanodevice with a biomolecular motor” in Science in 2000 [46, 47]. It is interesting to note that at the time this research was performed, Montemagno and his group were located at the Cornell University in Ithaca, NY. From this same university some 40 years before, Racker, Penefsky, and co-workers reported that they had isolated a soluble “factor” from beef heart mitochondria that hydrolyzed ATP [48]. They reported that this factor could restore ATP synthesis in mitochondrial membranes that had lost this ability during isolation. They called this interesting protein the “factor 1” or F1 for ATP synthesis. The Montemagno group used a substructure of the F1 ATPase from the thermophilic bacterium PS3 that contains only the basic rotor assembly consisting of the subunits ,
, and , similar to the experiments described by the Yoshida group [27]. In initial experiments, procedures for the specific attachment and positioning of the nanoelectromechanical systems (NEMS) were tested [47]. Using electron beam lithography, an array pattern was etched on a 25 mm coverslip. The coverslips were then patterned with metal substrates such as gold, copper, or nickel. A synthetic peptide containing a polyhistidine tag as described above was allowed to attach to the metal-coated coverslips. The peptide had a microsphere covalently attached to the opposite side, and laser tweezers were used to test the strength of the attachment to the metal surface. Nickel was found to be the most promising candidate, and, therefore, in their following paper [46], the group presented a method to generate nanofabricated Ni posts of a diameter of 50–120 nm and a height of 200 nm. Ni posts were chosen as a “stand” for binding the ATPase motor to prevent problems that are associated with “dragging” the “propeller” unit in close proximity to the base of the motor. Nickel propeller rods were generated and their dimensions were optimized for optical detection and minimal friction during the rotation process. The propellers were then coated with biotinylated peptides that also carried histidine tags. The polyhistidines allowed binding of the peptides to the Ni rods, while the biotinylation allowed

88

Nanomotor F1 -ATPase

engineering and in natural sciences, to see the future and limitations of use for such highly intriguing devices.

GLOSSARY

Figure 7. Diagram of a nanoelectromechanical system as developed by the Montemagno group, (for more details see [46]). An F1 substructure containing 3
3  is immobilized via His-tags onto Ni post structures with a diameter of 50–120 nm and a height of 200 nm. Subunit  was biotinylated and using the biotin–streptavidin–biotin construct, a spacer is formed that binds to prefabricated Ni rods that have been covered with His-tagged oligopeptides. Upon addition of ATP, the ATP-driven rotation of the  subunit can be visualize as a rotation of the Ni rod.

the interaction of the propellers with F1 that carried a streptavidin protein at the  subunit. Functional NEMS were constructed by sequential addition of the individual components: F1 -ATPase was biotinylated at its  subunit through specific modification of engineered cysteine residues in the appropriate position. The biotinylated F1 was placed onto the Ni posts by virtue of the histidine tags that were located at the
subunits of the constructs. Next, streptavidin was bound to the biotin molecules attached to the  subunit and finally the Ni propellers decorated with biotinylated peptides were added and assembled onto the motor. One model for an appropriate design is shown in Figure 7. Finally, and most ingeniously, the F1 part of the NEMS was further modified to contain a chemical switch that allowed the system to be turned on or off, without having to run the motor out of its power source, ATP [49]. Using computational design methods [50–53] and molecular biological methods Hellinga and co-workers constructed a binding site for Zn2+ ions. Using the original construct of the motor with an actin filament attached to the  subunit, they showed that rotation occurred in the absence of Zn2+ ions, was inhibited in the presence of Zn2+ , and could be reestablished when Zn2+ was removed from the mixture. A very similar approach was used by Hisabori and co-workers [54] who introduced a chemical switch into the  subunit that could be turned off in the presence of oxidants such as CuCl2 and switched back on upon reduction with dithiothreitol, a reducing agent, and thioredoxin, which is found to be a natural regulator of the ATPase that is found in chloroplasts.

6. OUTLOOK The first steps for the ATP synthase into the “nano-world” have already been successfully performed. Whether it will be used as a pump in nanoscale chemical reaction chambers, a three-step switch to modulate flow of fluids or electricity, or even a motor to drive nanosubmarine structures, it will be solely up to the imagination of researchers, both in

Adenosine-5′ -diphosphate (ADP) Corresponds to ATP with one less phosphoryl group. Adenosine-5′ -triphosphate (ATP) A biological molecule that is used in all organisms for short-term energy storage. Biotinylation Chemical linking of biotin to another biomolecule. His-Tag A series of (usually) six histidine residues that are genetically attached to recombinantly produced proteins. The histidine residues form complexes with Ni2+ ions and allow affinity purification of the corresponding proteins. Inorganic phosphate (Pi ) Salt of phosphoric acid. Micromolar (
m) One micromole of a compound dissolved in 1 liter of a solvent. One micromole equals 10−6 mole. Nanoelectromechanical system (NEMS) An inorganic particle (here a Ni rod) that is linked to a biological system (here the F1 -ATPase). Ni-Nitrilo triacetic acid (NTA) Nitrilo triacetic acid that has Ni2+ ions chelated to the carboxylic acid moieties. The reagent is commonly used for affinity chromatography to specifically bind proteins that have oligo histidine tags attached.

ACKNOWLEDGMENTS The author thanks Dr. John G. Wise for critically reading the manuscript and preparing the artwork.

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Encyclopedia of Nanoscience and Nanotechnology

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Nanoparticle Drug Delivery to the Brain K. Ringe, C. M. Walz, B. A. Sabel Otto-von-Guericke Universität Magdeburg, Magdeburg, Germany and Nanopharm AG, Center for Neuroscience Innovation and Technology, Magdeburg, Germany

CONTENTS 1. Introduction 2. Transport of Molecules Across the Blood–Brain Barrier 3. Transport Mechanisms of the Blood–Brain Barrier 4. Nanoparticles as a Drug Delivery Tool for Brain Targeting 5. Preparation of Nanoparticles 6. Purification 7. Stability 8. Sterilization 9. Characterization 10. Drug Loading 11. Drug Release 12. Body Distribution of Nanoparticles—Brain Targeting 13. Mechanism of Nanoparticle Transport Across the Blood–Brain Barrier 14. Conclusion Glossary References

1. INTRODUCTION The blood–brain barrier (BBB) protects the brain against toxic substances that circulate in the bloodstream. Although this is life-supporting protection for the brain, the existence of the BBB is a severe limitation for the delivery of most drugs to the brain because they do not cross the BBB in sufficient amounts. A large number of potentially useful drugs, such as cytostatics and central nervous system (CNS)active agents, do not cross the BBB at all or in insufficient

ISBN: 1-58883-063-2/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

quantities. However, for therapeutic reasons methods to increase the bioavailability of drugs in the brain are needed to deliver drugs to the brain which are usually blocked from entering the brain by the BBB. One possible way to achieve this goal is to attach drugs to nanoparticles and thus transport them across the BBB. Nanoparticles are solid colloidal particles, ranging in size from 1 to 1000 nm (usually 200–300 nm), and they are a rather useful “drug delivery system” to target drugs to the brain. Here, we review the structure and the role of the BBB and describe the manner whereby molecules normally pass through the BBB. Furthermore, we will discuss how nanoparticles can be prepared and purified and review their physicochemical properties and drug release mechanisms. We then discuss the evidence that nanoparticles can be used to deliver drugs to the brain in the living animal and document their usefulness in some animal models.

2. TRANSPORT OF MOLECULES ACROSS THE BLOOD–BRAIN BARRIER In some cases potentially useful compounds to treat brain disorders are injected into the bloodstream or given orally, but they do not reach the brain at all or not in sufficient amounts (insufficient bioavailability). Therefore, therapeutic efficiency to treat brain diseases is diminished or prevented because systemic administration of the drug does not lead to an effective brain concentration [1–4]. There are many reasons why this may be the case: the molecules may be too large, they have unfavorable physiochemical properties (such as polar functional groups), they may be metabolized by enzymes before reaching their target (the brain), or they may be extruded at the cerebrovascular endothelium well before reaching the brain cells (neurons) upon which they should act. The major reason why drugs do not reach the brain is the existence of the BBB [5–7]. To develop methods to overcome this barrier, a good understanding of its nature is required.

Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 7: Pages (91–104)

92 2.1. The Physiology of the Blood–Brain Barrier The BBB is not one single structure or membrane in the brain, but it is created by the way the blood vessels in the brain are organized. Thus, understanding the BBB requires an understanding of the anatomy and physiology of the blood vessels in the brain. Both large and small capillaries form a richly branched and complex network throughout the entire brain tissue. Like a chimney made of individual bricks, the brain blood vessels consist of a monolayer of endothelial cells that are connected with each other by tight junctions (zonulae occludentes) [8]. The part of the cell’s membrane facing the bloodstream is called the “luminal” membrane [9–11], and the side which is exposed to the actual brain tissue is called the “abluminal” membrane. This part faces the extracellular liquid of the brain parenchyma where pericytes and endfeet of astrocytes surround the blood vessels. The most important site of the BBB lies at the cerebral microvessels, that is, the very fine vessels that have extremely small diameters. Because endothelial cells are very polarized, that is, essentially similar to the epithelium, they exhibit very low pinocytic activity and possess a high number of mitochondria that are needed for the multiple energy-dependent active transport mechanisms found in endothelial cells [12]. Peripheral vessels in the rest of the body can much more easily transport molecules across their membrane because they are fenestrated and have many active transcellular transport mechanisms. In contrast, in central blood vessels of the brain, even small molecules like antibiotics have great difficulty crossing the barrier and only a limited number of molecules can actively cross the endothelial cells. Here, the endothelial cells use specific transport systems to allow the influx of glucose, iron, amino acids, peptides, small organic acids, and others. This is necessary so that substances which are critical for brain metabolism and function can gain fast and efficient access to the brain via specific energy-dependent carrier mechanisms at the endothelium [13].

Nanoparticle Drug Delivery to the Brain

[17–19]. Pericytes have an important role in the function of the BBB. They are responsible for the maintenance of the barrier function and the stability of the vessel [20].

2.3. The Role of Astrocytes Astrocytes (which are brain glia cells) also contribute to the BBB, and they are attached with their endfeet to the pericytes and the endothelial cells. Astrocytes are glial cells responsible for the homeostasis and the ion regulation in the brain [20], but their endfeet cover the blood vessels only partially. In contrast to endothelial cells and pericytes, astrocytes are not connected to other cells by tight junctions, and they do not have a common basal membrane. Therefore, polar molecules (such as proteins) can enter the interstitial liquid and be directly transported to the pericytes and the endothelial cells [21]. That astrocytes are important for the induction and maintenance of the BBB properties can be deduced from the following observations in cell cultures: in the presence of astrocytes or medium conditioned by astrocytes, endothelial cells express markers important for BBB characteristics and develop tight junctions [9–11]. On the other hand, endothelial cells promote the development and differentiation of astrocytes. This interaction between both cell types actually occurs even when there is no contact between the two cell types, indicating that some soluble, extracellular factors are mediators of BBB development.

3. TRANSPORT MECHANISMS OF THE BLOOD–BRAIN BARRIER Although the BBB is a fairly “tight” structure when “unfriendly” molecules try to enter the brain, it does have several mechanisms to allow “friendly” molecules to get in. Among them are active, carrier-mediated transport mechanisms for relatively small molecules, an absorptive-mediated endocytosis mechanism for positively charged peptides, and receptor-mediated endocytosis mechanisms specific to certain peptides. For the structure of the BBB see Figure 1.

2.2. The Role of Pericytes

3.1. Transport of Anionic Compounds

Pericytes, which are located on the abluminal side of the endothelial cells, are also part of the BBB. Pericytes are a physiological heterogeneous cell population and are found on all microvessels in nearly every organ [13], but they never cover the entire blood vessel. The pericytes, which are located on the “brain side,” are encapsulated by the basal membrane of the endothelial cells, and they are responsible for the synthesis and release of different components of the basal membrane and the extracellular matrix such as collagen and glycosaminoglycocan [14]. The basal membrane of the endothelial cells and that of the pericytes are closely attached to each other so that both cells have a common basal membrane [15]. Electron microscopy studies have revealed fenestrations between pericytes and endothelial cells [16], and pericytes have contractile properties that may play a role in the regulation of the blood flow. Several molecules are involved in these contractile functions such as actin, myosin, tropomyosin, vimentin, and desmin

Various anionic compounds are transported across the BBB by the monocarboxylic acid transporter (MCT) [22, 23]. Lactic acid, for example, is transported by a specialized mechanism and not by nonionic passive diffusion [24, 25].

mitochondria pericytes bloodvessel astrocytes

Vesicles bloodstream endothelial cell

Figure 1. The blood brain barrier (BBB).

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Nanoparticle Drug Delivery to the Brain

MCT1 is present in the BBB and acts as a transport mechanism for lactic acid and other monocarboxylic compounds [26].

3.2. Transport of Cationic Compounds Cationic compounds enter the brain by passive diffusion and also by carrier-mediated transport, which is believed to be the mechanism of action whereby several drugs cross the BBB [27–32]. An endogenous hydrophilic amine, choline, has been demonstrated to be taken up by a carrier-mediated transport mechanism [29–31], and a carrier-mediated amine transport system is likely to be responsible for transport of cationic compounds across the BBB.

3.3. Transport of Peptides Because peptides are usually relatively large, hydrophilic, and unstable, efficient permeation into the brain generally does not occur [33]. However, certain relatively small peptides are transported by carrier-mediated transport mechanisms, and others cross the BBB by transcytosis including receptor-mediated transcytosis and absorptive-mediated transcytosis.

3.4. Carrier-Mediated Transport of Peptides Because the transport of glutathione across the BBB is saturable [34, 35], carrier-mediated transport that has a high efficiency comparable to the brain uptake of single amino acids such as phenylalanine and cysteine is probably involved.

3.5. Absorptive-Mediated Endocytosis Absorptive-mediated transcytosis is triggered by electrostatic interactions between the positively charged moiety of the peptide and the negatively charged plasma membrane surface region [36–39]. If one attempts specific targeting to the CNS, absorptive-mediated transcytosis is not expected to be useful, because absorptive-mediated transcytosis or endocytosis also functions in other tissues such as kidney and liver [38].

3.6. Receptor-Mediated Endocytosis To get peptides to cross the BBB they need to be manipulated in a manner such that penetration into the brain is achieved. Sometimes this is achieved by synthesis of chimeric peptides. They are formed by covalent binding of the nonpermeable but pharmacologically effective portion of the peptide to an appropriate vector that can be transported across the BBB [38]. In this case, the chimeric peptide is first transported into the brain endothelial cytoplasm by receptor-mediated or absorptive-mediated endocytosis. The intact chimeric peptide is then transferred into the brain’s interstitial space by receptor-mediated exocytosis. Subsequently, the binding between the vector and the pharmacologically active peptide is cleaved and, finally, the released peptide exerts its pharmacological effect in the brain [36, 38, 40, 41].

3.7. Efflux by P-Glycoprotein Several anticancer drugs such as vinca alkaloids and anthracyclines exhibit lower accumulation in the brain than would be expected from their lipophilic properties [42, 43]. Furthermore, tumor cells show a resistance to anticancer drugs such as anthracyclines and other nonrelated compounds [44]. This multidrug resistance is accompanied by overexpression of the transmembrane P-glycoprotein and a decrease of drug concentration in the resistant cells compared with that in drug-sensitive cell lines [45, 46]. P-glycoprotein molecules are located at the luminal side of the endothelial cells and their function is to serve as an energydependent efflux pump and transport various drugs out of cells, thus decreasing their accumulation in the cytoplasm, and, as a consequence, reducing their efficiency [46–48]. P-glycoprotein has a very broad substrate specificity [49–51].

3.8. Transport of Drugs across the BBB Given the highly selective nature of the BBB, the question arises as to how drugs that usually do not cross the BBB can still be delivered to the brain. An estimated 99% of all potential drugs are clinically useless because the BBB prevents them from getting into the brain. Thus, finding ways to overcome the BBB are of great clinical significance. There are two fundamental ways to get drugs into the brain. The first and most invasive method is application of the drug directly into the brain. This can be done by intracerebral injection or infusion or by artificial drug delivery systems such as polymer implants that release drugs in a sustained manner [52]. For example, anticancer drugs are often applied by intraventricular infusion, but this is a rather invasive technique with high risks. In view of the rapid turnover of the cerebrospinal fluid, however, the pharmacological compound is rapidly removed from the brain into peripheral blood vessels and the diffusion-dependent concentration in the parenchyma is far below desirable levels. The second and most favorable method is to manipulate or “trick” the BBB, so that neurologically active compounds can be given systemically by oral, intramuscular, or intravenous application. Here, several different approaches are possible: osmotic opening of the BBB or pharmacologically by raising the lipophilicity of the drug using chimeric molecules or by attaching drugs to nanoparticles [53].

3.9. Osmotic Opening of the BBB The BBB can be opened by osmosis or by biochemical and pharmacological means [54–56]. Application of hyperosmotic mannitol and arabinose solutions results in the local reversible destruction of tight junctions, thus increasing the permeability of the endothelial cells. For example, hyperosmolar urea solution withdraws water from the endothelial cells and leads to shrinkage of the cells and consequently to an opening of the tight junctions. As one can easily imagine, the major disadvantage of this method is that the brain loses its protection from neurotoxic substances for a certain period of time, which results in significant unwanted side effects such as brain edema [54–56].

94 A similar approach is the infusion of a vasoactive substance such as bradykinin or leukotriene, which increases vesicular transportation activity of the endothelial cells.

3.10. Pharmacological Approaches Among the pharmacological approaches the most common one is increasing the lipophilicity of the drug and using chimeric proteins as well as cationized antibodies. Chimeric proteins can be transported via receptor-mediated or adsorptive-mediated transcytosis [57, 58]. Prodrugs are an excellent example of such drug manipulations. With this method, the original compound is manipulated to make it more lipid-soluble, providing greater brain penetration. However, increased lipid solubility may significantly alter pharmacokinetic parameters such as clearance and half-life, which, for chlorambucil derivatives, is undesirable [58]. The third and in our mind the most desirable method to get a drug across the BBB is the novel technique of nanoparticle drug delivery. Compounds can be attached to or incorporated into nanoparticles, which serve as a universal “drug delivery system,” allowing many pharmacological agents to cross biological barriers.

4. NANOPARTICLES AS A DRUG DELIVERY TOOL FOR BRAIN TARGETING Over the last few years work in the laboratories of Kreuter [59, 60] and Sabel [61–64] has demonstrated the usefulness of nanoparticles as a universal tool to deliver drugs to the brain. The evidence is consistently mounting that important diseases of the brain can be treated by a combined nanoparticle/drug approach, and brain tumor treatment, in particular, has been accomplished in animal models. A variety of experiments have been carried out to date using various animal species and different behavioral paradigms and disease models, all of which substantiate the value of nanoparticles as a novel drug delivery method. To understand the usefulness and potential of nanoparticle technology for drug delivery to the brain, we shall first describe methods of preparation, the mechanism of drug binding and release, and evidence of toxicity and efficacy. We will also briefly discuss practical matters that are important for clinical use of nanoparticles such as sterilization procedures, stability, and purification issues and then discuss the evidence indicating their usefulness as a tool for delivery of drugs to the brain.

Nanoparticle Drug Delivery to the Brain

the brain drug uptake, and the stability of the drug in the plasma [65].

5.1. Emulsion Polymerization Emulsion polymerization is one of the most rapid and most frequently used methods for nanoparticle preparation. Here, the monomer is added to a continuous phase, usually an aqueous phase at room temperature under constant stirring conditions. It is also possible to use an organic phase as the continuous phase. The polymerization can be initiated either by free radicals or by ion formation. The polymerization is initiated by the reaction of a monomer molecule with an initiator molecule. Triggers for the initiation of the reaction can be ultraviolet (UV) light, hydroxyl ions, or high-energy radiation. The polymer chain starts to grow when these initiated monomer ions or monomer radicals react with other monomer molecules. Additional monomer is solubilized in surfactant micelles or emulsified in larger droplets. After completion of polymerization, the reaction mixture is filtered, neutralized, and purified by centrifugation to remove any residual monomer. An example for an anionic process is the preparation of “poly(alkylcyanoacrylate) nanoparticles” and an example for a free radical-initiated emulsion polymerization is the manufacturing of polymethyl methacrylate nanoparticles [66]. The process of emulsion polymerization has numerous advantages. Compared with other methods, it is rapid and in general there is no need to use stabilizers and surfactants. In addition, for industrial requirements it is easily scaled up [67]. In contrast, with the requirement of UV light, radiation, or free radicals to initiate the polymerization process, the incorporation of proteins and peptides during the polymerization is not possible. Furthermore, if one wishes to scale up this procedure, the need for purification of the nanoparticles via dialysis and centrifugation represents a problem [68]. The mechanism of an anionic polymerization is shown in Figure 2.

Initiation CN

CN H O

+

HO

OBu O Monomer (BCA) Polymer Chain Growth

CN HO

CN CN

BuO2C

OBu O

CO2Bu HO

5. PREPARATION OF NANOPARTICLES There are different methods to manufacture nanoparticles: (1) emulsion polymerization, (2) interfacial polymerization, (3) solvent evaporation, (4) solvent deposition, and (5) denaturation. The properties of nanoparticles vary with different polymers, stabilizers, and surfactants used during the manufacturing process. Each excipient added may have an influence on the bioavailability of the drug carried,

OBu O

(n-1)-times

CN CN CH2 n CO2Bu CO2Bu

Termination HO H+ (Acid)

CN CN CH2 n H CO2Bu CO2Bu

Poly (butylcyanoacrylate) (PBCA)

Figure 2. Mechanism of polymerization.

Nanoparticle Drug Delivery to the Brain

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5.2. Interfacial Polymerization

emulsion. Then both phases are emulsified using a homogenizer. The size of the forming particles depends on the stirring velocity, slit width, and power of the homogenizer. Then the particles are hardened by cross-linking with an aldehyde, by heat denaturation, or by cooling below the gelation point [75–77].

To achieve interfacial polymerization, monomers are polymerized at the interface between two immiscible phases. Interfacial polymerization takes place in a medium consisting of an aqueous and an organic phase, which are homogenized, emulsified, or micro-fluidized by vigorously mechanical stirring. Al Kouhri Fallouh et al. [69] introduced the formation of polyalkylcyanoacrylate nanocapsules. In this process the monomer and the drug are dissolved 1 in a mixture of oil and ethanol (oil/ethanol: 101 to 200 ) and then slowly added through a small tube or needle to an aqueous phase containing surfactants (poloxamer 188 or 407 or phospholipids). The oil used can be Miglyol or benzylic acid. The primary disadvantage of this method is the occurrence of strong shear forces. This excludes the possibility of adding proteins and peptides during the polymerization process for incorporation purposes. The monomer spontaneously polymerizes and forms nanocapsules that consist of an oil droplet and a polymeric shell [69]. An advantage of this process is that the drug is encapsulated into the nanocapsule and not just adsorbed onto the surface. This would protect it from enzymes, thus preventing premature biodegradation before it reaches the blood brain barrier.

5.3. Solvent Evaporation The solvent evaporation method is a well-established and frequently used method for the manufacturing of particles with sizes above 1
m and also sizes of less than 1000 nm. In this process the preformed polymer and the drug are dissolved in a volatile, water-immiscible organic solvent. This organic phase is then added to the aqueous phase under stirring, and the organic solvent is removed by heating and/or under reduced pressure. The polymer precipitates and forms micro- or nanospheres instantaneously, containing the drug dispersed in the polymer matrix network. The particles are then purified by filtration and centrifugation [70]. Examples of this process are the manufacturing of poly(lactic acid) nanoparticles and poly(lactic-coglycolic acid) nanoparticles [71, 72].

6. PURIFICATION All processes mentioned above require purification except for the emulsion polymerization process in some cases, when no surfactant and no organic solvents are used to produce nanoparticles. In general, the organic solvent is removed under reduced pressure and the resulting particles are purified by ultracentrifugation, ultrafiltration, gel chromatography, dialysis, or a combination of these methods. The choice of the appropriate purification method depends on the release properties of the nanoparticles. Inappropriate purification methods can lead to the loss of biologically active agent. Stabilization of the nanoparticles is usually achieved by lyophilization using a cryoprotector (such as mannitol) to prevent agglomerations [66].

7. STABILITY The stability of poly(butylcyanoacrylate) nanoparticles was examined in water, in phosphate-buffered saline, in acidic medium (0.01 or 0.1 N HCl), and in human blood serum [78, 79]. The authors found that in acidic medium no formation of agglomerates occurred and no degradation took place. The nanoparticles could therefore be stored in acidic medium for several months. In contrast, when suspended in water or phosphate-buffered saline, the nanoparticles agglomerate. Nanoparticle polymers did not degrade in solution as indicated by the fact that they kept their size constant. In human blood serum no formation of agglomerates was observed, and nanoparticles were stable for 8 days. This result supports the possibilty of the use of nanoparticles for intraveneous administration, because microembolisms due to agglomeration are not expected.

5.4. Solvent Deposition In this process the polymer, e.g., poly(dl-lactide), and phospholipids are dissolved in a volatile organic solvent such as acetone. Then a solution of the drug in benzyl benzoate is added to the organic phase and the reaction mixture is poured into the water phase, which contains poloxamer 188 under moderate stirring conditions. Nanocapsules consisting of an oily core and a poly(lactic acid) shell are formed instantaneously. The organic solvent is then removed under reduced pressure. Partial removal of water also occurs [73, 74].

5.5. Denaturation Nanoparticles can also be produced by denaturation of natural macromolecules such as albumin and gelatin in an oil emulsion. For this procedure the macromolecule is dissolved in an aqueous solution and the drug is entrapped in an oil

8. STERILIZATION An important prerequisite for the use of nanoparticles clinically is sterilization of the nanoparticle/drug complex. The possibility of sterilizing poly(butylcyanoacrylate) nanoparticles was studied by Sabel et al. [80]. Nanoparticle suspensions and nanoparticle powders were submitted to autoclaving (121
C for 20 min with or without cooling to 70
C afterward) or treated with formaldehyde (60
C). The nanoparticles were prepared using different stabilizers, such as dextran 70,000, poloxamer 188, and polysorbate 85. In most cases the authors detected a significant increase in particle size. For lyophilized nanoparticles no powder was suitable for preparing injectable suspensions. In particular, the resuspension of nanoparticle powders caused problems, which could not be overcome by intensified sonication. Under certain conditions poloxamer 188 suspensions and polysorbate 80 suspensions led to injectable nanoparticle

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suspensions. In summary, sterilization of nanoparticles after fabrication is possible under certain conditions, but the favored way to obtain aseptic material seems to be the production of nanoparticles under aseptic conditions.

0.01 N HCl 4h

9. CHARACTERIZATION The most important feature of nanoparticles is their small size. Therefore, some understanding is needed of how to manipulate and measure the size of nanoparticles. There are many different parameters that influence the size of particles during the manufacturing procedure. These are the pH of the reaction medium, the stirring velocity, the slitwidth, and the duration of ultrasonification. Besides size, there are also other physical parameters important for nanoparticles such as density, molecular weight, crystallinity, release, and degradation properties. The surface charge, hydrophilicity, and hydrophobicity significantly influence the body distribution of nanoparticles and, respectively, the bioavailability of the bound drug. Kreuter [66] reviewed the most common physicochemical methods for the characterization of nanoparticles. The size of nanoparticles is determined using photon-correlation spectrometry. This method, which quantifies light scattering, determines the hydrodynamic diameter of the nanoparticles via Brownian motion. It is important to verify the results obtained by this method using electron microscopy, because larger particles, such as dust or accidential microbial contamination, could lead to incorrect results [81, 82].

10. DRUG LOADING Drugs can be loaded onto nanoparticles by adding them to a solution that contains previously prepared nanoparticles or by adding them to the reaction mixture during the polymerization process. Both methods can supply (1) a solid solution of the drug in the polymer [83, 84], (2) solid colloidal nanoparticles with dispersion of the drug in the polymer [85], (3) adsorption of the drug onto the surface of the nanoparticle [86], (4) chemical binding of the drug to the polymer [87], or (5) no binding or incorporation at all. Figures 3 and 4 show the two possible ways of drug loading. The amount of bound drug and the type of interaction of drug and nanoparticles depend on the chemical structure of the drug and the polymer and the conditions of drug loading. The determination of the adsorption isotherm is one

PBS buffer 4h

Adsorption experiment nanoparticles (circle) and pharmaceutical active compounds (filled triangles) in PBS buffer

compounds adsorbed on the surface of nanoparticles

Figure 3. Drug loading of nanoparticles by adsorbtion.

Encapsulation experiment Growing chain of PBCA (curved line) by anionic polymerization in the presence of drug (filled triangles) and BCA monomer (short double line)

Drugs adsorbed and encapsulated on/in nanoparticles

Figure 4. Drug loading of nanoparticles by encapsulation.

possible way to detect the type of binding and the binding rate (mg drug/mg nanoparticle) [88]. Linear sorption isotherms characterize solid solutions [84] and Langmuiror S-type isotherms characterize surface adsorption [89]. Because nanoparticles are colloidal systems, precise determination of the drug content can be a problem. Therefore, the most reliable way is to separate the nanoparticles from the solution containing unbound drug by ultracentrifugation or gel filtration [90]. The amount of bound drug can be determined by subtracting the drug content in the supernatant from the primary amount of drug present in the suspension [66].

11. DRUG RELEASE For manipulation of the rate and the timing of the drug release from nanoparticles, a good understanding of the mechanisms of drug release is needed. There are five possible methods for drug release: (a) desorption of drug bound to the surface, (b) diffusion through the nanoparticle matrix, (c) diffusion through the polymer wall of nanocapsules, (d) nanoparticle matrix erosion, or (e) a combined erosion–diffusion process [66]. The pharmacokinetic analysis of drug release from nanoparticles can be described by a biexponential function Ct = Ae−t + Be−t where C is the concentration of drug remaining in the nanoparticles at time t, A and B are system characteristic constants, and  and  are rate constants that can be obtained from semilogarithmic plots. Gupta et al. [91] analyzed the mathematical problems of drug release using doxorubicin as the model drug. They proposed two main pathways of drug release. First, there is a rapid release of drug from the nanoparticles, which could stem from drug adsorbed on the nanoparticle surface. Then a slower, more controlled release takes place, which is possibly related to nanoparticle degradation or diffusion of the drug through the nanoparticle shell. Not only are the diffusion coefficient and the biodegradation rate main factors in drug release, but the biological environment also is important. Plasma proteins could be adsorbed onto the surface of the nanoparticles, so that an additional diffusion barrier is formed. On the other hand, nanoparticles could bind to

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2a

1

2b

2 Drug

Polymeric matrix

Drug Polymeric matrix Figure 5. (1) Initial rapid desoption of drug from the nanoparticle surface; (2) Controlled release of drug by diffusion through the nanoparticle matrix and polymer wall. The release is dependent on the nanoparticle biodegradation of the polymer shell.

biological membranes, so that the transport of drugs through these membranes is facilitated. Hence, the results obtained by in vivo and in vitro drug release experiments are very different. Nevertheless, in vitro drug release experiments are very important for quality control reasons; see Figures 5 and 6 [66, 92, 93].

11.1. Ideal Properties of Polymeric-Based Nanoparticles Before nanoparticles can be considered as a realistic drug delivery method, there are several properties the system needs to fulfill [94]. These are the following: • • • • • • • • •

stable in blood nontoxic nonthrombogenic nonimmunogenic noninflammatory no activation of neutrophils biodegradable avoidance of the reticuloendothelial system applicable to various molecules, such as small molecules, proteins, peptides, or nucleic acids (platform technology) • scalable and inexpensive manufacturing process. Because poly(butylcyanoacrylate) nanoparticles possess these properties they were reported to be useful tools for drug delivery to the brain in the several in vivo experiments. In addition, they exhibit very low (if any) toxicity and are considered to be relatively nontoxic. Their toxicity toward hepatocytes is rather low with an LD50 at about 0.4 mg/2 × 106 cells [95]. The LD50 in mice is 230 mg/kg after intraveneous application [96].

12. BODY DISTRIBUTION OF NANOPARTICLES—BRAIN TARGETING Before discussing the evidence that nanoparticles are indeed useful to deliver drugs to the brain, we need to consider their fate after being injected into the body.

Figure 6. Combined nanoparticle erosion diffusion process. 2a: Diffusion of drug through the polymeric matrix and shell; 2b: Drug release through the biodegradation of the nanoparticle.

12.1. Fate of Nanoparticles in the Body After intraveneous injection, nanoparticles are taken up very rapidly by the reticuloendothelial system (RES) and distribute especially into the liver (60–90%) and spleen (2–10%) and, to a minor degree, into the bone marrow. The RES consists of phagocytic cells originating from the bone marrow. The cells exist in the whole body, but their highest concentration is found in the liver (Kupffer cells), spleen, and bone marrow. Despite their great usefulness to target the brain, because of their high uptake by the RES after intraveneous injection, only a limited proportion of the nanoparticles actually reach the brain [97, 98]. Unless their surface is modified by special coatings (described below), nanoparticles themselves are of little value for delivery of drugs to the brain.

12.2. Poly(butylcyanoacrylate) Nanoparticles to Permit Transfer across the BBB In recent years Kreuter et al. [59, 60] and Schroeder et al. [61–64] applied a special procedure to permit brain targeting of nanoparticles. This was accomplished by altering their surface with surfactants. Specifically, polymeric nanoparticles are coated with different hydrophilic surfactants. So far only poly(butylcyanoacrylate) nanoparticles possess the potential to transport drugs across the blood–brain barrier in vivo [99]. The most common method is to first fabricate the nanoparticles; then the drug is bound by adsorption on the surface of the nanoparticles or by forming a solid solution or dispersion. Thereafter, a surfactant is added to the nanoparticle/drug complex. Poly(butylcyanoacrylate) nanoparticles have an average diameter size of about 200–300 nm and are very rapidly biodegraded [97, 100]. Figure 7 shows the two pathways of biodegradation of these nanoparticles. The main pathway consists of enzymatic cleavage of the butylester group of the polymer. The polymeric acid is then formed, and butanol is formed as well. Both metabolites are water soluble and will be excreted by the kidneys. During the other minor pathway, the polymer chain is degraded and formaldehyde is formed in traces, too low to be of physiological concern [101]. The first drug that was successfully delivered to the brain with this approach was the hexapeptide enkephalin, dalargin (Tyr-d-Ala-Gly-Phe-Leu-Arg). These studies were carried out first in the laboratory of Kreuter and subsequently and independently in the laboratory of Sabel.

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Nanoparticle Drug Delivery to the Brain

Reaction times of rats in hot-plate-tests after i. v. administration of Dalargin with & without nanoparticles

latency period [sec]

30 25 20 15

Dalargin on coated PBCA-Nps

10

Dalargin adsorbed on PBCA-Nps Dalargin alone

5 5

15

nanoparticles alone

30

time after in

45

jektion / m in

90

Figure 8. Central analgesic effect of dalargin-loaded nanoparticles coated with polysorbate 80 after i.v. injection. Figure 7. Biodegradation of PBCA-nanoparticles.

12.3. Behavioral Evidence That Nanoparticles Can Deliver Drugs across the BBB Using Dalargin Dalargin is an enkephalin-type peptide that has analgesic (pain-reducing) effects when injected directly into the brain. However, when given intravenously, it does not cross the BBB and no analgesia occurs [59, 102]. Studies to investigate the targeting of dalargin to the brain were carried out using the tail-flick test [59, 102] as well as the hot-plate test [61, 103]. Both tests are useful to quantify pain perception as a behavioral model of drug activity in the brain. When the rat tail is lightly pinched, the rat withdraws the tail by flicking it to the side. If an effective analgesic is given, the flicking does not occur because the rat feels no pain. Thus, one can quantify experimentally analgesic effects of a drug. In the hot-plate test the situation is similar: when placed on a hot plate, the animals will lick their paws. Time to tail flicking and time to paw withdrawal are very sensitive and reliable measures of pain perception and can thus be used to quantify analgesia. To evaluate the usefulness of nanoparticles crossing the BBB, dalargin was bound to nanoparticles and injected into animals, which were then tested for analgesia. To be sure that drug alone or nanoparticles alone had no analgesic effect, groups of animals that received different treatments were compared: (1) dalargin alone; (2) polysorbate 80 alone; (3) poly(butylcyanoacrylate) nanoparticles alone; (4) a mixture of dalargin and polysorbate 80; (5) a mixture of dalargin and poly(butylcyanoacrylate); (6) a mixture of all three components, dalargin, polysorbate 80, and nanoparticles, mixed immediately before injection; and (7) a suspension of dalargin bound to nanoparticles without coating. After intravenous (i.v.) injection into mice, none of the groups showed an analgesic effect. Only dalargin bound to poly(butylcyanoacrylate) nanoparticles coated with polysorbate 80 produced a significant antinociceptive effect [59, 61, 102, 103]. This clearly showed that dalargin had

crossed the BBB. Figure 8 shows the antinociceptive effect after i.v. administration of polysorbate 80-coated nanoparticles loaded with dalargin using the hot-plate test [61]. Apparently the coating with polysorbate 80 was the critical step in achieving the effect. This finding raised the question whether any other coating material may be useful as well. Therefore, different coating materials in combination with the nanoparticles were used to study the specificity of the coating effect to deliver dalargin to the brain. It was found that polysorbate 20, 40, and 60 coatings have similar, but weaker, analgesic effects compared with polysorbate 80 coating. Poloxamers and poloxamines as well as surfactants of the Cremophor and Brij series [polyoxyethylene-(23)laurylether] had no effect [60]. Thus, with a particular set of coating materials nanoparticles effectively delivered drugs to the brain after i.v. injection.

12.4. Oral Application of Peptides using Nanoparticle Technology In the clinical setting it would clearly be desirable to avoid having to inject nanoparticles but rather to make them available also as an oral method for drug delivery. The efficacy of drug delivery to the brain using dalargin-loaded poly(butylcyanoacrylate) nanoparticles after oral application was studied by Schroeder et al. [62]. Different nanoparticle formulations containing dextran 12,000, poloxamer 188, or polysorbate 85 as stabilizer loaded with dalargin were used. No additional coating was used. The formulations were given intraveneously and orally. When polysorbate 85 was used as a stabilizer without coating, a significant analgesic effect occurred after i.v. injection as well as after oral application. Figure 9 shows the analgesic effect after oral application of polysorbate 85-stabilized nanoparticles loaded with dalargin. These results suggest that nanoparticles can also be used as a new tool for oral drug delivery of peptides [62].

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Nanoparticle Drug Delivery to the Brain

latency period [sec]

30

25

Reaction times of rats in hot-plate-tests after oral administration of Dalargin with & without nanoparticles Dalargin, adsorbed on Tween 85-coated nanoparticles Dalargin untreated

20

15

10

5 30

45

60

90

120

150

time after injection / min

Figure 9. Central analgesic effect of polysorbate 85-stabilized nanoparticles loaded with dalargin after oral administration.

12.5. Nanoparticles as a Universal Method for Drug Delivery Across the BBB Next the question arose whether such effects can only be achieved with the test drug dalargin or whether nanoparticles are a universal tool for delivery of drugs to the brain. Therefore, different antinociceptive agents, such as kytorphin [63] and loperamide [104] that normally cannot penetrate the BBB, were also tested using nanoparticles. Similarly to the dalargin experiments, analgesic effects of these drugs were observed. Drug solutions and uncoated nanoparticles, which served as controls, had no significant effect on analgesia, but a significant analgesic effect was obtained when nanoparticles coated with polysorbate 80 and polysorbate 85-stabilized nanoparticles without coating were used [63]. Pharmacokinetic studies of amitriptyline, a tricyclic antidepressant, bound to polysorbate 80-coated poly(cyanoacrylate) nanoparticles showed an enhancement in brain area under the curve (AUC) and a reduced serum AUC after i.v. injection. Similar results were also obtained with polysorbate 85-stabilized nanoparticles without coating [63]. AUC is the area under the curve of concentration versus time after adsorption of 20.0 mg/kg amitriptyline onto the surface of the nanoparticles after i.v. injection of amitriptyline-loaded nanoparticles in mice. The amitriptyline concentrations in serum and brain were determined after 5, 20, and 60 min after i.v. injection. To better understand the mechanisms of action of the injected nanoparticle/drug complex, it is necessary to know its fate after injection. To this end the bioavailability and body distribution of radioactively labeled [3 H]-dalargin bound to poly(butylcyanoacrylate) nanoparticles coated with polysorbate 80 were studied by Schroeder et al. [64]. The studies were performed by comparing unbound 3 H-labeled dalargin with bound dalargin after i.v. injection into mice. The level of radioactivity in brain preparations was three times higher after i.v. injections of 3 H-labeled dalargin bound to poly(butylcyanoacrylate) nanoparticles and coated with polysorbate 80 after 5 and 20 min. In addition, radioactivity levels in the liver were decreased [64]. These results are compatible with the known time course of the analgesic

effect found in behavioral studies 5 and 15 min after oral versus i.v. application [61, 62]. The increased dalargin level in the brain and the enhanced serum levels led to the conclusion that the drug is stabilized by the nanoparticles. This finding is also supported by the decreased liver levels. The nanoparticle formulation thus protects the labeled peptide from rapid degradation and uptake by the RES [64], thus permitting higher brain concentrations. The question also arises whether these findings hold true only for analgesia studies or whether they generalize to other disease models as well. Here, a study by Alyautdin et al. [105] is of interest. They provoked the development of epileptiform seizures using tubocurarine bound to polysorbate 80-coated poly(butylcyanoacrylate) nanoparticles. Tubocurarine, a quaternary ammonium salt that is unable to penetrate the BBB, provokes epileptiform seizures upon direct injection into the brain. An in-situ rat brain perfusion technique was used and the electroencephalogram (EEG) was recorded. Tubocurarine-loaded polysorbate 80-coated nanoparticles caused the appearance of EEG seizures after 15 min. None of the controls, such as a tubocurarine solution, tubocurarine-loaded nanoparticles without polysorbate 80 coating, or a mixture of polysorbate and tubocuraine, affected on the EEG. In conclusion, only polysorbate 80-coated nanoparticles were able to transport tubocurarine across the BBB.

12.6. Influence of Nanoparticles on the Metabolism of Drugs The use of poly(butylcyanoacrylate) nanoparticles as a transport system of antiepileptic drugs, such as valproic acid, was investigated by Schroeder et al. [106]. The authors evaluated the increase in the brain-to-serum ratio of the drug to reduce dose-related side effects in the periphery by using nanoparticles. Changes in the metabolism of valproic acid were also investigated. Mice were given four different i.v. injections: (1) valproic acid alone, (2) valproic acid + nanoparticles (dextran-stabilized), (3) valproic acid + nanoparticles (dextran-stabilized) + Tween 80, and (4) valproic acid + nanoparticles (polysorbate 85-stabilized). Twelve mice were decapitated 5, 20, and 60 min after i.v. injection. The blood was allowed to clot, and serum was taken after centrifugation. The brains were removed, cleaned, and frozen until analysis. The brain and serum levels of valproic acid and its metabolites were determined using a modified gas chromatography–mass spectroscopy assay [107]. It was found that the serum kinetics and the brain tissue levels of valproic acid did not change by administration of valproic acid/nanoparticle formulations compared with the drug alone. However, nanoparticles did influence the metabolism of valproic acid. They inhibited the metabolic degradation of the drug by mitochondrial -oxidation but did not influence any other metabolic pathway. It was concluded that nanoparticles reduce the toxic side effects of valproic acid therapy by selectively blocking a metabolic pathway. Thus, nanoparticles may serve as a tool to change drug metabolism, probably through a sustainedrelease mechanism, in a desirable manner.

100 12.7. Nanoparticles as a Method to Delivery Cytostatic Agents to Treat Brain Tumors In another line of research, drugs to treat brain tumors were investigated. Gulyaev et al. [108] bound doxorubicin to nanoparticles and then examined their body distribution after i.v. injection to rats. Rats were given four different formulations of doxorubicin (DOX): (1) DOX in saline, (2) DOX in polysorbate 80 in saline, (3) DOX bound to poly(butylcyanoacrylate) nanoparticles, and (4) DOX bound to poly(butylcyanoacrylate) nanoparticles overcoated with polysorbate 80. The two doxorubicin solutions showed a similar body distribution and no significant difference between plasma and organ (brain, liver, spleen, heart, or kidney) concentration. For both nanoparticle preparations a significant decrease in the heart concentration was observed. This is a very important finding, because the use of doxorubicin in the treatment of cancer is limited by its heart toxicity, which had also been noted by Couvreur et al. [109]. Only with the polysorbate 80-coated nanoparticle formulation was a high concentration of doxorubicin (>6
g/g) achieved in brain and plasma. The low plasma level and brain concentrations (0.1
g/g, below the detection limit) of the free drug without nanoparticles are caused by their rapid uptake by the RES [110–112]. In addition, polysorbate coating reduced the concentration of doxorubicin in the liver, spleen, and lung [108]. When taken together, these results suggest again that polysorbate 80-coated nanoparticles are a useful drug delivery vehicle for brain targeting. This and other studies by Gelperina et al. [113] described below open new possibilities for the treatment of brain cancer. To evaluate the efficacy of a DOX–nanoparticle formulation, Gelperina et al. [113] investigated the treatment of rat brain tumors using doxorubicin-loaded, polysorbate 80-coated poly(butylcyanoacrylate) nanoparticles. To test efficacy, rats with intracranially transplanted glioblastoma 101/8 cells were treated with a DOX–nanoparticles formulation in the dose of 3 × 1 5 mg/kg. After 6 months these animals were killed and a beneficial effect was documented by histological examination of the brain. In the untreated control group all animals died within 17 days after implantation of cancer cells into the brain. In the remaining four groups [(1) nanoparticles + polysorbate (Ps), (2) DOX in saline, (3) DOX + Ps, and (4) DOX + nanoparticles] only one group (DOX + Ps) showed a long-surviving animal. This could have been due to the fact that the BBB might have been partially disrupted as a result of tumor growth. In conclusion, this study provides another indication that polysorbate 80-coated nanoparticles are a useful tool for drug delivery to the brain.

12.8. Other Approaches with Particles for Drug Delivery to the Brain Nanoparticles are not the only method to increase drug bioavailability. Another approach to reduce RES uptake and to overcome the BBB is the preparation of magnetic microspheres combined with the application of a magnetic field to the brain of rats after intracarotid injection [114]. Two different types of microspheres of 1–2
m diameter size were

Nanoparticle Drug Delivery to the Brain

prepared: magnetic neutral dextran and cationic aminodextran microspheres. Both kinds of microspheres are prepared by an emulsification process using polysorbate 80 as the emulsifier. The magnetic particles were then injected into the carotid arteries of healthy rats and rats with implanted brain tumor (gliom-2/RG-2). A magnetic field was then applied to the brain. The rats were killed after 30 min and 6 h, and the magnetic particle concentration in the tissues was determined by atomic absorption spectroscopy. In healthy rats only low brain concentrations but high lung and spleen concentrations were found for both microspheres. In tumor-bearing rats, the brain concentration of magnetic cationic particles was increased compared with that of neutral particles. In general, these experiments with magnetic microspheres resulted in increased brain concentrations and decreased concentrations in peripheral organs, but did not show any significance because of the high variability among the groups.

13. MECHANISM OF NANOPARTICLE TRANSPORT ACROSS THE BLOOD–BRAIN BARRIER Different mechanisms are described to explain the nanoparticle-mediated drug transport to the brain, including creation of a concentration gradient, a general surfactant effect, opening of the tight junctions, endocytosis, and inhibition of the efflux system [99]. Among them the most likely mechanism is the receptor-mediated endocytosis of nanoparticles. Lück et al. [115] found that apolipoprotein E (apo E) adsorbs on the surface of polysorbate 20-, 40-, 60-, or 80-coated nanoparticles after 5 min in human plasma at 37
C. After separation of the particles from the serum by centrifugation, the adsorbed plasma proteins were desorbed and analyzed by two-dimensional gel electrophoresis. For polysorbate 20-, 40-, 60-, or 80-coated nanoparticles, apo E was found in the serum. In contrast, without coating or with overcoating of nanoparticles using poloxamers 338 and 407, Cremophor EL, or Cremophor RH40, no adsorption of apo E was observed. These results correspond to the findings that only polysorbate 20-, 40-, 60-, or 80-coated nanoparticles induced an antinociceptive effect using dalargin [60]. Kreuter et al. [116] studied the involvement of apo B and E in the mechanism of nanoparticle transport across the BBB. For i.v. injection into mice, poly(butylcyanoacrylate) nanoparticles loaded with dalargin were coated with apolipoproteins AII, B, CII, E, or J without or after precoating with polysorbate 80. In addition, nanoparticles loaded with loperamide were coated with apo E alone or after precoating with polysorbate 80. Furthermore, the antinociceptive effect of polysorbate-coated dalarginloaded nanoparticles was measured in ApoEtm1Unc and C57BL/6J mice. The authors used the tail-flick test to determine the antinociceptive threshold. It was found that dalargin and loperamide-loaded nanoparticles coated with polysorbate 80 and/or with apo B or E induced the analgesic effect. Nanoparticles with polysorbate-precoating and apo B or E overcoating achieved a significantly higher analgesic effect. In addition, with the apo E-deficient ApoEtm1Unc mice, the effect was notably reduced compared with that in

101

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C57BL/6J mice, from which the ApoEtm1Unc mice were derived. The results led to the conclusion that apo B and E are involved in the mediation of the transport of drugs bound to poly(butylcyanoacrylate) nanoparticles across the BBB. These results and also the studies of Lück et. al. [115] indicate that after i.v. injection apo E and/or B is anchored by the polysorbate on the surface of the nanoparticles [116]. Apo B and E are known to bind to lipoprotein receptors on the surface of cells [117, 118]. Low-density lipoprotein receptors have been identified in rat and monkey brains [119]. They also exist in the brain capillary endothelial cells [119, 120]. Polysorbate 80-coated nanoparticles adsorb the apolipoproteins after i.v. injection and thus seem to mimic lipoprotein particles that are able to interact with members of the low-density lipoprotein receptor family and are taken up via receptor-mediated endocytosis. Bound drugs may be further transported into the brain by diffusion [116].

14. CONCLUSION Many drugs affecting the brain or spinal cord either do not cross the BBB at all or do not cross it in pharmacologically effective amounts. As a consequence, some drugs affecting the brain have undesirable peripheral side effects that pose a clinical problem. The severe disturbance caused by cytostatic agents used for the treatment of brain tumors are a dramatic example of this point. It is therefore desirable to have a method available whereby drugs can be delivered to the brain and spinal cord more effectively. Nanoparticle technology is a very valuable method to deliver drugs across the BBB: nanoparticles have a diameter of about 200 nm and they are suspended in an aqueous solution. Depending on the method of the polymerization, drugs are either attached to the surface and/or are incorporated into poly(butylcyanoacrylate) particles. Subsequently, this drug–particle complex is covered by a suitable surfactant (such as polysorbate 80). This complex is then injected intravenously or given orally. Nanoparticles can be stored either in lyophilized form or in solution. In lyophilized form they are stable for at least 2 years; in neutral solution they are just stable for several days. In acidic solution nanoparticles are stable for at least several months. The primary advantage of nanoparticles is their ability to adsorb different drugs because a large variety of compounds can be delivered to the brain. Advantages over other methods of delivering drugs to the brain are that (1) they do not open the BBB, (2) potentially any drug can be delivered (hydrophilic or hydrophobic), and (3) the drug does not need to be altered. Furthermore, nanoparticles are known to be nontoxic. Neither the polymer nor the surfactants have any known toxic effect. Efficacy of the nanoparticle approach has been demonstrated by tests with an analgesic peptide, dalargin, as well as with several other drugs, including cytostatic agents (e.g., doxorubicin). Dalargin normally does not cross the BBB because it only has an analgesic effect when injected directly into the brain. However, when bound to nanoparticles, a marked analgesia is seen when it is given peripherally.

In summary, nanoparticles are a very useful and universal method to deliver drugs to the brain. Industrial applications of the nanosphere technology would have several benefits: • Nanoparticles deliver drugs to the brain that normally do not cross the blood–brain barrier. • They reduce peripheral side effects of (approved) drugs that cross the BBB by increasing the relative dose of drugs reaching the brain; • Nanoparticles can also be used as a screening tool. Delivering drug candidates to the brain by nanosphere technology for initial screening of CNS activity obviates direct CNS injections. It also reduces the need for altering drugs to allow their passage through the BBB, which decreases drug development costs significantly. Furthermore, drugs that come off patent protection can be protected again when used in combination with new drug delivery tools such as nanoparticles. Nanoparticles thus open new possibilities for the treatment of disorders of the brain that were previously inconceivable. The value of nanotechnology for medicine is therefore obvious. We are confident that nanotechnology will make a major contribution to the advancement of drug treatment by helping drugs to be targeted more efficiently to specific organs, such as the brain. This may also be a means to attack previously untreatable disorders such as brain tumors and other neurodegenerative diseases.

GLOSSARY Adsorption Binding of substances to a solid surface. Aldehyde [alcohol + New Lat. dehydrogenatum, dehydrogenated], any of a class of organic compounds that contain the carbonyl group, and in which the carbonyl group is bonded to at least one hydrogen; the general formula for an aldehyde is RCHO, where R is hydrogen or an alkyl or aryl group. Bioavailability After intraveneous or oral administration a drug is distributed throughout the body in different concentrations in several organs. Chromatography Resolution of a chemical mixture into its component compounds by passing it through a system that retards each compound to a varying degree; a system capable of accomplishing this is called a chromatograph. Colloid A mixture in which one substance is divided into minute particles (called colloidal particles) and dispersed throughout a second substance. The mixture is also called a colloidal system, colloidal solution, or colloidal dispersion. Familiar colloids include fog, smoke, homogenized milk, and ruby-colored glass. Cryoprotector Compound such as a sugar that prevents the nanoparticles from the formation of agglomerates. Denaturation Term used to describe the loss of native, higher-order structure of protein molecules in solution. Most globular proteins exhibit complicated three-dimensional folding described as secondary, tertiary, and quarternary structures. Dialysis Transfer of solute (dissolved solids) across a semipermeable membrane. Strictly speaking, dialysis refers

102 only to the transfer of the solute; transfer of the solvent is called osmosis. Dialysis is frequently used to separate different components of a solution. Dispersion Mixture in which fine particles of one substance are scattered throughout another substance. A dispersion is classified as a suspension, colloid, or solution. Generally, the particles in a solution are of molecular or ionic size. Enzyme Biological catalyst; enzymes are proteins that accelerate the rates of reactions while experiencing no permanent chemical modification as a result of their participation. Evaporation Change of a liquid into vapor at any temperature below its boiling point. For example, water, when placed in a shallow open container exposed to air, gradually disappears, evaporating at a rate that depends on the amount of surface exposed, the humidity of the air, and the temperature. Free radical A molecule or atom that contains an unpaired electron but is neither positively nor negatively charged. Free radicals are usually highly reactive and unstable. They are produced by homolytic cleavage of a covalent bond. Ion A neutral atom or group of atoms becomes an ion by gaining or losing one or more electrons or protons. Because the electron and proton have equal but opposite unit charges; the charge of an ion is always expressed as a whole number of unit charges and is either positive or negative. Isotherm Line drawn on a map connecting points of equal temperature. Each point reflects one temperature reading or an average of several readings over a period of time. Lipid A broad class of organic products found in living systems. Most are insoluble in water but soluble in nonpolar solvents. The definition excludes the mineral oils and other petroleum products obtained from fossil material. Major classes of lipids include the fatty acids, the glycerol-derived lipids, the sphingosine-derived lipids, the steroids and their derivatives, the terpenes and their derivatives, certain aromatic compounds, and long-chain alcohols and waxes. Phospholipid Lipid that in its simplest form is composed of glycerol bonded to two fatty acids and a phosphate group. The resulting compound called phosphatidic acid contains a region (the fatty acid component) that is fatsoluble along with a region (the charged phosphate group) that is water-soluble. Polymerization Reaction to create a chemical compound with high molecular weight consisting of a number of structural units linked together by covalent bonds. Precipitation A process in which a solid is separated from a suspension, sol, or solution. In a suspension such as sand in water the solid spontaneously precipitates (settles out) on standing. In a sol the particles are precipitated by coagulation. Surfactant A surface-active compound with a hydrophilic and a lipophilic moiety. Suspension Mixture of two substances, one of which is finely divided and dispersed in the other. Common suspensions include sand in water, fine soot or dust in air, and droplets of oil in air.

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Encyclopedia of Nanoscience and Nanotechnology

www.aspbs.com/enn

Nanoparticle Layers in Multilayers Diana Nesheva Bulgarian Academy of Sciences, Sofia, Bulgaria

CONTENTS 1. Introduction 2. Vapor Deposition of Thin Films 3. Continuous Nanoparticle Layers 4. Discontinuous Nanoparticle Layers 5. Concluding Remarks Glossary References

1. INTRODUCTION Over the past several decades, there has been rapidly increasing interest in the preparation of nanometer-sized materials such as superlattices, quantum wires, and quantum dots. This enhanced interest is justified because these materials show a great variety of new properties with respect to three-dimensional ones. Nanostructured or nanophase materials can be classified into four categories according to the shape of their structural constituents: nanophase powders, nanostructured films (including single-layer, multilayer, composite film, compositionally graded film, etc.), monolitic nanostructured materials, and nanostructured composite. The nanostructured materials can contain crystalline, quasicrystalline, and/or amorphous phases. The search for ultra-thin materials (nanostructured films), in particular, semiconductors, can be traced quite far back (for a review of early work up to 1975, see [1–3]). However, the motivation for their production went up sharply when new types of devices were predicted [4, 5]. Studies of ultra-thin semiconductor layers and multilayer structures containing ultra-thin films have since then increased progressively. Single and multiple quantum wells, single- and double-barrier tunneling structures, incoherent multilayer tunneling structures, etc. have been prepared [6–10] as some of them have been used in production of various devices such as mobile phones, semiconductor photomultipliers, and lasers, etc. [11, 12]. It is important to notice that in crystalline superlattices (periodic multilayer structures built of two consecutively deposited materials) disorder and scattering must be low enough to allow building up of coherent superlattice bandstates and, thus, to prevent destruction of

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the phase coherence by interface fluctuations. This requirement means that for building up crystalline superlattices, pairs of materials have to be used with a difference in the lattice constants smaller that 1%. Thus, only a limited number of pairs can be applied in the superlattice preparation. In the beginning of the 1980’s, it was shown [13] that superlattices could also be fabricated from amorphous semiconductors (a-Si:H, a-Ge:H, SiOx , SiNx , etc.). The lack of long-range order in the structure of amorphous materials induces a great number of defects such as bond-length and bond-angle fluctuations, dangling and floating bonds, etc. This fact, along with the flexibility of amorphous materials, strongly reduces the requirements for matching lattice constants of the constituent materials and makes possible application of a great variety of materials in the fabrication of amorphous multilayers (a-MLs). Regular a-MLs, based on a-Si:H and a-Ge:H, have been prepared by a variety of rather simple and cheaper set-ups (glow-discharge [13], magnetron sputtering [14], plasma- and photochemically enhanced chemical vapor deposition [15–17] techniques), as compared to molecular beam epitaxy [18, 19] applied for crystalline MLs. It has been shown that applying bandgap engineering, new properties can be achieved, based both on classical effects, connected mainly with the influence of the interlayer barriers [20–25], and quantum-size effect (QSE) when the layers are sufficiently thin and the period (or the well layer width) is comparable with the de Broglie wavelengths of the charge carriers (electrons and holes) [20, 26–30]. Four-fold coordinated a-Si:H, a-Ge:H, and similar materials keep the rigid tetrahedrally bonded structure of the respective elemental crystalline semiconductors. In chalcogenide materials coordination number (that is, the number of the nearest neighbors) varies between 2 (for a-S, a-Se, a-Te, and their alloys) and 10) regardless of reaction time, and it was composed of CuCl(s) and CuCl2 (s). This is contrary to the much lower chlorine content obtained without Table 8. Mass distributions of desorbed gases from thermal etching and photon-induced etching of copper at various conditions. Mass distribution Thermal etching Species

860 K

Cl Cu CuCl CuCl2 Cu2 Cl Cu2 Cl2 Cu2 Cl3 Cu3 Cl2 Cu3 Cl3

9 20 51 — 83 10 — 25 100

28

UV laser1

920 K

0.26J/cm 532 nm

27 68 514 — 82 14 — 27 100

28 273 89 121 284 10 282 141 100

2

0.66J/cm 355 nm — 47 8 5 6 13 35 60 100

UV lamp 2

CuCl04 CuCl12 340 nm 340 nm 410 — 100 2330 130 100 550 130 100

350 — 100 2350 280 150 2380 270 100

Nanoscale MRAM Elements

473

Etch Rate (Å/min)

3000 1 2000 Etch Rate with UV Cl content 1000

0

Chlorine Content in CuClx

2 4000

0 0

1

2

3

UV Intensity (arb. units) Figure 9. The effect of UV intensity on etch rate of copper and chlorine content in the copper chloride at Cl2 /N2 = 1.5, 2 mTorr, 500 W ICP source power, and room temperature. Adapted from [6], D. E. Heim et al., IEEE Trans. Magn. 30, 316 (1994) and [8], R. E. Fontana et al., IEEE Trans. Magn. 32, 3440 (1996). © 1994 and 1996, IEEE.

450 E tch

0

N iF e 10C l 2 /5A r 200W rf 2m T orr

D eposition

-500

350

250 -1000

d c B ias (-V )

E tch R ate (Å /m in )

500

W / UV W /O U V d c B ias

-1500 0

200

400

600

800

150 1000

IC P Source P ow er (W ) N iF eC o 10C l 2 /5A r 200W rf 2m T orr

800

350 W / UV W /O U V dc B ias

400

250

dc B ias (-V )

450

1200

E tch R ate (Å /m in )

UV illumination. However, this result is attributed to the fact that the copper surface is easily chlorinated under UV illumination because UV photons promote the chemistry at the surface and lower the activation energy. Choi and Han reported the activation energy of 0.12 eV, which is much lower than the energy of 1.6 eV required to sublime CuCl(s) to Cu3 Cl3 (g). This confirms that the dry etching with UV illumination is not a simple thermal desorption, but a nonthermal etch mechanism due to the presence of UV photons. Figure 9 shows the effect of UV intensity on etch rate and the chlorine content in the copper chloride, adapted from the experiments by Kwon et al. They measured etch rates and Cl contents with varying UV intensity at Cl2 /N2 = 1.5, 2 mTorr, 500 W ICP source power, and room temperature. The etch rates increased linearly with UV intensity up to certain point and then remained almost constant, while the Cl concentration in the copper chloride was independent of UV intensity and maintained at 1.2–1.3, implying coexistence of CuCl(s) and CuCl2 (s). The insensitivity of chlorine atomic ratio to the UV intensity indicates that the UV photon energies used in their experiment are enough for the surface chlorination to occur and to form CuClx having x > 10. The photon-assisted etch of the copper chloride layer occurs very quickly since the CuClx layer has low reflectivity but high absorption depth (see Table 2) and absorbs most UV photons as soon as the layer is formed. The increase in etch rate with UV intensity is believed to occur because the photonassisted removal rate of copper chlorides is faster than the deposition rate of CuClx , indicating that the deposition rate of copper chloride controls the overall etch process. However, at higher UV intensity the CuClx formation rate is also increased due to the increased photon flux, and is thus in equilibrium with the photon-assisted etch rate. Figure 10 shows the effect of ICP source power in our reactor on etch rates of Ni08 Fe02 (top) and Ni08 Fe013 Co007 (bottom) with or without UV illumination in Cl2 plasmas at 10 sccm Cl2 /5 sccm Ar, 200 W rf chuck power, 2 mTorr, and room temperature. In these experiments an unfiltered 400 W Hg arc lamp was used for UV irradiation. Details of the experiment are described elsewhere. There is net

E tch

0 D eposition

0

200

400

600

800

150 1000

IC P Source P ow er (W ) Figure 10. The effect of ICP source power on etch rates of NiFe (top) and NiFeCo (bottom) with or without UV illumination in Cl2 plasmas at 10 sccm Cl2 /5 sccm Ar, 200 W rf chuck power, 2 mTorr, and room temperature.

deposition observed on NiFe, indicating the rate of formation of metal chlorides is greater than their removal rates. This result also implies that reaction products such as NiClx and FeClx are not absorbing UV photons. The increase in the formation rate of metal chlorides is attributed to the increased chlorine radicals with UV illumination and the chemistry promoted at the surface by photons. In contrast to NiFe, NiFeCo showed an overall increase in etch rate with UV illumination, especially at moderate ICP source powers (500–800 W). This may be attributed to two factors: (1) lower binding energy of NiFeCo than NiFe (for example, see the Fe–Co phase diagram; addition of Co to Fe lowered the melting point of FeCo alloy) and (2) greater absorption capacity of UV photons by CoClx than by NiClx and FeClx . The latter is unlikely because Ni, Fe, and Co are elements all in the same period and the same group so that the alloys and metal chlorides have similar optical properties (Tables 2 and 3), and furthermore the atomic ratio of Co (i.e., 0.07) is too small to affect the overall optical properties of etch products. However, to clearly understand the effect of UV illumination on the dry etching of magnetic materials, more systematic studies, in particular, the dependence of etch rates on optical properties of NiClx , FeClx , and CoClx , need to be conducted. With the UV-enhanced process, very clearly defined features can be patterned into Cu, as shown in the scanning electron micrographs of Figure 11. The etching was

Nanoscale MRAM Elements

474

Plasma chemistry The combination of gases used to create reactive etch products with the sample upon creation of a plasma. Plasma etching Use of a reactive plasma to etch controlled amounts of a sample exposed to the plasma; also called dry etching.

REFERENCES Figure 11. SEM micrographs of features etched into Cu layers on Si, using ICP Cl2 /Ar discharges.

performed at 75
C in Cl2 /Ar in this case, whereas to achieve similar rates without UV illumination required etch temperatures ≥150
C. An etch mechanism with UV illumination was proposed to better understand the ICP etching of copper and magnetic materials. The photodissociation of Cl2 provides a chlorine-enriched environment near the surface, and UV photons promote the chemistry at the copper surface, leading to fast deposition of metal chlorides on the surface with low activation energy. The proposed model predicts that surface chlorination under UV irradiation produces copper chlorides having Cl content equal to or greater than the stoichiometric ratio (i.e., x ≥ 1). The overall etch process of metals with UV illumination is limited by absorption of UV radiation, which is determined by optical properties of the metal chlorides. The proposed etch mechanism showed gaseous etch products are CuCl, CuCl2 , Cu2 Cl, Cu2 Cl2 , Cu2 Cl3 , Cu3 Cl2
and Cu3 Cl3 , verified with reported mass spectrometry data [8] and the dominant gas species are CuCl2 and Cu2 Cl3 in the etching with UV illumination. The Cl2 –ICP etching of magnetic materials with UV illumination showed no enhancement in etch rate for NiFe but a substantial enhancement for NiFeCo mainly due to lower binding energy of NiFeCo. However, to clearly understand the effect of UV illumination on the dry etching of magnetic materials, more systematic studies have to be carried out in terms of the absorption of UV photons by NiClx , FeClx , and CoClx .

5. CONCLUSIONS Nanoscale patterning of MRAM elements and other magnetic structures is possible using high density plasma etching, combined with appropriate lithography. The choice of plasma chemistry is determined by the materials used in the structure, and both corrosive and noncorrosive chemistries are available.

GLOSSARY High density plasma A discharge with an average ion density above approximately 1011 ions per cubic centimeter. Ion-induced damage Any disruption of the properties of a material by the energetic ions that bombard its surface during dry etching. Magnetic random access memory A form of nonvolatile magnetic memory that is promising for data storage.

1. G. A. Prinz, in “Ultra-Thin Magnetic Structures II” (B. Heinrich and J. A. C. Bland, Eds.). Springer-Verlag, Berlin, 1994. 2. C. H. Tsang, R. E. Fontana, Jr., T. Lin, D. E. Heim, B. A. Gurney, and M. L. Williams, IBM J. Res. Develop. 42, 103 (1998). 3. C. H. Tsang, J. Appl. Phys. 69, 5393 (1991). 4. R. White, IEEE Trans. Magn. 28, 2482 (1992). 5. J. M. Daughton, P. Bade, M. Jenson, and M. Rahmati, IEEE Trans. Magn. 28, 2488 (1992). 6. D. E. Heim, R. E. Fontana, Jr., C. H. Tsang, V. Speriosu, B. A. Gurney, and M. L. Williams, IEEE Trans. Magn. 30, 316 (1994). 7. M. Parker, K. Coffrey, J. Howard, C. H. Tsang, R. E. Fontana, Jr., and T. Hylton, IEEE Trans. Magn. 32, 142 (1996). 8. R. E. Fontana, S. MacDonald, C. H. Tsang, and T. Lin, IEEE Trans. Magn. 32, 3440 (1996). 9. B. A. Everitt, A. V. Pohm, and J. M. Daughton, J. Appl. Phys. 81, 23639 (1997). 10. S. Wang, F. Liu, K. D. Maranowski, and M. H. Kryder, IEEE Trans. Magn. 26, 1689 (1989). 11. S. Wang, E. Louis, F. Wolfson, R. Anderson, and M. H. Kryder, IEEE Trans. Magn. 30, 3897 (1994). 12. H. Takano, H. Fukuoka, M. Suzuki, K. Shiiki, and M. Kitadu, IEEE Trans. Magn. 27, 4678 (1991). 13. H. Gokan and S. Eho, J. Vac. Sci. Technol. 18, 23 (1991). 14. M. J. Vasile and C. J. Mogab, J. Vac. Sci. Technol. A 4, 1841 (1986). 15. R. Giridhar, Jpn. J. Appl. Phys. 35, 6347 (1996). 16. C. Tsang, M. Chen, T. Yogi, and K. Ju, IEEE Trans. Magn. 30, 281 (1994). 17. F. C. M. J. van Delft, J. Magn. Magn. Mater. 140–144, 2203 (1995). 18. K. Kinoshita, K. Yamada, and H. Matutera, IEEE Trans. Magn. 27, 4888 (1991). 19. M. Balooch, D. S. Fischl, D. R. Olander, and W. J. Siekhaus, J. Electrochem. Soc. 135, 2090 (1988). 20. D. S. Fischl and D. W. Hess, J. Vac. Sci. Technol. B 6, 1577 (1988). 21. D. W. Hess, Plasma Chem. Plasma Proc. 2, 141 (1982). 22. B. Khamsehpour, C. D. W. Wilkinson, and J. N. Chapman, Appl. Phys. Lett. 67, 3194 (1995). 23. I. Nakatani, IEEE Trans. Magn. 32, 4448 (1996). 24. P. M. Levy, J. Magn. Magn. Mater. 140–144, 485 (1995). 25. P. M. Levy, Solid State Phys. 47, 367 (1994). 26. See, for example, IBM Storage Division Web site, http:// www.storage.ibm.com/hardsoft/diskdrdl/technolo/gmr/gmr.htm. 27. B. El-Kareh, “Fundamentals of Semiconductor Processing Technology.” Kluwer Academic, Boston, 1995. 28. D. M. Manos and D. L. Flamm, “Plasma Etching: An Introduction.” Academic Press, Boston, 1989. 29. P. Singer, Semiconductor Int. 154 (July 1996). 30. B. Gorowitz, R. J. Saia, and E. W. Balch, in “VLSI Electronics Microstructural Science” (N. G. Einspruch, S. S. Cohen, and G. Gildenblat, Eds.), Vol. 15, Chap. 4. Academic Press, Orlando, 1987. 31. A. K. Sinha, H. S. Lindenburger, D. B. Fraser, S. P. Murarka, and E. N. Fuls, IEEE Trans. Electron Devices. ED-27, 1425 (1980). 32. T. M. Mayer, J. M. E. Harper, and J. J. Cuomo, J. Vac. Sci. Technol. A 3, 1779 (1985). 33. “CRC Handbook of Chemistry and Physics,” 72nd ed. CRC Press, Boca Raton, FL, 1989.

Nanoscale MRAM Elements 34. M. A. Liebermann and A. J. Lichtenburg, “Principles of Plasma Discharges and Materials Processing.” Wiley, New York, 1994. 35. K. B. Jung, E. S. Lambers, J. R. Childress, S. J. Pearton, M. Jenson, and A. T. Hurst, Jr., Appl. Phys. Lett. 71, 1255 (1997). 36. S. J. Pearton, T. Nakano, and R. A. Gottscho, J. Appl. Phys. 69, 4206 (1991). 37. R. J. Shul, M. L. Lovejoy, D. L. Hetherington, D. J. Rieger, J. F. Klem, and M. R. Melloch, J. Vac. Sci. Technol. B 13, 27 (1995). 38. R. J. Davis and E. D. Wolf, J. Vac. Sci. Technol. B 8, 1798 (1990). 39. G. S. Oehrlein, Y. Zheng, D. Vender, and O. Joubert, J. Vac. Sci. Technol. A 12, 323 (1994). 40. J. Mau, J. Vac. Sci. Technol. B 6, 652 (1987). 41. D. A. Danner, M. Dalvie, and D. W. Hess, J. Electrochem. Soc. 134, 669 (1987). 42. J. W. Lee, J. Hong, and S. J. Pearton, Appl. Phys. Lett. 68, 847 (1996). 43. S. J. Pearton, J. W. Lee, E. S. Lambers, J. R. Mileham, C. R. Abernathy, F. Ren, W. S. Hobson, and R. J. Shul, J. Vac. Sci. Technol. B 14, 118 (1996). 44. F. Ren, W. S. Hobson, J. R. Lothian, J. Lopata, J. A. Caballero, S. J. Pearton, and M. W. Cole, Appl. Phys. Lett. 67, 2497 (1995). 45. J. W. Lee, J. Hong, E. S. Lambers, and S. J. Pearton, J. Vac. Sci. Technol. B 15, 652 (1997). 46. K. B. Jung, E. S. Lambers, J. R. Childress, S. J. Pearton, M. Jenson, and A. T. Hurst, Jr., J. Vac. Sci. Technol. A 16, 1697 (1998). 47. K. B. Jung, J. Hong, H. Cho, J. R. Childress, S. J. Pearton, M. Jenson, and A. T. Hurst, Jr., J. Electron. Mater. 27, 972 (1998). 48. See, for example, “High Density Plasma Sources” (O. A. Popov, Ed.). Noyes, Park Ridge, NJ, 1994. 49. Y. B. Hahn, to be published. 50. B. Vavra, Honeywell SSEC, Plymouth, MN, private communication.

475 51. See, for example, G. S. Oehrlein and Y. Kurogi, Mater. Sci. Eng. R 24, 153 (1998). 52. J. M. Daughton, Thin Solid Films 216, 162 (1992). 53. T. Osaka, T. Homma, K. Saito, A. Takekoshi, Y. Yamazuki, and T. Namikawa, J. Electrochem. Soc. 139, 1311 (1992). 54. M. Jimbo, K. Komiyama, and S. Tsunashima, J. Appl. Phys. 79, 6237 (1996); J. Magn. Magn. Mater. 165, 308 (1997). 55. J. A. Caballero, W. J. Geerts, F. Petroff, J.-V. Thiele, D. Weller, and J. R. Childress, J. Magn. Magn. Mater. 177–181, 1229 (1998). 56. K. B. Jung, H. Cho, Y. B. Hahn, D. C. Hays, T. Feng, Y. D. Park, J. R. Childress, and S. J. Pearton, Mater. Sci. Eng. B, 60, 101 (1999). 57. H. Yoda, H. Iwasaki, T. Kobayashi, A Tsutai, and M. Sahashi, IEEE Trans. Magn. 32, 3363 (1996). 58. H. Kanai, K. Yamada, K. Aoshima, Y. Ohtsuku, J. Kane, M. Kanamine, J. Toda, and Y. Mizoshita, IEEE Trans. Magn. 32, 3368 (1996). 59. W. P. Jayasekara, S. Wang, and M. H. Kryder, J. Appl. Phys. 79, 5880 (1996). 60. C. H. Tsang, T. Lin, S. MacDonald, N. Robertson, S. Santini, M. Duerner, T. Reith, L. Vo, T. Diola, and P. Arnett, IEEE Trans. Magn. 33, 2866 (1997). 61. K. Fukuda, M. Sakai, N. Yamanaka, A. Iijima, and M. Matsuzaki, IEEE Trans. Magn. 30, 3891 (1994). 62. W. P. Jayasekara, J. Grant, J. A. Bain, A. E. T. Kuiper, and M. H. Kryder, IEEE Trans. Magn. 33, 2830 (1997). 63. N. Fukushima, H. Katai, T. Wada, and Y. Horiike, Japan. J. Appl. Phys. 35, 2512 (1996). 64. R. E. Lee, J. Vac. Sci. Technol. 16, 164 (1979). 65. J. W. Lee, S. J. Pearton, C. J. Santana, J. R. Mileham, E. S. Lambers, C. R. Abernathy, F. Ren, and W. S. Hobson, J. Electrochem. Soc. 143, 1093 (1996).

Encyclopedia of Nanoscience and Nanotechnology

www.aspbs.com/enn

Nanoscopic Optical Tracers Wolfgang Schaertl Universität Mainz, Mainz, Germany

Sabine Schaertl Evotec OAI AG, Hamburg, Germany

CONTENTS 1. Introduction 2. Optical Micro- and Nanorheology 3. Optical Nanotracers in Drug Development 4. Concluding Remarks Glossary References

1. INTRODUCTION “Nano” signifies one of the most important scientific topics of modern physics, chemistry, and the life sciences. It promises interesting technological developments in the near future, especially in the fields of information technology and modern drug discovery. From a fundamental point of view, nanoscopic probe particles provide the means to explore the structural and dynamic natures of matter on a tiny length scale and improve our understanding of physicochemical processes on a fundamental level. In this chapter, we will describe the use of specially designed nanoscopic particles in optical tracer experiments. These studies comprise the exploration of transport phenomena in dense interacting colloidal systems, polymer melts, etc. on a micrometer length scale, elucidating for instance interparticle interactions or the mechanism of complex transport processes. A variety of different optical techniques to address these fundamentally important problems has been developed during the last one to two decades, ranging from direct microscopic observation of probe particles [1–5], automatized via modern computers, to more complex fluorescence spectroscopic [6–11] or light-scattering [12–20] techniques. Each technique requires special optical properties of the probe particles, which have to be designed accordingly. For example, nanoscopic probes suitable for fluorescence techniques have to be chemically modified with fluorescent dye molecules or semiconducting metal clusters. On the other hand, the probe particles have to be prepared in such a way that they do not influence the behavior of ISBN: 1-58883-063-2/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

the surrounding sample itself. These restrictions provide a major challenge for chemical synthesis, which is rewarded by the scientific knowledge one can get from experiments with nanoscopic optical tracers. A second use of nanoscopic optical tracers lies in modern drug discovery. Potential drugs are identified by their ability to interact with biochemical molecules, which is monitored in an in vitro assay where a preferrably fluorescent probe is used for detection. Here, nanobeads can be used to generate or enhance a signal. Fluorescence confocal single molecule detection [21–27] applied to drug discovery allows the use of highly miniaturized sample volumes and accurate detection of biochemical interactions, and the combination with nanobeads expands the range of applications. Our contribution is organized as follows: In a first section about optical microrheology, we will start with a short overview of the theoretical background of transport processes in soft condensed matter systems. This part will mainly cover the relationship between standard dynamicalmechanical relaxation experiments using a conventional rheometer, and the information one may get from the optical nanotracer experiments. We will conclude this section with a review of the optical techniques used for optical nanotracing, also providing some illustrative experimental examples taken from the recent literature. The second section of our contribution will deal with the use of nanoparticles in pharmaceutical drug discovery and diagnostics. Here, we will mainly consider recent developments in high throughput drug discovery using fluorescence detection techniques.

2. OPTICAL MICRO- AND NANORHEOLOGY 2.1. Diffusion of Nanoscopic Probe Particles and Mechanical Spectroscopy Only seven years ago [28], Mason and Weitz set the basis for so-called optical microrheology [28–34]. They have shown that by determination of the single particle trajectories of

Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 7: Pages (477–491)

Nanoscopic Optical Tracers

478 tiny probe particles embedded in a complex fluid, it is possible to extract the frequency-dependent linear viscoelastic moduli, that is, the flow and elastic properties, of the sample. This new approach provides some important advantages, such as extended frequency range and the ability to probe the dynamic within a micrometer length scale. The latter is especially important for structurally heterogeneous systems, where conventional rheology only can provide a meaningless average result. The motion of a probe particle dispersed in a complex viscoelastic fluid is described by a generalized Langevin equation [35–41]: ˙ mvt = fR t −




t 0

t − v d

(1)

˙ with m the particle mass and vt the time derivative of the particle velocity. fR t is the random forces acting on the probe particle and includes both stochastic Brownian forces exerted on the probe particle by thermally incited density fluctuations within the fluid, and, in the case of higher concentrations of probe particles, direct interactions between individual particles. The integral term represents the viscous damping or friction of the fluid and incorporates a generalized time-dependent memory function t, which basically includes the viscoelastic moduli of the fluid. For a complex viscoelastic fluid, the fluctuation-dissipation theorem, which describes the relation between the stochastic density fluctuations driving the probe particle motion and the viscous damping of this motion due to energy dissipation (Note: Both effects are caused by the same stochastic Brownian force fR t. The so-called fluctuation-dissipation theorem connects diffusive mobility and viscous friction.), is given by fR 0fR t = kB T t

(2a)

with fR 0fR t the time-correlation function of the stochastic force and kB T the thermal energy. For a simple viscous fluid, the memory function t is replaced by the shear viscosity 0 , and Eq. (2a) becomes fR 0fR t = kB T0

(2b)

Based on Eqs. (1) and (2a), it can be shown that the viscoelastic memory function t is related to the velocity autocorrelation function v0vt and hence to the mean squared displacement of the probe particle r 2 t [28]. After Laplace transformation, a generalized Stokes–Einstein relation (GSER) is obtained:  = s s ˜ Gs =

kB T  asr˜2 s

(3)

 with s the frequency in the Laplace domain, Gs the vis˜ coelastic modulus, s the frequency-dependent viscosity of the complex fluid, a the radius of the probe particle, and r˜2 s its mean squared displacement. For a viscous fluid, the probe particle is freely diffusing, and its mean squared displacement is simply given by 2

r˜ s = 6D/s

2

(4)

In this case, the viscosity is independent of frequency s, and Eq. (3) becomes the well-known Stokes–Einstein equation relating self-diffusion coefficient and shear viscosity 0 : 0 =

kB T 6aD

(5)

In conventional rheological measurements, the complex ′′ dynamic-mechanical modulus G∗  = G′  + iG , with G′  the elastic or storage modulus representing the elasticity of the sample and G′′  the loss modulus representing the viscous flow properties of the sample, is measured typically with an oscillatory shear rheometer [42]. A thin film of the sample (thickness about 0.1–1 mm, diameter a few cm) is deformed periodically with a motor, and the resulting stress transferred by the sample to a transducer is measured (see Fig. 1). It is important to note that the stress and, correspondingly, the viscoelastic moduli of the sample usually depend on the deformation frequency . To illustrate the significance of the viscoelastic moduli, let us regard the two extreme cases: For an elastic solid body, suchas a rubber ball, which, upon stress, shows neither flow nor permanent deformation, G′  ≫ 0 and G′′  = 0. On the other hand, for a simple viscous fluid, suchas water or very dilute solutions, G′  = 0 and G′′  ≫ 0, and, upon stress, all energy is dissipated into the sample. Complex fluids, suchas concentrated colloidal dispersions, polymer gels, etc., have both elastic and viscous components.  To compare Gs obtained from microrheological measurement with G∗  determined by conventional rheology, one could, in principle, calculate first the Laplace trans form and then the Fourier transform of Gs. In their first  experiments, Mason and Weitz preferred to fit Gs by a functional form and determined G∗  by analytic continuation of this fitted form. The authors have verified the validity of the sketched formalism by three different experimental examples: (1) A highly concentrated (56 vol%) colloidal suspension of silica particles of radius 210 nm in ethylene glycol studied by diffusing wave spectroscopy (DWS), a special light-scattering technique that will be discussed further beyond; in this case of a concentrated colloidal dispersion studied by DWS, probe particles and sample are identical: The viscoelastic behavior is mainly determined by direct interactions between the nanoscopic colloidal particles. (2) An emulsion of uniformly sized oil droplets of radius 530 nm, stabilized with a surfactant and suspended in water, volume fraction of the droplets 62%; here, as in transducer

sample

motor Figure 1. Sketch of a typical oscillatory shear rheometer.

Nanoscopic Optical Tracers

case of example (1), probe particles and sample are identical. (3) An entangled polymer solution of high molecular weight polyethylene oxide dissolved in water, containing a small amount (2 vol%) of nano-sized polystyrene latex spheres of radius 210 nm as optical probe particles; in this last example of a polymer gel, the latex probe particles only serve to visualize the viscoelastic behavior of the polymer network but do not influence it. In all three cases, Mason and Weitz [28] found excellent agreement between the viscoelastic moduli determined by standard rheological measurements and by the new microrheological approach using optical tracer techniques. Here, it is important to mention that the generalized Stokes–Einstein equation ( Eq. (3)), which relates the single probe particle dynamics to the complex viscoelastic modulus, is only valid at certain length scales and within a limited frequency regime [43–47]: If the medium is inhomogeneous on the particle length scale, the tracer particle will follow the easy way, and its dynamics will predominantly sample local regions that provide the least resistance to deformation. Therefore, these soft cavities are oversampled. Only if the size of the probe particle is much larger than the characteristic length scale of the viscoelastic fluid, the single-particle dynamics reflect the overall viscoelasticity of the dispersing medium. For this reason, optical probes for microrheological measurements are usually several hundred nanometers in size. A recent experimental development provided a solution to this problem: By simultaneous determination of the correlated displacement of two probe particles [48, 49] separated by a distance that is large compared both to the particle size and the characteristic length scale of the viscoelastic medium, using for example optical video microscopy, the result becomes independent of both size and shape of the probe particles. This correlated two-particle displacement, also called two-point microrheology, directly reflects the bulk viscoelasticity of the medium and does not suffer from the length scale restrictions present in studies of single-particle dynamics in microscopically heterogeneous media. The GSER (Eq. (3)) is not only limited to probe particles larger than the characteristic length scale of a heterogeneous viscoelastic medium, for example a polymer network, but is also restricted in respect to the frequency window L <  < U : The lower frequency L is given by the longitudinal compression mode of the polymer network, and the upper frequency cutoff originates from fluid inertia effects. Due to the important perspectives for the experimentalist, the validity of the GSER has recently become a very important subject in the field of theoretical physics. For a more detailed discussion, which is far beyond the scope of this contribution, we therefore refer to the literature [35, 36, 40, 41, 44–47]. We have tried to sketch how the microscopic dynamics of an optical probe, also called microrheology, and conventional rheological techniques are connected. This formalism, developed just a few years ago, opens up a rich field for the experimentalist: Now, not only can the dynamics of optical probes be used to study simple viscous fluids where the Stokes–Einstein equation holds (Eqs. (4) and (5)), but it is also possible to investigate complex viscoelastic samples and

479 even to determine the viscoelastic moduli in a frequency regime not accessible by conventional rheological methods.

2.2. Experimental Techniques In this section, we will try to illustrate the importance of optical microrheology by a presentation of various recently developed experimental methods. The interested reader is also referred to a short but comprehensive review about optical microrheology techniques by Mukhopadhyay and Granick [50] that has just been published. All these techniques have in common the fact that their fundamental experimental quantity is the mean squared displacement of a nano- to micron-sized probe particle determined by optical methods. However, they differ strongly in time and length resolution, as well as in the optical properties of their probe particles. Depending on the scientific problem, the suitable technique or even a combination of various methods has to be chosen carefully.

2.2.1. Optical Video Microscopy In optical video microscopy [1–5], the motion of a nanoscopic probe particle is directly observed with the help of an optical microscope. Images of the particle positions are recorded with a video camera and fed to a personal computer. The major advantage of this technique is that it is capable of tracking many probe particles simultaneously. For this reason, it also allows one to measure the correlated motion of two individual particles necessary for the 2-point microrheology [49] mentioned above. Another advantage is the very small sample volume necessary for microscopic studies (100 nm) and, more crucially, the limited time resolution of modern video hardware (ca. 0.001–0.01 seconds). Therefore, the technique is not suited to study very elastic fluids, where rapid particle motion on a very short length scale is to be expected. In general, currently only the long-time or, correspondingly, the low-frequency regime of the dynamic mechanical modulus G∗  of a viscoelastic fluid can be studied by videomicroscopy. In the near future, new technical developments, for example high speed cameras and faster computers, will enhance the time scale of this technique to much shorter times (higher frequencies). Standard optical microscopic techniques are limited to very thin samples, restricting the observable particle motion to two dimensions. Therefore, well-suited samples are biological monolayers or bilayers, such as cell membranes. Here, optical microscopy, where already one single particle can be detected, is much better suited than light scattering techniques, which, due to the low contrast of an individual particle, need to average the signal from many probes, and therefore are only suited for bulky samples. The restriction of optical microscopy to two dimensions can be overcome by confocal microscopy [51–55], which, although on a very slow time scale of seconds, allows one to change the plane of focus systematically within a sample, thereby creating a three-dimensional microsopic image. For videomicroscopy, it is necessary to distinguish clearly the probe particles from the surrounding medium by sufficient optical contrast. This optical contrast of the

Nanoscopic Optical Tracers

480 probe particles may be based on fluorescence (fluorescence microscopy), for which purpose the probes have to be labeled with fluorescent dyes or even semiconducting metal clusters. The latter are much better suited because of their higher stability in case of irradiation [56–59]. It is also possible to tune the wavelength of both excitation and fluorescence via the size of the metal clusters [60, 61]. Alternatively, dark field microscopy [62, 63] may be applied, where the probe particles are distinguished from the surrounding medium by their enhanced light scattering power. Compared to conventional optical transmission microscopy, both the fluorescence and the dark field techniques have the advantage that tracers even much smaller than the wavelength of light (400–800 nm) are clearly visible and therefore can be used as probe particles. Next, let us consider a recent example of single particle tracking by optical microscopy: The diffusion of individual fluorescent tracer particles has been studied in thin (d = 2–3 m) concentrated colloidal suspension layers [5]. For this purpose, a few fluorescent tracers (100 nm fraction); (B) unfractionated colloids immobilized on a glass slide surface by using mercaptopropyl trimetroxysilane; and (C) unfractionated colloids immobilized on a glass surface by using polylysine. Laser wavelength = 633 nm; excitation intensity = 3 mW; data integration time = 1 s; and R6G concentration = 1 × 10−7 M. Reprinted with permission from [144], D. J. Maxwell et al., Chem. Mater. 13, 1082 (2001). © 2001, American Chemical Society.

SERS experiment performed in silver or gold colloidal solution [75, 149]. Spectra were excited by an argon-ion pumped continuous wave Ti:sapphire laser operating at 830 nm with a power of about 100–200 mW at the sample. A microscope attachment was used for laser excitation and collection of the Raman scattered light. The analyte was provided as a solution at concentrations smaller 10−11 M, which was added to the solution of small colloidal clusters [75]. In the single-particle SERS studies [80], nanometer-sized silver particles were used to amplify the spectroscopic signatures of adsorbed single molecules enormously. Simultaneously, the size-dependent properties of the nanostructures could be examined at the single-particle level. A silver colloid with adsorbed rhodamine 6G molecules was used [80], immobilized on polylysine coated glass surfaces (average silver particle size of about 35 nm). A very small number of Ag nanoparticles, called “hot particles,” exhibited unusually high enhancement efficiencies. For single rhodamine 6G molecules adsorbed on the selected nanoparticles, the intrinsic Raman enhancement factors were on the order of 1014 to 1015 . Based on these findings, a SERS screening and enrichment method was reported for exploring the size and shape

diversities of nanometer-scale colloidal particles [19]. The described highly active nanoparticles can be used in singlemolecule spectroscopy, ultrasensitive chemical analysis, and nanomaterials design [144].

4.3. SERS as a Probe to the Chemical Nature of the Nanoparticle Surface There is a complementary effect on SERS studies in the sense that it can be focused on the study of the internal modes of the adsorbates or on the adsorbate–metal surface modes, providing information on the type of surfaces of a specific nanometal. The correlation between the optical enhancement with the morphological characteristics of metal nanoparticles makes SERS a potential technique for nanomaterials design [80]. In this sense, standard molecular adsorbates can be used to discriminate specific particles sizes of nanoparticles assemblies. In this context, there is interest to extend SERS studies to a variety of metal surfaces. This is particularly interesting when associated with the study of catalytic processes occurring at various metal surfaces. A possible approach which has been investigated involves the use of ultrathin metals coating a SERS active substrate (Ag or Au) [157]. Although in these cases valuable information about the metal surfaces can be obtained, there is also the possibility to have enhancement of the Raman signal from the adsorbate in contact with the active SERS substrate or at the metal/metal interface. The ideal situation, and also the most difficult to obtain, is to get the SERS spectrum on a wide range of bare metal surfaces (i.e., in a situation analogous to the SERS obtained when Ag and Au substrates are used). This has attracted considerable attention since the observation of the C–O stretching band from CO adsorbed

Nanostructured Metals in Surface Enhanced Raman Spectroscopy

712

5. PERSPECTIVES

568

2 cps

~2188 2094

484

549

0.0 V ~2025

491 540

2076 –0.2 V

~1995 494

+0.2 V

2061

538

–0.4 V

~1972 2041

444 536

–0.8 V

447 2056

–1.0 V

454

2056 –1.4 V

300

500

700

900

1700

1900

2100

2300

Wavenumbers (cm–1)

Figure 9. Potential-dependent surface Raman spectra from CO adsorbed irreversibly at a roughened Pt electrode. Reprinted with permission from [157], Z. Q. Tian et al., J. Phys. Chem. B 101, 1338 (1997). © 1997, American Chemical Society.

on a platinized Pt electrode [158]. Since then considerable efforts have been made to obtain SER spectra using bare Pt electrodes, although low signal intensities were generally observed [157]. Some of these limitations will tend to be overcome with advances in Raman instrumentation. An elucidative example of this was the use of confocal microprobe Raman spectroscopy and a electrochemical pretreatment of Pt electrodes to extend the detailed surface Raman studies to bare Pt substrates, using SCN− and CO as the adsorbates (Fig. 9) [157]. Another approach to extend SERS studies to other metal surfaces involves the nanoengineering of specific metal substrates. For example, metal nanorod arrays with high SERS activity have been used as a diagnostic tool to metal nanowires with specific cross sections [159]. By analysis of SERS spectra, namely the band frequency shifts and the intensity of specific probe molecules (e.g., pyridine, SCN− ) adsorbed onto metal surfaces, one may conclude with special electronic properties of the metal nanostructures [159]. A major drawback that has limited SERS as a tool for nanometal design is that the high Raman enhancement has been limited to silver, gold, and, to a lesser extent, to copper. It should be noted that in the latter case [159], due to the nanorod morphology, SERS activity was observed even for metals which usually are non-SERS active such as in the case of several transition metals, including nickel and cobalt. In this case, two-dimensional arrays of metal nanowires (15–70 nm) were prepared by a template synthesis method involving the electrodeposition of the respective metal into nanoholes of the anodic aluminum oxide, followed by removal of the film. SERS on net transition metals has been studied [160] (e.g., Pt, Ru, Rh, Pd, Fe, Co, Ni, and their alloys) by developing various roughening procedures. An approach that replaces the randomly roughened surface with ordered nanorod arrays of transition metals was introduced as a promising class of highly SERS-active substrates [160].

The chemical control of the properties of metal nanostructures associated with recent developments on Raman spectroscopic methods has increased the possibility to apply this technique in innovative contexts. For example, the extension of SERS studies to other metal surfaces rather than Ag and Au, by tailoring specific metal nanostructures, will provide new insights about the mechanisms behind the SERS effect. The study of size-dependent properties of nanometals by SERS screening at the single-molecule level will provide novel knowledge on the understanding of the mechanisms behind surface modification and self-assembly methods. Using single-molecule SERS, the size-dependent properties of the nanostructures can be examined at the single-particle level, and, simultaneously, the spectroscopic features of adsorbed single molecules are enormously amplified. The combination of these complementary effects will give an increasing importance of single-molecule SERS for future research in the fabrication of nanodevices containing nanometals and molecular units.

GLOSSARY Metal nanoclusters Nanoparticles composed of up to hundreds of atoms, with dimensions typically less than 3 nm in diameter, which are stabilized with capping organic ligands. Metal nanocrystals Large nanoparticles which may have dimensions superior to 100 nm, constituents of most of the metal colloids employed in SERS. In metal nanocrystals the internal crystalline structure is similar to the macrocrystalline lattice but it shows distinct physical and chemical properties from the bulk materials and from nanoclusters of metallic atoms. Raman spectrum When monochromatic light of frequency 0 is incident on a transparent sample and the scattered light is dispersed by a monochromator and subsequently measured in intensity, the spectrum of the inelastically scattered radiation (the Raman spectrum of the sample) is obtained. Single-molecule SERS SERS measured on a single molecule using single-metal nanoparticles or aggregates of nanosized metal particles, giving stronger enhancement of the Raman signal up to 1014 . The extremely large SERS enhancement seems to be a very local effect with high spacial confinement, and the single analyte has to find a special hot area (for strong field enhancement) or a hot site (for electronic enhancement). Surface enhanced Raman scattering (SERS) Refers to the observation that for certain molecules adsorbed on specially prepared metal surfaces a Raman spectrum is obtained whose intensity is enhanced by a factor of up to 106 . The large enhancement factors in SERS are obtained through a combination of an electromagnetic effect and chemical interactions between the adsorbate molecule and the surface. Surface modification Derivatization of the metal particle surface using either an inorganic phase, an organic ligand, or both. The derivatization process should not disturb the integrity of the metal core.

Nanostructured Metals in Surface Enhanced Raman Spectroscopy

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Encyclopedia of Nanoscience and Nanotechnology

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Nanostructured Organic Light-Emitting Diodes Thien-Phap Nguyen Université de Nantes, France

Gilles Horowitz Université Denis-Diderot, Paris, France

CONTENTS 1. Introduction 2. Organic Electroluminescence 3. Nano-Organic Light-Emitting Diodes 4. Conclusion Glossary References

1. INTRODUCTION Light emission from organic materials has been known for a long time. One of the most amazing examples of organic light comes from a small insect known as a firefly. It emits light by a chemical process produced by its own biochemistry and the light emission is then called bioluminescence. What is remarkable is the efficiency of the conversion process, which is very high, close to unity, and at this stage it is not possible for scientists to obtain a similar performance with all the techniques they have. Some fish living in deep oceans can also emit light by bioluminescence. Light can be also generated in organic materials by other conversion processes. When the excitation source is light, the process is called photoluminescence. Similarly, if the origin of the excitation is chemical, thermal, or electrical, the terms chemiluminescence, thermoluminescence, or electroluminescence are used to designate the light emission. In electroluminescent devices, the electrical excitation of the material is provided by an external voltage source. A current flows through the device and, at a sufficient level of supplied energy, the light emission process starts in the emitter ISBN: 1-58883-063-2/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

and the device emits light to the external environment. Electroluminescence in organic materials was first done experimentally in 1963 on anthracene monocrystals by Pope et al. [1] who obtained light emission by using a high applied voltage (400 V). Such a bias was considered too high and the materials were therefore not suitable to be used for everyday-use applications. In 1987, Tang and Van Slyke [2] using thin film deposition techniques and organic materials fabricated the first light emitting diodes (LEDs), which operated at low bias. A few years later, in 1990, Burroughes et al. [3] demonstrated that a well known conjugated polymer, poly(p-phenylene vinylene) (PPV), could emit light in a diode configuration with an applied voltage less than 20 V. Since those first experiments, the science of polymer and organic LEDs has progressed greatly. Talented chemists, physicists, and engineers have contributed to the development of new materials and new device designs, enabling the fabrication of devices with high performance: various colors, low turn-on voltage, long lifetime, low energy consumption, and great brightness. The physics of these new electronic devices have also been intensively studied and during the last decade; many new concepts were built using the basic knowledge from classical semiconductor devices. In parallel, nanotechnology science has emerged and is advancing constantly. In the late 1960s, Moore’s law predicted that the number of transistors on a chip would roughly double every 18 months and that was verified over four decades. At the beginning of 2000, we have entered in the nanosize era. Advances in manipulating nanosized materials have already allowed improvements in electronic devices such as computer data storage, batteries, solar cells, and light emitting diodes. Understanding the potential market of nanosized devices, many countries have concentrated their efforts in developing research programs in nanoscience.

Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 7: Pages (717–739)

718 The conjugation of both technologies led to a new field of research: that of nanosized polymer and organic LEDs (OLEDs). In reality, the devices studied have a size ranging from several nanometers (nm) to several micrometers (
m). Classical photolithography used in computer chip industry can provide a common size of 200 nm and is still very popular in designing electronic devices. Recent progress in patterning techniques has allowed features as small as 10 nm to be obtained with high definition and ordering. Such a tiny object is not easy to handle and even if several devices could be produced, the mass production still needs further investigation to control them, especially in the design of the surface on which will be implanted the nanocomponents and the electrical connection between them. With the development of nano-objects, the electronic properties of the materials will change from classical physics to the less familiar quantum physics. New optical and electrical properties of nanosize materials have been discovered and more are expected to be found in the near future. Study of micro- and nano-OLEDs has only been investigated for a few years, starting with composites made of a polymer matrix containing inorganic nanoparticles. These systems were first fabricated to obtain the light emission of both the electroluminescent polymer and the nanoparticles. The second generation of small OLEDs has benefitted from the progress in patterning technology to allow fabrication of ordered arrays of pixels. This chapter is organized as follows. In the first section, we shall give the state of the art of OLEDs showing different aspects: materials, physical processes including the light emission, charge carrier transport, and degradation mechanisms. The second section deals with the nano-OLEDs where different technologies will be described. Some aspects of the physical processes in nanosize materials will be treated. In the last part, the potential applications of nanoOLEDs are discussed.

2. ORGANIC ELECTROLUMINESCENCE The aim of this section is to present the current state of the art in organic electroluminescence. Emphasis will be given to the way the device works and to the various issues that govern its operating process.

2.1. Operating Mode Electroluminescence (EL) is a nonthermal emission of light from a solid traversed by an electrical current. EL in organic materials was first observed in anthracene single crystals as early as 1963 [4]. The crucial issues of the process and in particular the requirement of a double injection of charge (electrons and holes) were identified two years later [5]. Today, the most generally accepted mechanism for describing organic EL does not fundamentally differ from this early analysis. The basic device for organic EL is the diode, composed of one or several organic layers sandwiched between two conducting electrodes. The sequential steps of the conversion of electricity to light in an OLED are schematized in Figure 1. At the outset of the process, there is an injection of electrons and holes from the electrodes at each side of the

Nanostructured Organic Light Emitting Diodes

Figure 1. The four steps of the conversion of electricity to light in an organic light-emitting diode.

diode. The carriers are then driven toward the interior of the organic layer by the electric field generated by the voltage applied to the device. Recombination of charges of opposite sign occasionally occurs when these charges meet, leading to the formation of electron–hole pairs, which rapidly decay to bound excitons. At this stage, a crucial parameter is the exciton bounding energy; excitons in organic materials are generally regarded as strongly bound excited molecules, but this is still controversial, as will be detailed in the following. Light is eventually emitted when excitons deactivate to ground state. The overall efficiency of the diode results from that of each step; therefore, each of them needs to be optimized. The steps will now be analyzed in more detail.

2.1.1. Charge Injection Injecting charge from a highly conducting (the electrodes) into a poorly conducting (the organic layer) medium is a difficult task. In principle, charge transfer between two media occurs isoenergetically. Accordingly, there are two elementary issues in charge injection: energy level alignment and injection processes. Energy Level Alignment This subject has been recently reviewed in detail by Ishii et al. [6]. The levels implied in charge injection from a metal into an organic layer are not of the same nature at both sides of the interface. When gathered together to from a solid, atoms and molecules see their discrete quantum energy levels widening into alternatively allowed and forbidden bands. In metals and degenerate semiconductors, the highest energy allowed band is only partially filled with electrons up to the so-called Fermi level, which constitutes therefore the level of interest in this case. The corresponding energy is the work function, m , which measures the distance between the Fermi level and the vacuum level (VL), the latter being defined as the energy of an isolated electron at rest at infinite distance from the solid. In a molecular solid, molecules interact only through weak van der Walls forces, so that it is generally accepted that bands are narrow and the highest occupied molecular orbital (HOMO) and lowest unoccupied MO (LUMO) are only slightly displaced from their value in individual molecules.

Nanostructured Organic Light Emitting Diodes

719

The number of interest is therefore the distance that separates the HOMO and LUMO levels from the vacuum level, that is, the ionization potential IP and electron affinity EA. Because IP and EA are very sensitive to surface state, their estimation is a difficult task. Several techniques require ultra high vacuum, such as ultraviolet (UV) photoelectron spectroscopy. Other techniques comprise Kelvin probe and electrochemical measurements. In the latter case, care must be taken because several corrections, involving solvatation effects, must be brought to the crude data. Finally, we have to mention internal photoemission, which is in principle a direct method but presents a major drawback: it requires the fabrication of a metal–semiconductor junction and its reproducibility is often uncertain. In principle, the value of EA can be obtained directly by inverse photoemission spectroscopy, a method that suffers from radiation damage of the organic material. Nevertheless, the most popular way for estimating EA consists of subtracting from IP the HOMO–LUMO gap as deduced from optical absorption measurements (optical gap EgOPT ). However, it must be noted that the optical gap may differ from the true energy gap (corresponding to the energy required to promote an electron from the HOMO to the LUMO level). To understand this difference, we have to go a little deeper in the description of energy levels in a molecular solid. As stated, the IP and EA of the solid slightly differ from that of the isolated molecule. The difference comes from the polarization energy (P+ and P− for holes and electrons, respectively) induced by the ionized molecule in the surrounding molecules. This energy is sometimes referred to as the “polaron binding energy.” Similar stabilization energy exists for an electron–hole pair (or exciton), which is also often called the exciton binding energy. Only if this exciton binding energy strictly equals P+ + P− does the optical gap equal the electronic gap. When the metal and the organic layer are put in contact, the VL at the interface is shared by both media and barriers p for hole (of height B  and electron injection (of height Bn  appear. For the perfect contact depicted in Figure 2a, the magnitude of the barrier height follows the Schottky–Mott rule, where m is the work function of the metal: p

B = IP − m Bn = m − EA

(1)

In molecular solids, which are primarily insulators, the Fermi level is located somewhere in between the HOMO and LUMO levels. With a Fermi level at exactly midgap, we

Figure 2. Energy level alignment at a metal/organic interface: (a) ideal case; (b) in the presence of a surface dipole.

see that the junction in Figure 2a is not in electrical equilibrium. However, equilibration would require charge redistribution, which is difficult in practice because the number of available mobile charges in the organic layer is very low. This is the more true as most OLEDs are made of very thin organic layers, which reduces further the amount of charge available. For these reasons, the simple scheme of Figure 2a remains the one most usually adopted to describe energy level alignment in organic diodes. Nevertheless, Figure 2a only corresponds to the ideal case. In actual systems, a dipole layer may form at the interface. Possible origins of this dipole are chemical reaction, charge transfer across the surface, or rearrangements of electronic charge. An abrupt shift  of the energy levels is associated with this dipole layer, as shown in Figure 2b, which leads to a similar change of the barrier heights. Note that this shift can also be viewed as a change of the metal work function that can be used to purposely adjust the energy level alignment. From the previous analysis, it emerges that several strategies can be envisioned to tune the energy levels at both sides of a metal–organic junction. • Interpose a buffer layer between the electrode and the electroluminescent layer to reduce the barrier height. In practice, a hole injecting material presents a high ionization potential, while an electron injecting material is characterized by a low electron affinity. This strategy was proposed in 1987 by Tang and Van Slyke [2] and many of such materials have been identified since then. • Modify the work function of the electrode by an appropriate surface treatment. Various examples of such treatments will be described in the following. The energy scheme of a typical multilayer OLED is shown in Figure 3. The terms “hole transport layer” (HTL) and “electron transport electron” (ETL) were first introduced by Adachi et al. [7] in 1988 and are widely used today to designate the two buffer layers. However, we note that these terms are somewhat confusing because these layers inject rather than transport the charges from the electrodes to the light-emitting medium. These injecting layers may also play the role of blocking layers for the charges of opposite sign. Figure 3 does not account for the electric field that appears in the device when applying an external voltage. This is shown in Figure 4 in the case of a one-layer device. The far right image of this figure corresponds to forward bias where emission of light occasionally occurs.

Figure 3. Energy diagram of a multilayer OLED. HTL: hole transport layer; EL: emissive layer; ETL: electron transport layer.

Nanostructured Organic Light Emitting Diodes

720

Figure 4. Energy diagram of an unbiased and biased one-layer OLED.

Injection Processes The ideal case of perfect energy alignment at both interfaces is practically never fulfilled in practice. In most real cases, charges have to pass a potential barrier before penetrating the organic layer. This interfacial process must not be confused with charge transport, which will be dealt with in a following section. As most organic semiconductors (SCs) actually behave as insulators, there are basically two injection processes: Schottky emission and field emission. The former corresponds to thermionic emission across the metal–insulator interface. The corresponding current density is given by Eq. (2). Here, A∗ is the effective Richardson constant, F is the electric field, q is the absolute electron charge,  is the permittivity of the organic layer, k is Boltzmann’s constant, and T the absolute
temperature.  is a characteristic factor given by  = q/4, where  is the permittivity of the medium. (Note that the same constant is encountered in the Poole–Frenkel effect that will be dealt with in the next section.)   q √ q j = A∗ T 2 exp − B + (2)  F kT kT The second mechanism, which is often referred to as the Fowler–Nordeim process, occurs under high applied electric field. In that case, electrons can tunnel through the triangular barrier that forms when the diode is polarized. The probability for tunneling depends strongly on the height and width of the barrier but is independent of the temperature. The corresponding current density is given as follows, where m∗ is the charge effective mass:  √ ∗  4 2m qB 3/2 2 j ∝ F exp − (3) 3e
F A useful way of checking whether field-induced injection is involved consists of plotting the logarithm of I/F 2 as a function of the reversed electric field. The main difference between the two mechanisms resides in their temperature dependence; the tunnel process is temperature independent, while the Schottky mechanism is thermally activated. It must be pointed out that, because parameters involved in Eqs. (2) and (3) such as the Richardson constant and effective mass are not well known in most organic SCs, a quantitative check of the charge injection process remains hazardous.

2.1.2. Charge Transport Although organic SCs have been identified for more than 50 years, charge transport in these materials is still the subject of great debate. A prominent issue of charge transport in organic SCs is the very low mobility of the charge carriers.

The main methods for measuring charge carrier mobility are time of flight (ToF), analysis of the current–voltage curves of single carrier diodes in the space charge-limited current (SCLC) regime, and fabrication of a field-effect transistor (FET) structure. As shown in Table 1 for the typical case of PPV, the hole mobility stands in the 10−8 –10−6 cm2 /V s range. Even lower values have been reported for electron mobility. This low mobility implies that the corresponding mean free path is substantially shorter than the intermolecular distance, which excludes the dominant charge transport mechanism encountered in most metals and conventional semiconductors, that is, diffusive transport in delocalized states. Among the various models that have been put forward to explain this very low mobility, two classes emerge. One covers the models based on trapping, which assumes that charge transport is limited by a given distribution of traps in the energy gap. Second are the fielddependent mobility models, which implies an exponential dependence of the mobility on the square root of the electric field. The mobility model was first set on the basis of the observed mobility-field dependence of time-of-flight data. As the general dependence resembles that of the Poole–Frenkel mechanism, the model is often referred to as the “Poole–Frenkel-like” law because experimental data do not quantitatively agree with the classical Poole–Frenkel emission model. Because the density of mobile charges in organic SCs is extremely low, the current rapidly becomes limited by charges injected from the electrodes. In this space charge limited regime, the current density is given as follows, where
is the charge mobility and d is the thickness of the organic layer: j=

9 V2
 3 8 d

(4)

The SCLC is strongly affected by the presence of charge traps. The expression depends on the energy distribution of the traps. One of the most frequently invoked distributions is the exponential distribution. If the density of trapped charges largely exceeds that of free charge and the Fermi occupancy function is a step function, the SCLC is given by [11] j = q l−1
Nc



2l + 1 l+1

l+1 

l  l + 1 Hb

l

V l+1 d 2l+1

(5)

Here, Hb is the density of traps and l = Tc /T , where Tc is a characteristic temperature that describes the steepness of the distribution. Table 1. Hole mobility of undoped PPV determined by various methods. Polymer PPV PPV MEH-PPVa a

Mobility (cm2 /V s) 10 10−7 –10−8 5 × 10−6 −8

Method [Ref.] ToF [8] FET [9] SCLC [10]

MEH-PPV—poly[2-methoxy,5-(2′ -ethylhexyloxy)-1,4-phenylene vinylene].

Nanostructured Organic Light Emitting Diodes

721

The field-dependent mobility model dates back to the 1970s [12]. It has become common practice to analyze mobility data in terms of the empirical equation due to Gill [13]: √  q   F
F  =
0 exp − 0 + kT kTeff 1 1 1 = − Teff T T0 

(6)

T0 is the temperature at which Arrhenius plots of
T  intersect and  is the previously defined Poole–Frenkel factor. The physics of the field dependence relies on disorderinduced localization of charges. The field-dependent term arises from the fact that charge transport is governed by tunneling from one localized state to another; the transfer occurs through tunneling, a process that can be assisted by the electric field. Such a mechanism is similar to the Poole–Frenkel effect. However, the exact expression for  strongly depends on the distribution of the traps, so that it noticeably differs from the conventional Poole–Frenkel factor. Furthermore, the derivation of the constant cannot be carried out by analysis. A widely used expression is that derived by Bässler [14] by performing a statistical Monte Carlo computation based on a Gaussian distribution of localized levels. The energetic disorder is depicted by the standard deviation , while that of the geometric dispersion is given by . The general expression of the field-dependent mobility is given by √       2 2 2 exp C − 2 F (7)
=
0 exp − 3 kT kT More recently, Garstein and Conwell [15] and Novikov et al. [16] have proposed an alternative approach to the problem. The model, termed the correlated disorder model, assumes that the potential viewed by a charge carrier presents slowly varying spatial fluctuations. These variations occur because the energy of neighboring sites is correlated; that is, the energy of one site depends on the energy of the nearest sites. Because of these correlations, the energy difference between two sites is limited by an effect of spatial averaging. As in the case of the model of Gaussian disorder presented previously, the mobility is calculated through numerical Monte Carlo simulation:   

    3 2 aF 3/2 − exp C0
=
0 exp − 5 kT kT (8)

Here, C0 = 0 78 in a three-dimensional case,  measures the energy disorder ( = 2, and a is the intersite distance.

2.1.3. Charge Recombination and Light Emission Charge Recombination The problem of charge recombination has received much less attention than charge injection and light emission. Charge recombination is a bimolecular reaction that obeys a second order kinetic of the following form, where n and p are the density of electron

and holes, respectively [17]: dp dn = = np dt dt

(9)

The most widely recognized mechanism of charge recombination is of Lagevin type, that is, diffusion controlled [18]. Such a mechanism is characteristic for materials in which the charge carrier mean free path is smaller than a critical distance defined by the Coulombic capture radius rc = q 2 /4kT . For typical organic emitting materials, rc amounts to around 20 nm at room temperature, while the mean free path compares to the distance between conjugated sites, which is of the order of a few nanometers. The recombination factor in Eq. (9) is given as follows, where
n and
p are the electron and hole mobility:

=

q 
+
p   n

(10)

From Eqs. (9) and (10) it can be seen that increasing recombination can be obtained by increasing charge mobility but also requires the density of electrons and holes be as close to each other as possible. The latter issue demands a balanced injection rate for both charges, which is probably one of the more difficult requirements for high performance devices. Light Emission Charge recombination leads to the formation of electron–hole pairs that rapidly decay to excitons. The nature of the excitons in conjugated organic materials is the subject of great controversy that is still alive today. The debate has been the subject of a whole volume [19] published in 1997, which develops the two opposing aspects of the controversy. In essence, an exciton is an electron– hole pair where the two charges are linked together through Coulomb interaction. The strength of the link, also called exciton binding energy, is strongly material dependent. In conventional inorganic semiconductors the effective mass is lower than the free electron mass and the dielectric constant is high, so the binding energy is weak (that is, comparable to kT at room temperature) and the exciton extends over several lattice sites. (This weakly bond exciton is frequently termed Wannier exciton.) Hence, exciton effects are unimportant except at low temperature. On the other hand, excitons in molecular crystals are tightly bound and are localized on a single molecule, thus forming a so-called Frenkel exciton [20]. Because of the weakness of intermolecular interactions, the Frenkel exciton model is widely accepted in materials made of small molecules. This is not the case for polymers, where there exists a conflict between strong intrachain and weak interchain interactions. Estimating the exciton binding energy is in principle quite simple [21]; it merely amounts to the difference between the energy gap and the optical gap. However, there are several difficulties hidden behind this simple definition. The first one is that both quantities are chain length dependent. Only for sufficiently long chains do they come to limiting values independent of the length. Another problem arises from the tendency of conjugated chains to relax when charges are added. This point has already been evoked earlier in this chapter. A consequence of this relaxation is that the energy gap is reduced by a quantity P+ + P− , where P+ and P− are

722 polarization energies, also called polaron binding energies. Because the polarization energies amount to tenths of an electronvolt, the estimation of the exciton binding energy may substantially differ depending on whether, on breakup, the exciton dissociates directly into a pair of polarons rather than a free electron and a free hole that subsequently relaxes into polarons. Part of the controversy rests on this still unresolved point. Frenkel excitons in organic semiconductors can also be viewed as excited molecules that can travel over the solid through a mechanism of energy transfer. Because the Frenkel exciton propagates, it can generate energy bands, the width of which is determined by the transfer rate from one molecule to the next. Frenkel excitons can be singlet or triplet, depending on the respective spin parity of its constituents. During the mechanism of electroluminescence, excitons are a result of the recombination of two charges of reverse sign, the spin of which is distributed at random. A generally accepted concept is that this feature limits the electroluminescence yield to 25%. The argument is based on simple spin multiplicity; for recombination of a pair of charges, they are four microstates in total, with three triplet states and only one singlet state. As the ground state is usually singlet, radiative decay from a triplet state is spin forbidden, so that the theoretical quantum yield of OLEDs is limited to 25%. However, quantum efficiency up to 50% has been recently reported in MEH-PPV based diodes [22]. Two kinds of argument have been invoked to explain this behavior. The first one is to assert that excitons in some organic semiconductors (mainly polymers) are weakly bound (Wannier excitons). In that case, exciton effects can be neglected and quantum yields up to 100% be envisioned, like in the case of inorganic LEDs. Such an argumentation falls within the general controversy evoked previously. The second analysis assumes Frenkel-type excitons [23]. The ratio between the number of singlet excitons and the total number of excitons can be expressed as  = S / S + 3 T , where S and T are the cross sections for singlet and triplet formation. The quantum mechanical argument is that interchain correlation effects of bond-charge type distinguish the cross sections for singlet a triplet states. Calculations show that in the case of PPV, the ratio S / T may be as high as 3, thus leading to a quantum yield of 50%. An alternative approach to improve quantum efficiency consists of using phosphorescent materials [24]. In these materials, the luminescence comes from the radiative decay of the triplet state. In that case, the theoretical limit of the quantum yield is 75%. One way would therefore consist of adding phosphorescent compounds to the luminescent layer of the diode. However, this method has many problems. Because the decay from a triplet state is forbidden by selection rules, the lifetime of triplet excitons is very long. This means that all the phosphorescent sites may become occupied and therefore unavailable for energy transfer. Moreover, the long lifetime also increases the risk of nonradiative deactivation at some defect, or through triplet– triplet interactions. A group at Princeton University [25] has used a different methodology where both singlet and triplet excitons transfer energy from the electron–hole pairs. As shown in Figure 5,

Nanostructured Organic Light Emitting Diodes

Figure 5. Phosphorescent sensitized OLED. Left: schematic structure of the device. The structure comprises a HTL (TPD), a hole blocking layer (BCP) and an ETL (Alq3 . The emitting layer is made of 10 layers of CBP alternatively doped with Ir(ppy)3 (10%) and DCM2 (1%). Right: proposed transfer mechanism in the emitting layer. S stands for singlet, T for triplet, and ISC for intersystem crossing. Förster transfers are represented by solid arrows and Dexter transfers by dotted arrows. Reprinted with permission from [25], M. A. Baldo et al., Nature 403, 750 (2000). © 2000, Macmillan Magazines Ltd.

the emissive layer is made of a set of alternating layers that contain either a phosphorescent sensitizer or a fluorescent dye embedded in a host material. As a result, both singlet and triplet excitons are generated. Moreover, the energy of the triplet state in the phosphorescent dye is higher than that of the singlet in the fluorescent dye, so that energy transfer occurs from the triplet to the singlet, which then emits light. A quantum yield of nearly 100% thus has be obtained. However, the system presents several drawbacks. One is the need for a number of downhill energy steps, which results in the energy of the emitted light being much lower than that of the charge pair. For this reason, green or blue light would be difficult to obtain. The second problem concerns the energy transfer. Energy transfer between molecules in a solid may occur through two basic mechanisms: dipolar (Förster) or contact (Dexter). The former is long range and authorizes change of spin configuration, while the latter is short range and an exciton transferred this way retains its spin multiplicity. This second mechanism should therefore be avoided because it would lead to the formation of the nonemitting triplet exciton in the fluorescent dye.

2.2. Materials One of the unique aspects of organic chemistry is its ability to produce new molecules at a high rate. Organic electroluminescence is a very active research topic that involves a great number of teams in both academic and industrial laboratories worldwide. Since the emergence of organic electroluminescence, dozens of new compounds aimed at being used in OLEDs have been synthesized each year. For these reasons, a comprehensive review of the materials used in organic LEDs would be far beyond the scope of this chapter. It would also not be very helpful, because it is difficult

Nanostructured Organic Light Emitting Diodes

723

to predict which compounds will lead to real applications. We will therefore restrict ourselves to a few representative molecules. Note that many of them are already commercially available.

2.2.1. Emitting Materials Emitting materials can be sorted into polymers and short molecules. Recall that organic electroluminescence was first observed in a molecular crystal, anthracene, in 1963. This early device already presented encouraging quantum efficiency. However, its operating voltage of around 1000 V made its development unlikely. It is only with the advent of thin film devices that commercial application could be envisioned. Polymers [26] and small molecules [27] based devices emerged almost simultaneously at the turn of the 1980s. This breakthrough was actually made possible after the synthesis of the first conducting polymer in 1977: polyacetylene (PA) [28]. At that time, the unique property that fascinated chemists and physicists was the ability of the polymer to become conducting upon doping by a charge donating of withdrawing agent, hence the name “conducting” polymers. PA has a serious drawback: it is highly unstable in ambient air, but many other conjugated polymers were soon discovered. Their molecular formula is given in Figure 6. The finding of electroluminescence in one of them, PPV, drastically changed the perspective. The more promising property of this class of materials moved from “being a conductor when doped” to “being a semiconductor when undoped.” A very interesting issue in conducting polymers is the possibility of substituting side groups to the main chain in order to modify some of its physical properties. For example, unsubstituted PPV is infusible and insoluble in most organic solvents, thus making it very difficult to process in thin solid films. Some of its substituted compounds are sketched in Figure 7. Now the most popular, MEH-PPV, which is soluble, has largely helped in developing OLEDs based on PPV. Similarly, it has been theoretically predicted that substitutions with electron donating or withdrawing groups could allow a tuning of the frontier (HOMO and LUMO) levels [29], thus favoring energy level alignment at one or both electrodes. The HOMO and LUMO shifts calculated for compounds I and II in Figure 7 are displayed in Table 2. Substitution with a donor group (OCH3 , compound I) leads to a destabilization (positive shift) of the levels, while substitution with an acceptor group (CN, compound II) induces stabilization (negative shift).

Figure 7. Molecular structure of PPV and poly[2-methoxy,5-(2′ -ethylhexoxy)-1,4-henylene-vinylene] (MEH-PPV). Compounds I and II are models used to see the effect of electron donor and acceptor on the frontier levels (see Table 2).

A critical issue with low molecular weight organic compounds stems from their tendency to crystallize readily and hence form polycrystalline layers when deposited in thin films. This has the following detrimental effects on the performance of EL diodes: (1) exciton recombination occurs at grain boundaries, which considerably reduces the quantum yield; (2) films are not free of pinholes, leading to short circuits; (3) although data on that matter are relatively scarce, the polycrystalline structure might also be responsible for the lack of long-term stability of the devices. The original structure developed by Tang and van Slyke was made of two layers. The first one was an aromatic diamine and the second one was tris(8-hydroxyquinoline) aluminum (Alq3 . The morphology of the films, as measured by transmission electron microscopy, was found to be amorphous for the first layer and microcrystalline for the second one. This probably explains the tremendous success of Alq3 as an emissive layer in OLEDs made of small molecules. The molecular structure of Alq3 is given in Figure 8. More recently, Shirota [30] developed a general strategy to conceive and synthesize amorphous molecular materials. Starting from the simple picture that nonplanar structures should prevent crystal packing, Shirota proposed a new concept, the -electron starburst, for the design of amorphous molecular materials. Typical examples are shown in Figure 9. (Note that Alq3 also presents a nonplanar configuration.)

2.2.2. Electrodes The basic rules for choosing materials for electrodes are quite simple: high work function for the anode (hole injecting) and low work function for the cathode (electron injecting). To that, we must add an obvious requirement; that is, Table 2. Calculated shifts (in eV) of the HOMO and LUMO levels for derivatives I and II with respect to the unsubstituted PPV.

Figure 6. Molecular structure of most popular conducting polymers. Trans-PA; polythiophenes; PPV; poly-dialkyl-fluorene.

Derivative

HOMO

LUMO

Eg

PPV I II

+0 27 −0 99

+0 08 −1 17

3.24 3.06 3.11

Note: The energy gap Eg reported in the last column corresponds to the difference between the HOMO and LUMO levels (after [29]).

Nanostructured Organic Light Emitting Diodes

724

Figure 8. Molecular structure of tris(8-hydroxyquinoline aluminum).

at least one of the electrodes must be transparent to let light get out of the device. Transparent conducting materials mainly include degenerate oxides. Although there have been some reports on OLEDs with aluminum-doped zinc oxide (AZO) [31], practically all OLEDs use indium-tin oxide (ITO) as the anode. A probable reason for that is that ITO coated glass is also widely used in liquid crystal displays. In most cases, the organic layers are deposited on top of ITO during the fabrication of the device. In the course of the process, the surface state of the electrode is of primary importance because it controls crucial parameters such as energy level alignment and the absence of short circuits. In a recent paper, Kim and co-workers have investigated how surface treatments modify the performance of OLEDs [32]. The various treatments and their effect on the work function and roughness are summarized in Table 3. The desired issues are (1) high work function to improve hole injection in the organic layers; (2) low sheet resistance to reduce ohmic losses; (3) low average roughness to avoid short circuits. An analysis of the data in Table 3 shows that the oxygen plasma treatment appears to be the best one. This was further confirmed by measuring the lifetime of the diode, which was substantially improved after an oxygen plasma treatment of the ITO surface. Conducting polymers such as polyaniline [33] have been envisioned as alternative transparent anodes. The polymers present the advantage of a better interfacial matching with organic semiconductors. However, the sheet resistivity of these polymers remains too high for practical use. Hybrid anodes that combine the higher conductivity of ITO with the properties of the polymer have been shown to bring improvements in terms of efficiency, lifetime, and turn on voltage. The best example is the ITO/poly(3,4-ethylene dioxythiophene) (PEDOT) anode. PEDOT is now a commercially available polymer. In its most widely used form,

Figure 9. Molecular structure of typical amorphous molecular materials: 4;4′ ,4′′ -tris(diphenylamino)triphenylamine (TDATA); 1,3,5-tris(diphenylamino)benzene (TDAB); 2,4,6-tris(diphenylamino)-1,3,5-triazine (TDATz); 1,3,5-tris(4-diphenylaminophenyl)benzene (TDAPB).

the polymer is doped with another polymer, polystyrenesulfonate (PSS), Figure 10. A unique feature of this mixture is its large stability under its doped conducting form. Electroabsorption measurements [34] have shown that the improvements partly originate from an increased work function, so that PEDOT also plays the role of a hole injecting material. An alternative way of modifying the work function of ITO is the use of self-assembled monolayers (SAMs). The principle of this modification rests on the use of dipolar molecules. Molecules used in SAMs also comprise a functional group prone to induce chemisorption on the surface. In the case of ITO, it has been shown that both carboxylic acid and preferably phosphonic acid can induce the formation of SAMs [35]. Both types of SAMs have been used to modify the ITO

Table 3. Work function, sheet resistance, and roughness of variously treated ITO substrates.

Mechanical

Wet Dry Combined Note: After [32].

Surface treatment

Work function (eV)

Sheet resistance (/

Roughness (nm)

as-received paper rubbing Teflon rubbing ultrasonic RCA aquaregia (10′ /20′ /30′ ) oxygen plasma (5′ /10′ /15′ ) argon plasma (5′ /10′ /15′ ) aquaregia (20′ )/oxygen plasma (10′ ) oxygen plasma (10′ )/aquaregia (20′ )

4.5 4.2 4.2 4.35 4.35 4.6/4.3/4.7 4.35/4.75/4.75 4.5/4.5/4.55 4.6 4.7

16.1 16.3 16.5 15.5 19.6 18.5/23.5/28.6 16.4/15.0/16.4 16.7/17.3/17.0 27.7 >30

2.6 2.3 2.4 3.4 2.4 3.8/8.4/8.8 1.4/1.4/2.1 10.9/15.4/23 6.0 1.8

Nanostructured Organic Light Emitting Diodes

725 a a

P OH a

HN2

O

O ON2

P OH

OH

OH

TCPA

4-NPPA

O

O

P OH

P OH

a

OH

OH AMPA

Figure 11. Molecular structures of the SAMs used to modify ITO electrodes: (tirchloromethyl)phosphonic acid (TCPA); (4-nitrophyl)phosphonic acid (4-NPPA); (aminomethyl) phosphonic acid (AMPA); (2-chloroethyl) phosphonic acid (2-CEPA).

Figure 10. Molecular structure of PEDOT and PSS.

electrodes in OLEDs [36, 37]. The shift in work function is interpreted as originating from the dipole moment induced by the SAM. According to this model, the work function shift  is determined by the change in electrostatic potential V created at the surface by the dipolar moment
,  = −qV = −qN




(11)

Here, N is the surface density of molecules and  the permittivity of the SAM. Table 4 compares the calculated and measured work function change by four various molecules adsorbed on ITO. The measurements were performed with a Kelvin probe. The molecular structures of the SAMs are given in Figure 11. Because the cathode is most generally deposited at the end of the fabrication process, surface treatments cannot be performed and the only criterion for selecting a metal for the cathode is its work function, which must be as low as possible (electronegative metal). Table 5 gives the work function of various metals used as cathode. According to Table 5, metals such as calcium or sodium appear to be the best choice. Unfortunately, these metals are also highly reactive and making devices with them requires a very efficient protection against ambient air. To date, the best compromise seems the use of an alloy between low work function and noble metal, such as Mg:Ag. Improved electron injection was obtained by inserting a thin (0.5–10 nm) insulating film of lithium fluoride (LiF) between a stable metal cathode (mainly Al) and the emitter layer. The mechanism behind the enhanced injection is not fully understood. Interpretations include tunnelling [38], removal of interface states at the cathode–organic interface, and reduction of the barrier height to electron injection [39]. Table 4. Calculated and measured work function shift (in eV) of ITO modified by SAMs. SAM 4-NPPA TCPA 2-CEPA AMPA

2-CEPA

Dipole moment D

Calculated

Measured

5 73 1 76 1 69 −1 43

0 303 0 185 0 179 −0 140

0 720 0 221 0 212 −0 179

Note: The molecular structure of the SAMs is shown in Figure 11. Dipole moments are calculated at the PM3 semi-empirical method (taken from [37]).

2.2.3. Charge Transport Agents Although the terms “electron transport” and “hole transport” layers are universally used in the community of organic light-emitting diodes, it must be stressed that these expressions are somewhat misleading. In essence, an electron (hole) transport material would be that in which high electron (hole) mobility is encountered. This is not the case in OLEDs. Instead, ETLs and HTLs are made of chemical agents that favor electron (hole) injection. For this reason, some recent papers make a contradistinction between charge transport and charge injecting materials. In reality, both terms designate the same class of materials, since charge carrier mobility is low in practically all these organic semiconductors. One of the most widely used electron transport agent remains the already invoked Alq3 , which is most often used as both ETL and emissive layer. A few alternatives have been proposed since then. At present, the main representatives of electron transport agents are derivatives of oxadiazole. One of these, PBD, is shown in Figure 12. The difficulty in finding organic electron transport materials probably comes from the fact that low electron affinity is usually associated with high chemical reactivity. Note that some polymers, such as polypyridine [40], have also been reported as electron transporting agents. Hole transport materials are much more common. These comprise both short molecules and polymers. A very popular hole transport agent is N N ′ -diphenyl-N N ′′ -bis(3methylphenyl)(1,1′ -biphenyl)-4,4′ -diamine or TPD [7], the molecular formula of which is indicated in Figure 13.

Table 5. Typical low work function metals. Metal Al Ca In Li Mg Na Sm

Work function (eV) 4 28 2 87 4 12 2 9 3 66 2 75 2 7

Nanostructured Organic Light Emitting Diodes

726

Figure 12. Molecular oxadiazole (PBD).

scheme

of

2-(4-biphenylyl)-5-phenyl-1,3,4-

2.3. Performance To conclude this section, we give here a brief outlook of the current performance of organic light emitting diodes.

2.3.1. Color It is often claimed that one of the unique advantages of OLEDs is the possibility of generating practically all colors. However, this statement must be somewhat tempered. A characteristic of organic luminophores is to present a wide emission spectrum. This is detrimental when dealing with color displays, where red, green, and blue emitters with welldefined chromaticity are needed, but turns out to an advantage in the case of white light emission. These two extreme cases will now be dealt with in sequence. The development of color displays based on inorganic light-emitting diodes has long been impeded by the lack of blue emitting devices. By contrast, blue OLEDs have been realized since the early beginning [41]. To date, dozens of blue light emitting molecules and polymers have been identified. Strangely enough, the problem with OLEDs concerns the red emitters; most of them are actually orange, which is not favorable for making good quality color displays. Two approaches have been used to overcome this difficulty. One is to use organometallic complexes based on rare earths, mainly europium, which is one of the best-known red emitters [42, 43] with four sharp emission peaks, the dominant one being centered at 618 nm. It is worth pointing out that in this case, the emitting element is the rare earth ion, which is at variance with other organometallic complexes such as Alq3 where the emitting part is the ligand. The sharp emission in rare earths comes from electron transitions between 4f bands. For symmetry reasons, these transitions are forbidden in the free ions but may become allowed when the symmetry of the ion is removed by an asymmetrical external crystal field such as that provided by an appropriate ligand. Generally, the complex is embedded in a polymer matrix that can act as an energy transferring system for the complex. After exciting the polymer, energy cascades through the ligand to the central rare earth ion, which eventually emits light. We note that organic diodes have also be made with another rare earth, erbium [44, 45], that emits in the near infrared at 1.54
m, a wavelength of importance in

Figure 13. Molecular formula diphenylbenzidine.

of

N ,N ′ -bis(3-methylphenyl)-N ,N ′ -

telecommunications because it corresponds to a minimum of losses in optical fibers. The second strategy for red light devices is the use of small amounts of an efficient luminophore for this color dispersed in an electroluminescent material that emits at higher energy. One speaks in that case of “dopant” (or guest) in a host material. Representative examples of doping materials are laser dyes such as 4-dicyanomethylene-2-methyl-6-(pdimehylaminostyryl)-4H-pyran (DCM) [46]. Like in the case of the rare earth complexes, emission results from a Förster energy transfer from the matrix (typically Alq3  to the dye. The first report on white OLED was published in 1994 [47]. White light is obtained by mixing several (most often three) emitting materials with complementary emitting spectra. In this configuration, the wide luminescent spectra of organic compounds become advantageous. Various structures have been used to realize white OLEDs, among them blends, multiple layers, and doped matrices. In essence, the basic principles that govern the operating mode of these diodes do not differ from those of the one-color diodes. Note that white phosphorescent diodes have also been reported [48].

2.3.2. Yield The yield of an electroluminescent device can be defined in various ways. The quantum yield q represents the ratio of the number of emitted photons to the number of injected charge carriers. The overall yield can be decomposed into a product of factors that mirror the yield of each step of the process; hence q = 1 2 3 , where 1 = (number of emitted photons)/(number of singlet excitons), 2 = (number of singlet excitons)/(total number of excitons), and 3 = (number of excitons)/(number of injected carriers). The first term corresponds to the photoluminescence (PL) quantum efficiency of the emitting material. Note that high PL yield (higher than 50%) can be achieved in organic solids. As discussed, the second term is in principle limited to 25%, but there is both experimental and theoretical evidence for possible higher yields. Finally, the third term mainly depends on the rate of carrier recombination. A crucial issue for high recombination rate is a balanced injection of electrons and holes. A distinction has been made by Greenham et al. between the internal and external yield [49]. To understand this concept, one must recall that all photons produced in the diode do not actually leave the emitting layer; some of them are trapped by a process of total internal reflection. Using Snell’s law, they determined that the internal quantum yield, which accounts for the total number of photons produced, is greater than the external quantum yield, for directly emitted light, by a factor of 2n2 where n is the refractive index of the emitting material. Note that this correction is much more important in inorganic semiconductors than in the organic ones, the refractive index of which generally ranges between 1.5 and 2. However, the technologically important parameter is the power efficiency, that is, the ratio of the output light power (in lumens) to the input electrical power (in watts). It is worth noting that the early device of Pope and co-workers made of an anthracene single crystal presented a reasonably good quantum yield of a few percent but a desperately

Nanostructured Organic Light Emitting Diodes

poor power efficiency because its operation required very high voltages. Current OLEDs operate at low voltage, which considerably increases the power yield of the diodes. Among other issues, high power yields are obtained by using very thin films; the overall thickness of current diodes does not exceed 100 nm.

2.3.3. Degradation Device stability is a major concern for OLEDs. This problem has known increased interest, as the development of organic electroluminescence is becoming an industrial challenge. Studies have focused on two widely used structures: ITO/poly(para-phenylenevinylene)/Ca and ITO/Alq3 /(Al or Mg:Ag) (with occasionally TPD as hole transport layer). Two different degradation mechanisms have been identified [50]. The first corresponds to a uniform long-term decay in electroluminescence yield. The half-time of the best current OLEDs, defined as the time elapsed before the luminance of the device falls to half its initial value, may amount to up to a few thousands of hours. In the second process, the degradation manifests itself through the formation of dark (i.e., nonemissive) spots that gradually cover the surface of the diode [51]. The formation of these dark spots is greatly reduced when the device operates in an inert atmosphere. For this reason, great care must be taken to avoid exposure of OLEDs to oxygen or moisture during their fabrication. Among the various origins for degradation that have been put forward, we can mention: • Crystallization of the charge transporting layers [52] may occur. As stated, the best performance is obtained with amorphous materials. A likely origin for crystallization is Joule heating. Note that an improvement of the luminescence yield also results in a reduction of the Joule current. • Evidence has been given that the dark spot formation is associated with the cathode/Alq3 interface [53]. A major cause is cathode delamination. Another origin for dark spots is oxidation of the cathode/organic interfacial region. The role of traces of oxygen in this process is strongly suspected. • Degradations may also occur at the ITO/organic interface. The main cause is diffusion of indium out of the oxide electrode. It has been suggested to replace the ITO anode with AZO [31], another transparent conducting oxide. Diffusion of zinc also occurs in this case, but to a lesser extent than indium out of ITO. A general conclusion of these degradation studies is that preventing exposure of the device to oxygen and moisture during its entire fabrication process is of primary importance. It is also worth pointing out that any improvement in the performance of a device most generally comes with an increase of its lifetime.

3. NANO-ORGANIC LIGHT-EMITTING DIODES The term “nano-OLEDs” designates organic light emitting diodes having nanometric size (i.e., from several nanometers to several tens of nanometers). Making such devices with

727 controlled properties is still difficult because the fabrication technique of OLEDs has not yet been entirely mastered. Moreover, the technology for nanosize classical semiconductors is still in the process of development, despite remarkable progress made in this field in recent years. Several researchers, however, have tentatively fabricated OLEDs of submicrometer size with moderate success. The basic techniques are borrowed from semiconductor technology, although the particular properties of organic materials could allow special preparation and applications of devices. In 2001, the limiting size for nanodevices was reported to be about 250 nm [54] although it recently has been demonstrated that nanocontacts of 10 nm could be realized by nanoimprint technology [55]. We shall first review the different techniques used in conventional semiconductor technology to fabricate nanosize devices.

3.1. Technology of Nanostructures 3.1.1. Lithography The key drivers for semiconductor industry have been lithography. This technique employs optical projection printing: the image of the mask is projected on a semiconductor wafer that has been coated with a photosensitive layer or photoresist (Fig. 14). After exposure to UV light, this layer, which becomes soluble in a developing fluid, is removed so that a pattern emerges on the substrate upon development by appropriate solvents. This pattern is a resist layer for further etching or ion implantation process and allows defined geometries for the devices to be obtained. The resolution of the pattern depends on the quality of both the resist material and the mask fabrication. The former should exhibit high imaging contrast whereas the latter should be well defined, resolved, and placed with accuracy. The resolution of a lithography system is usually expressed as a function of the wavelength  of the radiation used to Resist Semiconductor

a

UV light Mask

b

c d

e

f

Figure 14. Schematic overview of an optical lithography process: (a) semiconductor covered with light sensitive resist; (b) exposure to UV light; (c) the expose region becomes soluble; (d) reproduction of the pattern on the resist layer; (e) etching of the semiconductor; (f) washing of the resist; the pattern is transferred to the substrate.

Nanostructured Organic Light Emitting Diodes

728 project the image and the numerical aperture F , d = k1

 F

Stamp

(12)

where k1 is a constant whose value depends on the process being used, typically 0.5 for integrated circuit manufacturing, and F varies in the range of 0.5–0.6. To achieve a low resolution, short wavelengths are used, for instance, with excimer laser sources or very short wavelengths from ultraviolet radiation (100–140 nm). The main drawback of these techniques is a large absorption of the radiation used by the materials, and the resist layer should be relatively thick. Alternative technique consists of using an electron beam as a radiation source and a membrane with holes in it as a mask (electron beam lithography). The electron beam is absorbed by the solid part of the membrane and passes through the holes in the membrane. In this way, patterns can be designed on the resist layer. The resolution limit is based on the intermolecular force between exposed and unexposed molecules, which prevents the exposed molecules from being dissolved in the developer solution. Heating of the mask by the electron beam may cause distortion in the final pattern, which can be defined with a resolution lower than 100 nm.

3.1.2. New Technologies The conventional lithography techniques provide highly resolved geometries to devices but require specific preparation steps, which are not always convenient for the fabrication processes. Several techniques recently developed can be used in replacement of traditional lithographic processes with success, especially for organic and polymer based devices. (a) Scanning probe arrays: This technique makes use of the scanning probe of a scanning force microscopy system to pattern the surface of a layer by affecting its surface chemistry. A bias current is applied to the tip of the probe and generates an electrical field in the surface under test and modifies its structure. This modification produces relief images that can be used for circuit pattern. A large number of scanning tips in array arrangement would be needed to design circuits by this technique. (b) Nanoimprinting lithography (NIL): This technique uses a stamping or moulding process to replicate a pattern from a master. It consists of transferring a pattern by a mechanical mold to a layer deposited on a hard substrate (Fig. 15). A stamp with the desired nanofeatures is usually fabricated by a conventional lithography technique. The material to be printed is a polymer, which is deposited on a substrate. The stamp and the substrate are put into conformal contact and the system is molded by heating it at a temperature above the glass temperature Tg of the polymer. The stamp and the substrate are then cooled down to a temperature just below Tg and separated. The polymer film left on the substrate can be used as a device or a mask for further patterning operation. Several commercial products are fabricated by using this process, for instance, compact disks. Resolution as small as 10 nm over large areas could be realized by this

Polymer Substrate

a

b

c

d

Figure 15. Schematic overview of the nanoimprint technique: (a) initial setup; (b) conformal contact; (c) cooling and mold removal; (d) patterned polymer layer.

technique [56]. For practical use, there are two considerations. The first one is the alignment accuracy of the patterns, which can be important especially for small size and highly resolved circuits. The second issue is the accuracy in the size of the mold that should be as good as that of the pattern.

3.2. Polymers in Nanotechnology Polymers are perfectly adapted for nanotechnology because of the length scale of their chains. In addition, ease of processing and the ability to incorporate chemical functionality to the backbones make polymers ideal building blocks for nanosize systems [57]. In the NIL technique, a polymer such as poly(methyl methacrylate) or PMMA is used as a thin thermoplastic film to pattern nanosized designs on semiconductor substrates. After imprinting the polymer film, the pattern is transferred to the substrate by etching. The quality of the process depends on several parameters such as Tg temperature, viscosity of the polymers, and adhesion of the polymer to the substrate [58]. An alternative technique using polymer to design patterns is microcontact printing (
CP). Because the process does not employ hard polymers, it is called a soft lithography technique. It consists of printing a monolayer of a material from a stamp [made of poly(dimethyl siloxane) or PDMS] on a substrate (Fig. 16). The background or left space on the substrate can be later filled with a self-assembled monolayer, producing a patterned surface. The resolution obtained by this technique can reach 100 nm [59]. Several other particular techniques have been developed to pattern electroluminescent devices. They will be described in the next section. We mention here a special technique using an electrical field to pattern thin polymer film [60]. It consists of depositing a thin film on an electrode and then applying an electrical field to the polymer through another electrode, kept at a distance of 100 nm from the surface at the film, the system being kept at a temperature above the Tg temperature of the polymer. The electrical field will induce displacement charge density at the surface of the polymer, producing a periodic pattern.

Nanostructured Organic Light Emitting Diodes

3.3. Dispersed Nano-OLEDs Making nanosized LEDs can be carried out by using a polymer host matrix in which electroluminescent nanoparticles are incorporated. These devices are known as hybrid structures and the nanoparticles are responsible for the light emission. The nanoparticles may be organic or inorganic. Guha et al. [61], for instance, used fluorescent dyes such as (cou3-(2′ -benzothiozolyl)-7-N ,N -diethylaminocoumarin marin 7), 3-(2′ -benzothiozolyl)-7-diethyl-aminocoumarin (coumarin 6), and DCM dispersed in a PMMA matrix. The thin films obtained by conventional deposition techniques were brought into contact with a GaN based LED. Light emission from the inorganic material is absorbed by the organic particles, which in turn emits light. Alternatively, inorganic nanocrystals can also be used in a electroluminescent polymer to obtain light emission from both materials. Schlamp et al. [62] deposited cadmium selenide (CdSe) or cadmium sulphide (CdS) nanocrystals from a chloroform solution onto a PPV thin film to form a disordered matrix of nanocrystals. Devices made with the combination of the two layers show either nanocrystal-only EL or a combination of nanocrystals and polymer EL, depending on the nanocrystal layer thickness. Several other inorganic nanoparticles have also been used in a polymer matrix in order to fabricate electroluminescent devices: ZnS [63], ZnS:Mn [64], porous silicon [65], carbon nanotubes [66], etc. Generally speaking, such a composite used as an emitter exhibits a higher conductivity than that of the polymer film alone. Charge carrier mobility is also improved in the composite. However, it is rarely possible to obtain light emission from both materials when using an electroluminescent polymer matrix. On the other hand, the nanocomposite systems show significant porosity [67], which may be a drawback for the fabrication of flexible devices. Another technique to fabricate micro- and nano-OLEDs was proposed by Granström et al. [68] using poly[3-(4octylphenyl)-2,2′ -bithiophene] or PTOPT as an emitter. This

729 technique consists in filling the pores of a microfiltration membrane with PEDOT, which is a conducting polymer. The filled pores then will be used as an electrode with a defined size (10–14 nm). The emitting polymer is spin-coated on top of the membrane-contact structure and a metal is evaporated onto it to form the diode (Fig. 17). Light emission has been obtained from the polymer with dot size of about 100 nm. It should be noted that only 20 to 25% of the diodes fabricated by this technique have worked and the quantum efficiency was estimated to be less than 0.1%. A second diode structure has also been realized by the same authors using the same emitting polymer [69]. The nanosize of the diode in this case was obtained by taking advantage of the phase separation in polymer blends. The size of the emitting polymer islands was experimentally determined by varying the proportion of the components. PTOPT was mixed with PMMA in proportion of 5% PTOPT and 95% PMMA by weight and the solution was spin coated on the PEDOT contact. The size of the nanodiodes is comparable to that obtained by the previous technique.

3.4. Ordered Nano-OLEDs The realization of dispersed nanodiodes has demonstrated that it is possible to fabricate nano-OLEDs, but in practice, a better organization of the devices is needed for displays. Therefore, the conventional techniques used in semiconductor technology are applied to pattern the polymer emitting films. In standard photolithography, the use of solvents to remove the soluble part of the photoresist film may dissolve and swell the organic layer. In addition, UV light can damage the emitter. Methods that do not require lithography have been recently developed for patterning polymer thin films. These methods can be classified into two principal categories: soft lithography and inkjet printing. Other techniques are also available but their applications are limited.

3.4.1. Masking Technique This technique is the simplest way to produce arrays of OLEDs. A metal mask is put in contact with the substrate and the organic layer is evaporated through the slits of the

Stamp Polymer Substrate

a

(a)

b

c (b)

d Microcontact

Lift-up

Figure 16. Schematic overview of the microcontact printing techniques: (a) initial setup; (b) conformal contact; (c) stamp removal; (d) patterned polymer. In the microcontact technique, the stamp is dipped in the polymer solution before contact with the substrate. In the lift-up technique, the polymer film is deposited on the substrate before contact with the stamp.

Figure 17. Fabrication of nanodiodes using PTOPT as an emitter, deposited into a polycarbonate membrane: (a) diode structure; (b) photograph of emitting nano-LEDs. Reprinted with permission from [69], M. Granström et al., Synth. Met. 76, 141 (1996). © 1996, Elsevier Science.

730 mask and forms a well defined pattern on the substrate. Generally, there is a close but not direct contact between the mask and the substrate in order to avoid scraping of the organic layer. The formed thin films have high definition geometry but their size is important. Simple pixel arrays of Alq3 based diodes were fabricated by Jabbour et al. [70] using an electrochemically patterned mask or an electron microscope grid. Mori et al. [71] used a simple sliding mask to fabricate RGB (red green blue) pixels, each of them is 120
m wide (Fig. 18). The masking technique was used to fabricate planar OLEDs or surface cells [72]. In this configuration, electrodes were deposited on a polymer substrate with a gap in between using a shadow mask. The cell configuration can be a single gap cell [73] or interdigited one [74, 75]. The gap between the electrodes is a few micrometers wide and the light intensity is proportional to the total length of the electrode. In poly(3-(2′ ,5′ -bis(1′′ ,4′′ ,7′′ trioxaoctyl)phenyl)-2,2′ bithiophene) planar based diodes, a turn-on voltage of 6 V was sufficient to run a device with an electrode separation of 10
m. The major advantage of such diodes over sandwich ones is that they are less sensitive to pinhole formation and may avoid electrical short in operation. However, the width of the LEDs is relatively large, of the order of a few micrometers, and it is not possible at this stage to reduce further the size of devices. Nevertheless, these diodes could be used to realize dot matrix displays.

3.4.2. Standard Lithography The technique conventionally used in inorganic device manufacture was successfully applied to polymer LEDs by several authors to fabricate microsize diodes. For instance, Lidzey et al. [76] deposited a photoresist layer onto the emitting layer [poly(2,5-dialkoxy-p-phenylene vinylene)] and exposed the film to UV radiation through a contact mask. After development and washing, the exposed resist was removed and metal electrode was deposited forming micropatterned arrays of 5
m diameter devices on a 7
m

Nanostructured Organic Light Emitting Diodes

pitch. The authors reported a loss of 35% of the photoluminescence efficiency that they attributed to the modification of the polymer during the photoprocessing. To avoid such a problem, a solution was proposed by Nagayama et al. [77] who have used a conventional lithographic method but instead of depositing the resist on the emitting layer, they fabricated arrays of cathode separators directly on the ITO substrate. These arrays of 30
m width will act as a shadow masks in the vacuum evaporation process of the organic layer and the cathode to form the devices. The principle of the process is shown in Figure 19. This method can be also applied to fabricate polymer based diodes [78]. In this case, the polymer films were cast before patterning the cathode separation barriers. An insulator can be inserted between the emitter and the substrate to prevent edge defects, which may lead to electrical shorts between the cathode and the anode. Standard lithography is also applied to pattern the anode, especially the ITO substrate. The cathode cannot be patterned the same way because the organic layer would be damaged under the high temperature at which the photoresist is baked. The emitting layer usually dissolves in developers. After deposition of the emitting layer by a conventional technique on the patterned ITO film, the cathode layer is evaporated through a mask to form the diodes. The size of the ITO pattern and that of the metallic electrode define the diode size. This technique was used for fabrication of photodiodes with poly(3-hexylthiophene) and 1-(3-methyoxycarbonyl)propyl-1-phenyl(6,6)C61 blend as an active layer [79]. The ITO layer was patterned into strips 450
m in width and aluminum was deposited on a strip 635
m wide forming an array of small pixels that could be deposited onto a flexible substrate material. Hosokawa et al. [80] used a similar technique to fabricate RGB multicolor displays, but instead of sizing the diode by fixing the size of the cathode layer, they used the photolithographic process to form ribs on the ITO substrate for the electrode separation. Next, organic layers and cathodes were Resin Anode Substrate

a

UV light Photo mask

b

Cathode separator

Organic layer

Cathode

Figure 18. Nano-RGB pixels deposited by a sliding mask technique. Reprinted with permission from [71], K. Mori et al., Displays 22, 43 (2001). © 2001, Elsevier Science.

c

d

e

Figure 19. Deposition of nano-OLEDs using the cathode separator technique: (a) initial setup; (b) exposure to UV light; (c) formation of the cathode separators; (d) deposition of the organic layer; (e) deposition of the cathode.

Nanostructured Organic Light Emitting Diodes

sequentially deposited on the ITO film within the space left between the ribs. Resolution less than 100
m could be obtained using this technique. Based on the same principle, Tian et al. [81] fabricated Alq3 devices of 300
m width using oblique deposition of the cathode to avoid overheating of the emitting layer. The lifetimes of these diodes were found to be significantly improved. An original technique of shadow masking was proposed by Py et al. [82], who fabricated the mask directly on the inorganic substrate with overhanging edges. They used a stack of dense SiO2 , porous SiO2 , and Si3 N4 , deposited on a ITO substrate. To obtain the mask, a photoresist layer was patterned on the stack and was transferred by acid etching. Because of the different rates of dissolution of the insulators, the porous SiO2 will be undercut and an overhanging profile is formed under the Si3 N4 layer, which acts as an integrated mask. Rows of 1.54
m width could be filled with Alq3 to form an array of OLEDs by this technique. These techniques are convenient for most of the soluble polymers or evaporated organic materials. For polymers such as PPV, which need a thermal conversion process at high temperature, these techniques are not adapted because of the possible damage of the resist. Visconti et al. [83] used a method based on UV holographic lithography and plasma etching to produce patterning of PPV. This technique consists of making a mask pattern by holographic lithography using an argon laser (363.8 nm) on the resist layer, which is deposited on the polymer film. By rotating the interferometer around the laser axis, the authors could obtain planar arrays of squares, triangles, and diamonds on the resist layer. Next, the patterns are transferred to the PPV film by a reactive ion etching process. By carefully controlling the etching rate, the resist layer was removed and continuous PPV stripes with a width of 200 nm could be formed.

3.4.3. Soft Lithography Standard lithography has disadvantages in OLED fabrication, mainly because it cannot provide efficient control over the chemistry of patterned organic surfaces. A number of techniques have been developed for fabricating micro- and nanostructures using an elastomeric stamp or mold to transfer the pattern to a substrate. The elastomer stamp is usually fabricated by patterning a silicon substrate with a prepolymer of PDMS. After curing, the stamp is peeled off from the substrate. These techniques, called soft lithography, include
CP, microinjection molding in capillaries (MIMIC), replica molding, and microtransfer molding [84]. To minimize the defects of the pattern, the soft lithography techniques make use of the self-assembly of the molecules. This property of the molecules to be organized into stable configuration is based on the principle that at a final state, their organization is at thermodynamic equilibrium and therefore tends to reject any defect that could be formed. One of the best-known examples of self-assembly is the self-assembled monolayer, which is formed by self-organization of functionalized organic molecules on an appropriate surface. Soft lithography techniques have been used by Grandlund et al. [85] to fabricate arrays of OLEDs. The arrays were formed by patterning the conducting polymer PEDOT/PSS layer deposited on an ITO substrate using the
CP

731 technique. After deposition of the active polymer layer [poly(3-(2-butyloxy-5-octylphenyl))], they used the MIMIC technique to pattern the polymer film, and finally, a layer of aluminium was deposited over the active layer to form arrays of OLEDs. The size of each diode was 100 × 100
m2 , which has a similar performance to that of standard devices. A similar technique has been used by Nüesch et al. [86] to pattern the ITO anode (Fig. 20). A elastomeric PDMS stamp was fabricated to the desired pattern and then immersed in a 3 × 10−3 M solution of (tetrabutylammonium) hydroxide in ethanol or water. The stamp is then pressed onto the ITO substrate. The base will react with the conducting oxide film, resulting in the formation of a solid ionic double layer at the oxide surface and leading to a change in its work function [87]. The devices were obtained by depositing a TPD/Alq3 double layer onto the ITO film and the cathode LiF/Al was finally evaporated to form the diodes. The patterned ionic layer will inhibit the positive charge injection from the anode and only the organic film corresponding to the unpatterned parts of the ITO substrate will emit light. A luminance of about 100 cd/m2 was obtained with a driving bias of 6.5 V for such a diode. This method has the advantage in that it will avoid handling of the organic film, which may cause damage to the devices. Arrays of OLEDs with a period of 200 nm were reported by Wang et al. [88], who used nanoimprint lithography at 150  C in vacuum. The emitting layer was Alq3 doped with 2 wt% DCMII dye molecules, which has high luminescence efficiency. The patterning process in vacuum was found to preserve the optical property of the organic layer by preventing the residual oxygen from contaminating it. Arrays of about 400 nm width were realized by Nyberg et al. [89] using poly(3-(2′ -methoxy-5′ -octylphenyl)thiophene) as an emitting layer. Making use of this method, an insulating layer was use to separate the cathode from the anode, the pattern being obtained on the insulating layer and the cathode. The emitting film was deposited in the space left between two

V

light emission

Figure 20. Fabrication of nano-OLEDs with Alq3 as an emitter, using a soft-lithography technique to pattern the ITO substrates. Reprinted with permission from [86], F. Nüesch et al., Appl. Phys. Lett. 75, 1799 (1999). © 1999, American Institute of Physics.

Nanostructured Organic Light Emitting Diodes

732 successive arrays and the diodes have a quantum efficiency similar to standard sandwich devices (0.002%). It is also possible to pattern the metal cathode layer directly using soft lithography. This technique makes use of silicon stamp to pattern the cathode layer by applying pressure onto the surface of the diodes (cold-welding process [90]). The stamp was previously patterned with raised areas in the shape of the regions on the electrode that were to be removed. When this was done, the left areas on the substrate can be used as arrays of LEDs. The active material used in this fabrication was Alq3 with an electron transport layer made of 4,4′ -bis(N -naphthyl)(N -phenyl-amino)biphenyl. The measured performance on 1 mm diameter diodes is comparable to those obtained in Alq3 based LEDs and no apparent degradation of the emitting layer was observed during the cathode patterning process. The different soft lithography techniques have demonstrated that they can be applied to the OLED technology without producing significant damage to the organic layer and the performances of the nano- and microdiodes are generally comparable to those of standard ones. Devices of small size and high definition could be obtained by these techniques as compared to standard lithography. Recent investigations have demonstrated that patterns with 10 nm features could be prepared [91]. However, it should be noticed that industrial production requires rapid and reproducible patterning, and parallel techniques of fabricating devices are more adequate for manufacturing nanostructures. Soft lithography methods are well adapted to serial fabrication of devices in laboratory research work or lithographic masks.

3.4.4. Inkjet Printing This technique is particularly adapted for solution processable materials and appears to be the most interesting for fabrication of devices with highly resolved patterns [92, 93]. The emitting layer can be produced by two different methods. For the first technique, the film is directly deposited by printing on the substrate. For the second, the polymer is preliminarily spin-coated onto the substrate. Then a solution containing the dopant is dropped over the films, allowing the dye diffusion into the host layer. Inkjet printing can be performed in a continuous way or in a drop-on-demand (or impulse) mode. The difference between the two modes is in the pattern size and the printing accuracy, the drop-on-demand mode allowing smaller size patterning and a better accuracy. This process can be performed by using either a bubble jet or a piezoelectric technique. In the bubble jet technique, the ink droplet is pulled out of the nozzle by the pressure of a vapor bubble that is locally formed by thermal heating. This technique therefore needs water as a solvent for the material. In the piezoelectric technique, the ink droplet is mechanically pumped out of the nozzle by applying a voltage to a piezoelectric crystal. This technique can be applied to polymers dissolved in organic solvents. Notice that many nozzles can operate in parallel to achieve high speed printing, resulting in a low cost production of devices.

Most of the materials used for inkjet printing belong to the polycarbazole (PVK) and the phenylene vinylene families. Light emitting diodes with low turn-on voltage were fabricated by Hebner et al. [94] using PVK doped with coumarin dyes. Soluble derivatives of PPV such as MEHPPV [95] and poly[5-methoxy-(2-propanoxysulfonide)-1,4phenylene vinylene] [96] also used successfully make use of the printing technique. Figure 21 shows the polymer light emitting fabrication process and a logo created by inkjet printing using MEH-PPV as an active layer. The size and the quality of the printed pattern depend on several factors. First, the size of standard nozzles is in the range of 20–30
m, which produces at best dots of about 25
m in size [97]. Second, the resolution of the pattern depends greatly on the viscosity of the ink and its ability to bind to the substrate. Generally, a low viscosity is needed to prevent rapid drying of ink and clogging of nozzles. Therefore, additives should be incorporated to the ink when using soluble dyes for color emission. On the other hand, ink droplets should not spread on the substrate before they are absorbed and dried (few seconds to several minutes). This condition implies that the ink viscosity should be sufficiently high and the surface of the substrate should be rough enough to limit spreading of the ink and blurring of the image. Finally, the printed pattern should be of a uniform thickness to avoid possible electrical shorts and the uniformity of the layer depends greatly on the quality of the material used. Indeed, the pinhole formation in printed patterns is usually observed and to improve the quality of the emitting devices, additional layers are used. These layers of course have their usual function but are useful to prevent shorts. For instance, PEDOT doped with PSS was used (a)

Glass

(b)

Glass

ITO

ITO

UCLA PLED

Printed CP logo

Cathode EL polymer

(c)

Conducting polymer EL

Figure 21. Fabrication of nano-OLEDs with MEH-PPV as an emitter, using an inkjet printing technique to design a logo. Reprinted with permission from [95], J. Bharathan and Y. Yang, Appl. Phys. Lett. 72, 2660 (1998). © 1998, American Institute of Physics.

Nanostructured Organic Light Emitting Diodes frame

mesh

stencil

Mg:Ag

12 inch

as a hole transport layer in printed OLEDs with polyfluorene and PPV as emitters [98]. Improved techniques and materials [regioregular poly(3-hexylthiophene-2,5 dyil)] have demonstrated that good quality patterns could be realized without buffer layers [99]. The inkjet technique has several undeniable advantages in that a pattern of any size and/or shape can be reproduced directly on the substrate. Problems encountered in the technique include uniform thickness of the printed layer, pinhole formation, and viscosity of the solution. Even with these problems, the technique appears to be one of the most promising for patterning organic devices in the future.

733

Alq3 TPD: polycarbonate ITO/Glass

4 inch

3.4.5. Special Techniques Besides the techniques currently used for fabrication of small devices previously mentioned, several others have been also carried out with success to pattern organic diodes. First, a variation of the lithography technique was used by Noach et al. [100], who used a 193 nm excimer laser to ablate first the ITO substrate through a mask. After deposition of the polymer film and the metal electrode, the grid was then rotated orthogonally to the direction of the ITO strips and the laser was used to ablate the metal layer and partially the polymer. Arrays of 20
m square pixels were reported with improved luminance as compared to standard thin film LEDs. This technique requires, however, careful control of the laser operation to obtain the desired results. For printing techniques, an alternative method has been applied by Pardo et al. [101] to fabricate logos using MEHPPV as an emitter (Fig. 22). This technique, called screenprinting, consists of using a nylon fabric as a screen through which the ink (solution) is deposited on an ITO substrate. The screen is in direct contact with the ITO film or close to it (≈1 mm). The shape of the screen can be defined by using an epoxy to hide parts of the fabric that will not be printed. Multilayer diodes can then be formed on the screen by conventional deposition techniques. The technique is relatively simple and allows a high printing speed with a good resolution, below 100
m. Birnstock et al. [102] reported that very a low turn-on voltage (3 V) was obtained in screenprinted OLEDs using a polyfluorene derivative, without pattern caused by the fabric. More specific techniques have been recently developed to obtain nanosize OLEDs. These techniques can be divided into two main categories: the first one uses optical means to obtain a light emission from the organic material and the second is a special preparation of the substrate to pattern the devices. The nanodevices can be patterned by light [103]. The technique used consists of fabricating a standard diode and then irradiating it by an intense light beam (laser) through the transparent substrate. An alternative voltage is simultaneously applied to the device during the irradiation (several minutes). It was observed in Alq3 based diodes that electroluminescence was induced by the light beam irradiation and a memory effect was obtained: the device continued to emit light during a week. This observation suggests that the illumination facilitates the charge injection and their transport through the device, leading to the formation of excitons. However, the memory effect induced by the light is not well

Figure 22. Fabrication of nano-OLEDs with MEH-PPV as an emitter, using a screen printing technique to design a logo. Reprinted with permission from [101], D. A. Pardo et al., Adv. Mater. 12, 1249 (2000). © 2000, Wiley-VCH.

understood. This technique allows patterning the diodes by moving the light beam on the surface of the substrate. A variation of the previous technique was used by Micheletto et al. [104] with a laser light of a modified scanning near field optical microscope setup. The device studied was a ITO/poly-3(2-(5-chlorobenzotriazolo)ethyl)thiophene/Al diode. The cathode is the tip of the microscope, which acts as a nanosize electrode. It allows stimulation of very small areas of the active polymer and locally complete LEDs are formed. By this technique, it was possible to study diodes of size about 100 nm and significant differences in the light emission of these diodes with that of standard devices were observed. It should be noticed that the technique does not allow one to obtain permanent devices but may be helpful for studying properties of small size diodes. Based on the same principle, other optical instruments were modified and used to study very small areas of OLEDs. For instance, diaminotofluorbiphenyl based diodes were studied with a scanning tunneling microscope [105] and 1,3,4-oxadiazole moiety modified alkoxy ring substituted poly(p-phenylene vinylene) LEDs by atomic force microscopy [106]. Highly ordered OLED heterostructures were fabricated by Marks et al. [107] using a special preparation of the

Nanostructured Organic Light Emitting Diodes

734 substrate. This technique is called nanosphere lithography (NSL). It consists of making a special mask deposited directly on the substrate (Fig. 23). First, a self-assembled layer of triarylamine was deposited on the ITO substrate in order to obtain a smooth and uniform surface. Then a layer of hexagonally close-packed carboxy-terminated polystyrene beads was formed on the obtained surface, playing the role of a mask. Diodes were fabricated by evaporation of Alq3 as an emitting layer and TPD as a hole transporting layer. Regular pattern prismatic posts with 90 nm sides were obtained, which emit a light similar to that of macroscopic diodes without a significant shift of the EL maximum. However, an overall light intensity was found to be two orders lower than that of standard diodes, working in similar bias conditions. This technique provides very regular small size diodes.

3.4.6. Concluding Remarks Many techniques have been invented or borrowed from the inorganic material technology to fabricate nano-OLEDs. The size of the devices ranges from several tens of nanometers to several micrometers. Generally, the performance of small size diodes is similar to that of conventional ones. However, it should be noted that the size of the devices can influence the physical process involved in transport and light emission of the diodes. These particular aspects will be examined. Moreover, although most of techniques used give reliable and reproducible results, only a few of them are suitable for industrial fabrication, which requires low cost, mass production, and high performance devices. Finally the technique used should also suit most of the organic materials to allow the fabrication of multiplayer and multicolor devices, which are necessary for the realization of displays.

3.5. Applications: Matrix Displays Applications of OLEDs in the field of displays can be divided into two types: active matrix and passive matrix. These displays differ from each other in their structure and in the controlling process. A passive matrix has a simpler

structure than an active matrix, but its control is less efficient than that of an active one.

3.5.1. Passive Matrix Displays Principle Passive matrix displays consist of an array of picture elements or pixels deposited on a substrate. The pixels are patterned by one of the techniques described in previously. They are formed at intersections of rows (X horizontal) and columns (Y vertical) lines. To switch on a particular pixel (X Y ), electrical signals are applied to the X and Y lines, with a positive bias to the anode and a negative bias to the cathode. Each pixel is composed of a light emitting diode, whose color is designed by the choice of the emitting material. For a white pixel, three red, green, and blue subpixels are necessary. The brightness of a pixel is controlled by setting the current through each individual diode to the desired value. Current Cross-Talk The circuit scheme of a OLED passive matrix is shown in Figure 24. Each pixel is switched on when a bias higher than its turn-on voltage is applied. However, because of the electrical connections between the diodes, which are connected to the same row or to the same column, parallel conduction paths occur when a selected pixel is switched on. In other words, a dc current cross-talk exists and may cause unwanted light in the matrix. There are several sources of cross-talk [108]: (i) the display resolution which creates more conduction paths when it is high, (ii) the diode rectification ratio, which reduces the cross-talk when it is high, and (iii) the diode reverse leakage current, which increases the stray light when it is high. Circuit simulation performed by Braun et al. [109] indicates that a current driver is more suitable than a voltage driver to address pixels. Furthermore, the electrode resistance, the diode leakage current, and the location of faulty pixels will strongly influence the image uniformity and the power consumption of the display. The cross-talk problem can be minimized by using a carbon underlayer placed between the ITO and the hole transport layer [110]. This layer insulates the electrodes and thus lowers the leakage current, preventing the occurrence of cross-talk. Design Aspects for Displays In a passive matrix display, each line of the picture is addressed sequentially for a short time. The forward biased pixels will emit light while those nonaddressed are kept at zero or reverse bias. To avoid possible flicker effects, the scanning period should

Al 300nm AlQ 50nm TPD 40nm PS Beads SA monolayer ITO Glass

Figure 23. Schematic overview of the NSL. Reprinted with permission from [107], T. Marks et al., Synth. Met. 127, 29 (2002). © 2002, Elsevier Science.

Figure 24. Schematic circuit of an OLED passive matrix.

Nanostructured Organic Light Emitting Diodes

be smaller than 1/XVr sec, where Vr is the video rate (Vr = 25 images sec−1 for PAL standard). However, because the scanning period is very short, the emitted light intensity should be high enough to allow the eye to see a picture with a normal brightness. This condition implies that the average luminance perceived on the screen should be multiplied by a factor equal to the number of lines (X) to obtain the real luminance of the diodes. Beside this consideration, other factors should be taken into account in the calculation of the device luminance. For a monochrome display, one should compensate the loss in emission due to the use of a contrast filter and to the faulty pixels [111]. For instance, to obtain an average of 100 cd/cm2 in a display of 120 lines, with 20% of faulty pixels, the required luminance of the diodes is 37,500 cd/cm2 . For a color display, a factor of 12 higher peak luminance would be needed because each pixel is composed of three RGB subpixels that have a reduced area, a reduced scanning time, and an increased number of lines. Of course, such a high luminance of the devices will require a high power consumption leading to a high power dissipation by Joule effect that should be reduced, for instance, by dividing the anode line into different sectors, each driven by independent synchronous circuitries. Displays Passive matrix displays were fabricated and studied by using polymer or organic materials as an emitter. They utilize a simple structure, which is suited for low cost, low information applications such as alphanumeric displays. The techniques for the realization of the devices are different depending on the material used. For polymers, standard and soft lithography are well adapted for making small size pixels. Inkjet printing is also convenient for polymers, especially soluble ones, which can be deposited into determined size pixels. For organic materials, vacuum evaporation with the use of a special masking technique is often adopted. Monochrome displays are currently fabricated by many companies. The first realization was the seven-segment prototype fabricated by Cambridge Display Technology using a PPV derivative. In 1997, Pioneer launched their passive matrix displays of 256 × 64 dots for automotive applications, based on Alq3 diodes. In 2000, Motorola fabricated a cellular phone screen with passive matrix OLED displays (Timeport P8767) from Pioneer. Researchers from Huyndai LCD presented a 2.4 in. blue monochrome display for mobile application, with 160 × 160 pixel resolution and an average brightness of 30 cd m−2 [112]. High resolution and full color displays have been developed in recent research. In 1997, Hosokawa et al. [80] fabricated an organic display of 5 in. with 320 × 240 pixels (256 gray scale) which was followed by a full color display of 10 in. with VGA resolution [113]. The pixel surface was 330 × 320
m2 . Pure RGB color passive matrix displays were developed by Pioneer with 320 × 240 pixels of size of 330 × 330
m2 and a luminance of 150 cd m−2 [114, 115] using a high accuracy moving system mask to deposit RGB emitters. Despite the progress made in this field, the passive matrix displays need to be driven under pulsed conditions at high current density, which is not suitable for high resolution and high information content applications such as videos or graphics. For such applications, active matrix displays are used.

735 3.5.2. Active Matrix Displays Principle In an active matrix display, each pixel element can be addressed independently via the associated thin film transistors (TFTs) and capacitors in the electronic backplane (Fig. 25). There are two TFTs employed for driving an OLED: a drive transistor and an address transistor. To address a particular pixel, the proper row is switched on and then a charge is sent down to the correct column. A storage capacitor at the designated pixel receives this charge and is able to hold the charge until the next refresher cycle. The addressed transistor acts as a switch for the drive transistor by holding a voltage on the gate of the latter. The OLED pixel has to be biased with a constant current and is thus connected to the drain of the drive TFT mounted in series with the diode. The current can be supplied to the diode during the whole frame time and the current density is much smaller than that needed to drive a passive matrix display. Other advantages of the active matrix are no cross-talk problems, continuous excitation, low power consumption, and integrated drive electronics. Design Aspects for Displays Active matrix displays are currently fabricated using amorphous or polysilicon deposited on glass or plastic substrates although conjugated polymer has been also proposed to drive OLEDs [116, 117]. Poly-Si can be deposited at low temperature but has several drawbacks, including low electron mobility and variation in electrical properties, leading to difficult control of the current density at each pixel. Several techniques can be used to improve the performance of Si TFTs, including low temperature crystallization or excimer laser annealing [118, 119]. However, these techniques require drastic control of the substrate, which make them difficult to put into practice. A four-transistor circuit has been proposed to remedy these drawbacks [120, 121] (Fig. 26). This circuit makes use of the gate voltage of a TFT to control the data current level at a given value, regardless the TFT voltage threshold, resulting in constant output current density which switches on the pixel. A luminance uniformity and an improved performance at low luminance levels were obtained in the 16 × 16 pixel display prepared for this study. It should be noted that p-type TFTs are more adapted for driving OLEDs due to the fabrication process used for the organic diodes. In fact, the use of an n-type TFT would require the anode (ITO) of the diode to be deposited on the organic layer, which can damage the emitter. Displays Although the feasibility of OLED active matrix displays was demonstrated a few years ago [122, 123], it is known that one TFT pixel electrode configuration cannot be used because of the continuous excitation during the frame period. Therefore, a production of TFT substrates is needed

Figure 25. Schematic circuit of an OLED active matrix.

Nanostructured Organic Light Emitting Diodes Idata

736 VDD Source Line

Select Line Vselect

T4

Data Line

Cs

B

T2

T1

T3

A

T5

Cdiode

Iout

OLED

Cathode

Figure 26. Schematic circuit of a four-TFT OLED active matrix. Reprinted with permission from [121], Y. He et al., Jpn. J. Appl. Phys. 40, 1199 (2001). © 2001, Institute of Pure and Applied Physics.

to develop active matrix displays. Using organic materials, Pioneer Corp. has fabricated a 2 in. device with 176 × 192 dots targeted at mobile telephones and a 3 in. device with 320 × 320 dots targeted at personal digital assistants (PDAs) [124]. A 160 × 160 pixel display is usually considered sufficient for a square PDA screen. Dawson et al. [125] described a prototype of QVGA screen (320 × 240 pixels) using a fourtransistor autozeroing pixel driver. An alternative approach has been proposed by eMagin by fabricating OLEDs on silicon microdisplays [126]. Instead of low temperature polysilicon or amorphous silicon, the driving circuit is directly integrated within the silicon wafer using CMOS technology. Full color SVGA (852 × 3 × 600 pixels) displays have been realized with a high brightness (>100 cd m2  and a high lifetime (>10000 hrs) and can be used in applications such as wearable PCs, cell phones, and digital cameras. Another technique for driving the pixels has been proposed by Seo et al. [127] using a simple circuit (capacitance and rectifying diode) and providing a good control of the gray scale. Attempts to fabricate active matrix displays on flexible substrates have been performed by several research teams but no prototype has yet been proposed. These realizations need a low temperature process to implant TFT on plastic substrates (150  C for polyethylene terephthalate and 200  C for polyethersulphone).

3.6. Physics of Nanosize Devices It is tempting to believe that the background we know from conventional solid-state physics can be applied without difficulty to nanodevices. However, the size of the objects involved in nanotechnology is such that the structure may significantly influence the physical processes that occur in devices [128]. In the field of OLEDs, several aspects can be considered. First, from the electrical point of view, because of the small size of the devices, the current density would be very large. There will be a problem of energy dissipation

(intensity and mechanisms) inside the structure which at this time is not clearly understood. On the other hand, the charge injection processes are believed to dominate in molecular OLEDs contrarily to molecular junctions [129], in which injection cannot occur because of the minute thickness involved (a few nm). Nevertheless, it is known that the injected charges modify the electrostatic potentials at the interface and chemical interactions can occur between the organic material and the electrode. The effects of these processes on the transport can be enhanced in very small size devices and this still needs to be elucidated [130, 131]. Second, from the optical point of view, the size of the devices may influence the emission properties of the organic materials. In the nanometer range, quantum confinement effects are expected to blueshift the optical absorption edge with decreasing material size. Small Si crystallites of 5 nm are found to emit intense blue light [132]. The optical response and charge transport in electronic polymers can be drastically changed by a small variation in local order in the materials, for instance by modifying the substituent group [133]. Experiments performed in Alq3 of 10–15 nm sizes clearly show that the PL spectra of the material are blueshifted and the shift direction depends strongly on the size of the sample [134]. In large size samples, the formation of dimers or multimers is probable and their strong interaction results in an increase of the gap between the excited states, producing a redshift of the PL. In smaller size samples, the organic molecules would resemble monomers and the PL spectra are blueshifted. The effects of the intermolecular interactions on the photophysical and transport properties of organic semiconductors can also be investigated through the nanoengineering of the materials, by modifying the structure of conjugated dendrimers [135] so as to understand the physical mechanisms involved within the nanostructures. The miniaturization of the devices requires much research on new physical issues, which include, among others, the hot electron effect, the phonon effect, the quantum noise effect, the purity effect, and those effects already mentioned.

4. CONCLUSION With the intensive research of recent years, the development of organic devices has attained a level which allows industrial applications to be commercialized, especially in the display field. Electronic companies have started to fabricate small screens for cell phones and handheld computers which compete with those using conventional techniques. Organic materials have several undeniable advantages over classical semiconductors. In particular, their very high luminance is a definite asset in display applications. These materials are also well adapted to nanotechnology, resulting from the ease of the deposition technique, which allows any shape and size of the devices to be manufactured. Not only can conventional methods developed for semiconductor technology be applied to polymers and organic materials, but also new ones (inkjet, screen printing) have been invented to fabricate nanosize devices. These techniques benefit from the unique physical properties of the materials (solution, flexibility) that are not evident in conventional semiconductors.

Nanostructured Organic Light Emitting Diodes

High-resolution displays need very small size pixels. Technically speaking, organic diodes of submicrometer size can already be fabricated with an acceptable performance. However, the question of tolerance still remains a problem. Fluctuations in size and in structural properties of the emitting layer may severely affect the quality and performance of the diodes and need to be limited to an acceptable level. Furthermore, under normal working conditions, the tiny devices have to dissipate a considerable amount of energy in regard to their size. The stability of the emitting materials is therefore the key for the fabrication of reliable displays. For the commercialization of these products, mass production would need a simple, low cost, and reproducible process for fabricating the emitting layer. At present, inkjet or screenprinting using polymers appears to be the best technique for making emitting devices. Another concern in the field of nano-OLEDs is the interconnections. The devices in matrix displays need to be driven by appropriate circuits that require reliable electrical contacts. Although this problem can be solved by techniques used in conventional electronics, it has been proved that a number of faulty pixels exist because of failure in electrical connection. The development of organic nanodiodes has been accompanied by new physical issues that have to be further investigated. In addition to the power dissipation in these devices, the electrical transport process, the light emission, and the interface between the emitter and the electrodes have a new and different aspect as compared to conventional and standard diodes. Not only does the size influence these properties, but also new phenomena occur, especially in the optical processes, which are not yet clearly understood. According to many observers, the recent progress in microelectronics technology has confirmed Moore’s law and this trend will continue to obey the law until the year 2010. Projections will then have to be reformulated. Further research and development appear necessary to replace the conventional semiconductors in the near future. Organic materials are good candidates, at least in the field of optoelectronics, due to their excellent emission properties. As regards nanotechnology, they are quite suitable to the processes and technologies used for the fabrication of nanodevices. There is great expectancy that these materials will have a bright and brilliant future in a new nanoelectronics era, when the ultimate limitations of the component size will be reached.

GLOSSARY Electroluminescence Emission of light from a material when excited by an electrical mean (applied voltage). The light is generated by recombinations of excitons. Exciton A pair of electron-hole generated in a material by an external source (light, electrical mean) and bound together by electrostatic attraction. An exciton can be a singlet (the electron and hole have spins in opposite directions) or a triplet (the electron and hole have spins in the same direction).

737 Lithography Printing technique that puts detailed patterns on a flat surface of a substrate. In the classical photolithographic process, an image of the desired pattern is projected onto the surface of the substrate, which is coated by a thin layer photosensitive resist. The bright parts of the resist film become soluble by a chemical reaction with the light, whereas the dark parts remain insoluble. After contact with a developer solution, the soluble part of the resist is removed. The pattern is transferred onto the substrate by a chemical etching of its surface, which preserves the protected parts by the resist film. Other lithographic techniques include electron-beam lithography, soft X-ray lithography, atomic-beam holography. Nanoimprint Printing technique using a stamp of nanometer size to transfer a polymer film onto a solid substrate surface. The formed polymer film is then used either as an active layer in devices or as a mask in a conventional lithographic process. Pixel A picture element. In OLED technology, a pixel is determined by the part of the emitting layer where the cathode and anode overlap. A high display resolution needs small size and closely spaced pixels.

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Encyclopedia of Nanoscience and Nanotechnology

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Nanostructured Surface Modifications for Biomedical Implants Shane A. Catledge, Marc Fries, Yogesh K. Vohra University of Alabama at Birmingham, Birmingham, Alabama, USA

CONTENTS 1. Introduction 2. Nanostructured Diamond Coatings 3. Nanostructured Hydroxyapatite Coatings 4. Nanostructured Metalloceramic Coatings 5. Conclusions Glossary References

1. INTRODUCTION With the advancement of modern materials science, many times a single material does not possess the desired properties for certain applications. For example, some materials have desired bulk properties (chemical, mechanical, electrical, etc.) but their surface properties are inadequate. In these cases, a combination of two or more materials or a modification of the bulk material is adopted. Surface modification is basically a process in which the surface of a material is chemically, physically, or mechanically altered so that the surface properties are changed from that of the original bulk. Materials surfaces are commonly modified by techniques involving, for example, deposition of some additional material as a thin coating or implantation of energetic ions to alter the local atomic bonding. In addition, multilayer or functionally graded structures can be engineered to provide a more viable transition from the bulk to the surface. Novel materials whose microstructure can be engineered to contain features with nanometer-scale dimensions have become quite popular, especially in the last two decades. These “nanostructured” materials can exhibit enhanced mechanical, electrical, magnetic, and/or optical properties compared to their conventional micrometer-scale (or larger) counterparts. Nanostructured (NS) materials contain a large volume fraction (greater than 50%) of defects such as grain ISBN: 1-58883-063-2/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

boundaries, interphase boundaries, and dislocations, and this strongly influences their chemical and physical properties. The Vickers hardness of electrodeposited nickel, for example, increases from 140 to 650 when the grain size is reduced from the microcrystalline range to about 10 nm [1]. Similarly, NS ceramics tend to be tougher and stronger than coarser grained ceramics. The synthesis and control of materials in nanometer dimensions can provide access to new levels of material properties and device characteristics that were previously unattainable, and work is rapidly expanding worldwide in attempts to exploit the opportunities offered through nanostructuring. Terms with the prefix “nano”—nanostructured, nanocrystalline, and nanophase, for example—have often been used interchangeably to describe materials with nanometerscale dimensions. However, it is important to distinguish between different structural forms of materials containing nanometer-size features. Defined broadly, the term nanostructured is reserved for materials characterized by structural features of less than 100 nm in average size. Nanostructured materials can take the form of powders, dispersions, coatings, or bulk materials. One rapidly evolving class of NS materials is that of nanocomposites in which nanometer-size particles or whiskers act as reinforcements in a matrix composed of conventional-size grains or amorphous material. For example, hard composite coatings composed of nanocrystalline (10–50 nm) TiC grains imbedded in an amorphous carbon matrix (about 30 vol%) have shown a fourfold increase in toughness compared to nanocrystalline single-phase TiC [2]. Such coatings can be designed to provide adequate compliance through the controlled formation of dislocations and nano- and microcracks once stresses exceed the elastic limit, while still maintaining high hardness and eliminating catastrophic failure typical of hard, brittle materials. For purposes of this chapter and to avoid confusion with other “nano” terminology, we define nanocrystalline as a more specific subcategory of NS materials characterized by nanometer-size grains without the presence of conventional-size grains or an intergranular amorphous phase.

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Nanostructured Surface Modifications for Biomedical Implants

The tremendous impact on the biomedical community by the unique properties offered by NS materials has stimulated intense research to evaluate the possibility of using them in the design of orthopedic and dental implants.

1.1. Orthopedic Implants Over 450
000 total knee and total hip replacement operations were performed in the United States in 1994 with an anticipated increase of 10% per year [3]. The typical useful life for a replaced joint is between 10 and 15 years [4]. Complications arising from wear include component loosening, deleterious biological responses, osteolysis, mechanical instability, decreased joint mobility, increased pain, and ultimately implant failure. Therefore, revision surgery is frequently necessary, particularly in younger, more active patients. If the useful life of the implant were extended (to upward of 40 years) considerable patient suffering could be eliminated and a substantial amount of health care dollars could be saved. It has been shown [5] that the wear rate of implant components is noticeably lower when articulated against ceramic materials such as zirconia than for metallic materials. Unfortunately, zirconia devices are three times more expensive than their metallic counterparts. Common drawbacks to ceramic devices are brittleness, geometrical limitations, and catastrophic failure modes. These physical limitations have made manufacture of hips difficult and knees impossible; there are currently no available femoral knee components made from solid ceramics. Thus, the major goal is to develop coating technology that can reduce the friction and wear in mating total joint replacement components, thus contributing to their significantly improved function and longer life span.

1.2. Dental Implants It is estimated that currently there are approximately 10 million people in America, the majority of them women, who suffer pain and dysfunction in and near the temporomandibular joint (TMJ). In previous decades, TMJ implants were fabricated of polymeric materials, including the Vitek and Silastic TMJ implants. The primary problem area with these implant systems was wear and deterioration of the components. The almost 100% failure rate of these implants after 3 years lead to a recall of these devices. Revision surgery is needed in most of these patients due to excessive loss of bone and function, and there is currently no fully successful implant system available. Currently, the two devices most commonly used for TMJ restoration are: (1) cobalt– chrome metal on metal devices and (2) polyethylene condyle on a titanium alloy shaft articulating against a curved cobalt– chromium plate (glendoid-fossa component) as shown in Figure 1. Although the patient’s own bone can be used to rebuild a portion of the deficient area around the TMJ, lost function is not restored in many cases and an artificial device is necessary. Metal-to-metal TMJ implants fabricated to date have also exhibited loosening problems because of the type of sliding and rotational motions involved, and metal debris is seen in fairly high amounts in the joint area. Another problem with the TMJ devices which leads to higher than expected wear (primarily the fretting type)

Figure 1. The components of a temporomandibular joint dental implant. The photograph shows a long titanium alloy shaft with a round condylar head made out of polyethylene. This polyethylene condyle articulates against a cobalt–chromium curved metal plate (glendoidfossa component) shown in the top right hand corner of the photograph. The Ti-alloy screws shown are used to attach the shaft to the supporting bone. We have selected this device as a case study for nanostructured bioengineered diamond and calcium phosphate ceramic coatings. Reprinted with permission from [148], S. A. Catledge et al., J. Nanosci. Nanotechnol. 2, 293 (2002). © 2002, American Scientific Publishers.

is the lack of stable fixation in bone, as retaining screws can come loose allowing the implant move out of its ideal position. The ceramic coatings discussed in this chapter will address the issues of wear and loosening in these devices by nanostructural modification of the implant surfaces, which will allow improvement of existing articulations utilizing metal–metal and metal–polymer implants. This approach will enhance screw and component fixation through bone-tohydroxylapatite interactions and hopefully lead to the development of a more successful TMJ implant design. Further background can be obtained from reviews on the subject (see [6
7]). In this chapter, we focus on the following areas of cutting edge research: 1. Nanostructured bioengineered diamond coatings on cobalt–chrome and titanium alloys that will increase the life span of a variety of implant devices to upward of 40 years. Nanostructured diamond and diamondlike carbon coatings have great potential for use as biomedical implants due to their extreme hardness, wear resistance, low friction, and biocompatibility characteristics. Nanostructured diamond produced by chemical vapor deposition (CVD) techniques and comprised of nanosize diamond grains has particular promise because of the combination of ultrahigh hardness, improved toughness, and good adhesion to titanium alloys. The structure and properties of these coatings are easily tailored to the desired application by appropriate choice of feedgas chemistry and other deposition conditions. 2. Nanostructured hydroxyapatite coatings on metals that will promote better attachment to the bone while optimizing abrasion resistance, bond strength, and the dissolution rate. Hydroxyapatite (HA) is a bioactive

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ceramic with a crystal structure similar to native bone and teeth minerals. It has generated great interest in the search for advanced orthopedic and dental implant materials as it elicits a favorable biological response and forms a bond with the surrounding tissues. However, applications of HA are currently limited to powders, coatings, porous bodies, and non-load-bearing implants due to processing difficulties and the poor mechanical properties of conventional HA. Nanostructured processing applied to hydroxyapatite-based materials is used to achieve the desired mechanical characteristics and enhanced surface reactivity for multifunctional implant systems tailored toward different hard tissue replacements. It has allowed chemical homogeneity and microstructural uniformity to be achieved for HA so that fully dense bioceramics can be generated at low sintering temperatures with a significant reduction in flaw size. The nanometer-sized grains and high volume fraction of grain boundaries in nanostructured HA have been found to increase osteoblast adhesion, proliferation, and mineralization. 3. Nanostructured metalloceramic coatings that will provide continuous variation from a nanocrystalline metallic bond at the interface to the hard ceramic bond on the surface. Bonding of functionally graded, NS metalloceramic coatings gradually changes from metallic to primarily covalent with increasing ceramic material toward the surface. One advantage of the graded bonding structure is the ability to overcome adhesion problems associated with ceramic hard coatings on metallic substrates while exhibiting enhanced surface hardness and wear resistance. The NS metalloceramic coatings have a smooth surface finish that is retained in vivo, leading to a higher wear resistance.

Japan [13] for rendering economically viable growth rates, that the scientific community was finally convinced of the feasibility of low pressure diamond synthesis. It is well known that diamond is the hardest known material. In fact, it is in the market of abrasives and cutting tools that diamond has found its most prominent and economically sustaining niche. Other conventional, hard bulk materials such as cubic boron nitride can reach, at best, about 47 GPa (only about 47% diamond hardness). Granted, appropriate engineering of the chemistry and microstructure of materials has led to a new class of synthetic superhard materials with exciting potential. For example, epitaxial [14] and polycrystalline [15] superlattices of transition metal nitrides can reach hardness of 50 GPa when the lattice period decreases to 5–7 nm. Carefully designed composites containing nanocrystals of a hard transition metal nitride imbedded into an amorphous silicon nitride matrix has led to claims of achieved hardness greater than 50 GPa with the possibility of approaching the 70–100 GPa range for diamond [16
17]. However, the extremely wide range of synthetic carbon structures attainable by low pressure deposition techniques has resulted in coatings with measured hardness ranging from 10 (amorphous carbon) to 100 GPa (crystalline diamond) [18–20]. For this reason, carbon-based coatings with a myriad of different structural forms and ascribed names such as diamond, diamondlike carbon, nanostructured diamond, and tetrahedral amorphous carbon continue to dominate the superhard material arena. It is not surprising that these coatings are particularly suited for, and to some extent already commercially realized, in wear resistant applications such as in the machining of nonferrous materials using diamondcoated carbide cutting tools. Recent advances have led to NS diamond coatings exhibiting a unique combination of high hardness, high toughness, and low friction. These and other carbon coatings continue to be actively investigated with respect to the scientific issues (growth mechanisms, structure, etc.) and technological issues (large-area deposition, adhesion onto metallic substrates, etc.) involved. While there are several deposition techniques for producing hard carbon films (e.g. ion beam, pulsed laser, cathodic arc, etc.), we will focus on the use of CVD as it pertains to NS diamond growth. Chemical vapor deposition using hydrogen-rich, hydrocarbon-containing gases has been the most successful method of producing metastable diamond films of high crystallinity. Work by Lander and Morrison [21] at Bell Labs showed in 1966 that a diamond surface saturated with hydrogen maintains the bulk terminated diamond lattice to the outermost surface layer of carbon atoms. Without the hydrogen atoms to terminate the carbon dangling bonds, the surface reconstructs into more complex structures. In 1971 Angus et al. [22] showed that atomic hydrogen could be used as a cyclic etching step to remove unwanted graphite deposited during CVD of diamond. However, the importance of atomic hydrogen used during the diamond growth process itself was realized predominantly by Fedoseev et al. [23] in the USSR, during the mid to late 1970s. In this way, atomic hydrogen could simultaneously (i) stabilize the diamond growth surface, (ii) preferentially etch graphitic and other nondiamond carbon, and (iii) create new growth sites on the surface via hydrogen-abstraction reactions.

2. NANOSTRUCTURED DIAMOND COATINGS Diamond growth from the gas phase was reported as early as 1911 by von Bolton [8] using acetylene in the presence of mercury vapor at 100
C. However, the first documented report of diamond growth at low pressures, which was subsequently confirmed by others, was the work of William G. Eversole at the Union Carbide Corporation. In the period between 26 November 1952 and 7 January 1953, Eversole achieved diamond growth on a diamond seed crystal using carbon monoxide as a source gas. These findings were documented in 1956 [9]. This predates the first documented, reproducible synthesis of diamond by a high pressure, high temperature process by scientists at the General Electric Company in 1955 [10]. The enormous success of this technique of producing diamond where it is thermodynamically stable, along with the impractically low growth rates initially observed for low pressure synthesis of diamond, delayed further development of the low pressure techniques. There also still remained a strong feeling that diamond grown at pressures where it is a metastable phase was somehow thermodynamically forbidden. It was not until the late 1970s, when advances were made in the USSR [11
12] for yielding continuous films using hydrogen and methane mixtures and in

744

Nanostructured Surface Modifications for Biomedical Implants

This allowed much higher growth rates and permitted the nucleation of new diamond crystallites on nondiamond substrates. The reader is referred to a review by Angus and Hayman [24] for a more comprehensive description of the diamond growth process involving hydrogen-rich, hydrocarbon-containing gases and the corresponding roles of atomic hydrogen.

3% mixture [25
26]. Adhesion of conventionally grown diamond films on metallic substrates is a concern because large thermally induced residual stresses provide a critical driving force for the propagation of cracks in the rather unforgiving and brittle nature of the film. In this example, the nanostructured nature of the film shown in the right side of Figure 2 is induced by the addition of large amounts (10% of methane flow) of nitrogen to the feedgas mixture. The grain size of the NS film as measured by X-ray diffraction is 15 nm and the surface roughness is 27 nm root-meansquared (rms) value, an order of magnitude less than the microcrystalline film. By improving the surface finish of the initial predeposited substrate to within 10 nm (rms value), we have achieved NS diamond films with surface roughness as low as 15 nm [26]. As compared to the microcrystalline film, the Raman spectrum of the NS film reveals a weaker diamond peak (ca. 1332 cm−1 , pronounced scattering in the 1350–1550 cm−1 region associated with an increase of sp2 -bonded carbon, and an additional peak at 1140 cm−1 . It should be noted that the intensity scales on the Raman spectra of Figure 2 are not the same and that the diamond peak intensity for the NS film is a factor of three lower than that for the microcrystalline film. It has been shown that the weaker diamond peak is caused by a reduction of grain size to the nanometer scale [27], and that the increased sp2 bonded carbon is due to increasing -bonds at the grain boundaries in the nanocrystalline films [28]. The additional peak at 1140 cm−1 has been attributed to scattering from nm-sized diamond grains [29]. As measured by X-ray photoelectron spectroscopy (XPS), the NS diamond films grown by adding large amounts of nitrogen to the feedgas mixture do not contain a substantial nitrogen concentration. The elemental depth profile by XPS is shown in Figure 3 for a NS diamond film grown on Ti-6Al-4V alloy. Each scan step included oxygen 1s, vanadium 2p, titanium 2p, nitrogen 1s, bulk carbon, carbidic carbon, and aluminum 2p specific scans. The collected data

2.1. Structure A conventional mixture used to produce high phase purity microcrystalline diamond films by CVD using hydrocarboncontaining precursors is about 1 to 3% methane in a balance of hydrogen. Other deposition parameters such as substrate and gas-phase temperature, as well as the choice of substrate material and how it its surface is prepared, can affect the film structure and morphology. However, the former mixture will typically produce a rough, faceted diamond surface comprised of micrometer-size grains. For many applications, a rough surface is undesirable as it can cause severe abrasion during sliding against other materials. By appropriate choice of feedgas types and concentrations, it is possible to manipulate the diamond growth process to produce NS films with high hardness and smooth, wear-resistant surfaces. Figure 2 shows an example of the difference in microstructure between microcrystalline and NS diamond films produced by microwave plasma CVD. Both films were grown by Catledge and Vohra [25] on a titanium alloy (Ti-6Al4V) using an unconventionally high methane concentration of 15%. The microcrystalline film was grown under plasma conditions allowing sufficient production of atomic hydrogen via elevated gas pressure (125 Torr), along with very low levels of nitrogen impurity in the feedgas. In this way, the high methane concentration can lead to an increase of nucleation and growth rates without a substantial decrease in diamond quality. An added benefit of the high methane concentration is an improvement of diamond-to-titanium adhesion when compared to the more conventional 1 to

100

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Figure 2. Scanning electron microscope images and Raman spectra of CVD diamond films grown with mixtures of (a) H2 /CH4 with flow ratio of 500/88 and (b) H2 /CH4 /N2 with flow ratio of 500/88/8.8. Both films were grown using a chamber pressure of 125 Torr and an unconventionally high CH4 fraction (15 vol%). The smooth nanostructured film in (b) results from the addition of nitrogen to the feedgas mixture. Reprinted with permission from [148], S. A. Catledge et al., J. Nanosci. Nanotechnol. 2, 293 (2002). © 2002, American Scientific Publishers.

O 0

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Figure 3. Elemental concentration depth profile of NS diamond film measured by XPS. The three predominant elements in the interface region on the right side of the graph include film carbon (labeled “DLC” here), Ti, and carbidic carbon. The profile represents a diffuse film/substrate boundary.

Nanostructured Surface Modifications for Biomedical Implants

745

show the classic pattern for a diffuse interlayer boundary, with bulk carbon decreasing in proportion to TiC and metallic titanium with increasing depth. The proportion of carbidic carbon in the sample decreases starting at the point where bulk titanium overtakes bulk carbon as the primary species detected. The ratio of titanium to carbidic carbon is roughly 2:1 from the onset of detection of titanium up to the point where it makes up about 30% of the total volume, indicating that metallic titanium is present along with TiC throughout the interface region. Oxygen is present in the interface region at a mean value of 3% for the last 8160 s of sputtering time. This finding indicates that the titanium surface is not completely etched bare during exposure to the hydrogen plasma. It is likely that amorphous, nonstoichiometric titanium oxides exist within the interface as has been detected in other diamond/titanium systems. The XPS data reveal only trace quantities of nitrogen, suggesting that the dramatic changes observed in film morphology and structure with nitrogen feedgas addition are due not to nitrogen incorporation, but to the result of gas-phase and surface reactions involving nitrogen related species such as CN. Due to the small grain size of NS diamond films, a significant fraction of the carbon atoms is situated in the grain boundaries. It is believed that the grain boundary carbon is responsible for the absorption and scattering of light in these films, their electrical conductivity, and their electron emission properties [30]. Simulations by Keblinski et al. [31] have revealed important structural differences between the grain boundaries of phase pure nanocrystalline diamond and those of silicon, and these findings may partially explain the remarkable properties of nanocrystalline diamond films. In contrast to silicon, carbon can form both sp2 - and sp3 hybridized electronic states. The greater bond stiffness of diamond combined with its ability to change hybridization in a disordered environment results in more ordered grain boundary structures in diamond than in silicon. This comes at the expense of many carbon atoms in the grain boundary (typically 70–80%) being only threefold-coordinated. The competition between structural disordering and local hybridization change, which is absent in silicon, implies that the high degree of structural disorder in the mostly fourfoldcoordinated silicon grain boundaries is replaced by bondcoordination disorder in the mostly threefold-coordinated, structurally less disordered diamond grain boundaries. Due to the different numbers of bonds per unit area across the grain boundary and degrees of sp2 hybridization on high and low energy grain boundary planes, it was shown that nanocrystalline diamond (likely to contain a large fraction of high energy grain boundaries) may be mechanically stronger than coarser grained diamond (containing a significant fraction of low energy grain boundaries) or even perfect crystal diamond. The implication of this is that the dominating brittle-fracture mode in nanocrystalline diamond might be intra- rather than intergranular. Finally, Keblinski et al. showed that the threefold-coordinated grain boundary carbon atoms were poorly connected to each other, and therefore any type of graphitelike electrical conduction through the boundaries is not likely unless “bridging” impurities provide the missing connections. A final note regarding structure involves a discussion of how the nm-sized diamond grains may be distributed in the

film and whether a second or third phase is present beyond the grain boundaries. In other words, it may be possible to have a nanocomposite film comprised of nm-sized diamond (and perhaps also graphitic) grains imbedded in a surrounding amorphous carbon matrix. Such films, if designed properly, could be remarkably hard and tough. To the authors’ knowledge, the only reported nanocomposite-like films based purely on carbon have been achieved through postdeposition annealing of diamondlike amorphous carbon (a-C) films [32]. This results in nm-sized regions of high density a-C embedded in a lower density a-C matrix. The hardness in this case was reported to increase by 15% (to 88 GPa) due to the nanocomposite structure. A few other reports have shown diamond nanocrystallites sporadically imbedded within amorphous carbon [33
34]. However, a uniform microstructure with controlled dispersion of a nanodiamond phase within a surrounding amorphous carbon matrix is not yet reported.

2.2. Processing Routes A range of processing routes to CVD NS diamond films exist, but they all have in common the deposition of nanometer-size grains and a film surface roughness that is typically about an order of magnitude lower than that of microcrystalline diamond films. It is possible that early observations of nanocrystallinity, or at least of the apparent degradation of diamond film quality resulting from nanocrystallinity, was concluded to be a result of gas-phase contamination by nitrogen. It is well known that nitrogen is a common impurity in natural diamond and that it can influence physical properties such as optical transparency as well as electrical and thermal conductivity [35]. In 1993, Badzian et al. [36] reported deliberate use of N2 in place of H2 to determine its effect on CVD diamond growth. They concluded that the mixture of CH4 + N2 resulted in a disordered diamond structure likely to be caused by surface processes involving atomic nitrogen. Nitrogen was not incorporated into the film to the amount detectable by Auger electron spectroscopy and XPS. Although not identified as containing nanocrystalline diamond grains, Raman spectroscopy of the films produced by Badzian et al. have similar features to those of NS diamond. In addition, their diamond X-ray diffraction (XRD) peaks were broad, suggestive of reduced grain size. Work by Locher et al. [37] and Jin and Moustakas [38] followed to study the influence of varying amounts of nitrogen in conventional CH4 + H2 mixtures for CVD diamond growth and revealed dramatic changes in structure and morphology. The addition of small amounts (40– 200 ppm) of nitrogen results in a pronounced 100 texture with nearly coplanar surface facets and improved crystalline diamond quality as determined by Raman spectroscopy. It was established that much higher nitrogen additions led to a deterioration of film quality which according to Locher et al., became “nanocrystalline.” The potentially beneficial properties of such films (such as improved wear resistance and electron emission) appear not to have been recognized at that time. In fact, the films may have been determined to be inferior due to the apparent lack of diamond phase purity.

746 Since the work of Locher et al., many researchers have investigated the influence of nitrogen addition on CVD diamond growth and realized that unique properties (such as enhanced electron field emission [39] and improved toughness [26]) can result from the nanostructured films. The evolution from micro- to nanocrystalline diamond grains has prompted considerable investigation into the mechanisms responsible for the nitrogen-induced transformations. For hydrogen-rich reactant gases, the importance of methyl radicals to the diamond growth process is well known [40]. It is likely that the relative concentration of CH3 and CN species is of crucial importance to the growth mechanism and observed changes in morphology. According to Bohr et al. [41], for small N2 additions CN and HCN can efficiently abstract adsorbed H atoms creating vacant growth sites and improving diamond crystal quality by reducing carbon supersaturation. With larger N2 additions, the increased supply of CN and HCN enhances the abstraction of adsorbed H leading to reconstruction of the diamond surface, because adsorbed CN or nitrogen species are not able to stabilize the diamond structure at the surface efficiently. This “reconstruction” appears to manifest itself as a reduction of crystal size with a corresponding increase of sp2 -bonded carbon, most of which is presumably located at the grain boundaries. Recent gas-phase simulations [42] indicate that there exists a critical N2 /CH4 feedgas concentration, above which changes in the CH3 /CN ratio are minimal. The trend in the modeled CH3 /CN ratio corresponds well to the experimentally observed changes in diamond crystallinity and surface roughness [25]. This suggests that above a critical N2 /CH4 ratio, saturation of CN will not induce any further change in the surface structure. While it has been shown that nitrogen incorporation is higher in {111} growth sectors than in {100} sectors by a factor of 3–4 leading to different growth rates of these faces [43], the overall low level of nitrogen incorporation (90% Ar) plasmas and elevated reactant gas pressures (100 Torr) that the C2 concentration is extremely intense compared to atomic hydrogen, while the concentration of methyl radicals is immeasurably low [53]. This is in contrast to the case of conventional (hydrogen-rich, low methane) plasmas

Nanostructured Surface Modifications for Biomedical Implants

Figure 4. Plan-view TEM image of a diamond film prepared from an Ar/CH4 plasma at 100 Torr showing that the diamond film consists of nanocrystalline grains ranging from 3 to 20 nm. The inset image shows a sharp ring pattern of selected area electron diffraction, indicating that the diamond grains have a random orientation. Reprinted with permission from [51], D. Zhou et al., J. Appl. Phys. 83, 540 (1998). © 1998, American Institute of Physics.

in which the CH3 radical predominates. The relatively high C2 plasma emission compared to atomic hydrogen or CH species is illustrated in an optical emission spectrum (Fig. 5) for an Ar-rich plasma (99% Ar, 1% CH4 ) at a gas pressure of 100 Torr. The film growth rate and C2 emission intensity were also observed to increase with increasing reactant gas pressure. These results, along with the fact that the films can be grown in hydrogen-poor or hydrogen-free plasmas, led to a modified explanation for growth involving the carbon dimer C2 , which is believed to be the precursor for nucleation and growth of nanocrystalline diamond in this composition regime. It was suggested that with C2 as the growth species, no hydrogen abstraction reactions are required, partly because insertion of C2 into surface C–C bonds is energetically favorable with low activation barriers. Growth rates for the nanocrystalline diamond films produced from argon-rich plasmas tend to be low, especially for compositions considered to be optimum for yielding small grain size and low surface roughness. For example, conditions required to reduce the rms surface roughness of the film to about 30 nm (e.g., 97% Ar, 2% H2 , 1% CH4  yield a growth rate of only about 0.3 m/hr [50]. According to Gruen, the reduction in growth rate may be due in part to the activation energy associated with forming a nucleus of critical size [54]. In order to produce NS diamond films at significantly higher growth rates, and to achieve better adhesion and toughness to metal-carbide forming substrates, Catledge and Vohra developed a process [55] using a mixture of unconventionally high CH4 concentration (15% of total flow) with N2 (1.5% of total flow) in a balance of H2 at a reactant gas pressure of 125 Torr and substrate temperature of 800–850
C. In this way, NS diamond films with rms roughness of as low as 15 nm can be grown [26]. The C2

Nanostructured Surface Modifications for Biomedical Implants

747

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Figure 5. An optical emission spectrum of an Ar/CH4 plasma running with 1 vol% CH4 and 99 vol% Ar as the reactant gas at a chamber pressure of 100 Torr; (b) plots of growth rates of nanocrystalline diamond films and emission intensities of C2 from the Ar/CH4 plasmas vs reactant gas pressures ranging from 55 to 150 Torr. Reprinted with permission from [51], D. Zhou et al., J. Appl. Phys. 83, 540 (1998). © 1998, American Institute of Physics.

emission was found to increase with increasing CH4 flow and with increasing gas pressure [56], leading to higher nucleation and growth rates. The growth rates for micro- and nanostructured films grown with the 15% CH4 concentration were 2.4 and 1.8 m/hr, respectively [57]. The strong influence of the CN radical in causing nanocrystallinity was confirmed by the correlation of its modeled composition in the gas phase [42] with the degree of nanocrystallinity as determined experimentally [18] for diamond films grown with different N2 additions. For a given CH4 feedgas concentration, there exists a critical N2 feedgas concentration, above which the change in the CH3 /CN ratio is minimal. The change in the CH3 /CN ratio with increasing N2 /CH4 ratio is shown in Figure 6 and illustrates a “knee” in the curves, defining the critical N2 concentration. The knee becomes more evident when using a higher CH4 /H2 feedgas ratio. It was observed experimentally that the same critical N2 feedgas concentration exists, above which a further decrease in diamond crystallinity and surface roughness of the grown diamond films is minimal. Recently, Sharda et al. [58] have produced NS diamond films with surface roughness in the 15–30 nm range by using biased enhanced growth (BEG) in a microwave plasma CVD system. This unique technique relies on a combination of two growth processes acting simultaneously during deposition. One process involves the surface-related hydrogen abstraction reactions typical for diamond deposition using conventional hydrogen-rich plasmas. In addition, shallow

0 0.0

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Ratio N2/CH4 Figure 6. Gas-phase equilibrium plot of the ratio of CH3 to CN as a function of N2 /CH4 feedgas ratio as simulated for conditions of diamond growth using an H2 /CH4 /N2 mixture with 1 and 15 vol% CH4 . The chamber pressure was 125 Torr. Reprinted with permission from [42], R. Corvin et al., Appl. Phys. Lett. 80, 2550 (2002). © 2002, American Institute of Physics.

subsurface implantation of energetic carbon ions caused by the continuous application of a dc bias voltage to the substrate produces a disordered structure containing a high concentration of sp3 carbon in the films. The BEG process takes advantage of subsurface implantation of carbon ions to produce a smooth NS diamond film while the process involving hydrogen abstraction reactions helps to etch away graphitic carbon deposits. Relatively low substrate temperatures (400–700
C) were shown to be useful for this growth regime in obtaining optimal NS diamond content and film hardness. While the three major processing routes for NS diamond growth discussed in this chapter can be used to produce hard and smooth films, there are likely to be differences in structure, primarily with regard to the relative amounts of sp3 - and sp2 -bonded carbon, the degree of crystallinity, and the amount of hydrogen incorporation in the film. These factors will no doubt influence the mechanical properties of the film such as hardness, adhesion, and wear resistance.

2.3. Mechanical Properties As grain size decreases to the nm range, the mechanisms for plastic deformation change. In particular, dislocation activity is reduced and the creation of new dislocations is made difficult as the grain size reaches the lower end of the nanoscale ( b . Now one can immediately obtain a relation between the laser fluence and material parameters needed to reach the ablation threshold Fthreshold = 43 ne ls b . A typical binding energy for the majority of solids is a few electron volts and therefore, the typical absorbed laser fluence for ablation threshold is around 0.5 J/cm2 . One can see that ablation by long or short laser pulses occurs under very different conditions. In order to ablate the same amount of material with a short pulse, one should apply a larger laser intensity approximately in inverse proportion to the pulse duration. For example, laser ablation with a 100-fs pulse requires the intensity to be above 1013 W/cm2 [31–33, 65], while with 10-ns pulses, the same material is ablated at much lower intensities, ∼108 – 109 W/cm2 [31]. The depth of material ablated per single short laser pulse is proportional to the skin depth, whereas in the case of long pulse ablation, the characteristic ablation depth is proportional to the heat conduction length per pulse ∼ atp 1/2 , where a is the thermal diffusivity (cm2 /s) of the target material. Correspondingly, the number of particles evaporated per pulse differs by several orders of magnitude. It has been shown [33, 65] that at laser intensities in excess of 1013 W/cm2 , practically any target material is ionized during the subpicosecond pulse time. Following ionization, the laser energy is efficiently absorbed by free electrons due to

Nanostructures Created by Lasers

inverse Brehmsstrahlung and resonance absorption mechanisms and does not depend on the initial state of the target. Consequently, the interaction of a laser pulse with both metals and dielectrics proceeds in a similar way. The efficient evaporation of dielectrics and the formation of atomic beams of ablated atoms is now possible using short and intense laser pulses. Since additional energy, ∼10 eV/atom, is required for ionization, it is obvious that the ablation threshold for dielectrics must be higher than that for metals. Indeed, the experiments show that the ablation threshold for dielectrics is typically ∼2 J/cm2 [33].

3.2. Ablation Rate and Deposition Rate The most efficient ablation will be achieved if all the absorbed energy is used in ablation only, and any losses and overheating of the plume are avoided. In this case, the instantaneous ablation rate (the ablation rate during the pulse) can be easily estimated as the absorbed laser intensity divided by the binding energy n abl ≈

AI0 atoms/cm2 /s

b

In fact this ablation rate is close to the experimentally measured value for the optimum ablation mode. This is the highest rate from all available ablation methods. The values for the instantaneous ablation rate span from 1032 atoms/cm2 /s for short, ∼100-fs pulses, to 1027 atoms/cm2 /s for the nanosecond pulses. The total number of atoms evaporated per single pulse with the total energy Elas is given by AElas /b . The laser energy per short pulse is in the order of ∼J, while in the nanosecond pulses it reaches 1 J. Thus, the ablation rate per pulse, with the pulse duration ranging from nanoseconds to femtoseconds, is correspondingly ∼1012 – 1018 atoms/pulse. Taking into account the different pulse repetition rates (up to 100 MHz for the short pulses and 10– 30 Hz for the long nanosecond pulses) one can see that the average flow of laser-ablated atoms is N ∼ 1019 –1020 atoms/s near the ablation surface. This figure, along with the temperature and ionization state of the vapor, defines the initial conditions for the formation of new structures in a chamber. Let us consider the use of the atomic flow for the deposition of thin films on a substrate placed at a distance d from the target in an evacuated chamber. The film growth rate for the formation of a film with a number density na is defined as N /2d 2 na . Thus, taking the average target to substrate distance of 10 cm and the number density of solid 1023 atoms/cm3 the deposition rate for the formation of amorphous films with laser ablation can reach several tens of nanometers per second.

3.3. Criterion for the Full Atomization of Ablated Vapor The phase state of the ablated vapors is determined by the conditions of evaporation, that is, it depends on the amount of laser energy absorbed in the ablating material. The energy delivered by a laser is spent on the breaking of interatomic bonds and on the kinetic energy of atomic expansion. If this kinetic energy is low, the vapor expands slowly, and therefore it can be condensed back near the target shortly after

793 the laser pulse termination. We shall determine the magnitude of the kinetic energy sufficient for keeping the plume expanding into a vacuum in a gas state of non-interacting atoms. One can estimate the energy threshold necessary to achieve full atomization of the ablated plume on the basis of thermodynamic arguments similar to those used for establishing the criterion for complete vaporization of a material in an unloading stage after the action of a strong shock wave [66]. In this case all the nonequilibrium processes related to the energy transfer to ions are assumed to be completed before the expansion begins. The target material after the termination of the pulse experiences adiabatic expansion. The adiabatic expansion from a solid state to the gas state can be described by the conventional relation between the gas energy, pressure P , and gas volume, V , but with a volume-dependent exponent (so called the Gruneisen coefficient). In order to get the final stage of expansion as a gas state, the adiabatic curve in the PV plane must pass higher than the critical point, Pcr $ Vcr , separating the states of a homogeneous phase (atomized vapor) from states with a mixture of phases (gas and condensed liquid droplets). Given these constraints, it can be determined that the energy delivered by the laser per ablated atom must be approximately three to four times larger than the binding energy. Therefore, the absorbed laser energy density necessary to transform the ablated material into an atomized vapor should exceed the ablation threshold in accordance with the condition F > 4Fthr .

3.4. Damage and Condensation Thresholds If the total energy delivered by the laser is close to the binding energy, total ∼ b , then a solid experiences only a small density decrease from the standard solid density of the target material. The pressure in the material is comparable to the bulk modulus. Therefore, the final state of the target affected by the laser at this energy level might be considered “damaged,” having cracks, flakes, etc. in the laser focal spot depending on the initial state of the target (such as the presence of defects, impurities, etc.). If the deposited energy is in the range b < total < (3–4)b , then the final state of the expanding vapors may lie in the region of the pressure–volume parameter space where the mixture of phases is energetically favorable. The condensation of vapor into liquid droplets in a course of expansion in a vacuum may occur when the absorbed laser energy is within Fthr < F < (3–4)Fthr .

3.5. Ionization State and Velocity Spectrum of Ablated Ions Ionization of a solid target material during the ablation process and the ionization of ablated vapors occurs due to processes of photoionization, multiphoton ionization, and ionization by electron impact (avalanche ionization) [66]. As ionization proceeds, the vapor is converted into a highdensity plasma whose properties can eventually dominate the physics of the laser–vapor interaction. If the laser–matter interaction occurs at a high intensity, which is typical in ablation by femtosecond laser pulses, the full first ionization is completed during the first few femtoseconds at the

794 beginning of the laser pulse [65–68]. Afterward the interaction proceeds with the plasma. The energy distribution of the ions in the ablated flow appears to be non-Maxwellian. It can be roughly approximated as a two-bump distribution composed of the slow and fast parts. Experimental and theoretical studies have demonstrated that the energy distribution of outflowing ions is highly dependent on the ratio of the maximum intensity in the main laser pulse to the intensity in the prepulse (the so-called contrast ratio) [69]. It has been observed that for 100-fs laser pulses in the laser intensity range of 1014 –1016 W/cm2 , the ion energies vary from 100 eV to 20 keV [69]. Therefore, the interaction of an ionized flow, either with an ambient gas in the chamber resulting in cluster formation or with a substrate leading to the formation of a nanofilm, proceeds in a different way, as has been confirmed by experiments which are discussed below. We should stress that all parameters of a hot atomic flow which affect the process of a nanocluster formation can be controlled and steered in a desirable manner.

4. FORMATION OF NANOCLUSTERS IN A VACUUM The whole process of nanostructure formation can be separated tentatively into the following stages. First, laserablated atomic vapors (or plasma) are produced to form a plume. Then, the laser plume expands into a vacuum and cools in the experimental chamber. The nanostructure formation process (nucleation) is composed of vapor–vapor, vapor–filling gas, vapor–substrate, and cluster–substrate interactions. Finally, the resulting product is annealed and cooled. In this section, we concentrate on the processes of nanostructure formation, taking the parameters of ablated vapors (plasma) as the initial conditions. Then, we discuss the characterization of the structure produced and relate the structural and material features to the formation conditions resulting from vapor–gas–substrate coupling. We start from the most studied process of thin film deposition in an evacuated chamber. Recently a huge variety of different structures were deposited by the laser ablation method including refractory and complex materials. The literature covering this topic comprises thousands of references [i.e., 70, 71]. Our goal in this review is to point out relations between the properties of the atomic beam, the ambient gas, and the conditions created in the chamber to the properties of the emerging nanostructure. Such relations, when properly understood, would allow the control and prediction of the formation process. Therefore, we concentrate on several structures where this relation has been at least partly revealed. We also mention recent achievements in the quality and in the efficiency of thin film deposition, which makes the pulsed laser deposition technique more attractive for industrial applications.

4.1. Deposition of Nanometric Films in a Vacuum Laser ablation has been successfully used for thin film deposition during the last 3 decades with the use of conventional nanosecond, 10- to 30-Hz lasers [70–72]. However, due to

Nanostructures Created by Lasers

poor control over the laser beam parameters in these lasers, the surface quality (abundance of droplets) and material properties (for example, the sp2 /sp3 bond ratio in carbon films) would differ from one laser installation to another with seemingly similar parameters. In addition, the deposition rate with lasers running at a repetition rate of 10–30 Hz was too low for most industrial applications. The recent advent of short-pulse, high average power, high repetition rate lasers resulted in the elimination of these drawbacks of laser deposition. Progress in the understanding of the ablation process led to control over the pulse time shape (elimination of the prepulse), over the spatial distribution of the intensity across the laser focal spot (tophat distribution), and over the temperature of the ablated ions. Now full control of the ablated plume parameters, at least in principle, can be provided. Future developments will determine whether it will be possible to make this process cost effective and to scale it to the industrial level.

4.1.1. Interaction of Hot Atoms with a Substrate in a Vacuum Let us describe the succession of processes accompanying thin film deposition in a vacuum. We consider, for example, the flow of carbon atoms forming diamond-like carbon films on a substrate (conventionally the substrate is a silicon or silica) in a high vacuum, P = ∼10−6 –10−7 Torr, which corresponds to a density of air molecules of ∼ 2 × 109 – 1010 cm−3 . A short-pulse laser with a high repetition rate produces 1019 –1020 atoms/s, which destroys the vacuum after several seconds of operation [32, 73–75]. Therefore, continuous chamber evacuation is necessary in order to maintain constant conditions during the long, 30- to 120-min deposition process. Continuous chamber evacuation at a rate of 2 × 103 liters/s maintains the number density of particles in the chamber at an approximately constant level of na ∼ 2 × 1010 cm−3 [73]. Under these conditions, the mean free path for the particles (carbon atoms and air molecules) is l ∼ 1/na  = 5 × 104 cm, assuming that the cross section of atom–atom collisions is  ∼ 10−15 cm2 . Hence, one can suggest that there is no influence from any collisions in the chamber on the film formation process at the substrate and no cooling of the carbon atoms under this vacuum condition. Thus, the films of any material are formed due to direct vapor–substrate interaction at the vapor’s temperature, which approximately corresponds to the target surface temperature. Note that these conditions are appropriate for the formation of sp3 carbon bonds assuming T > 103 K. However, not all of the collisions between the ablated atoms and the substrate lead to the sticky attachment of an atom to the substrate. Some atoms can rebound from the substrate or from the chamber walls, cool down, and flow around the vacuum chamber [3, 73, 76]. Some small deposition of the ablated material on the rear side of the substrate may serve as direct experimental evidence of this effect. Another important factor for deposited film formation is the pressure on the substrate during the film building process. This pressure consists of two components: kinetic pressure, Pkin , and thermal pressure, Pth . The momentum transferred to the substrate by the incoming flux of atoms (ions) determines the kinetic pressure. However, the kinetic

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pressure is small in comparison to the thermal pressure, which depends on the average temperature of the substrate. The average temperature on the substrate surface generated by the impact of the ablated flow can be calculated through the maximum temperature on the target surface, Tmax , the laser repetition rate, and the pulse duration [73]. The thermal pressure and average temperature on the substrate were estimated as 20 kbar and 1600 K, respectively, for the 120-ns pulse laser and 40 kbar and 3000 K for the 60-ps laser by Gamaly et al. (1999, 2000) [31, 73]. These pressure and temperature values are close to the range of parameters most appropriate for the carbon-to-diamond phase transition to occur under equilibrium conditions. One can see that an increase in laser intensity will increase the energy of the ablated ions and consequently will increase the temperature and pressure on the surface of the substrate, thus affecting the conditions for thin film formation.

4.1.2. Experiments: The Material Properties of the Films Produced High average power, high repetition rate Nd:YAG lasers ( = 1
064 m) were used for laser ablation of carbonaceous targets and deposition experiments [73, 75]. Laser radiation with parameters of 60 ps, 3 × 109 W/cm2 , and 76 MHz is absorbed well (∼85%) by a graphite target and produces an almost fully ionized laser plume with a surface temperature (average over many pulses) in the range from 2500 to 3500 K [73]. Thin carbon film deposition was performed in a chamber evacuated to 10−7 Torr on a mica substrate. The surface morphology of carbon films with a thickness of 25–120 nm has been investigated with an atomic force microscope [73–75, 77]. Films with thicknesses of 20–25 nm appear to be almost atomically smooth with the surface root mean square (rms) roughness around 0.4–1 nm [73, 75]. The optical bandgap of 0.5–0.7 eV extracted from ellipsometry measurements and Raman spectra indicated that the deposited films had properties similar to the diamond-like amorphous carbon (a-C) films. Studies of the influence of laser intensity in the range 1014 –1016 W/cm2 and wavelength in a range of 400–1000 nm on the properties of deposited films unveiled several interesting phenomena [73–76]. The energy distribution of ions which were ablated with short (around 100 fs), intense (in excess of 1014 W/cm2 ), and prepulse free laser pulses has a pronounced two-bump form composed of a main thermal part, Eth , and a fast part, with energy 3–5 Eth [74]. Studies of the deposited films revealed that the transmission of the films increases with increasing laser intensity, while the ratio of sp3 to sp2 bonds decreases, being evidence of a less diamond-like character. The bandgap for these films determined with ellipsometry measurements was 0.85 eV, which supports the assumption of the amorphous nature of the films. Experiments using an intense short-pulse, high repetition rate laser demonstrated, along with atomic surface quality, an extremely high deposition rate up to a few micrometers/hour [73, 75], exceeding that for all other available methods of thin film deposition. It is instructive to compare with a deposition rate using a long pulse (∼17 ns), low repetition rate (10–20 Hz) KrF laser (248 nm, 5–125 J/cm2 ),

795 where the deposition rate for the production of amorphous carbon films with high surface quality (rms roughness of 0.6 nm) constitutes 0.3–0.6 micrometers/hour [77].

4.2. Deposition of Complex Films Laser ablation can be used to produce films of complex materials with the same stoichiometry as the original target. Provided that the laser intensity is chosen such that the bonds with the highest binding energy can be destroyed, laser ablation can produce an atomized beam containing the whole mix of constituent atoms. As a result, the laser plume contains a mixture of atoms with exactly the same atomic content and with the same atomic ratio as in an original target. Therefore the deposition process maintains the same stoichiometry in the deposited film or in a nanocluster as in the ablated target. As an example of complex structures being successfully deposited, we mention chalcogenide glasses (As2 S3 [34] and high-temperature superconducting ceramics [78–80].

5. NANOCLUSTERS PRODUCED THROUGH THE INTERACTION OF ABLATED VAPOR WITH NOBLE GAS The ideal mode of formation for any nanostructure is bottom-up or atom-to-atom attachment in a proper place in space, and at the proper rate in time, in order to form clusters with desirable characteristics. To approach this mode, one should be able to control the formation process on a space scale of angstroms and on a time scale less than a picosecond. An atomic beam for cluster formation can be created by laser ablation with short (picosecond and subpicosecond) successive laser pulses, with the repetition rate up to 100 MHz. In this case, the shortest controllable time scales are the laser pulse duration and a time gap between the pulses. The smallest controllable number of atoms is the number of atoms evaporated per single laser pulse. Of course, the decrease of a single pulse duration and increase of the repetition rate will lead to a smaller controllable time scale and number of particles per pulse. In principle, there is no upper (lower) limit: in the ultimate limit of extremely short pulses and the highest possible repetition rate, one has atom-by-atom evaporation with as short as necessary time control and consequently an atom-to-atom attachment process of cluster formation. The process of nanocluster formation is composed of several stages, namely, the formation of a laser-produced flow of hot atomic vapors, plume propagation, diffusion, cooling/heating in a chamber, a cluster nucleation process, and a final stage of annealing, cooling, and stabilization. In what follows, we describe all the formation stages of individual clusters and compare with experimental data where available. We briefly discuss size-dependent cluster material properties and the internal structure of nanoclusters. We then discuss interactions with the substrate and the formation of cluster-assembled films.

796 5.1. Nucleation, Growth, and Annealing It is instructive to consider the simplest case of the formation of clusters composed from one element. The most studied cases are those of carbon cluster and metal cluster formation. We consider, for example, the thoroughly studied carbon cluster formation process in a noble gas filling of the experimental chamber. There are also many studies of cluster formation in a reactive gas atmosphere [7–9, 81]. The processes of cluster formation in reactive gases are more complicated and less developed. Therefore, we restrict ourselves to interactions between atomic beams with noble gas. Many features of the formation process that we describe are common for the formation of clusters of different elements. We should note that many essential details of cluster formation mechanisms have still not been uncovered, and some of the proposed mechanisms are questionable. There is no clear understanding or mutual agreement about the onset of the nucleation process, the progression toward cluster building, or growth termination. Many theoretical models have been proposed. But due to the lack of in-situ diagnostics, no experimental validation of the proposed mechanisms has been obtained to date. However, the general picture of cluster formation can be presented in a reasonable scenario. In the following we present a qualitative picture of cluster formation based on kinetic and thermodynamic arguments.

5.1.1. Nucleation and Growth The cluster formation mechanism appears to be simple from first appearances. The hot vapor of ablated atoms rapidly expands in a cold gas. Thus, the thermodynamic approach of fast vapor condensation into minidroplets, that is, clusters, seems straightforward. Close examination, however, reveals that the process is too fast in comparison to the equilibration time. The vapor density is relatively low, and the atom-toatom collision time is not negligibly small in comparison to the characteristic time of the process. Thus caution should be exercised in applying the thermodynamic approach for describing the cluster formation process. In the following, we discuss and compare the thermodynamic and kinetic descriptions of the cluster formation process. Thermodynamic Approach—Condensation Nucleation is a process through which clusters of a new phase grow inside an initial phase, which has been heated above the phase transition temperature. In thermodynamics the nucleation process describes the early stages in phase transformation, such as condensation of gases during expansion or solidification of melts. The expanding vapor (plasma) of ablated atoms during interaction with a cold gas or substrate can be transformed into a supersaturated state. This state is thermodynamically unstable. Therefore, a vapor– liquid phase transition develops leading to the formation of nuclei of the new phase, minidroplets of liquid. If some fast annealing process can suddenly terminate further growth of these droplets, then nanoclusters can be formed. The nuclei of the new phase are formed due to fluctuations in an unstable system. A nucleus can continue its growth only in cases where its radius exceeds a definite critical value. Classical condensation theory [82] predicts well the critical size of a nucleus when a liquid droplet forms,

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starting the fast process of the phase transformation under the conditions of local thermodynamic equilibrium. The small seeds (nuclei) of a new phase are created in the overheated, initially homogeneous, vapor phase due to fluctuations [82]. Such seeds are unstable structures because the formation of an interface between two phases is energetically unfavorable: to create a seed, the work to overcome the surface tension for the formation of a nucleus needs to be spent. The seeds with a size less than the critical value decay into the initial phase. The seeds with a size exceeding the minimum critical radius start to grow up, rapidly becoming the centers of the fast transformation into a new phase. The critical radius of a seed can be obtained from the condition of minimization of the free energy of a seed assuming that it has the form of a spherical droplet. Physically, this condition is equivalent to the balance between the surface tension and the thermal pressure. The critical radius of the seed is expressed through the temperature of the overheated phase, T , as [82] 2' 2' rcr = ′ ≈ P −P na T − Tmelt

where ' is the surface tension between the liquid and gas, P ′ is the transient pressure in a gas, and P is the pressure corresponding to the liquid–gas equilibrium: P = na Tmelt . One can consider seed formation as the attachment of a single atom (or monomer) to the seed center, with a characteristic thermal velocity th ∼ 2T /M 1/2 . This approach allows the estimation of the cluster size under conditions close to those in equilibrium. There have been numerous attempts to improve a classical theory of cluster formation by molecular beams under nonequilibrium conditions without considerable success. Review and discussion of these theories by Milani and Iannotta (1999) is available [3]. The critical radius is directly proportional to the surface tension between the liquid and gas phases and inversely proportional to the pressure of the expanding vapor. Therefore, as one can easily estimate from the above formula, the nanometer size clusters can be formed via the condensation process only in a very dense vapor with a density a few times, 3 to 10 times, lower than the solid density. It means that the formation of nanoclusters by vapor condensation from the supersaturated state might occur in a region very close to the ablated target. Note that the above description of minidroplet formation applies to a monoatomic homogeneous vapor in thermal equilibrium. Let us now compare the above model to the experimental data of cluster formation. Hot silicon vapor was produced by laser ablation (ArF laser,  = 193 nm, 15 ns, 1–3.9 J/cm2 ) of a monocrystalline silicon sample [83]. Silicon clusters with a diameter in the range of 1–4 nm were formed through interaction with a flow of pure helium (at pressure from 1 to 4 Torr). The silicon target was used as a substrate where the nanoclusters were collected. Patrone et al. and Marine et al. [83, 84] found that cluster size grows in direct proportion to the increase in laser fluence. However, the increase in laser fluence results in increases in the near surface temperature and pressure of vapors. Thus, in thermodynamics, it should result in a decrease in the critical radius of the nucleus of the new phase and therefore make easier the growth of large droplets. It was also demonstrated that the cluster size

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decreases as the distance from the laser focal spot increases. The temperature at the substrate decreases as the distance from the focal spot increases. In accordance with the classical theory of expanding vapor condensation [66, 82], this must result in an increase in the number of critical nuclei for condensation, which is in contradiction to the experimental observation. The vapor condensation model has also been mentioned by Sattler [85], in relation to carbon nanotube formation, as a possibility for forming half-fullerene seeds for the further construction of nanotubes. One can note that condensation leads to the formation of a disordered (liquid) droplet. The complicated internal structure is a result of a microscopic atom-to-atom interaction. One can conclude that the direct application of the thermodynamic approach for explanation of the transient processes of nanocluster formation looks rather questionable. It allows an estimation of an approximate cluster size at best. Let’s now consider the kinetic approach to the cluster building process. Kinetics of Vapor–Gas Interaction The flow of atomic carbon is created by laser ablation near the surface of a target. The carbon cloud expands, carbon atoms collide with the filling gas atoms, exchanging energy, diffusing, and finally forming a mixture of carbon and filling gas with some average transient density and temperature. Thus, the conditions for the formation of clusters—“the primeval soup”—are created. The number density and temperature of this mixture change with the distance from the target. It is quite different near the target and near the substrate, several centimeters away. The processes of collision, diffusion, and atom-to-atom (atom-to-cluster, cluster-to-cluster) attachment can be described qualitatively on the basis of a simple kinetic theory [54, 86–87]. Depending on the masses of ablated atoms and the atoms of the filling gas, the processes of energy exchange will occur at different rates. If the masses of colliding atoms are comparable (for example, carbon flow with an argon fill), the carbon can loose a significant part of its energy even in a single collision. Hence, efficient energy equilibration occurs after several collisions: the carbon vapor is cooling down and the argon gas is heating up. The main processes which contribute to changes in the density of carbon atoms in the cluster formation zone are the following: delivery of atomic carbon by the target ablation, carbon losses due to diffusion out of the formation zone, and carbon consumption in the cluster formation process. On the basis of kinetic considerations, the scenario of carbon cluster formation in a carbon–argon mixture created by the high repetition laser has been suggested. We point out that the main features of this scenario are applicable to the cluster formation of any other element. Kinetics: Nucleation by Monomer Addition Laser ablation creates an almost continuous inflow of hot carbon atoms and ions, with an average temperature of a few electron volts, into the experimental chamber. The shock wave generated by each pulse rapidly decelerates in the ambient gas atmosphere, and further propagation of hot atoms proceeds by diffusion. Initially the ambient gas is at room temperature (or the temperature of the furnace). The continuous inflow of hot carbons increases the partial density of carbons in the chamber, along with the temperature in the mixture.

797 When the carbon vapor temperature and the number density reach the level where the probability of carbon–carbon attachment becomes significant, the formation of carbonaceous clusters begins. The carbon consumption rate during this formation process significantly exceeds the evaporation rate due to laser ablation. Therefore, the carbon number density rapidly decreases to the value at which the formation process terminates. Thus, the ablation rate, target parameters, pressure, and properties of the ambient gas determine the formation time and, accordingly, the size of the cluster formed. Continuing laser evaporation leads again to an increase in the carbon number density to a value sufficient to resume the next cycle of cluster formation. It has been suggested by Gamaly et al. [87] that the cluster formation process is composed of periodic stages of heating and cluster formation, with the time period depending on the initial argon density, the evaporation rate, and on the carbon attachment reaction rate, which in turn is a function of the temperature and density of the atomic carbon. It is clear that the average temperature of the ambient gas depends on the laser repetition rate. For example, in the case of a high repetition rate laser [73], during the short period of cluster formation (in comparison to the heating period), the argon gas does not cool down but maintains a temperature approximately equal to that required for cluster formation. As a result, the average temperature in a carbon– argon mixture appears to be high enough for formation of sp2 and sp3 bonds, as experimentally observed. The maximum number of atoms in a cluster (or the maximum cluster size) from the kinetic viewpoint is directly related to the cluster formation time defined above. The characteristic time for N atomic cluster assembly in an argon–carbon mixture can be estimated under the assumption that the main building process is dominated by single atom attachment to a bigger cluster, taking the attachment cross section to be equal to the geometrical cross section for elastic collisions. This time is directly proportional to the ambient gas density and inversely proportional to the square of the partial density of single carbon atoms. These predictions qualitatively comply with the experimental data that small clusters (∼6 nm, 104 atoms) are preferably formed at a low gas pressure of 1 Torr [37, 73], while carbon nanotubes (106 atoms) are formed at pressures of 300–500 Torr [27–30, 87]. Therefore, the kinetic approach can qualitatively predict the formation time and the size of the nanocluster. However, kinetic theory, as well as thermodynamics, fails to explain fundamental issues relevant to the internal structure of the nanoclusters and their unusual material properties already observed experimentally, for example, why clusters having a particular number of particles (magic numbers) are more abundant, which features of the formation process are responsible for the intricate structure of a cluster, and what are the reasons for the formation of crystalline or amorphous clusters.

5.1.2. Cluster Annealing and Stabilization Laser ablation creates a dense homogeneous mixture of hot ablated atoms and atoms of an ambient gas that proved to be the most appropriate medium for the formation of threedimensional clusters. The homogeneous mixture has high

798 symmetry—it is almost isotropic. Kinetics and thermodynamics theories can qualitatively explain why the hot atoms can form a cluster of a definite size, like an amorphous snowball, during the many “sticky” collisions. However, it is well known that nanoclusters have different and sometimes very complicated structures. A fundamental question then arises, namely, how does the transition from such a disordered gas phase to the highly symmetric molecule of fullerene [19], or a carbon nanotube [20, 21], or even the more complicated structural unit of carbon nanofoam [37] take place? The most natural answer may be found in the general theory of phase transitions for condensed matter, in the breaking of the initial high symmetry of a homogeneous gas and in the formation of primary seed structures displaying the specific symmetry obtained in the final structure. Formation of a three-dimensional cluster breaks the initial high symmetry in the cluster formation zone. In the genesis of fullerene, C60 , for example, a lower symmetry cluster, pentagon or hexagon, displaying an axis of rotation of a higher order (5 and 6) is created. From the chemical point of view, the substance in the nanocluster formation zone is a random mixture of different low-dimensional carbon clusters (monomers, dimers, trimers, five- and six-membered rings, etc.) formed in the process of stochastic “sticky” collisions of carbon atoms in the carbon-ambient gas mixture. All of these clusters have a lifetime strongly dependent on the temperature. Generally, this lifetime increases with decreasing temperature. Simultaneously, the spatial amplitude of fluctuations decreases when the temperature falls to the critical temperature and below. The critical temperature is the characteristic temperature at which the particular structure begins to stabilize and becomes rigid [88]. The jump in the order parameter (a singularity), which manifests the appearance of a new symmetry, also occurs at this temperature. The free energy of a newly formed cluster at T < Tc must include, in addition to thermal energy, the internal (strain) energy which is absent from a totally disordered state. The configuration entropy of a cluster also characterizes its particular structure. The minimization of the free energy determines the critical temperature for the defect-mediated phase transition from a disordered gas phase [89, 90] or, for the case considered here, the optimum temperature for nanocluster formation. This critical temperature, or rather optimum temperature for nanostructure formation, was found experimentally: for carbon nanotube formation this temperature is approximately 1200–2000 K [29, 40, 43]. For fullerene formation this temperature as seen in molecular dynamics simulations [91] lies in the range of 2000–3000 K. The formation of three-dimensional carbon clusters can be understood in terms of a phase transition from a disordered to an ordered phase by the introduction of a specific defect assembly or seed with a new structure. In the case of fullerene formation, it is associated with the appearance of pentagon-shaped, or five-wedge, disclinations. This is similar to the conventional scenario seen for disorder–order transition phenomena in the growth of crystalline structures [88, 89]. The appearance of a disclination—a singularity in order parameter—in a hot mixture of unassociated carbon atoms echoes arguments presented by Anderson that “the fluctuations do become of quasi macroscopic size and

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dimension at the critical point


” [88]. The defect in this context is a means for replacing the symmetry of an initial phase with that of a new one. We should note that most of the studied threedimensional carbon clusters display very complicated internal structure. For example, fullerenes and fullerene-like structures are embedded with pentagons, which are units relevant only to surfaces of positive curvature. It is likely that carbon clusters, which include surfaces with negative curvature where heptagons are the responsible topographic elements, have also been identified experimentally [37].

5.2. Electronic and Structural Properties of Individual Nanoclusters Many intrinsic properties of a particular bulk material, become dependent on the size of a system when the cluster size decreases to several nanometers. The thermodynamic and electrodynamic arguments which apply to the infinite system (when one can ignore boundary effects) become invalid for the description of the properties of very small particles. The unique features of nanoclusters are directly related to their small size. That size lies between the atomic size and the macroscopic dimensions of many particles in a bulk structure. There are at least two main consequences for the physical and chemical properties resulting from size. First, a nanocluster is a system of many, but a limited, number of particles, say 10–104 , and behaves as a large atom with discrete energy levels. Second, accompanying a decrease in cluster size, the ratio of the surface to volume increases. In this case, the surface phenomena dominate the electronic and optical properties of a cluster. For example, in a cluster containing 1000 atoms, about a quarter of the atoms lie close to the surface, suggesting that these atoms may strongly influence the cluster properties.

5.2.1. Critical Cluster Size It is crucial for understanding the properties of nanoclusters to know at what cluster size (or at what number of atoms in a cluster) the material properties of an atomic system approach those of the bulk structure. Moreover, it is important to understand if all the material properties are changing at the same critical “threshold” size or if different properties change at different cluster sizes. It was theoretically predicted [92] that small metal clusters (n < 10) would have a face-centered cubic (fcc) structure, while in bulk, the structure is body-centered cubic (bcc). It was observed later on [93] that a structural evolution from amorphous to fcc, and subsequently to bcc, structure occurs in tungsten when the number of atoms in a cluster increases, in agreement with Tomanek et al. [92]. The critical cluster size for metallic chromium nanoclusters is determined to be 490 ± 100 atoms, and for Mo nanoclusters it is in the range of 1460–3900 atoms for the cluster–bulk transformation in a structural sense to be completed [94]. The surface-to-volume ratio is huge for small clusters and therefore the surface energy contribution dominates in the total cluster energy. The fcc structure is more compact than the bcc and thus provides a lower surface energy and overall lower total energy

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of a cluster. As will be shown in the next section, the critical cluster size appears to be different for different materials and for different properties.

5.2.2. Size Effects Quantum Size Effects A system of particles in a finite volume has discrete energy levels. In general the distances between energy levels decrease exponentially with increases in the number of particles. In bulk, the interference of electronic wave functions results in a band structure. However, at the opposite limit, when the size of the system decreases to the nanometer scale, the energy bands split again into energy levels. For example, the difference in energy between the electronic levels, , in a small metal cluster increases in inverse proportion to the size of the cluster, R, as  ∼ F /R, where F is electron Fermi velocity [95]. If the applied electric field is small in comparison to the interatomic field eER ≪ , and the frequency of the external field complies with condition  ≪ F /R, then the small metallic particle behaves in such a field like an atom with a certain polarizability. A moderately small cluster possesses a larger polarizability than that following from the classical polarization of a metal sphere. Size-dependent photoluminescence of silicon nanoclusters has been observed experimentally where the cluster size ranged from 1 to 3.5 nm [83, 84]. Analysis of the internal structure of the silicon clusters using high-resolution transmission electron microscopy (HRTEM) revealed that clusters had a crystalline structure and nearly spherical shape [84]. When the cluster sizes were decreased from 3.5 to 1 nm, the peak in the luminescence spectrum shifted from 750 to 300 nm. Neutral silicon clusters ranging in diameter from 1 to 20 nm were produced by laser ablation of a silicon target in an ambient atmosphere of helium at a pressure of 8 Torr and extracted into a vacuum as a cluster beam. The cluster beam was then scattered by an argon beam flowing in a direction perpendicular to the cluster beam. Clusters of different sizes were deposited onto substrates positioned at different distances from the axis of the cluster beam. On the substrate placed directly on the beam axis, spherical isolated clusters with a mean diameter of 10 nm were deposited. The average size of the clusters decreases as the distance from the axis of the cluster beam increases. The nanocluster films exhibit a strong red photoluminescence after being exposed to air. The energy of the photoluminescence peak changes between 1.42 eV (845 nm) and 1.72 eV (700 nm) depending on the substrate position: the farther from the cluster beam axis, the higher the energy. Wu et al. [96] relate the observed energy shift to the quantum confinement of carriers in surface-oxidized silicon nanocrystals. A blue shift in the energy of the photoluminescence peak, of up to 2.1 eV, in surface-oxidized porous silicon quantum dots was also observed by another research group when the size of the dot decreased from 3 to 2 nm [97]. These observations qualitatively comply with the effect of increasing the distance between the energy levels while the cluster size decreases. Note that such a luminescence has not been observed in bulk silicon.

799 Formation Energy It was experimentally determined that the energy for the formation of individual clusters depends on their size and shape. Tin nanoclusters containing from 95 to 975 atoms were formed by laser ablation of tin in a helium atmosphere [98]. For one type of tin clusters it was found that the formation energy was proportional to (1.64 ± 0.04 eV) × N −1/3 , indicating compact spherical-like shapes. Another class of clusters had almost constant formation energy of 0.4 ± 0.05 eV. The theory developed for elongated neutral silicon clusters indicates [99, 100] that the surface-to-volume ratio of in these clusters is constant, which indicates that the formation energy was independent of size. It was suggested that the second type of cluster has a quasione-dimensional geometry. Thus, in the first type of cluster, the surface energy changes with the change in the number of atoms in the cluster, while in the second cluster type, the contribution of the surface energy to the total cluster energy is the same for clusters of different sizes. The experiments [98] clearly demonstrate the strong influence of surface energy on the formation energy of a cluster: the smaller the cluster is, the easier it is to form. Melting Temperature: Solid-like to Liquid-like State Transition It has been demonstrated both experimentally and theoretically that the melting temperature of nanoparticles and nanorods is significantly lower than that for the bulk material (see, for example Wang et al., 2002 [101] and references therein). The melting point of platinum nanowire was found to be 400  C [102] (the bulk value 1772  C), while the melting temperature of 4.6-nm-thick palladium was 300  C, which is drastically lower than the bulk value of 1552  C [103]. Through molecular dynamic simulations [101], the melting temperature of gold helical cylindrical nanowires was found to be ∼1100 K, that is, lower than the bulk value of 1357 K, but higher than that of gold nanoclusters. Usually equilibrium melting starts from the surface and then propagates into the interior. Surface atoms have the fewer nearest neighbors and weaker binding, which may lead to a lower melting temperature at the surface than that for the bulk. Large surface-to-volume ratios and quantum size effects are the two major factors believed to be responsible for this dramatic decrease in the melting temperature of nanoclusters compared to the bulk value. In contrast, it was found that the interior melting temperature in gold nanorods appeared to be lower than that of the atoms on the surface. Melting starts from the interior atoms, while surface melting occurs at relatively high temperature. This unique thermodynamic behavior, compared to the above description, is closely related to the helical structure of the nanorod. In this case, surface melting is responsible for the overall melting of the structure, and the effect of higher interior melting temperature entirely relates to the complicated internal structure of a rod [101]. The transition from a solid-like to a liquid-like state for finite systems, where the surface and boundary effects are dominant, is not as well defined as that for a bulk solid. The transition may exhibit the intermediate state of the coexistence of different structural phases (isomers) of the same cluster [104]. The solid–liquid phase transition in a system with a finite number of particles is described in terms

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800 of a potential energy surface [105]. Stable clusters correspond to minima on the potential energy surface. If a cluster acquires sufficient energy, the transition from one isomeric form of a cluster to another corresponds to a “jump” over the saddle-like potential barrier separating the minima. The more liquid-like a cluster becomes (the higher the temperature and internal energy), the shorter the time for a transition from one isomeric form to another. One can define the transient state as a state when the lifetimes for the different isomeric forms of a particular cluster become comparable [104]. The lifetime of cesium halide clusters with different spatial arrangements of constituent atoms were observed using temperature-dependent photoelectron spectra and applying the pump-probe technique [104]. The clusters were produced in a laser vaporization source. A plume of laser-ablated cesium halide vapor was swept through a temperature-controlled nozzle by a flow of helium. The clusters were formed through helium–vapor interaction and then mass selected using time-of-flight mass spectrometry. The anions of desired mass were directed into a magnetic bottle, where the electrons were then detached by the action of 1- to 2-ps-long probe laser pulses, and the electron spectra were measured. Three different isomers of cesium halide consisting of four cesium atoms and three iodine atoms were identified: cube, flat ladder, and ring. The transition between these structures proceeds in the following succession: cube → ladder → ring. At a temperature ∼500 K, the lifetime for all three isomers become of the same order of magnitude of several tens of picoseconds. Therefore this temperature can be considered the cluster melting temperature: at this temperature all three isomers are continuously transforming to each other, thus making any particular structure indistinguishable, as in a liquid drop. From the measurements, the time for this phase transition to occur was estimated to be in the range of ∼100 ps. One may note that the melting temperature for the bulk cesium halide is 900 K. Adsorption Energy Two other important microscopic parameters, which depend on the cluster size, are the adsorption energy and the bond distance of single atoms on surfaces. The adsorption energy, or energy of an interaction of an ad-atom and the surface, increases as the number of atoms decreases. Conversely, when the number of atoms in a system increases, this energy converges to the final constant value corresponding to the bulk solid [106]. For example, the adsorption energy for a copper atom on a four-atom copper cluster comprises 3.6 eV, whereas the adsorption energy saturates at 2.7 eV for clusters with a number of atoms larger than 56 [106].

5.2.3. Dielectric Function for a Single Metal Cluster The qualitative dependence of the dielectric function of a single metal cluster on its size can be understood on the basis of simple arguments of general physics. Let us assume that the dielectric function for the metal cluster in an external electric field with frequency  has the same form as the

function for a conventional metal, for example, having the Drude form [63]: =1−

2pe   + ieff

here pe = 4e2 ne /me 1/2 is the characteristic electron plasma frequency, ne , me are the electron number density and electron mass, respectively, and eff is the effective frequency of electron collisions with the lattice, which is responsible for the energy dissipation. We assume that the cluster of radius R contains N atoms of a metal with one conductivity electron per atom. One can reasonably suggest that all conductivity electrons fill the whole volume of the cluster homogeneously like a jellium [2, 107, 108]. The electron number density can be expressed as ne = Ne/ 4/3R3 , thus giving the dependence of the plasma frequency on the cluster size. One can see that the energy dissipation of an external electric field imposed on a small cluster also depends on the size of the cluster. Indeed, in a nanometer size metallic sphere, the mean free path of an electron between collisions significantly exceeds the cluster diameter lmfp ≫ R. Therefore, the electron can loose its energy only in collisions with the cluster. The characteristic frequency of this process is proportional to F /R. Hence, the effective frequency of energy dissipation is eff ∼ AF /R, where A is a dimensionless proportionality coefficient. It was shown that the classically derived 1/R law also follows from quantum mechanical calculations (see the thorough discussion of this problem and references by Krebig and Vollmer (1995) [107]). It appears that this law represents a fundamental quantum size effect; it also reflects the surface-to-volume ratio. These simple relations show how the optical properties of metal nanoclusters can be controlled by their size, which suggests many applications. We should note that the dielectric function of a single isolated cluster has not yet been determined experimentally.

5.2.4. Static Polarizability of a Single Metal Cluster From the viewpoint of classical electrodynamics [63], a metal sphere in an external static electric field E acquires an induced dipole moment P = R3 E, which is proportional to the volume of the sphere. However, close consideration of the dipole moment even in frames of a simple jellium model shows that electrons are spilled out of the cluster boundary (defined as R ∼ N 1/3 ) at a distance *, depending on the nature of the metal. Usually, this distance is * ∼ 1
3– 1.5 Å. Thus, the nanocluster dipole moment is expressed as P = R + * 3 E. These estimations, in the frame of a simple jellium model, are well supported by quantum mechanical calculations [107]. The important conclusion follows that the small metal sphere possesses a polarizability larger than that predicted by classical electrodynamics due to the effective increase in the cluster radius caused by spilling out the electric charge. The change in polarization can be controlled by the size of the particle. This effect was observed experimentally [2] with reasonably good agreement with the theory.

Nanostructures Created by Lasers

5.2.5. Shell Model for a Simple Metal Cluster The abundance mass spectra of alkali metal clusters produced and detected by Brack (1993) [108] revealed a striking feature: clusters with a particular mass value, containing a specific number of atoms—“magic numbers”—appeared to be much more abundant in comparison to the average mass of the clusters produced. It is established now that this characteristic abundance pattern holds up even for clusters containing several thousand atoms [2, 108]. It was recognized that the abundance pattern reflects the electronic structure of the cluster and is indicative of the most stable clusters. Clusters of metal atoms are considered a unified edifice having a common electronic structure, with all valence electrons belonging to all constituent atoms and filling corresponding shells that are characterized by specific quantum numbers for such an edifice as a whole. Therefore, maxima in the mass abundance spectra have been identified as clusters with closed electronic shells. Just as for atoms, the electronic system of a cluster with exactly the right number of electrons to complete a shell is very stable. If one more atom is added to a cluster with a closed shell, the valence electrons of this extra atom will occupy the higher energy state, and hence the stability of the new cluster is reduced. The reduced stability is reflected in reduced abundance, which explains the experimentally observed drops in the cluster abundance spectra after each shell-closing number [2]. The theory also predicts that closed-shell clusters have a spherical shape, while open-shell clusters are significantly distorted. Molecular dynamics and quantum chemical calculations later supported the initial simple theories, revealing fundamental physical features of the shell model. The theory of the cluster shell model is now well developed, with many predictions experimentally confirmed (for comprehensive review, see de Heer (1993) and Brack (1993) [2, 108] and references therein). While it is difficult to determine the cluster size and shape experimentally, through measurements of the optical properties of the clusters it is possible to make some conclusions about the influence of shape on the properties of the clusters.

5.2.6. The Affinity between the Internal Structure, Material Properties, and Formation Conditions of Nanoclusters The discovery and studies of new nanostructured carbon phases, such as fullerenes [19, 51] and nanotubes [20, 21, 56], has opened a new era in materials science. It has been discovered that minute changes in the spatial arrangement of carbon atoms in the space scale of tens of angstroms can profoundly change the electronic properties of these systems from a semiconductor to a metal [110, 111], from a conductor to a superconductor [112, 113], and even from diamagnetic to ferromagnetic [114], with a drastic difference from the bulk properties of graphite, diamond, or amorphous carbon. One could expect that structural rearrangements at the nanometer scale might also change the properties of other materials in ways similar to those with the carbonaceous structures. To date thorough studies have been performed with carbon nanoclusters. Below we concentrate on structural and material properties in connection with the relevant

801 formation conditions of carbonaceous clusters and clustered films. Laser ablation was used to generate carbonaceous nanoclusters under different experimental conditions: in the ambient gas at different pressures; with additional gas heating; and with different catalysts. A broad variety of different nanostructures have been created which now form the family of “fullerenes.” This family includes single-shell fullerenes, C60 and Cn [19], multiwalled hollow nanoparticles (fullerene onions), single-wall and multishell carbon nanotubes [20, 21, 29, 56], hypothetical carbonaceous structures with negative curvature [115–118], carbon nanohorns [119], and carbon nanocones [120]. Both the nanocluster formation energy and kinetic factors define the formation conditions and therefore the abundance of the particular nanocluster [118, 121]. The primary product of the interaction between the laser-produced plume and a noble gas is a complicated network of different nanostructures mixed together and interconnected. In order to study the individual nanotubes the meticulous processes of separation and purification of the primary material are used [21]. Another method of cluster selection and separation is to preionize the clusters using a special short-wavelength laser and then to selectively remove clusters with an applied electric field [2, 3, 45, 122]. Cage-like Structures A plume of carbon atoms and ions ejected during the laser ablation of a graphite target was made to interact with a noble gas buffer [45, 122]. Carbon clusters created in such an interaction were then detected by a mass spectrometer. The measured abundance spectra may be regarded as an accumulated “snapshot” of salient features in the nucleation and growth of carbon clusters in a time sequence. A typical mass spectrum of positively charged clusters is bimodal [45, 122]. The peaks in the mass abundance spectra correspond to clusters of enhanced stability. The maximum in the first group of clusters (n < 30) corresponds to clusters comprising 11 carbon atoms, while the maximum in the second group (30 < n < 100) relates to the famous fullerene, C60 , molecule consisting of 60 carbons [19, 122]. Any closed-shell-like exclusively carbon cage is referred to as a fullerene [123]. The fullerenes are viewed as graphitic sheets distorted by inclusions of topological defects, such as five-membered rings, or pentagons. The simplest ball is a pentagonal dodecahedron comprising 20 carbons. The appearance of a pentagon is the signature of a curved surface with positive Gaussian curvature. C60 , which is the most stable, and central to the fullerene family, consists of 12 pentagons and 20 hexagons. The range of clusters is composed of one- and twodimensional structures (linear and ring clusters, n = 3–20) along with three-dimensional clusters, like the closed cage of the fullerene molecule. Multiwalled hollow nanoparticles (nested fullerenes or onions) can be also formed under similar conditions [123]. All these clusters are formed in an almost homogeneous mixture of carbon and noble gas atoms at pressures of several hundred Torr and temperatures of 1000–2000 K. The estimates of the scale of the temperature for fullerene formation may be made from the self-energies of nanoclusters [118, 121]. The additional energy that it is necessary to spend for fullerene formation, in comparison

802 to the flat graphite sheet, ranges from 0.6 to 0.4 eV/atom [118, 121]. This means that the optimum temperature for the formation of such clusters can be in a range of several thousand degrees Kelvin. This estimate qualitatively complies with the experimental measurements. The relative population of a particular cluster is governed by cluster growth kinetics. In turn these kinetics depend on the transient partial number density of carbon atoms in the carbon–noble gas mixture and the transient temperature in the cluster formation zone. Therefore, one can conclude that under isotropic conditions, no cluster of preferential symmetry can be formed but only the simple clusters, or clusters with a high symmetry of the order 5 and 6, like fullerenes. Carbon Nanotubes Another carbon nanocluster, the nanotube, is also produced by laser ablation at high pressure in an almost homogeneous mixture of carbon atoms, noble gas atoms, and a metal catalyst at a temperature of around 1000–2000 K. The required optimal ambient gas pressure was found to be around 500 Torr for the formation of carbon nanotubes, while at 100 Torr the efficiency of carbon nanotube formation was drastically reduced. Carbon nanotube can be imagined as a graphitic sheet rolled up and stitched without seams. Therefore, nanotubes consist entirely of sixfold rings, hexagons. The straight nanotube possesses an axial symmetry, which is apparently absent in the zone of formation. However, it was observed that carbon nanotubes formed in a homogeneous carbon–noble gas mixture were only formed in the presence of metal catalysts at a concentration of ∼1% of the total carbon content. These catalysts are usually transitional metals, such as cobalt, iron, or nickel or a mixture of them. Thus, there is strong experimental evidence that a catalyst is responsible for the formation of axially symmetric structures. It may be that catalytic particles are either atoms or metallic clusters containing many atoms; however, there is no thorough theoretical explanation of catalyst action in the formation process. Nanotubes in general are helical, meaning that the tube is twisted around its axis. In the spirit of defects and energy arguments, one can assume that tubules grow helically with the introduction of a screw dislocation, as metal “whiskers” grow [113]. The theory shows [110, 111] that a chiral tube can be generated in such a way that no distortion of bond angles is introduced. This distortion relates only to the cylindrical curvature of a tube. Helicity is responsible for one of the most striking properties of nanotubes. Depending on chirality one third of the tubules will be metallic and two thirds semiconducting. The existence of metallic and semiconductor nanotubes has been observed experimentally [124]. Raito et al. [111] have suggested that a large fraction of metallic tubules might be formed if the initial seed for the tube cap is centered around a pentagon. However, the proper conditions for the preferential formation of such seeds needs to be formulated. These properties imply many important applications in the future. For example, one can imagine nanometric conducting wires, microscopic metal– semiconductor devices for nanoelectronics or photonics, and many other possibilities. Nanotubes also possess extraordinary strength, with the highest Young modulus of all known materials. This was deduced from the observation of temperature vibrations of freestanding tubes in a transmission electron microscope [125].

Nanostructures Created by Lasers

It follows from molecular dynamics calculations and a simple elasticity approach [118, 121] that the energy necessary for the formation of tubes consists entirely of the energy required to bend a graphite sheet into a tube, which is ∼0.2 eV per carbon atom. Comparison to the fullerene selfenergy implies that the tubes are more stable than fullerenes. Another conclusion is that the temperature required for nanotube formation may be somewhat lower than that for the creation of fullerenes and may be around 2000 K, which qualitatively complies with the experimental data presented in Section 2. Structural Units of Carbon Nanofoam According to theoretical predictions [115–118], hypothetical carbonaceous structures with negative, or hyperbolic, Gaussian curvature, branded “schwarzite,” are more complex than fullerenes (elliptic curvature) and buckytubes (parabolic curvature). Sevenfold rings (heptagons) are the topological elements (disclinations) responsible for the generation of schwarzite structures. The exact shape of a single negative disclination is not yet known; however, calculations show that heptagons, in terms of local structure, are energetically less costly (more stable) than pentagons, with the self-energy per carbon in a range of 0.1–0.15 eV/atom [118, 121]. This also means that the temperature conditions for hyperbolic structure formation may be close to those for carbon nanotubes. It has been suggested that the complicated spatial structure of schwarzites might result in unusual electronic properties. Recently, low-density cluster-assembled carbon nanofoam was produced by laser ablation of glassy carbon in an argonfilled chamber at a pressure range of 0.3–1 Torr [37, 114]. Diffusion-limited aggregation of carbons in the carbon– argon mixture and the subsequent fast quench resulted in a unique, fractal, all-carbon foam deposited on a substrate. Preliminary studies revealed the presence of a hyperbolic schwarzite structure, rather than the expected nanotube-like structures. The foam structure was characterized by scanning electron microscopy, transmission electron microscopy, HRTEM, small-angle X-ray scattering, Raman spectroscopy, EELS, Rutherford backscattering, and surface-area measurements [37, 54, 114]. These studies revealed that the foam is made of a web-like fractal network of randomly interconnected clusters, 6–9 nm in diameter, as can be seen in Figure 8. HRTEM images demonstrated that individual clusters possess an internal periodic structure with a period of ∼5.6 Å. The spatial variation of sp2 /sp3 bonding across a single cluster was mapped using a PEELS with a spatial resolution of 1 nm [37]. These results indicate that sp2 -bonded carbons prevail in the core region of clusters, whereas sp3 bonded carbons dominate near the cluster boundary. The measured high dc resistivity of the foam suggests that these sp3 -bonded carbon atoms are responsible for sticking the clusters together. The most salient property of the foam is its unusual magnetic behavior. The freshly produced foam is strongly attracted to a permanent magnet, just like a metallic dust, which demonstrates the existence of an intrinsic positive magnetic moment. Only the structural rearrangement of carbon atoms in the foam can be a reason for the dramatic change in the magnetic properties of this all-carbon system. Electron spin resonance measurements gave the density

Nanostructures Created by Lasers

10 nm

100 nm

Figure 8. Transmission electron micrograph of carbon nanofoam (left) showing that the foam is assembled from 6-nm clusters. The SEM image (right) shows the web-like structure at lower magnification.

of unpaired spins up to 1.5 × 1020 spins per gram, or one unpaired spin per several hundred carbon atoms. The ferromagnetic behavior exhibited by the new phase of carbon is extremely unusual in comparison to all known allotropes of carbon. Graphite, diamond, fullerenes, multiwalled carbon nanotubes, and single-walled carbon nanohorns possess a diamagnetic susceptibility in the range of −10−5 –10−6 emu/g. It seems natural to suggest that the observed ferromagnetic behavior can be traced to the complex microstructure of the foam. The origin of magnetism in cluster-assembled carbon foam has been theoretically studied using a geometry which contains hyperbolic, negatively curved surfaces [114]. The basic structural unit is a tetrapod that exhibits many of the structural features observed in experiments. The core structure consists of warped sp2 -bonded carbon segments terminated by sp3 carbon atoms at the hydrogen-passivated edges of the four extremities. In a tetrapod, like in other schwarzite-related structures, tubular segments of 0 Gaussian curvature coexist with convex segments of hyperbolic, saddle-like regions of negative Gaussian curvature. The radius of curvature in this basic unit is close to 6 Å, which is consistent with the superstructure found in the diffraction pattern. The tetrapod-like building blocks can be assembled into a rigid foam structure with a very low density that compares to the measured density of 2–20 g/cm3 . The threefold

803 coordinated carbon atoms in the sp2 regions form a network of hexagons and heptagons only. These trivalent carbons are sterically protected within the system of single and double bonds imposed by the sp3 -terminated tetrapod and occur in groups of three. The number of unpaired spins was found to be robust with respect to size and boundary shape variations within the tetrapod. However, this number depends sensitively on the bonding topology in the regions of the negative Gaussian curvature. Subclusters (tetrapods) containing 264 and 336 carbon atoms have been considered, and the predicted magnetic moment in a C264 tetrapod agrees well with the experimental observation. This is the first time to our knowledge that trivalent carbon radicals embedded into hyperbolic surfaces have been identified in an undoped all-carbon nanocluster prepared under specific conditions by laser ablation. Stabilization of carbon radicals by steric protection has been known since the synthesis of triphenylmethyl by Gomberg in 1900 [126]. The ferromagnetism found in these complex nanoclusters occurs as a consequence of nanometer-sized conducting segments containing atoms with different electronic configurations. It appears that a careful preparation of conditions for nanocluster formation by laser ablation may lead to similar changes in the structural and electronic properties of different materials. Fractal Nanoclusters Nucleation of a new phase is one of the processes where the fractal nature of the object often manifests itself. The generally accepted models for cluster growth include diffusion-limited aggregation, cluster–cluster assembling, homogeneous nucleation by monomer addition, and others. All the models assume that the nucleus, the seed of the new phase, has a spherical shape on which the further assembling of the structure occurs. Experimental evidence has been presented by Zenkevich et al. [127] which shows that gold clusters of ∼5 nm in diameter have a fractal structure with fractal dimension of D = 1
33 ± 0
08. These clusters were deposited on the surface of highly oriented pyrolitic graphite by laser ablation using an Nd:YAG laser with the following parameters of ablation:  = 1
06 m; 15-ns pulse duration; 25-Hz repetition rate; average intensity ∼109 W/cm. The authors [127] suggested that the shape and dimension of the clusters are determined by the rate at which atoms arrive at the surface where the formation occurs and by the symmetry of this surface. It was proposed that the formation of clusters proceeds under highly nonequilibrium conditions by the attachment of an ad-atom to the fractal nucleus.

6. CLUSTER-ASSEMBLED MATERIALS With the laser technology that is currently available, it is possible to ablate any existing material—refractory metals, complex composites, and dielectrics—if the laser parameters are chosen according to the properties of the material. The proper choice of laser parameters and conditions in the experimental chamber (pressure of the ambient gas or vacuum) defines the mass distribution in a cluster flow. The size of the clusters produced ranges from several atoms to tens of thousands of atoms per cluster. Clusters then can be deposited on a substrate to form a cluster-assembled film [3].

804 Films of clusters embedded in various codeposited matrices have been produced [128]. Very often such a film possesses material properties drastically different from those in the bulk of the initial material. Cluster networks can be classified into two categories [5]. The first one comprises clusters embedded in a host matrix and well separated from each other. The properties of such structures depend on the properties of the individual clusters and that of the host matrix. The dielectric properties of the cluster-embedded composites depend on low and easy-tochange filling factors (∼0.01 vol fraction of clusters) and on cluster-to-cluster contacts and connections. The second category includes cluster networks—sponge, froth, or foam-like structures—with properties which are drastically different from those of isolated clusters and which strongly depend on intercluster connections and interactions.

Nanostructures Created by Lasers

the beams was centered on C20 , C60 , and C900 . These films have a highly porous nanostructured morphology resulting from a random stacking of incident clusters. The density of the films is around 1 g/cm3 , which is much lower than that of conventional carbonaceous structures. The most interesting structure appears to be C20 “amorphous” film with a shortrange order of 15 nm, with pure sp3 hybridization and the absence of any long-range order. Similar films were produced with silicon cluster beams with the size distribution centered on Si50 . It is suggested that the presence of a large number of pentagons may significantly change the electronic structure of the clusters. These silicon films also have a granular structure and they are highly porous. The most unusual feature of these films is a strong visible luminescence at ∼750 nm comparable to that seen in porous silicon and recently observed in 3.5-nm silicon clusters [83, 84].

6.1. Cluster-Assembled Films The flow of nanoclusters hits a substrate and starts building a deposit. First of all we shall distinguish between cases when the cluster-assembled film grows on a substrate in a vacuum [3, 32, 33] and in a noble gas-filled chamber [37, 83, 84, 114]. Molecular dynamics simulations of film growth by energetic cluster impact in a vacuum have shown the influence of cluster energy on the morphology of the film [129]. It is now widely accepted that the energy of a cluster must be sufficiently low in order to prevent the splitting of a cluster during cluster–substrate impact. The straightforward idea of “random paving” on a substrate seems to be in contradiction to experiments: it appears that film morphology depends on the cluster size [128]. Indeed, gold, antimony, and silver clusters, comprising 250–300 atoms, 2 nm in diameter, form large branched and well-separated islands with definite long-range order when deposited on a graphite surface. The presence of an evaporation cell in the deposition chamber allows the production of films with clusters embedded into different matrices. Harbich et al. [130, 131] produced films of mass-selected metal clusters (Agn and Aun ) embedded in various solid matrices of Ar and Kr using this technique. Gold clusters, comprising 250–300 atoms, embedded in various matrices (SiOx , LiF, and MgF2 ) are randomly distributed over a film surface. It was demonstrated that the cluster volume fraction of Au clusters embedded into a SiOx matrix can be easily changed from 2 to 11% [128]. Therefore, films with variable dielectric function can be produced for a range of optical applications. Another interesting application relates to the deposition of transitional metal clusters onto different substrates to produce magnetic films for high-density memory devices and spin electronics. Films with the size-controlled clusters of iron, cobalt, and nickel have recently been produced [128]. The incident free cluster size distributions were centered on Fe150 , Co300 , and Ni300 . Cluster-assembled films with thicknesses up to 100 nm were produced. These films have a granular structure with a grain size of 3–5 nm, slightly larger than the size of the incident cluster size resulting from the diffusion and coalescence of clusters. Cluster-assembled films about 100 nm thick were produced with carbon cluster beams. The mass distribution in

6.2. Magnetic Properties of Cluster-Assembled Films Monodispersed cobalt nanoclusters, with cluster sizes varying from 300 to 9000 atoms, were produced by the clusterbeam technique [132]. These clusters were embedded in Cu and SiO2 substrates, where the cobalt volume concentration varied from 10 to 50%. The magnetization of cobalt in such structures is always lower than the bulk value. This magnetization increases with increasing cluster size and decreases with increasing Co concentration for a given cluster size. Calculations of intercluster exchange interactions are used to qualitatively explain the magnetization data as a function of Co concentration in good agreement with the experimental results [132].

6.3. Nonlinear Optical Properties of Cluster-Assembled Films It was found [133] that Si films deposited by laser ablation exhibit a nonlinear refractive index change, as high as n = −0
5 at a wavelength of  = 532 nm for films with an average thickness of 200 nm. These films consist of large droplets composed of crystallites with hexagonal wurtzite symmetry and with nanoclusters interspersed between them. The crystallographic symmetry of these droplets was observed with Raman spectroscopy, as well as linear and nonlinear optical measurements, when the films were annealed under various conditions. The authors attribute the large nonlinear refraction coefficient to the hexagonal wurtzite symmetry of the crystallites, which raises the possibility of developing very efficient nonlinear optical devices [133]. However, the origin of this nonlinearity is not fully understood.

6.4. Electrical Conductivity of Nanoclusters and Cluster-Assembled Materials: Quantum Charge Transport and Localization Another interesting property of the nanocluster-assembled system relates to electrical conductivity. It appears that the “conductivity quantum,” or conductivity scale of 2e2 /h, plays

Nanostructures Created by Lasers

an important role in the electric conductance through the “bottle necks” connecting the nanoclusters in the clusterassembled systems. Simple scaling illustrates the appearance of the “conductivity quantum” or “resistance quantum,” h/e2 , when one considers the charge transport at the atomic space and time scales. The motion of electrons with charge e, mass m, and number density n in an applied electric field E of high-frequency  generates the current density 2

j = en ≈

e n E ≡ E m v + i

This is Ohm’s law, where v stands for the electron collision frequency responsible for the energy dissipation (or resistance 1/). The full current, I = jS, flowing through the sample with a cross section S, and length L, and containing a total number of electrons N = nSL, can be presented in the form e2 N e2 N I≈ V E≈ mvL mvL2 We assume  ≪ v, which always holds for metals, and E ∝ V /L (where V is a potential). The resistance R, can be expressed as R≈

NV mvL2 = I e2

Considering all parameters at atomic scales, that is, taking the collision frequency as the same order of magnitude as the atomic frequency,   e2 /aB , and L  aB , where aB =
2 /me2 is the Bohr radius, one obtains the quantum unit of resistance as
R0 ≈ 2 e This unit comprises 2.5812 × 104 ohm. Most probably this value of conductance (resistance) separates two different regimes of high and poor conductivity, giving the percolation and localization regimes [134]. The conductivity in nanowires of atomic dimension behaves in the jump-like manner of quantum charge transport. The electrical conductivity of small silicon clusters (n = 1–10, 13, 20) placed between atomistic aluminium and gold leads has been investigated using the ab initio nonequilibrium Green’s function formalism [135]. All clusters display metallic conductance ranging between one and two quantum units, 2e2 /h. The transport properties of these cluster junctions may be understood in terms of both the band structure of electrodes and the electronic states of the cluster, modified by the lead environment and size effects. The resistance in this system is R ∼ R0 . Carbon nanofoam composed from well-defined carbon clusters of 6–9 nm in diameter, randomly interconnected in a web-like fractal structure, demonstrates a different limit case for conductivity [49]. The resistivity of the as-deposited foam, measured in the voltage range ±100 V, demonstrates nonlinear current–voltage characteristics with strong hysteresis. The resistivity of the foam after annealing is equal to 1–3 × 109 1/cm at room temperature and 1–10 × 1013 1/cm at 80 K, which is similar to that of amorphous diamondlike films. Thus, resistance of the foam exceeds R0 by many

805 orders of magnitude. One can assume that the electrons in a foam are strongly localized in nanoclusters, and the electron conductivity has a tunneling character.

6.5. Photoluminescence in GaAs Nanoaggregates Laser ablation of a single crystal GaAs target in a vacuum or Ar gas has produced nanoclusters of GaAs [136]. Atomic force and transmission electron microscopy have shown that most of the clusters were spherical, with diameters in the range of 1 to 50 nm, with a peak size distribution between 5 and 9 nm, depending on the Ar gas pressure or laser fluence. X-ray diffraction, solid state nuclear magnetic resonance, Auger electron spectroscopy, electron energyloss spectroscopy, and high-resolution transmission electron microscopy revealed that these nanoclusters were randomly oriented GaAs crystallites. An oxide outer shell of ∼2 nm subsequently developed on the surfaces of the nanocrystals as a result of transportation of the cluster in air. Unpassivated GaAs nanoclusters exhibited no detectable photoluminescence. After surface passivation, these nanoclusters displayed photoluminescence energies less than that of the bulk GaAs from which they were made. These experiments suggest an abundance of sub-bandgap surface states in GaAs nanocrystals. Thus, this kind of nanocluster with a surface layer demonstrates that a decrease as well as an increase can be achieved with transition from the bulk to the nanoscale level. Such changes in the photoluminescence energy were similar to that observed with silicon clusters [83, 84].

7. PERSPECTIVES ON LASER ABLATION FOR CONTROLLABLE PRODUCTION OF NANOCLUSTERS Laser ablation has proven to be an efficient and flexible tool for the production of a large variety of novel nanoclusters with remarkable properties. These novel nanostructures include fullerenes, carbon and boron nitride nanotubes, magnetic nanofoam, metal clusters, silicon clusters, and a variety of cluster-assembled films and nanofilms. It is clear that this is only the beginning; many different and complex clusters can be created and tested for future applications. Generation of nanoclusters by laser ablation is already a well-controlled process where the ablation rate, temperature and ionization states of the ablated atomic flux, and the conditions of the laser plume and ambient gas interaction can be controlled with high precision. Moreover, it is now clear that control over these processes in time and space can be significantly improved by the use of short laser pulses, as short as a few femtoseconds, and high repetition rate (up to hundreds of megaHertz) lasers. There are also some obvious extensions for the use of laser ablation for simultaneous coevaporation of several different targets for deposition of complex films or preparation of unusual composites and alloys. The same technique can be used for the preparation of multilayered systems consisting of nanometer-thick layers of different materials, which may be regarded as a one-dimensional analog of cluster-assembled films.

806 Nanoscience and nanotechnology are still in their infancy. However, one can easily foresee many short-term and longterm applications for nanoclusters and cluster-assembled structures. The obvious short-term applications for cluster networks are in catalytic devices, systems with unusual and variable dielectric properties, and layers with controllable heat conduction. However, there will be also many longterm applications for nanoclusters, for example, as part of future nanodevices for nanoelectronics, nanophotonics, and spintronics. We may also mention nanowires of carbon nanotubes, nanometric metal–dielectric junctions, and ultra-low-capacitance devices comprising one or several nanoclusters, Coulomb-blockade structures where one-byone passage of a single electric charge between two neighboring particles can be regulated. The pulse duration, the intensity on the target surface, and the repetition rate can be precisely controlled in laser ablation, so precise and improved control over the ablated vapor can be achieved. Using lasers one can control heating and annealing rates on a space scale of micrometers and a time scale of femtoseconds. This improvement in the control of cluster formation conditions leads to realization of the atom-to-atom attachment mode of nanocluster building, increasing the possibilities for control over the cluster size and the internal structure of a cluster. Laser ablation is also a route for creating metastable allotropes of known materials where the unusual internal structure determines new material properties such as were seen in conducting carbon nanotubes or paramagnetic all-carbon nanofoam. Laser ablation has demonstrated the highest deposition rate in the production of thin films, of ∼10 m/h [73, 75], and the highest rate of production of a nanofoam of 1 cm3 /min. If lasers can be made cost effective and manageable under industrial conditions, then the industrial production of nanostructures with the use of lasers is a distinct possibility in the near future. Indeed, there is still a “plenty of room at the bottom” and lasers will help to fill it with new and amazing nanostructures.

GLOSSARY Ad-atom An additional atom attached to a nanocluster. Adsorption Process of attachment of ad-atom to a structure. Atomized flow Plume or cloud of atoms created by laser ablation. Binding energy The energy necessary to separate atoms from a molecule. It equals to the energy of vaporisation per atom. Critical cluster size The cluster size (or critical number of atoms in a cluster) at which the material properties of a nanocluster approach to those for the bulk structure. Femtosecond, picosecond, nanosecond Time units, respectively, 10−15 s, 10−12 s, 10−9 s, used to characterise fast laser-matter interaction processes such as laser ablation and nanocluster formation.

Nanostructures Created by Lasers

Laser Abbreviation of the “light amplification by stimulated emission of radiation.” Modern lasers are capable of transformation of any of existing materials to atomic state. Laser ablation Removal of material from a surface by means of laser irradiation. The term ‘laser ablation’ is used to emphasize the non-equilibrium vapour/plasma conditions created at the surface by intense laser pulse, to distinguish from ‘laser evaporation,’ which is heating and evaporation of material in conditions of thermodynamic equilibrium. Nanoclusters, or Nanoparticles Aggregates of atoms or molecules containing between a few and a few thousand atoms that have properties drastically different from those in bulk. The size of nanoclusters is in the range of 1–100 nm (1 nanometer = 10−9 m). Nanoparticle behaves as a large atom with discrete energy levels. With a decrease in cluster size the ratio of the surface to volume increases, and the surface phenomena dominate the electronic and optical properties of a cluster. Nanocluster-assembled film Films formed by clusters of desirable size and mass deposited on a substrate, or film of clusters embedded in various co-deposited matrices. Nucleation An initial process of cluster growth (formation of nucleus or seed) inside an atomic mixture by aggregation of atoms and clusters. Quantum charge transport The jump-like behaviour of charge transport between the nanoclusters connected by a “bottle neck” that contains a few atoms. It can be associated with a motion of a few single charges. Quantum-size effects, quantum confinement The changes in electronic and structural properties as the size of the system decreases to the nanometer scale where quantum effects become dominant—the energy bands split into energy levels. Self-assembly Formation of nanostructures from an atomic mixture where atoms bond due to inherent tendency of molecules and molecular clusters to interact and organize themselves into structures. Shell model for cluster electronic structure The cluster is a unified edifice (somewhat similar to a big “atom”) having electronic structure with all valence electrons filling the common “shells.” Filled shells correspond to most stable clusters. Maximums in the mass abundance spectra correspond to the clusters having the closed electronic shells. “Sticky” collision Inelastic atomic collision resulting in bonding of atoms.

ACKNOWLEDGMENT The authors acknowledge Dr. D. Golberg for providing HRTEM photographs of single wall carbon nanotubes for the present review. The authors are grateful to S. T. Hyde, A. G. Christy, and D. Tomanek for many useful discussions, and to K. Gamaly for careful proofreading of the manuscript. E. G. G. acknowledges the assistance of the Australian Research Council under the ARC Centers of Excellence program through the Centre for Ultrahigh bandwidth Devices for Optical Systems (CUDOS).

Nanostructures Created by Lasers

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Encyclopedia of Nanoscience and Nanotechnology

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Nanostructures Within Porous Materials Y. Kumzerov, S. Vakhrushev Ioffe Physico-Technical Institute, St. Petersburg, Russia

CONTENTS 1. Introduction 2. Porous Structures 3. Methods for the Preparation of Nanostructures Within Nanoporous Matrices 4. Properties of Nanostructures Based on Nanoporous Matrices Glossary References

1. INTRODUCTION The experimental implementation of new effects in the physics of nanostructures relies upon our ability to create new types of structures and devices. Our understanding of material processing in the pursuit of ultrasmall structures is steadily advancing. Epitaxial growth and lateral microstructuring techniques have made it possible to create low-dimensional electronic systems with quantum-confined structures, that is, quantum wells, quantum wires, and quantum dots. Nanostructures can also be obtained by confining a solid or a liquid within nanometer-sized pores of various porous materials. There are a lot of materials that incorporate into their structure systems of voids (nanometer pores), and, what is more, we may say that virtually all materials have some porous structure if they are not single crystals. When we fill such a porous material with some substances, we may prepare some types of nanostructures. Systems with nanoparticles embedded in a porous matrix via chemical coating have received some attention in recent years. In this case, the confined liquid materials penetrate into the pores by means of wetting processes. In the case of nonwetting there is a possibility of using a mechanical coating of inner surfaces of porous materials by forcing a nonwetting liquid into the pores by external pressure. The material coating the inner surfaces of the pores in different porous matrices may be of interest as a physical object with characteristic ISBN: 1-58883-063-2/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

nanometer sizes, that is, some new types of nanostructures. We emphasize some advantages of such nanostructures: 1. It is possible to prepare nanostructures with a large range of characteristic sizes (from approximately 1 nm to approximately 200 nm). 2. It is possible to prepare nanostructures with various geometries (two-dimensional (2D) film-like structures, 1D wire-like structures, 0D small particle-like structures). 3. It is possible to prepare nanostructures from various substances (metals, semiconductors, insulators, etc.). 4. It is possible to prepare nanostructures with a very large amount of nanomaterial (up to several cubic centimeters). This situation permits the use of some experimental methods (e.g., neutron scattering, heat capacity measurements, etc.) that require a large amount of nanostructures. It seems that such nanoobjects are similar to the wellknown nanocomposite materials, used very widely nowadays, and in some situations it is not so simple to distinguish them. We mean that nanocomposites are rather 3D objects demonstrating new special properties owing to some interaction or combination of properties intrinsic to the nanoporous matrix and to a substance introduced into nanopores. In the case of nanostructures within nanoporous matrices, we are mainly interested in the properties of a substance in nanovoids and take into account the porous matrix virtually only as some external support for such a nanostructure. Recently there have been a lot of investigations (more than 500 in the past 10 years) that can be considered to be concerned with nanostructures of this kind. At the same time, there are no reviews describing various aspects of the physics of nanostructures within porous materials. The objective of this chapter is to fill the gap in the existing literature. This chapter is organized as follows. Examples of nanoporous matrices are presented in Section 2 with some descriptions of their porous structures, including characteristic sizes of nanopores, distributions of characteristic sizes of nanopores, relative volumes of nanopores, etc. Section 3

Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 7: Pages (811–849)

Nanostructures Within Porous Materials

812 describes some methods for the preparation of nanostructures within nanoporous matrices, including mechanical methods for which such a characteristic as wetting is very important, and some chemical methods, electrochemical methods, etc. Section 4 is devoted to various nanostructures based on nanoporous matrices and to physical properties of such nanostructures and possible applications.

2. POROUS STRUCTURES 2.1. Porosity The “porosity” of a solid material means the existence of some free volume inside its structure that is not occupied by structural elements of this material. Such a porous volume can be divided ambiguously into elementary porous structures—pores, which may differ in their characteristic sizes, types of shape, and types of connections. They may be organized as an open porous system as to be isolated. The possibility of having different chemical compositions, different structural units, and different origins of porosity leads to a very large diversity of porous structures. The porous structures can be conventionally divided, according to their genesis, into two large groups: systems based on a composition of some solid elements with porous space situated between these elements and those based on extraction of some part of structural elements due to decomposition, dissolution, or leaching from a bulk nonporous material. Examples of the first group are tissues, paper, granules of sorbents and catalysts, porous ceramics, crystals of zeolites and chrysotile asbestos, etc. Examples of the second group are dry hydrates of metals, carbonized and activated coals, porous glasses, porous membranes, etc. The general characterization of a porous system is determined by the characteristic sizes of its pores and by geometrical factors. There are porous systems with strongly regular alternation of identical pores connected through identical channels and those in which the characteristic sizes of pores, their arrangement, and connections are stochastic. The quantitative characterization of porous materials can be based on: 1. The porosity of a porous system
, which can be defined as the relative volume of the porous space, that is, the volume of the porous space, V0 , divided by the total volume V :
= V0 /V . The relative volume of the nonporous skeleton is in this case 1 −
. Occasionally, such a parameter as
/1 −
 is used to estimate the porosity. For the existing porous materials the value of
may vary between virtually 0 to approximately 0.9. 2. The characteristic sizes of pores, which reflect the typical effective sizes of cross sections of the empty porous space and are the most important parameters controlling the main processes in a porous medium. To have a simple parameter, the complicated form of the porous space can be reduced to the simplest geometrical figures with some equivalent parameters (spheres or cylinders with characteristic diameters, etc.). According to the regulations of the International Union of Pure and Applied Chemistry (UIPAC) porous materials are named according to their characteristic pore sizes: submicroporous (diameter less than 0.4 nm), microporous

(diameter in the range 0.4–2 nm), mesoporous (diameter in the range 2–50 nm), and macroporous (diameter exceeding 50 nm). 3. The size distribution of pores. This characteristic is often stochastic and can be determined through such a function as the density of diameter distribution f D, where f D dD is the probability of finding pores with diameters in the range of D to D + dD
in the unit volume of a porous material. Naturally, f D dD = 1. There is a more practically interesting function V D—the distribution porous volume over
2of the 2 diameters. V D = D /D f D dD, where D2 =
2 D f D dD. 4. The inner surface of a porous material, which corresponds to the area of the interface between the porous space and the skeleton of the matrix. It can be defined as the relative surface S, that is, the internal surface area per unit mass or unit volume of a porous material (measured in m2 /g or m2 /cm3 ). For different porous materials, S may vary between about 10−2 and about 103 m2 /g. Naturally, real porous objects mainly have irregular and stochastic systems of nonidentical voids with parameters that are very difficult to calculate. In this case, a usual way to describe them is associated with attempts to reduce the porous system to various geometrical models. A simple variant is to reduce porous materials to systems of spheres, modeling the skeleton of a porous matrix, in which the empty space between these spheres is modeling the real porous space. In the simplest case of identical spheres with regular packing, the needed parameters are only the sphere radius R and the coordination number n, characterizing the density of packing. In this case, the main parameters for a porous medium can be found as [1]


=

262  n

S = 31 −
R−1

(1)

Unfortunately, the simplest geometrical models cannot describe the topologically complex space of real, irregular porous matrices. A stronger description of porous systems of this kind was given in [2], where it the porosity itself was regarded as a fundamental random variable, because the value of porosity
or the pore size distribution is not sufficient to characterize the complex pore-space geometry. The characterization is based on analyzing the local geometry on a mesoscopic scale, and the local geometry around a lattice point R is defined as the intersection of the pore space and the primitive cell at R. To define the local porosity, the characteristic function of an arbitrary set A is introduced as A r = 0 if r lies outside the set A and 1 if r lies inside the set A. The local porosity
R L at the lattice position R is defined for length scale L as  (2)
R L =  MC r R LPS r dr where  is the density of Bravais lattice points; MC r R L is the characteristic function of the measurement cell at R, having size L; and PS r is the characteristic function of

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the porous space. The integration is done over the porous medium. To define the local porosity distribution function, let 
 R L measure the probability of finding the local porosity
in the range from
to
+ d
in a cell of linear dimension L at a point R. If the porous medium is homogeneous, must be independent of R, and 
 R L = 
 L can be named the local porosity density at scale L. The bulk porosity
∗ can be determined as an integral over the entire volume or as an average over a statistical ensemble of measurement cells,
and, assuming “ergodicity,” 1 we have
=
R L →  = 0

 L d
, independent of R and L. Higher-order distribution functions n 
1  R1 
2  R2  
n  Rn  L measure the probability density of finding
1 in the cell at R1 ,
2 in the cell at R2 , etc. at scale L. A set of such functions gives full information about the statistical properties of a porous medium at scale L. The local porosity distribution 
 L depends on L. There is an intermediate length scale , the porosity correlation length, at which the local geometries are relatively simple, but, on the other hand, the single-cell distribution function has sufficient nontrivial geometric content to be a good approximation. More precisely, is determined by a two-cell distribution function, 2 
1  R1 
2  R2  L, which depends only on the distance R in the isotropic case, that is,

2 = 2 
1 
2  R L. Namely,

2 =  R2 CR 0d 3 R / CR 0d 3 R , where CR L is the porosity autocorrelation function at scale L:   1  1 
1 −
∗ 
2 −
∗  2 
1 
2 RLd
1 d
2 CRL = 0



0

1 0

 
−
∗ 2 
RLd


(3)

The local porosity distribution can be defined as 
 = 
 , the single-cell porosity at scale . The important aspect of 
 = 
  is that it is measurable with modern image-processing equipment. The procedure for observing 
 in homogeneous and isotropic media measures this

function on photographic images of thin 2D sections across the porous space. The local porosity distribution contains a good deal of geometrical information about the pore-space geometry, and it is optimal in the sense that it contains the maximum amount of information based purely on the porosity concept. The second geometric property to characterize local geometries is whether or not the pore space percolates. Let 
 denote the fraction of percolating cells with local porosity
. 
 can be called the local percolation probability. The two functions 
 and 
 constitute only a partial and approximate geometric characterization of the pore space, but they have rich geometrical content.

2.2. Characterization of Porous Media For the pore sizes of the nanometer scale there is no unique method yielding full information about the porous structure. We need to use various methods to extract the whole body of information of interest [1 3 4]. The most essential of these are listed in Table 1.

2.2.1. Electron Microscopy This is the well-known method for the study of porous structures (see [3 4]), frequently used as an additional method because of the laborious procedure of sample preparation, especially in the case of transmission electron microscopy. This method gives in its simplest form direct information about the sizes and shapes of pores, and about their connections, but only in some local positions. For more complete information, several measurements are needed for varying and averaging the positions on a sample, as are the feature-counting measurements on electron micrographs. As an example of a study of this kind, mention can be made of the fact that the fractal geometry was confirmed for the porous space in sandstone with the use of scanning electron microscopy (SEM) with manual feature-counting in SEM images [5]. For the same purposes, an automated technique

Table 1. Information about methods for porous media characterization. Minimum characteristic size

Method

Information that can be obtained

1. Electron microscopy

Amount, volume, and distribution of pores. Internal surface area. The possibility to determine the closed pores. There is only local information.

≈0.5 nm

Total porosity Internal surface area Volume and distribution of pores, internal surface area

≈0.5 nm ≈0.5 nm ≈1 nm

Volume and distribution of pores, internal surface area

≈1 nm

Pore sizes, internal surface area. The possibility to determine the closed pores. Nondestructive method

≈0.5 nm

Volume and distribution of pores, internal surface area

≈2 nm

2. Methods based on porous structure filling with wetting materials a. Pycnometry b. Monolayer and multilayer adsorption c. Capillary condensation 3. Methods based on porous structure filling with nonwetting materials (mercury porosimetry) 4. Small-angle scattering of X-rays and neutrons 5. Methods based on NMR a. Relaxation time measurement for confined liquids b. Pulsed field gradient NMR

Pore sizes, internal surface area

Nanostructures Within Porous Materials

814 has also been developed for making SEM measurements [6] with image digitizing, filtering, counting of geometrical features as a function of feature sizes, and fitting feature histograms.

2.2.2. Methods Based on Filling of Porous Structures with Wetting Materials Pycnometry This method for studying porous structures [3 4] is based on a comparison of the densities of porous materials with empty and filled porous space. The pores in this method may be very easily filled with a liquid that wets the internal surface of the porous space (in the simplest case this may be water) and thereby can penetrate all open pores. The difference between the densities of a sample with empty pores and the same sample with filled pores gives the total porous volume for this sample if the density of the wetting liquid is known. Thus this method permits one to determine the total porosity of porous materials. Monolayer and Multilayer Adsorption A study of adsorption of various gases by porous materials is a source of important information about the internal surface of a porous space (see [3, 4, 7–12]). This process can be described by isotherms of adsorption, that is, by the dependences of the volume of adsorbed substance on the relative pressure at a given temperature. The substance most frequently used for adsorption in nanoporous materials is nitrogen at 77 K. A theoretical description of monolayer adsorption is based on a model developed by Langmuir [13], in which the isotherm looks like V /Vm = Bp/1 + Bp

(4)

Here V is the volume of condensed sorbate, Vm is the maximum volume corresponding to the inner surface covered with a monolayer of sorbate, p = P /P0 is the relative pressure, P0 is the saturated vapor pressure, and B is a constant. From experimental data, V = V p, it is very easy to determine first Vm and then S, the internal surface area of the porous space, if we know the characteristic sizes of molecules for the sorbate used. Brunauer et al. [14] developed this model for multiple-layer adsorption. The isotherm of adsorption corresponds in this case to the equation (the so-called BET equation) V /Vm = Cp/1 − p1 + C − 1p 

(5)

where C ≈ expQ/RT , Q is the heat of adsorption, R is the gas constant, and T is temperature. This equation, when written in the form p/V 1 − p = 1/Vm C + pC − 1/CVm , is very convenient for the approximation of experimental data, because the dependence of p/V 1 − p on p, which can be obtained in experiment, is a straight line, which permits one to determine the coefficients 1/Vm C and C − 1/CVm and then to calculate Vm and C. It was established that experimental data are frequently in agreement with the BET equation, especially at relative pressures p in the range from approximately 0.05 to approximately 0.35.

Capillary Condensation When p = P /P0 is more than approximately 0.75, the pore space is filled by sorbate not through multilayer adsorption but through capillary condensation. This results from a decrease in the saturated vapor pressure over the curved surface of the wetting liquid in a capillary in comparison with the saturated vapor pressure over the planar surface of the same liquid, which leads to condensation of wetting liquids in the pores at p < 1. The condensed liquid volume can be calculated with the Kelvin equation (see [8 9]) lnP /P0  = −4V cos /DRT

(6)

where  is the surface tension of the liquid, V is the molar volume of condensed liquid,  is the wetting angle (at full wetting  = 0 and cos  = 1), D is the pore diameter, R is the gas constant, and T is the temperature. The experimental dependence V = V P  can be used to calculate, with the Kelvin equation, the dependence of the characteristic porous volume on pore diameter. A more exact description of capillary condensation needs to take into account the thickness of adsorption layers and the dependence of the surface tension on the curvature of the liquid meniscus (see [9]). The adsorption and desorption processes also exhibit a hysteresis depending on the geometry of the porous space. Commonly, practical calculations use the simplest form of the Kelvin equation and the desorption branch of the capillary condensation hysteresis. Some examples of such a study are the following: [15] for xenon adsorption on silica gel; [16 17] for adsorption of Ar, N2 , O2 , C2 H4 , and CO2 on model mesoporous adsorbents MCM-41; and [18] for the adsorption of xenon on Vycor porous glass. Some models have been proposed for describing the adsorption hysteresis on the basis of Monte Carlo [19] and molecular dynamic computer simulation [19 20], the density functional approach [21], the lattice gas model [22], and percolation theory [23].

2.2.3. Mercury Porosimetry This method is based on the possibility of filling porous materials under high pressure with liquids that do not wet the surface of the porous space (see, e.g., [3 4 24]). Owing to the property of mercury that it will not wet most porous materials, it has frequently been used for these purposes, and this method has been named “mercury porosimetry” (some other materials can also be used, see, e.g., [25], where the Wood alloy was employed). The pressure needed for filling is the well-known Laplace pressure. In the simplest case (for full nonwetting, when the wetting angle  is 180 ) it can be written as P = 4/D (, surface tension; D, pore diameter). At this pressure the entire porous volume of pores with diameters exceeding D is filled with nonwetting liquid. From the experimental dependences of filled porous volume on external pressure it is possible to calculate the distribution of porous volume over diameters. P = 4/D can be written as 4F /D2 = 4/D (F strength). For a cylindrical pore with length L this expression can be rewritten as 4F L/D2 = 4L/D or F L = DL ≈ S, where F L is

Nanostructures Within Porous Materials

815

the mechanical work done by the piston pressing liquid into the pore and S is the total surface area of the cylinder. In this form the above equation reflects the process of mechanical energy transformation during the process of filling into the surface energy S of dispersed liquid and permits one to determine the total surface area of the porous space. When there is some distribution of pore diameters, the surface area of the pore space can be determined from the experimental dependence of filled volume on the external pressure V P  S = −1/



V max

0

P dV

(7)

2.2.4. Small-Angle Scattering of X-Rays and Neutrons X-ray and neutron scattering is a powerful technique for studying crystalline materials. For a given wavelength , the scattering angles  for a lattice constant d are determined by the Bragg condition n = 2d sin , where n is an integer. In porous materials, the characteristic lengths L ≫ d, and the scattering features are observed at small angles. For example, for ≈ 015 nm and 2 nm < L < 100 nm the typical angles  are in the range from 5 to 7 . A theory has been developed for describing the X-ray and neutron scattering at small angles (see [26 27]), and such a study is very informative regarding porous structures at the nanometer scale (see [3, 4, 28–30]). According to a theory for scatterers bounded by a smooth surface, the limiting form of the scattered intensity must be proportional to q −4 , where q = 4 −1 sin/2. Some deviations from this dependence have been observed for various porous materials (sedimentary rocks, lignite coals, silica aerogels, porous glasses) and attributed to the existence of fractals (for fractals, see [31]) in the porous structure of these materials (see [32–38]). A difference between volume and surface fractals was established. In the former case, the scattering intensity Iq ∼ q −Dv , where Dv is the fractal dimension relating the mass M to the characteristic length L as ML ∼ LDv for a sphere of radius L. In the latter case, the scattering intensity Iq ∼ q Ds −6 , where Ds is the surface fractal dimension which relates the surface area S to length as S ∼ LDs for a sphere of radius L. The conventional dependence Iq ∼ q −4 corresponds to Ds = 2, that is, to a 2D geometry of porous surface space.

2.2.5. Methods Based on Nuclear Magnetic Resonance Measurement of Relaxation Time for Confined Liquids Relaxation time measurements can probe the local surfaceto-volume ratio for a porous space and thus can determine the average pore sizes and pore distributions [39–41] (see, also [42]). In this method, the relaxation of magnetization with time is measured after the application of an appropriate pulse sequence to a porous sample filled with some suitable liquid. An increased relaxation rate (either transverse or longitudinal) caused by the interaction of the solid surface with fluid molecules near the surface is assumed for molecules within a certain distance from the surface. For the liquid within a single pore, there is a single relaxation time

1/T = 1/TB + s/v /TS , where 1/T is the longitudinal or transverse relaxation rate; 1/TB and 1/TS are, respectively, the corresponding relaxation rates in the bulk or within from the surface; s and v are the surface area and volume of the pore. For the entire sample the contribution of relaxation rates from different pores to magnetization decay can be written in the continuum form, At =





0

P D exp−t1/TB +  /TS m/D dD

(8)

where At is reduced magnetization which depends on the NMR signal Et At = 1/21 − Et/E for a longitudinal inversion recovery sequence and At = Et/E0 for a transverse pulse sequence E is the echo signal upon full recovery and E0 is that at zero delay time), P D is the pore size distribution function, D is the pore diameter, s/v = m/D (the constant m depends on the pore geometry). Inversion of the experimental magnetization data for practical purposes may permit calculation of the function P D. In [41], the experimental P D data determined in relaxation time measurements with various porous glasses were compared with the experimental results obtained with measurements by the adsorption method and mercury porosimetry. Pulsed-Field-Gradient NMR Pulsed-field-gradient (PFG) nuclear magnetic resonance (NMR) is a versatile tool for studying the transport of fluids in porous media [43–47]. The PFG NMR technique can reveal structural properties of the porous medium by measuring the molecular transport, that is, by monitoring the restricted self-diffusion of the molecules. NMR, combined with an additional spaceand time-dependent magnetic field, so-called pulsed field gradients (PFGs), offers an opportunity to generate labeled molecules and to detect their mean displacements related to any transport process (the labeling is due to the Larmor precession  of nuclear spins associated with the molecules). The Larmor frequency z t can be written as z t = −B0 + gtz, where B0 is time-independent uniform magnetic field parallel to the z coordinate, gt is an additional time-dependent magnetic field with a field gradient oriented parallel to the z direction, and  is the gyromagnetic ratio of the nuclei under investigation. In such a magnetic field, the complex magnetization density mr t gets an additional z dependence,   t m′ r t = mr t exp −iz gt ′  dt ′ 0

(9)

If the magnetic field gradient gt is turned off after a time , the magnetization density is found to be embossed with a z-dependent factor m′ r t = mr t exp−igz

(10)

This phase factor represents the labeling of the molecules observed in PFG NMR diffusion studies. A length scale lPFG = 2k−1 (k = g) can be introduced, over which a significant change in the phase factor and, hence, the labeling of the diffusing molecules are achieved. The selfdiffusion process of the molecules observed smears out the

Nanostructures Within Porous Materials

816 originally present spatial distribution of phases. Measurement of this phase distribution after an observation time  allows evaluation of the self-diffusion of the molecules. This process is caused by a second magnetic field gradient pulse after a time , which has to refocus the special phase distribution introduced by the first pulse. Owing to the displacements of the molecules, caused by self-diffusion, the refocusing is not complete. The NMR signal observed, which follows from integration of the magnetization density over the sample volume, is reduced by the factor k  =



P z − z  expikz − z′ dz − z′ 

in comparison with the signal measured without a pulsed field gradient (P z − z′  ) denotes the probability density that a molecule is displaced by z − z′ within a time interval ). P z − z′   is given by the inverse Fourier transform of the NMR signal attenuation [48] and contains information about the geometrical features of the pore space, which affect the molecular motion of the pore fluids [49– 53]. The power of PFG NMR as a tool for the investigation of porous systems is based on the fact that lPFG and k can easily be controlled by choosing the appropriate values for the pulsed field gradient intensity g and width . lPFG values of less then 0.1 m (required, e.g., for 1 H NMR with  ≥ 1 ms and g ≥ 20 T/m) can be achieved with the current state-of-the-art PFG NMR spectrometers [54].

2.3. Porous Matrices 2.3.1. Matrices with Irregular Porous Structure Porous Glass A porous silica glass can be defined as a bicontinuous random structure of two interpenetrating percolating phases, namely the solid and the pore networks. The pores in the glasses are connected to each other, and the pore size distribution is narrow (see Fig. 1). Porous glass is available in standard forms such as tubing, rods, and sheets. It is mechanically hard and strong, nondusting, nonflaking, and chemically inert (for its physical and chemical properties, see [55–62]). The preparation methods and properties of various types of porous glasses are summarized in [63]

(see also [64–77]). Porous glass is often used for the filtration and separation of compounds. The open-cell network allows permeability on a selective basis—the species must be smaller than the microscopic pores to pass through a porous glass. A porous glass matrix can also be used in nuclear waste storage [78, 79] and optical applications [80]. The present status and future potential for porous glass applications are reviewed in [81]. The homogeneous pore diameters can be controlled to be, on the average, between 40 and 500 Å. A typical example of porous silica glasses is Vycor glass (Corning vycor brand 7930 [82]). Its standard chemical composition is as follows: 96% SiO2 , 3% B2 O3 , 0.40/a Na2 O, R2 O3 ± RO2 < 1% (R = mostly Al2 O3 and ZrO2 ). Its physical characteristics are given in Table 2. For Vycor porous structure, see also [29, 36, 37, 75, 83– 89]. Such a structure is obtained as a result of spinodal decomposition of the following two phases: SiO2 and B2 O3 + Na2 O. Vycor porous glass is prepared in three steps [90]. A melt composed of 75% SiO2 , 20% B2 O3 , and 5% Na2 O is quenched near (but below) its consolute temperature, inside the immiscibility gap. During the heat treatment, a slow liquid-liquid diffusion occurs, resulting in separation into two phases, rich in B2 O3 alkali oxide and in SiO2 . After the glass is heat-treated and annealed, the B2 O3 -rich phase is removed by leaching at about 100  C with acid, leaving an almost pure SiO2 skeleton. The resulting structure of the interconnected matrix has been interpreted in different ways. First the pore network was suggested to be a mass fractal, associated with 3D percolation clusters [91]. Next, Vycor glass was analyzed [85, 92] with the theory developed for the early stages of spinodal decomposition [93]. In this model, the phase separation occurs by growth of unstable longwavelength concentration fluctuations. The acid leaching removes the regions “poor” in SiO2 , creating an interconnected solid skeleton. The third proposed separation process is suggested to be driven by nucleation and growth of an almost pure SiO2 phase [37, 94, 95]. The Vycor glass must have a structure made up of a randomly packed assembly of spheroidal particles forming a connected and homogeneous solid network. The geometrical nature of the interfacial microstructure of the pore network has also been controversial. There have been discussions in the literature, regarding both the volume and surface fractal structures in Vycor glass [36, 37, 83–86, 91, 96, 97]. Most of the information

Table 2. Main physical characteristics of porous glasses. Parameter Approx. specific gravity (dry) Void space Internal surface area Avg. pore diameter (standard) Appearance Avg. modulus of rupture of abraded “A” rods, 25  C Young’s elastic modulus, 25  C Loss tangent at 25  C, 100 Hz Dielectric Constant at 25  C, 100 Hz Figure 1. Model of porous structure for porous glass.

Value 1.5 28% of vol. 250 M2 /g 40 Å Opalescent 6000 psi 25 × 106 psi 0.007 3.1

Note: Loss tangent and dielectric constant are affected by water in porous glass.

Nanostructures Within Porous Materials

related to the pore morphology has been obtained by means of transmission electron microscopy, adsorption methods, and small-angle scattering techniques. A study using a smallangle scattering technique [36] interpreted the power-law scattering at large q ∼q −4  to be a signature of scattering from a smooth interface [26]. However, some results [37] show an asymptotic behavior at large q, with power-law scattering of the form q −37 ± 01 . This noninteger exponent may be due to scattering from a rough pore interface. Xerogels and Aerogels Some other materials with an irregular porous structure are xerogels and aerogels. These materials are based on a gel that is on a suspension or polymer solution that behaves as an elastic solid or semisolid, rather than a liquid. A dried-out gel is termed a xerogel. A xerogel has an open porous structure at the nanometer scale. The porosity of this material is due to a random colloid aggregation process in the solution precursor. The classical models of their porosity-dependent properties are based on highly simplified geometrical structures like packed spheres or bottlenecked bubbles [7]. An aerogel is a special kind of xerogel in which the dried-out gel retains most of the original open structure. The most frequently used xerogels and aerogels are those based on SiO2 : silica gels and silica aerogels (for their production, see [98]). Their porous structure has been studied by various methods: gas/vapor adsorption (see [15]); mercury porosimetry (see [24], but this technique is generally not effective with aerogels); X-ray, neutron, and visible light scattering methods (see [99–108]); and numerical simulations [109–111]. Pores in various materials are either open or closed, depending on whether the pore walls are solid or porous themselves. A macroscopic example of an open-pore material is a common sponge. In a closed-pore material, gases or liquids cannot enter a pore without breaking it. This is not the case with an open-pore structure. In this instance, gases or liquids can flow from pore to pore with limited restriction, and eventually through the entire material. It is this property that makes aerogels effective materials for gas-phase catalysts, microfiltration membranes, and substances for chemical vapor infiltration. Physical properties of typical silica aerogels are listed in Table 3. Table 3. Physical properties of silica aerogels. Apparent density

0.003–0.35 g/cm3

Internal surface area

600–1000 m2 /g

% solids

0.13–15%

Mean pore diameter

≈20 nm

Primary particle diameter Coefficient of thermal expansion Dielectric constant

2–5 nm

Sound velocity through the medium

(2–4) ∗ 10−6 ≈1.1 100 m/s

Most common density is about 0.1 g/cm3 . As determined by nitrogen adsorption/desorption. Typically 5% (95% free space). As determined by nitrogen adsorption/desorption. Determined by electron microscopy. Determined with ultrasonic methods. For density 0.1 g/cm3 . Very low for solid material. For density 0.07 g/cm3 . One of the lowest velocities for a solid material.

817 Nanoporous Particle Track-Etched Membranes In 1962, Price and Walker [112, 113] made an interesting observation that the tracks in a material damaged by the passage of heavy charged particles through insulators can be revealed by chemical etching to form pores. The tracks that traverse the specimen are seen to be quite uniform and about 700 Å in diameter. Bean et al. [114] described an electrical method for subsequent pore growth during etching and a theory describing the rate of pore enlargement. They used clear muscovite that was cleaved to thicknesses between 3 and 8 m. Irradiation was accomplished from a sample of spontaneously fissionable 252 Cf. About 105 tracks/cm2 were formed in 16 h. The process of pore growth was monitored by measuring conductance across a thin sample. In summary, this study demonstrated that pores in mica, with radii from 30 Å to many micrometers can be created and monitored. A similar technology has been developed for polymeric track and other membranes [115–121]. The technology consists of irradiation of thin polymer foils with accelerated heavy ions, sensitization, and chemical treatment, resulting in the formation of uniform micro- or nanopores in the polymeric matrix. The pores are straight cylindrical channels with a clearly defined diameter. The surface pore density is also precisely predetermined by irradiation conditions. Special etching procedures give pore channels as small as 15–50 nm. The pore shape can also be changed at will. At the Joint Institute of Nuclear Research (Dubna, Russia) [115, 116] the irradiation of polymer foils is carried out on a U-400 cyclotron. It furnishes an opportunity to perform a homogeneous treatment of large sample areas. Accelerated Kr and Xe ions with energies of 4–6 MeV/amu are available.

2.3.2. Matrices with Regular Porous Structure Zeolites Zeolites are nanoporous crystalline solids with well-defined structures [122–126]. Generally, they contain silicon, aluminum, and oxygen in their skeleton. Many zeolites occur naturally as minerals and are extensively mined in many parts of the world. Others are synthetic and are made commercially for specific uses [126–129]. Natural and synthetic zeolites are typically powders with a characteristic size less than 10−2 cm. Because of their unique porous properties, zeolites are used in a variety of applications with a global market of several million tons per annum. Their major applications in the world are in petrochemical cracking, ion exchange (water softening and purification), and separation and removal of gases and solvents. Other applications are in agriculture, animal husbandry, and construction. Zeolites are often also referred to as molecular sieves. A defining feature of zeolites is that their frameworks are made up of 4-connected networks of atoms. One way of thinking about this is in terms of tetrahedra, with a silicon atom at the center and oxygen atoms at the corners. These tetrahedra can then be linked together by their corners to form a rich variety of structures. The framework structure may contain linked cages, cavities, or channels, which are roughly between 3 and 15 Å in diameter (see Fig. 2). The centers of zeolite cages (or channel axis) are arranged in space with crystalline order, which allows preparation of ensembles with size-calibrated clusters and/or atomic diameter wires with long-scale macroscopic ordering [130]. In all,

Nanostructures Within Porous Materials

818

with uniform pore sizes up to approximately 30 nm. These materials are synthesized in acidic media to produce highly ordered, 2D hexagonal silica block-copolymer mesophases. Calcination at 500  C gives porous structures with pore sizes from 4.6 nm to 30 nm, pore volume fractions up to 0.85, and silica wall thicknesses of 3.1 nm to 6.4 nm.

Figure 2. Zeolite cages for NaA (left) and NaX (right) matrices.

130 different framework structures are now known [131]. In addition to those having silicon or aluminum as the tetrahedral atom, other compositions have also been synthesized, including the growing category of nanoporous aluminophosphates known as ALPOs. The structural properties of some typical zeolites are listed in Table 4 [122, 130]. Mesoporous Molecular Sieves There are new kinds of nanoporous materials with regular systems of nanovoids, the so-called mesoporous molecular sieves, such as MCM-41 [132–137] and SBA-15 [138], which have many desirable properties for application as separation media (see also [139–145]). Members of this family of materials, designated MCM-41, were first observed in electron micrographs of products from hydrothermal reactions of aluminosilicate gels in the presence of quaternary ammonium surfactants. The material possesses a regular array of uniform, hexagonally shaped channels with narrow pore size distribution, the dimensions of whcih can be tailored in the range from 16 Å to 100 Å or more through the choice of surfactant, auxiliary chemicals, and reaction conditions. The pore walls are composed of amorphous silica, as indicated by X-ray diffraction measurements. MCM-41 has been used as a model system for sorption isotherms of various gases. The BET surface area is ≥1000 m2 /g with exceptionally high sorption capacities. The range of pore volumes for MCM-41 samples is 0.7– 1.2 cm3 /g (porosity of up to 80%). The use of amphiphilic triblock copolymers to direct the organization of polymerizing silica species has resulted in the preparation of wellordered hexagonal mesoporous silica structures, SBA-15,

Artificial Opals Natural opal is known as a precious stone with beautiful colors due to its structure, which is really a natural diffraction grating for visible light [146–149]. It consists of identical silica spheres with a very narrow size distribution (for its structure, see also [150–153]). There are now artificial opals [147, 154, 155] that also consist of identical silica spheres with diameters D varying from 150 to 900 nm [156]. The size uniformity of these spheres allows their assembly in a close 3D lattice, usually with FCC symmetry (see Fig. 3). There are empty voids between neighboring spheres, which, in turn, form their own regular lattice. There are two types of interpenetrating voids in the opal lattice: 8-fold-coordinated large voids, each connected with eight 4-fold-coordinated small voids. The large void has the form of a truncated tetrahedron with four windows to four large voids. The diameters of spheres inscribed in the larger and smaller voids are d1 = 041D and d2 = 023D, respectively. The diameter of a circle inscribed in the triangular window is d3 = 015D. The density of voids in opal is typically 1014 cm−3 . The porosity of the ideal package of spheres is 26% of the whole volume. The main opal spheres consist of smaller spheres 30–40 nm in diameter, which in turn are composed of particles 5–10 nm in diameter. Thus, the total porosity of opals may approach 59%, constituted by the 26, 19, and 14% porosity corresponding to the lower hierarchy of size [157]. The actual porosity of the opal may be either above or below this value, depending on the synthesis history (sintering conditions, interstitial cement). Chrysotile Asbestos Asbestos is a general term for a number of naturally occurring, fiber-rich minerals. The minerals are silicates, which means that the crystal structure is built up around SiO4 , frequently with a high concentration of magnesium, iron, or alkali metals [158, 159]. There are a number of health issues associated with exposure to asbestos [160, 161]. Chrysotile asbestos (chemical formula Mg3 Si2 O5 (OH)4 ) is the only type of asbestos that can be

Table 4. Structural properties of typical zeolites. Property

Zeolite NaX

Zeolite NaA

Zeolite NaM (mordenite)

Chemical formula

Na86 [(AlO2 86 (SiO2 106 ]32 × 8H2 O

Na12 [(AlO2 12 (SiO2 12 ]29H2 O

Na87 [(AlO2 87 (SiO2 393 ]24H2 O

Lattice of voids

Diamond-like with lattice constant 25.4 Å

Cubic with lattice constant 12.27 Å

Parallel channels with distance between their axes of 13–14Å

Diameter of voids

13 Å

11.4 Å

Diameters of channels 6.7–7 Å

Diameter of window between voids Relative volume of voids

7–8 Å

4.2 Å

42% of the total volume (there are some small voids with relative volume of 8%) 1.91 g/cm3

40% (there are some small voids with relative volume of 7%) 1.96 g/cm3

1.41 g/cm3

1.49 g/cm3

Density with adsorbed water Density without water

20%

2.13 g/cm3

Nanostructures Within Porous Materials

Figure 3. Packing of silica spheres in opal matrix.

decomposed by acids. It is a regular set of closely packed, parallel, ultrathin dielectric tubes with external diameters of about 20–25 nm. Its color may be white, gray, green, or yellowish. Currently chrysotile asbestos is the only type of asbestos mined on a large scale. The biggest deposit of asbestos mined now is located in the Urals (Russia) [162]. The mineral structure is described as a layer of partially hydrated MgO bound to a corresponding SiO2 . Since the MgO layer cannot adapt properly to the SiO2 layer, being larger, the thin double layer rolls up into very thin tubes, with the magnesium oxide layer outermost. The fibers are therefore hollow cylindrical tubes with an outer diameter of 200–250 Å and an inner diameter of 20–50 Å [158, 159] that are convenient for nanowire preparation (see Fig. 4). The density of chrysotile is 2.4–2.6 g/cm3 . The surface area depends on the distribution of fibers and may vary within 4–50 m2 /g, which is more than the corresponding variation in other fibrous textile materials. The refractive index along the fibers is 1.531–1.541 [159, 163, 164]. The lowtemperature magnetic susceptibility of Canadian chrysotile obeys the Curie law, and Rhodesian chrysotile has an antiferromagnetic Weiss constant of about 1 K. The apparent paramagnetism of chrysotile may be due to the presence of iron compounds, such as magnetite, as impurities [165]. The pH reaction of chrysotile corresponds to Mg(OH)2 in water in that a 0.5% chrysotile suspension free of CO2 has a pH of 10.33. The determination of the lattice parameters of chrysotile has been beset by unusual difficulties, as a result of the peculiarities of its diffraction pattern [166, 167].

Figure 4. System of nanowires within the channels of chrysotile asbestos.

819 For example, no single crystals of the mineral are available, and the finest fiber specimen that can be examined gives a diffraction pattern with the full symmetry of a rotation photograph. Warren and Bragg [168] suggested a structure based on amphibole-like silicate chains. Warren and Herring [169] and Aruya [170] pointed out that the diffuse reflections of chrysotile are similar to cross-grating reflections and, therefore, assumed that the mineral has a disordered layered structure. Modern structural results were obtained by Whittaker [166] at a time when electron-microscopic results appeared to be well established, but before the theory of diffraction by cylindrically curved layers was worked out. The types of structure that can be formed by cylindrically curved layers have been classified, and their diffraction effects have been discussed systematically [171–175]. The typical specimen studied by Whittaker [176] was a fiber pencil (17 mm long and 014 × 007 mm in cross section) from Bell’s mine, Thetford, Québec, Canada. All of the reflections from this specimen are in the positions expected for a monoclinic cylindrical lattice with parameters a = 1465 ± 001 Å b = 92 Å c = 534 ± 001 Å  = 93 16′ ± 1′ . Some other types of chrysotile have also been studied by Whittaker [177–179] (for lattice parameters of chrysotile reported by different authors, see [180–184]. The porous structure of asbestos has been studied by Pundsak [185, 186]. The void fractions observed experimentally were on the order of 6%. The water vapor adsorption-desorption data demonstrated that, in all of the samples, more than 80% of the void volume is in pores with radii less than 30 Å. Similar experiments have been carried out by Naumann and Dresher [187] with the use of nitrogen adsorption-desorption. A direct observation of porous structure in asbestos with the use of high-resolution electron microscopy was done by Yada [180, 188]. It was found that the outer diameter of the microfibers ranges from about 150 to 1000 Å, and the average value is about 500 Å. Most of the fibers were actually found to be hollow tubes with central holes 50–80 Å in diameter. The most frequent values of the outer and inner diameters of the samples showing a sharp distribution are 220–270 Å and 50–80 Å, respectively. None the tubes observed are simple cylindrical ones, but consist of spirally wound layers. Perfect concentric cylindrical layers were also found. The proportion of chrysotile fibers that are not hollow is very small. It was demonstrated that short uniform fibers of chrysotile asbestos exhibit strong interparticle forces parallel to the fiber axis, which result in aggregation of the fibers into distinct geometrical shapes [189]. Carbon Nanotubes The discovery of fullerenes provided exciting insights into carbon nanostructures. Carbon nanotubes are the most striking example. Carbon nanotubes were discovered by Iijima in 1991 during a study of the surfaces of graphite electrodes used in electric arc discharge [190]. Numerous novel and exceptional properties have been observed or predicted for these systems [191–200]. The basic structural unit of a carbon nanotube is a graphitic sheet rolled into a cylinder, with the tube tips closed by hemispherical or polyhedral graphitic domes. The aspect ratios of nanotubes vary with diameter, but the average length may be several micrometers. Experimentally, carbon nanotubes can be classified into two types: single-walled carbon

820 nanotubes (SWCNTs) and multiwalled carbon nanotubes (MWCNTs). SWNTs consist of single graphene cylindrical walls with diameters ranging between 1 and 2 nm. MWNTs have thicker walls consisting of several coaxial graphene cylinders separated by a spacing of 0.34 nm, which is close to the interlayer distance in graphite. The outer diameters of MWCNTs range between 2 and 25 nm, and the inner hollows, between 1 and 8 nm. Individual SWCNTs have a uniform diameter, although, when formed, they also show a strong tendency to pack together in large bundles. The very long cavities of carbon nanotubes have a special potential due to their high aspect ratio, and they can be used as templates for the fabrication of elongated nanostructures [201–205]. It may be noticed that there are some artificial noncarbon nanotubes based on MoS2 , WS2 , NiCl2 , etc. (see [206–210]). Some properties and the main methods for the synthesis of noncarbon nanotubes, as the results of experimental and theoretical studies, are discussed in [211].

3. METHODS FOR THE PREPARATION OF NANOSTRUCTURES WITHIN NANOPOROUS MATRICES 3.1. Filling with Wetting Liquids Filling of nanovoids in porous matrices with various substances can be done from the molten state. In this situation, the possibility of filling the nanovoids strongly depends on such a characteristic of a system formed by the molten substance and the nanoporous matrix as wettability (see [212, 213]). If a liquid substance wets the inner surface of nanovoids it penetrates into these nanovoids and can organize inside the nanoporous material nanostructures whose shapes and sizes reflect the geometry of the porous space. So, to prepare nanostructures of this kind, we need in the simplest case only to melt some substance wetting the nanoporous matrix and to put this nanoporous matrix into this melt. There are many examples of nanostructures prepared in this way. First of all it should noted that water very frequently wets porous materials (and may even condense inside the nanopores from air) and so can be studied as a nanostructure [214–222]. Simple liquids like N2 , O2 , H2 , Ar, Ne, and CO have been introduced into nanopores of mainly Vycor porous glass [223–229] as superfluid liquids 3 He and 4 He [230–242] (zeolites have long been used as molecular sieves for wetting liquids). Various liquid crystals have also been studied in the confined geometry of the nanoporous space (mainly in nanopores of Vycor porous glass) [243– 253]. Nanostructures have been prepared from the wetting liquid state or wetting solutions from organic materials and polymers [254–262], ferroelectric materials NaNO2 and KH2 PO4 [263–265], and fullerenes [266–268]. Carbon nanotubes have also been filled under the action of capillary forces in molten media [201, 203, 269] (see also [204, 205]).

Nanostructures Within Porous Materials

material and on the effective diameter of nanopores and corresponds to the formula for the Laplace pressure, P = 4/D, where  is the surface tension and D is the diameter. In preparation of nanostructures within porous matrices, we need to put a porous matrix into the melt of some substance and to compress this system up to the pressures corresponding to the Laplace pressure, when the liquid substance fills the pore space and forms a nanostructure reflecting the geometry of nanovoids (see Fig. 5). This method of nanostructure fabrication is similar to the process of mercury porosimetry and, in the case of mercury-based nanostructures, the fabrication process exactly coincides with such a porosimetry. The characteristic surface tensions and the needed pressures (Pc ) are presented in Table 5 for some liquid substances introduced into nanoporous matrices. When the external pressure is decreased after filling, the liquid nanostructures are unstable because of a nonwetting situation, and some breaks appear even within nanovoids with uniform shapes. The nanostructures are in this case similar to some sets of isolated nanopatricles. However, the probability of breaking is lower if the external pressure is decreased after the system is cooled to the temperatures below the melting point, and the nanostructures may be continuous in this case. Nanostructures may be fabricated by filling Vycor porous glass with various metals at low temperatures of melting. Nanostructures have been prepared from Hg and Ga metals [270–276], In metal [277–281], and BiPb alloy [282–284]. Regular systems of nanovoids in zeolites [130, 285–288] and opals [153, 289–292] have also been filled with metals and other materials. Nanotubes of chrysotile asbestos have been filled under high pressure with Hg [293– 297], In [298], Sn [299], Bi [300], Te [301], and InSb [300– 303]. For this type of nanostructure preparation, there is an interesting question: What is the minimum diameter of nanopores for which this method can be used? This question is associated with such fundamental problems of capillary phenomena as determination of the local structure and properties of interface layers (so-called Tolman length

3.2. Filling with Nonwetting Liquids To fill porous matrices with liquids that do not wet the inner surface of porous space, it is necessary to apply some external pressure, which depends on the surface tension of liquid

Figure 5. Process of porous matrix filling with molten material under high pressure.

Nanostructures Within Porous Materials

821

Table 5. Surface tensions and typical needed pressures for filling of porous matrices with nonwetting liquids. Liquid material (melt) Bi Hg Pb Se Te Sn In Ga

Surface tension (Erg/cm2 )

Pc (kbar, for D = 100 Å)

Pc (kbar, for D = 20 Å)

372 465 440 105 179 530 556 706

1.49 1.86 1.76 0.42 0.72 2.12 2.22 2.82

745 93 88 21 36 106 111 141

[213]), static and dynamic properties of the interphase interaction [212], capillary phenomena in extremely thin channels, or transition from capillary to diffusion phenomena. The experimental results from filling, with liquid metals, of channels of atomic-scale diameters in zeolites under high pressure [130, 286, 304–306] demonstrated that the interface transition layer has a thickness of about 1–1.5 Å, and the formula for the Laplace pressure can be used even for diameters of about 10 Å, in which this pressure approaches a value of (20–30) × 103 atm. Capillary effects in this situation are a direct manifestation of the transformation of the mechanical energy (mechanical work done by a piston pressing some nonwetting liquid into a porous matrix) to the surface energy of a material highly dispersed in the pore space. Zeolites that contain liquid metals in their channels are heterogeneous systems with very high surface energy (one can estimate the energy capacity to be up to 200 kJ/liter) and can be used for simple direct storage of mechanical energy [305– 309]. This high energy capacity (roughly 103 times greater than that of a spring) corresponds to that of an electrochemical storage unit, but, unlike the latter, it does not require an electric motor to produce mechanical work. Hydrocapillary storage units are sources of high-pressure liquid and can be used in transport, for example, with highly efficient hydraulic motors with high specific power (about 0.1 liter/kW) [307].

3.3. Chemical Methods for Filling of Nanoporous Materials When some substance cannot be introduced into nanopores from a melt (such a situation is typical of materials with a high melting point), there are a lot of opportunities to prepare nanostructures through some chemical reactions inside the nanoporous space filled with various solutions (or vapors) of the components needed for such a reaction. Two main features characterize this method. First, it is not universal in comparison with the methods based on capillary phenomena and, therefore, requires in any particular case some special chemical approach that may be different from those employed. In the conventional bulk situation (a chemical reaction in the confined geometry of a nanoporous space may be not the same as in bulk). Second, such a method does not permit filling of the entire porous volume, because it is necessary to remove products of chemical reactions, and, as a result, the filling factor may be lower. A variety of chemical methods are based on electrolysis in an electrolyte introduced into the nanoporous system.

Metal-organic chemical vapor deposition (MOCVD) has been used to prepare GaAs and InAs nanoparticles from organogallium and organoindium compounds in Vycor porous glass [310, 311], InP nanoparticles in Vycor glass [312], and InP nanowires from trimethyl indium within asbestos nanotubes [313]. Other semiconducting compounds have been prepared in porous glass [314, 315]; CdS, CdSe, PbS, and PbSe compounds have been synthesized with the photochemical method [316]. The antiferromagnetic material MnO [317], like Fe compounds [310], has been introduced chemically into porous glass. Three-dimensional regular systems of Si and Si-Pt [318–322], GaN, InN, InGaN [323–326], and VO2 [327] nanostructures have been fabricated in the void sublattice of a synthetic opal. The idea of using zeolites and mesoporous materials for the growth of quantum dots and wires has been proposed [328], and different nanostructures were synthesized within nanovoids of such porous materials as metals [329, 330], nanostructured metal sulfides [331], Ge [332], noble metal [333] nanowires, CdS nanorods [334], oxides [335], and organic materials and polymers [336–339]. Chemical reactions inside carbon nanotubes are described in [204, 205]; in particular, silver nitrate (AgNO3 ) has been introduced (melting point 212  C) into single-wall carbon nanotubes and decomposed into pure silver by thermal treatment at 400  C, and the transformation of AuCl3 in multiwalled carbon nanotubes into its base metal was described as an example of observation of reduction as a transformation of NiO to nickel metal. Similarly, encapsulated crystals of pure Pd [340, 341] have been prepared inside carbon nanotubes. Apart from hydrogen reductions, other kinds of reactions have been carried out inside carbon nanotubes. An example is the formation of cadmium sulfide crystals with hydrogen sulfide at 400  C [342]. Electrodeposition has mainly been used for filling of some nanoporous membranes. Bi and Pt nanowires have been prepared in nanoporous anodic aluminum oxide [343–345] as Fe and Co nanowires [346] within nanoporous membranes and Ni nanowires in a porous Si matrix [347].

4. PROPERTIES OF NANOSTRUCTURES BASED ON NANOPOROUS MATRICES 4.1. Optical Properties Artificially structured nanomaterials within porous matrices have attracted interest as objects of an optical study, because of the opportunity to observe quantum confinement, such as molecular-like discrete spectra, which exhibit strong size dependence, and some other effects, not associated with quantum confinement, which may be useful for different applications.

4.1.1. Quantum-Confinement Effects Theoretical descriptions of the electronic structure of such nanostructures have advanced from considering a simple particle in box models to much more sophisticated approaches, including finite well effects, Coulomb interactions, nonparabolicity of the conduction band, confinementinduced mixing of valence subbands, etc. (see [348]). The simplest approach is based on the model of a spherical

822 quantum well with an infinite potential barrier, assuming a parabolic dispersion of electron and hole bands. The carrier energies are quantized and can be determined for semiconductors from the expression   h 2 2 e h
l n /2me h a2  (11) El n = 2 where Ele n Elh n  is the electron (hole) energy reckoned from the bottom of the conduction (valence) band,
l n is the nth root of the first-order spherical Bessel function, me mh  is the electron (hole) effective mass, and a is the nanoparticle radius. The absorption spectrum consists of narrow peaks with spectral positions     h 2 2 h
l n /2mr a2  (12) l n = Eg + 2 2 where mr = me mh /me + mh  and Eg is the energy gap for the bulk material. The absorption edge, which can be designated the energy gap for a nanoparticle, corresponds to the lowest transition and is shifted in comparison with the bulk situation. Because of quantum confinement, the gap increases as a−2 with decreasing nanoparticle size. The first three roots
l n are  l = 0 n = 1 449 l = 1 n = 1 576 l = 2 n = 1. So the absorption edge is given     h 2 2 h  /2mr a2 (13) 01 = Eg + by 2 2 . Because in semiconductors the hole mass is typically much greater than that of the electron, the electron levels are much more sparse than the hole levels. Estimation of the absorption edge shift gives a value of about 25 meV for a = 5 nm and me = mh = m0 (m0 is the free electron mass). So the absorption edge shift due to quantum confinement can be observed in nanostructures within nanopores only a few nanometers in diameter or in semiconductors with sufficiently small effective mass of carriers. Luong and Borelli [349] have shown that III–V (GaAs, GaP) nanocrystallites in Vycor porous glass, introduced by metalorganic chemical vapor deposition, exhibit size-dependent shifts in the absorption and emission spectra, indicative of the quantum confinement. Optical properties of GaAs confined in mesoporous matrix MCM-41 also were studied [350]. Exciton absorption and luminescence spectra of PbI2 nanocrystals [351] incorporated into porous glass by a lowtemperature method (from solution) also demonstrated a short-wavelength shift due to quantum confinement. Indium phosphide has been deposited in 4-nm and 15-nm Vycor porous glass by the reaction of trimethylindium with excess PH3 [312]. The absorption spectra of InP in a 4-nm porous glass have an onset at approximately 750 nm and reach a maximum at 500 nm. This sample is clearly blue-shifted with respect to the 15-nm sample, which displays a more broadened spectrum with an onset well before 1000 nm and a maximum at 700 nm. For comparison, bulk InP would show a sharp transition near 918 nm. Such a behavior of the absorption edge is consistent with quantum confinement. A broad absorption edge was attributed to a distribution of crystal

Nanostructures Within Porous Materials

sizes, since it has been observed that a 10% change in particle size results in broadened, featureless spectra. A strong quantum confinement effect has been found for nanowires within chrysotile asbestos nanotubes, for GaAs [352–354], CdSe [354, 355], and InP [354]. The polarized absorption spectra of GaAs nanowires demonstrated bands at energies of 1.8 eV and 2.2 eV for both polarizations (the absorption is stronger for light polarized along the wire), the bandwidths being ∼0.1 eV. Asbestos is transparent in the spectral region considered. Thus, all of the bands can be attributed to optical transitions in the GaAs nanowires. The energy of the first transition between the highest valence subband and the lowest conduction subband of a cylindrical quantum wire with infinite bandgap discontinuity can be estimated. If we take as a room-temperature energy gap Eg = 144 eV for bulk GaAs, we obtain the quantum-wire energy gap and the first transition energy to be ∼1.8 eV. This value correlates well with the spectral position of the 1.8-eV band. The band at 2.2 eV can be assigned to a transition between the valence band subbands split off by the spin-orbit coupling and the first conduction subband. The polarized absorption spectra of CdSe nanowires also display stronger absorption for light polarized parallel to the wires and weaker absorption for light polarized perpendicular to the wires. The broad band peaked at about 1.87 eV was observed and can be attributed to intersubband transitions in the cylindrical CdSe quantum wires. This band displays a blue shift of about 0.14 eV relative to the bulk CdSe absorption edge (the energy gap of the bulk CdSe is 1.73 eV at room temperature), which corresponds to the quantumconfinement energy shift of the first intersubband transition (for me = 012m0  a = 35 nm).

4.1.2. Metallic Composite Medium The optical properties of metallic nanostructures within nanoporous matrices have been described mostly in the framework of the Maxwell-Garnett theory [356], which is a simple treatment of composite materials, addressing the shape but not the size of a particle. It provided the first theoretical basis to explain the resonant absorption (or dielectric anomaly), which is characteristic of systems of this kind. In the Maxwell-Garnett theory, the effective dielectric function eff of a composite medium is related to the polarizability of a single metal particle via the Clausius-Mossotti equation [357], that is, eff − i /eff + 2i  = 4/3N0

(14)

where N is the number density of metal particles, 0 = R3 m − i /m + 2i  i is the dielectric function of the dielectric host, m is the dielectric function of the metal, and R is the radius of the metal sphere. From this equation follows the relationship between the dielectric function of the metal-insulator composite and the dielectric functions of its constituents eff − i /eff + 2i  = f m − i /m + 2i 

(15)

where f = 4 3 NR3 /3 is the volume fraction of metal spheres.

Nanostructures Within Porous Materials

In such a way the optical properties of a composite porous glass with Ag have been studied [358] by measuring the reflectance between 10,000 and 40,000 cm−1 . It was shown for samples with different sizes (mean radius from about 2.5 nm up to about 45 nm) that the red shift, broadening, and reduction of the peak in reflectance can be successfully compared with theoretical predictions. In a similar way nanoscopic gold cylinders of controlled radius (from 30 nm to 60 nm) and aspect ratio were studied; these were prepared via electrodeposition of the metal within the pores of anodically grown porous aluminum oxide membranes [359]. Maxwell-Garnett’s original work addressed spherical inclusions, and it is for this specific geometry that the factor of 2 appears in the denominators. This factor is also called the screening parameter and, in general, is denoted by k (see, [360]). Hence, while k = 2 for spheres, long needlelike particles with their axes of revolution aligned with the direction of light incidence have a k value approaching unity. On the other hand, k tends to infinity for thin flat disks with an axis of revolution perpendicular to the direction of light incidence. The Maxwell-Garnett-calculated spectra are in qualitative agreement with experimental data for Ag in porous glass, which show dependence on both size and shape. Polarized optical spectra of long nanowires made of Hg, Bi, and InSb have been studied in the spectral range 0.5– 3 eV [300]. These wires were prepared within channels of chrysotile asbestos by filling the channels with molten material under a pressure of up to 10 kbar. A high absorption anisotropy has been observed. This was explained in terms of the Maxwell-Garnett theory with depolarization factor k dependent on the nanowire orientation with respect to the electric field vector of incident light.

4.1.3. Interaction Between Filler and the Porous Matrix In the case of nanostructures within porous materials, based on wetting liquids, the optical properties have attracted much attention because of the possibility of making some important conclusions about the phase state of encapsulated molecules and the possible mechanism of interaction between the filler and the active centers of the matrix, situated on the inner surface of pores, such as the molecular mobility of liquids within the nanopores. In such a way, the reorientational and vibrational dynamics of ethylene glycol and its homologous systems, possessing different numbers of OH groups per molecule, have been studied [257, 258] (see also [361]). The above systems have been studied in bulk and in the confined state within a porous glass matrix with pores 2.5 nm in diameter by means of light scattering (Raman and Rayleigh). By a comparison of the results obtained, evident influence of the chemical and physical traps on the molecular mobility was shown. The infrared absorption and Raman measurements, performed in the O-H stretching region, allowed identification of the intramolecular, H-bond subband and related various subbands to different intermolecular environments originating from the existence of the H-bond potential [362]. The optical properties of the 4-n-alkyl-4′ -cyanobiphenils (nCBs, where n is the number of carbon atoms in the alkyl radical n = 5 8) confined to porous glasses with four different mean pore sizes (2, 4, 54,

823 and 90 nm), have been studied [255]. It has been shown that the interaction of nC8 molecules with the pore surface is accompanied by the formation of hydrogen bonds between the SiOH group on the glass pore surface and the cyano group of the nCB monomer. In contrast, in the case of benzophenone confined to porous glass, weak OHSi hydrogen bonds are formed. Phosphorescence spectra of benzophenone encapsulated in the inner space of mesoporous aluminosilicate molecular sieves of the MCM-41 type (the channel diameter is about 4 nm) have been analyzed at 4.2–200 K [254]. A comparison of these spectra with the spectra of a bare MCM-41 matrix, pure benzophenone, and benzophenone incorporated into the porous glass led to conclusions about the phase state of encapsulated molecules and the possible mechanism of interaction between the filler and active centers (of the Si-OH type) on the inner surface of pores. The main influence exerted by the strong dipolar interactions on the dynamics of hydrogen-bonded liquids (propylene glycol) diffusing within 2.5-nm and 7.5-nm pores of a sol–gel porous glass has been demonstrated [363] by depolarized light-scattering spectroscopy. The experimental spectra measured as a function of temperature revealed unambiguously the slowing down of the collective reorientational processes triggered by the confinement effects. In addition to intermolecular interactions, an interaction mechanism of induced absorption has been identified in porous Vycor glass filled with liquid H2 by measuring the infrared absorption [364]. Infrared spectra have been studied for pyridine adsorbed on porous glass [365], and it was established that physical adsorption occurs by hydrogen bonding of pyridine to SiOH and B-OH groups via a nitrogen atom. Absorption in the far infrared region has been used to investigate surface vibrations in NaCl crystals dispersed in porous glass [366]. The experimental results were in good agreement with the theory predicting a gap between the limiting frequencies of the longitudinal and transverse optical surface vibrations in very small ionic crystals. Optical methods have also been used to study the interaction between liquid crystals and the inner surface of porous matrices [250, 252, 367, 368]. Dynamic and static light-scattering measurements in a nematic liquid crystal, pentylcyanobiphenil (5CB), confined in silica porous glasses with an average pore size of 100 nm (volume fraction of pores 40%) and 10 nm (volume fraction of pores 27%), demonstrated significant changes in the physical properties of confined liquid crystals [252]. The nematic-isotropic phase transition temperature is depressed by 0.6 K in 100-nm pores, compared with the bulk value, and this phase transition is not detected at all in 10-nm pores. It was found that even at about 20 below the bulk melting point the relaxation processes in a confined liquid crystal are not frozen. The infrared absorption spectra of 5CB dispersed in porous glass and molecular sieves of the types Si, Al-MCM-41 and Cu-Si, Al-MCM-41 (pore diameter of about 4 nm) have been investigated in the region of fundamental and overtone vibrations [367]. The mechanism of interaction between a part of 5CB molecules and the active centers of the porous interface was estimated. In this case, a strong enough interaction occurs between the cyano groups of 5CB and the hydroxy groups of the channel surface. It was also shown that another part of the 5CB molecule exists in the liquid-crystal state, and its

824 amount depends on the size and nature of the pores. Photon correlation spectroscopy was used to investigate nematic liquid crystals dispersed in porous matrices with randomly oriented interconnected pores (porous glasses) and parallel cylindrical pores (Anopore membranes) [250]. Investigation of liquid crystals in cylindrical pores, together with studies in random porous matrices, made it possible to separate the effect of random structure and domain formation from the contributions due to the existence of a liquid crystal–solid pore wall interface and the effect of the finite pore size in relaxation of the order parameter or director fluctuations.

4.1.4. Luminescence, Phosphorescence, Spectral Kinetics Interface phenomena in nanostructures formed within porous matrices have also been studied with the use of luminescence, phosphorescence, spectral-kinetic techniques, etc. (see [266, 267, 313, 369–376]). An enhanced and broadband photoluminescence behavior of fullerene (C60 )-doped porous glasses has been observed [371]. By means of photoluminescence and photoluminescence-excitation spectroscopy of C60 dopant in surface-unpassivated and -passivated porous glasses, it was shown that the interaction of C60 with the silica surface is quite strong (see also [267]) and that the modified C60 molecules contribute only in the orange-red region (1.9 eV) of the observed photoluminescence spectrum. The luminescence spectra of a number of polypyridine ruthenium (II) complexes adsorbed on the surface of a porous glass have also been studied [372]. Experimental data on the decay of the excited state of adsorbates were adequately described within the framework of a two-exponential model. Special features of the spectral luminescence parameters measured were accounted for by inhomogeneous broadening of spectra of luminophores arranged under heterogeneous conditions on the glass surface. The revealed features of luminophore quenching in heterogeneous conditions [373] were explained within the framework of a model analyzing two subsystems of adsorbed luminophores. Different mechanisms of quenching were considered, and a conclusion about the dynamic character of luminophore quenching in a porous glass was made. A comparative study of Raman, optical absorption, and photoluminescence spectra in 3D regular ensembles of InP quantum wires [313, 369, 377] revealed the dependence of the optical properties of these quantum wires on interfacial effects, namely, atomic interactions in the wires, and wire-matrix and wire-wire interactions. InP quantum wires have been produced in channels of chrysotile asbestos (wire diameter D = 8 nm, distance between wires A = 40 nm), MCM-41 mesoporous framework silicate (D ≈ 3 nm, A ≈ 34 nm), and AlPO4 -5 zeolite (D ≈ nm, A ≈ 1 nm) by a two-stage gasphase substitution reaction of the metal-organic compound trimethylindium [378]. InP wires in chrysotile asbestos are virtually isolated from one another; in other words, there is no wire-wire interaction. The spacial separation between the channels in MCM-41 is small enough (channel wall thickness of 0.8 nm) to allow effective coupling between nanowires. Taking into account that only one InP molecule can fit to the diameter for AlPO4 -5 zeolite, it appears natural to assume that the interaction between the AlPO4 -5

Nanostructures Within Porous Materials

matrix and InP is the strongest among all of the hosts considered. A comparison of optical data for these three matrices demonstrated that the wire-matrix interaction distorts the InP lattice, broadens the electronic density-of-states spectrum of the wire in the vicinity of the energy gap, and redistributes the relaxation of photoinduced excitations among states belonging to the wire itself and to defects in the matrix bound to the wire. The migration of triplet excitations of complex molecules in a confined geometry was studied in [374–376]. The results of investigation of the decay kinetics of phosphorescence and delayed fluorescence of disordered chrysene and chrysene in porous matrices were presented. The study of triplet-triplet annihilation kinetics allows an understanding of transport in disordered films, polymers, and membranes and of paradigms of heterogeneous chemical kinetics. It is also a tool for studying the topology, morphology, and structure of molecular aggregates, strands, pores, and domain boundaries. Porous glasses represented as chaotically arranged spheres and natural mineral chrysotile asbestos represented as hollow cylinders packed parallel to one another were used as matrices. An investigation of delayed luminescence of disordered chrysene and chrysene in porous matrices has shown that the triplet excitation transport in these systems at T = 77 K is dispersive in nature. The annihilation kinetics of triplet excitations is described by a rate coefficient that depends on time according to a power law. The exponent is determined by the microscopic structure of a sample and its geometry. In the case of chrysene in porous matrices, the annihilation kinetics of triplet excitations is determined by the matrix geometry and varies slightly with increasing temperature. An analysis of the decay kinetics of delayed luminescence from chrysene in porous glasses in comparison with chrysotile asbestos has led to a conclusion that the topology of the porous network of porous glasses is similar to that of the 3D percolation cluster.

4.1.5. Structure of Clusters and Nanochains in Zeolites Zeolites, which possess a regular system of cavities with a diameter of about 1 nm, are very appealing, in that they permit the preparation of arrays of unisized nanoclusters in the cavities. There are a lot of questions about the kind of structures that may be stabilized inside the zeolite pores. Some of these have been solved by applying optical spectroscopy methods to clusters of chalcogens (sulfur, selenium, tellurium) introduced into the pores of zeolites NaA and NaX (see [319, 379–387]). Chalcogens are good materials for the preparation of this kind of cluster, because they can easily be introduced from the melt or adsorbed into zeolite nanovoids, and their optical properties can be studied in the visible and near-UV spectral ranges, in which zeolites are transparent. For sulfur clusters it has been shown by Raman scattering and optical absorption spectra [382] that the main molecular unit of sulfur in the NaA zeolite is the most stable sulfur molecule, namely, the S8 crown-like ring. NaA with selenium has been examined by Raman [380, 381, 383, 384, 386, 387] and optical absorption [379, 381, 385–387] spectroscopies. The whole body of data obtained

Nanostructures Within Porous Materials

shows that some kind of Se ring molecules, rather than chain molecules, are stabilized. The NaA zeolite with Te has also been studied by Raman [380, 386] and optical absorption [386] spectroscopies. Similar to the case of Se clusters, the experimental data obtained indicate that, probably, Te ring molecules are stabilized. A more detailed study of Raman spectra [388] yielded evidence in favor of the stabilization of S8 , Se8 , Se12 , and Te8 ring molecules in the NaA zeolite. S8 and Se8 molecules are well known to exist in the condensed state, but there has been no information about the stabilization of Se12 and Te8 rings under conditions different from those in the zeolite NaA cavities. A possible reason for this stability is the good compatibility of the size and symmetry of Se12 and Te8 with the size and symmetry of cavities in the NaA zeolite. Strong and broad low-frequency bands in the Raman spectra of a NaA zeolite with sulfur and selenium were attributed to librations of ring molecules in the cavities. To obtain information about the symmetry of the Raman-active vibrations and the orientation of clusters in zeolite cavities, Raman microprobe polarization measurements have been performed (usually microcrystalline powder samples were studied) [389]. The dependences obtained correspond to S8 rings with the D4v point group symmetry, with their fourfold axes aligned with the fourfold axes of zeolite NaA, and Se12 rings with the D3d point group symmetry, with their threefold axes oriented along the threefold axes of the zeolite. The possibility of determining the ratios between the Raman tensor components of vibrations of zeolite-confined clusters was demonstrated. There are zeolites, such as mordenite, cancrinite, and AlPO4 -5, which are very attractive for the preparation of 1D systems. The chalcogen guest materials (sulfur, selenium, tellurium) have been introduced into the cavities of these zeolites, and the structure of chain-like nanostructures within the pores has been studied by optical methods (see [381, 384–386, 390] for mordenite matrix, [391–393] for cancrinite matrix, and [394–396] for AlPO4 -5 matrix). Polarized Raman and optical absorption spectra of natural mordenite single crystals containing sulfur, selenium, or tellurium within 1D channels (channel diameter 0.7 nm) have been studied. The bands in the Raman and absorption spectra, which are polarized along the channel direction, are attributed to helical chains. The helical chains and ring molecules (S6 , S8 , Se6 , Te6 ) coexist in the mordenite channels. The chains contribute to absorption spectra only for the E c polarization. Correspondingly, the resonance enhancement of Raman spectra of the chains is working for cc-polarization, and so Raman bands of the chains are active in this polarization. Ring molecules absorb light for all possible polarizations, and so the molecule vibrations are active for the aa-, bb-, and cc-polarizations. The ratio between the concentrations of chains and rings can be related to some kind of regular arrangement between chains and rings inside a channel. Polarized Raman, optical absorption, and luminescence spectra of cancrinite crystals possessing parallel nanochannels with Se inside have been investigated. It was shown that − Se is stabilized in the form of Se2− 2 and Se2 dimers situated at the center of the channel and oriented along the channel. When present in high concentration, the Se2− 2 dimers show a tendency to organize linear chains. At low temperatures,

825 − quite strong interdimer bonding for both Se2− 2 and Se2 was observed. The additional Raman bands were attributed to vibrations of linear Se2− 2 chains distorted by the incommensurate potential of cancrinite. Strong near-infrared polarized luminescence was observed. Photoionization of dimers was shown to be an important step in the mechanism of the luminescence. From Raman spectra of selenium incorporated into the channels of AlPO4 -5 zeolite single crystals (AlPO4 -5 is a molecular sieve with nearly cylindrical channels with diameter of 0.73 nm) it has been concluded that single helical chains and Se8 molecules are formed inside the channels. The temperature dependence of the Raman spectrum of single helical Se chains was studied. Dramatic changes in the spectra owing to structural transformations in this 1D system were observed. The chains are ordered at 77 K. Onedimensional Se shows transformations of the chains from the ordered state at low temperatures to weakly and strongly disordered states at higher temperatures. A phase transition from a weakly to a strongly disordered state is accompanied by structural relaxation of the chain. The structural transformations observed in single Se chains can be regarded as an example of how a nearly 1D system confined in a nanochannel behaves.

4.1.6. Nonlinear Optical Properties The potential of quantum-confined semiconductor nanoparticles for nonlinear optical and electro-optical applications has been anticipated [397–399]. Experimentally, the nonlinear optical properties of nanoparticles in porous glass have been studied for GaAs [400, 401], InP [402], and Cu2 O [315]. Time-resolved pump/probe Z-scan experiments (for the Z-scan technique, see [403]) using 1064-nm 100-ps pulses have been performed to determine the temporal characteristics of the optical nonlinearities of GaAs nanocrystals. The buildup and decay of the nonlinearities were instantaneous, compared with the duration of the excitation pulses. Singlebeam Z-scan experiments were also used to measure the two-photon absorption coefficient, , and bound electronic nonlinear refractive index, , of the quantum-confined crystals. The ratio / is greater by approximately a factor of 10, compared with bulk GaAs. In the case of InP nanocrystals, the magnitudes of nonlinearities in a 15-nm sample were found to be similar to those in bulk InP, whereas for a 4-nm sample the ratio / was a factor of 14 greater, compared with that in bulk InP. Carrier confinement to a single dimension must also lead to enhanced optical nonlinearities [397], and, therefore, the nonlinear optical properties of quantum wires have attracted much attention. Nanowires in channels of chrysotile asbestos (GaAs, CdSe, InP) have been intensively studied in this regard [354, 404–411]. The experiments used the pump and probe method to measure the differential transmission DT = T  − T0 /T0 , where T  and T0  are the transmission spectra of the excited and unexcited samples. Nonlinear optical absorption at discrete frequencies (bleaching bands) has been observed for GaAs quantum wires with an average diameter of about 6 nm. The induced decrease in absorption was accounted for by filling of the quantum-well energy levels

826 of quantum wires with nonequilibrium carriers (saturation effect). Strong ( 3 ≈ 10−8 e.s.u.) and fast (relaxation time ≤50 ps) third-order optical nonlinearity has been revealed. The nanowires within chrysotile asbestos demonstrate pronounced excitonic behavior with enhancement of excitons, with the binding energies ranging from 120 to 260 meV.

4.1.7. Photonic Crystals The concept of a photonic crystal whose behavior with respect to photon waves is similar to that of a dielectric crystal with respect to electron waves has been advanced by Yablonovich [412] and John [413]. In periodic dielectric structures with a period close to the wavelength of electromagnetic waves, these waves undergo Bragg diffraction, and a stop band is formed for modes propagating in a given direction. If the stop bands for all propagation directions overlap in some frequency range, a photonic gap can be created, in which the density of photonic states is zero. It has been shown that synthetic opals [414–417], like opallike films formed from polymethyl methacrylate beads [418], possess the properties of photonic crystals throughout the visible spectrum. Moreover, because of their regular porous structure, opals can be used as matrices for the fabrication of regular arrays of nanosized systems in the voids between the spheres constituting opal, which may also possess photonic stop bands. The voids between the silica spheres may comprise up to 26% of the total volume of the opal material. This makes it possible to change the optical contrast coefficient  = /s 1/2 , where s 1/2 and 1/2 are, respectively, the bulk refractive indices within the SiO2 spheres and outside them [419]) by filling the voids with different substances. According to the theoretical estimations [419], a complete photonic bandgap may exist at  ≥ 28. In pure opals, where  is considerably lower, the formation of the complete photonic bandgap is, apparently, impossible. Therefore, materials with a high dielectric constant should be used to fill the voids. In a similar way nanosystems of CdS particles [420] have been prepared: GaN, InN, and InGaN particles [323–326]; Si particles; VO2 particles [327]; and photonic crystals made of nematic liquid crystals [421]. Moreover, after filling of the original opal matrix, SiO2 can be removed chemically, and opal replicas can be prepared from different materials [422–424]. This operation yields a 3D semiconducting lattice, which occupies up to 26% of the total volume of the material and is surrounded by a “matrix” of air spheres that occupy the remaining 74% of the volume. The potential applications require control of the photonic gap structure in real time under external effects. It has been proposed [421, 425] that the opal pores be filled with liquid crystals, which allow tuning of characteristics of the photonic bandgap structure through an electro-optical effect in the liquid crystal, occurring when an electric field is applied. It has been demonstrated [327] that the photonic bandgap structure can be controlled via the metal-semiconductor phase transition in VO2 embedded in opal. A controllable and reproducible variation of the photonic bandgap properties of the opal-VO2 composite during heating and cooling in the temperature range 60–90  C was achieved. This is due to the change in the dielectric constant of VO2 upon the phase transition. It was suggested

Nanostructures Within Porous Materials

that a phase transition in this material and, hence, the photonic bandgap tuning in the opal-VO2 composite can also be observed under ultrafast laser pulses.

4.1.8. Laser Media Based on Nanoporous Materials New optical media have been developed on the basis of nanoporous materials, mainly porous glasses, for both optoelectronic applications [426] and laser elements [427]. New types of lasers have been fabricated by the incorporation of active dyes into porous glasses [428–434]. Molecular sieves can host some laser active dyes, too. Pyridine-2 molecules have been introduced into the channel pores of nanoporous AlPO4 -5 zeolite [435]. It was established that many effective dye molecules, such as rhodamines, do not fit into the pores, but the amount of encapsulated dyes can be raised by modifying the structure of the dyes so that they could match the host templates. The resulting microlasers have properties that depend on the size and shape of microcavities. For dyes that fit into the pores, partial regeneration of the photoinduced damage has been observed.

4.1.9. Materials for Optical Data Recording Filling of porous media with photosensitive materials has been used to prepare new media for optical data recording (silver-containing porous holograms). With these materials, one can make a volume holographic record with high diffraction efficiency [436–442]. Deep 3D holograms with large physical thickness, allowing postexposure amplification and a posteriori alteration of the grating parameters, were obtained. The sol–gel technology for making glass has made it possible to synthesize a new class of porous materials, monolithic xerogels. Xerogels have a more uniform porosity, which is an important advantage in data recording. It has been shown that holograms with a diffraction efficiency of nearly 100% can be obtained upon an exposure of about 0.1 J/cm.

4.2. Electronic Transport 4.2.1. Superconductivity Superconducting Properties of Metals in the Confined Geometry of Porous Glass The first studies of superconductivity in confined geometries of porous glass were concerned with the development of new artificial hard superconductors [443, 444]. New superconducting nanostructures were fabricated by pressing mercury into porous Vycor glass placed in mercury in a small balloon and compressed hydrostatically for 20 min at 3300 atmospheres, the pressure required to force the mercury into the Vycor glass. By measuring the weight gain, it was found that 10% of the total volume of the sample, whose interconnected pores were approximately 3 nm in radius, was filled with mercury. The superconductivity was measured with the magnetic induction technique. The measurements of magnetization and critical current demonstrated a large enhancement of the critical magnetic field and critical current in comparison with their bulk values. The critical current density was ∼104 amps/cm2 , and the critical magnetic field, ∼40 kOe at 2.1 K (the critical magnetic field for bulk mercury at 2.1 K is 320 Oe).

Nanostructures Within Porous Materials

827

This size effect may arise when the characteristic sample size is made comparable to, or less than, the bulk coherence length 0 and the magnetic field penetration depth 0 . For bulk mercury, 0 ≈ 200 nm and 0 ≈ 43 nm, and, therefore, the observed enhancement is not surprising. Furthermore, the superconductivity of some other metals (In, Sn, Pb, Tl, Ga) within nanopores of porous glass was studied [445–447]. Measurements of the critical magnetic field and transition temperature of superconducting indium in porous glass have been made with a low-frequency mutual-inductance technique [446]. Pore diameters from 6.5 to 25 nm were used. It was found in these measurements that the critical magnetic field Hc depends strongly on D, the pore diameter of the glass. Below t = 05 t ≡ T /Tc  Tc critical temperature) Hc can be represented as approximately Hc = 3415 ± 401 − t 2 /D100 ± 014 , where Hc is measured in kOe and D in Angstroms. This is in agreement with the predictions of Hc2 made by de Gennes and Maki [448, 449] for type II superconductors in the dirty limit under the assumption that the electron mean free path is proportional to D. According to the de Gennes-Maki theories, Hc2 0 = 3/2 2 0 / 0 l

(16)

where 0 is the flux quantum, 0 is the coherence length of the pure metal, and l is the electron mean free path. Near t = 0, de Gennes and Maki obtained Hc2 087 L 0Hc 01 − t 2 /l

(17)

where L (0) is the London penetration depth in pure metal at t = 0. The dependence of Tc on D is conveniently represented as Tc − Tcbulk = 1 − 0028/D, where D is in Angstroms. It was supposed that the change in Tc may be due to strain, mean free path, or surface effects. Experimental results on the transition temperature of indium, thallium, and lead grains of various sizes in porous glass, together with preliminary measurements on other metals [447], have been interpreted in terms of changes in the phonon spectrum, which alter the electron-phonon coupling constant. McMillan [450] has shown that the transition temperature of simple metals can be raised by reducing the Debye temperature. It has been suggested [451, 452] that, in small crystallites, the phonon spectrum is appreciably modified by a greater proportion of low-frequency surface phonons, and this is the reason for the shifts in Tc in granular or disordered materials. For these purposes the phonon spectra of gallium and tin embedded in porous glass have been studied with the Mössbauer technique [453, 454]. In [281], superconducting metals within porous glass were described as granular superconductors, that is, as superconductors consisting of small grains that are separated spatially but connected by electron tunneling. Abeles et al. [455] have carried out a calculation for a 1D model of a granular superconductor, with the grain boundaries represented by -function barriers. They found that the material behaves like a homogeneous dirty superconductor, with a critical field given by de Gennes-Maki theory, but with an effective mean free path l = D /1 − , where D is the grain size and is the transmission coefficient for electrons incident on a -function barrier. Some experimental results and results derived from this theory for metals in porous glass are given in Table 6.

Table 6. Parameters of superconductivity for metals in porous glass.

Indium

Lead Tin Thallium

D (Å)

Tc (K)

Hc2 (kOe)

0 (105 cm)

31 60 80 32 58 31 59 32

4.24 4.05 3.96 7.05 7.15 4.97 4.25 2.65

69 39 29 96 55 54 39 48

35 37 375 085 083 172 200 117

l (Å) 0042 0036 0036 0120 0120 011 0104 0175

131 217 290 384 690 342 440 559

It has been shown that Pb-Bi alloys embedded in a porous glass [282, 283, 456] can be used in some applications because of their very large critical magnetic field (for Pb-40%Bi Hc2 was about 120–125 kOe at 4.2 K). The transition temperature was about 7.8 K for porous glass with a 6-nm pore diameter. Measurements of the critical current density for Pb-40%Bi alloy in porous glass with an average pore diameter of 3.5 nm have been made in a transverse magnetic field and demonstrated a typical critical current density of about 105 A/cm2 in a zero magnetic field and 104 A/cm2 at 90 kOe. For Pb-Bi alloy in porous glass with a 2-nm pore diameter [456], the critical temperature was found to be 6.2 K, and Hc2 (0) was 230 kOe (as estimated by extrapolating from 210 kOe, the highest field used in measurements). Interestingly, the last value is greater that the so-called paramagnetic limit introduced by Clogston [457] and Chandrasekhar [458]. They pointed out that the electron Zeeman energy in the normal state can make a significant contribution to Hc2 determined at high enough fields. At magnetic fields stronger than Hp = 0 /2 B 1/2 (where 0 is the energy gap of the superconductor and B is the Bohr magneton) superconductivity must be impossible, since the free energy of electrons in the normal state is equal at Hp to the superconducting condensation energy. For PbBi alloy, Hp is about 120 kOe, and so the experimental value of Hc2 for this material in porous glass exceeds the paramagnetic limit. The explanation was found in the framework of the theory [459], including the effects of spin-flip scattering induced by spin-orbit coupling. Gallium has been introduced under a pressure of 14 kbar from a melt into porous media, such as cellulose, corundum powder, synthetic zeolites (NaA, NaX), and porous glass [271]. In the temperature range studied (4.2–16 K), two superconducting transitions were observed in the range from 6.1 to 6.4 K and between 6.8 and 7.2 K. The first transition was ascribed to the metastable phase -Ga, and the second, to another metastable phase, named -Ga. These phases were previously observed in thin films and in gallium emulsions [460, 461] (Tc of the ordinary phase of gallium is 1.08 K). The major part of gallium in porous glass was not superconducting above 4.2 K. At 4.2 K, a broadened signal was observed, which could hardly be suppressed with a magnetic field. This signal was identified with the “tail” of some low-temperature (Tc < 42 K) transition of gallium into the pores. Further study of the superconductivity of gallium embedded in nanoporous materials (various porous glasses and opal) was performed [462–466] to reveal how the size and configuration of pores influence the superconducting

828 features, because it was found previously that many general superconducting properties of porous glasses filled with metals occur because of the interplay of strong and weak links between metallic nanoparticles in pores. The superconductivity was studied with a superconducting quantum interference magnetometer with a 7-T solenoid in the temperature range 1.7–20 K. Single and double superconducting phase transitions were observed for different samples. Magnetization hysteresis loops were also measured and found to be dependent on the size and geometry of the pores. The changes in magnetization below about 6.4 K were analyzed in terms of models for granular superconductors, while the alterations in magnetization near 7.1 K were regarded as resulting from a superconducting phase transition in a coexistent structural modification of confined gallium. X-ray diffraction measurements confirmed the presence of such an additional gallium modification. The results obtained suggest that studies of magnetization at low temperatures can be used to get information about the geometry of the pore network and distribution of Josephson links in porous composite materials. A double resistive superconducting transition has also been found for indium within 5.6-nm-pore Vycor glass [467] (see also [468, 469]). The interconnected network of pores occupied approximately 30% of the total sample volume. From the broadening of the X-ray diffraction lines, a characteristic crystalline size of about 35 nm is inferred, which is significantly larger than the pore size of the Vycor. Furthermore, the X-ray diffraction measurements do not reveal a second phase. At the same time, the zero-field resistive transition shows a two-step temperature dependence with maximums in the derivative dR/dT at 3.99 and 4.03 K (Tc of bulk indium is 3.40 K). In a magnetic field, two fundamentally different transitions were observed by means of electric transport and magnetic susceptibility measurements. It was concluded that the presence of two distinct transitions is an intrinsic effect associated with the microstructure of indium in the porous Vycor glass. The superconducting transition temperature of an In-impregnated porous glass with 3.8-nm pore diameter has also been measured as a function of a hydrostatic pressure of up to 3.74 kbar [280]. All measurements were performed with a sample inside a Be-Cu pressure cell. The mean Tc increased above the value characteristic of bulk In by 17%. Its pressure derivative dTc /dp was determined to be −28 ± 06 × 10−5 K/bar less than the effect of pressure in bulk indium. It was concluded that the increase in the critical temperature and the smaller effect of pressure on the critical temperature for In-impregnated porous glass, compared with bulk indium, are both due to the softening of the phonon spectrum, resulting from the increased surface-to-volume ratio of the pores. Superconducting Properties of 3D Arrays of Weakly Coupled Nanoparticles within Opal Arrays of nanosize superconducting metal particles have been prepared by impregnation of the opal matrix with molten metal (In, Pb, Sn, Ga, and PbBi alloy) under high hydrostatic pressure [153, 289–292, 470]. The shape of the metal grains is an exact copy of the void configuration, since the metal occupies the entire free volume of the matrix, and so a 3D replica of the matrix can be formed. In accordance with

Nanostructures Within Porous Materials

the matrix structure [150], each section consisting of two adjoined grains contains a constricted region that can be considered a weak link (in the sense of superconducting properties), that is, an element of the S-c-S (S, superconductor; c, constriction) type, and so the proposed material contains a regular array of identical Josephson junctions. Owing to the matrix, these elements are arranged in a crystalline manner and form a macrosystem. The density of weak links in this material is about 1014 cm−3 . The interest in systems with a large number of Josephson junctions has been growing because of the practical demand. Microwave generators, receivers, and other devices based on a single Josephson junction are limited in their application because of their inability to emit powerful radiation in the generator mode and their liability to saturation in a weak external field in the detector mode. In-series connected Josephson junctions are very promising for application as power sources of microwave radiation for space communications, widedynamic-range detectors, parametric Josephson amplifiers, voltage standards, etc. Their main advantage is the coherent addition to the output signal from each element of an array. Microwave generators using coherent oscillations of an array of 40 or 100 Josephson junctions have been fabricated with good performance: emitted power of up to 10−6 W and frequencies of up to 300 GHz; moreover, the phase-locked emission linewidth was less than 5 kHz [471, 472]. In addition, an increase in the dynamic range of detectors in proportion to N 2 is observed for N in-series connected junctions [473]. The results obtained with opal-based Josephson junction arrays show that the materials prepared behave like continuum Josephson media exhibiting mutual phase locking. The following dependences were measured: resistance versus temperature, RT ; critical current versus temperature, Ic T ; and current–voltage characteristics. The measured detector response to an external radiofrequency signal were compared with RT  and dR/dT dependences and current–voltage characteristics. The microwave sources in use covered the range from 0.5 to 10 GHz. To separate the amplitude- and frequency-dependent response components from the total detector signal, amplitude-modulated radiation and frequency-modulated radiation were used. Magnetic properties of the system in a weak magnetic field H < 150 Oe, namely, the dependences Ic H  in dc and ac magnetic fields, shift of the superconducting transition temperature, and distortions of the voltage–current characteristics and responses, were also studied. The resistive transition demonstrated a shift toward higher temperature. For the In-based system, the critical temperature was shifted to T R = 0 = 3446 K, compared with that in bulk In (Tc = 340 K). Taking into account the experimental dependences of Tc on the diameter of superconducting nanoparticles, one can estimate the related size of In grains to be 50 nm. This value corresponds to the void size. The critical current density of each bridge was on the order of 104 A/cm2 , which is about 10 times less than the characteristic bulk value, and the sample-average critical current density was about 102 A/cm2 . An oscillating dependence of the critical current on the external magnetic field has been observed. Conventionally, such a dependence corresponds to trapping of flux quanta in the lattice cells of a phase

Nanostructures Within Porous Materials

coherent array of Josephson junctions. For a Sn-based system the periods of the observed oscillations, H1 = 3 Oe in a weaker magnetic field and H2 = 22 Oe in a stronger field, were smaller than the critical field in bulk Sn (Hc 0 = 306 Oe) at T = 342 K, fixed in the experiment. Therefore, this effect can be regarded as resulting from quantum interference in a regular lattice of magnetic vortices. These data were fitted using the relation HD2 /4 = 0 0 is the flux quantum). The first period corresponds to a lattice of loops with effective diameter D = 2500 nm. When a state with 4 flux quanta per loop is achieved, the system jumps to a state with loops 1000 nm in diameter. Both periods correspond well to multiples of the silica sphere diameter (250 nm). The typical voltage–current characteristics of the samples under investigation look like the curves observed for bridge-type Josephson junctions, which obey the resistively shunted junctions model. Typically, the hysteresis loop of the voltage–current characteristic takes place at T < Tc . However, other specific features of the voltage–current curve were found: switching between some fixed states in the resistive branch of the voltage–current characteristics; irreversibility of voltage–current characteristics (that is, any shift of the operating point along the resistive branch forward and back results in a hysteresis loop); an “anomalous” hysteresis loop at temperatures that are low but close to Tc , that is, the downward branch of voltage–current characteristics branch passes above the upward branch [153, 289, 290]. As for the last phenomenon, upon cooling the magnitude of this hysteresis first reaches a maximum and then gradually decreases and turns into the “normal” one. Moreover, the stronger the current through the sample I > Ic , the greater the “anomalous” difference between the upward and downward branches of the voltage–current characteristics. The response to microwave radiation shows no Shapiro steps in the voltage–current characteristics of a sample exposed to external radiation; that is, there is no selective detection typical of separate junctions. However, the origin of detection of the radiofrequency signal is Josephson-related rather than classical. The frequency-modulated response curve differs significantly from the amplitude-modulated one both in magnitude and in shape; that is, the sample exhibits frequency-dependent properties. So, a Josephsonlike behavior of such a system was demonstrated, but, at the same time, some disadvantages were found: the indefiniteness of its structure, related to the polycrystalline nature of artificial opal-like matrices, and the uncertainty of the type of interjunction interaction due to the close displacement of Josephson junctions. Superconductivity in Metallic Nanowires The nanochannels of chrysotile asbestos matrix have been filled under high pressure with superconducting metals (Hg, In, Sn, Ga, Pb), and the superconducting transitions of a complete series of such samples have been studied by the contact method [293–299, 474, 475]. Relieving the external pressure after filling of asbestos channels with liquid metals led to a loss of sample conductivity because of some oozing of liquid metals from the pores due to the nonwetting instability. It was, therefore, essential to study the system directly under high pressure, using autonomous chambers where the pressure was kept. Each sample contained about

829 106 parallel nanowires with the same diameter and length of about 0.5 cm, separated from one another by an insulator (asbestos) layer 30 nm thick. For such a system the temperature dependence of resistance in the region of the superconducting transition has a temperature spread T , which is due to fluctuations significant for such thin elements (width of the critical region). It is known that fluctuations smear the superconducting transition, so that the resistance smoothly decreases from the normal-state value RN to zero in some finite temperature region. In the low temperature region, the fluctuations destroy the superconductivity and result in the appearance of finite conductivity. In the high-temperature part of the superconducting transition, an additional conductivity correction associated with fluctuation electron pairing appears. For mercury nanowires of 8-nm diameter the temperature smearing of the transition is T ∼ 04 K (from ∼49 K to ∼53 K). Measurements performed on mercury nanowires with diameters of 2 nm [294] have shown that their superconducting transition is smeared from ∼2 K to ∼6 K, that is, T ∼ 4 K. Some attempts to describe theoretically the fluctuation-smeared superconducting transition have been reported [476–480]; they are reviewed in [481]. The dimensionless smearing of the superconducting transition due to fluctuations in the 1D case (for ultrathin wires) was estimated to be t1 ≡ T /Tc = F /kTc kF3 0D2 −1

(18)

where F is the Fermi energy, h/2kF is the Fermi momentum, 0 =  0 l1/2 , 0 is the coherence length, l is the mean free path for electrons, D is the diameter, and Tc is the critical temperature. For macroscopic D (∼001 cm), the dimensionless smearing can be calculated as t ∼ 10−12 , and so no influence of fluctuations can be observed. For D = 6 nm, t is about 10−1 , and for D = 2 nm, t ∼ 1, which is in agreement with experimental data for mercury nanowires for Tc ≈ 4 K. It is not quite clear how to determine the critical temperature Tc for such a temperature-smeared superconducting transition. This parameter was determined for superconducting nanowires within chrysotile asbestos channels from the temperature dependence of resistance, using theoretical descriptions of the fluctuation-smeared superconducting transition. In the low-temperature range, the temperature dependence of resistance can be written as RT  = RN /t1 9/4 exp−−/t1 3/2 

(19)

where  = T − Tc /Tc is dimensionless temperature. Tc can be obtained by comparing the above dependence with experimental data. The temperature dependence lnRT /RN −2/3 in the low-temperature part of the superconducting transition is linear and equal to zero at Tc . A good agreement with such a dependence was observed for all of the samples studied, and the Tc values were determined for different superconductors. The critical temperature Tc can also be calculated from the high-temperature part of the superconducting transition, where the temperature dependence of the resistance corresponds to the theoretical dependence  − N /N = −3/2

(20)

830 where T  ≡ 1/RT  and N ≡ 1/RN . In this case, the dependence  − N /N −2/3 vs. T is linear and equal to zero at Tc . There was also a good agreement of such a dependence with experimental data, and Tc parameters determined for the two sides (low- and high-temperature) of superconducting transitions were the same. This is an interesting experimental result, because the theoretical descriptions of the low- and high-temperature parts of the superconducting transition (and, therefore, the experimentally obtained Tc parameters) are independent. Such a result indicates that this Tc corresponds to a physical quantity that can be designated the critical temperature for a smeared superconducting transition. Dependences of Tc on diameter D have been measured for mercury, tin, and indium nanowires with diameters of 2 to 15 nm [152, 299]. The critical temperature of tin nanowires increases with decreasing diameter (up to 5.2 K), and the Tc D dependences for mercury and indium nanowires show maximums. For mercury nanowires, Tcmax = 46 K at D = 4 nm; for indium nanowires, Tcmax = 65 K at D = 25 nm. The current-induced breakdown of superconductivity in nanowires within asbestos nanotubes has been studied [293, 294], and some discrete steps in voltage–current characteristics were observed. It was suggested that they correspond to nonequilibrium processes in superconducting nanowires, associated with formation of the so-called phase-slip centers (see [482, 483]), studied for superconducting whiskers and nanobridges. The voltage–current characteristics of mercury nanowires are strongly nonlinear in the superconducting region, and further cooling (T < 29 K) gives rise to a falling region [295]. It was found that the distinguishing features of the characteristics observed are the N-type shape and the existence of an upper limit to the oscillation frequency. The frequency dependence of the characteristics was investigated with a relaxation oscillator in which the sample served as the active element. The N-type region of the characteristics was accounted for by the appearance of a thermal resistive domain associated with local heating of the sample by the current. The heat capacity of mercury and indium nanowires in the temperature range of the superconducting transition has been measured [296]. Experiments have been carried out on mercury nanowires with different diameters (from 2 up to 15 nm) and indium nanowires with a diameter of 5 nm, obtained by forcing the metal into the channels of chrysotile asbestos. A nonstationary method has been used (similar to that in [484, 485]) from the variation of the nanowire resistance in the region of the superconducting transition under the influence of a thermal flux modulating the temperature of the sample at a frequency of 25 Hz. This method fails to give the absolute values of the heat capacity and yields only its temperature dependence in the region of the superconducting transition smeared, because of fluctuations, over a considerable temperature interval. Three heat capacity peaks were observed in the region of superconducting transition for nanowires, and only one jump, in the bulk metal. This splitting of the heat capacity peak grows with decreasing nanowire diameter and vanishes when the nanowires are thick. These distinctive features of the heat capacity of metal nanowires cannot be accounted for by the coexistence of

Nanostructures Within Porous Materials

different crystal modifications with different critical temperatures (for mercury, -Hg with Tc = 415 K and -Hg with Tc = 395 K are known), because, first of all, there are three of them, and, furthermore, the temperature dependence of the heat capacity of indium nanowires, which do not have any different crystal phases, also displays three peaks. To explain the observed effect, it was suggested that the heat capacity peaks result from the electron system splitting into a series of subbands associated with spatial quantization and having their own different critical temperatures. In such a system, both the superconducting and the Peierls phase transitions (exhibiting different heat capacity features) are also possible [297, 486]. Critical magnetic fields have been measured for superconducting mercury nanowires [474, 475]. For nanowires 6 nm in diameter, the critical magnetic field extrapolated to T = 0 was 65 kOe for a magnetic field aligned with the nanowires and 36 kOe for a field oriented in the perpendicular direction. For mercury nanowires with a 2-nm diameter the critical magnetic field along the nanowires for T = 0 was 220 kOe, which exceeds by approximately a factor of 500 the value for bulk mercury. What is more important, this value is approximately three times the paramagnetic limit [457, 458] (77 kOe at T = 0). Such a large enhancement of the critical magnetic field can be explained in the framework of the theory, taking into account the spin-orbit scattering on the inner surface of asbestos channels [487].

4.2.2. Weak Localization in Nanowires The electronic transport properties of thin wires in the temperature and field regime have been the object of numerous studies, mainly because of localization effects that strongly depend on the spatial dimensionality. In a 3D system, localization of all of the electronic states does not occur until the randomness exceeds a certain nonzero level. However, it has been shown for 1D systems [488, 489] that any amount of disorder, no matter how small, would make all of the states localized, and this would lead to vanishing conductivity at T = 0. For not strictly 1D systems (i.e., wires) it has been shown [490, 491] that the electronic states will be localized with a localization length Lloc equal to a wire length corresponding to an impurity resistance of h/e2 ≈ 258 kOhm. Thus, any wire with a resistance greater than this value, which is longer than the localization length, will have a thermally activated conductance at low temperatures and be an insulator at absolute zero. At high temperatures, an electron will experience frequent inelastic collisions with phonons. Each of these collisions will cause the electron to jump from one localized state to another, and the localization will have no effect on the conductance. The effect of localization will be felt when the mean free path for inelastic scattering is comparable to the localization length. At finite temperatures the resistance will be given by R = R0 + R, where R/R = Li /Lloc  R0 is the temperature-independent impurity resistance, Li is the distance to which an electron diffuses between inelastic collisions (Li = D i 1/2 ), D is the electron diffusion constant (due to elastic collisions), and i is the inelastic scattering time. Experimentally, the localization effects in thin wires have been studied in metals for samples fabricated with a method based on the substrate

Nanostructures Within Porous Materials

step technique, in which a wire is formed in the corner of a step ion-milled into a substrate (see [492–495]). As for nanostructures within porous matrices, localization effects have been observed for mercury nanowires with diameters of 2 to 10 nm within the channels of chrysotile asbestos [496]. In the temperature range 10–50 K, the experimental data for Hg nanowires are well described by a R ∼ T −3/2 dependence (for 25-Å nanowires Rmax /R0 ≈ 04). Below 6 K, the superconducting fluctuations govern the conductivity. As for nanowires with larger diameters, their negative temperature derivative of resistivity also corresponds to the R ∼ T −3/2 dependence, but R/R0 decreases with increasing diameter. From the R/R0 ∼ T −3/2 dependence it follows that i ∼ T −3 . According to [490], such a temperature dependence of the inelastic scattering time may be due to scattering on 3D phonons. This is not surprising, since the nanowires are embedded in the dielectric matrix and are, to some extent, in contact with it, so that part of the phonons in such a composite medium may be three-dimensional. At 10 K, R/R0 ∼ 045  ∼ 3 ∗ 10−5 !cm (this value is determined from the ratio R300 /R10 and the resistivity of liquid mercury, ∼10−4 !cm), D = vF l/3 ∗ 10 cm2 s−1 (vF ∼ 108 cm/s, l is the mean free path for elastic collisions, determined from the temperature dependence of resistance). From these data, it can be found that i ∼−10 s at 10 K. The localization length (D i1/2 ) at 10 K is about 3 ∗ 10−5 cm, which satisfies the localization criterion for these nanowires. More recently, localization effects have also been studied in Bi nanowires. The semimetal Bi is often selected for such studies because the electron density is about five orders of magnitude smaller than that in the conventional metals. Furthermore, the very small effective mass of electrons in Bi results in a large spatial extension of the electron wave functions; the effects of reduced dimensionality can, therefore, be seen in samples with dimensions on the order of 100 nm. Bi nanowires have been electrodeposited into nanometer-size cylindrical pores in polycarbonate membranes [497], introduced by pressure injection of a liquid Bi melt [498, 499] (see also [500]) and by vacuum evaporation [501] into the nanochannels of an anodic alumina template, and injected into porous Vycor glass by the application of hydrostatic pressures of 5 kbar [502]. The anodic alumina templates, having an array of parallel nearly cylindrical channels, were produced by anodizing aluminum substrates in acid solutions (for nanowires within these templates, see also [503–505]). The diameters of the pores in alumina templates are uniform to within 10% over the channel length (40–64 m) from approximately 30 nm up to approximately 200 nm for different samples with average spacing between nanochannels of about 100 nm. In pores of polycarbonate membranes, Bi nanowires with diameters of 2000, 1000, 400, and 200 nm were fabricated, with wire densities of, respectively, 2 ∗ 104  2 ∗ 105  1 ∗ 106 , and 3 ∗ 106 wires/mm2 . In the Vycor porous glass, the average pore diameter was about 6 nm. Measurements of the resistance of Bi nanowire arrays with different wire diameters have been carried out over a wide range of temperatures and magnetic fields. An increase in resistivity and a large positive magnetoresistance were observed. The additional magnetoresistance was ascribed [501] to a transition from 1D localization at a low field to 3D localization at a high field, when the magnetic length becomes smaller than the

831 wire diameter. Most of the experimental results obtained in [499] are in good agreement with the theory and are accounted for by the electronic subband structure of quasi1D Bi nanowires. Evidence that localization effects occur at low temperatures (T < 40 K) was obtained, but it was established that the localization effects are not the dominant mechanism affecting either the resistivity or the magnetoresistance in the temperature range 20 K < T < 300 K. In Bi nanowires, 6 nm in diameter, in Vycor glass [502], no strong localization was observed, and this composite was a basically a good conductor. The observed temperature rise at low temperature and the associated magnetoresistance were interpreted in terms of weak localization.

4.2.3. Thermoelectricity in Bi Nanowires Bi nanowires are of special interest for thermoelectric applications owing to the unique properties of bulk Bi, such as its small electron effective mass components, high anisotropy of its Fermi surface, and low thermal conductivity of Bi. Theoretical calculations predict that nanowires of bismuth must have an enhanced thermoelectric figure of merit [506] (see also [507, 508]), defined by ZT = S 2 T /k, where S is the thermoelectric power (Seebeck coefficient),  is the electrical conductivity, and k is the thermal conductivity. For a material to be a good thermoelectric cooler, it must have a high figure of merit, ZT . With known conventional solids, a limit for the figure of merit is obtained, and modification of any one of the parameters adversely affects the other transport coefficients, so that the resulting ZT does not vary significantly. Currently, the highest ZT 1 at 300 K is observed in the Bi2 Te3 compounds. It has been demonstrated that quantum wires have a strongly different ZT , since the electrons are confined to a single dimension. This increase is due mainly to the change in the density of states. In addition, there is enhanced phonon scattering from the wire surfaces. This must reduce the lattice thermal conductivity and, hence, lead to higher ZT . According to calculations, an array of nanowires with diameters on the order of 7 nm, oriented along the trigonal direction, could have a figure of merit of ∼2 at 300 K. Single-crystal bismuth nanowires 200 nm in diameter (embedded in porous anodic alumina) have been used to measure the thermoelectric power and longitudinal magneto-Seebeck coefficient, and the first data on thermoelectric power, taken on an array of bismuth nanowires, were presented [509]. The temperaturedependent thermopower data are consistent with the partial electron and hole thermopower values calculated using the carrier Fermi energies obtained from Shubnikov-de Haas oscillations on the same samples.

4.2.4. Luttinger Liquid-Like Behavior in Semiconductor Nanowires InSb nanowires with a diameter of about 5 nm (a length of about 0.1 cm) have been prepared within the channels of chrysotile asbestos [300, 302] by filling with InSb melt at 550  C under a high pressure of 15 kbar. These nanowires are stable at room temperature, even after the pressure is removed. The temperature dependence of their zero-field electric conductance GT  is a power function of temperature, GT  ∼ T  , in the temperature interval 1.5–300 K

832 [302], with the exponent  ranging from ≈2 to ≈7. Current– voltage characteristics of such nanowires are nonlinear and follow at low temperatures the power law I ∼ V  [302]. A similar behavior has been observed for 5-nm Te nanowires [301]. For InSb nanowires with 5-nm diameter and carrier effective mass m∗ = 0014–02me (possible range of effective masses for bulk InSb), the energy spacing between the first and the second quantum levels was E = h2 /2m ∗ d 2 = 800–20000 K ≫ T for the temperature range examined. So the electron band structure is in this case essentially one-dimensional. Thus, the samples studied consist of long quantum wires with one or few quantum conduction channels. The electron–electron correlation, negligible in the 3D case, predominates in the 1D case [510]. As a result, the physical properties of a 1D metal are expected to be dramatically different from the properties of the conventional metals with a Fermi liquid of electrons. One of the most significant consequences of the correlation effect is the absence of quasi-particle excitations in 1D metals. Instead, collective excitations associated with separate spin and charge degrees of freedom develop in the 1D case [511]. In the absence of long-range interactions, a 1D liquid (so-called Luttinger liquid) is formed [510, 511], whereas the long-range Coulomb interaction leads to a 1D Wigner crystal [512]. Charge transport is of a collective nature in this case and cannot be described by the conventional kinetic equation. The following temperature dependence of conductance, G ∼ T  , has been predicted for tunneling between two drops of a pure Luttinger liquid, and nonlinear current–voltage characteristics, I ∼ V  [513], are similar to those observed in InSb nanowires. It was suggested that, in multiple InSb samples prepared within asbestos nanotubes, long-range interactions between electrons in each wire may be screened by the Coulomb interaction of these electrons with electrons of neighboring wires. This leads to short-range intrawire electron–electron interaction, which is a basic assumption of the Luttinger liquid theory. Transport properties of individual nanowires are determined by impurities and weak links (e.g., constrictions) appearing in the fabrication process. The number of such weak links can be estimated, and it corresponds to ≈103 weak links/cm per nanowire. The magnetoresistance of InSb nanowires has been studied over the temperature range 2.3–300 K in magnetic fields of up to 10 T [303]. The magnetic field leads to a 20% increase in the exponents  and  at H = 10 T. The magnetoresistance is positive; current suppression by up to an order of magnitude was observed at T < 5 K and H = 10 T. This may result from breaking of spin-charge separation in the 1D electron system, which is a novel mechanism of magnetoresistance. The results of an experimental investigation of the thermoelectric properties of InSb and Te nanowires (diameter 5 nm) [301] support the Luttinger liquid model. The thermopower S of InSb nanowires is characterized below T ≈ 250 K by a linear temperature dependence ST  GT  ∼ T 28 . For Te nanowires, ST  exhibits a metallic behavior but is not linear in any temperature interval and changes sign at T ≈ 180 K (GT  for Te nanowires is ∼T 33 ). Such a behavior of the transport properties is typical of neither semiconductors nor metals and corresponds, at least qualitatively, to the Luttinger liquid model [514], which predicts

Nanostructures Within Porous Materials

a metallic behavior for the temperature dependence of thermopower (see also [515]).

4.3. Magnetic Properties The influence of reduced physical dimensions on magnetic entities is of both fundamental and technological interest. Mainly motivated by technological interests, techniques for fabrication and characterization of magnetic nanoscaled systems have been developed. Physical vapor deposition techniques, followed by lithography of everincreasing resolution, are usually considered to represent the ultimate technique for producing nanoscale magnets. However, well-crystallized nanomagnets can also be fabricated by a different method. In this method, thin wires of magnetic metals with large aspect ratios are electrochemically synthesized within the voids of anodic oxide films on aluminum [516] (Co and Co-Ni alloy) and track-etched polymer membranes [517] (Co, Ni). Nickel nanowire arrays have been fabricated by electrodeposition into the nanopores with lateral dimensions as small as 30 nm [518, 519]. The porous templates were fabricated by nuclear track etching. Particle tracks were formed in 5- m-thick mica wafers by exposure to ∼6 meV  particles from a 100 Ci Cf-252 source in a chamber at a pressure of about 10−3 Torr. Interesting properties are expected to appear when the geometrical dimensions of the wires become comparable to a characteristic length scale, such as domain wall width or exchange length, and to mesoscopic dimensions, such as domain width. In bulk magnetic systems, the correlation length increases with temperature and diverges at the bulk transition temperature Tc . When one or more dimensions in the system are small, the growth of is eventually limited by the smallest dimension d, and the system displays a lowered transition temperature Tc d owing to finite-size effects. For Ni nanowires with diameters of 500 to 30 nm [519], the measured Tc d values obey the finite-size scaling relation Tc  − Tc d/Tc  =  0 /d , where = 094 and 0 = 22 Å. The measured correlation length 0 = 22 Å is close to the value of 20 Å reported for thin polycrystalline nickel films. Large coercive fields have been observed for assemblies of ferromagnetic Ni cylinders with diameters ranging from 35 to 250 nm, produced by electrodeposition in nanoporous membranes [520]. At low temperature these coercive fields could be attributed to the curling mode of magnetization reversal, with account taken of the distribution of wire diameters and orientations. The coercive field of the nanowires of smaller diameter decreases from 1500 Oe to 200 Oe at 300 K nearly linearly. The magnetoresistance of similar nanowires has been measured at room temperature [521, 522]. The full magnetoresistive hysteresis loop was studied as a function of the angle between the applied field and the wire direction. The anisotropic magnetoresistance and magnetic properties of arrays constituted by similar objects have also been studied by other authors [523–526]. A giant magnetoresistance of about 15% has been observed at room temperature in a nanostructured material consisting of multilayer magnetic nanowires (Co/Cu) formed by electrodeposition into nanometer-sized pores of a template polymer membrane [527].

Nanostructures Within Porous Materials

833

The classical antiferromagnet MnO has been embedded in a porous glass with an average pore diameter of about 7 nm [317]. MnO was synthesized from manganese nitrate solution by the chemical bath deposition method. The temperature evolution of the crystal and the magnetic structure of MnO under the “confined geometry” conditions were examined by means of neutron diffraction. It was demonstrated that a magnetic order similar to that observed in the bulk appears in regions smaller than the average size of nanoparticles. However, the ordered magnetic moment of 3.84 B /ion was noticeably smaller than that in the bulk. The magnetic phase transition was found to be second-order with elevated Néel temperature, in contrast to the discontinuous first-order transition in the bulk. The experimentally observed temperature dependence of the magnetic moment was mT  ∼ 1 − T /TN  with TN = 122 K and  = 034. The critical index  is close to those expected for phase transitions in the classical 3D Heisenberg model.

4.4. Freezing and Melting in Confinement: Structure of Solid Phases The confinement effect on freezing and melting (f/m) has been of considerable theoretical and experimental interest for many years. As early as 1888, J. J. Thomson proposed that the freezing temperature of a final particle would depend on the properties of the surface [528]. The first experiments on f/m in confined geometry (CG) were reported in the beginning of the last century [529–536]. Confinement usually results in depression of the f/m phase transition. Considering the difference in the Helmholtz free energy between liquid and solid in the pore, one obtains [537] G = Ali − si + VGm 

(21)

where Gm is the free energy of fusion, li is the substrateliquid energy, and si is the substrate-solid interfacial energy. A is the total interfacial area between the material and substrate and V is the total value of the confined material. The energies of any other interfaces in the system are ignored. Gm is given by Gm =

T Hf Tm − T Sm = Vm Vm Tm

(22)

where Sm is the entropy of melting, T is the melting point of the confined material, Hf is the heat of fusion, and vm is the molar volume. The differences in molar volume and heat capacity between solid and liquid are ignored. Analyzing Eq. (21), one can determine two different characteristic temperatures [537, 538], T1 = Tm −

A Vm Tm si − li  V Hf

(23)

where A/V is geometry dependent and can be written as A/V = /r, where  = 3 for a sphere of radius r and  = 2 for a cylinder of radius r. T1 corresponds to the equilibrium condition, when the energy of the completely liquid particle is equal to the energy of the completely solid particle. So T1 represents [538] a thermodynamic lower bound for the

melting temperature. However, taking into account kinetic arguments, one can obtain a second characteristic temperature equal in the case of a cylindrical pore of radius r T2 = Tm −

3Vm Tm si − li  rHf

(24)

T2 corresponds to the vanishing of the energy barriers between solid and liquid. It represents a thermodynamic upper bound for the melting temperature. It is most likely that the freezing will take place around T2 , and the melting around T1 . Following [537], we should emphasize that the influence of the material of the pore on the confined substance was completely neglected in the treatment considered above. The situation in the case of f/m phase transition is more complicated than that in the case of liquid/vapor. Wall effects on solid structure are expected to have a long-range character. The structure of the solid in confinement can be different from that the bulk. In the following paragraphs we will present a brief summary of experimental studies of the f/m in CG (for a more detailed review see, e.g., [537] and references therein). The first experimental results for f/m in confinement were mostly related to the f/m of water adsorbed on different hydrogels [529, 530]. The essential freezing-point depression was found for several different liquids on silica gel [536], and in the case of water adsorbed on 1.1-nm silica gel no freezing was found down to 208 K [539]. Scientific activity in the field essentially increased with the appearance of porous glasses, xerogels, and more recently channel matrices like MCM-41. f/m was studied for different types of materials. Properties of gases and some of liquids embedded by absorption from vapors strongly depend on the degree of filling, f . At low filling the pore condensate exists as an adsorbate on the pore walls [227]; at higher filling the pore center is filled. So a distinction should be made between the layers absorbed on the pore walls and the fluid or solid in the central part of the pore.

4.4.1. Inert Gases Inert gases (IGs) except helium (see Section 4.7) are the simplest substances to be studied in CG. In [540] suppression of the Tm for Ne in Vycor (d = 54 nm) (as well as for H2 and D2 ) was found, and estimation of the solid-liquid surface energy was found to be 2.6 mJm−2 . The 1.8 K difference between Tm = 225 K and Tf = 207 K (freezing temperature) was found and was attributed to the nucleation effects. In [228] f/m of neon and argon (together with H2 and O2 ) in Vycor and a silica xerogel were studied by combined heat-capacity and ultrasonic methods. Depression of the f/m was confirmed, but essential irreversibility of the freezing was found. It was demonstrated that any solid that forms, even in very small amounts, remains frozen until warmed well above the onset of solidification. Melting, however, is complete at a well-defined temperature between the onset of freezing and the bulk Tm . This fact was used as an indication that freezing is controlled by the pore geometry and not by nucleation kinetics. The width of the freezing region was attributed to the distribution of the pore sizes. Adams et al. [541] saw such measurements as providing a “spectrometer

834 of pore size.” Wallacher and Knorr [542] presented results of elaborate heat capacity and vapor pressure study of Ar in Vicor. Measurements were performed for various filling and sample histories. It was demonstrated that first and second monolayers on the pore walls do not participate in f/m, whereas for other layers, in particular for the third one, a delayering transition was observed in the case of incomplete filling. Structures of frozen IG in CG were studied by X-ray diffraction [543, 544]. In the case of complete filling for pores down to 6 nm, a crystalline structure was revealed. Ar 2.2-nm and 2.5-nm diffraction patterns were similar to those of amorphous solids. For Ar in 7.5-nm gelsil in the case of incomplete filling diffraction patterns changed from amorphous at low f ≤ 04 to crystalline at f > 04 [544]. The structure of the solid phase of Ar and Kr in Vicor [545] was interpreted as a disordered hexagonal close packed with phase transition to the fcc one at T /Tf ≈ 05. In [544] this result was argued, and the structure of confined solid Ar was described in terms of fcc structure similar to that of the bulk, but with numerous stacking faults.

4.4.2. Diatomic Compounds: N2
O2
CO In general f/m of diatomic gases in confinement is similar to the IG [228, 537]. In [546] a picosecond optical technique was used to study f/m of O2 in Vicor. For low filling (less than two monolayers) no freezing was found. For pore sizes 2.2 nm ≤ d ≤ 5.2 nm, Tf followed the 1/d law (see Eq. (23)). f/m hysteresis was especially well pronounced at 2.2 nm and 2.8 nm. A – solid-solid phase transition was observed, and the transition temperature T was also depressed as 1/d. A neutron diffraction study [547] demonstrated that the crystallites were considerably larger than the pores (about 10 times). An expected suppression of the melting temperature was also observed for nitrogen and CO. The crystal structure of CO is identical to structure of the bulk, with a crystallite size twice that of the mean pore diameter. In the case of N2 and CO in 2.5-nm MCM-41 [537], it was suggested that the structure was either amorphous or liquid.

4.4.3. Metals Unlike the cryogenic and H-bonded fluids, liquid metals usually do not wet the pores, and so there are no layering processes. For liquid mercury in the porous glasses, which has a high surface tension, it was demonstrated that the size of the solid clusters was temperature independent and equal to the pore diameter [276]. The main features of f/m transitions in Hg are broadening of both transitions and the existence of large thermal hysteresis, as demonstrated by neutron diffraction, NMR, and acoustic [274] measurements. It was shown that the freezing process was irreversible, but melting consisted of reversible and irreversible temperature regions. Combined use of longitudinal and transverse acoustic waves made it possible [274] to come to a conclusion about the origin of different behavior on melting. The broadening of melting was explained by the formation of a liquid layer on the mercury solid surface, whereas freezing was shown to be driven by the pore geometry with no visible precursor effects.

Nanostructures Within Porous Materials

Few papers were published that related to the study of liquid metals in zeolites (Hg and Ga) [287], with cavities about 12 Å in diameter, and mordenite (Hg and Bi), with an average channel diameter of about 6.6 Å [548]. In 12-Å zeolites, well-defined jumps in temperature dependences of electric conductivity and peaks in the temperature dependences of the specific heat were observed and were considered to be evidence of the melting/freezing phase transition, with strong depression of the melting point. This result, which was rather surprising for such small clusters, was interpreted as evidence of the strong suppression of the fluctuations near the melting point related to the possible interaction between individual drops. In the case of the mordenite channel, the main result was demonstration of the possibility of producing monatomic metallic chains in the channels of the dielectric matrix; m/f transition was not searched for in this case. Bogomolov et al. [549] have reported the study of onedimensional metallic filaments produced by embedding of liquid mercury in the channels of natural chrysotile asbestos with diameters of 20–100 Å. It was demonstrated that as the filament diameter is reduced the phase transition region shifts toward low temperatures (shifts value follows the ∼1/d law) and becomes diffuse over a large temperature interval (the width of the transition region follows the ∼1/d 2 law). The hysteresis between the melting and the solidification decreases and vanishes at d ≈ 20 Å. Data analysis based on the Imry-Scalapino theory of the fluctuation effect on the first-order phase transition has demonstrated that the contribution of the fluctuations to the transition broadening does not exceed 1 K for the smallest diameters. Heat capacity measurements of In in PG demonstrated essentially different behavior on melting and freezing (the heat capacity peak is much stronger for melting than for cooling). Careful differential scanning calorimetry (DSC) study of In in porous silica glasses with mean pore diameters from 6 to 141 nm has demonstrated [538] that, in agreement with Eq. (23), the melting temperature is reduced in inverse proportion to the pore size. In the smallest pores (8.2 and 18.2 nm) the latent heat of fusion was found to be about one-third to one-half of the bulk value. In was crystallized in the tetragonal phase identical to the bulk phase, but with a uniform lattice expansion of 0.5%. Unlike mercury, in the case of indium the crystallite size in 5.6-nm Vycor was about 20 nm, which is considerably larger than the pore size. Liquid gallium in porous glasses and opals was extensively studied by electrical resistance measurements [550], X-ray diffraction [275, 550, 551], NMR [552–554], and acoustical [555, 556] methods. In contrast with mercury in porous glass, the size of confined gallium crystallites was estimated to be 22 nm, which was significantly larger than the pore size (≈4 nm) [275]. Within the limits of experimental accuracy this size was nearly temperature independent. Only a slight tendency to the peak narrowing (i.e., size increase) was observed on cooling. The authors concluded that since the size of crystallites was about constant during the melting, the broadening cannot be attributed to the particle size distribution. Nor can it be explained in terms of the pore size distribution, since the gallium crystallites were much larger than the pores. As in the case of mercury, it was proposed that the broadening is related to the formation of the

Nanostructures Within Porous Materials

liquid around the particles. Information about the crystal structure of the solid gallium confined in the porous glasses is contradictory. In paper [551] several modification were found upon Ga solidification in the 4-nm porous glass, while in [275] only a single phase was found down to 20 K, and below this temperature the appearance of the second phase was reported. Both modifications reported in [275] were different from the known bulk gallium structures. In the case of Ga confined in opal, four different modifications were reported [550]. Two of them were similar to those observed in the porous glass and so were different from bulk, whereas two others were identified as -Ga and disordered -Ga. An interesting effect was reported for the f/m of disordered -Ga. Melting-freezing hysteresis for this modification was found to depend on the temperature of prewarming.

4.4.4. Water As mentioned above, water was the first material used to study the f/m transition in a confined geometry. A number of methods were used for its study, including DSC [557], neutron diffraction [557–559], and NMR [560, 561]. The studies of water freezing in the porous materials (silica gel, porous glasses, and activated charcoal) showed a freezing point depression consistent with two or three layers of nonfreezing water on the pore surfaces [537, 560]. In some cases freezing resulted in the formation of confined crystallites with a structure different from that of the bulk. In particular, cubic ice was shown to form in pores at 260 K. This modification was known before only at high pressure conditions. In samples with 2-nm pores, water remained liquid down to 251 K. On lowering of the pore size from 50 nm to 4 nm, the predominant ice modification changed from hexagonal to cubic [562]. NMR studies of water confined in glasses with different hydrophobicities (treated with hexamethyldisilazane) have demonstrated an increase in the melting point depression with increase of hydrophobicity. In the case of the most hydrophobic samples water was unable to penetrate the pores. Such behavior is consistent with the larger contact angle of the water-ice interface on the treated glass substrate [537]. In [562] the low-temperature (down to 173 K) structure of water in MCM-41 with d = 33- and 3.5-nm structure was found to be incompatible with neither cubic nor hexagonal ice. X-ray diffraction experiments performed on water confined in 2.4 nm and 4.2 nm MCM41 demonstrated that water freezes abruptly in the middle of 4.2-nm channels and more gradually in 2.4-nm channels [563]. As in the porous glasses, a disordered liquid-like layer was found. In contrast to porous glasses, no hysteresis was found in MCM-41 materials. This results in the conclusion that large f/m hysteresis in other matrices can be attributed to a network effect [537].

4.4.5. Organic Liquids For organic liquids confined in porous glasses, depression of the freezing temperature is typically observed. For cyclohexane in silica glass the temperatures of both f/m transition and the transition from the plastic to the brittle crystal are decreasing [564, 565]. Booth and Strange [566] demonstrated that for pores smaller than 5 nm, the plastic crystalline phase was replaced with a structurally disordered phase with high rates of diffusion. No freezing was

835 observed in the case of 2,4,6-trinitrotoluene in 2.5-nm and 5-nm gelsil glasses and in 10-nm and 20-nm glasses a bulklike orthorhombic structure was formed [567]. Systematic studies of CCl4 and nitrobenzene in silica glasses and silica gel (4–100 nm) [537, 568, 569] showed a good linear correlation between the melting-point depression and the inverse pore diameter. Takei et al. [569] found no changes in the transition temperature resulting from silanizing the pores with hexadimethylsilazane. The same linear dependence was observed in [570] for cis-decalin, trans-decalin, cyclohexane, benzene, chlorobenzene, naphthalene, and n-heptane in silanized silica glasses (4–73 nm). No freezing was observed for cyclohexane or cis-decalin in 4-nm pores [537, 570]. Essentially different behavior was observed in the case of f/m of organic liquids in MCM-41 materials. Morineau et al. reported differential scanning calorimetry measurements of cyclohexane, benzene, toluene, o-terphenyl, and m-toluidine confined in 4-nm MCM-41 [571]. Only a moderate decrease (not exceeding 6 K) of the f/m temperature was observed. In the presence of a few percent excess liquid, crystallization of the confined part was found to be sensitive to the presence of crystal outside the pores. The absence of supercooling of the confined part was explained by a freezing mechanism induced by the outside part. Glass transitions in confined toluene, o-terphenyl, and m-toluidine were nearly unaffected by confinement.

4.5. Dynamics Confinement strongly affects dynamical properties of the embedded materials, especially liquids (for the solid phase the problem is much less studied). Especially well studied are water and H-bonded systems [572, 573]. For many H-bonded fluids crystallization is easily suppressed in confinement, and these systems are considered as glass-forming materials. In general there are several mechanisms that can influence the molecular dynamics: • Structural effects due to (i) geometrical obstacles in the finite volume [574] and (ii) a reduced density resulting from the difficulty in packing molecules. In the case of diffusion the existence of dead-ended pores became important. • Surface effects: Interaction of liquids with the surface results in the formation of two (interfacial and bulklike) [575] or even three [576] (consisting of molecules having solidlike, interfacial, and bulklike dynamics, respectively) layers. • Finite-size effects due to spatial heterogeneity of the confined material–when the length scale of confinement becomes smaller than an intrinsic length scale related to the dynamics of bulk material. Such a situation is typical in glass formers when the glass transition temperature, is approached. Dynamics of confined materials are studied by several methods: dielectric spectroscopy [574, 575, 577–579], nuclear magnetic resonance (NMR), optical spectroscopy (Raman and dynamic light scattering) [573], and neutron spectroscopy [573, 579] are most important.

Nanostructures Within Porous Materials

836 4.5.1. Dielectric Properties in Confinement Dielectric properties of confined systems are crucial for many applications. Dielectric spectroscopy is appropriate for the investigation of polar materials and covers a large dynamical range from dc to microwaves [574, 580]. The difficulty with the interpretation is that neither the permittivity of the filler, p , nor that of the matrix, m , but a volumeaveraged value, eff , is obtained. eff can be presented as [574] eff =

1 − f m + fp Ep /Em 1 − f  + f Ep /Em

(25)

where f = Vp /Vtotal is the volume filling factor, Ep is the electric field averaged over the filler volume, and Em is the electric field averaged over the matrix volume. The ratio Ep /Em and thus the measured effective permittivity depend on the microstructure, that is, the topology, degree of order, and dimensionality. This problem is discussed in detail in [574]. In general we can formulate the following main results: • 3D confinement (droplets): The values of eff and the relaxation frequency relax depend on the exact spatial distribution of the particles. In the case of dilute inclusions of strongly polar materials, relaxation strength eff ≪ "p becomes independent of "p . With increasing disorder or filling factor F , eff increases, while the frequency shift of eff decreases. Agglomeration gives rise to a broadening of the relaxation peak [581]. In the case of asymmetric relaxations described by the Havrilak-Negami (HN) formula, HN =  +

 1 + i/0 1− 

(26)

with shape parameters  and , the shift of the relaxation frequency increases with increasing asymmetry ( < 1). Similar to the symmetric case, it decreases with increasing disorder or filling factor. The slopes of the low- and high-frequency sides of ′′  are unchanged. • 2D confinement (channel-like pores running through the whole sample; real porous systems with a high amount of dead ends and/or a fractally rough surface should be considered as an intermediate 2D-3D case): In the case of noncrossing pores, eff ≃ p  eff ∝ p . The high-frequency side of ′′  is slightly flattened. In the case of a network of interconnected pores the form of electric relaxation is hardly distinguishable from that of bulk material. In the most important case of real porous systems, the following basic features can be formulated [574]: The effective relaxation strength increases linearly with p for large enough values: eff ≃ ap + b. The effective relaxation frequency roughly equals that of the filler, eff /p ≃ 1. The shape of the relaxation is preserved on the lowfrequency side of the peak and is weakly modified on the high-frequency side.

• 1D confinement (films or multilayer structures): The situation depends on the orientation of the layer. In the case of layers oriented parallel to the film, the characteristics resemble those of a 2D confinement, and in the perpendicular case, the 3D confinement. The molecular dynamics of confined liquids in the frequency range from 10−6 to 1012 Hz is characterized by the superposition of different relaxation processes that take place on a local scale (-relaxation) and cooperative fluctuations (-relaxation, dynamic glass transition). In most cases an additional relaxation peak appears, which is usually ascribed to the Maxwell-Wagner-Sillars (MWS) polarization appearing when a slightly conducting liquid is enclosed in an insulating material [577, 582]. Experimental dielectric results were obtained for several different confined systems. In nitrobenzene in CPG, Vycor, and MCM-41 [582], already mentioned above, two relaxation components were found in the liquid state at about 5 ∗ 10−3 s and 10−4 s, both of simple Debye relaxator shape. The slow one has been attributed to the MWS polarization, and the fast to the relaxation of the contact layer. The response of the bulk fluid was out of the experimental range. Nitrobenzene is not a glass former, and neither component demonstrates essential temperature dependence. The dynamic behavior of glass formers is essentially different. Several glass-forming liquids were studied, among them N -methyl--caprolactam (NMEC) (nonassociating liquid) [577, 583, 584], propylene glycol (PG) and its oligomers (PPG) [578, 579, 584], salol [575], pentylene glycol [575], and glycerol [575]. Experimental dielectric spectra typically contained a MW peak plus one or two relaxation peaks. Peaks are broadened as compared with a simple Debye relaxator and asymmetric; the shape is consistent with the HN formula. In the case of two relaxation peaks a slow process was unambiguously attributed to the interface dynamics. This fact was confirmed by modifying the porous glass surface (silanizing with trimethylchlorosilane) [577], which results in weakening of liquid (NMEC) to the surface and in the nearly complete suppression of the slow peak. Liquids with two (PG) or three (glycerol) hydroxy groups were shown to exhibit only one relaxation process [575]. This was interpreted in terms of a shell model of a bulklike phase and an interfacial layer including molecular exchange between the two subsystems. For all components relaxation times were temperature dependent [575, 577, 579], following the Vogel-Fulcher-Tammann (VFT) relation [585, 586] m

= −1 m = A expDT0 /T − T0 

(27)

where m is the position of the maximum of the dielectric loss peak, A is the prefactor, D is the fragility parameter (higher values of D correspond to stronger glass formers), and T0 is the Vogel temperature. A fit of dielectric data to the VFT equation is often used to determine the glass transition temperature Tg , based on m Tg  = 100 s. In such a definition Tg is exactly dynamic, determined by the whole set of VFT variables. Some published results are summarized in Table 7. For interface components relaxation is always retarded; as clearly seen from a comparison of prefactors, Tg for the interface layer is essentially lower than that for bulk. However, there is no regular change of Vogel temperature, even for the interface layer. The  relaxation of the liquids

Nanostructures Within Porous Materials

837

Table 7. Parameters of VFT equation for dielectric relaxation. System PG(bulk) [579] PPG-400(bulk) [579] PPG-725(bulk) [579] PPG-4000(bulk) [579] PG(conf., inner) [579] PPG-400(conf., inner) [579] PPG-725(conf., inner) [579] PPG-4000(conf., inner) [579] PG(conf., interface) [579] PPG-400(conf., interface) [579] PPG-725(conf., interface) [579] PPG-4000(conf., interface) [579] NMEC(bulk) [583] NMEC(confined) [583] Salol(bulk) [575] Salol(confined 7.5 nm) [575] Salol(confined 5 nm) [575]

A (ps)

D

T0 (K)

Tg (K)

195 9 32 123 892 84 49 116 02 07 06 11 ∗ 10−6 023 0062 01 18 ∗ 10−3 017

184 78 83 70 191 93 90 69 116 98 127 66 338 374 48 80 53

1123 1604 1603 1646 1154 1580 1578 1661 114 155 147 174 1423 1306 194 177 185

1668 1964 1971 1974 1713 1977 1973 1990 188 215 221 244 1735 1611 222 215 214

Tg (K)

T0 (K)

+45 +13 +02 +16 +212 +186 +239 +466

+31 −24 −25 +17 +17 −54 −133 −96

−124

−117

−7 −8

−17 −9

Note: Tg = Tgconf − Tgbulk  T0 = T0conf − T0bulk .

in the inner pore space is much less affected by confinement and the results of different authors are controversial, as one can see from the data in Table 7. Conducting Liquids in Porous Media In many natural inhomogeneous materials, such as brine-saturated sedimentary rocks, giant values (about 106 ) of low-frequency dielectric permittivity were observed (“dielectric anomaly of rocks”). A similar result was obtained for brine-saturated porous alumina ceramics [587], where Re ≈ 2 ∗ 105 was reported for the porosity 0.193. This anomaly was analyzed [587–589], and the best agreement was obtained for the model considering a system of pores separated by thin walls. In [590] giant growth of  was observed on heating of NaNO2 ferroelectric confined in 7-nm porous glass (up to 108 at 100 Hz and T > 550 K). This effect was explained by an essentially broadened melting transition. In a very recent paper [591] the temperature evolution of structure in a restricted geometry was studied for the ferroelectric NaNO2 embedded in a porous glass, and it was shown that this CM forms a kind of interconnected cluster, probably of the dendrite type, with a practically temperatureindependent average size of about 45 nm. Above Tc the volume “premelted” state is formed, manifesting itself in a sharp growth of the thermal motion parameters, softening of lattice, and increase of lattice volume. In such a case the possible appearance of ionic current due to oxygen jumping diffusion is proposed as a reason for the observed giant growth of dielectric permittivity. On cooling below Tc macroscopic polarization and potential barriers suppress the lattice softening, and the normal ferroelectric phase exists. There is very limited information on the behavior of ferroelectric materials in confinement. In [263, 265, 592] sodium nitrite and Rochelle salt embedded in 7-nm porous glass were studied. Only a very small negative shift of transition temperature was found in contrast to the dispersed BaTiO3 and PbTiO3 [593]. Substantial broadening of the transition was reported and interpreted as an effect of the fluctuations. In [263, 592] KDP embedded in artificial opal and porous

glass was studied. A fast increase of the transition temperature with decrease of pores size was observed. The most plausible explanation is coupling of the embedded materials with the pore surface.

4.5.2. Diffusion Hindered transport in restricted geometries is of theoretical and practical interest because of its relevance to many important processes, such as chromatographic separation of polymers, enhanced oil recovery, membrane separation, and polymerization in the presence of heterogeneous catalysts [594]. In an early paper on the study of molecular diffusion by forced Rayleigh scattering in porous media, published more than 15 years ago [595], the diffusion of an azobenzene molecule in Vycor was reported to be two orders of magnitude slower than in free unbound solution. The authors succeeded in separating chemical heterogeneity and geometrical disorder and developed a detailed fractal model relating pore size distribution to self-diffusion. In another paper [596] the diffusion of polystyrene in 74.5-nm porous silica glass was studied by dynamic light scattering. Adsorption of polymer was excluded by silanizing the surface. Decay of long-wavelength fluctuations was governed by a single “macroscopic” relaxation rate. It was found that the correlation length depends not only on the pore geometry but on the hydrodynamic radius RH of the polystyrene molecule as well. Samples with number-averaged molecular weights of 35,000 and 93,000 corresponded to RH ≈ 4 nm and RH ≈ 75 nm, respectively. The following description was proposed for an effective macroscopic self-diffusion coefficient D D = f RH /RP D0 = DP

(28)

where  is the intrinsic conductivity (hindrance factor) of the porous medium (T = 1/ is called tortuosity), D0 is the bulk diffusion coefficient, RP is the average pore radius, and DP is the diffusion coefficient within the pores for the

Nanostructures Within Porous Materials

838 short times or distances. An intrapore short-distance translational diffusion coefficient can be effectively measured with incoherent quasi-elastic neutron scattering [597], though we do not know any paper in which coefficient f was analyzed on the basis of a comparison of D with DP from neutron data. A rough estimate of  ≈ 075 was given in [596] with estimations for f of 0.92 and 0.83, and 4 nm and 7.5 nm for RH , respectively. Diffusion of polystyrene with molecular weights of 2500–13,000 in 2-nm Vycor glass with a porosity
≈ 028 (ratio of polymer free-solution radius to the glass pore radius from 0.017 to 1.4) was studied with dynamic light scattering [594]. Strong dependence of the D /D0 on RH /RP was confirmed, and an estimation of  = 03 to 0.7 was obtained. Such an estimation is in good agreement with calculations in the frames of model of medium composed of random structural elements (pores) chaotically connected with one another [598]  = 1 − 23 1 +
1 −
3/2

(29)

This yields  = 048 for
= 028. The extremely small  value obtained in [595] was explained in [594] by incomplete suppression of the adsorption on the pore walls. A limiting case of diffusion in the very narrow pores was considered in [599]. Diffusion of tetrafluoromethane (diameter of molecules 0.47 nm) in the AlPO4 -5 zeolite (channel diameter on the order of 0.73 nm) was studied by pulsed field gradient NMR. AlPO4 -5 zeolite is traversed by parallel channels. It was demonstrated that in this case the mean square displacement # 2  increases in proportion with the square root of observation time, in contrast to the ordinary diffusion when # 2  ∝ t. This observation corresponds to the regime of “single-file” diffusion, when the molecules are unable to pass each other. Measurements provide a diffusion coefficient D on the order of 5 ∗ 10−7 m2 s−1 , which is about 2 orders of magnitude larger than in other zeolites [600]. The observed phenomenon was explained in [599] as the effect of molecular guidance by the channels, resulting in the enhancement of molecular mobility in one-dimensional channels in comparison with higher-dimensional pore networks. Self-diffusion properties of plastic formers succionitrile and cyclohexane confined in porous glasses [601, 602] and in MCM-41 [603] were studied. In the confined liquid, above freezing the diffusion coefficient is essentially lower than in the bulk, similar to the other confined substances considered above. However, on freezing, the diffusion coefficient in bulk drops down by about 4 orders of magnitude. In the confined material two phases develop, namely, a plastic phase in the center of the pore and a liquid-like component with D about 3 orders of magnitude higher than in the bulk.

4.6. Liquid Crystals Liquid crystals (LCs) are often considered as ideal objects for the study the effects of confined geometry. Kralj et al. [249] have explicitly formulated the main advantages of LCs as model systems for such research: (i) LCs exhibit a variety of phases with different degrees of orientational or translational order; (ii) there exist different kinds of transitions between these phases; (iii) they are typical representatives

of soft materials (their response to perturbations induced by the confining matrix is pronounced and long-ranged); (iv) LCs and the host materials do not interact chemically; and (v) both LCs and the host matrixes are in most cases transparent, and consequently samples can be studied by a variety of optical methods. Key to understanding the large part of confinement effects on LCs is an interaction of the LCs with surfaces [604]. In the case of the nematic LC this interaction is usually described in terms of the preferred orientation of the nematic director at the surface called the “easy direction” and the strength of the interaction. The easy direction is the direction of the director at which the surface energy is minimal. The strength of the interaction is determined by the so-called anchoring strength, which tells what torque is needed to move the orientation of the director from the easy direction. Anchoring properties of the surface strongly affect both static and dynamic characteristics of LCs. The influence of the confinement on the LCs is related to the contribution of the LC/matrix surface to the free energy. This effect is usually described in the framework of the Landau-de Gennes theory [605, 606], with the surface term described as  → Fs = fn + fs d 2 − r (30) with the nematic contribution fn described as [607]  −  → 3 → n− e 2 − 1 + W2 S 2 fn = −W1 S 2 where W1 and W2 are positive surface anchoring constants, − → n determines the nematic director field, S is the nematic → orientational order parameter, and − e is the easy direction. The linear term is concerned with the direct interaction between the surface and LC molecules, and the S 2 term is due to the fact that LC molecules have fewer neighbors at the surface [249]. The smectic contribution fs is presented as [249] fs = −Wp  cos − s  where Wp is a positive constant. We will follow [249] in describing possible LCs structure in the simplest case of the cylindrical cavities of radius R and length Ld or the cavities that can be presented as a space between two concentric cylinders of radii R0 and R0 + 2R, respectively. Two extreme cases can be considered: homeotropic anchoring (the LC molecules tend to be aligned along the surface normal) and planar anchoring (the molecules are forced to lie in the limiting plane, where all directors are equivalent). The case of planar anchoring corresponds to the homogeneous structure (Fig. 6(i)) or the homogeneous structure with point defects (Fig. 6(ii)). In the case of homeotropic ordering one expects formation of the escaped radial (Fig. 6(iii)) [249, 608] or escaped radial with point defects (Fig. 6(iv)) structures. In the limiting case of strong homeotropic anchoring, structures (iii) and (iv) are transformed into the planar radial structure (Fig. 6(v)) [249, 608, 609]. In this case the bend nematic deformation, characteristic for structures (v) and (iv), is absent and the director field radially streams from the center of the cylinder with a line defect along the cylinder axis.

Nanostructures Within Porous Materials

Figure 6. Model director structures. (i) Homogeneous. (ii) Homogeneous with point defects. (iii) Escaped radial. (iv) Escaped radial with point defects. (v) Planar radial structure. For the type (v) cavity the  (foldirector field is either radially distributed or perpendicular to R. lowing [249]).

An important effect is related to the quenched disorder in the LC-matrix nanocomposites. The matrix in this case not only geometrically confines the LCs but also induces a random orienting field that fixes the direction of the order parameter near the surface of the matrix [610]. The randomness is determined by the geometry of a confining porous matrix. Maritan et al. [611] were the first to associate the effects of the porous media with that of a random field. Their theoretical considerations supported the early experimental results of [612, 613] reporting the light scattering and calorimetry measurements of confined LCs. It was demonstrated that the first-order phase transition observed in bulk LCs was replaced by a smooth evolution to a glassy state, with the correlation length not exceeding the characteristic pore size. More elaborate (renormalization group) theoretical treatment of the problem of confined nematics was recently reported by Feldman [610]. He has demonstrated that in the case of weak disorder a state with quasi-longrange order can be formed. However, in the case of strong disorder the topological defects drive the system into the glass state, in which the orientation of the director is determined only by the local random potential. Influence of randomness to a large extent is governed by the ratio between the average pore radius R and the nematic correlation length n . In [249] estimations were made for the controlled porous glass matrix, and it was shown that the effects of randomness become important for R < n , where the noncorrelated curvatures of cylindrical voids are the main origin of randomness. Properties of the confined LCs have been extensively studied by different experimental techniques such as NMR [249, 614], light scattering [604], dielectric spectroscopy [615], X-ray diffraction [246], etc.

839 In particular it was shown that in small pores, as already mentioned, isotropic-nematic (I-N) phase transition is replaced by a gradual evolution of the nematic order [249, 612–614]. However, in the case of large enough pores (R ≥ 25 nm for pentylcyanobiphenil (5CB) in controlled porous glass [249]) the I-N phase transition is discontinuous. In this case TI-N can be shifted either upward or downward, depending on the size of the cavity and on the ordering properties of the cavity surface. In the mentioned example of 5CB in CPG, with a decrease of TI-N with TI-N =
Ibulk -N − 13 ± 03 ∝ 1/R [249]. T =∝ 1/L (L is the mean free
Iconf I-N -N path in the empty regions), scaling was observed for LCs in aerogel matrix [616]. It should be mentioned that in many cases the surface-induced paranematic order is observed in the isotropic phase [614]. The nematic-smectic-A phase transition is usually more affected than the I-N one [249]. It was demonstrated for the octylcyanobiphenyl (8CB) in controlled porous glass [246, 249] that 8CB was confined to anopores (200 nm in diameter) [617] and aerogels (mass densities  = 008060 g · cm−3 ) [616]. In the case of porous glasses, LC-surface interaction was modified by silanizing the surface. According to [249], silane-treated surface exhibits homeotropic anchoring and nontreated surface planar anchoring. In nontreated samples the smectic order parameter temperature dependence is similar to that in bulk LCs, with the order parameter reduced by a few percent [246]. In the case of nontreated surface pretranslation, smectic ordering is observed. Temperature dependence of the smectic correlation length sm , similar to that in magnetic systems with random fields, was observed for both treated and untreated samples [246]. sm was gradually increased by lowering the temperature from the nematic phase and saturated at sm ≈ R. In the case of anopores the surface was either untreated or lecithin-treated. The rough untreated surface inhibited the smectic growth, whereas in the case of the lecithin-treated surface the smectic layers were initiated at the surface [617]. Dynamics of LCs is strongly affected by confinement. Broadband dielectric spectroscopy of 5CB and 8CB in porous glasses (10–100 nm) has revealed a number of differences between bulk and confined behavior [618]. Similar to those of confined liquids (see 4.5.1), all observed relaxation processes are of the non-Debye type but can be well described by the Havriliak-Negami equation, (26). The relaxation processes in confined LCs are not frozen, even at temperatures about 20 below bulk crystallization temperatures. Confinement resulted in the appearance of two new relaxation processes not observed in the bulk LCs. One of the processes is related to the presence of the surface layer; the origin of the other is not clear yet. Dynamics of the nematic-isotropic phase transition was studied with time-resolved transient grating optical Kerr effect measurements [619]. Nonexponential decay and drastic decrease in the relaxation time of the order parameter fluctuations were observed in the pretransitional temperature range. This result is in contrast with data of Wu et al. [612], who observed below bulk TI/N slowing down of the critical fluctuations described by the Vogel-Fulcher law. Dielectric spectroscopy was also used to study the smectic-A to smectic-C* transition in W314 LCs confined in aerogels ( = 008 and 017 g · cm−3 ) [615]. In addition to

Nanostructures Within Porous Materials

840 the Goldstone collective mode, an additional relaxation process related to the surface layer was found with decreasing, strength while the strength of the Goldstone mode increased on cooling.

4.7. Helium in Confinement The problem of quantum liquids (He and hydrogen) is too broad to be covered as a small part of a more general review, so we will indicate just some of the main topics related to this problem. As early as 1956, the first studies of Vycor glass as a superleak were reported in [620]. Later on, solidification [537, 541], superfluid transition [621–624], dynamics [625, 626], and other properties were studied in great detail. A paper by Adams et al. [541] remains the most detailed study of the P -T phase diagram of 4 He confined in the Vycor glass for 0.8 K < T < 25 K and P ≤ 60 bar. No solidification was found for P < 363 bar, and it was shown that at T = 08 K, solid and liquid may coexist for 36.3 bar < P < 380 bar. The line of superfluid phase transitions was shifted to lower temperatures for about 0.2 K but remained parallel to that in bulk liquid He. In [623] the temperature dependence of the superfluid density S was examined in the critical region for 4 He in Vycor glass. It was shown that superfluid density follows a power law in reduced temperature, S ∝ # , with the exponent # ≈ 067, in numerical agreement with the bulk value. Later [624] S   dependences were checked for He in Vycor (full filling and films) xerogel (full and film) and aerogel, and values of # from 0.63 to 0.91 were obtained. Different critical exponents indicate different universality classes. Moreover, Mulders et al. [627], analyzing earlier published data on S and specific heat temperature dependences, have demonstrated apparent violation of the hyperscaling relation 3# = 2 − . We are not aware of any reliable explanation of the described facts. Recently several papers were published that attempted to solve the puzzle of confined helium properties by microscopic measurements. In [626] Sokol et al. report the results on an inelastic neutron scattering study of roton excitations in two different porosity aerogels. Crossover in the temperature dependence of the roton energy gap was observed at T ≈ 19 K, which was explained in terms of length scales of confinement and the roton mean free path. It was suggested that the roton mean free path determines the spatial scale above the crossover temperature, while below it the temperature dependence of the roton energy is suppressed. Some very recent inelastic neutron scattering results on He in xerogel glass were presented in [625]. In spite of the huge total number of publications, we believe that there is still no comprehensive understanding of the problem.

GLOSSARY Confinement Restriction of some material to a given volume; can be one-dimensional (films), two-dimensional (filaments), or three-dimensional (isolated particles). Phase transition Change of a substance from one phase (the type of a system, such as solid, liquid, gas, superconductor, ferromagnet, etc.) to another. Also known as phase transformation.

Porosity The existence of some free volume inside a solid material structure, which is not occupied by structural elements of this material. Size effect The effect of size of a piece of material on its properties. Wettability The ability of any solid surface to be wetted when in contact with a liquid; that is, the surface tension of the liquid is reduced so that the liquid spreads over the surface.

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Encyclopedia of Nanoscience and Nanotechnology

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Nanostructuring at Surfaces Using Proteins Michael Niederweis Friedrich-Alexander Universität Erlangen-Nürnberg, Erlangen, Germany

Stefan H. Bossmann Universität Karlsruhe, Karlsruhe, Germany

CONTENTS 1. Introduction 2. S-Layer Proteins 3. Porins from Gram-Negative Bacteria 4. The Porin MspA from Mycobacterium smegmatis 5. Conclusion Glossary References

1. INTRODUCTION The information age can be characterized by its everincreasing demand of ultrafast computer systems, which resulted in the expectation of an exponential success in miniaturization, which is known as Moore’s “law” [1]. Although more conventional techniques, such as (deep) UVpatterning [2], X-ray proximity [3], or ion-beam projection lithography [4] are being optimized and installed in industrial development and production units, it is apparent that the successful design of nanoscale systems will require entirely new materials, processes, and device architectures. In order to meet this challenge, a wide range of methods for the nanostructuring of (mostly metal-) surfaces [5] was developed during the last two decades. This research endeavor is particularly dedicated to the development of advanced hardware. However, other commercial applications of (bio-)nanosystems are of increasing importance as well; for instance bio- and medical sensing systems [6] and optical devices [7]. The most advanced technologies today ISBN: 1-58883-063-2/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

are commonly described as electrochemical nanostructuring (by tip-induced metal deposition or oxidation) [8] and atomic force microscope (AFM) lithography [9]. Electrochemical methods are based on the technology of the scanning tunneling microscope (STM) [10]. However, until now the most significant disadvantage of electrochemical nanostructuring and AFM Lithography is that nanostructuring has to be performed atom-by-atom or fragment-by-fragment, respectively. Consequently, the defined nanostructuring of surfaces has been time-consuming and expensive. Therefore, the generation of well-defined nanostructures by protein or macromolecule deposition on two-dimensional surfaces would represent a considerable advantage compared to the technologies previously mentioned. Especially the use of proteins has many advantages [11]. Proteins are, in comparison to synthetic polymers, much more “intelligent” materials, because they are able to interact site-specific with each other as well as with possible ligand molecules or substrates [12]. Furthermore, proteins permit the harvest of the results from very many of years of evolution for nanotechnical purposes [13]. Even better, the genetic technology of site-directed mutagenesis permits the introduction of specific features for tailor-made nanotechnological application into the protein-based assemblies.

1.1. Design and Future Applications of Quantum Dots Recent developments in nanotechnology offer applications in very different areas, such as electron tunneling (superconduction) at feasible temperatures [14], (photo) electro-catalysis [15], the development of quantum computers [16], as well as novel photoelectrochemical devices, using the effect called “plasmon-resonance” of an array of nanoparticles or -wires [7]. To date, the most developed nanosystems for quantum applications consisted of

Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 7: Pages (851–867)

852 doped carbon-nanotubes [17] and doped zeolites [18]. However, both template materials lead inevitably to at least some degree of electrical connection between the embedded nanoparticles. Therefore, possible quantum effects could be cloaked by unwanted electrical connection of the individual quantum dots. In this case, we cannot expect “real quantum effects” when these materials are used for advanced electrocatalysis. The use of a stable protein as nanotemplate for the stabilization of nanoparticles and -wires would provide an electrically insulating matrix for the consequent electrosynthesis [19] of metal-nanoparticles or nanowires. Furthermore, at least some proteins possess the ability of self-organization under in-vitro conditions. A straightforward approach to the generation of stabilized nanoparticles consists of the use of nanotemplates, which act as “hosts” for the nanoparticles [20]. These nanoscopic particles are generated by reduction of metal salts by chemical processes [21]. Protein-stabilized nanoparticles represent an ideal quantum-dot system, having the big advantage that the exterior of the synthesized Au, Ni, or Pt-nanoparticles or -nanowires will be embedded by the protein, serving as an ideal insulator. Since only the openings of the metal-filled nanochannels or nanopores will be open to the supernatent buffer or the substrate, real quantum effects could occur. Besides quantum effects, protein-based nanodots may permit the observation of very large electrical field effects, since the electrical field at the top of a metal-doped protein channel will easily exceed 106 Vcm−1 .

1.2. S-Layer Proteins and Porins Two groups of bacterial proteins are of a special interest for the design of future nanotechnology: the S-layer proteins and the porins. S-layer proteins form two-dimensional crystalline surface arrays and have been identified in hundreds of different species from nearly every taxonomic group of walled eubacteria and are also present in many archeabacteria [22]. S-layer proteins from numerous species were isolated and characterized and are, in principle, available for technical applications. Porins are channel proteins in bacterial outer membranes and allow the diffusion of small and hydrophilic compounds [23–26]. In contrast to the S-layer proteins, various porins have been intensively studied with respect to their biophysical properties [27–29]. The mechanisms and the triggering factors of the channel-opening are of especially great interest because of possible applications of ion- and diffusive channels [30–34]. Furthermore, the crystal structures of some porins of Gram-negative bacteria have been solved and the diffusion of ions through porin channels have been computer-simulated [35]. Channel porins from Gram-positive bacteria and especially from Mycobacteria [36] are of special interest with respect to their application in nanotechnology because of their unique channel lengths [37]. Since the structures (and especially also the functions) of bacterial porins have been optimized in evolution, we might as well use these highly versatile biological structures directly, instead of mimicking their structures and working principles in chemical membrane and surface models. Nevertheless, it must be noted that evolution was not

Nanostructuring at Surfaces Using Proteins

directed toward any applications in nanotechnology, but rather headed for an optimized influx of nutrients while providing maximal protection at the same time. Therefore, we have to proceed with great care on this path. It is apparent that the chemical stability of bacterial proteins (S-layer subunits and porins) against thermal and photochemical decomposition reactions must be sufficient in order to permit a successful application in nanotechnology [38]. The porin MspA isolated from Mycobacterium smegmatis possesses a superior chemical stability and can, principally, be used as a chemically synthesized polymer [39]. It possesses very distinct properties and forms nanochannels (not open “pore” structures like those found within S-layer lattices) of approximately 2.5 nm in diameter and 10 nm in length [37]. Furthermore, MspA can be reconstituted in various environments just as lipid bilayers, polymers, and hydrophobic surfaces. Therefore, the formation of nanochannels cannot only be achieved within one defined environment, like in the case of pore formation within S-layer lattices, but can be achieved in virtually any hydrophobic environment. This approach is considerably more versatile with respect to nanotechnology applications. In this respect, it is very fortunate that MspA has a very high tendency to form pores in artificial environments and that these pores were, at least in the examples known to date, of comparable geometric extensions. MspA nanochannels are hydrophilic in their interior and strongly hydrophobic in their exterior. Due to the electrically insulating nature of the pore walls and their geometric dimensions, the pores formed by the MspA porin from Mycobacterium smegmatis represent a serious challenge to carbon nanotubes as host systems for nanotechnological applications. This chapter is describing the most important developments in the field of nanotechnology on surfaces employing proteins. It consist of the following sections: (2) S-Layer Proteins; (3) Porins from Gram-Negative Bacteria; (4) The Porin MspA from Mycobacterium smegmatis. In each section, a comprehensive description of the most striking biochemical and biophysical properties is provided, before we discuss the applications as well as the application potential of the proteins of interest in nanotechnology at surfaces and surface structures.

2. S-LAYER PROTEINS The surface of many bacteria is covered by two-dimensional crystalline arrays of proteins or glycoprotein subunits, which are commonly referred to as “S-layers” [22, 40]. Consequently, S-layer proteins belong to the most abundant proteins in prokaryotes comprising up to 15% of the total cellular protein [22]. Although considerable knowledge has accumulated on the structure, assembly, biochemistry, and genetics of S-layers, relatively little information is available about their specific functions [41]. S-layers are thought to function as molecular sieves, protective or adhesive coatings or ion traps. Furthermore, in all bacteria that possess S-layers as exclusive cell wall components, the cell shape is determined by the (glyco)proteins [41]. Whereas the S-layer proteins from archaebacteria and Gram-negative eubacteria are not connected to their cytoplasmic or outer membranes, respectively, the S-layer

Nanostructuring at Surfaces Using Proteins

proteins of at least some Gram-positive eu- and archaebacteria are indeed chemically linked [42]. As it can be seen from the examples provided in Figure 1, considerable variations in structure, complexity, and lattice symmetry of Slayer proteins exist. However, many S-layers are similar with respect to their chemical composition, formation principles, biophysical properties, and molecular size distribution. The thickness of S-layers ranges from 5–25 nm [40]. The outer surface appears often to be smooth, whereas the inner surface is more corrugated [43]. Structural investigations of S-layers in vivo and after recrystallization on various substrates were performed using a combination of very different techniques, such as metal-shadowing, negative staining, ultrathin-sectioning, freeze-etching, scanning probe microscopy experiments, and underwater atomic force microscopy [22]. Structural information was obtained down to the subnanometer range. Consequently, the formation principles of two-dimensional S-layer protein arrays and their self-repeating structures are known [44]. S-layer lattices, which form an array of protein or glycoprotein subunits, possess either oblique (p1, p2), square (p4), or hexagonal (p3, p6) symmetry (see Fig. 2). The symmetry class in which the S-layer proteins crystallize is strongly dependent on the bacterial species, but not on the experimental conditions of the crystallization process. The experimental conditions only determine whether the formation of wellordered lattices at surfaces does occur or not. One of the results from the structure elucidation of S-layers is that they form highly porous mesh works with a porosity in the range between 30–70%. The assemblies of identical protein or glycoprotein subunits possess masses in the range of 35,000 to 230,000 Dalton and exhibit pores of identical size and morphology. Many S-layers feature two or even more distinct classes of pores in the range of 2–8 nm. The subunits of most S-layers interact with each other during the process of S-layer formation through noncovalent forces including hydrophobic interactions, hydrogen bonds, ionic bonds, and the interaction of polar groups [40]. The chemical composition of S-layer (glyco)proteins from all phylogenetic branches was found to be surprisingly similar [40]. The typical S-layer is composed of an acidic protein or glycoprotein, possessing an isoelectric point in the region from pH 3 to 5. Since the isoelectric point of a protein results from the superposition of the isoelectric points of those amino acids, which are exposed to the aqueous electrolyte, it is very interesting to take a look at the chemical composition. Typical S-layer proteins have high amounts of glutamic and aspartic acid. Together, they account for 15 mol%. The lysine content of S-layer proteins is in the range of approximately 10 mol%. Thus, ionic amino acids make up about a quarter of the total composition of S-layer proteins. This finding indicates clearly the importance of ionic interactions during the formation of the S-layer lattice structure. It is noteworthy that the content of sulfur-containing amino acids in the S-layer proteins is close to zero. Interestingly, the main fraction of amino acids of S-layer proteins is hydrophobic in nature. It is even more interesting that hydrophobic and hydrophilic amino acids do not form extended clusters, but alternating segments with a more hydrophilic region at the terminal N-end. Information regarding the secondary structures of S-layer

853

Figure 1. The structures of bacterial cell walls. (A) Archaebacteria; (B) gram-negative eubacteria; (C) gram-positive archae- and eubacteria [22]; and (D) legend.

854

Figure 2. Symmetries of S-layer lattices (schematic representations).

proteins was obtained by using circular dichroism measurements, FT-IR-spectroscopy, and especially from secondary structure prediction based on the available protein sequence data [45]. In a typical S-layer, up to 70% of the proteins form
-helices and 20% form -sheets. Aperiodic foldings and -turn contents account for most of the missing fraction. In many of the S-layers, the N-terminal regions, which are among the parts of the protein-sequence self-organized as
-helices, are able to recognize distinct structures in the underlying cell envelope [46]. Because of the noncovalent nature of the bonds between the subunits, which are hydrophobic as well as ionic in nature, the growth of the S-layer, which is in most of the investigated cases surrounding the whole bacterium, proceeds very rapidly. One can approximate that a coherent S-layer at the surface region of an average cell is formed by the supramolecular interaction of approximately 5 × 105 protein or glycoprotein subunits. For S-layered bacteria with a generation time of 20 min, approximately 500 copies of the S-layer subunits have to be synthesized inside the cell, translocated and integrated into the S-layer per second [22] (Fig. 3). Because of their unusual building mechanisms and dynamics, S-layers can been described as “dynamic closed surface crystals,” with the intrinsic capability to assume a structure of low free energy during cell growth and also during their growth and assembling processes at membranes and artificial surfaces.

2.1. Applications of S-Layer Proteins at Surfaces The physicochemical properties and especially the permeability of S-layer cell envelopes are of a profound interest because they offer (a) an insight into the function principles of the bacterial transport mechanisms, and (b) the possibility of designing permeability filters for nano- and biotechnological applications [22, 47].

Nanostructuring at Surfaces Using Proteins

Figure 3. Oblique S-layer lattice of Bacillus stearothermophilus Adapted with permission, from [22], M. Sara and U. B. Sleytr, Prog. Biophys. Molec. Biol. 65, 83 (1996). © 1996, Elsevier Science.

2.2. S-Layer Proteins as Permeability Barriers S-layer proteins from mesophilic and thermophilic Bacillaceae were studied in detail. Opposite to the underlying peptidoglycan-containing “wall skeleton,” no net negative surface charge was determined. The charge density found in the native S-layer from B. sphaericus was 1.6 carboxylic acid functions per nm2 . However, the free carboxylic acid functions are neutralized by free amino groups of lysine. The presence of an approximately equimolar amount of amino groups and carboxylic acid groups in the pore areas of many Bacillaceae, prevented the adsorption of charged macromolecules inside the pores. Therefore S-layers from Bacillaceae can be used as suitable antifouling coatings. Furthermore, permeability studies performed on the same S-layers, demonstrated that, in spite of the considerable differences in the lattice types, the molecular weight cutoff was 30,000–40,000 Da [48]. This data is in agreement with the assumption of a pore diameter of approximately 4–5 nm.

2.3. S-Layer Ultrafiltration Membrane For the synthesis of S-layer ultrafiltration membranes (SUMs), [49] either cell wall fragments with adhering S-layer proteins or previously isolated self-assembling Slayer subunits are used. Also in this case, S-layers from Bacillaceae possess ideal physical and chemical properties. The fixation of S-layers at microfiltration membranes can be achieved using a pressure procedure. Then the S-layer lattices on top of either the microfiltration membrane or the cell fragment adhering to the microfiltration membrane are crosslinked with glutaraldehyde, and thereafter the Schiff bases are reduced employing sodium borohydride as reagent. Depending on the very defined structures of S-layer lattices on surfaces, the rejection curves of S-layer-SUMs are distinctly

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Nanostructuring at Surfaces Using Proteins

steeper than of microfiltration membranes made of amorphous polymers. Again, a molecular weight cut-off of 30,000–40,000 was found. This is not surprising because the molecular weight rejection effect is achieved by the pore structure of the S-layer lattice.

B. sphaericus CCM 2120 can bind anionic, cationic, zwitterionic, and noncharged macromolecules. Note that only the surface of Thermoanaerobacter thermohydrosulfuricus is glycosylated [22].

2.5. Semifluid Membranes 2.4. Chemical Modification of S-Layers The crosslinking procedure using glutaraldehyde produces eventually a net negative charge. Carbodiimide activation offers the opportunity to link carboxylic acids to a manifold of chemical reagents and groups [50]. Thus, either a strong net negative charge or a strong positive net charge can be achieved. Also the hydrophobicity of SUMs could be modulated following the same experimental approach. It is of special importance that the distinct geometry of the self-repeating S-layer lattice did not change noticeably when the free carboxylic acids are chemically modified. S-layer glycoproteins offer the same opportunities via the activation of their glycan chains either by periodate oxidation or cyanogens-bromide activation. A recent example of this versatile strategy was the application of S-layer-coated liposomes for entrapping and binding of functional molecules: The S-layer protein from Bacillus stearothermophilus PV727P2 was recrystallized on positively charged unilamellar liposomes of an average diameter of 180 nm formed by dipalmitoyl phosphatidylcholine (DPPC), cholesterol, and hexadecylamine (HDA) (molar ratio: 10/5/4) [51]. The S-layer subunits possess the molecular weight of 97,000 and form a two-dimensional lattice of oblique symmetry. Crosslinking was achieved using glutaraldehyde. Then, the free carboxylic groups were activated with 1-ethyl-3-(dimethylaminopropyl)-carbodiimide (EDC). This reagent has the advantage that it can be successfully employed also in aqueous solutions. The crosslinking process could be observed employing S-layer–coated carbonic anhydrase containing liposomes (SCALs). Whereas the crosslinking reaction proceeded exclusively between adjacent S-layer subunits within the two-dimensional lattice at the outer surface of the liposomes, the enzyme carbonic anhydrase, located inside the liposomes, was not effected by the chemical treatment as it could be demonstrated using SDS-polyacrylamide gel electrophoresis (SDSPAGE). When the crosslinking of the S-layer subunits was performed using Bis(sulfosuccinimidyl)suberate (BS), evidence for heterologous crosslinking between the S-layer protein and membrane incorporated HDA was found. The supramolecular as well as the highly specific binding of molecules and polymers to S-layer lattices can also be achieved by using noncovalent forces. Important factors determining the nature and the selectivity of the binding are the S-layer lattice type, the geometric sizes (or the vander-Waals radii, respectively) of the morphological units and the chemical nature, the physicochemical properties, and the distribution of binding sites on the array. An example for this binding type is the binding of polycationic ferritin (PCF) on the S-layer lattice of B. coagulans E38-66 [52]. The hexagonally ordered S-layer lattices from B. stearothermophilus PV72 and Thermoanaerobacter thermohydrosulfuricus L111-69 [53] and the square S-layer lattice from

A simple and straightforward method for generating coherent S-layers on lipid films is the injection of isolated S-layer protein subunits in the subphase of the Langmuir–Blodgett (LB)-trough. The crystallization of the two-dimensional S-layer lattices begins at several nucleation points and proceeds underneath the preformed phospholipid or tetraetherlipid films until coalescence of the single crystal domains occurs. Generally, the orientation of S-layers, which can be crystallized on any kind of surfaces, is determined by the anisotropy of their physicochemical surface characteristics. The more hydrophilic surface, which possesses net negative charges, is usually directed towards the negatively charged or zwitterionic head groups of phospholipid or tetraetherlipid films. Since the direction is determined by the charged head groups embedded in the S-layer structure, the more hydrophobic “outer” face (with respect to its natural orientation adhering to the bacterial cell) is directed toward the water phase during its formation. However, ordered phases with adhering S-layers can be either turned or transferred onto organic, ceramic, or metal supports. It is noteworthy that the fluidity of the lipid films, which were previously used as self-assembled mono- or bilayers is a very critical parameter for generating coherent S-layer lattices. When the formation of S-layers adhering to lipid films is achieved, crosslinking can be performed using glutaraldehyde. The latter procedure increases the mechanical stability of the S-layers on lipid film remarkably. In a very similar manner, so-called semifluid membranes can be generated [54]. In these cases, where free carboxylic or amine groups are left after the crosslinking procedure using glutaraldehyde, lipid molecules of the LB film can be chemically linked to the S-layer protein lattice. The linking of the S-layer protein subunits to individual lipid molecules, which interact nevertheless with all lipid molecules forming the lipid monolayer or bilayer, decreases the lateral diffusion (Fig. 4). Consequently, the fluidity of the whole membrane assembly decreases. Using standard procedures, a manifold of functional biomolecules (for instance, ion channels, molecular receptors, proton pumps, or porins) can be integrated in semifluid membranes. Depending on the structure and hydrophobicity of the biomolecules, the integration into the lipid film can be achieved either before the chemical fixation of the adhering S-layer lattice or after this procedure. Because of the flexibility of this experimental approach, this technology has a big potential to initiate a broad spectrum of developments in the fields of optical or electronic nanodevices, diagnostics in medicine, and life science engineering. The application of S-layer–coated liposomes for entrapping and binding of functional molecules via the avidin- or streptavidin-biotin bridge demonstrated this potential [54]. Two biotin residues accessible to avidin binding were bound to every S-layer subunits within the crosslinked S-layer lattice. Using biotinylated ferritin, which serves as an excellent electron paramagnetic resonance (EPR) marker, it could

856

Figure 4. Schematic representation of a “semifluid” membrane, composed of an S-layer lattice possessing binding sites for lipid molecules and a lipid mono-/bilayer.

be demonstrated that a well-ordered layer of straptavidin formed on the accessible surface of the S-layer coated liposomes. The same strategy also proved valuable when biotinylated antihuman IgG was attached via streptavidin to the biotinylated S-layer–coated liposomes (Fig. 5). The biological activity of the S-layer bound antihuman IgG was confirmed

Nanostructuring at Surfaces Using Proteins

using the enzyme-linked immunosorbent assay technique (ELISA). A similar strategy was used for the immobilization of the enzymes invertase (Mr 270,000) and glucose oxidase (Mr 150,0000) at the S-layers of B. stearothermophilus PV72 and T. thermohydrosulfuricus L111-69 [54]. The labeling density corresponded to 2–3 enzymes per hexametric unit cell of the S-layer lattice. This finding corresponded to the formation of a monomolecular enzyme layer on the surfaces of both Llayer lattices. Immobilized invertase retained approximately 70% of its enzymatic activity in the nonimmobilized state, glucose oxidase approximately 35%. When spacer molecules were used (4-amino butyric acid or 6-amino caprotic acid), the measured activity of glucose oxidase increased to about 60%. The use of spacers obviously prevented the binding of whole enzymes or partial enzyme structures within the S-layer pores and is especially advantageous for the generation of enzyme assays.

2.6. S-Layer Based Amperometric and Optical Biosensors As already pointed out, a broad range of amperometric and optical bioanalytical sensors have been developed using suitable S-layer lattices as nanoscale immobilization matrix. The concepts of enzyme-immobilization and the manufacture of SUMs have already been discussed. For the fabrication of a single enzyme sensor, for instance a glucose sensor, glucose oxidase was bound to the surface of a S-layer ultrafiltration membrane. The electrical connection to the sensing layer was achieved by sputtering a nanoscopic gold or platinum layer onto the S-layer bound enzyme layer. The whole sensor assembly is then usually stabilized using a conventional gold or platinum electrode, by which the electrical contact to the nanolayer is achieved. In this configuration, the analyte reaches the immobilized enzyme through the pores of the S-layer (Fig. 6) [55, 56].

2.7. Molecular Nanotechnology Using S-Layers One important and very successful approach towards the molecular nanotechnology of the future consists in the generation of so-called “self-assembled monolayers” (SAMs) at metal (especially gold)-, silicon-, or highly oriented pyrolithic graphite (HOPG) surfaces [57]. Self-assembled monolayers are formed by chemically attached lipids, which are bound to these surfaces in such a density that

Figure 5. Schematic representation of a liposome, which is coated with an S-layer lattice. The S-layer subunits are chemically linked to functional macromolecules, such as enzymes.

Figure 6. Schematic representation of an amperometric biosensor. (A) microfiltration membrane; (B) multiplayer, consisting of enzyme loaded S-layer fragments; (C) sputtered metal layer.

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Nanostructuring at Surfaces Using Proteins

cooperative effects, just as two-dimensional condensation, occur. Therefore, SAMs are highly ordered and can serve as substrates for the binding and/or incorporation of hydrophobic substrates of all kinds. A very interesting alternative to the formation of SAMs is provided by the recrystallization of S-layer subunits of surfaces, which are suitable for nanofabrication. Silicon or gallium arsenide wafers are two examples for the successful creation of an ordered S-layer on a semiconductor material. S-layer lattices have a great potential for the development of molecular manufacturing procedures and biological nanoresists. A first success using recrystallized S-layer lattices on semiconductor materials was achieved by the method of deep ultraviolet irradiation (DUV) [58] (Fig. 7). This method is principally related to the conventional negative photoresists, which will not be able to satisfy the hardware needs of the information age. However, it can be regarded as an example for the modern nanotechnology yet to be developed, because it uses the self-replication properties of S-layer lattices for lateral nanopatterning of wafer surfaces. The method of deep ultraviolet irradiation employs the argon-fluorine (ArF) excimer- (or more correctly, exciplex-) laser system as a coherent light source. The current restriction in the availability of optimal mask systems only permits the generation of submicron structures. Exposure with deep ultraviolet photons, followed by the treatment with an aqueous buffer solution leads to the complete removal of the S-layer lattice located on top of the wafer material. It is very likely that the absorption of high energy photons causes chemical transformations of the amino acids, which are forming the S-layer subunit proteins. Possible photoreactions are Norrish I and II reactions [59], as well as photoinitiated oxidation reactions, which produce water-soluble groups such as carboxylic acids and alcohols. Because of this deep UV-induced chemical transformation, the ability of the S-layer subunits to form ordered lattices is greatly diminished. If the exposure time is optimized, the exposed S-layer surfaces can be completely removed by this procedure. It is noteworthy that the unexposed S-layer surface areas retain their structural and, therefore, their functional integrity.

2.8. Synthesis of Semiconductor and Metal Nanoparticles Using S-Layer Templates As pointed out earlier, the use of organic and inorganic templates for the synthesis of semiconductor and metal nanoparticles is a very promising strategy. S-layer lattices represent ideal templates, because they represent highly ordered pore structures [57]. By choosing the right S-layer type, nanopores can be obtained. These nanopores can support either the crystallization of inorganic nanoparticles or their chemical or electrochemical reduction [54]. Inorganic superlattices of cadmium sulfide (CdS) with either oblique or square lattice symmetries were fabricated by exposing self-assembled S-layer lattices to Cd2+ -ion solutions. After cation-exchange, a slow reaction with hydrogen sulfide was carried out. Precipitation of CdS was confined to the nanopores only and, therefore, the resulting CdSdoped S-layer superlattices possessed the same symmetry as the S-layer lattices used as templates. Using this method, extended arrays of a very defined nanostructure, extending to 5 × 104 nm2 could be fabricated [60]. A similar procedure resulted in the generation of a square superlattice of uniform 4–5 nm-sized gold particles with a 12.8 nm repeat distance [61]. The key steps of this procedure were the induction of thiol groups to the S-layer and the exposition of the resulting template to a tetrachloroauric acid (H[AlCl4 ]) solution. Electron irradiation under transmission electron micrograph (TEM) conditions led to the initial formation of a grainy gold layer covering the whole surface of the S-layer. The shape of the gold particles resembled the morphology of the pore region of the S-layer. Crystalline Au(O)-particles were found. However, they did not follow a crystallographic pattern. This approach to nanopatterned metal-coated S-layers did not only work with H[AlCl4 ], but also employed PdCl2 , NiSO4 , KPtCl6 , Pb(NO3 2 , and K3 [Fe(CN)6 ] [54]. Principally, any combination of S-layer lattice symmetries (oblique, square, or hexagonal), -lattice dimensions and pore sizes with a suitable nanomaterial (metal, metal oxide, or semiconductor particle) can be achieved.

3. PORINS FROM GRAM-NEGATIVE BACTERIA

Figure 7. DUV (193 nm)-patterned S-layer coated surface (550 × 550 nm). (For the original images, see [58]).

Porins are channel proteins in bacterial outer membranes and allow the diffusion of small and hydrophilic compounds. Their properties are under intensive investigation [23–26]. Numerous biotechnological applications of porins from Gram-negative organisms were reported [62, 63] with respect to biochemical [64–66] and medicinal [67] applications. Porins from E. coli or other Gram-negative bacteria are stable channel-forming proteins, but they dissociate into inactive monomers above temperatures of 55–70
C [68–70]. Therefore, their application in nanotechnology at surfaces are limited. We want to describe one very promising application of a porin from a Gram-negative organism in more detail here, because of its prospects for future developments: Nanoreactors based on polymerized ABA-triblock copolymer vesicles have been successfully designed [71]. They

858 consisted of stable nanocapsules from an ambiphilic poly(2methyloxazoline)-block-poly(dimethylsiloxane)-blockpoly(2-methyloxazoline) triblock copolymer (PMOXAPDMS-PMOXA) [72]. In perfect structural analogy to the S-layer proteins, these artificial block copolymers consist of separated hydrophilic and hydrophobic polymer segments. Therefore, the PMOXA-PDMA-PMOXA-triblock copolymer aggregates spontaneously in dilute solutions into vesicular structures. Depending on the experimental conditions, the size of the polymer-triblock vesicles can be controlled in the range from 50–500 nm [73]. Again, in a further analogy of the S-layer lattices, the resulting nanocapsules can be further stabilized by subsequent crosslinking polymerization of the reactive end groups. The result is a “supermacromolecule,” in which all the individual block copolymers are connected by covalent bonds. The polymer triblock vesicles were used to encapsulate a model enzyme -lactamase in its interior [74]. To create a nanoreactor, the very thick triblock copolymer shell (d = 10 nm) has to be overcome in order to feed the enzyme with a suitable substrate. However, owing to their higher hydrophobic thickness, the triblock copolymer shells are even less permeable than conventional phospholipid bilayers. This situation is a typical case where the application of a suitable channel porin is requested, because the PMOXA-PDMA-PMOXA triblock copolymer behaves in aqueous buffer solutions principally like a higher molecular weight analogue of conventional lipids. However, the block copolymer membranes are approximately twice as thick as conventional bilayers. The bacterial porin OmpF forms trimeric channels in the outer membrane of E. coli [75] and was chosen to provide a pathway through the block copolymer membrane. The high flexibility and the conformational freedom of the triblockcopolymer membrane permits its adaptation to the specific requirements of the bacterial porin [76]. If the OmpF porin can retain its specific geometric and dynamic conditions, it will retain its “natural” functions. After the spontaneous

Figure 8. Scheme of a nanoreactor consisting of the crosslinked PMOXA-PDMA-PMOXA triblock copolymer, the bacterial porin OmpF, and the encapsulated enzyme -lactamase [74].

Nanostructuring at Surfaces Using Proteins

reconstitution of OmpF in the triblock copolymer shells, the encapsulated enzyme -lactamase was successfully “fed” using the antibiotic ampillicin as model substrate, resulting in the “production” of ampicillinoic acid (Fig. 8). The latter, in contrast to ampillicin, is able to reduce iodine to iodide. This offers the opportunity to observe the reaction progress monitoring the Vis-absorption of the iodine/starchcomplex. A high activity of -lactamase was retained within the nanoreactors, which represent a perfect model for the nanoreactor technology of the future. Upscaling of a nanoreactor system is easily possible because of the very favorable diffusion conditions in the nanoscopic scale.

4. THE PORIN MspA FROM MYCOBACTERIUM SMEGMATIS 4.1. The Mycobacterial Cell Envelope The mycobacterial cell envelope forms an exceptionally strong permeability barrier rendering mycobacteria naturally resistant to a wide variety of antimicrobial agents. This is due to its unique structure [77]. The arrangement of the various layers of the mycobacterial cell wall is shown schematically in Figure 9. The innermost layer of the envelope is the cytoplasmic membrane of about 4 nm thickness. Outside this membrane is the so-called “cell wall skeleton,” a giant macromolecule entirely surrounding the bacterial cell,

Figure 9. Structure of the mycobacterial cell envelope The inner leaflet of the outer membrane is composed of very long-chain fatty acids, the mycolic acids, which are covalently linked to the arabinogalactanpeptidoglycan copolymer The mycolic acids differ in length and modifications. The outer leaflet is formed by a great variety of extractable lipids such as trehalose-dimycolate (“cord factor”), lipooligosaccharides, sulfolipids, glycopeptidolipids, phenolic glycolipids and glycerophospholipids. It should be noted that bilayer formation of mycolic acids is only possible, when the cross-linked glycan strands and the arabinogalactan strands run in a direction perpendicular to the cytoplasmic membrane. The inner membrane is mainly is mainly composed of convential phospholipids. The thicknesses of the inner and outer membrances are derived from electron microscopic images of mycobacterial cell envelopes and are drawn to scale.

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Nanostructuring at Surfaces Using Proteins

and consisting of peptidoglycan (a structure of oligosaccharides formed from disaccharide units of N-acetylglucosamine and N-glycolylmuramic acid crosslinked by short peptides), arabinogalactan (a complex branched polysaccharide), and mycolic acids (long-chain, 2-alkyl-3-hydroxy fatty acids). Associated with the cell-wall skeleton, but not covalently attached to it, are a large variety of other lipids. Substantial evidence for the organization of the mycolic acids in a second lipid bilayer in addition to the cytoplasma membrane was presented by Nikaido et al. [78]. X-ray diffraction measurements on purified mycobacterial envelopes, free of plasma membranes ( 100 nm) is typical for a deposited pattern that was only investigated by TEM for a short time (less than 60 s).

4.7. Formation of Dendrites and Stars In Figure 18, dendrites and “stars” generated by deposition of MspA for 175 ± 5 s at 40 ± 5
C at the chosen carbon surface are shown. The comparison of the occurrence of this micropattern at very low TEM exposition times (t < 60 s) and after 300 s of electron beam treatment reveals polymerization of MMA included in the formed micropattern. The average thickness of the formed dendrites and stars was approximately 110 to 120 nm in the beginning of the TEM characterization, whereas the thickness decreased to 25–30 nm after 300 s of continuous electron beam exposure. In addition to the observed polymerization process, evaporation of water and MMA molecules into the high vacuum can be detected. Consequently, the diameter of the TEM beam of approximately 3000 nm can be seen in Figure 18 (300 s). However, this behavior is typical for all micropatterns investigated in this study. In all cases, the geometries initially formed during MspA deposition are retained during

Figure 17. Microletters formed by deposition of MspA/P(MMA)/buffer at the carbon surfaces (TEM image, three different deposition experiments).

Figure 18. Dendrites and stars formed by deposition of MspA/ P(MMA)/buffer at the carbon surface (TEM image) after z1 , due to adhesive forces. The slope of the elastic part of the curve gives the required sensitivity, Sz . Assuming that the laser beam is well positioned above the probing tip, the normal and lateral forces are related to the voltage VN , and the difference between the horizontal signals, VL , on the photodetector by the following relations: FN = cN Sz VN

FL =

3 h c SV 2 Ll z L

(3)

The normal spring constant cN can be evaluated with alternative methods. Cleveland et al. attached tungsten spheres to the tip, which changes the resonance frequency f0 according to the formula [18]
1 cN (4) f0 = 2
M + m∗

2.2. Force Calibration in Friction Force Microscopy Force calibration is relatively simple for rectangular cantilevers [2]. Due to possible discrepancies with the geometric values provided by manufacturers, it is recommended to use optical and electron microscopes to determine the width w,

Figure 5. Sketch of a typical force vs distance curve. The tip approaches the sample from right to left. At z = z1 the tip jumps into contact. Further moving results in an elastic bending of the cantilever. Due to adhesive forces, the tip jumps out of contact at z2 > z1 .

Nanotribology: Friction Force Microscopy

882 In (4) M is the mass of the added object and m∗ is a certain effective mass of the cantilever, which depends on its geometry. The spring constant can be deduced from the frequency shifts corresponding to the different masses attached. Hutter and Bechhoefer [19] observed that the constant cN is related to the area of the power spectrum of the thermal fluctuations of the cantilever, P . The correct relation is cN = 4kB T /3P , where kB = 138 × 10−3 J/K is the Boltzmann constant and T is the temperature [20]. Cantilevers with different shape require finite element analysis, although in few cases analytical formulas can be derived. Neumeister and Ducker [21] obtained approximate analytical expressions for the normal and the lateral spring constant of V-shaped cantilevers. Surfaces with well-defined profiles are useful in-situ tools for calibration [22]. In such a case the the horizontal and vertical components of the total force revealed by the photodetector differ from the normal and lateral components with respect to the surface, FN and FL . The geometric relations between these components are used to determine the conversion ratio between volts and nanonewtons as well as the coefficient of friction. In some cases an adequate estimation of the radius of curvature of the tip, R, is required. This quantity can be evaluated with a scanning electron microscope. Otherwise, well-defined structures such as step sites [23] or whiskers [24] can be imaged. The image of these high-aspect ratio structures is convolved with the tip shape. A deconvolution algorithm that allows extracting the radius of curvature of the probing tip was proposed by Villarrubia [25]. Finally, when calibrating the instrument one must be aware that the accuracy of the piezoelectric scanners is limited by instrumental drifts [26] and typical piezoelectric effects such as nonlinearity, hysteresis, creep, and variation of sensitivity with the applied voltage [27, 28]. An accurate analysis of the errors occurring in the calibration of the lateral forces is given in [29].

2.3. Other Techniques Beside the atomic force microscope, the surface force apparatus (SFA) and the quartz crystal microbalance (QCM) are useful instruments in nanotribology. The surface force apparatus [30, 31] consists of a pair of mica sheets, which are pressed together and reciprocally translated under pressure (Fig. 6). The contact area and distance between mica surfaces can be measured by optical or capacitive techniques with a resolution of 2 Å. The normal and lateral forces are deduced from the deformation of springs. The SFA is commonly used to detect the behavior of lubricant liquids between the two surfaces in contact. As an example, the layering of liquids in discrete strata was observed as a function of the applied load [33]. O’Shea et al. observed a similar effect with an AFM [34, 35]. In such a case, the layering of liquid molecules on graphite and mica surfaces caused stiffness oscillation as the tip–sample distance was varied. The quartz crystal microbalance, which is commonly used to measure thin film growth, was first applied to nanotribology by Krim and Widom [36]. The QCM consists of a single crystal of quartz, which oscillates in a shear mode with a high quality factor Q. The sliding friction of adsorbed films

F(D) f (t)

σ

V

F
D

f

A

σ Ds

η

Dk

Figure 6. Diagram of a surface force apparatus. Two smooth mica surfaces are separated by a molecularly thin lubricant film. The springs represent any device used to measure the normal and lateral forces between the surfaces. Reprinted with permission from [32], B. Bhushan et al., Nature 374, 607 (1995). © 1995, Nature Publishing Group.

is related to the frequency shift and the broadening of the resonance peak of the crystal. Unfortunately, the instrument can reveal only very low friction forces and its application is limited to systems like rare-gas solids on metals [37]. In Section 6.5 we will see how the quartz crystal microbalance was used to detect electronic contributions to friction.

3. MECHANICS OF SLIDING NANOCONTACTS 3.1. Load Dependence of Friction The lateral force, FL , between two surfaces in reciprocal motion depends on the size of the real area of contact, A, which is usually a few orders of magnitude smaller than the apparent area of contact. From the analysis of several experimental data Bowden and Tabor concluded that friction is proportional to the real area A [38]: FL = A

(5)

The mean lateral force per unit area, , is called the shear strength. In a first approximation, it does not depend on the normal pressure. Bowden and Tabor assumed that the asperities of the two surfaces in contact are deformed plastically while sliding. In such a case the asperities of the two surfaces are compressed until the applied pressure, p, equals a certain yield value, p∗ . The resulting area of contact is thus A = FN /p∗ , and the well-known Amonton’s law is obtained: FL = FN , where  = /p∗ is the coefficient of friction. The same idea can be extended to contacts formed by many asperities, and it leads again to Amonton’s law. The simplicity of this analysis explains why most of the friction processes

Nanotribology: Friction Force Microscopy

883

where K = 3E ∗ /4, E ∗ being an effective Young’s modulus, related to the Young’s moduli, E1 and E2 , and the Poisson’s numbers, 1 and 2 , of the sphere and plane, by the following relation: 1 − 12 1 − 22 1 = + ∗ E E1 E2

(7)

The result A ∝ FN2/3 does not agree with Amonton’s law, A ∝ FN . However, a linear relation between FL and FN can be derived for contacts formed by several asperities in some important cases. For example, the area of contact between a flat surface and a set of asperities with an exponential height distribution and the same radius of curvature, R, is proportional to the normal force [5]. The same conclusion holds approximately for a Gaussian height distribution. However, the hypothesis that the radii of curvature are the same for all asperities is not realistic. A general model proposed by Persson predicts that the contact area is proportional to the applied load for a large variety of elastoplastic contacts formed by surfaces with arbitrary roughness [6]. Further effects are observed if adhesion between the asperities is taken into account. If the range of action of the adhesive forces is smaller than the elastic deformation, Eq. (6) is extended by the Johnson–Kendall–Roberts (JKR) model [40] to the expression  2/3  2/3  R FN +3
R+ 6
RFN +3
R2 AFN  =
K (8) where is the surface tension between sphere and plane. The real area of contact at zero load is finite and the sphere can be detached only by pulling it away with a finite force. This is also true in the opposite case, where the range of action of adhesive forces is larger than the elastic deformation. In such a case the relation between contact area and load has the simple form  2/3  2/3 R FN − Foff (9) AFN  =
K where Foff is the negative load that is required to break the contact. The Hertz-plus-offset relation (9) can be derived from the Derjaguin–Muller–Toporov (DMT) model [41]. To discriminate between the JKR or DMT models Tabor [42] introduced a non-dimensional parameter, 1/3  9R 2 (10)

= 4K 2 z30

where z0 is the equilibrium distance in contact. The JKR model can be applied if > 5; the DMT model holds when

< 01. For intermediate values of , the Maugis–Dugdale model [43] is consistent with experimental results. The tip of a friction force microscope is a single asperity sliding on a surface. The previous discussion suggests a nonlinear dependence of friction on the applied load, provided that continuum mechanics can be applied down to nanometer scales. Schwarz et al. [44] observed that the Hertz-plus-offset relation (9) holds on graphite, diamond, amorphous carbon, and C60 in argon atmosphere (Fig. 7). Well-defined spherical tips with radii of curvature of tens of nanometers were used. The probing tips were obtained by contaminating standard silicon tips with amorphous carbon in a transmission electron microscope. In order to compare the tribological behavior of different materials, Schwarz et al. introduced an effective coefficient of friction,  which does not depend on the tip curvature. The highest C,  was found on C60 and the lowest on friction coefficient C graphite. Various groups measured friction vs load curves in UHV in agreement with JKR theory [45–47]. Different materials such as ionic crystals, mica, and metals were considered. Meyer et al. used an original two-dimensional (2D) histogram technique [45]. The normal load is increased or decreased while imaging, which allows one to correlate lateral and normal forces with improved statistics. Carpick et al. extended the JKR relation (8) to include nonspherical tips. For example, in the case of an axisymmetric tip profile z ∝ x2n , with n > 1, the increase of friction becomes less pronounced with increasing n [46].

3.2. Estimation of the Contact Area In contrast to other tribological instruments, like the surface force apparatus, the area of contact cannot be directly determined with the friction force microscope. An indirect estimation of the contact area is achieved by contact stiffness measurements [48]. Figure 8 shows a series of two springs corresponding to the microscope tip apex pressed

frictional force FL [nN]

were related to plastic deformation for a long time. However, plastic deformation provokes a quick damage of the surfaces under pressure, which is not so frequently observed while sliding. Thus, the morphology of the surface must be affected by less disruptive mechanisms of deformation. Elastic deformation can be easily described in the case of a sphere of radius R pressed against a flat surface. In such a case the contact area is [39]  2/3 R FN2/3 (6) AFN  =
K

6

4

2

0 0

2

4

6

8

10

12

normal force FN [nN]

Figure 7. Friction vs load curve measured on amorphous carbon with a well-defined spherical tip in argon atmosphere. The data are fitted with the expression (9). Reprinted with permission from [44], U. D. Schwarz et al., Phys. Rev. B 56, 6987 (1997). © 1997, American Physical Society.

Nanotribology: Friction Force Microscopy

884 klever = ∆Z

kcontact

= klever kcontact ∆X Figure 8. (a) Normal and (b) lateral stiffness of the contact between tip and surface. Reprinted with permission from [49], R. W. Carpick et al., Appl. Phys. Lett. 70, 1548 (1997). © 1997, American Institute of Physics. z against the sample. The effective constant keff of the series is given by

1 1 1 = z + z keff kcontact cN

(11)

where cN is the normal spring constant of the cantilever, z and kcontact is the contact stiffness. This quantity is related to the radius of the contact area, a, by the simple relation z = 2aE ∗ kcontact

(12)

where E ∗ is the effective Young’s modulus introduced in z Section 3.1. Unfortunately, typical values of kcontact are order of magnitudes larger than cN , and a practical application of Eq. (11) is not possible. Carpick et al. [49] and Lantz et al. [50, 51] extended this idea to lateral deformations. According to several models, the lateral stiffness of the contact between a sphere and a flat surface is [52] x = 8aG∗ kcontact

(13)

where the effective shear modulus G∗ is defined by 2 − 12 2 − 22 1 = + G∗ G1 G2

(14)

G1  G2 are the shear moduli of sphere and plane. The contact between tip and sample can be modeled again by a x series of springs (Fig. 8b). The effective constant keff of the series is now given by 1 1 1 1 = x + x + x keff kcontact ktip cL

(15)

where cL is the lateral spring constant of the cantilever, and x kcontact is the lateral stiffness of the contact. As suggested by Lantz et al., Eq. (15) includes the lateral stiffness of x the tip, ktip , which can be of the same order of the lateral x spring constant. The effective spring constant keff is determined by scanning the surface and measuring the slope of the lateral force vs displacement curve (Section 5.1). Once x kcontact is known, the contact radius, a, is easily estimated with Eq. (13).

Carpick et al. applied their method to a silicon nitride tip sliding on muscovite mica in air, whereas Lantz et al. studied the contact between NbSe2 and graphite in UHV. The relations between spring constant and load were fitted by the JKR and the Maugis–Dugdale models respectively. The same models were also consistent with independent measurements of friction vs load. Thus, the hypothesis that friction is proportional to the contact area held in the applied range of loads (up to FN = 40 nN in both experiments). Another way to estimate the contact area is based on the measurement of the contact conductance, which is proportional to the contact area. Enachescu et al. used silicon cantilevers coated with tungsten carbide to measure both conductance and friction on boron-doped diamond as a function of the applied load [53, 54]. The load dependences of both friction and conductance were fitted independently with the same model (DMT), which was a further confirmation of the hypothesis (5).

4. FRICTION EXPERIMENTS ON THE NANOMETER SCALE Friction force microscopy is mainly applied to characterize the response of a surface to the localized stress exerted by the probing tip. The large variety of materials investigated by FFM includes solid lubricants, carbon and silicon compounds, ferroelectrics, and even ice. The role of the environment in such a contest is essential. Ambient air, controlled atmosphere or liquids [55], can drastically influence the values of friction forces, as well as their dependence on the scan load and velocity. Only ultra-high-vacuum friction results from the direct interaction of two materials in contact. Atomic-scale experiments in UHV will be discussed later in Section 6. In the same section we will also consider experiments dealing with friction anisotropy and other minor effects.

4.1. Material Contrast Revealed by Friction Force Microscopy Due to their lubricity properties, self-assembled monolayers (SAM) and, in particular, Langmuir–Blodgett (LB) films are among the most studied materials in nanotribology. LB films can be easily prepared by transferring any desired number of layers on smooth substrates, as silicon wafers or mica, where they form densely packed structures. Figure 9 shows the first FFM measurements on LB films realized by Meyer et al. [56]. Two bilayers of Cd–arachidate were transferred on a silicon wafer. Friction is lower on the areas covered by the lubricant film, and it does not depend on the film thickness. The load dependence of friction is weak, and wear appears when the normal load exceeds 10 nN. Furthermore, small islands of bilayer height could be moved in their entirety, which made possible a direct measurement of the shear strength between the bilayers. The measured value of  = 1 MPa was in agreement with SFA experiments at low loads [57]. Overney et al. [58] studied more complex LB films, formed by mixtures of hydrocarbons and fluorocarbons. Fluorocarbons were observed to be less effective in reducing friction than hydrocarbons, which was again in agreement

Nanotribology: Friction Force Microscopy

(a)

885

(b)

Figure 9. (a) Topography of two bilayers of Cd–arachidate on a silicon wafer. (b) Friction map shows increased friction on the substrate compared to the substrate. Friction is the same on the single and on the couble bilayer. Frame sizes: 2 m. Reprinted with permission from [56], E. Meyer et al., Phys. Rev. Lett. 69, 1777 (1992). © 1992, American Physical Society.

with SFA measurements. Frisbie et al. [59] studied the relation between friction and chemistry on SAMs and found different contrasts when the tip was coated with different functional groups. An extended study with the same purpose was performed by Green et al. [60]. A detailed overview on this topic was given by Carpick and Salmeron [61]. Carbon surfaces were first observed by Mate [62], who studied friction on C60 , amorphous carbon, hydrogen terminated diamond, and graphite. The highest friction was found on C60 , and the lowest on graphite, which is in agreement with the results by Schwarz et al. (Section 3.1). Buzio et al. [63] applied the idea of the effective friction coefficient introduced by Schwarz et al. to characterize friction on nanostructured carbon films with self-affine morphology. Perry et al. [64] observed that friction on amorphous carbon films increases with increasing hydrogen content. These results are of great interest in the hard disk drive industry, where carbon protective coatings are applied. Lüthi et al. [65] investigated friction on C60 islands deposited on NaCl in UHV. Again C60 revealed high friction. Furthermore, the islands could be moved over the substrate without breaking and with extraordinary low shear strength  = 005–0.1 MPa (Fig. 10). This result suggested to the authors

that C60 islands might be used as a sled-type transport system on the nanometer scale. Silicon and silicon oxides have a fundamental role in semiconductor industry. Apart from their electronic properties, mechanical properties are interesting in the development of microdevices, where low friction is required to minimize power consumption. Scandella et al. [66] examined a silicon surface structured by standard photomask lithography and found that friction on hydrogen passivated silicon was larger by a factor 2 than friction on silicon oxide. Teuschler et al. [67] patterned silicon surfaces with a conductive tip, which was subsequently used for characterizing friction. Friction was higher on the modified areas, where the formation of silicon oxide was enhanced. The apparent contrast with the experiment of Scandella et al. is probably due to different crystallinity of the samples. Studies on III–V semiconductors were reported by Garcia and co-workers. Tamayo et al. [68] detected chemical variations of indium alloys with 3 nm resolution. Changes of 10% in indium composition were clearly distinguished in air. Measurements with submonolayer sensitivity were performed on quantum dot structures [69]. Friction force microscopy was also applied to investigate ferroelectric materials. Lüthi et al. [70] and Eng et al. [71] observed significant contrasts between neighboring domains of opposite polarization in friction force maps acquired on GASH (guanidimium aluminum sulphate hexahydrate) and TGS (triglycine sulphate), respectively. On TGS Bluhm et al. measured different friction coefficients, depending on the polarization, the asymmetry of the surface potentials, and also the orientation of the crystallographic lattice with respect to the scan direction [72]. On GASH, the contrast was related only to structural differences, which modify the surface potential experienced by the probing tip. The electrostatic interaction between tip and sample did not affect the friction force significantly. To conclude this overview, we should also mention the studies of friction on a nanometer thin ice film grown on mica by Bluhm et al. [73]. A friction coefficient  = 060 was measured in a temperature range from −24 to −40  C, which is comparable to the values obtained in macroscopic experiments [38]. The squeezing of the water layer out of the contact, which was observed in noncontact mode, suggested that dry friction was probably revealed. Other effects like pressure melting and frictional heating were found to be not relevant.

4.2. Role of the Environment

Figure 10. (a)–(g) Sequence of topography images of C60 islands on NaCl. An island is rotated and translated from one location to another. Frame sizes: 530 nm. (h) Summary of the movement of the C60 island. Reprinted with permission from [65], R. Lüthi et al., Science 266, 1979 (1994). © 1994, American Association for the Advancement of Science.

A humidity increase in ambient air leads to the formation of water layers on hydrophilic surfaces and to a consequent capillary interaction between tip and surface [74]. The influence of capillary condensation in FFM measurements was first studied by Binggeli and Mate [75], who found a substantial decrease of friction at 70% humidity on a hydrophilic silicon oxide surface. On less hydrophilic amorphous carbon films and lubricated silicon oxide, the decrease was not observed. Systematic studies of humidity dependence on mica were performed by Schumacher et al. [76]. The formation of an ordered layer of adsorbed water at 40% humidity led to a strong increase in friction. The Hertzian

886 dependence FL ∝ FN2/3 was also observed. However, friction decreased above 60%, probably because water acted as a boundary lubricant. Putman et al. [77] found out the relation FL ∝ FN2/3 on mica and glass in ambient conditions, whereas friction increased linearly with the normal load in N2 or Ar atmosphere. This result was explained assuming that the tip roughness was smoothed by a condensed water film, which led to a single asperity contact at high humidity and to a multiasperity contact at low humidity. Capillary condensation leads also to different velocity dependences of friction on the nanometer scale. This effect is discussed in Section 6.3. We should also mention that friction in aqueous solutions depends on the pH [78, 79]. Thus, in principle, it might be possible to differentiate chemical species on a surface simply by changing the pH value of the surrounding medium.

4.3. Topographic Effects Another factor to take into account when measuring friction with an atomic force microscope is the contribution of the topography to the lateral force signal, which in such a case is not simply proportional to the friction force acting on the probing tip. We have already seen how a surface with wellknown local slope the topographic contribution can be used to calibrate the lateral forces (Section 2.2). This is not the case with rough surfaces, where the slope variations, combined with local variations of the contact area, can lead to ambiguous results. These problems have been addressed by Bhushan and co-workers [80, 81]. A particular topography effect is observed at the step edges of crystal surfaces. Meyer et al. [56] found a significant increase of friction at such locations on a NaCl surface in UHV. The same increase was observed when a step was crossed up- or downward (Fig. 11). This result states that the most important role is not taken by simple geometric effects, but by enhanced interaction at the step locations (Schwöbel barriers).

Nanotribology: Friction Force Microscopy

5. FRICTION ON THE ATOMIC SCALE Friction forces on the atomic scale are characterized by a typical sawtooth behavior, which reflects the structure of the underlying lattice. This phenomenon is due to the stick-slip movement of the probing tip, and it can be well described by a classical model developed by Tomlinson in 1929 [10]. Theoretical studies of stick-slip on the atomic scale were reported by various groups [82–91]. Here, we first derive the main results of the Tomlinson model in one and two dimensions. Thermal effects, which slightly affect these results at room temperature, will be discussed in Section 5.2.

5.1. The Tomlinson Model The motion of the AFM tip is ultimately related to the atomic structure of the surface and the elastic deformations of the cantilever. The shape of the tip-surface interaction potential, U x y, depends on several factors like the chemical composition of the two materials and the atomic arrangement on the tip apex. For sake of simplicity, we will start the analysis in the one-dimensional case and consider a sinusoidal profile with the periodicity of the atomic lattice, a, and a peak-to-peak amplitude E0 . In Section 3.2, we have shown how the elasticity of the cantilever and of the contact area can be described in an unique framework introducing the effective lateral spring constant keff . If the cantilever moves with a constant velocity V along the x direction, the total energy of the system is then given by Etot x t = −

E0 2
x 1 cos + keff Vt − x2 2 a 2

(16)

Figure 12 shows the energy profile Etot x t at two different instants. When t = 0 the tip is localized in the absolute minimum of Etot . This minimum slightly increases with time due to the cantilever motion, until the tip position becomes unstable at a certain time t = t ∗ . The critical position x∗ at t = t ∗ is determined by equating to zero the second derivative 2 Etot x t/ x2 , which gives   1 2
2 E0 a (17) = x∗ = arccos − 4 keff a2 The coefficient compares the strength of interaction between tip and surface with the stiffness of the system. The

Figure 11. Friction image of NaCl. Increased friction is observed on the step sites, both going down and up the steps, which indicates that friction at the step edges is not dominated by geometric effects. Reprinted with permission from [56], E. Meyer et al., J. Vac. Sci. Technol. B 14, 1285 (1996). © 1996, American Vacuum Society.

Figure 12. Energy profile experienced by the AFM tip (black circle) at t = 0 (dotted line) and t = t ∗ (continuous line) The tip is dragged by the cantilever, which moves rightward with a constant velocity V . The tip does not move significantly until it suddenly “jumps” at the critical time t = t ∗ .

Nanotribology: Friction Force Microscopy

887

stick-slip is observed only if > 1 (i.e., if the system is not too stiff or the interaction is strong enough). In what follows, we assume that ≫ 1, as usually observed in the experiments. When t = t ∗ the tip suddenly “jumps” into the next minimum of the potential profile. Just before jumping, the lateral force is [92] F∗ =

keff a 2


(18)

Figure 13 shows the lateral force FL as a function of the cantilever position, X. When the cantilever is moved forward, the lower part of the curve in Figure 13 is obtained. If, at a certain point, the direction of motion of the cantilever is suddenly inverted, the force follows the profile in the upper part of the curve. The area of the friction loop obtained by scanning back and forth gives the total energy dissipated. The slope of the sticking part of the loop is equal to keff [92]. In two dimensions, the energy of the system is given by Etot r t = U r +

keff Vt − r2 2

(19)

where r = x y and V is the scan velocity. For example, Figure 14 shows the total energy corresponding to a periodic potential of the form   2
x 2
y 2
x 2
y E +cos cos +E1 cos U xy = − 0 cos 2 a a a a (20) The stability of the equilibrium can be discussed introducing the Hessian matrix  2  U 2 U  x2 + keff x y    H = (21)    2 U 2 U + keff y x y 2 When both eigenvalues 1 2 of the Hessian are positive the position is stable. Figure 15 shows such regions for a potential of the form (20). The tip follows the cantilever adiabatically as long as it remains in the (++)-region. When the tip is dragged to the border of the region, it suddenly jumps into the next (++)-region. Thus far we have implicitly assumed that the tip is terminated by only one atom. It is also instructive to consider the

Figure 14. Energy landscape experienced by the AFM tip in 2D.

case of a periodic surface sliding on another periodic surface. In the Frenkel–Kontorova–Tomlinson (FKT) model the atoms of one surface are harmonically coupled with their nearest neighbors. Let us examine the case of quadratic symmetries, with lattice constants a1 and a2 for the upper and lower surface respectively (Fig. 16). In such a context the role of commensurability is essential. In one dimension Weiss and Elmer [94] predicted that friction should decrease with decreasing commensurability, the minimum of friction being reached when a1 /a2 equals the golden mean z¯ = 1 + 1 + 1 + · · · −1 −1 = 0618. In two dimensions Gyalog and Thomas [95] studied the case a1 = a2 , with a misalignment between the two lattices given by an angle . When the sliding direction changes, friction increases from a minimum value corresponding to the sliding angle  = /2 to a maximum value, which is reached when  = /2 +
/4. The misfit angle  is related to commensurability. Since the misfit angles giving rise to commensurate structure form a dense subset, the dependence of friction on  should be discontinuous. The numerical simulations performed by Gyalog agree with these conclusions (Fig. 17).

5.2. Thermal Effects on Atomic Friction Although the Tomlinson model gives a good interpretation of the basic mechanism of the atomic stick-slip, it cannot explain some minor features observed in the experiments. 3.0

2.5

2.0

1.5

1.0

0.5

0.0 0.0

Figure 13. Friction loop obtained by scanning backward and forward. The slope of the sticking part of the loop gives the effective spring constant keff .

0.5

1.0

1.5

2.0

2.5

3.0

Figure 15. Regions on the x y plane labeled according to the signs of the eigenvalues of the Hessian matrix (21) with the potential (20). Reprinted with permission from [93], T. Gyalog et al., Europhys. Lett. 31, 269 (1995). © 1995, EDP Sciences.

Nanotribology: Friction Force Microscopy

888

0,4

F L (nN)

0,3 0,2 0,1 0,0 Figure 16. The FKT model in 2D. Reprinted with permission from [95], T. Gyalog and H. Thomas, Europhys. Lett. 37, 195 (1997). © 1997, EDP Sciences.

For example, the peaks of the friction loop shown in Figure 2a have different heights, which is not the case in Figure 13. Another effect is observed if the scan velocity V is varied. In Section 6.3 we will see that the mean friction force measured in UHV conditions increases with the logarithm of V (Fig. 18). Also this result cannot be interpreted without further assumptions in the model. Let us focus again on the energy profile in Figure 12. At any time t < t ∗ , the tip jump is prevented by the energy barrier Et = Exmax  t − Exmin  t, where xmax t corresponds to the first maximum observed in the energy profile, and xmin t is the actual position of the tip (Fig. 19). The quantity E decreases with time, or, equivalently, with the frictional force FL , until it vanishes when FL = F ∗. Close to the critical point the energy barrier can be approximated as EFL  = F − FL 

(22)

where F ≈ F ∗ . However, at a finite temperature T , the jump can occur before the critical value FL = F ∗ is reached [9]. The most probable value of FL , when the jump occurs, is estimated with the master equation   Et dpt = −f0 exp − pt (23) dt kB T In (23), p is the probability that the tip does not jump and f0 is a characteristic attempt frequency of the system. Using 1.3

1

2

3

4 5 In ν (nm/s)

6

7

8

Figure 18. Mean friction force vs scanning velocity on NaCl(100) at FN = 044 nN (+) and FN = 065 nN (×). Adapted with permission from [9], E. Gnecco et al., Phys. Rev. Lett. 84, 1172 (2000). © 2000, American Physical Society.

the approximation (22) the condition of highest probability of jumping, d 2 pF /dFL2 = 0, yields [9] FL v = F ∗ −

kB T V ln c

V

(24)

with Vc =

f 0 kB T keff

(25)

Thus, the lateral force increases logarithmically with the sliding velocity. However, when the jump occurs very close to the critical point x = x∗ the approximation (22) does not hold. This is the case at high velocities, where the probability pt does not change significantly, until it suddenly falls down to zero when t → t ∗ . Thus, friction is expected to be constant at sufficiently high velocities, which agrees with the classical Coulomb’s law. This topic is still under investigation.

5.3. Molecular Dynamics Simulations of Friction and Wear Several authors interpreted sliding friction on the atomic scale with molecular dynamics (MD). Even if huge differences in time-scale make impossible a direct comparison between simulations and real experiments, MD simulations can reveal atomic mechanisms not directly accessible by experiment. Landman et al. [96, 97] predicted atomic-scale

1.2 E (x,t)

(a)

∆E

(b)

1.1 1.0 0.9

∆E xmin xmax

0.8 –30

0

30

60

90

x

F* FL

120

Figure 17. Friction as a function of the sliding angle  in the 2D FKT model. Reprinted with permission from [95], T. Gyalog and H. Thomas, Europhys. Lett. 37, 195 (1997). © 1997, EDP Sciences.

Figure 19. (a) The tip jump in the Tomlinson model at any time t < t ∗ is prevented by an energy barrier Et. (b) Energy barrier E as a function of the lateral force FL . The dashed line close to the critical value corresponds to the linear approximation (22).

Nanotribology: Friction Force Microscopy

889

stick-slip for Si and CaF2 tips sliding on surfaces of the same materials. Harrison et al. [98] observed stick-slip with a weak load dependence for two hydrogen-terminated diamond (111) surfaces, which is in a certain agreement with the experiments by Germann et al. discussed in Section 6.1. Sørensen et al. [99] predicted the occurrence of wear in the case of a copper tip sliding on Cu(100) surfaces (Fig. 20), whereas Cu(111) appeared more resistant. Even this conclusion was somehow confirmed experimentally (Section 6.1). Shluger et al. observed that the scanning process is accompanied by strong displacements of the surface ions inside the lattice and by their transient or permanent adsorption onto the tip at low loads (till 1 nN) [100–102]. Another simulation by Livshitz and Shluger [103] suggested that the adsorbed material adjusts itself leading to an effect of selflubrication of the tip (Fig. 21). This result may explain why periodic structures can be observed experimentally also at rather high loads. Ohzono and Fujihira [104, 105] considered friction between an ordered organic monolayer of n−alkane molecules and a rigid slider with a single protuberance. Incommensurability and tip size comparable to the molecular size were found to be important conditions in imaging the molecular lattice. A few MD simulations focused on the connection between friction and wear on the nanometer scale. Buldum and Ciraci [106] considered the processes of nanoindentation and sliding of sharp and blunt nickel tips on copper. In the case of the sharp tip quasi-periodic variations of the lateral force were observed, due to stick-slip involving phase transition. One layer of the asperity was deformed to match the substrate during the first slip and then two asperity layers merged into one through structural transition during the second slip. In the case of the blunt tip the stick-slip was less regular. Different mechanisms were observed when the tip is harder than the underlying sample. Komanduri et al. [107] considered an infinitely hard Ni indenter scratching single crystal aluminum at extremely low depths (Fig. 22). In such case a linear relation between friction and load was found, with a high coefficient of friction  = 06, independent of the scratch depth. Nanolithography simulations were performed by Fang et al. [108], who investigated the role of the displacement of the probing tip along the direction of slow

(a)

(b)

(c)

(d)

Figure 20. Snapshot of a Cu(100) tip on a Cu(100) substrate during sliding. (a) Starting configuration; (b,c,d) snapshots after two, four, and six slips. Reprinted with permission from [99], M. R. Sørensen et al., Phys. Rev. B 53, 2101 (1996). © 1996, American Physical Society.

Mg2+ O2–

F–

Li+

Figure 21. Regular structure of ions adsorbed on a MgO tip sliding on a LiF surface. Reprinted with permission from [103], A. I. Livshits et al., Phys. Rev. B 56, 12482 (1997). © 1997, American Physical Society.

motion between a scan line and the next one. A certain correlation with FFM experiments on silicon films coated with aluminum was found. More complex simulations of nanoindentation are presented in [109–112].

6. FRICTION EXPERIMENTS ON THE ATOMIC SCALE 6.1. Experimental Overview Figure 23 shows the friction map obtained by Mate et al. on graphite on the atomic scale [8]. The periodicity of the lateral force is the same as of the atomic lattice of the sample. The series of friction loops in Figure 24 reveal the stick-slip effect discussed in Section 5.1 The applied loads are in the range of tens of N. According to the continuum models introduced in Section 3 these values correspond to contact diameters of 100 nm. A possible explanation for the atomic

Figure 22. MD simulation of a scratch realized with an infinitely hard tool. Reprinted with permission from [107], R. Komanduri et al., Phys. Rev. B 61, 14007 (2000). © 2000, American Physical Society.

Nanotribology: Friction Force Microscopy

890 a

b

WIRE SPRING CONSTANT = 2500 N/m a) LOAD = 7.5â10–6 N

2.0

FRICTIONAL FORCE (10–7 N)

0.0 –5.0 5.0

0.0 –2.0

b) LOAD = 2.4â10–5 N A

B 2.0

0.0

0.0

–5.0

10.0

2.5 Å

C

c) LOAD = 5.6â10–5 N

–2.0

4.0

5.0

2.0

0.0

0.0

–5.0

–2.0

–10.0

–4.0

0.0

5.0

10.0

15.0

WIRE DEFLECTION (Å)

5.0

20.0

X SAMPLE POSITION (Å) Figure 24. Friction loops on graphite acquired with (a) FN = 75, (b) 24, and (c) 75 N. Reprinted with permission from [8], C. M. Mate et al., Phys. Rev. Lett. 59, 1942 (1987). © 1987, American Physical Society.

1

2

3

4 5 Distance (nm)

6

7

8

1

2

3

4 5 Distance (nm)

6

7

8

Lateral Force (arb. units)

features observed at such high loads is that graphite flakes were detached from the surface and adhered to the tip apex [113]. Another possibility is that the contact between tip and surface consisted of few nm-scale asperities and the corrugation was not entirely averaged out while sliding. The load dependence of friction found by Mate et al. was rather linear, with a small friction coefficient  = 001. The UHV environment reduces the influence of contaminants on the surface and leads to more precise and reproducible measurements. Howald et al. obtained a series of results on ionic crystals with a home-built AFM apparatus in UHV [114]. In Figure 25 a friction map recorded on KBr(100) is compared with a theoretical map deduced from the 2D-Tomlinson model [115]. The periodicity a = 047 nm corresponds to the spacing between equally charged ions. No

Lateral Force (nN) 3.0

Figure 23. First atomic friction map acquired on graphite with a normal force FN = 56 N. Frame size: 2 nm. Reprinted with permission from [8], C. M. Mate et al., Phys. Rev. Lett. 59, 1942 (1987). © 1987, American Physical Society.

Figure 25. (a) Measured and (b) theoretical friction map on KBr(100). Reprinted with permission from [115], R. Lüthi et al., J. Vac. Sci. Technol. B 14, 1280 (1996). © 1996, American Vacuum Society.

individual defects were observed. This is a common aspect to all friction measurements on the atomic scale. One possible reason is that the contact realized by the probing tip is formed by many atoms, which superimpose and average their effects. Molecular dynamics simulations show that even a single-atom contact may cause rather large stresses in the sample, which lead to the motion of defects far away from the contact area. In a picturesque frame, Meyer et al. said that “defects behave like dolphins that swim away in front of an ocean cruiser” [116]. Howald et al. [117] detected atomic-scale friction on the reconstructed Si(111)7×7 surface. The observation of atomic features was only achieved after coating the tips with polytetrafluoroethylene, which has lubricant properties and does not react with the dangling bonds of Si(111)7×7 (Fig. 26). Bennewitz et al. [118] observed atomic stick-slip on metallic surfaces. Regular features were obtained on the closed-packed Cu(111), whereas sliding on Cu(100) produced irregular and irreproducible patterns (Fig. 27). Molecular dynamics suggested that wear occurs more easily on the Cu(100) [110]. This conclusion was achieved with copper tips in computer simulations. The assumption that copper covered the tip apex used in the experiment was supported by current measurements. Atomic stick-slip on diamond was observed by Germann et al. [120]

Nanotribology: Friction Force Microscopy

891 (a)

(b) fx 1.58 Å

4.6 Å

2.74 Å

9.2 Å

fx

fy 5.2 Å

5.2 Å

fy

3.16 Å

2.5 Å

(c)

2.5 Å 2.74 Å stick point

Figure 26. Topography and (b) friction image of Si(111)7 × 7 measured with a PTFE coated Si tip. Reprinted with permission from [117], L. Howald et al., Phys. Rev. B 51, 5484 (1995). © 1995, American Physical Society.

6.2. Friction Anisotropy The importance of the misfit angle in reciprocal sliding of two flat surfaces discussed in Section 5.1 was first observed by Hirano et al. [126] in the contact between two mica sheets. Friction increased when the two surfaces formed

1.58 Å X 3.16 Å

with an apposite diamond tip, prepared by chemical vapor deposition, and, a few years later, by van der Oetelaar and Flipse [121] with standard silicon tips. The values of friction had huge discrepancies corresponding to the presence or absence of hydrogen on the surface. Morita et al. [122, 123] measured friction on MoS2 with a 2D-FFM apparatus, which could reveal forces even perpendicular to the scan direction. The features in Figure 28 correspond to a zigzag walk of the tip, which is consistent with the 2D-Tomlinson model [86, 87]. Analogous studies were conducted on mica and NaF [124]. The 2D stick-slip on NaF was detected with normal forces lower than 14 nN, whereas loads up to 10 N could be applied on layered materials without damage. The zigzag walk on mica was also observed by Kawakatsu and Saito [125] with an original 2D-FFM with two laser beams and two quadrant photodetectors.

slip motin

Y

Figure 28. (a) Friction force on MoS2 acquired by scanning along the cantilever and (b) across the cantilever. (c) Motion of the tip on the sample. Reprinted with permission from [123], S. Fujisawa et al., Phys. Rev. B 51, 7849 (1995). © 1995, American Physical Society.

commensurate structures, in agreement with theoretical results. In more recent measurements with a monocrystalline tungsten tip on silicon, Hirano et al. [127] observed superlubricity in case of incommensurability. Overney et al. [128] studied the effects of friction anisotropy on a bilayer lipid film and found that different molecular alignments resulted in significant variation of friction. Liley et al. [129] observed islands of a lipid monolayer on mica, consisting of domains with different molecular orientation (Fig. 29). The angular dependence of friction reflected the tilt direction of the alkyl chains of the monolayer revealed with other techniques. In their experiments on C60 islands (Section 4.1) Lüthi et al. found that friction is independent of the sliding direction. This was not the case in other experiments by Sheehan and Lieber [130], who observed that the misfit angle is relevant when MoO3 islands are dragged on the MoS2 surface. In such a case, sliding was possible only along low index directions. The weak orientation dependence found by Lüthi et al. was probably due to the large mismatch of C60 on NaCl. Another example of friction anisotropy is given by carbon nanotubes. A dramatic increase of friction was observed when a nanotube was moved in the directions corresponding to commensurate contact with a graphite surface [131].

6.3. Velocity and Temperature Dependence of Friction Figure 27. Friction images of (a) Cu(111) and (b) Cu(100). Frame size: 3 nm. Reprinted with permission from [119], R. Bennewitz et al., Trib. Lett. 10, 51 (2001). © 2001, Plenum Publishing Corporation.

The velocity dependence of friction was investigated relatively late. Zwörner et al. observed that friction between silicon tips and diamond, graphite, or amorphous carbon is

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–0.5 –0.7 –0.9 –1.1

–0.5 –0.7 –0.9 –1.1

Figure 29. Friction images of a thiolipid monolayer on a mica surface. Reprinted with permission from [129], M. Liley et al., Science 280, 273 (1998). © 1998, American Association for the Advancement of Science.

constant with scan velocities, V , of few m/s [132]. Friction decreased when V was reduced below 1 m/s. On lipid films on mica, Gourdon et al. [133] found a critical velocity Vc = 35 m/s, which discriminated between an increasing friction and a constant friction regime (Fig. 30). Although these results were not explained with thermal activation, we argue that the discussion in Section 5.2 gives the correct interpretative key. A clear observation of a logarithmic dependence of friction on the micrometer scale was reported by Bouhacina et al. [134] on triethoxysilane molecules and polymers grafted on silica with sliding velocity up to V = 300 m/s The result was explained with a thermally activated mica fluid arm 5 arm 4

300

LFM signal (a.U.)

250 200 150 100 50

0

0

2

4 6 velocity (µm/s)

8

Eyring model, which does not differ significantly from the model discussed in Section 5.2 [135, 136]. The first measurements on the atomic scale were performed by Gnecco et al. [9] and Bennewitz et al. [118] on sodium chloride and copper in UHV. In both cases a logarithmic dependence of friction was observed up to V = 1 m/s, in agreement with Eq. (24). Higher values of velocities were not explored, due to the limited range of the scan frequencies accessible with the FFM on the atomic scale. Riedo et al. [137] realized the importance of the surface wettability in the velocity dependence of friction. A logarithmic increase in controlled atmosphere was only observed on hydrophobic surfaces. Hydrophilic surfaces, on the contrary, revealed a logarithmic decrease of friction with velocity, which was related to thermally activated nucleation of water bridges between tip and sample asperities. The rate of such a decrease depends drastically on humidity. Thus far we have used thermal activation to explain the velocity dependence of friction. The same mechanism predicts also that friction should change with temperature. According to the master equation (23) the probability of a tip jump is reduced at low temperatures T until it vanishes when T = 0. In this limit case, thermal activation is excluded and the lateral force FL is equal to F ∗ , independently of the scanning velocity V . Stick-slip processes at low temperatures have not been reported at our knowledge. However, a significant increase of the mean friction with decreasing temperature was measured by He et al. [138]. Neglecting the logarithmic contributions, Eq. (24) predicts F ∗ − FL  ∼ T for the temperature dependence of friction, which is in agreement with the experimental results.

6.4. Dissipation in Noncontact Atomic Force Microscopy Energy dissipation is also observed when the AFM is operated in noncontact mode (NC-AFM); that is, the cantilever is excited close to its resonance frequency and the energy required to keep the oscillation amplitude constant is monitored [139]. The origin of this additional dissipation is manifold. Apparent energy dissipation may arise from inharmonic cantilever motion, artifacts from the phase controller, or slow fluctuations round the steady-state solution [140, 141]. Velocity dependent dissipation is observed in case of electric- and magnetic-field mediated Joule dissipation [142, 143]. Hysteretic dissipation due to atomic instabilities [144, 145] and hysteresis due to adhesion [146] can also play a role. Energy dissipation can be also measured by exciting the torsional oscillation of the cantilever [147]; in the future it is not excluded that the energy losses observed with FFM and NC-AFM will be considered in a unified frame. A detailed review of dissipation phenomena in noncontact force microscopy is given by [148].

10

Figure 30. Velocity dependence of friction on mica and on lipid films with different orientation (arms 4 and 5) and in a fluid phase. Reprinted with permission from [133], D. Gourdon et al., Trib. Lett. 3, 317 (1997). © 1997, Plenum Publishing Corporation.

6.5. Electronic Friction The role of the electrons in friction processes was first suggested by Persson [149]. If small particles of mass m are adsorbed on a thin conducting film the electronic friction

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force FL el = mel v gives rise to an additional resistivity (26)

7. WEAR ON THE NANOMETER SCALE If the normal force FN applied with the AFM exceeds a critical value depending on the tip shape and the material under investigation, the surface topography is permanently damaged. Among several examples of tip-induced wear of a surface [11, 65, 115, 153–158], wear of the tip was also reported [159, 160]. In some cases wear can be exploited to create patterns with well-defined shape. This is the subject of nanoindentation and nanolithography.

7.1. Nanoindentation Nanoindentation is performed by increasing and then decreasing the normal load with a hard tip without scanning. The Berkovich indenter, formed by a three-sided diamond pyramid, is the most common tool for such a purpose. The indentation pit can be subsequently characterized with the AFM. Nanohardness is calculated by dividing the loading force by the projected residual area of the indentation. The geometry of the tip is the most important source of uncertainty in this kind of measurements [161]. Nanohardness tends to decrease when the normal load increases. However, hard and fragile materials react in a different way. For example, Bhushan et al. found that nanohardness falls when FN = 35 mN for Si(111), but not on Si(100) [162]. Besides hardness, the Young’s modulus can be obtained from the slope of the unloading curve [163]. A loaddisplacement curve obtained on Si(100) is shown in Figure 31. The hysteretic appearance means that deformation is not fully elastic. For compliant materials such as polymer blends, magnetic tapes, etc. both loading and unloading curves do not differ.

40

250 30 200

20 10 0

150

0

1

2

3

4

5

6

100 50 0 0

5

20

10 15 Displacement (nm)

25

Figure 31. Load-displacement curves at different loads for Si(100). Reprinted with permission from [162], B. Bhushan et al., Philos. Mag. 74, 1117 (1996). © 1996, Taylor & Francis, Ltd.

atomic scale (Fig. 3). Before discussing the few experimental results reported on such a level, we should mention here the importance of nanoscratching in realizing well-defined patterns thanks to the precise control of the tip movement made possible by the piezoelectric elements of the AFM. In such a way, for example, superconducting nanoconstrictions (Josephson junctions) [164], or surface quantum wells [165], were created. The first atomically resolved images of the damage produced by scratching the AFM tip on an ionic crystal surface were reported by Gnecco et al. [11]. In Figure 3a a small mound grown at the end of a groove on KBr is shown under different magnifications. The groove was created a few minutes before imaging by repeated scanning with the normal force FN = 21 nN. The image shows a lateral force map acquired with a load of about 1 nN; no atomic features were observed in the corresponding topography signal. Figure 3b shows that the debris extracted from the groove recrystallized with the same atomic arrangement of the undamaged surface. Although it is not straightforward to understand how the wear process was initiated and how the tip transported the debris, important indications are provided by the profile of the lateral force FL recorded while scratching. Figure 32 shows some friction loops acquired when the tip was scanned laterally on 5 × 5 nm2 areas. The mean lateral force multiplied by the scanned length gives the total 0 –10 –20

FL (nN)

where n is the number of conduction electrons per unit volume, na is the coverage of the adsorbed particles, and d is the film thickness. Experiments in agreement with this effect were performed by Krim et al. [37], who related the tribological properties of thin adsorbed films to changes of the Q-factor of a quartz crystal microbalance. In such way, it was found that slip times for ethane and ethylene monolayers adsorbed on silver and chemisorbed oxygen/silver surfaces are different, arguing that electronic contributions to friction should be considered whenever conducting surfaces are involved [150]. More recently, Dayo et al. [151] proved that friction of incommensurate N2 on lead drops abruptly at the superconducting transition temperature Tc ≈ 5 K, which was related again to an electronic contribution to friction. Further experiments are discussed in the review article by Mason [152].

Silicon (100)

60

300 50

Load (µN)

mna  = el ne2 d

350

–30 –40

I II III IV V

–50 –60

dFL

–70

dx

–80 0

7.2. Nanolithography If the AFM tip is scanned with high load, debris can be removed from the underlying surface. Although this technique does not differ from ploughing commonly used in agriculture, the results can be surprising when observed on the

1

2

3

4

5

x (nm) Figure 32. Friction loops acquired while scratching the KBr surface on 5 nm long lines with different loads FN = 57 to 22.8 nN. Reprinted with permission from [11], E. Gnecco et al., Phys. Rev. Lett. 88, 215501 (2002). © 2002, American Physical Society.

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thermal activation. The number of defects created in the contact area AFN  is [167]   E (27) Ndef FN  = tres n0 AFN f0 exp − kB T

(a)

(b)

Figure 33. (a) Lateral force images of the pits produced with FN = 57 to 22.8 nN. Frame size: 150 nm. (b) Detailed image of one of the pits with pseudo-atomic resolution. Frame size: 20 nm. Adapted with permission from [11], E. Gnecco et al., Phys. Rev. Lett. 88, 215501 (2002). © 2000, American Physical Society.

energy dissipated in the process. The results of the tip movement are the pits in Figure 33a. Thanks to the resolution obtained in the lateral force images (Fig. 33b), the number of removed atoms can be directly estimated from the maps. This allowed us to evaluate that 70% of the dissipated energy went into wear-less friction. Figures 32 and 33 clearly show that the damage increased with increasing load. On the other hand, varying the scan velocity between 25 and 100 nm/s did not produce significant changes. A different kind of wear was observed on layered materials by Kopta and Salmeron [166], who removed layers from a muscovite mica surface with the normal force FN = 230 nN (Fig. 34a). Fourier filtered images acquired on very small areas revealed the different periodicities of the underlying layers, which reflect the complex structure of the muscovite mica (Fig. 34b, c). To interpret their results, Kopta and Salmeron assumed that wear of mica initiates from atomic defects. When the defects accumulate beyond a critical concentration, they grow to form the scars shown in Figure 34. Such a process was once again related with

where tres is the residence time of the tip, n0 is the surface density of atoms, and f0 is the attempt frequency to overcome the energy barrier E to break a Si–O bond (this quantity depends on the applied load). When the defect density reaches a critical value, a hole is nucleated. The friction force during the creation of a hole was also estimated with thermal activation, which led to the formula [167] 2/3 2/3 FL = cFN − Foff 2/3 + FN expB0 FN 

(28)

The first term on the right gives the wear-less dependence of friction in the Hertz-plus-offset model (Section 3.1); the second term is the contribution of the defect production. The agreement between Eq. (28) and the experiment is clearly visible in Figure 35.

7.3. Tribochemical Wear Like friction, wear is also influenced by the surrounding environment. Nakahara et al. [168] could induce degradation of the cleavage steps on the hygroscopic crystal NaNO3 at humidity higher than 45%. Diatomic steps splat into monatomic steps and the material was dragged to the terrace above. After repeated scanning, rows of material were piled up. Humidity-dependent layer removal was also observed by Thundat et al. [169] on lead pyrophosphate by scanning at humidity >25%. In such a case the increase of capillary forces at high humidity was proposed as the wear mechanism, instead of the sample dissolution.

7.4. Metallic Nanocontacts An interesting case of wear processes is provided by nanometer-sized metallic contacts under stress. If the contact is smaller than the mean free path of the electrons, the conductance is given by the Landauer–Buttiker formula [170] G=

2e2  T h k k

(29)

–6

fricition force in nN

40

B

–7 –8

30

–9 –10 –11

20

18.0

18.5 19.0 {L in nN}2/3

10 50 Figure 34. (a) Topography image of an area scratched on muscovite mica with FN = 230 nN. (b,c) Fourier filtered images of different regions. Reprinted with permission from [166], S. Kopta and M. Salmeron, J. Chem. Phys. 113, 8249 (2000). © 2000, American Institute of Physics.

60

70 80 total load in nN

90

Figure 35. Friction vs load curve during the creation of a hole in the muscovite mica. Reprinted with permission from [166], S. Kopta and M. Salmeron, J. Chem. Phys. 113, 8249 (2000). © 2000, American Institute of Physics.

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20 AFM cantilever conductance (2e2/h)

cantilayer beam 15 gold sample

gold tip

10

5

(a) 0 2

(b)

force (nN)

0 ∆F –2 –4 –6 –8 –10 0.0

0.5 1.0 tip displacement (nm)

1.5

Figure 36. (a) Conductance and (b) force during the elongation of a gold nanowire. Reprinted with permission from [171], G. Rubio et al., Phys. Rev. Lett. 76, 2302 (1996). © 1996, American Physical Society.

where Tk is the transmission probability for the kth electron conduction channel. The number of channels is proportional to the contact area, and Tk is close to 1, so that the conductance G is proportional to the contact area. Rubio et al. [171] brought into contact a tip and a sample of gold to form a single asperity contact. A small bias voltage was applied and the current through the contact was measured. Figure 36a shows the conductance of a tip, which was pulled back from the sample after the formation of the contact, and Figure 36b shows the corresponding force. The conductance changes stepwise, and each step is associated with a relaxation in the normal force FN , which, otherwise, increases elastically. Each jump can be associated with an atomic rearrangement of the contact, which changes the number of conduction channels.

8. CONCLUSIONS We have emphasized the variety of friction and wear processes occurring in different physical systems, which have been investigated with the atomic force microscope. The unique capability to detect and control forces between a sharp nanometer-sized tip and a surface could reveal processes occurring on surfaces in motion down to the atomic scale, and a lot of information could be extracted also at a fundamental level (load and velocity dependence of friction). Considering that it is practically impossible to report all the results currently obtained by friction force microscopy around the world, we mainly focused on some original

experiments, which, in our opinion, led to a better understanding of friction and wear processes on the nanometer scale. The scenario can be extended by further readings from books and review articles on this subject [61, 116, 172–175]. Even if the experiments discussed constitute a significant breakthrough in our understanding of tribology, much work is still to be done. Subjects like temperature dependence of friction or friction changes in phase transitions require further investigation. The subject of friction and wear on the nanometer scale is extremely wide, and we believe that the observation of nature and the needs of technology will suggest new exciting experiments in this field.

GLOSSARY Amonton’s law The Amonton’s law states that friction is proportional to the applied load. It is verified in macroscopic friction experiments. Atomic stick-slip Mechanism in which the friction force between a sharp tip and a crystal lattice repeatedly builds up and then quickly slips at each atomic site. Coulomb’s law of friction The Coulomb’s law of friction states that kinetic friction is independent of the sliding velocity. It is approximately fulfilled in macroscopic friction experiments. Derjaguin-Muller-Toporov (DMT) model Model for contact and friction which includes the effect of asperity adhesion forces. The range of action of adhesive forces is assumed larger than the elastic deformation. Frenkel-Kontorova-Tomlinson model Model for friction which considers a layer of atoms connected to a rigid upper plate via springs. The layer feels a spatially periodic potential. The plate is driven by a constant velocity. Johnson-Kendall-Roberts (JKR) model Model for contact and friction which includes the effect of asperity adhesion forces. The range of action of adhesive forces is assumed smaller than the elastic deformation. Maugis-Dugdale model Model for contact and friction which includes the effect of asperity adhesion forces. Its range of applicability lies inbetween the JKR and the DMT model. Quartz crystal microbalance Piezoelectric transducer which allows a mass change to be converted into a resonant frequency change. Surface force apparatus Device used to measure the interaction force between two macroscopic surfaces as a function of surface separation. Tomlinson model Model for friction which considers a single atom connected to a rigid upper plate via a spring. The atom feels a spatially periodic potential. The plate is driven by a constant velocity.

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Nanotribology of Carbon Films F. L. Freire Jr., R. Prioli Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro, Brazil

CONTENTS 1. Introduction 2. Amorphous Carbon Films 3. Force Microscopy 4. Nanotribology Results 5. Conclusions Glossary References

1. INTRODUCTION Amorphous carbon films are made of clusters of sp2 hybridized carbon atoms, with typical size of 1 nm, connected to each other by sp3 -hydridized carbon atoms. The electronic and optical properties of these materials are mainly controlled by the size of the sp2 clusters, while the mechanical properties are given by the degree of interconnectivity of the amorphous skeleton, that is, the fraction of sp3 -hybridized carbon atoms present in the matrix [1]. Film properties can be tuned by choosing the deposition technique with the appropriate deposition conditions. Among the different deposition parameters, the energy of the impinging ions plays the most important role and controls the sp2 /sp3 -hybridized carbon atoms fraction. In this way, films with properties typical of polymers, polymer-like films, or of graphite or diamond, graphite-like and diamondlike films, respectively, can be synthesized. On the other hand, the incorporation of elements such as nitrogen, silicon, or fluorine can optimize some of these properties [2] or even induce the formation of new nanostructured materials, such as the fullerene-like carbon films, films with strongly interacting curved graphene planes. The fullerene-like structure results from curving of the graphene planes induced by nitrogen incorporation and is similar to that found in carbon nanotubes and fullerenes [3]. The study of the nanometer scale of the physical phenomena related to the interaction of surfaces in contact and in relative motion, nanotribology, was made possible with the invention of the atomic force microscope in 1986 [4]. These phenomena are extremely important in situations ISBN: 1-58883-063-2/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

like manipulation of atoms and molecules in surfaces, as well as in the operation of electromechanical devices. For example, it was recently demonstrated that the knowledge of the energy dissipation mechanism when an atomic force microscope tip scratches the surface of a hard film might be useful for surface chemical and mechanical modifications with high spatial resolution [5]. For complete understanding of the phenomena involved, basic studies on the friction laws in nanoscale are necessary. In the last decade, with the development of friction force microscopy, the study of wear and friction properties of the materials has received increasing attention [6, 7]. Despite this, the study of the lubricant and tribological properties of carbon-based films and other nanostructured materials is still in the beginning stages and deserves more work for a complete description of the tribological processes on the nanometer scale. In the next sections, we will briefly review present knowledge on the properties and structure of amorphous carbon films as well as current applications. We will follow with a short discussion of the basic concepts involved in both atomic force microscopy and friction force microscopy. After that, we will discuss recent results on the tribological properties of carbon-based films. We will devote special attention to the effects of the incorporation of hydrogen and nitrogen into amorphous carbon (a-C) films.

2. AMORPHOUS CARBON FILMS Carbon films are presently being used in a wide variety of applications. In particular, films deposited by magnetron sputtering, plasma-enhanced chemical vapor deposition (PECVD) and filtered cathodic vacuum arc (FCVA) are used as protective overcoats for automotive components, shaving blades, biomedical implants, and computer hard disks [1]. The use of hydrogenated carbon films as the interconnect dielectric in ultra-large scale integrated chips was also proposed [8]. In addition to these many applications, a-C films are materials with considerable interest from an intrinsically basic point of view, and they have been the subject of intensive research in the last three decades. Since the pioneering work of Aisenberg and Chabot [9], hyperthermal (energies ∼1–1000 eV) carbon-containing

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Nanotribology of Carbon Films

900 species have been extensively used for the synthesis of a-C films [10]. The subplantation model suggests that the deposition of hyperthermal species is a shallow implantation process, where the incorporation of carbon species in the subsurface layers followed by large internal stresses is the dominant mechanism, responsible for the formation of a sp3 carbon rich dense phase, the diamond-like phase [11–13]. The energy of the impinging species plays the main role in the control of the carbon bonding hybridization. In fact, the evolution of the dense phase in a-C films occurs by a preferential displacement mechanism. It occurs when the incident ion energy is sufficient for the displacement of atoms with low displacement energy, Ed , the sp2 -hybridized carbon atoms, but it is insufficient for the displacement of high Ed atoms, the sp3 -hybridized carbon atoms. In subplantation, the increased density stabilizes sp3 hybridization over sp2 hybridization. For some experimental conditions, a-C films with up to 80% of carbon atoms with sp3 hybridization can be obtained. These films are called tetrahedral amorphous carbon (ta-C) films and can be hydrogenated or not. For films deposited by FCVA using C+ beams, the maximum fraction of sp3 hybridization occurs at around 100 eV [14], which is in good agreement with subplantation model predictions [11]. Amorphous carbon films present important properties that are closely related to the film microstructure [15]. Following Robertson [1], the sp3 bonds are responsible for the high hardness, which can reach ∼80 GPa (Young’s modulus of 700–800 GPa) in ta-C films grown by filtered arc and laser ablation methods, and because sp2 bonds are weaker than sp3 bonds, the respective  states of these bonds lie closer to the Fermi level, controlling the gap size and the optical properties of the materials. By choosing the deposition technique and the appropriate deposition parameters, the ratio between carbon atoms in sp2 and sp3 hybridization can be tuned and the film properties can be controlled. The incorporation of hydrogen in the amorphous skeleton also plays an important role, as is illustrated in Figure 1. In this figure, a ternary phase diagram of the amorphous carbon–hydrogen system is presented. Besides the 100% sp3 (diamond) and 100% sp2 (graphite) phases, a-C films with the fraction of sp3 bonding in the range between 5 and 80% can be produced. The hydrogen content of these films can vary from 0 to 50 at.%. The amorphous hydrogenated carbon (a-C:H) films can be deposited by both sputtering and PECVD techniques in a large range of sp2 /sp3 -hybridized carbon atom ratios. Depending on the deposition conditions, substrate-bias voltage, substrate temperature, pressure, and gas precursor atmosphere, they can be either diamond-like (sp3 -rich films) or graphitic-like (sp2 -rich films). However, a-C:H films with high H content (∼50 at.%) and a high fraction of carbon atoms with sp3 hybridization have a polymeric character. The region of larger H content is forbidden, because this corresponds to molecules, not a continuous network solid. Recently, it was shown that the subplantation model could be applied to describe the mechanisms of a-C:H growth by PECVD. In fact, the internal stress and hardness of a-C:H films deposited by radio frequency (rf)-PECVD in pure methane atmosphere show a dependence with the self-bias that is well described by the subplantation model. In this case, hardness and stress presenting

sp3

ta-C ta-C:H

a-C:H sputtered a-C(:H)

sp2

H

Figure 1. Ternary phase diagram of the amorphous carbon–hydrogen system. Reprinted with permission from [63], J. R. Robertson, Thin Solid Films 383, 81 (2001). © 2001, Elsevier Science.

maxima at around −100 V of self-bias voltage, Vb , for films deposited at 1 Pa [16]. At this pressure the energy of the impinging ions is essentially eV b , where e is the electron charge. One way of changing a-C:H film properties is through the incorporation of different elements such as N, F, and Si during the film growth. The incorporation of Si, for example, stabilizes sp3 carbon bonds and improves the thermal stability of a-C:H films [17]. The incorporation of fluorine in a-C:H films has also attracted interest in the last few years. Despite the remarkable lubricant properties of poly(tetrafluoroethylene), recent research on fluorine incorporation into a-C:H films is mainly motivated by its electrical characteristics. In fact, to improve the switching performance of future ultra-large scale integrated circuits, insulator films with dielectric constants lower than that of SiO2 are needed to reduce the capacitance of interlayer insulators [8]. Fluorinated amorphous carbon (a-C:H:F) films have been proposed as possible candidates due to their low dielectric constant [18–22]. These films can be plasma deposited in a wide compositional range, the film fluorine content being determined primarily by the precursor atmosphere [19]. It has been found that the dielectric constant decreases with an increase in the F/H ratio of the precursor atmosphere for films deposited by PECVD [19]. However, the poor thermal stability of a-C:H:F films inhibits their application as a low K dielectric in semiconductor devices, because important thickness reduction was observed for annealing temperatures higher than 300 C [22]. Notwithstanding the interest in the dielectric properties of fluorinated amorphous carbon films, not much attention has been paid to the effect of fluorine incorporation on the mechanical and tribological properties of a-C:H films [23–26]. Similarly, the effect of ionic bombardment during a-C:H:F film growth has not been investigated in great detail [25, 27]. The incorporation of fluorine increases the film surface energy, and because

Nanotribology of Carbon Films

one makes the choice of the appropriate set of deposition parameters a hard, anti-adhesive, and low friction coating can be deposited with a high deposition rate [28]. In the last few years, an important portion of the research effort on a-C:H films was dedicated to the study of the nitrogen incorporation [29, 30]. The main purpose of this research effort was the intention to synthesize the -C3 N4 solid, proposed by Liu and Cohen [31], structurally analogous to -silicon nitride (sp3 -carbon atoms bonded to sp2 nitrogen) and with mechanical properties comparable to those of crystalline diamond. Many attempts to synthesize -C3 N4 samples have failed: high pressure–high temperature techniques produced only graphitic materials [32, 33], and the film deposition techniques usually produce amorphous films [34, 35]. In fact, only in a few cases was the presence of some small crystalline grains embedded in an amorphous matrix reported [36, 37]. In these cases, an electron diffraction pattern somehow related to the predicted one was obtained from those grains. The difficulties in synthesizing -C3 N4 were tentatively explained by molecular dynamics calculations showing that strong nitrogen incorporation into the amorphous carbon network catalyzes carbon undercoordination, which in turn causes the nitrogen to develop CN double and triple bonds [38]. Electron energy loss spectroscopy measurements support these calculations, because they show that nitrogen incorporation into amorphous carbon films, as also observed in amorphous hydrogenated carbon films [39], induces an increase in the fraction of carbon atoms presenting sp2 -hybridization [40]. Results provided by neutron and X-ray diffraction experiments also revealed that nitrogen incorporation induces a transformation of carbon hybridization from sp3 to sp2 states, with the presence of both C N and C N bonds [41, 42]. Nitrogen incorporation into a-C:H films was found to modify the structure and properties of these films. Concerning the mechanical properties, a reduction on the internal compressive stress was observed, with minor changes in the mechanical hardness [43–45]. Concerning the modification of electrical and optical properties, it was found that nitrogen could electronically dope a-C:H films with the simultaneous reduction of the electronic defect density. This makes possible the use of a-C:H:N films as a semiconductor material [46, 47]. In an attempt to avoid the metastability of -C3 N4 , a new approach was tried: the growth of superlattices involving very thin layers, a few nanometers thick, of carbon nitride and transition metal nitrides, the last one providing a lattice-matched structural template to seed the growth of the -C3 N4 phase. The production of a hard (∼50 GPa) and fully crystalline carbon nitride composite material was claimed to be achieved [48, 49]. In a recent publication, a detailed structural characterization of this material was performed, but, unfortunately, despite the fact that the presence of sp3 -hybridized carbon was revealed by several analytical techniques, Raman and electron energy loss spectroscopies [50], it was not possible to clearly determine the presence of the -C3 N4 phase. Despite the difficulties in synthesizing crystalline -C3 N4 or any other crystalline structure of carbon nitride, amorphous carbon–nitrogen films, a-CNx , especially those deposited by reactive sputtering, are very interesting because

901 of their application as protective coatings. In fact, a-CNx films with hardness of ∼20 GPa have been obtained by using different configurations of sputtering deposition systems: direct current (dc)- or rf-magnetron, ionized magnetron, and unbalanced dc-magnetron [51–53]. The substrate bias is the relevant parameter to optimize the mechanical and tribological properties of the films: a negative substrate bias is necessary for the production of hard a-CNx films with improved tribological properties. The results of hard disk durability tests show that carbon–nitrogen coatings have greater wear resistance than pure argon-sputtered carbon films [54, 55]. As a consequence, a-CNx films are currently being used as the protective coating on many commercial hard magnetic disk systems [56]. The effects of the substrate temperature on the film microstructure were also investigated. As a general rule, films deposited at low temperatures onto a floating substrate are amorphous, and the nitrogen content and the deposition rate decrease with increasing deposition temperature. Cuomo and collaborators [57], based on infrared (IR) absorption spectroscopy results, proposed a structure for a-CNx films deposited by rf-sputtering onto a floating substrate that they called paracyanogen-like, a solid polymer form of cyanogen, (CN)n . This material is formed by aromatic rings with C N and C N bonds, connected to hydrogen or CN radicals. On the other hand, high-resolution transmission electron microscopy experiments performed on a-CNx films deposited at temperatures higher than 250  C revealed the presence of distorted graphite-like structures consisting of buckled and curved basal planes, giving rise to a fullerenelike microstructure [58]. Fullerene-like carbon (FLC) films with strongly interacting graphene planes have the unique properties of being hard and extremely elastic [3, 58]. The curving of graphene planes facilitates the formation of sp3 bonds between intersecting graphene planes, resulting in a predominantly covalent sp2 network. The highly elastic nature (up to 90% elastic recovery after indentation) of the FLC films makes it difficult to extract hardness values with the nanoindentation technique. However, the Young’s modulus of FLC thin films measured using the surface acoustic wave method is approximately 500 GPa [3]. FLC films can be deposited using magnetron sputtering [58], laser arc [59], and localized high-pressure arc discharge (LHPA) [3]. In magnetron sputtering, high growth temperature (for formation of graphene sheets) and approximately 15% nitrogen in an Ar + N2 atmosphere are required for the formation of the fullerene phase [58]. The presence of nitrogen in a hexagonal graphite lattice favors the formation of pentagons, inducing curvature in the graphene planes. In the laser arc and LHPA techniques, the fullerene-like structure results from the covalent interlinking of large fullerenes, nanotubes, and nanoparticles emitted from the cathode during the discharge. Concerning the application of a-C films as tribological coatings, the protection of the hard magnetic disk deserves special attention, because it represents a unique combination of the latest technologies in tribology, thin film deposition, fluid mechanics, magnetism, and materials science. A schematic view of a hard magnetic disk is presented in Figure 2. With the recent development of magnetic

Nanotribology of Carbon Films

902

Together with an important effort to extend to lower thickness the current coating technologies, that is, carbon nitride films deposited by pulsed magnetron sputtering [62], a lot of effort has been devoted to preparing a new generation of coatings, the ta-C films, based on mass selected ion deposition techniques [63], which are supposed to be able to fulfill all the requirements to achieve the goal of 100 Gbits/inch2 .

GMR read/write head

Air gap Lubricant

Magnetic space

3.1. Atomic Force Microscopy

Carbon Co-based magnetic layer

3. FORCE MICROSCOPY

Disk

Substrate

Figure 2. Schematic diagram of a hard magnetic disk and head.

devices, specially after the introduction of the magnetoresistive readers, the areal bit density in hard disks increased more than 60% a year, density that increased even faster in the last few years after the introduction of the giant magneto-resistive read technology. Today, even using a conservative approach, the goal of 100 Gbit/inch2 could be achieved in less than 4 years from today [60]. As the recording density grows, reader stripe dimensions are vanishing. Head/magnetic media spacing must be reduced to achieve those densities. In fact, coatings that are around 1 nm thick will be needed, as shown in Figure 3, together with very restrictive conditions on surface roughness and lubricant layers. The spacing between the slider and the disk is steadily reduced and the disc revolutions per minute is heading toward 20,000 and beyond [61]. With the current load–unload technology, the overcoat is expected to provide some tribological protection together with protection against corrosion that requires a dense coating with low defect density. Under these conditions, drive performance improvement has to be necessarily combined with mechanical and tribological durability.

Figure 3. Variation of the carbon coating thickness on disk and sliders, the magnetic space, and the fly height with storage density. Reprinted with permission from [63], J. R. Robertson, Thin Solid Films 383, 81 (2001). © 2001, Elsevier Science.

A variety of instruments can be used to study friction, but it was after the invention of atomic force microscope (AFM)/friction force microscope (FFM) in the late 1980s that the field of tribology has gained new impulse. The force microscope has made possible the study of very low friction forces in a precise way. The instrument working principle of the AFM/FFM is very simple: a small tip is brought into contact with a surface, in a very controlled way, and scanned over the surface. While scanning, the normal and lateral movements of the microscope tip can be acquired. The normal movement of the tip is related by Hook’s law to the normal force while its lateral movement, caused by the moment of the friction force acting on the tip–surface interface, is related to the friction forces. In Figure 4, a typical AFM/lateral force microscope (LFM) scheme is presented. Usually, the samples are placed on the top of a piezoelectric tube ceramics that is going to control the lateral scan and the normal movements of the sample related to the tip. When scanning, the tip movement is measured by a position-sensitive photodetector. Although the top minus bottom (T − B) output from the detector is proportional to the tip normal displacement, the left minus right signal (L − R) is proportional to the torsion of the AFM tip. To keep the normal forces between the AFM tip and the sample constant during the scan, the T − B signal is compared with a reference value. Its difference, called error signal, is then used by the microscope feedback system to

Figure 4. Schematic diagram of an atomic force microscope.

Nanotribology of Carbon Films

correct the distance between the tip and the sample, keeping the normal force constant during the whole image. If the feedback system is turned off, the piezoelectric ceramics are no longer moved in the normal direction, keeping the sample’s height nearly constant. On this operational mode, the cantilever deflections are recorded as a function of the sample position. These two operational modes are then called constant force and constant height modes and have in common the fact that the total normal force, acting between the tip and surface atoms, is repulsive. In general, images with “low” resolution or large scan areas are performed in the force constant mode while high resolution images are acquired in the constant height mode. In Figure 5 we present two examples of these extreme cases and show an image obtained from an a-C film deposited by sputtering and an image obtained from a highly oriented pyrolytic graphite (HOPG) surface. The AFM also has two additional modes that are called the noncontact and tapping mode. In both cases, instead of acquiring the direct bending of the cantilever tip, the amplitude, phase, or frequency from a mechanically vibrated tip is acquired. This signal is again compared with a reference value and its error is used by the feedback system to correct the sample height. While in the tapping mode the force

Figure 5. (a) Amorphous carbon film deposited by sputtering using bias voltage of −50 V and (b) boric acid single crystal (H3 BO3 ) images obtained by the AFM.

903 sensed by the vibrated tip ranges from attractive to repulsive, in the noncontact mode the forces are predominately attractive. A typical force curve obtained in an AFM is presented in Figure 6. In such an experiment, the sample is moved upward or downward with the use of the piezoelectric ceramics while the cantilever deflection is acquired. In region 1, the tip is far from the sample surface, thus no effective force is sensed by the AFM tip. As the sample is moved upward, that is, the distance between tip and sample decreases, the cantilever tip bends toward the sample (region 2), indicating that the forces between them are attractive. As the sample keeps moving upward, the tip comes close to the surface so that the net interaction force becomes repulsive (region 3). As the sample is moved downward, the tip remains in contact with the sample surface, due to its adhesion to the surface (region 4), until the force at the cantilever overcomes the tip–surface adhesion. The reader has to note that the attractive forces between tip and surface during its approach are caused mainly by Van der Waals forces, the repulsive forces are caused by the repulsion of the tip–surface atom’s electronic clouds, and finally, the tip–surface adhesion is caused mainly by the capillary condensation of water between the tip and the surface. As mentioned above, the tip movement can be translated into forces by Hook’s law. Therefore, the calibration of the AFM cantilever and its displacement sensor for friction forces is essential for the successfully measurement of friction forces. First, the elastic normal bending and torsion constants of the cantilever have to be calculated, which is usually done with measurement of the cantilever’s

Figure 6. Typical force curve obtained with an AFM.

Nanotribology of Carbon Films

904 dimension by electronic microscopy and the use of a wellknown static mechanics procedure [64]. Then, the displacement sensor can be calibrated to translate the normal and torsion bending angles in normal and friction forces [65].

3.2. Friction Force Microscopy The energy that is dissipated at the interface when two materials are brought into contact and move with respect to each other is determined by the friction forces acting at the materials’ interface. As defined, friction is always regarded as the force that opposes the movement of the surfaces. It was studied a long time ago by prominent scientists such as Leonardo da Vinci, Guillaume Amonton, and Charles A. Coulomb, among others [66]. They stated that friction is independent of the surface’s contact area, that it is proportional to the normal forces acting between the surfaces, and that the kinetic friction is independent of the surface’s relative velocity. Unfortunately, these laws seem to be no longer valid. As observed by Mate et al. [67], the lateral movement of the scanning tip on a surface is shown to follow an atomic scale stick and slip behavior. The result obtained from a HOPG surface is shown in Figure 7. Here it was shown how the frictional force behaves during the stick and slip process as the surface is rastered in the xy plane. In this experience the sample is moved back and forth with the velocity of 40 nm/s in the x direction and 0.2 nm/s in the y direction. The critical friction force before the first slip occurs varies, depending on the position of the tip with respect to the graphite lattice. The slips occur where the image suddenly changes from bright to dark. Figure 7 clearly illustrates how the atomic structure of the surfaces influences the frictional properties of the tip–surface interface. The image shows the periodicity of the HOPG surface potential.

The atomic scale stick and slip is believed to be responsible for the energy dissipation at the tip–surface interface. In such a case, a mechanism introduced by Tomlinson in 1929 [68] can be used to explain the energy dissipation. He proposed that some irreversible process in the passage of one atom past another must exist to explain the energy dissipation in pure conservative potentials. The stick–slip movement of the scanning tip can be simulated in either one or two dimensions. Usually, a simple oscillator model as proposed by Tomlinson is used to simulate the FFM images in which the microscope tip slides over the corrugation of an atomically flat surface. This has been mainly performed in periodic potentials, generally described by sinusoidal potentials [69]. The calculations show that the FFM images present the surface potential periodicity instead of atomic resolution [70] and that the cantilever stiffness and scanning direction are important to the friction force images [71, 72]. The movement of the microscope tip can be understood by an analysis of the system’s potential energy [6, Chap. 4]. The tip sticks in a surface minimum, until the elastic force in the tip–surface system overcomes friction. Then the tip jumps directly to the next surface minimum, leading to an atomically periodic stick–slip movement, as represented in Figure 8. As a consequence, only part of the surface potential is probed by the microscope tip, leading to images that contain only the periodicity of the analyzed surface. Recently, it has been shown that the FFM resolution is governed by the quotient between the average potential interaction energy and the average elastic energy stored on the tip before the jumps. It was also shown that there is an optimal velocity with which the scanning tip better senses the surface potential [74]. Studies on the influence of the normal force on friction revealed that at low normal forces, in contrary to what is observed in the macroscopic scale, the friction forces strongly depend on the real tip–surface contact area [75]. Friction is observed to be proportional to the contact area,

8

Potential Energy

6

4

2

0

-2 -4

-2

0

2

4

LFM cantilever position Figure 7. The frictional force in the x direction as a function of x and y. The intensity of the image is scaled to the friction force with the bright areas corresponding to 1 8 × 10−6 N. Only scans in the left-to-right direction are shown. The size of the image is 2 to 2 nm2 , and no correction from piezoelectric scanners was done. The load is 5 6 × 10−6 N, and the wire spring constant is 2.5 kN/m. Reprinted with permission from [67], C. M. Mate et al., Phys. Rev. Lett. 59, 1942 (1987). © 1987, American Physical Society.

Figure 8. The system’s total potential energy as a function of the LFM cantilever position. The dashed and solid lines represent the potential, while the gray and black dots represent the microscope tip position. Note that, as the cantilever is scanned, its tip gets pinned in a local surface minima (dashed line) until the elastic energy is high enough to overcome the friction barrier (solid line). Thus, the tip slides to the next surface minima (gray → black balls).

Nanotribology of Carbon Films

and the proportionality coefficient is defined as the interface shear strength. It has been shown by Kaneko et al. [76] that, if the microscope tip does a multiasperity contact with a surface, the dependence of friction with the normal force becomes linear because the contact asperities can increase with an increase in the normal force. They have also shown that if the tip does a single asperity contact with the surface, the relations between the friction and the normal forces are no longer linear. A change from multi-asperity to single asperity contact is shown to be caused by the capillary condensation of water on the microscope tip. The influence of the environmental conditions on the friction experiments is not restricted to changes in the kind of tip sample contact. The role of water condensation was investigated in detail for silicon wafers, and the results for the friction forces revealed the importance of the surface energy in defining the thickness of the water film and its effects on the friction forces [77]. It was shown by Riedo et al. [78] that the capillary condensation of water strongly influences the dependence of friction on the scanning velocity. The formation of a capillary bridge increases the adhesion between the tip and a surface, leading to an increase in the force necessary to move the tip with respect to the surface. As the scanning tip moves faster, the time that the system has to built up the capillary decreases, leading to a decrease in the force necessary to move the tip on the surface. In fact, the dependence of friction on the scanning velocity may be explained with a combination of three different models. At very low scanning velocity (v → 0), the energy dissipation is shown to be mainly caused by the nonlinear dynamics of the moving parts [79–81]. At higher velocities, friction is shown to present a logarithmic dependence with velocity. This logarithmic dependence is explained by a combination of thermally activated stick–slip behavior [82, 83] and the kinetics of nucleation of water bridges between the moving parts [78]. In force microscopy the main energy dissipation process that is believed to occur when the tip is scanning on a surface is phononic excitation. Whereas at very low scanning velocities, the nonlinearity of the tip motion together with the coupling of its 2 degrees of freedom, is responsible for the energy exchange between its vibration modes [84, Chaps. 1, 6, and 7], at higher velocities, the discontinuous nature of the sliding tip movement is able to excite the normal modes of vibration on the scanned surface, raising its temperature.

4. NANOTRIBOLOGY RESULTS 4.1. Adhesion When two surfaces in vacuum or in a gaseous environment come close, they usually experience attractive forces, such as Van der Waals forces. Once in contact, they are inevitably deformed because of their finite elasticity. Contact between two solid bodies can be described by the model of Johnson, Kendall, and Roberts (JKR) [85] or by the model of Derjaguin, Muller, and Toporov (DMT) [86]. Both models are based on an earlier analysis by Hertz [87], who considered two elastic bodies in contact under an external load but ignored attractive forces. In the JKR approach, the effective

905 steady-state pressure in the contact area is assumed to be the superposition of the elastic pressure and of the attractive surface forces, which acts only over the contact area. As a result, a tensile force is necessary to separate the adhering surfaces. For two spherical particles this pull-off force is given by FJKR = 3R

(1)

where  is the effective solid surface energy and R is the reduced radius of curvature of the two surfaces (R = R1 + R2 /R1 R2 ). The DMT model is an alternative model that also accounts for noncontact forces in the vicinity of the contact area. It predicts a slightly higher pull-off force of FDMT = 4R

(2)

Both models are limiting cases of a more general description [88]. The JKR model is appropriate for large, soft bodies with high surface energy, and for hard solid bodies with low surface energy, the DMT model should be applied [89, 90]. For an AFM tip interacting with a carbon film surface, we can model the tip–surface interaction as a sphere contacting a flat surface, the DMT theory describes the adhesion force as Fad = 2RWad

(3)

where R is the radius of curvature of the sphere and Wad is the work of adhesion defined as Wad = 2tip surface 1/2

(4)

where  is the surface free energy of the tip and of the surface [91]. From this model it is seen that adhesion forces scale directly with the radius of curvature of the tip. Therefore, to correct for changes in tip geometry and to probe the inherent properties of the carbon film surface, one needs to normalize the adhesion forces by the radius of curvature of the AFM tip [92]. When two surfaces come in contact, contact occurs on a large number of asperities. To develop a fundamental understanding of friction and wear mechanisms in lubricated contacts, experiments in a single asperity contact need to be conducted. The development of the atomic force makes possible the investigation of the adhesion forces and its influence on the tribological performance of coatings in a single asperity contact regime. One of the first discrepancies between the macroscopic behavior and the friction on the nanometer scale was revealed by studies designed to investigate the dependence of friction forces with the contact area. The fundamental friction law, first proposed by da Vinci and reproposed by Amonton more than three centuries ago, can be written as FF = FL

(5)

where FF is the friction force,  is the friction coefficient, and FL is the normal load force. The friction coefficient is constant for a given pair of materials in a wide range of

Nanotribology of Carbon Films

906 loads and independent of the apparent contact area. This condition is fulfilled when the contact area, A, is proportional to the normal load. It was shown that for rough surfaces (multiasperity contact) in an elastic regime, it occurs if the asperities follow a statistical height distribution [93–95]. Moreover, when the normal load increases and plastic deformation occurs, an increase of the contact area is verified so that the relation contact area, A ∼ FL , remains valid and so follows Amonton’s law. In a single-contact regime the situation is different. In fact, load-dependent studies of frictional properties of graphite, diamond, amorphous carbon, and fullerene thin films were performed in argon atmospheres and ambient conditions by Wiesendanger and collaborators [96] using specially prepared silicon tips with well-controlled tip point shape and radius. Their results reveal that in the low load regime, that is, in a regime where wear and plastic deformations can be neglected, the friction force did not follow direct dependence with the applied load. The data were explained using a theoretical model based on a Hertziantype tip–surface contact, which predicts a dependence of the contact area with the normal force of A ∼ FL2/3 [87]. With this result, the authors show that friction is proportional to the contact area and that the shear stress was constant within the applied pressure, leading to a FF ∼ FL2/3 dependence of the measured frictional forces. These experiences showed that single asperity contact mechanical models are valid for tip radii down to a few nanometers, at least when the tip has a well-defined tip–surface contact area. In nanoscale the normal force must take into account the attractive adhesion forces FN = FL + Fa

(6)

where FN is an effective normal force that takes into consideration both the normal load FL and the adhesion force Fa . The adhesion force is taken as the maximum negative bending force of the cantilever on the tip approach curve. Many experimental works are devoted to determination of the adhesion forces in carbon film surfaces and many other surfaces [92]. In a pioneer investigation, Binggeli and Mate [97] showed that the adhesion force measured in different ambient, relative humidities ranging from 80 to 98%, can be considered as a constant for a-C films deposited by sputtering. The effects of hydrogen on adhesion force of a-C:H films were carefully investigated by Perry and collaborators [98]. They showed that the adhesion force increases with the hydrogen content in films deposited by sputtering in Ar–H2 atmospheres. Because they used a tip with the same chemical composition, oxidized tungsten in this case, they concluded that the observed increase arises from an increase in the surface free energy of carbon films that follows the hydrogen content in the films. The friction coefficient measured in the same samples also increased with the hydrogen content, following the adhesion force behavior. The effect of nitrogen incorporation was also investigated for films deposited by ion beam sputtering using a second argon beam as an assistance beam [55]. The authors, using an AFM with a Si3 N4 tip, operating in air, showed an increase from 25 to 32 nN for adhesion forces measured in

a-C and a-CNx films, respectively. Despite higher adhesion at the interface, a-CNx films showed a smaller friction coefficient than did a-C films—0.14 and 0.28, respectively. The contact radius calculated using the Hertz model was about 0.2 nm and almost equal for both coatings. The authors concluded that the shear strength of CNx was lower than that of carbon and could partially explain why friction is lower in CNx than in carbon films.

4.2. Friction As previously mentioned, the laws that control the friction at the macroscopic scale are well known: the friction force (FF ) increases with the applied normal load (FL ) and it is independent of both the contact area and the velocity [66]. The studies carried out since the invention of the friction force microscope reveals that some of these laws are no longer valid on the nanometer scale. To investigate this new experimental domain, the study of carbonbased materials occupies a special place. A recent review of tribological properties of carbon films shows that, in all environments, the macroscopic tribological behavior of these films was controlled by an interfacial graphitic transfer layer formed during friction [99]. However, in nanoscale, those energy-dissipating mechanisms are far from being well understood. Some authors claimed that the dissipation of friction energy could take place by phonon excitation [100]. A second proposed mechanism takes into consideration the dissipation via electron–hole pair excitation [101]. Amorphous carbon films represent a remarkable opportunity to investigate friction mechanisms because materials with different microstructures, the sp2 /sp3 ratio, for example, can be easily synthesized. The FFM experiences showed that single asperity contact mechanical models are valid for tip radii down to a few nanometers, but only when the tip has a well-defined tip– surface contact area. These experimental results also show that, in nanoscale, the normal force must take into account the attractive adhesion forces; that is, FN = FL + Fa . Wiesendanger and collaborators [96] show that, for measurements performed in argon atmospheres, the friction in C60 films is higher than those for a-C films and diamond surfaces. In ambient air, the friction is higher than friction forces measured in a water-free ambient. For atmospheric exposed surfaces, a-C films have friction higher than that for diamond. In both cases, the lowest friction forces were always determined for HOGP samples. Following this first work, several other groups performed a comparative study of the friction properties of different carbon-based films. Among them we mention the investigation performed by Riedo and collaborators [102]. They studied diamond-like films with different fractions of sp3 hybridized carbon atoms and CNx films with different contents of nitrogen (0 2 < x < 0 3), both deposited by laser ablation. The Raman results obtained from the samples show that, depending on the laser fluence, the content of sp3 hybridization can be controlled, and it is higher for films deposited at the higher power laser in a nitrogen-free atmosphere. These films have 53% sp3 -hybridized carbon atoms and are called diamond-like carbon (DLC). The FFM measurements were performed in ambient conditions using a

Nanotribology of Carbon Films

907

silicon nitride tip. To avoid plastic deformation, the loads were restricted to 20 nN. As was observed before by Bushan and Sundarajan [103, 104], the topographical images of CNx and a-C films obtained simultaneously with the friction force images revealed that the friction forces map essentially follows the surface topography, as can be seen in Figure 9. In this figure the topographical image of a CNx film was compared with the friction image in the forward and backward scan direction taken simultaneously. In Figure 10, we show the friction forces for HOGP, CNx , and DLC films for an applied load of 12 nN. The figure shows the forward and backward scans with the friction force being proportional to the difference between the two. It is clear from the figure that the friction force in HOPG is by far the lowest one and that the friction force measured on the CNx film is of the same order of magnitude as the one obtained from a DLC, but slightly lower. The authors claimed that the friction forces obtained from a-C films with sp3 fractions in the range of 34–53% are equal within experimental errors. Similar behavior was observed for CNx films with different nitrogen content; that is, in this case the friction forces are independent of the amount of nitrogen incorporated in the films.

Figure 10. Friction forces for the samples of (a) graphite (HOPG), (b) CNx , and (c) DLC. Each graph presents a scan width of 50 nm and two force signals corresponding to foreword and backward scans. Reprinted with permission from [102], E. Riedo et al., Surf. Sci. 477, 25 (2001). © 2001, Elsevier Science.

Figure 9. Topographical image (top) of a CNx film taken simultaneously with a friction image in the forward (→) and the backward (←) scan direction (middle and bottom image, respectively). Reprinted with permission from [102], E. Riedo et al., Surf. Sci. 477, 25 (2001). © 2001, Elsevier Science.

The investigation of the friction force as a function of the normal load reveals that CNx film results show linear dependence between the friction force and the load force, indicating a multiasperity contact, while the results obtained from a-C films nicely follow a two-thirds power law, FF ∼ FN2/3 , as expected from a single asperity contact. Because a similar silicon nitride tip is used in all instances, the differences observed between DLC and a-CNx films can be attributed to the lower surface roughness of the former. Because on nanoscale the Amonton’s law FF = FL is no longer valid, the friction coefficient defined in that way is not well suited for comparing tribological behavior of different materials in the case of single asperity contact. The friction coefficient was determined by the linear regression of FF versus FN , that is, taking into account the adhesion forces, and the following results were obtained:  = 0 009 ± 0 003 for HOPG,  = 0 167 ± 0 03 for CNx films, and  = 0 208 ± 0 03 for DLC films. These results seems to support the phonon mechanism as the dominant one for energy dissipation, because the friction coefficient in DLC films is independent of the sp3 fraction films, and, more important, the DLC films have

Nanotribology of Carbon Films

908

0.8

(c)

0.6

2

sp fraction

a higher friction coefficient compared with HOPG. If an electron–hole excitation mechanism played an important role, the opposite behavior should be expected. Thin CNx films, 1–10 nm thick, deposited by ion beamassisted deposition (IBAD) were investigated by friction force microscopy [105]. Raman spectra from these films are quite similar to those obtained from films deposited by laser ablation and mentioned previously, suggesting the same microstructure [102]. Forward–backward scan cycles were obtained and the friction coefficient determined in the wear-less regime (load of 1 N) is on the order of 0.12, a value that increases to 0.22–0.24 for higher loads (10 N). No thickness dependence was observed in the range of 1–10 nm. These values for the friction coefficient were on the same order as the previous ones. Khurshudov et al. [55] using an AFM equipped with a silicon nitride tip (10–20 nm radius) also measured the friction forces for a-CNx (x = 10 at.%) films deposited by IBAD. The measurements were performed at a velocity of 10 m/s and at ∼60% of relative humidity and show that the friction force measured for a-CNx films was systematically 20% lower when compared with the friction force measured in a-C films deposited by the same technique, confirming the general trend showing that the friction force (or friction coefficient) measured in CN films is slightly smaller compared with the values obtained from a-C films deposited with the same technique using similar deposition conditions. Films with different contents of nitrogen deposited by PECVD, a-C:H(N) films, were also investigated by friction force microscopy using a silicon nitride tip with measurements performed in air [106]. The results are summarized in Figure 11. It is clear from this figure that, despite a substantial increase of the sp2 fraction upon nitrogen incorporation

roughness (nm)

0.4 0.3

(data taken from Ref. 107), the friction coefficient is constant, supporting the idea that phonon excitation is the dominant energy dissipation mechanism. The increase in film surface roughness with the increase of the sp2 fraction was observed before for a-C films deposited by C+ beams [108] and seems to play a secondary role in the definition of friction forces in this case. A comparative FFM study of a-C films deposited by different techniques was carried out by Sandararajan and Bushan [109]. Films deposited by electron cyclotron resistance (ERC)–chemical vapor deposition (CVD) using ethylene as a precursor gas, rf sputtering of a graphite target in argon atmosphere, FCVA, and direct ion beam deposition from methane dissociation were studied. The results for the friction coefficient were obtained with a diamond tip at a 4 m × 4m scan size in a load regime where no wear was observed. The results for friction coefficients were determined for films with thickness in the range of 3.5–20 nm. The thinner films have higher friction coefficients independent of those deposited using the same technique. These results contradict the results obtained by Bai et al. [105] for CNx films mentioned above. The systematic investigation of the coating failure by the AFM topography image reveals the direct correspondence between high friction and coating failure area. This problem is critical in the case of sputtered carbons films, where reliable coatings with thickness below 5 nm could not be obtained. The fundamental laws of tribology predict that the friction is independent of the velocity. Friction force microscopy measurements on carbon-based compounds have also been performed to investigate this question on the nanometer scale. In a first report, Zwörner et al. [110] determined that the friction forces are constant over a wide range of velocities. Metal-containing carbon films, Me–C:H, with Me = Au and W were also investigated, and the results show that in the range of 0.1–10 m/s, the friction force measured by the FFM is constant [111]. In another investigation, constant friction coefficients were reported for ta-C and FLC films in the velocity range of 0.1–40 m/s [112]. The results are shown in Figure 12. In this case, the ta-C films were deposited by FCVA while the fullerene-like carbon films were deposited using an unfiltered LHPA discharge,

0.2

0.18 (b)

0.1

0.3 0.2 (a)

0.1

0

5

10

Friction coefficient

friction coefficient

0.15

0.12

0.09 ta-C FLC

15

Nitrogen content (at. %)

0.06 0

2

Figure 11. Fraction of carbon atoms in sp hybridization (a), surface roughness (b), and friction coefficient (c) for a-C:H:N films deposited by PECVD. Reprinted with permission from [106], R. Prioli et al., J. Vac. Sci. Technol., A 14, 2351 (1996). © 1996, American Vacuum Society.

10

20

30

40

Scanning velocity ( µm/s) Figure 12. Friction coefficient as a function of the scanning velocity for ta-C and FLC films [102]. The lines are only to guide the eyes.

Nanotribology of Carbon Films

between two mechanisms, the cohesive forces responsible for the stick and slip movement and the kinetics nucleation of water meniscus between the moving parts. Experimental data obtained in air from a-C:H and a-C:H:F films deposited by PECVD are shown in Figure 13 [117]. The results clearly show the existence of the logarithmic velocity dependence. It is observed that the increase of the hydrophobicity of the carbon–fluorine films, represented in this case by the contact angle, is responsible for the progressive increase of the slope of the friction forces dependence with velocity, in agreement with the model proposed by Reido et al. [78]. The dependence of the friction coefficient with the surface energy is illustrated in Figure 14, where the friction coefficient obtained from hydrogenated carbon films deposited by sputtering [98] and a-C:H and a-C:H:F films deposited by PECVD are plotted as a function of the contact angle [97]. The friction coefficients were determined by the linear regression of FF versus FN , that is, taking into account the adhesion forces, and show a clear correlation with the surface energy: the higher the contact angle, the lower the friction. These results for the friction coefficient show the importance of the study of the adhesion forces and capillary condensation for the complete description of the friction behavior. The first systematic investigation of this problem was carried out by Binggeli and Mate [97, 118]. In Figure 15 their results for both the friction coefficient and adhesion force as functions of the relative humidity are presented for a-C films and silicon dioxide. The sliding speeds were on the order of micrometers per second. The slope of the friction versus load curve provided the friction coefficient and the extrapolation to zero loads, the adhesion force. In this experiment, the linear dependence between friction and applied load was an indication of the multiasperity contact among the AFM tip and sample surface. The results show that the friction coefficient decreases for silicon oxide surface but not for carbon films upon the increase of the relative humidity. The same behavior was observed for the adhesion force. The difference between the two samples was explained in 12

Friction force (nN )

introducing the carrier gas (nitrogen) via a 1 mm hole in the graphite (99.99% purity) target. The friction force measurements were carried out using an AFM operated in the friction force regime. The friction force (forward and reverse cycles) images were acquired at constant normal load, and the total normal force is composed of the adhesion force between tip and sample surface and the applied load. The cantilever-bending constant and the calibration method proposed by Liu et al. [66, 113] were used to obtain the absolute values of the friction coefficients. Nanostructured carbon films deposited by supersonic cluster beam were also studied by friction force microscopy [114]. These clusters have a fullerene structure and linear and planar structures [115]. The friction coefficients reported are in excellent agreement with the values obtained for FLC films [112]— = 0 12 ± 0 2—considering that the values reported for the nanostructured films depend on the region of the sample and the size of the clusters and varies from 0.10 to 0.14, the higher value being obtained from films deposited with the larger clusters. Gnecco et al. [83] determined a logarithmic increase of the friction force with the velocity for ultrahigh vacuum friction force microscopy measurements performed on NaCl (100) single crystals. These results were interpreted in terms of a thermally activated stick and slip behavior and the friction being due to the cohesive forces between the two surfaces in contact. It was shown that these forces increase with the scanning velocity and this logarithmic dependence was explained by a modified one-dimensional Tomlinson model [68]. Similar velocity dependence, that is, a logarithmic increase of the friction forces within the velocity was observed for DLC coated silicon substrates for friction force microscopy measurements performed on air [116]. A recent investigation carried out by Riedo et al. [78] showed that the presence of water in the ambient air changes this situation. In fact, they investigated the friction dependence of amorphous carbon films with different surface energy and showed that the friction forces were velocity dependent, confirming the logarithmic character of this dependence. However, not only increasing behavior was observed. For other materials, such as CrN films, a decrease in the friction forces with velocity was verified. This fact occurs when the measurement is performed in air and the dependence with the velocity becomes stronger for atmospheres with higher humidity. In this situation, capillary effects due to water vapor condensation must be taken into consideration. In a humid environment, the force resulting from the condensation capillary liquid bridges at many different points along the tip–sample contact area is responsible for a velocity dependence force. When the tip is at a fixed position, this capillary force increases as a function of time, because of the continuous formation of liquid bridges at the tip–sample interface. When the tip is scanning the sample surface, the time available for liquid bridges decreases as a function of the velocity, and so, the capillary forces. Hence the capillary forces acts in opposition to atomic stick and slip, causing a decrease of friction with increasing velocity. This effect obviously depends on the hydrophobicity of the sample surface. For hydrophilic surfaces, this mechanism can be predominant and friction decreases with velocity. The velocity dependence behavior observed experimentally can be understood as a competition

909

10

8 o

θ = 95

o

θ = 72

6 1

10

100

Velocity (µm/s) Figure 13. Friction coefficient as a function of the scanning velocity for films with different contact angle:  = 95 for a-C:H film and  = 72 for a-C:H:F film [106]. The lines are only to guide the eyes.

Nanotribology of Carbon Films

910

terms of the hydrophilic nature of the oxide, where water molecules are strongly bounded to hydroxyl groups. The friction coefficient for a-C films is nearly constant and equal to 0.3. A similar experiment was performed for a lower relative humidity regime (0–60%) and showed a slight increase of the adhesion force upon a humidity increase [92]. This apparent contradictory behavior can be explained as follows. For very low relative humidity, there is an increase in the number of the meniscus bridges, which results in a progressive increase of the friction. It occurs more or less independently on the surface energy of the samples. When the relative humidity is higher, the hydrophobicity of the film surface plays the decisive role. The influence of hydrogen content in a-C:H films tribology is important in either the macroscopic or nanoscopic scale. In fact, in a review article by Erdemir [119] the role of hydrogen in the tribological behavior of diamond and

diamond-like films was extensively discussed. This article showed that, for films deposited by PECVD in CH4 –H2 atmospheres, the friction coefficient measured by conventional techniques in dry nitrogen (humidity = 0%) can be extremely low ( = 0 003) when the samples were grown in a very high H/C ratio in the precursor atmosphere (H/C = 10). On the other hand, it can be very high ( = 0 65) when measured in a hydrogen-free film. With an increasing the humidity, the friction coefficient of the hydrogen-free film dropped to 0.25 and for the film deposited in a hydrogen-rich atmosphere the friction coefficient increased to 0.06. The superlubricity of the a-C:H films was explained in terms of the almost complete elimination of covalent bonds at the carbon film surface by hydrogen passivation of carbon dangling bonds [119, 120]. The C H bonds (stronger than C C bonds) inhibit the covalent interaction with the atoms of the counterface materials and, thus, cause low adhesion and friction. These arguments must be valid on the nanometer scale. In Figure 16 the results obtained by friction force microscopy from a-C:H films deposited in CH4 + H2 atmospheres by ECR–CVD [121] are shown. The friction coefficients obtained by Erdemir and collaborators [122] are also presented. The trend observed for both sets of data are the same: a decrease in the friction coefficient for films deposited in a hydrogen-rich atmosphere. It is interesting to note that films with high hydrogen content (up to 40 at.%) deposited by sputtering in Ar–H2 atmospheres [98, 123] show exactly the opposite behavior; that is, the friction coefficient increases with the hydrogen content of the films. The different effects of the plasma film surface interaction in the case of Ar + H2 mixtures in a sputtering chamber and in the case of hydrocarbon–H2 mixtures in PECVD deposition are still not well understood. Probably they are responsible for the behavior observed for the a-C:H films, because the dangling bond density in the uppermost surface layer of a-C:H films certainly depends on the deposition technique used.

Figure 15. Friction coefficient and normalized adhesive forces during sliding as a function of relative humidity. Two typical measurement series for clean silicon wafers with silicon oxide and amorphous carbon are shown. Adhesive forces have been normalized by setting the lowest value to 1 to account for different tip radii in the separate experiments. Reprinted with permission from [97], M. Bingelli and C. M. Mate, Appl. Phys. Lett. 65, 415 (1994). © 1994, American Institute of Physics.

Figure 16. Friction coefficient as a function of the hydrogen content in CH4 -H2 atmospheres. Reprinted with permission from [121], T.-H. Fang et al., Thin Solid Films 396, 166 (2001). © 2001, Elsevier Science.

friction coefficient

0.8

ref. 98

0.6

ref. 112

0.4

0.2

0.0 40

50

60

70

80

90

100

o

contact angle ( ) Figure 14. Friction coefficient as function of the contact angle for a-C:H films deposited by sputtering [108] and a-C:H and a-C:H:F films deposited by PECVD [106].

Nanotribology of Carbon Films

The demands resulting from the continuous increase of the storage density of computer hard disks and from the reduction of the loads and dimensions used in microelectromechanical systems; that is, thinner protective and anticorrosive coatings with lower surface roughness, together with the spreading of the use of the AFM motivate a large experimental effort to understand the wear behavior, in nanoscale, of carbon-based films deposited by different techniques [124]. In fact, it was demonstrated that it is possible to enter in a subnanometer scratching resistance testing regime using a standard AFM with diamond-tipped cantilevers [103]. As was also discussed before for the friction studies, a comparison of results obtained by different groups is not straightforward because the authors frequently did not report a complete structural characterization of the films under investigation. The comparison of the absolute values of wear data, the scratch depth, for example, is nontrivial, because sometimes not taken into account is the fact that the constant applied force on the cantilever cannot overcome the extra resistance force arising from the larger tip–surface contact area at deeper groove depths. On the other hand, some authors explicitly take into consideration the blunting of the tip when presenting their data [109]. Hydrogenated carbon films are a good example of this situation. These films can be deposited by sputtering with different hydrogen content by changing the ratio between Ar and H2 gases in the camera. The control of the hydrogen content can also be achieved in a-C:H films deposited by PECVD techniques by changing the hydrocarbon–hydrogen precursor gas mixtures. Hydrogenated films deposited by sputtering were investigated by Jiang et al. [123]. The 25 nm thick sputtered films were scratched with an AFM diamond tip with a loading force of 28 N and were imaged by the same tip after 16 wear cycles. The results show that the scratch depth increases from 4 to 30 nm with the increase of hydrogen content in the films, which varies from 2 to 40 at.%. The scratch depth of 30 nm measured for the hydrogen richest film means that the film is completely removed by the AFM tip. Nanoindentation measurements show that the hardness decreases with the increase in the hydrogen content from 9 to 6 GPa. A similar investigation was carried out by Wiens et al. [125]. From similar tests, they show that the scratching resistance decreases with the amount of hydrogen incorporated in the film for loads of 17 and 23 N. Sputtered hydrogenated carbon films were also studied by Anoikin et al. [126]. They deposited 10 nm thick a-C:H films onto AlMg/NiP/Cr/Co-based magnetic layer smooth disks (average surface roughness of 0.5 nm). The tip velocity was 1 m/s and the load force was in the range of 10–15 N. The films were deposited in Ar (a-C films), Ar + H2 (a-C:H films), and Ar + N2 (a-C:N films), and the amount of hydrogen and nitrogen was measured and Raman analysis was performed on each sample. Despite the fact that it is not possible to obtain the sp2 /sp3 ratio directly from the Raman results, the position of the G-band can be used, in a qualitative way, to infer an increase (shift to higher wavenumbers) of the amount of sp2 -hybridized carbon atoms in the film or of the size of the graphitic domains [127]. The results are resumed in Table 1. They show that for films with nearly the

Table 1. Hydrogen content, G-band position, and scratch depth for several a-C films [123].

Materials a-C a-C:H a-C:N a-C (IBAD) Graphite [127]

H content (at.%)

G-band position (cm−1 )

Scratch depth (nm)

13 5 25 4 9 1 18 9 —

1582 1575 1569 1535 1584

14 7 4 0 5 —

same amount of hydrogen, the scratch depth decreases when the sp2 fraction increases. When we compare the results for scratch depth obtained for films deposited by sputtering with those obtained by ion beam deposition of hydrocarbon species, in the same experimental conditions, this correlation is even clearer. The results obtained from sputtered films and presented in Table 1 show a direct correlation between hardness and the scratch depth, considering that films with higher sp3 fractions usually have higher hardness [15 63]. Hydrogenated carbon films deposited by ECR–microwave plasma CVD were also studied for different chemical composition [121]. In this case the precursor atmosphere was a mixture of H2 and methane, and the authors varied the amount of hydrogen in the mixture from 0 to 71%. The wear depth as a function of the number of wear cycles is presented in Figure 17. A load of 100 N was applied, and each sample was submitted to 20 wear cycles. The wear rate decreases with the hydrogen content of the films. In this work, Raman results were presented and clearly show that a-C:H films have an increasingly graphitic character when the gas precursor mixture became richer in hydrogen: the G-band shits to higher wavenumber and its width reduces upon the increase of the amount of H2 in the plasma atmosphere. The Raman results suggest a hardness reduction upon the hydrogen incorporation. The same group investigates the effect of the self-bias voltage in films deposited by ECR–microwave plasma CVD using a CH4 (50%)–H2 (50%) mixture [128]. Again the Raman result revealed an 25 29% CH4+71% H2 71% CH4+29% H2 100% CH4

20

Scratch Depth (nm)

4.3. Wear

911

15

10

5

0 0

5

10

15

20

Wear cycles Figure 17. Wear depth as a function of the number of cycles for different hydrogen content in CH4 -H2 atmospheres. Reprinted with permission from [121], T.-H. Fang et al., Thin Solid Films 396, 166 (2001). © 2001, Elsevier Science.

Nanotribology of Carbon Films

912 increase in the graphitic character of the films upon the self-bias increase. The wear test performed under a load of 200 N, revealed the better wear resistance performance for the a-C:H film deposited at the higher bias voltage. Because the amount of hydrogen effectively incorporated in the films is not reported in this article, as well as the film hardness, it is difficult to compare these results with other data reported in the literature that shows an opposite behavior, especially in the case of the hydrogen content of the films. A systematic investigation of the wear resistance for a-C films deposited by different techniques was carried out by Sundararajan and Bhushan [109]. Films deposited by ECRCVD, sputtering, FCVA, and direct ion beam deposition were studied. They performed the scratch test using a pyramidal diamond tip mounted onto a platinum-coated stainless steel of stiffness of 40 N/m. The test consisted of 10 cycles over a scan length of 5 m with a velocity of 10 m/s and at a given load. In Table 2 we compare the data obtained at a load of 60 N for films with the same thickness, 20 nm. Despite the lack of structural characterization of the tested samples, we can expect, as also claimed by the authors, that the film hardness closely follows the sp3 -hybridized carbon atom fraction. As previously discussed the results listed in Table 2 revealed that the scratch depth increases when the film hardness decreases. Sundararajan and Bhushan [109] also performed wear tests. In this experiment, the tip scans a 2 m × 2 m area at a required load at 4 m/s for a certain number of cycles. Then, the normal load was lowered to 1 N, and the scan size was set to 4 m × 4 m to image the wear region. A detailed description of this procedure can be found in Ref. 129. Wear is not uniform, but it is initiated at the nanoscratches, indicating that surface defects (with high surface energy) act as initiation sites [103]. The wear test results showed that films 20 nm thick deposited by FCVA and ECR–CVD have excellent wear resistance for loads up to 80 N. These deposition techniques provide films with similar performance even for thickness as low as 5 nm, but in this case for a maximum load of 20 N. For very thin films, 3.5 nm thick, ECR–CVD deposited films have better performance. In fact, a-C films 3.5 nm thick deposited by FCVA are easily delaminated. On the other hand, 20 nm thick films deposited by ion beam deposition show a negligible wear depth for tests at 60 N. For higher loads, the film is completely removed by the AFM tip. However, thinner ion beam deposited films have better wear behavior than the films deposited by a filtered cathodic arc and a performance quite similar to the one obtained by films deposited by ECR–CVD. In fact, for films 5 nm thick, the Table 2. Hardness, elastic modulus, and scratch depth for carbon films prepared by different deposition techniques [1090000].

Material

Deposition technique

Hardness (GPa)

Elastic modulus (GPa)

Diamond a-C a-C:H a-C:H a-C:H

— FCVA ECR-CVD Ion beam Sputtering

100 24 22 19 15

1000 240 180 140 140

Scratch depth (nm) — ∼0 1 8 20

better performance was obtained for ion beam deposited films that show wear depths of around 2 nm for loads of 25 N. At this load the AFM tip completely removed the films deposited by the other techniques. For thickness of 3.5 nm, both ECR–CVD and ion beam deposited films have the same performance under loads of 20 N. On the other side, sputtered carbon films have the worst wear resistance, independent of the thickness. The results obtained for thicker films show that at least for a-C thick films the wear depth, as well as the scratch depth, closely follows the film hardness. However, for thinner films different behavior was observed. The better wear performance was obtained for ion beam and ECR–CVD deposited films that have an elastic modulus similar to that of the silicon substrates, whereas films deposited by a cathodic arc have the higher elastic modulus. This fact suggests that thinner coatings share load with the substrate, causing its deformation. Then, cracks can be created and propagate, resulting in the film delamination. The high internal stress of the cathodic arc deposited coatings aids propagation of cracks and facilitates spreading of the failed region compared with other coatings [130]. In this way, an analysis of the wear depth for very thin films must take into account the critical load required to fail the coating during the test. ta-C films were studied by Martínez et al. [131]. The films were deposited by filtered cathodic vacuum arc. The wear test was performed with an AFM equipped with a diamond tip that scans an area of 3 m × 3 m with a scanning frequency of 1 Hz. To obtain films with different hardness the substrate voltage was varied from −20 to −350 V. Films with thickness of around 100 nm were scratched with loads of 10 and 40 N and the scratch depth can hardly be measured with the diamond tip and was estimated to be of the order of 1 nm, similar to those reported in Table 2 for films deposited by FCVA with 20 nm, and much lower than the 27 nm for bare silicon previously reported by Bushan and Koinkar [132]. These results confirm the high wear resistance of thick ta-C films and show a direct correlation between film hardness and wear resistance. A scratch test can also be performed with very low loads and soft tips such as the silicon nitride tip to obtain information about the wear mechanism in hard carbon films. An AFM 3D image of a scratch profile on a ta-C film is shown in Figure 18 [112]. In this case 30 nm thick films were deposited by FCVA with a bias of −80 V applied to the substrate to produce films with an sp3 /sp2 ratio of about 80%. The scratch test was performed using a Si3 N4 tip of k = 0 77 N/m, scanning velocity of 2 m/s, 1024 cycles, and a total normal force of 470 nN. The image was obtained with the same tip used to scratch the surface. The scratch depth as a function of the normal load was plotted in Figure 19 for ta-C films. In the macroscopic scale, wear of ta-C films is strongly influenced by a shear layer of graphite that is built up at the interface of the slider tip and the ta-C surface during sliding. Although this graphitic layer may reduce the dissipated energy at the interface, it may also increase the surface wear. As the normal force is increased, the friction force also increases, leading to larger energy dissipation at the tip–surface interface [133]. However, on a nanometer scale, the presence of a low-density layer sp2 surface layer, approximately 1 nm thick for ta-C

Nanotribology of Carbon Films

913 0.4

Scratch dept h (nm)

0.3

0.2

0.1

0.0 0

1000

2000

3000

4000

5000

Scratch cycles

Figure 18. The result (topography image) of a scanning scratch test on a ta-C film performed with a Si3 N4 atomic force microscope tip of k = 0 77 N/m, scanning velocity of 2 m/s, 1024 cycles, and a total normal force of 470 nN [102].

films deposited with ion energy of ∼100 eV, at the surface of the film due to the subplantation mechanism during film growth probably plays an important role [134]. This layer may be easily worn during the scanning process leading to the wear observed at the film surface. It is proposed that most of the wear observed at the ta-C films surface is caused by the removal of this low-density layer already present at the film surface. In fact, the measurement shows that after the complete removal of this layer the wear process stops and the wear depth remains constant, despite the increase of the normal force. The influence of the number of scanning cycles on the ta-C wear can be seen in Figure 20. The normal force applied by the tip on the surface was kept constant at 470 nN and the humidity was 43%. The wear depth increases for scanning cycles up to 512 (forward + backward scans), above which it remains constant. This fact is in agreement with the hypothesis mentioned above that the microscope

Scratch depth (nm)

0.3

0.2

0.1

0.0 0

100

200

300

400

500

Normal load (nN) Figure 19. The scratch depth as a function of the normal load for ta-C films [102]. The line is only to guide the eyes.

Figure 20. The influence of the number of scanning scratch cycles on the wear of ta-C films [102]. The line is only to guide the eyes.

tip only removes the low-density graphitic layer present at the ta-C film surface. The effect of the film composition on the wear resistance has received increasing attention with the introduction of carbon–nitrogen films as protective coatings. One of the first efforts to establish a comparison between the scratch resistance, in nanoscale, of amorphous carbon films and carbon– nitrogen films was that of Miyake and collaborators [135]. They measured the wear depth as function of the load of films deposited by reactive ion-plating. In the range of loads from 50 to 100 N, they show that for nitrogen-containing carbon films the wear depth was on the order of one tenth of the depth measured in carbon films deposited using the same technique. More recently, a study of sputtered carbon–nitrogen films was performed by Wiens and collaborators [136]. Argon– nitrogen atmospheres were used to sputter a graphite target and the substrate was not biased. For films with nitrogen content between 6 and 18 at.%, the scratch depth under loads of 5 N decreases from 1 to 0.7 nm. The same test performed with loads of 3 N shows a decrease of the scratch depth from 0.5 to 0.3 nm. The scratch test was done using a diamond tip and scanning velocity of 0.2 m/s. Raman analysis carried out in these samples suggested that the films with higher scratch resistance have lower sp2 content. The same group [137] performed a more detailed investigation and the wear behavior of a-CN films deposited by FCVA was studied. They found an opposite behavior for the scratch depth upon nitrogen incorporation into sputtered films and FCVA-deposited films. For sputtered films, nitrogen incorporation reduces the scratch depth and for FCVA-deposited films it results in an increase of the depth. Unfortunately the authors did not report the values either for elastic modulus of sputtered films or for the position of the G-band for nitrogen-incorporated FCVA-deposited films. The results are presented in Table 3. Carbon–nitrogen films deposited by ion beam-assisted deposition were also studied [105]. The films have a nitrogen content of 11 at.% and the hardness is 22 GPa. The wear depth for 10 nm thick films submitted to a load of 10 N is on the order of 1 nm. These values are higher than those obtained by Wiens et al. [125] for sputtered films with

Nanotribology of Carbon Films

914

Table 3. Nitrogen content, elastic modulus, Raman G-band position, and scratch depth for a-CN films deposited by sputtering and filtered cathodic vacuum arc techniques.

Deposition technique

Nitrogen content (at.%)

Elastic modulus (GPa)

G-band position (cm−1 )

Scratch depth (Å)

FCVA FCVA FCVA FCVA Sputtering Sputtering Sputtering Sputtering Sputtering

0 6 12 5 14 5 0 6 8 5 14 18

480 400 150 120 — — — — —

1558 — — — 1584 1580 1579 1578 1575

0 7 0 8 1 5 1 5 4 3 5 3 7 3 2 3

Note: The wear test was performed using a diamond tip at a normal load of 2.8 N [136, 137].

Scratch d epth (nm)

0.4

0.3

0.2

0.1

0.0 0

100

200

300

400

500

Table 5. Friction coefficient for CNx films (N content of the order of 10 at.%) measured by FFM in air. Friction coefficient Materials a-C:H films deposited by PECVD [106] a-C films deposited by ion-assisted sputtering [55]a a-C films deposited by laser ablation [102] a

a-C

a-CN

0 22 ± 0 05 0.28

0 25 ± 0 06 0.14

0 21 ± 0 03

0 17 ± 0 03

Experimental errors are not quoted by the authors.

similar nitrogen content. The possible explanation for this large dispersion of data can be found in the formation of the fullerene-like structure in nitrogen–carbon films deposited by sputtering and many other techniques [58]. In this case the high elasticity of the materials certainly influences the wear resistance of the films. It is possibly more important when low loads were applied. We investigated the case of FLC films deposited using an unfiltered localized high-pressure arc discharge [112]. The scratch test was performed using a Si3 N4 tip of k = 0 77 N/m and scanning velocity of 2 m/s. The scratch depth as a function of the normal load is shown in Figure 21. The wear of the surface was verified only when we scratched the surface with normal forces of at least 200 nN. Increasing the normal force beyond this point leads to an increase of the wear depth. The resistance to scratching of FLC films may be attributed to the high elasticity nature of the films [3]. The tip may deform the surface while scanning, but this mechanical change is promptly restored due to the high film elasticity. Once a permanent surface modification is achieved the film wear is influenced by the energy dissipated at the tip–surface interface and increases with the applied normal load.

Normal Load (nN) Figure 21. The scratch depth as a function of the normal load for FLC films [102]. The line is only to guide the eyes.

Table 4. Friction coefficient for several carbon based materials measured by FFM in air. Materials a-C films deposited by resistive evaporation [96] a-C films deposited by ion assisted sputtering [55]a a-C films deposited by ion assisted sputtering [114] a-C films deposited by laser ablation [102] Diamond [96] ta-C deposited by FCVA [112] ns-C (small clusters material) [114] ns-C (large clusters material) [114] FLC films [112] HOPG [102] HOPG [114] HOPG [96] a

Experimental errors are not quoted by the authors.

Friction coefficient 0 45 ± 0 04 0.28 0 22 ± 0 02 0 21 ± 0 03 0 25 ± 0 06 0 15 ± 0 03 0 10 ± 0 04 0 14 ± 0 05 0 12 ± 0 03 0 009 ± 0 003 0 004 ± 0 001 0 0012 ± 0 0009

5. CONCLUSIONS The development of friction force microscopy in the last years resulted in significant progress in the understanding of either the basic friction laws and in the tribological performance of several coatings. Among those coatings, hard carbon films occupy a special place. Concerning the basic friction law, it was clear that in nanoscale the friction forces depended on the contact area and that the relation between friction and load forces was no longer linear. In addition, it was shown that the velocity dependence behavior of the friction forces could be understood as a competition between two mechanisms—the cohesive forces responsible for the stick and slip movement and the kinetics nucleation of water meniscus between the moving parts—resulting in a logarithmic dependence of friction with the scanning velocity. The friction coefficients measured in air by friction force microscopy for several carbon-based materials are listed in Table 4. It was clear that, despite the large discrepancies among the different experimental reports, the friction coefficient for HOPG is at least 1 order of magnitude lower compared with the friction coefficient obtained from a-C films. Among those different films, the nanostructured carbon films and the fullerene-like carbon films have lower friction coefficients while diamond-like carbon films show

Nanotribology of Carbon Films

friction coefficients similar to the one measured in diamond surfaces. The incorporation of hydrogen was also investigated, but it is very difficult to determine its role precisely. In fact, if on one side, the deposition of a-C:H films by PECVD in highly hydrogen diluted atmospheres resulted in a decrease of the friction coefficient due to the complete saturation of surface dangling bonds, the opposite effect was observed for a-C:H films deposited by sputtering, where the increase of the hydrogen content in the films resulted in higher friction coefficient. On the other side, the incorporation of nitrogen, as a general rule, induced a slight reduction in the friction coefficient as one can see in Table 5. Concerning wear behavior, scratch tests performed on carbon films thicker than 10 nm revealed that the wear resistance of these materials increased with the film hardness. For carbon–nitrogen films, the situation is more complex and the dispersion of the experimental data can be attributed to high elastic recovery of the films. It is due to the presence of nitrogen in a hexagonal graphite lattice that favors the formation of pentagons, inducing curvature in the graphene planes, responsible for the elastic behavior of the films. It is of importance also for fullerene-like films. For these materials, when low loads are applied the elastic deformation of the films can drastically reduce the wear when the sample surface is scanned with an AFM tip.

GLOSSARY Adhesion A consequence of the forces that act at the materials’ contact area to causes their sticking. Atomic force microscopy/microscope (AFM) A microscope able to observe surfaces at atomic and molecular scale by measuring the interaction forces between a sharp tip and a surface. Friction Force opposing relative motion of two objects that are in contact. Friction force microscopy/microscope (FFM) A microscope able to measure the friction forces between a sharp tip and a sample surface at atomic and molecular scale. Fullerenes Molecular forms of pure carbon, with a cagelike structure of carbon atoms. The number of atoms ranges from 60 up to a few hundred carbon atoms. Nanotribology The science and technology of interacting surfaces in relative motion at atomic and molecular scales. This includes friction, wear, adhesion, and lubrication. Sputtering Method used to deposit thin films in which a plasma is used. The plasma ions are used to bombard the target atoms that will condense out on a substrate, placed inside the deposition chamber, depositing a film. Thin films Films with thickness less than 100 . Wear The removal of material from surfaces in relative motion as a result of surface contact or abrasive or chemical action.

ACKNOWLEDGMENTS This work was partially supported by the Brazilian agencies Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Coordenação de Aperfeiçoamento de

915 Pessoal de Nível Superior (CAPES), and Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ).

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Encyclopedia of Nanoscience and Nanotechnology

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Nanotubes for Nanoelectronics Zhi Chen University of Kentucky, Lexington, Kentucky, USA

CONTENTS 1. Introduction 2. Progress in Nanoelectronics Prior to Nanotubes 3. Synthesis and Electrical Properties of Carbon Nanotubes 4. Single-Electron Transistors 5. Field-Effect Transistors, Logic Gates, and Memory Devices 6. Doping, Junctions, and Metal–Nanotube Contacts 7. Nanotube-Based Nanofabrication 8. Summary Glossary References

1. INTRODUCTION Carbon nanotubes (CNTs) have emerged as a viable electronic material for molecular electronic devices because of their unique physical and electrical properties [1–7]. For example, nanotubes have a lightweight and record-high elastic modulus, and they are predicted to be by far the strongest fibers that can be made. Their high strength and high flexibility are unique mechanical properties. They also have amazing electrical properties. The electronic properties depend drastically on both the diameter and the chirality of the hexagonal carbon lattice along the tube [8–10]. Carbon nanotubes were discovered by Iijima in 1991 at the NEC Fundamental Research Laboratory in Tsukuba, Japan [1]. Using a transmission electron microscope (TEM), he found carbon tubes consisting of multiple shells (see Fig. 1). These early carbon tubes are called multiwall nanotubes (MWNTs). Since then, extensive research has been focused on synthesis and characterization of carbon nanotubes. In 1993, Ijima’s group [11] and Bethune et al. [12] at IBM Almaden Research Center at San Jose, California, synthesized carbon nanotubes with a single shell, called single-wall nanotubes (SWNTs). Because of their simple and well-defined structure [13], the single-wall nanotubes serve

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as model systems for theoretical calculations and for critical experimental studies. Since then, the physical and electrical properties of carbon nanotubes have been studied extensively. Only a few years ago, people began to utilize carbon nanotubes’ unique electrical properties for electron device applications. Up to now, there has been no extensive review to cover the progress in nanoelectronic devices using carbon nanotubesy. In this chapter, I aim to present extensive review on progress in electronic structure and transport properties of carbon nanotubes and nanoelectronic devices based on carbon nanotubes ranging from quantum transport to fieldeffect transistors. This chapter is organized as follows. It begins with brief review of the progress in micro- and nanoelectronic devices prior to carbon nanotubes (Section 2). Then the synthesis and physical properties of carbon nanotubes will be discussed in Section 3. Nanoelectronic devices based on carbon nanotubes including single-electron transistors (SETs), field-effect transistors, logic gates, and memory devices will be reviewed in Sections 4 and 5. The chemical doping, junctions, and metal–nanotube contacts will be described in Section 6. Finally, nanofabrication based on carbon nanotubes including controlled growth and selective placement of nanotubes on patterned Si substrates will be reviewed in Section 7. Since the discovery of carbon nanotubes, over 1000 papers on carbon nanotubes have been published. It is unlikely that every paper will be included in this chapter, because most papers dealt with synthesis, physical, and chemical properties of nanotubes. In this chapter, I will focus on electrical properties of nanotubes, nanoelectronic devices constructed with nanotubes, and nanotube-based nanofabrication.

2. PROGRESS IN NANOELECTRONICS PRIOR TO NANOTUBES In 1959 Richard Feynman delivered his famous lecture, “There is Plenty of Room at the Bottom.” He presented a vision of exciting new discoveries if one could fabricate materials and devices at the atomic and molecular scale. It was not until 1980s that instruments such as scanning tunneling microscopes (STM), atomic force microscopes (AFM), and near-field microscopes were invented. These instruments

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b

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on the surfaces of materials [17]. Later the STM was used to modify surfaces at the nanometer scale and the manipulation and positioning of single atoms on surface was achieved [18]. In 1993, Crommie et al. [19] eloquently demonstrated with a “quantum corral” where the STM can be used not only to characterize the electronic structure of materials on a truly quantum scale, but also to modify this quantum structure. This suggested that the STM and AFM might be used for atom-by-atom control of materials modification, leading to atomic resolution. This potential motivated researchers to attempt to use STM and AFM for nanolithography [20–25]. This task has not been easy due to the irreproducibility of the modifications, the slow “write” speed, and the difficulty of transferring such fine manipulations into functioning semiconductor devices [21]. Until now, reliable fabrication and robust pattern transfer for linewidths below 10 nm has not been achieved yet.

2.2. Metal-Oxide-Semiconductor Field-Effect Transistors Figure 1. Cross-section images of carbon nanotubes by a highresolution TEM. Reprinted with permission from [1], S. Iijima, Nature 354, 56 (1991). © 1991, Macmillan Magazines Ltd.

provide “eyes” and “fingers” required for nanostructure measurement and manipulation [14]. The driving force for nanoelectronics is the scaling of microelectronic devices to nanoscale, which is the engine for modern information revolution. The microelectronics revolution began in 1947 when John Bardeen, Walter H. Brattain, and William Shockley of Bell Telephone Laboratories invented the first solid state transistor, the Ge point-contact transistor [15]. Solid state transistors had far superior performance, much lower power consumption, and much smaller size than vacuum triodes. People began to produce individual solid state components to replace the vacuum tubes in circuits in a few years after the invention. In 1958, Jack Kilby of Texas Instruments conceived a concept for fabrication of the entire circuit including components and interconnect wires on a single silicon substrate [16]. In 1959, Robert Noyce of Fairchild Semiconductor individually conceived a similar idea [15]. This concept has evolved into today’s very-large-scale integrated circuits or “microchips,” which consist of millions of transistors and interconnect wires on a single silicon substrate. The major driving force for this revolutionary progress is miniaturization of transistors and wires from tens of micrometers in the 1960s to today’s tens of nanometers. The scaling down of transistor and interconnect wires led to more and more transistors being incorporated into a single silicon chip, resulting in faster and more powerful computer chips. With the success in microelctronics and of the semiconductor industry, it is natural to consider extending the micrometer size devices to nanometer size devices.

As early as the 1920s and 1930s, a concept for amplifying devices based on the so-called field effect was proposed with little understanding of the physical phenomena [26, 27]. After 30 years, the field-effect transistor based on the SiO2 /Si structure finally became practical [28]. Since that time, the metal-oxide-semiconductor field-effect transistor (MOSFET) has been incorporated into integrated circuits and has grown to be the most important device in the semiconductor industry ranging from memory chips, microprocessors, and many other communication chips. Figure 2a shows the structure of an n-channel MOSFET. It consists of p-type Si, heavily doped n+ source and drain, and an insulated gate. When the gate voltage is zero, the region underneath the gate oxide is p-type. There are two pn+ junctions near the source and the drain. When applying a voltage across the source and the drain, either of the two pn+ junctions is reverse biased. Thus the transistor conducts no current. When the gate voltage is larger than zero but less than its threshold voltage, depletion happens underneath the gate oxide, which is still not conductive. When the gate voltage is larger than its threshold voltage, an inversion layer (n-type) is induced underneath the gate oxide, which forms a conduction channel connecting both source and drain. Thus the transistor conducts current. The typical I–V curves for an n-MOSFET with a gate length of 0.25 m and a width of 15 m are shown in Figure 2b. The driving force behind this (b)

(a) VS

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Drain n+

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Figure 2. (a) Schematic structure of a Si MOSFET used in various microchips for digital signal processing and (b) its current–voltage characteristics.

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remarkable development is the cost reduction and performance enhancement of integrated circuits (ICs) due to the continuous miniaturization of transistors and interconnect wires. The continuous scaling of transistors and the increase in wafer size has been and will continue to be the trend for the semiconductor industry. The transistor gate length (feature size) has been dramatically reduced for the past three decades [29, 30]. The lateral feature size or linewidth of a transistor has been shrunk by almost 50 times from about 10 m to the 100 nm range, allowing over 10,000 times more transistors to be integrated on a single chip. Microprocessors have evolved from their 0.1 MHz ancestors used for watches and calculators in the early 1970s to the current 2 GHz engines for personal computers. Memories have grown from 1-Kb pioneers used almost exclusively for mass storage in central computers to the 128/256-Mb dynamic random access memory commonly used in personal computers today. Most advanced chips on the market now have feature sizes of 100 nm. According to the Semiconductor Industry Association’s International Technology Roadmap for Semiconductors [31], the feature sizes for lithography were projected as follows: 130 nm in 2001, 100 nm in 2003, 80 nm in 2005, 35 nm in 2007, 45 nm in 2010, 32 nm in 2013, and 22 nm in 2016. The wafer size has increased from 2 inches in the early 1970s to the current 12 inches. Therefore, the performance of ICs has been dramatically improved, and the cost for manufacturing has been dramatically reduced. However, the device scaling is approaching its limit. It was suggested that MOS device scaling might not be extended to below 10 nm because of physical limits such as power dissipation caused by leakage current through tunneling [32–34]. In addition, once electronic devices approach the nano- and molecular scale, the bulk properties of solids are replaced by the quantum-mechanic properties of a relatively few atoms such as energy quantization and tunneling. It is therefore important to search for alternative devices for Si MOS devices.

2.3. Quantum-Effect Devices In order for a transistor-like device to operate on the nanoand molecular scale, it would be advantageous if it operated based on quantum mechanical effects. Even though the study of single-electron charging effects with granular metallic systems dates back to the 1950s [35, 36], it was the research of Likharev in 1988 that laid much of the groundwork for understanding single-charge transport in nanoscale tunnel junctions [37, 38]. When a small conductor (island) is initially neutral, it does not generate any appreciable electric field beyond its border. In this state, a weak external force (due to electric field) may bring in an additional electron from outside. The net charge in the island is (−e) and the resulting electric field repulses the following electrons which might be added. In order to have an electron to be added it needs to overcome the charging energy and its kinetic energy. Thus, the electron additional energy Ea is given by Ea = Ec + Ek Here Ec is the charging energy that is given by Ec =

e2 C

where e is the charge of electron and C is the capacitance of the conductive island. The kinetic energy is expressed as Ek =

1 g F V

where g F  is the density of states on the Fermi surface and V is the volume of the island. For the island diameter > 2 nm, Ec ≫ Ek . Thus Ea ≈ Ec =

e2 2C

For the 100 nm-scale island, Ea is of the order of 1 meV, corresponding to ∼10 K in temperature. If the island size is reduced to below 10 nm, Ea approaches 100 meV, and some single-electron effects become visible at room temperature. Among quantum-effect devices, single-electron transistors have been most extensively studied [38–40]. The basic structure of a SET is shown in Figure 3a. An island or quantum dot is placed between two electrodes (source and drain) with the third electrode (gate) is placed by its side. When a voltage is applied, an electron tunnels onto the island and the charging energy is increased by Ea ≈ e2 /2C and this increase acts as a barrier to the transfer of any further electrons. At small source–drain voltage, there is no current. The I–V characteristic is shown in Figure 3b. The current is blocked from −Vc to Vc , called Coulomb blockade. When the source– drain voltage is increased and reaches a level greater than Vc , where the energy barrier is eliminated, electrons can cross the island and the current increases with the applied voltage. The threshold voltage Vc is a periodical function of gate voltage. Coulomb charging effects were originally observed in metallic film by Gorter in 1951 [35]. The first successful metallic single-electron transistor was made by Fulton and Dolan in 1987 [36]. They used a relatively simple technique in which two layers of aluminum were evaporated in-situ from two angles through the same suspended mask formed by direct e-beam writing. Since then, single-electron transistors have been demonstrated in numerous experiments using a wide variety of device geometry, materials, and techniques. SETs based on metallic nanodots were fabricated. Chen et al. [41] reported that SETs with metal dots of 20–30 nm and gaps of 20–30 nm were fabricated by ionized beam evaporation. The electrical results showed clear Coulomb blockade at temperature as high as 77 K. Novel lateral metallic SETs can be based on gold colloidal particles. These particles are very uniform in size and can be obtained in a range (b)

(a)

I Gate –V/2

V/2

Source

Drain

–VC

VC V

Island

Figure 3. (a) Schematic structure of a capacitively coupled singleelectron transistors and (b) its source–drain dc I–V curves.

922 of sizes. The devices can be fabricated by placing the particles in the gap between the source and drain. Klein et al. [42] obtained the Coulomb blockade characteristics based on gold colloidal particles at 77 K. Nakamura et al. [43] fabricated Al-based SETs, which operated at 100 K. Shirakashi et al. [44] fabricated Nb/Nb oxide-based SETs at room temperature T = 298 K). The further reduction of the tunnel junction is performed by scanning probe microscope (SPM)based anodic oxidation. The Coulomb blockade characteristics were clearly shown at room temperature. Single-electron effects have also been observed in a number of semiconductor based structures. The first device was realized by squeezing the two-dimensional electron gas (2DEG) formed at the AlGaAs/GaAs heterostructure [45]. It consists of a pattern of metal gates evaporated onto the semiconductor surface. The voltages were applied to the gates to squeeze the 2DEG so that islands and tunnel barriers were formed. Coulomb blockade can be observed if the regions are sufficiently squeezed. Coulomb blockade effects have also been demonstrated on silicon based devices. A number of experiments have been reported on structures based on silicon-on-insulator (SOI). This is particularly important because silicon processing technology is the mainstream technology in the semiconductor industry. The silicon based SET technology can be easily integrated into the mainstream technology once it is successful. Ali and Ahmed [46] showed the first SOI-based SETs with clear Coulomb blockade. Leobandung et al. [47] also demonstrated silicon quantum-dot transistors with a 40-nm dot. The Coulomb blockade was clearly seen at temperature of 100 K. Takahashi et al. [48] and Kurihara et al. [49] scaled the silicon-based SETs to make significantly smaller islands and obtained Coulomb oscillation at temperatures approaching room temperature. Zhuang et al. [50] reported fabrication of silicon quantum-dot transistors with a dot of ∼12 nm with a clear Coulomb blockade at 300 K. Guo et al. [51] successfully fabricated a silicon single-electron transistor memory, which operated at room temperature. The memory is a floating gate MOS transistor in silicon with a channel width (∼10 nm) smaller than the Debye screening length of a single electron and a nanoscale polysilicon dot (7 nm × 7 nm) as the floating gate embedded between the channel and the control gate. Storing one electron on the floating gate screens the entire channel from the potential on the control gate and leads to a discrete shift in the threshold voltage, a staircase relation between the charging voltage and the shift. SETs based on Si nanowires have also been demonstrated [52]. It was shown that quantum wires with a large length to width ratio show clear Coulomb oscillations at temperatures up to 77 K.

3. SYNTHESIS AND ELECTRICAL PROPERTIES OF CARBON NANOTUBES 3.1. Synthesis of Carbon Nanotubes Although this chapter focuses on nanoelectronic devices, I still cover some of synthesis methods and approaches which may be helpful for interested readers. It should be

Nanotubes for Nanoelectronics

pointed out that I am unable to include all the papers in synthesis because extensive research has been conducted for growth of carbon nanotubes. Although multiwall carbon nanotubes were discovered in 1991 by Iijima, it is quite likely that such MWNTs were produced as early as the 1970s during research on carbon fibers [2]. The multiwall carbon nanotubes discovered in 1991 were obtained from the fullerene soot produced in an arc discharge [1]. As early as in 1986, Saito of the University of Kentucky studied the soot produced by a candlelike methane flame. A quartz fiber was inserted into the flame from the side and left there for a certain period of time [53]. When the fiber was raised to a certain height, a smooth film was coated on the fiber surface, which appeared to be brown in color. With increase of the sampling height beyond the critical height, the color of the deposited material changed from brown to black, and its surface appearance also changed from smooth to a rough and bumpy structure. The SEM analysis identified the rough surface material to be soot and the initial light brown material from the methane flame to be polyhedral-shaped crystal-like particles [54]. The deposit from the acetylene flame had a spiderweb shape of entangled, long, narrow diameter strings, of which the detailed structure remained unknown until recent TEM study [55]. It was a surprise that the recent TEM study showed that the entangled long strings synthesized in 1986 are carbon nanotubes, which were discovered later by Iijima in 1991. Recently Saito’s group repeated his 1986 experiments and synthesized CNTs using methane flames [56] and ethylene flames [57]. In 1993, Iijima and Ichihashi [11] synthesized single-wall carbon nanotubes of 1-nm diameter. Bethune and co-workers [12] also, at the same time, synthesized single-wall carbon nanotubes using cobalt catalyst. The research on carbon nanotubes really took off when Smalley and co-workers at Rice University found a laser ablation technique that could produce single-wall carbon nanotubes at yields up to 80% instead of the few percent yields of early experiments [58–60]. Kong and co-workers [61] at Stanford University used a chemical vapor deposition (CVD) technique to grow carbon nanotubes by decomposing an organic gas over a substrate covered with metal catalyst particles. The CVD approach has the potential for making possible large-scale production of nanotubes and growth of nanotubes at specific sites on patterned Si substrates [62, 63].

3.2. Electronic Structures of Carbon Nanotubes Just in one year after the discovery of carbon nanotubes, their electronic structures were theoretically studied based on local-density-functional calculation [8], tight-binding band-structure calculation [9, 10, 64]. Figure 4a shows how to construct a carbon nanotube by wrapping up a single sheet of graphite such that two equivalent sites of the hexagonal lattice coincide; that is, point C coincides with the origin (0, 0) [65]. The wrapping vector C, which defines the relative location of the two sites, is specified by a pair of integers n m that relate C to the two unit vectors a1 and a2 (C = na1 + ma2 ). A tube is called “armchair” if n equals m, and “zigzag” in the case m = 0. All other tubes are of the “chiral” type with a finite wrapping angle

923

Nanotubes for Nanoelectronics (c) Tubule Axis

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4

2

1

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5

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X

ir

(B) no. 10 T φ H

no. 7

no. 1

no. 8

1 nm

Figure 4. Relation between the hexagonal carbon lattice and the chirality of carbon nanotubes. (A) Construction of a carbon nanotube from a single graphene sheet by rolling up the sheet along the wrapping vector C. (B) Atomically resolved STM images of individually single-wall carbon nanotubes showing chirality. Reprinted with permission from [65], J. W. G. Wildoer et al., Nature 391, 59 (1998). © 1998, Macmillan Magazines Ltd.

 (0 <  < 30 ). Figure 4b shows the STM images of singlewall carbon nanotubes [65]. Tube 10 has a chiral angle  = 7 and a diameter d = 13 nm, which corresponds to the (11, 7) type of panel A. The dependence of the electronic structure of nanotubes on the tube indices n m can be understood by taking the two-dimensional graphene sheet as a starting point. In the circumferential direction (along C), the periodic boundary conditions C · k = 2q can be applied, where k is the wave vector and q is an integer. This leads to a set of allowed values for k, which can be substituted into the dispersion relations for the tube, with q representing the various modes. Electronic energy band structure calculations [3, 8–10, 64] predicted that armchair n = m tubes behave like metallic. For all other tubes (chiral and zigzag) there exist two possibilities. If n − m/3 is an integer, tubes are expected to be metallic, and if n − m/3 is not an integer, tubes are predicted to be semiconducting with an energy gap depending on the diameter. The energy gap can be expressed as Egap = 20 aC−C /d, where 0 is the C–C tightbinding overlap energy, aC−C is the nearest neighbor C–C distance (0.142 nm), and d is the diameter. Figure 5 shows the calculated energy band structure of zigzag nanotubes (12, 0) in (c) and (13, 0) in (d). [The geometric structure of the tubes and the first Brillouin zone of a graphene sheet are

shown in (a) and (b).] The tube (12,0) is metallic, satisfying the condition of n − m/3 being integer; and the tube (13,0) is semiconducting with an energy gap of 0.697 eV, which falls into the category of n − m/3 being noninteger. Figure 6 shows the calculated energy band gaps of tubes n 0 with n = 6–15. For n = 6, 9, 12, 15 [i.e., n − m/3 is integer], energy gaps are almost zero, and for n = 7 8 10 11 13 14, [i.e. n − m/3 is noninteger], the energy gaps are ranging from 0.6 to 1.2 eV. Figure 7 shows the calculated onedimensional (1D) electronic density of states for (a) a (9,0) nanotube and (b) a (10,0) nanotube [66]. The 1D density of state (DOS) of both nanotubes shows a series of spikes. Each spike corresponds to the energy threshold for an electronic subband caused by the quantum confinement of electrons in the radial and circumferential directions of nanotubes. The (9,0) nanotube is metallic and the (10,0) tube is semiconducting. Experimental measurements [65, 67] of the energy bands of nanotubes confirmed these theoretical calculations. Figure 8a shows a selection of I–V curves obtained by scanning tunneling spectroscopy (STS) on different tubes [65]. Most curves show a low conductance at low bias, followed by several kinks at larger bias voltages. Figure 8b shows 1.5

band gap (eV)

no. 11

Figure 5. (a) The geometric configuration for a single-wall carbon nanotube n 0. (b) The first Brilluoin zone of a graphite sheet and the wave vector allowed by the periodic boundary condition along the circumference for n = 6 (solid lines). Band structures of (c) (12,0) and (d) (13,0) single-wall nanotubes. Reprinted with permission from [9], N. Hamada et al., Phys. Rev. Lett. 68, 1579 (1992). © 1992, American Physical Society.

1.0

0.5

0

6

12

9

15

n

Figure 6. The energy bandgap as a function of the number of hexagons on the circumference for a single-wall nanotube n 0. Reprinted with permission from [9], N. Hamada et al., Phys. Rev. Lett. 68, 1579 (1992). © 1992, American Physical Society.

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(a)

(b)

Figure 7. Calculated one-dimensional electronic density of states for (a) a (9,0) nanotube and (b) a (10,0) nanotube. Reprinted with permission from [66], M. S. Dresshaus, Nature 391, 19 (1998). © 1998, Macmillan Magazines Ltd.

a

b

the dI/dV curves. There are two categories: the one has a well-defined gap values around 0.5–0.6 eV and the other has significantly larger gap values of ∼1.7–2.0 eV [65]. The gap value of the first category agrees very well with the predicted gap values for semiconducting tubes. As shown in Figure 9c, the energy gap decreases as the tube diameter d increases. This also agrees well with theoretical gap values obtained for an overlap energy 0 = 27 ± 01 eV, which is close to the value 0 = 25 eV suggested for a single graphene sheet [3]. The very large bandgaps observed for the second category of tubes, 1.7–2.0 eV, are in good agreement with the values of 1.6–1.9 eV obtained from one-dimensional dispersion relations for a number of metallic tubes with

n − m/3 being integer [65]. These metallic nanotubes are expected to have a small but finite DOS near the Fermi energy (EF ) and the apparent “gap” is associated with DOS peaks at the band edges of the next one-dimensional modes. Sharp van Hove singularities in the DOS are predicted at the onsets of the subsequent energy bands, reflecting the one-dimensional character of carbon nanotubes (see Fig. 7). The derivative spectra indeed show a number of peak structures (Fig. 8b). For semiconductors, it has been argued that

dI/dV / I/V  represents the DOS better than the direct derivative dI/dV, partly because the normalization accounts for the voltage dependence of the tunnel barrier at high bias [68, 69]. In Figure 9, dI/dV / I/V  is shown, where sharp peaks are observed, resembling that predicted for van Hove singularities. The experimental peaks have a finite height and are broadened because of hybridization of wave functions. Raman scattering experiments also support the one-dimensional subband of nanotubes [70, 71]. Resistivity measurements of armchair SWNTs also suggested their metallic behavior, consistent with the theoretical calculation [72, 73]. In addition, momentum-dependent high-resolution electron energy-loss spectroscopy was performed on purified SWNTs [74]. Two groups of excitations have been found.

–

c

–

Figure 8. (a) Current–voltage curves obtained by tunneling spectroscopy on various nanotubes. (b) The derivatives dI/dV show two groups: a semiconducting one with gap values around 0.5–0.6 eV and a metallic one with gap values around 1.7–1.9 eV. (c) Energy gap versus diameter of semiconducting chiral tubes. Reprinted with permission from [65], J. W. G. Wildoer et al., Nature 391, 59 (1998). © 1998, Macmillan Magazines Ltd.

Figure 9. (dI/dV)/(I/V) which is a measure of the density of states versus V for nanotube 9. The left inset displays the raw dI/dV data, and the right inset is the calculated DOS. Reprinted with permission from [65], J. W. G. Wildoer et al., Nature 391, 59 (1998). © 1998, Macmillan Magazines Ltd.

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One group is nondispersive and the energy position is characteristic of the separation of the van Hove singularities in the electronic DOS of the different types of nanotubes. The other one shows considerable dispersion and is related to a collective excitation of the -electron system [74]. As pointed out by Dresselhaus [66], these results [66, 67] showed a wide range of helicities for SWNTs which contradict the narrow distribution of chiral angles determined by Raman scattering experiments [71] carried out on SWNT ropes synthesized by the same technique. In addition, van Hove singularities (energy threshold for an electronic subband) were also clearly resolved [65] in the experimental DOS of both chiral and achiral nanotubes. The observation of these well-separated and clearly resolved sharp spikes in the DOS of SWNTs with chiral symmetry was not expected [66]. Further calculation of the  +  electron densities of states of chiral carbon nanotubes using a tightbinding Hamiltonian showed that the electronic structures of SWNTs with chiral symmetry are similar to the zigzag and armchair ones [73, 74]. Fluorescence has also been observed directly across the bandgap of semiconducting carbon nanotubes, supporting the theoretical calculation of energy band structure of carbon nanotubes [77]. Most SWNTs synthesized using the current technologies are ropes consisting of many individual SWNTs. The first-principle calculation of electronic band structure of close-packing of individual nanotubes (10,10) into a rope showed that a broken symmetry of the (10,10) tube caused by interactions between tubes in a rope induces a pseudogap of about 0.1 eV at the Fermi level [78]. This pseudogap strongly modifies many of the fundamental electronic properties of carbon nanotube ropes. Structures of molecular electronic devices ultimately depend on tuning the interactions between individual electronic states and controlling the detailed spatial structure of the electronic wave functions in the constituent molecules. It is amazing that the two-dimensional images of electronic wave functions in metallic SWNTs have been obtained using STS [79]. These measurements reveal spatial patterns that can be directly understood from the electronic structure of a single graphite sheet. This represents an elegant illustration of Bloch’s theorem at the level of individual wave functions.

3.3. Quantum Transport of Carbon Nanotubes The electrical transport experiments on individual tubes are highly preferred. The first measurements on individual nanotubes were carried out on MWNTs [80–84]. Langer et al. [82] reported on electrical resistance measurements of an individual MWNT down to a temperature of T = 20 mK. The conductance exhibited a ln T dependence and saturated at low temperature. A magnetic field applied perpendicular to the tube axis increased the conductance and produced aperiodic fluctuations. Their data also support two-dimensional weak localization and universal conductance fluctuations in mesoscopic conductors. These early studies on MWNTs suggested defect scattering, diffusive electron motion, and localization with a characteristic length scale of only a few nanometers. In addition, the electrical properties of individual MWNTs have been shown to vary strongly from tube to tube.

3.3.1. Ballistic Transport It came as a surprise when the first experiments on individual SWNTs showed that nanotubes could have delocalized wave functions and behave as true quantum wires [85, 86]. Electrical measurement indicates that conduction occurs through well separated, discrete electronic states that are quantum-mechanically coherent over long distance, at least >140 nm [86]. Theory predicts that the electrons flow ballistically through carbon nanotubes and that the conductance is quantized [87–90]. Quantized conductance results from the electronic waveguide properties of extremely fine wires and constrictions. When the length of the nanotube is less than the mean-free path of electrons, the electronic transport is ballistic (i.e., each transverse waveguide mode or conduction channel contributes G0 = 2e2 /h to the total conductance). Theoretical calculation indicates that conducting single shell nanotubes have two modes or two conduction channels [87–90]; this predicts that the conductance of a single-walled nanotube is 2G0 independent of diameter and length. Another important aspect of ballistic transport is that no energy is dissipated in the conductor and the Joule heat is dissipated at the contacts of metal and nanotubes. Conductance measurements on MWNTs revealed that only one conduction channel G0 exists in MWNTs, which conduct current ballistically over a length of 4 micrometers [91]. Recently, quantized conductance has been observed in SWNTs [92], which has two conduction channels 2G0 , in agreement with the theoretical calculation. Theoretical studies also suggests that conduction electrons in armchair nanotubes experience an effective disorder averaged over the tube’s circumference, leading to electron-mean-free paths that increase with nanotube diameter [93]. This increase should result in exceptional ballistic transport properties and localization lengths of 10 m. For (10,10) armchair nanotubes, the mean-free path of 7.5 m is obtained [93]. The fundamental reason for ballistic transport of carbon nanotubes is their perfect symmetric and periodic structure. It was shown that defects introduced into the nanotubes serve as scattering centers [94], which destroys the perfect structure. Theoretical calculation also showed that the absence of backscattering was demonstrated for single impurity with long range potential in metallic tubes [95–97] and a stepwise reduction of the conductance was inferred from multiple scattering on a few lattice impurities [98, 99]. Therefore, chemically doped semiconducting SWNTs may behave as diffusive conductors with shorter mean-free paths. It has been reported experimentally that mean-free paths of SWNTs are lower than the ones of reported structurally equivalent metallic SWNTs [100]. The backscattering contribution to the conductivity has been demonstrated to be more significant for doped semiconducting systems [101].

3.3.2. Other Transport Properties Zeeman Effect Tans et al. [86, 102] observed an excited state by applying a magnetic field perpendicular to the tube axis, which moved relative to the ground state at a rate corresponding to a g-factor of 2.0 ± 0.5, consistent with the expected free-electron Zeeman shift. Cobden et al. [103] later studied the spin state by applying a magnetic field along the tube axis of the nanotube rope. It is concluded that as

926 successive electrons are added, the ground state spin oscillates between S0 and S0 + 21 , where S0 is most likely zero. This results in the even/odd nature of the Coulomb peaks, which is also manifested in the asymmetry of the current– voltage characteristics and the peak height [106]. It is suggested that the g-factor of the Zeeman split is 2.04 ± 0.05 [104].

Nanotubes for Nanoelectronics

4. SINGLE-ELECTRON TRANSISTORS 4.1. Single-Wall Carbon Nanotubes

Aharonov–Bohm Effect When electrons pass through a cylindrical electrical conductor aligned in the magnetic field, their wavelike nature manifests itself as a periodic oscillation in the electrical resistance as a function of the enclosed magnetic flux. This phenomenon reflects the dependence of the phase of the electron wave on the magnetic field known as the Aharonov–Bohm effect [105], which causes a phase difference, and hence interference, between partial waves encircling the conductor in opposite directions. Theoretical studies showed [86, 106] that upon applying a magnetic field along the tube axis, the electronic structure of a carbon nanotube drastically changes from a metal to a semiconductor or from a semiconductor to a metal during variation of magnetic flux . The energy dispersion without the spin-B interaction is periodic in , with a period 0 , as a result of the Aharonov–Bohm effect. Magnetoresistance measurements were carried out on individual MWNTs, which exhibit pronounced resistance oscillations as a function of magnetic flux [107]. The oscillations are in good agreement with theoretical predications for the Aharonov–Bohm effect in a hollow conductor with a diameter equal to that of the outermost shell of the nanotubes. Significant electron–electron correlation has been observed in experiments [108]. Electrons entering the nanotube in a low magnetic field are observed to have all the same spin direction, indicating spin polarization of the nanotube. When the number of electrons is fixed, variation of an applied gate voltage can significantly change the electronic spectrum of the nanotube and can induce spin-flips [108].

In 1997, Bockrath et al. [85] reported the first single-electron transport of a single bundle containing 60 single-wall carbon nanotubes (10,10) with a diameter of 1.4 nm at a temperature of 1.4 K. The device structure (Fig. 10, left inset) consists of a single nanotube rope and lithographically defined Au electrodes. The device has four contacts and allows different segments of the nanotube to be measured. The device was mounted on a standard chip carrier and contacts were wire bonded. A dc bias (Vg  was applied to the chip carrier base to which the sample was attached. This dc bias can be used as gate voltage Vg to modify the charge density along the tube. Figure 10 shows the I–V characteristics of the nanotube section between contacts 2 and 3 as a function of temperature T . The conductance is strongly suppressed near V = 0 for T < 10 K. Figure 11A shows conductance G versus gate voltage Vg at T = 13 K. The conductance curve consists of a series of sharp peaks separated by regions of very low conductance. The peak spacing varies significantly. The height of peaks also varies widely with the maximum peak reaching e2 /h, where h is the Planck constant. The peak amplitude decreases with T (Fig. 11B) while the peak width increases with T (Fig. 11C). These phenomena can be understood based on Coulomb blockade effect described in Section 2.3. In this device, transport occurs by tunneling through the isolated segment of the rope. Tunneling on or off this segment is governed by the single-electron addition. The period of the peaks in gate voltage, "Vg , is determined by the energy for adding an additional electron to the rope segment. In the same year (1997), Tans and co-workers [86] at Delft University of Technology built molecular devices using a metallic (armchair) SWNT as a quantum wire. Figure 12 shows the structure of the device. An individual SWNT with a diameter of ∼1 nm is lying across two Pt electrodes with a separation of 140 nm. The third electrode located ∼450 nm

Luttinger Liquid Electron transport in conductors is usually well described by Fermi-liquid theory, which assumes that energy states of electrons near the Fermi level EF are not qualitatively altered by Coulomb interactions. In onedimensional systems, however, even weak Coulomb interactions cause strong perturbations. The resulting system, known as Luttinger liquid, is predicted to be distinctly different from its two- or three-dimensional counterpart [109]. Coulomb interactions have been studied theoretically for SWNTs [110, 111] and MWNTs [112]. Long-range Coulomb forces convert an isolated N N  armchair carbon nanotube into a strong renormalized Luttinger liquid [110]. At high temperatures, anomalous temperature dependence for the interaction, resistivity due to impurities, and power-law dependence for the local tunneling density of states were found. At low temperatures, the nanotube exhibits spincharge separation, signaling a departure from orthodox theory of Coulomb blockade. Experimental measurements of the conductance of bundles (“ropes”) of SWNTs as a function of temperature and voltage confirmed these theoretical studies [113].

Figure 10. The I–V characteristics at a series of different temperatures for the rope segments between contacts 2 and 3. Left inset: AFM image of the fabricated device where the bright regions are metallic contacts. Right inset: Schematic energy-level diagram of the two 1D subbands near one of the two Dirac points with the quantized energy levels indicated. Reprinted with permission from [85], M. Bockrath et al., Science 275, 1922 (1997). © 1997, American Association for the Advancement of Science.

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Nanotubes for Nanoelectronics

A

B

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0.5

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Figure 11. (A) Conductance G versus gate voltage Vg at T = 13 K for the rope segments 2 and 3. (B) Temperature dependence of a peak. (C) Width of the peak in (B) as a function of T . Reprinted with permission from [85], M. Bockrath et al., Science 275, 1922 (1997). © 1997, American Association for the Advancement of Science.

away from the nanotube functions as a gate. Their original idea is to build a single-electron transistor using a SWNT as a quantum wire. The electrical measurement was carried out at a low temperature of 5 mK. The typical current– voltage characteristics at various gate voltages are shown in Figure 13a. The coulomb charging effect is clearly observed. Coulomb charging occurs when the charging energy Ec =

e2 /2C ≫ kT. At low temperature, the Coulomb blockade effect can be observed. The two traces in Figure 13b were taken under identical conditions and show an occasional doubling of certain peaks. This bistability was regarded as the result of switching offset charges that shift the potential of the tube [86]. Chemical doping was used to achieve quantum dots and junctions for single-electron transistors [114]. Electrical measurements of the potassium (K) doped nanotube reveal single-electron charging at temperature up to 160 K [114]. The quantum dot is formed by inhomogeneous doping along the nanotube length [115–119]. The p–n–p junction

Figure 12. AFM tapping-mode image of a single-wall carbon nanotube on top of a Si/SiO2 substrate with two 15-nm-thick Pt electrodes. Reprinted with permission from [86], S. J. Tans et al., Nature 386, 474 (1997). © 1997, Macmillan Magazines Ltd.

Figure 13. (a) Current–voltage curves of the nanotube at a gate voltage of 88.2 mV (trace A), 104.1 mV (trace B), and 120 mV (trace C). Inset: more I–Vbias curves with Vgate ranging from 50 mV (bottom curve) to 136 mV (top curve). (b) Current versus gate voltages at Vbias = 30 V. Reprinted with permission from [86], S. J. Tans et al., Nature 386, 474 (1997). © 1997, Macmillan Magazines Ltd.

was obtained by chemical doping. The transport measurements of the junction showed that a well defined and highly reproducible on-tube single-electron transistor has been achieved [115]. It has been found that strong bends (“buckles”) within metallic carbon nanotubes [2] act as nanometer-sized tunnel barriers for electron transport [116]. Single-electron transistors operating at room temperature have been fabricated by inducing two buckles in series within an individual metallic SWNT by manipulation with an AFM [117, 118]. The island with a length of 25 nm has been achieved and the resulting SET clearly showed the Coulomb blockade effect at room temperature [118]. Room temperature SETs have also been fabricated from SWNTs using V2 O5 nanowires as masks for selective chemical doping [118]. Single-electron devices based on SWNTs with the lineshaped top gates [120], triple-barrier quantum dots [121], suspended quantum dots [122], field-induced p-type quantum dots [123], and kink-induced quantum dots [124] were fabricated. The microwave response of coupled quantum dots in SWNTs has also been measured [125]. The Coulomb oscillations for different microwave power were similar to those for different bias voltages without microwave. Collins and co-workers [126] investigated electrical transport by sliding the STM tip along a nanotube. Figure 14 shows the schematic procedure for measuring nanotube characteristics using a single STM tip. From a position of stable tunneling (Fig. 14A), the STM tip was initially driven forward ∼100 nm into the nanotube film (Fig. 14B). After retraction of the tip well beyond the normal tunneling range, nanotube material remained in electrical contact with the tip (Fig. 14C). Conductivity measurements were carried out by sliding the STM tip down along the nanotube while the tip remained electrically connected with the nanotube (Fig. 14D). The continuous motion of the tip allowed electrical characterization of different lengths of the nanotube. This technique results in a position-dependent electrical transport measurement along the extended lengths of selected nanotubes. A series of I–V curves were recorded

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Nanotubes for Nanoelectronics

A

B

Tunnel

Contact and adhesion

d = 1 nm

C

D

Retraction

Sliding contact

d = 20 nm d = 2 µm

Figure 14. Schematic of the procedure for measuring nanotube characteristics with a single STM tip. Reprinted with permission from [126], P. G. Collins et al., Science 278, 100 (1997). © 1997, American Association for the Advancement of Science.

with response characteristics consistent with the theoretical predictions. The extreme changes in conductivity were caused by contact with the localized nanotube defects that greatly altered the local N E. Although the injected current predominantly indicates a graphitic behavior for the nanotube rope, a nanotube defect at the contact point would obscure and dominate the transport characteristics. For example, the existence of a pentagon–heptagon defect in the otherwise perfectly hexagonal nanotube wall fabric can lead to sharp discontinuities in the electronic density state along the tube axis. It is possible to have one portion of the nanotube with metallic characteristics almost seamlessly joined to another portion that is semiconducting. This “junction” constitutes a pure-carbon Schottky barrier. The sliding STM probe indicates exactly this type of behavior as its position moves along the length of a nanotube by only a few nanometers, indicating the existence of a localized nanotube nanodevice.

4.2. Multiwall Carbon Nanotubes at positions 1600, 1850, 1950, and 2000 nm as shown in Figure 15. The first three curves are nonlinear but nearly symmetric. At a position of 2000 nm the I–V characteristics abruptly changed to a marked rectifying behavior (Fig. 15D). This response (Fig. 15D) was reproducible and persistent for positions up to 2300 nm before the nanotube was broken. It was suggested by Collins et al. [126] that the position-dependent behavior gives strong evidence for the existence of localized, well-defined, on-tube “nanodevices”

Although single-electron transistors were made first from SWNTs [85, 86], a few reports [127–132] can be found for fabrication of SETs using MWNTs. Roschier et al. [127] of Helsinki University fabricated single-electron transistors using MWNTs through manipulation by a SPM. Figure 16 shows the experimental procedure for rotating and moving a nanotube, and eventually the tube was set across the electrodes with a gap of ∼300 nm. The electrical measurements of the device were done at low temperatures

10

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A

B

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Figure 15. Different types of current–voltage characteristics, obtained for contact points at different heights of (A) 1600, (B) 1850, (C) 1950, and (D) 2000 nm along the carbon nanotube. Reprinted with permission from [126], P. G. Collins et al., Science 278, 100 (1997). © 1997, American Association for the Advancement of Science.

Figure 16. AFM images during moving process. The 410 nm long MWNT, the side gate, and the electrode structure are marked in the first frame. The last frame represents the measured configuration, where one end of the MWNT is well over the left electrode and the other end is lightly touching the right electrode. Reprinted with permission [128], L. Roschier et al., Appl. Phys. Lett. 75, 728 (1999). © 1999, American Institute of Physics.

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down to 4 K. The measured I–V curves display a 15 mV wide zero current plateau across zero-voltage bias as shown in Figure 17. The Coulomb blockade effect is clearly observed below a few Kelvin and the nanotube behaves as a SET. The asymmetry of the gate modulation, illustrated in the inset for Vbias = 10 mV, indicates a substantial difference in the resistance of the tunnel junctions. There is a clear hysteresis in the I–Vbias curve at T = 120 mK. It is suggested that this phenomenon can be attributed to charge trapping, in which single electrons tunnel hysteretically across the concentric tubes. Roshier et al. [128] later constructed lownoise radio-frequency (rf) single-electron transistors using MWNTs. Contact resistance between a metal and a nanotube is commonly on the order of quantum resistance RQ = h/e2 = 266 k%. Hence, quantum fluctuations do not destroy charge quantization and thus it is possible to construct sensitive electrometers based on electrostatically controlled single-electron tunneling. The rf-SETs are the best electrometers at present [133]. As reported by Schoelkopf et al. [133] of Yale University, the sensitivity √ of rf-SETs based on Al islands approaches 12 × 10−5 e/ Hz, near the quantum limit at high frequencies. However, at frequencies below 1 kHz, these devices are plagued by the presence of 1/f ' noise (' ∼1–2). The origin of 1/f ' noise is the trapping and detrapping of charges either in the vicinity of the island or on the surface of the nanotube or in the tunnel barrier [134, 135]. One way to reduce the 1/f ' noise in SETs is to avoid contact of the central island with any dielectric material. In research by Roshier and co-workers [128], a freestanding MWNT across two electrodes was used as the island. The MWNT was moved onto the top of the electrodes √ by an AFM tip. The 1/f ' noise of the SET is 6 × 10−6 e/ Hz at 45 Hz, close to the performance in the best metallic SETs.

4.0 0.1

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0

5. FIELD-EFFECT TRANSISTORS, LOGIC GATES, AND MEMORY DEVICES 5.1. Field-Effect Transistors The significance of the paper by Tans et al. [86] is not in the quantum effect, but in the gate-induced modulation of conductance of the metallic nanotube. Field-effect transistors were first demonstrated using a single semiconducting SWNT by Tans et al. [136], and using both a SWNT and a MWNT by Avouris et al. [137–140]. Figure 18 shows the structure of the carbon nanotube field-effect transistor (CNTFET) [137]. The two electrodes are separated by 300 nm and gate oxide (SiO2 ) is 140 nm. Figure 19 shows output characteristics of a SWNT-FET consisting of a single SWNT with a diameter of 1.6 nm for several values of the gate voltage. It is clearly seen that the source–drain current is modulated by electric field. The field effect of the MWNT-FET device was not observed [137]. The hole mobility is estimated to be 20 cm2 /V s. In 1999, Dai and co-workers [141] reported fabrication of FET using SWNTs controllably grown on substrates. Figure 20 shows the I–V curves at various gate voltages [141]. The asymmetry of the I–V curves was regarded as being inherent to the metal–tube–metal system. I–V curves after exchanging the source and drain show nearly unchanged asymmetry. These results suggest that the observed asymmetry is not caused by asymmetrical parameters such as different contact resistance at the two metal–tube contacts [141]. It was suggested that the asymmetry of I–V curves is due to high source– drain bias [141]. The transconductance was estimated to be 0.1 mS/m.

5.1.1. Scaling of CNTFET Theoretical studies [142] showed that the performance can be significantly improved if the channel length and gate oxide can be further scaled down. The I–V characteristics are similar to the ballistic Si MOSFETs except for the occurrence of quantized channel conductance. Because of ballistic transport, the average carrier velocity reaches 27 × 107 cm/s [145]. Theoretical studies [143] also show that the CNTFET can be scaled down to at least 5 nm. Because of the ballistic transport, there is no energy dissipation except at contacts, and terahertz operation may be possible. Recently Wind and co-workers at IBM [144] improved their CNTFET

0.2

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Au (source)

T = 22 K T = 0.12 K

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–40

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20

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Figure 17. Measured I–Vbias curves at different temperatures when the gate is at zero bias. The inset shows the gate modulation at Vbias = 10 mV (indicated by the arrow) at T = 120 mK. The enlargement in the lower right corner shows the hysteretic behavior of the current. Reprinted with permission from [128], L. Roschier et al., Appl. Phys. Lett. 75, 728 (1999). © 1999, American Institute of Physics.

Si (back gate)

Figure 18. Schematic cross-section of the FET devices. A single nanotube of either multiwall or single-wall type bridges the gap between two gold electrodes. The silicon substrate is used as back gate. Reprinted with permission from [137], R. Martel et al., Appl. Phys. Lett. 73, 2447 (1998). © 1998, American Institute of Physics.

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Figure 19. Output and transfer characteristics of a SWNT-FET: (a) I– VSD curves measured for VG = −6, 0, 1, 2, 3, 4, 5, and 6 V. (b) I–VG curves for VSD = 10–100 mV in steps of 10 mV. The inset shows that the gate modulates the conductance by 5 orders of magnitude (VSD = 10 mV). Reprinted with permission from [137], R. Martel et al., Appl. Phys. Lett. 73, 2447 (1998). © 1998, American Institute of Physics.

structure with top gate and very thin gate oxide (15 nm). Figure 21 shows the device structure and its output characteristics. A single-wall carbon nanotube with a diameter of 1.4 nm was used as a semiconductor nanowire. The source and drain were defined by e-beam lithography with a gate length of 260 nm. I–V curves show excellent saturation and on–off ratio of 105 . Table 1 shows a comparison of key device performance parameters for a 260 nm gate length p-type CNTFET with those of state-of-the-art Si MOS transistors, a 15 nm gate Si p-type MOSFET [145] and a 50 nm gate SOI p-type MOSFET [146]. It can be found that a CNTFET has superior performance over Si MOSFETs. A CNTFET exhibits a much higher ON current (Ion = 2100 A/m), reasonable OFF current (Ioff = 150 nA/m), and very high transconductance (2321 S/m). It should be noted that the transconductance of the 15 nm gate Si p-MOSFET is only 975 S/m [145].

5.1.2. High Mobility In [144], Wind et al. did not characterize the hole mobility during transport. I will analyze the hole mobility as follows. Because the I–V curves follow the classical transport model, the transconductance in saturation is expressed as [147] Gmsat =

p Cox W VG − VT 2L

V Figure 20. (a) Room-temperature I–V curves recorded with sample S1 for V in the range 3 to −3 V under various gate voltages. (b) I–V curves recorded after exchanging the source–drain electrodes. (c) Symmetrical I–V curves obtained by scanning V while biasing the two electrodes at −V /2 and V /2, respectively. Reprinted with permission from [141], H. Dai et al., J. Phys. Chem. B 103, 11246 (1999). © 1999, American Chemical Society.

where p is the hole mobility. L and W are the gate length and gate width separately. Cox is the gate oxide capacitance. VG is the gate voltage and VT is threshold voltage (−0.5 V). The gate width is considered to be half of the perimeter of the CNT (diameter = 1.4 nm). Thus the mobility can be calculated using p =

Gmsat 2L Cox W VG − VT

Based on the given data of the transistor structure, the hole mobility is 2018 cm2 V−1 s−1 . This is much larger than the ideal hole mobility in bulk Si (∼400 cm2 V−1 s−1 ) and 200 × higher than the hole mobility (12 cm2 V−1 s−1 ) derived from the 15 nm gate p-Si MOSFET [145]. These surprising data indicate the potential of carbon nanotubes for high-speed device application similar to III–V compound semiconductors such as GaAs. It was reported that SWNTs are extremely pure systems with large Fermi velocities of vF = 106 m/s and ballistic transport over long distance [65, 91, 148]. Considering its unique 1D quantum wire electronic band structure and ballistic transport over long distance, it is highly possible for SWNTs to have extremely high mobility.

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Nanotubes for Nanoelectronics

(a)

Gate Oxide

SiO2

Gate (Al or Ti)

CNT

Drain (Ti)

Source (Ti)

P–+Si

(b)

Figure 21. Schematic cross-section of top gate CNFET showing the gate and source and drain electrodes. (b) Output characteristic of a top gate p-type CNFET with a Ti gate and a gate oxide thickness of 15 nm. The gate voltage values range from −0.1 to −1.1 V above the threshold voltage, which is –0.5 V. Inset: Transfer characteristic of the CNFET for Vds = −06 V. Reprinted with permission from [144], S. J. Wind et al., Appl. Phys. Lett. 80, 3817 (2002). © 2002, American Institute of Physics.

The high mobility of nanotube transistors estimated by the present author has been confirmed by Rosenblat et al. [149] and Kruger et al. [150]. Rosenblat et al. [149] constructed a carbon nanotube transistor using an electrolyte as gate, which was inspired by the study of doping effects using electrochemical gating [150, 151]. Figure 22 shows the device structure [149]. Catalyst islands containing Fe(NO3 3 · 9H2 O, MoO2 (acac)2 , and alumina nanoparticles were defined on SiO2 . Carbon nanotubes were then grown by chemical vapor deposition. The source and drain with a separation of 1–3 m (channel length) were defined using Table 1. Comparison of key device performance parameters for a 260 nm gate length p-type CNTFET with those of state-of-the-art Si MOS transistors: a 15 nm-gate p-type Si MOSFET and a 50 nm gate p-type SOI MOSFET.

Types of transistors Gate length (nm) Gate oxide thickness (nm) Threshold voltage (V) ION (A/m) @ VDS = VGS − VT = 1 V IOFF (nA/m) Subthreshold slope (mV/dec) Transconductance (S/m)

CNTFET Si MOSFET SOI MOSFET [144] [145] [146] 260 15 −0.5 2100 150 130 2321

15 1.4 −0.1 265 ∼500 ∼100 975

50 1.5 −0.2 650 9 70 650

Source: Adapted with permission from [144], S. J. Wind et al., Appl. Phys. Lett. 80, 3817 (2002). © 2002, American Institute of Physics.

Figure 22. Optical micrograph of the device. Six catalyst pads (dark) can be seen inside the area of the common electrode. Correspondingly, there are six source electrodes for electrical connection to tubes. (b) AFM image of a tube between two electrodes. The tube diameter is 1.9 nm. (c) Schematic of the electrolyte gate measurement. A water gate voltage Vwg is applied to droplets through a silver wire. Reprinted with permission from [149], S. Rosenblat et al., Nano Lett. 2, 869 (2002). © 2002, American Chemical Society.

photolithography and a lift-off process. A micropipet is used to place a small (∼10–20 m) saltwater droplet (NaCl solution) over the nanotube device. A voltage Vwg applied to a silver wire in the pipet is used to establish the electrochemical potential in the electrolyte relative to the device. Then the electrolyte functions as a liquid gate. The output characteristics of the electrolyte carbon nanotube FET are similar to those in Figure 21. The transconductance of the transistor reaches its maximum ∼20 S at a gate voltage of −0.8 V. The mobility inferred from the conductance measurement is in the range of 1000 to 4000 cm2 V−1 s−1 . The maximum onstate conductance is also shown for the same samples. Values on the order of e2 /h are routinely obtained, within a factor of 4 of the theoretical limit of 4e2 /h. Fuhrer et al. [152] reported the hole mobility in a SWNT of 9000 cm2 V−1 s−1 , which is the highest value ever reported. In addition, the field effect is clearly shown even at a temperature of 5 K with a spikelike conductance, which is attributed to the van Hove singularities [153]. AFM tips were used to apply pointlike local gates to manipulate the electrical properties of an individual SWNT contacted by Ti electrodes [154]. The AFM tip contacting on a semiconducting SWNT causes depletion at a local point, leading to orders of magnitude decrease of the nanotube conductance, while local gating to a metallic SWNT leads to no change in conductance [154]. Theoretical study also suggests that a quantum dot is formed because of the induced ntype together with the p-type near the metal contacts when a positive gate voltage is applied on the p-type SWNT [155]. The induced quantum dot enhances the conductance.

932 Because the energy bandgaps of semiconducting SWNTs are inversely proportional to their diameter, large-diameter SWNTs have smaller energy bandgaps. Transistors made of large-diameter SWNTs exhibit ambipolar field-effect transistor behavior [156, 157]. Theoretical study showed that the energy gap of a semiconducting nanotube can be narrowed, when the tube is placed in an electric field perpendicular to the tube axis (e.g., in the FET case) [158]. This band-structure modulation may affect the electrical properties of CNTFETs. No experimental research has been reported regarding this phenomenon. For characterization of the semiconductor/oxide interface, capacitance–voltage measurement is usually carried out on MOS capacitors. Theoretical study showed that the calculated C–V curves reflect the local peaks of the 1D DOS in the nanotube [159]. This might be used for diagnose the electronic structure of nanotubes, providing a more convenient approach than STM. However, experimental measurement of the capacitance in nanoscale is not easy because the accumulation capacitance of a 1-m long nanotube MOS capacitor is only 1.5 × 10−4 pf or 1.5 pf/cm [159].

Nanotubes for Nanoelectronics A

B

C

5.2. Logic Gates In 2001, several groups [160–162] demonstrated logic circuits using carbon nanotube transistors. Bachtold et al. [160] showed inverter, NOR gate, static random access memory (SRAM), and ring oscillator. Derycke et al. [161] and Liu et al. [162] showed the CMOS inverter using both nand p-channel CNTFETs. Figure 23 shows individual device structure and layout [160]. Unlike the previous nanotube transistor structure using back gate, which applies the same gate voltage to all transistors, the transistor structure consists of a microfabricated Al wire with native Al2 O3 as gate insulator, which lies beneath a semiconducting nanotube that is electrically contacted to two Au electrodes. The channel length is about 100 nm and gate oxide thickness is about a few nanometers. This layout allows the integration of multiple nanotube FETs. The transistor is a p-type enhancement mode FET with transconductance of 0.3 S and on–off ratio of at least 105 . The transistor can operate at an ON current of 100 nA and an OFF current of 1 pA. The basic logic elements such as inverter, NOR gate, SRAM, and ring oscillator were constructed as shown in Figure 24. The inverter exhibits very good transfer characteristics. When input voltage is −1.5 V (logic 1), the output voltage is 0 V (logic 0). When the input voltage is switched to 0 (logic 0), the output becomes −1.5 (logic 1). Although the transition is not as sharp as a Si MOSFET, it is still competitive. Because this inverter is constructed using a single transistor, the standby current is still high. The ring oscillator shows good oscillation waveforms although the oscillation frequency is low in this pioneer stage. The inverters have been constructed using complementary nanotube FETs similar to Si CMOS structure (complementary MOS), leading to minimum standby power consumption [161, 162]. Figure 25 shows the CMOS inverter based on both n- and p-CNTFETs and its transfer characteristic [161]. A single nanotube bundle is positioned over the gold electrodes to produce two p-type CNTFETs in series. The device is covered by PMMA and a window is opened by e-beam lithography to expose part of the nanotube. Potassium is then evaporated through

Figure 23. Device layout. (A) Height image of a single-nanotube transistor, acquired with an atomic force microscope. (B) Schematic side view of the device. (C) Height-mode atomic force microscope image of two nanotube transistors connected by a Au interconnect wire. The arrows indicate the position of the transistors. Reprinted with permission from [160], A. Bachtold et al., Science 294, 1317 (2001). © 2001, American Association for the Advancement of Science.

this window to produce an n-CNTFET, while the other CNTFET remains p-type. The transfer characteristics show much better transition region (more steep slope).

5.3. Memory Devices A concept for molecular electronics exploiting carbon nanotubes as both molecular device elements and molecular wires for reading and writing information has been proposed [163]. Each device is based on suspended, crossed nanotube geometry that leads to bistable, electrostatically switchable ON/OFF states. The device elements are naturally addressable in large arrays by the carbon nanotube molecular wires making up the devices. These reversible, bistable device elements could be used to construct nonvolatile random access memory and logic function tables at an integration level approaching 1012 elements per cm2 , and an element operation frequency in excess of 100 GHz [163]. However, strictly speaking, these memory devices or logic gates are not made of CNTFETs. Several groups [152, 164– 166] reported fabrication of memory devices using nanotube field-effect transistors. Air-stable n-type, ambipolar CNTFETs were fabricated and used in nanoscale memory cells [164]. The n-type transistors are achieved by annealing nanotubes in hydrogen gas and contacting them by cobalt electrodes. Due to their nanoscale capacitance, CNTFETs

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Figure 24. Demonstration of one-, two-, and three-transistor logic circuits with carbon nanotube FETs. (A) Output voltage as a function of the input voltage of a nanotube inverter. Inset: Schematic of the electronic circuit. The resistance is 100 M%. (B) Output voltage of a nanotube NOR for the four possible input states (1,1), (1,0), (0,1), and (0,0). The resistance is 50 M%. (C) Output voltage of a flip–flop memory cell (SRAM) composed of two nanotube FETs. The two resistances are 100 M% and 2 G%. (D) Output voltage as a function of time for a nanotube ring oscillator. The three resistances are 100 M%, 100 M%, and 2 G%. Reprinted with permission from [160], A. Bachtold et al., Science 294, 1317 (2001). © 2001, American Association for the Advancement of Science.

are extremely sensitive to the presence of individual charges around the channel, which can be used for data storage that operate at the few-electron level [165]. Figure 26 shows the threshold voltage shift due to storage of charges (a,b,c), device structure (d), and the voltage signal (Vout ) due to charge storage [164]. In addition, the data-storage stability of over 12 days has been achieved [165].

6. DOPING, JUNCTIONS, AND METAL–NANOTUBE CONTACTS A key technology advancement for the success of semiconductor industry is achievement of n- and p-type doping, junctions, and Ohmic contacts between metal and

Figure 25. (a) AFM image showing an intramolecular logic gate. (b) Characteristics of the resulting intramolecular voltage inverter. The thin straight line corresponds to an output/input gain of one. Reprinted with permission from [161], V. Derycke et al., Nano Lett. 1, 453 (2001). © 2001, American Chemical Society.

Figure 26. (a)–(c) High vacuum I–Vg data at Vds = 05 mV. Device hysteresis increases steadily with increasing Vg due to avalanche charge injection into bulk oxide traps. (d) Diagram of avalanche injection of electrons into bulk oxide traps from the CNFET channel. (e) Data from CNFET-based nonvolatile molecular memory cell. A series of bits is written into the cell (see text) and the cell contents are continuously monitored as a voltage signal (Vout ) in the circuit shown in the inset. Reprinted with permission from [164], M. Radosavljevic et al., Nano Lett. 2, 761 (2002). © 2002, American Chemical Society.

semiconductor. It is critical to achieve doping, pn junctions, and Ohmic contacts for carbon nanotubes so that nanotube electronics may evolve into a large industry.

6.1. Chemical Doping Antonov and Johnson [167] observed current rectification in a molecular diode consisting of a semiconducting SWNT and an impurity. It was suggested that rectification resulted from the local effect of the impurity on the tube’s band structure. It is not clear what type of impurity it was. Lee et al. [168] reported doping of SWNTs by vapor-phase reactions with bromine and potassium. Doping decreases the resistivity of SWNTs at 300 K by up to a factor of 30 and enlarges the region where the temperature coefficient of resistance is positive, which is the signature of metallic behavior. It was reported [169, 170] that potassium (K) doping of SWNTs creates n-type carrier (electrons). The doping effects were studied using the transistor structure. The SWNT ropes were placed on top of Au electrodes that have 500 nm separation. The electrodes were fabricated on the oxidized n+ -Si substrate which serves as gate. The Au electrodes serve as source and drain. Figure 27 shows conductance vs gate voltage for an undoped nanotube rope (open circles) and an nanotube doped with potassium (solid circle) [169]. For the undoped nanotube, the conductance increases with decreasing gate voltage, indicating p-type behavior. For the K-doped nanotube, the conductance increases with increasing gate voltage, indicating n-type behavior. The typical values for the carrier density are found to be ∼100–1000 electrons/m and the effective mobility of electrons is eff ∼ 20–60 in early time [169]. Derycke et al. [171] reported two methods for conversion of SWNTs from p-type to n-type. The first method involves conventional doping with an electron donor and the second

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Figure 27. The conductance decreases with increasing gate voltage for an undoped sample (open circles), indicating p-type behavior. Left inset shows the energy band corresponding to this case. The conductance increases with increasing gate voltage after potassium doping at a high doping level (solid squares) and at a low doping level (solid circles). Right inset shows the energy band corresponding to this situation. Reprinted with permission from [169], M. Bockrath et al., Phys. Rev. B 61, R10606 (2000). © 2000, American Physical Society.

consists of annealing the metal nanotube contacts in vacuum to remove adsorbed oxygen. It has been found that the main effect of oxygen adsorption is not to dope the bulk of the nanotube, but to modify the Schottky barriers at the metal–semiconductor contacts [172, 173]. It also found that boron-doped MWNTs showed an enhanced room temperature conductivity [174]. However, theoretical calculation showed that H2 O adsorption on a SWNT reduces conductance [175].

Figure 28. An SWNT with modulated chemical doping. (A) Device scheme with the SWNT contacted by two Ni/Au electrodes. The right half of the SWNT is doped by evaporating K atoms (black dots) from an alkaline metal at 10−6 Torr. (B) Atomic force microscopy image of the SWNT recorded before PMMA coating of the left half and doping. The bright regions at the two ends are the electrodes. Dashed lines are drawn to highlight the later PMMA-covered region. (C) A band diagram for the system. Reprinted with permission from [176], C. Zhou et al., Science 290, 1552 (2000). © 2000, American Association for the Advancement of Science.

6.2. Junctions and Metal–Nanotube Contacts Zhou et al. [176] published the first attempt for controllable chemical doping of individual carbon nanotubes to achieve pn junctions. Figure 28 shows the device structure for potassium doping and the resulting energy band structure [176]. The SWNT used in the doping experiments has a diameter of ∼2 nm and a length of 3.5 m and is placed across two metal electrodes. A back gate is used to modulate the carrier concentration by applying voltage on the gate. A polymethylmethacrylate (PMMA) layer of 340 nm thickness covers the left half of the nanotube, leaving the right half exposed. Prior to doping, SWNT is a p-type semiconductor. Potassium doping of the SWNT is carried out in vacuum by electrical heating of a potassium source. Figure 29A shows the I–Vg curves [176]. When Vg < −1 V (Regime I), hole accumulation is achieved in the SWNT, leading to p+ in the PMMA protected area due to increase in hole concentration and n in the exposed region due to compensation of electrons. In Regime II, electron concentration begins to increase, resulting in p+ n+ junction. I–V curves of p+ n and p+ n+ junctions are shown in Figure 29B and C. In the forward bias regime, a nice pn junction diode is demonstrated. However, the reverse bias breakdown voltage is too small to be qualified as a diode [176]. Anyway, this is the first result showing some possibility for fabrication of nanotube-based pn junction diodes.

Figure 29. Electrical properties of the modulation-doped SWNT at room temperature. (A) Current versus gate-voltage I–Vg curve recorded under a bias voltage V = 1 mV. The drawings show the band diagrams in four regimes. (B) and (C) I–V curves recorded in Regimes I and II. The star and triangle in (A) marks the gate voltages for the I– V curves in (B) and (C), respectively. Reprinted with permission from [176], C. Zhou et al., Science 290, 1552 (2000). © 2000, American Association for the Advancement of Science.

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Nanotubes for Nanoelectronics

Based on theoretical calculation, Chico et al. [177] proposed metal/semiconductor or semiconductor/semiconductor junctions, made of SWNTs, and based on the introduction of topological defects in nanotubes. By introducing a pentagon and a heptagon into the hexagonal carbon lattice, two tube segments with different electronic structures can be seamlessly fused together to create semiconductor– semiconductor or metal–semiconductor junctions [172, 178, 179]. Two carbon nanotubes have also been fused together by high electric field [180]. The CNx /nanotube junctions have been synthesized by a microwave plasma assisted CVD method [181]. It is of particular interest that two SWNTs were crossed over each other to form junctions [182]. Theoretical study also suggests that negative differential resistance may be observed in metal–nanotube–metal structures [183]. Figure 30 shows the AFM image of a nanotube junction with a sharp kink of about 40 [172]. The kink consists of five to seven defects. Figure 31 shows the I–V characteristics of the kink metal–semiconductor junction [172]. The rectification effect is clearly seen in the figure. A model has been proposed for the kink-shaped carbon nanotube Schottky diode, where the gate voltage modulation is included [184, 185]. It has been observed that the nanotube Schottky diodes [172, 179] and the nanotube pn junctions [176] exhibit much lower reverse-bias breakdown voltage than conventional, micrometer-size Schottky diodes and pn junctions. A theoretical model has been proposed to describe the potential barrier shape in ultrasmall Schottky diodes [186]. It is suggested that for diodes smaller than a characteristic length lc (e.g., 80 nm for Nd = 1017 cm−3 ), Schottky barrier thickness becomes a function of the diode size. Consequently, the contribution of tunneling to the total conductance is dramatically enhanced, resulting in lower reverse breakdown voltage in nanoscale diodes [186]. The carbon nanotube “T” junction with heptagons or pentagons for joints has been proposed theoretically [187]. However, experimentally no “T” junction has been observed. Instead, “Y” junctions have been produced through an anodic aluminum oxide (AAO) template [188, 189] and directly on substrates [190–196]. Theoretical calculation confirms the rectification

Figure 30. Tapping-mode atomic force microscope amplitude images of examples of nanotube junction devices. (a) and (b) Nanotubes that contain a single kink of 36 and 41 respectively. (c) Illustration of the carbon-bond network of a kink junction constructed between an “armchair” tube and a “zigzag” tube, where 5 denotes a pentagon, 7 denotes a heptagon, and the atoms in the pentagon and heptagon are highlighted by dark balls. Reprinted with permission from [172], Z. Yao et al., Nature 402, 273 (1999). © 1999, Macmillan Magazines Ltd.

a

b

Figure 31. Current–voltage characteristics across the metal– semiconductor junction of (a), showing rectifying behavior. The data are taken at 100 K. The results at room temperature are similar, but the data are noisier. Inset in (a): the I–V curve for the upper straight segment measured at room temperature. In (a), the gate is grounded. In (b): the gate voltages from right to left are 2, 1, 0, −1, −2, and −4 V respectively. Inset in (b): expanded view of the small-current region which shows more clearly the onset of conduction for both bias polarities. Reprinted with permission from [172], Z. Yao et al., Nature 402, 273 (1999). © 1999, Macmillan Magazines Ltd.

effect of “Y” junctions [197–199]. When the positively biased metal–nanotube contact (source electrode) is locally gated with a negative gate voltage, a dramatic increase in transport current occurs because the Schottky barrier thickness is reduced due to accumulation of holes near the contact [200]. For the negatively biased metal–nanotube contacts, the gate voltage has no effect on transport because no Schottky barrier exists there [200]. Therefore, by positioning the gate locally near one of the contacts, the nanotube FET is converted into a rectifying diode [200]. Zhang et al. [201] fabricated the first real Ohmic contacts between SWNTs and Ti by solid solid reaction: C (nanotubes) + M (solid) → MC (solid), where M is metal. The reaction was performed at a temperature ranging from 800 to 1000  C in ultrahigh vacuum or an inert atmosphere to avoid volatile reactant [201]. The continuous transformation of the SWNT to carbide is controlled by the diffusion of

936 M to the C/M interface. The I–V curves showed a straight line when the bias voltage is swept from −1 to 1 V, indicating a true Ohmic contact [201]. The resistance at the contact is ∼0.3 k% [201], much better than the contact resistance (∼20 k%) for the direct metal/nanotube contacts [202, 203].

7. NANOTUBE-BASED NANOFABRICATION Carbon nanotubes exhibit Coulomb-blockade effects, ballistic transport, and field effects. Of particular importance is the field effect that may lead to the carbon nanotube electronics era. However, a critical issue for successful realization of carbon nanotube electronics is how to manipulate the nanotubes so that large-scale manufacturing is possible.

7.1. Manipulation of Nanotubes Using AFM and STM Since discovery of carbon nanotubes [1], for electronic device research, the majority of research has been focused on manipulation of carbon nanotubes using the STM or AFM [86, 118, 127, 163, 203–223]. Tans et al. [86] deposited SWNTs on the SiO2 /Si substrate which had patterned metal electrodes. An individual nanotube wire was put across the Pt electrodes, which was imaged by an AFM. Physical manipulation of nanotubes with the AFM tip, like rolling, sliding, bending, and buckling, has been used to investigate mechanical properties of nanotubes [211, 212]. Roschier et al. [127] positioned a semiconducting multiwalled nanotube between two gold electrodes at the SiO2 surface. The 410 nm long MWNT was manipulated and positioned on the gold electrodes by the AFM tip. Soh et al. [203] synthesized SWNTs on the patterned catalytic islands, which are contacted with metal pads. Lefebvre et al. [204] developed a method to assemble SWNT circuits using a tapping mode AFM. Nanotubes can be controllably translated, rotated, cut, and placed on top of one another by varying the tip–sample force and the tip speed. These operations can construct complex nanotube circuits. Of particular interest is that the suspended SWNT can be deformed locally by the AFM tip, leading to a decrease in conductance of the nanotube by two orders of magnitude [217–219]. This effect can be used to construct nanoelectromechanical devices. Tight-binding simulation showed that this effect is caused by the formation sp3 bonds because of the mechanical pushing action of the tip [217, 218]. Collins et al. at IBM [205] demonstrated a simple method for permanently modifying MWNTs by using current-induced breakdown to eliminate individual shells one at a time. Carbon nanotubes can withstand remarkable current densities, exceeding 109 A/cm2 , because of their strong carbon–carbon bonding. However, at high enough current nanotubes ultimately fail. In MWNTs, this failure occurs in air at a certain threshold power through the rapid oxidation of the outermost carbon shell. The mechanism for the breakdown initiation is the current-induced defect formation. By using the electrical breakdown technique, they can remove the MWNT shells one by one. This controlled breakdown technique is also performed with the help of STM or AFM. Study of the reliability and current carrying capacity showed that under high

Nanotubes for Nanoelectronics

current density (>109 A/cm2 ) no observable failure in the nanotube structure and no measureable change in the resistance are detected at temperatures up to 250  C and for time scales up to 2 weeks [224]. Although these processes and techniques are especially useful for study of nanotubes’ physical properties, they may not be appropriate for large-scale fabrication of nanotube-based devices and circuits with high yield.

7.2. Controllable Growth and Placement of Nanotubes Before we can think about building sophisticated nanotubebased circuitry, we must find how to grow the nanotubes in specific locations, orientations, shapes, and sizes, as well as how to construct nanotube devices at specific locations and how to connect nanotube devices with each other.

7.2.1. Vertically Aligned Carbon Nanotubes Li et al. [225, 226] reported the first large-scale synthesis of vertically aligned carbon nanotubes by using CVD catalyzed by iron nanoparticles embedded in mesoporous silca. Vertically aligned arrays of isolated tubes with spacing between the tubes of about 100 nm were controllable through the pores. This method has been extended to grow freestanding carbon nanotubes on glass substrates at lower temperature (