Electrophysical properties of porous and filamentous silicon and gas sensors based on them: monograph 9786010448032

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AL-FARABI KAZAKH NATIONAL UNIVERSITY

M. K. Ibraimov, S.B. Ikramova, A.O. Tileu

ELECTROPHYSICAL PROPERTIES OF POROUS AND FILAMENTOUS SILICON AND GAS SENSORS BASED ON THEM Monograph

Almaty “Kazakh University” 2020

UDC 621 LBC 22.33 I 10 Recommended by the Academic Council (Protocol №1 dated 28.09.2020) and Editorial and Publishing Council of KazNU al-Farabi (Protocol №1 dated 10.09.2020) Reviewers: PhD, associate Professor A.K. Saimbetov PhD Ye. Sagidolda

I 10

Ibraimov M.K. et al. Electrophysical properties of porous and filamentous silicon and gas sensors based on them: monograph / M.K. Ibraimov, S.B. Ikramova, A.O. Tileu. – Almaty: Kazakh University, 2020. – 107 р. ISBN 978-601-04-4803-2 The monograph is devoted to the study of the electrophysical properties of nanostructured porous and filamentous silicon with a theoretical description of new experimental results on the study of the morphology of silicon films containing vertical quantum nanofilms and the electrical properties of nanofilms. Possible methods of practical application of nanostructured silicon in electronics, radio engineering, and sensors are considered. A new method of selective gas sensor with porous silicon using the frequency dispersion of capacitances and time response characteristics of the sensor element is presented. The nonlinear characteristics of nanostructured silicon allow its use in chaotic signal generators. Recommended for students of physics specialties of universities, researchers who begin research in the field of nanoelectronics.

UDC 621 LBC 22.33

© Ibraimov M.K., Ikramova S.B., Tileu A.O., 2020 ISBN 978-601-04-4803-2

© Аl-Farabi KazNU, 2020

CONTENT INTRODUCTION............................................................................................... 4 Chapter 1. ELECTROPHYSICAL PROPERTIES OF NANOSTRUCTURED FILMS OF POROUS SILICON AND SILICON NANOWIRES AND THEIR PRODUCTION METHODS............ 7 Physical processes in nanostructured semiconductors and applications.... 7 Obtaining porous silicon and silicon nanowires and methods for measuring electrical characteristics...................................................... 21 Experimental results and discussion of the electrical characteristics of porous silicon......................................................................................... 28 Experimental results and a theoretical model of the electrical conductivity of silicon nanowires.............................................................. 33 Chapter 2. GAS SENSORS BASED ON NANOSTRUCTURED SILICON FILMS.................................................................................................................... 44 Sensor technologies for gas detection........................................................ 44 Gas sensors based on silicon nanowires..................................................... 49 Gas sensors based on silicon porous structures.......................................... 56 Chapter 3. NONLINEAR ELECTRICAL CHARACTERISTICS OF POROUS AND FILAMENTOUS SILICON AND CHAOTIC SIGNAL GENERATORS BASED ON THEM.................................................. 60 Frequency characteristics of modern nonlinear elements.......................... 60 Theoretical and schematic model of the chaotic signal generator.............. 67 Schematic description of the generator of chaotic signals on nanostructured films.............................................................................. 69 Statistical and nonlinear analysis of signal generators on porous silicon and silicon nanowires................................................................................. 71 CONCLUSION.................................................................................................... 81 References.............................................................................................................. 82 Appendix A............................................................................................................ 91 Appendix B............................................................................................................ 95 Appendix C............................................................................................................ 104

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INTRODUCTION Prospects for the use of nanostructured silicon films in electronic devices have caused the need to obtain information about the electrophysical parameters of these materials, methods for controlling the amount of electrical conductivity, properties of nanostructured silicon / metal and nanostructured silicon / crystalline silicon transitions, etc. Analysis of available literature sources has shown that, despite the large total number of publications on nanostructured semiconductors, many questions related to the electrophysics of porous silicon and silicon nanowires and structures based on them are unresolved. There is a lack of fundamental research on the mechanisms of electrical conductivity of nanoscale semiconductor structures. The capacitive (impedance) properties of structures with nanoscale silicon layers remain insufficiently studied. All of the above, supplemented by the practical technical necessity of using silicon nanostructured layers with specified electrophysical parameters in electronic devices, indicates the relevance of the study of the electrophysical properties of nanoscale structures of porous silicon and silicon nanowires. Also, as a result of the analysis of the current state of this topic, it turned out that it is relevant to use oxide materials as memristors, which can be used as faster-acting memory elements in comparison with the existing ones. Modern industrial and scientific research technology sets the task of searching and studying the possibilities of creating ultrasensitive sensor devices for monitoring the physical parameters of the environment and meteorological processes, for use in medicine and agriculture. Nanostructured silicon is an attractive material for these purposes because of their nanoscale effects and their unique electrical properties. The surface effect of nanostructured materials becomes dominant due to their large (fractal) surface of a given volume, which is useful for developing humidity and gas sensors. 4

Another urgent task is creating random signal generators based on nanostructured elements. One of the most effective ways to use chaotic signals in telecommunications systems is confidential signal transmission. At the same time, obtaining a chaos generator with the widest possible spectrum and managing the chaotic mode are technically complex issues. Interest in this topic continues to increase, as evidenced by the growing flow of scientific information, a large number of conferences and scientific schools on the problems of stochastics and chaos. There are two reasons for the long-standing popularity of the dynamic chaos problem. The first reason is the general interdisciplinary nature of this phenomenon. An independent section of nonlinear oscillation theory is formed by the efforts of specialists in various fields of knowledge. A fundamentally new natural science worldview is approved, indicating qualitatively different approaches to solving complex problems in the physics of nonlinear phenomena. The second reason is due to the wide range of experimental applications of deterministic chaos theory in various fields of knowledge. Having mastered the theory of chaos, the experimenters were able to create generators of chaotic self-oscillations and control their physical characteristics for the development of new practical and important technical devices. In order to create prospective information technologies for space activities and telecommunications, it provides great interest to use a signal with a broadband spectrum for the protection and transmission of information. Dynamic chaos expands the spectrum and thus increases the secrecy of the transmitted information. On the other hand, if you use dynamic chaos modulated by a useful signal as a carrier signal, the information capacitance and bandwidth of the communication channel increases by several orders of magnitude. Self-oscillating systems with semiconductor nanostructures can be used as new generators of chaotic signals. Therefore, in order to solve the scientific and technical problem it can be formulated in the following form: study of the electrical properties of semiconductor nanostructures and creation of chaotic signal generators based on porous silicon and silicon nanowires; make a nonlinear and statistical analysis of the operation of these generators to obtain optimal signal 5

generation modes; build a model of nonlinear dynamics of the vibrational properties of nanostructured films. Taking into account the relevance and importance of the abovementioned modern scientific directions, there is a need for a thorough analysis of theoretical and experimental studies of the electrophysical properties of nanostructured films of porous silicon and silicon nanowires, as well as research into the possibility of creating new applied devices based on them, such as a selective sensor device and a dynamic chaos generator. The research carried out in the framework of this work is related to prospective areas of modern electronic technology, which uses quantum-sized nanostructures, self-oscillating systems of dynamic chaos, and highly sensitive sensor devices.

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Chapter

1

ELECTROPHYSICAL PROPERTIES OF NANOSTRUCTURED FILMS OF POROUS SILICON AND SILICON NANOWIRES AND THEIR PRODUCTION METHODS Physical processes in nanostructured semiconductors and applications Currently, there is an increased interest in nanostructured semiconductor materials, which are considered as promising elements of nanoelectronics. One example of nanoscale structures with unique electrophysical properties is porous silicon (PS). The process of vaporization in obtaining porous silicon by electrochemical etching is very complex and there is still no single complete theory. It is known that when etching crystalline silicon in liquids containing hydrofluoric acid, so-called “channels” of etching are formed, which go deep into the crystalline silicon. Over time, the length and diameter of these channels will increase and, respectively, when reaching the size of several tens of nanometers, quantum-dimensional effects will be observed. Pore formation during electrochemical and conventional chemical etching is analogous. Several sequential and parallel reactions occur during the etching process. If we consider in more detail the reaction that occurs during etching, the silicon atoms dissolve in the liquid, and neutral silicon atoms are formed in parallel, which then expose secondary crystallization. 7

It is also worth noting that the concentration of neutral atoms will exceed the surface concentration of the original silicon. This means that neutral atoms in the event of secondary crystallization do not repeat the uniform sequence of the original crystalline silicon, moreover, as a result of quantum-dimensional expansion of the forbidden zone, the electrical resistance of these re-crystallized particles will be greater than that of the original silicon, and thus Islands resistant to dissolution are formed on the surface of the substrate. In this process, the original silicon substrate is dissolved and porous structures are formed. Geometric shapes and pore sizes, porosity and some physical properties of the film depend on the parameters of etching and electrolyte composition, the type of semiconductor, the degree of alloying. Potential applications of porous silicon and its electrophysical properties

Table 1

Application field The role of porous silicon Key properties Optoelectronics

Led Lightguide Field emitter Optical memory

Effective electroluminescence, Frequency tuning of the refractive index, the Emission of hot carriers, Non-linear properties.

Micro-optics

Fabry-Perot Filters Modulation of the refractive index, Structures with a photonic Regular array of macropores, band gap Highly nonlinear properties. All optical switching

Energy converters

Anti-reflective coating Photoelectrochemical cells

Low refractive index, Photo corrosion cells.

Environmental monitoring

Gas sensors

Sensitive properties to the environment.

Microelectronics Microcondenser The insulator layer Materials with low permittivity

High specific surface, High resistance, Electrical properties.

Thin film technology

Variable lattice parameters, High selectivity of etching.

Buffer layer in heteroepitaxy SOI wafers

Microprocessing Thick protective layer

Managed etching properties.

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Optoelectronic properties of PS and manufacturing technology for light-emitting diodes, light guides, photodetectors, photomodulators, and nanocomposites based on PS are described in [2]. In addition, in PS devices, electroluminescence is observed both in the infrared region and in the visible range with different efficiencies depending on the structure of the diode and the method of applying contacts [3]. The most interesting results were obtained in work [4] using devices where an electric bias is applied using a liquid electrode. High external quantum yield [5] and efficiency of injection electroluminescence [6] are the main attractive features of this system. On the other hand, the manufacturability of the device and its incompatibility with the microelectronic CMOS (complementary metal-oxide-semiconductor structure) system complicates the operation process. The easiest way to make an led on a PC is to apply a thin layer of metal to the surface [7] or from a transparent semiconductor, such as indium tin oxide (ITO) [8,9]. When using various Au-coated metals, the adjustment of the radiation line is observed with an improvement in the external quantum output next. In addition to optical properties, porous silicon has possible promising applications in modern microelectronics. An urgent task is to integrate the entire electronic system on a single chip, including analog and digital processing units. The search for compatible materials with the using integrated circuit brought to porous silicon. This promising candidate can provide localized isolations from different regions of the silicon substrate [10]. In the article [10], the authors consider the electrical properties of porous silicon, such as permittivity and conductivity at alternating voltage. To compare the results, you first need to determine the degree of porosity and characteristic dimensions using a scanning electron microscope. The porosity of the sample is affected by the composition of the electrolyte, the density of the supplied current, and, accordingly, the resistance of the substrate. The exposure time of the sample in the air after etching is also important. In particular, dry samples show a linear increase in conductivity as a function of frequency, while with traces of liquid they characterize a nonlinear frequency dispersion [11]. However, to stabilize the characteristics of the porous layer, it is sufficient to conduct annealing at a temperature of 300 ° C in a neutral atmosphere (argon and nitrogen). 9

The measured dielectric constant of different porous layers [10]

Table 2

Silicon type, orientation, resistance (Ohm * сm)

Porosity (%)

The thickness of the PS (um)

ε PS

P, (100), 5–10

80

70%) should also be considered, since the permittivity slightly affects the oxidation fraction. In figure 1, the filled circles correspond to low doping (< 1018 cm3), and the empty circles correspond to high doping of silicon wafers (> 10–18 cm–3). It is also known that porous silicon shows low electrical conductivity at constant voltage, for example, silicon with a porosity of 30% corresponds to the measured 10–7 S/cm[13]. This value decreases sharply after annealing [14]. The relative high porosity of samples from 60% to 80% shows electrical conductivity from 10–14 S/cm to 10–18 S/cm, respectively [15, 16].

Figure 1 – Dependence of the permittivity on the porosity of silicon [10]

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Measurement of volt-ampere characteristics in an alternating field and equivalent electrical circuits of samples with a porous silicon structure in the form of transistors are described in work [17]. The frequency dispersion of conductivity (σAC) in a variable field seems identical for silicon structures with low and high porosity. At high frequencies (10-100 kHz), σAC is directly proportional to ω. This behavior corresponds to the hopping transport of charge carriers. In this case, the electrons move randomly in the fractal silicon network under the influence of an electric field [10]. In addition, the effect of the electrolyte on the sample surface is noticeable at a frequency below 1 kHz [11]. Also, the authors of [18] claim that on PS layers with a porosity of 70% to 80%, the conductivity at a variable field corresponds 5*10-4 S/cm. Semiconductor nanostructures, especially silicon nanowires, have interested researchers both from a fundamental and technological point of view. They not only have interesting unique electrical and optical properties, but can also play an important role as connecting and functional components in the manufacture of future miniature nanoelectronic and optoelectronic devices. Here, as in porous silicon, the influence of size and dimensions on the electrical properties of semiconductor nanowires is of great importance. Until now, most scientific researchers have focused on the electrical properties of carbon nanotubes. Their remarkable molecular structures have shown themselves as ballistic conductors that can withstand a very high current density [19, 20]. In addition, nanodevices, like fieldeffect transistors were fabricated from individual carbon nanotubes. However, carbon nanotubes can behave like metal and semiconductor nanotubes. Therefore, semiconductor nanowires that are uniform in structure and size are very important. Silicon nanoparticles (CNP) are produced in two main directions, which include “top-down” and “bottom-up” methods. The most affordable and easiest option to get a CNP is the metal-assisted wet chemical etching (MAWCE) method (figure 2). MAWCE was first used in the etching of porous silicon coated with aluminum as an etching solution consisting of HF, HNO3 and Н2О in 1997 [21]. It was found that the manufacturing time was significantly reduced by the presence of an aluminum metal film on top of the silicon substrate. The authors later demonstrated a film where 12

they increased the reduction of HNO3 [21]. The MICE mechanism was further developed, Le, Bon and etc. explained the etching of Si substrate with a thin layer of noble metal sprayed on, HF, H2O2 and ethanol were used as the etching solution [22].

Figure 2 – Structure of manufacturing silicon nanowires using metal-induced chemical etching.

Figure 3 – Diagram of the metal-induced chemical etching. The grey part shows a noble layer of metal deposited on a silicon substrate.

The silicon substrate can be partially coated with a noble metal film (for example, Au, Pt, Ag), and placed in an etching solution consisting of HF and an oxidizer (for example, H2O2, HNO3). The noble metal acts as a cathode to catalyze the reduction of the oxidizer, producing many holes. After that, these holes are introduced into the valence band of the silicon substrate due to the higher electrochemical potential of the oxidants. Therefore, a silicon layer with a noble metal on the top is etched much faster than silicon without a noble metal coating. These different etchings occur at different rates depending on the type of noble metal, and leave behind a highly ordered array of wire-like structures (figure 3). 13

Figure 4 – Diagram of the metal-induced chemical etching process [23] ●- hole, – noble metal, – Si plate

Process 1: The oxidizer in the solution is predominantly reduced with the existence of a noble metal as a hole-generating catalyst; Process 2: The holes are generated by reducing the diffusion of the oxidizer through the noble metal and injected into the silicon, which is located at the border with the metal particles; Process 3: Silicon under the noble metal is oxidized with injected holes and therefore etched with HF solution, forming H2SiF6; Process 4: There is a high concentration of holes at the metalsilicon interface. As a result, silicon in contact with a noble metal is etched much faster than silicon without a noble metal coating; Process 5: When the ratio of oxidizer to HF is large, the hole generation rate is greater than the hole regeneration rate. Accordingly, the holes enter the silicon between the metal and the silicon. As a result of diffusion, silicon may be porous due to injection. Compared to other methods of manufacturing silicon nanofibers, MICE is gaining more and more interest for many reasons: MICE is a simple and cost-effective method for manufacturing silicon nanowires. The etching solution consists of commonly used chemicals, and the entire etching process is performed at room temperature in a chemical laboratory, without the use of any expensive equipment. Unlike many other manufacturing methods, such as steam-liquid-solid (SLS) or dry etching, where complex objects such as chemical vapor deposition (CVD) systems are required. MAWCE provides good control of the nanowire diameter, length, and crystal orientation. The geometry of the manufactured silicon 14

nanowires can be controlled during the manufacturing process. Since the cross section of the obtained Si nanowires is determined by the noble metal film, it can be precisely controlled using various methods of applying the metal film. The height of Si nanowires can be controlled by the etching time. As for the characteristics of the Si nanowire material, such as the crystal orientation and the concentration of the dopant, they are essentially the same as in a silicon substrate. However, in the way of growth of SLS, the crystal orientation of silicon nanowires depends on the diameter of the nanowires [24]. MAWCE allows you to make silicon nanowires vertically to the substrate. The growth direction of silicon nanowires grown by epitaxy (100) of the substrate using the SLS method is not vertical to the substrate. The quality of weakly doped Si nanowires made by MICE is very high. MAWCE can be used to produce anisotropic high elongation of weakly alloyed Si nanowires, without any damage to the lattice. For comparison, dry etching methods, such as deep reactive ion etching (DRIE), lead to jagged and inclined surfaces, and also cause defects in etched Si nanowires [25, 26]. In work [27], theoretical assumptions are made in some particular cases of electric current passing in semiconductor silicon nanowires. It is possible to use silicon nanowires as a field-effect transistor and increase the conductivity up to ~20 times using chemical modification of the SiOx surface [28]. When silicon is oxidized, the lattice periodicity is distorted, thus forming scattering centers for charge carriers. Therefore, scattering from defects becomes unavoidable and estimation of the limited transport of charge carriers is necessary. However, in a certain period of applied stress, the oxidation of surface atoms does not significantly change the transport properties of the nanowires. The researchers propose interesting theoretical models of both electronic and phonon transport in disordered and nanostructured semiconductors in both porous and filamentous materials, in which the conductivity is determined only by the properties of the conductor [29]. The beginning and development of this widespread theory can be found in the works of Landauer [30-32], Dates [33-35], and application in the work of Lundstrom [36]. In the Landauer-Datta-Lundstrom 15

model, the conduction channel is characterized by the density of States D(E-U), where E is the energy of the conductor States, and U is the self – consistent electrostatic potential of the gate, which allows the state to be shifted up or down the energy scale (figure 5).

Figure 5 – A typical electronic device with contacts characterized by flight times τ [29].

Figure 5 shows two ideal contacts that can quickly restore equilibrium in the process of electronic transport and are characterized by Fermi functions 𝑓𝑓� �𝐸𝐸� �

1 1 , 𝑓𝑓� �𝐸𝐸� � , 𝐸𝐸 � 𝐸𝐸�� 𝐸𝐸 � 𝐸𝐸�� exp � exp � ��1 ��1 𝑘𝑘𝑘𝑘 𝑘𝑘𝑘𝑘

(3)

where and – electrochemical potential. When the voltage V is applied, the decreases relative to the potential by a value of qV. The fly-by time τ gives an idea of how quickly electrons can leave the contact or conductor. For example, for nanoscale resistors and molecules, the flight time is controlled by the properties of the contacts. Since the quality of the two contacts may be different, the flight time for the two contacts has different values τ1, τ2. For convenience, the flight time can be expressed in units of energy . In the case of a single molecule as a conduction channel, γ acquires a simple physical meaning of broadening the energy levels of the molecule due to the finiteness of the electron lifetime at the molecular levels [29]. The communication channel has a zone structure, but this is not a mandatory condition [34]. The Landauer-Datta-Lundstrom model also considers electron and current densities in a conductor, Fermi distribution and electrochemical potentials, and densities of conductor states. 16

To begin with, if we consider a single contact with the conduction channel, in accordance with the electrochemical potential of EF1, it tries to replenish the conductor with electrons. As a result, when the number of electrons with energies between E and E+dE becomes equal, an equilibrium state is established between the conduction channel and the contact. (4) where D(E) means the density of States with energy E, f1(E) is the equilibrium Fermi function of the first contact. The process of establishing an equilibrium state between the first contact and the conduction channel is described by the kinetic equation (5) If the number of electrons in the conduction channel N’ is less than the equilibrium value , the rate of electron delivery dN’/dt to the conduction channel is positive, if more, then negative. If the second contact is connected to the conduction channel, equations (4) and (5) will be analogous. For simultaneous connection of a conduction channel with two contacts, the equation has the following form: .

(6)

For dynamic equilibria, the left side of the kinetic equation (6) is zero, and for the number of electrons in the conduction channel, we get: .

(7)

If we simplify equation (7) by equating , then the equation for the number of electrons in the conduction channel in differential form can be written as follows: (8) 17

By integrating over the entire energy spectrum, it is possible to obtain the number of electrons in the conduction channel at the dynamic equilibrium of two contacts with electric potentials and . The difference in these potentials is proportional to the voltage applied to the ends of the conductor: (9) For one-dimensional, two-dimensional, and three-dimensional conduction channels, the state density is proportional to the length L, area A, and volume of the conductor Ω: (10)

Figure 6 – Electronic transport in diffusion mode through a conductor of length L and cross-sectional area A. The traditional sign convention is used: the current I and the direction of electron motion are opposite [29].

As a result of the Landauer-Datta-Lundstrom model, the author of work [29] obtained two basic equations for electronic transport:

(11)

18

The above equations (11) express: the first – the number of electrons in a conductor in a dynamic equilibrium state through the density of states and Fermi functions; the second-the current through the time of flight and through the same characteristics that determine the number of electrons. You can also calculate the number of modes in two-dimensional conductors: (12) where

– valley degeneration [37]; – width of the conductor; – length of de Broglie wave.

Figure 7 – Comparative behavior of the density of States D(E) and the number of modes M(E) for one-dimensional, two-dimensional, and three-dimensional conductors [29].

In general, equation (12) shows how many de Broglie half-waves of energy E fit across the width of a two-dimensional conductor. The behavior of the density of states D(E) and the number of modes M(E) for one-dimensional (1D), two-dimensional (2D), and threedimensional (3D) conductors is shown in figure 7. If we consider the diffusion mode of conductivity, the specific surface conductivity of a long two-dimensional conductor does not 19

depend on the width W and length L of the conductor, and for short conductors it may depend. At the same time, for narrow conductors, the conductivity increases stepwise depending on the width of the conductor. The understanding of ballistic mobility was introduced by Schur [38] and is used in subsequent studies in the analysis of various devices [39, 40]. (13) (14) Equations (13) and (14) show ballistic and diffusion mobility. It can be seen that in diffusion mobility only the length of the ballistic mobility is replaced by the average length of the free run.

Figure 8 – Volt-ampere characteristic of single-wall carbon nanotubes in metal mode at three different temperatures [41].

Figure 8 shows a nonlinear volt-ampere characteristic of a carbon nanotube, where there is a linear section corresponding to a conductivity of 22 uS in small voltage offsets. According to estimates, the average free path gives =167 nm, which is much less than the physical length of the nanotube (1mkm) used in the experimental work. Accordingly, in such nanotubes, the transport is diffusive [29]. 20

Obtaining porous silicon and silicon nanowires and methods for measuring electrical characteristics Porous silicon (PS) is a material with a porous structure that can be formed by anodic electrochemical etching of monocrystalline silicon in electrolytes containing hydrofluoric acid (HF). There is also a method of chemical etching, which does not use the influence of an external electric field. In this paper, we applied these most common methods in the production of silicon nanowires and porous silicon. Although the PS was discovered in the late 50s of the XX century, significant interest in it was aroused only 30 years later due to the discovery of its unique optical properties, in particular, photoluminescence. Today, due to its unusual physical properties, the PS is considered a fairly promising material for modern semiconductor electronics. Electrochemical etching has three modes: galvanostatic (etching at constant current), potentiostatic (etching at constant voltage) and combined. An anode in the form of a silicon plate is placed in an electrochemical cell of the fluoroplast (figure 9). The electrolyte is a chemical liquid containing hydrofluoric acid (HF) and various organic additives. The cathode is a stable material to hydrofluoric acid (platinum, ultra-pure silicon).

Figure 9 – Etching mechanism [91].

21

a) b) Figure 10 – Micrographs of PS film obtained by scanning electron microscopy. a) – top view, b) – cross-section view

Figure 10 shows the results of scanning electron microscopy of the PS sample. The sample was obtained by electrochemical etching at a constant voltage of 10 V and a current of 15 mA. The etching time was 20 seconds. Ready-made p-n structures were used as the initial substrate, where the thickness of the p and n layers was 300 um and about 300 nm, respectively. At the same time, the n layer was strongly doped, its concentration was 1019cm-3. As can be seen from figure 10, the pore diameter has the order of 10 nm, and the order of the thickness of the porous film is about 250 nm.

a) b) Figure 11 – Results of scanning probe microscopy. a) two-dimensional image of the PS film, resolution 40:40 um; b) three-dimensional image of the PS film, resolution 40:40 um

In the course of this work, the morphology of the obtained films was studied using NTegra Therma scanning probe microscopy (SPM). 22

According to the SPM results, there is a strong heterogeneity of the PS film surface (figure 11). You can also notice that there are wirelike protrusions on the surface of the film [91]. Silicon nanostructures with different morphologies and properties can be manufactured at different ambient temperatures, with different deposition times on the catalyst surface and in different concentrations of etching fluids, as well as with different surface orientations of the substrate and doping levels. Crystalline   silicon 

SiNWs 

 

Figure 12 – Block diagram of the metal-induced chemical etching method.

Figure 12 shows a detailed block diagram of the MAWCE method used in this work. The method consisted of three stages: application of the catalyst to the surface of the substrate in the form of AgNO3 solution: HF, the process of chemical etching in a solution of H2O2: HF time of 40 minutes and removal of metal residues using HNO3 solution. As a result, samples of silicon nanowires were obtained. The initial substrate was a p-type boron-doped crystalline silicon with a charge carrier concentration of 1015 cm-3, a thickness of 300 um, and a plane direction (100). The surface resistance of the substrate was 10 Ohm mm2. Certain metal contacts were applied to the surface of the obtained samples. In this work, to measure the electrical properties, were obtained ohmic contacts, which were applied to the surface of samples in the” clean room “ of the Polytechnic Institute by Rensselaer sputtering method. The contact thickness was approximately 370 nm, where the thickness of the titanium layer is 20 nm, aluminum 300 nm and Nickel 50 nm. Figure 13 shows metal contacts on the surface of a silicon film with a porous structure. The contacts were of two different diameters. The same contact structure was used for silicon nanowires. 23

Figure 13 – Metal contacts on the surface of porous silicon and crystalline silicon.

There are several design considerations for measuring the signal quality in silicon nanowires (for example, changing resistance) and increasing the signal-to-noise ratio: The silicon nanostructures must be low-alloyed; The consistent resistance of the substrate must be kept to a minimum; The contact resistance between the silicon nanostructures and the metal electrodes should be kept to a minimum. That is, the contacts between the silicon nanostructures and the metal electrodes must be ohmic. For vertically positioned silicon nanostructures, the metal electrodes must be connected to the two ends of the silicon nanowires in such a way that the resistance of the silicon nanowires can be measured electrically. The metal electrode should be in full contact with the tip of the silicon nanowire, while the two electrodes should not be in contact, which could lead to a short circuit. To meet these requirements, there is a design of surface-contact structures, as shown in figure 14. 24

Figure 14 – Diagram of electrical contacts with vertically oriented Si nanowires: surface contact.

The measured resistance in a closed loop is the total resistance Rtotal = RNW + RSUB + RC1 + RC2,

(15)

where RNW and RSUB are the resistances of the nanowires and the substrate, and RC1 and RC2 are the contact resistances between the nanowires and the metal electrodes. To maximize the signal-to-noise ratio, RSUB, RC1, and RC2 must be kept to a minimum. To overcome the limitations of existing approaches in the manufacture of electrical contacts on the top of the sample (silicon nanostructures and PS), a suitable technique was used in this study. Ion deposition was used to apply a metal film of metal on the top of the sample. The diagram is shown in figure 15.

Figure 15 – Scheme of the ion sputtering method for obtaining surface contact.

As shown in figure 15, the metal is deposited on the sample in a vacuum chamber. A shadow mask with a diameter of 1 mm is placed just above the sample. Thus, the metal can be deposited and accumulated on the test sample without getting on the substrate.

25

Table 3 Technical characteristics and appearance of the analyzer Agilent 4156B Precision Semiconductor Parameter Analyzer Technical parameters

Values

Range of operating currents

±100 fA to ±100 mA

Operating voltage range

0 V to ±100 V

Software

Desktop EasyEXPERT software

Appearance

Measurement error

From 10 pA to 10 nA is ±12% From 100 nA to 100 mA is ±2.5%

Measurements of the volt-ampere characteristics of nanostructured films were performed using the Agilent 4156B Precision Semiconductor Parameter Analyzer (table 6) and the NI ELVIS II+ universal station volt-ampere analyzer (table 4). Table 4 Technical characteristics and appearance of the analyzer of volt ampere characteristics of the universal station NI ELVIS II+ Appearance

Technical parameters

Values

Range of operating currents

±40mA.

Operating voltage range

– 10 V to + 10 V.

Software

LabVIEW

The minimum increment of base current

0.48 uA

A precision LCR Meter E4980A (table 5) was used to measure capacitance-voltage characteristics, impedance, and frequency dispersion. 26

Table 5

Technical characteristics and appearance of the precision meter LCR Meter E4980A Technical parameters

Values

Operating frequency range

from 20 Hz to 2 MHz

The basic error of measurement

0,05%

High-speed measurements

5,6 ms

Software

LabVIEW

Appearance

In the LabVIEW software environment, an interface was developed for automating measurements and recording with subsequent processing of numerical data (figure 16). The interface consists of a front panel and a chart block. In the block diagram, the program is developed in graphical form. The front panel shows variables and a graphical representation of the results. The front panel and the chart block are synchronized with each other. Also, the front panel additionally displays numerical data of the results. Experimental measurement data is transmitted to a personal computer from a semiconductor analyzer. Numerical data of voltage and current are also recorded in a text file, from where we can carry out further data processing. The LabVIEW graphical programming environment was also used to control the impedance measurement process. A user interface was developed for automating the measurement and a corresponding block diagram that displays the source code of the program. This program was used to measure the volt-Farad, frequency characteristics, and time changes in the electrical properties of nanostructured porous silicon and silicon nanowires. During the measurement, the samples were placed in a special dark box to isolate them from sharp external disturbances. The measured signals are sent to the computer via the communication port. All commands and measurement parameters are set on the front panel, the source code for changing the interface is located in the block diagram of the virtual instrument. 27

Figure 16 – Interface of the LabVIEW program for measurement and signal processing.

Experimental results and discussion of the electrical characteristics of porous silicon For a detailed understanding of the processes occurring in nanofilms, it is necessary to know the physical basis of electrical phenomena in them. The electrical properties of nanofilms themselves can have immediate practical applications. For example, porous silicon nanofilms can be used, along with semiconductor diodes, to produce chaotic, broadband, high-frequency oscillations in electronic circuits. The hierarchical structure of the nanofilms can create a set of potential barriers of the electric field. Theoretical and experimental studies of electron tunneling processes in multi – barrier structuressuperlattices with specified regular forms of potential distribution are known [92]. It is noted that the tunneling process is also resonant: electrons whose energy is close to the barrier’s own quantum energy levels pass through the potential barrier. If the structure of the barriers is not strictly ordered, for example, fractal, then the proper energy levels are unknown, and the resonant effect is difficult to distinguish. This is necessary to estimate the intensity of electron transmission by the barrier. 28

For this purpose, it is interesting to study the process of electron tunneling in nanofilms with a fractal, cluster structure, where the structure of the potential barrier is complex. First, the electrical properties of a porous silicon nanofilm were investigated. Figure 17 shows the change in the current I passing through nanoscale silicon structures by the voltage V applied to different structural surfaces (Me/porous Si/n-Si) of the thin film. The voltage characteristic depends on how the voltage is applied: with a sequential increase in its absolute value, or with a decrease. After passing a current whose strength is about 0.5 mA, the structure and properties of the nanowires change, in particular, the electrical resistance of the nanowires increases. As a result, when the same absolute value is applied again, the current strength will be less than in the original case. This can be seen from figure 17, which is obtained when applying a voltage from-7 V to +7 V in increments of 0.9 V. This pattern is observed with repeated measurements (10 in total). After the equilibrium state is established, the initial electrical properties of the nanowires can be restored, but after a long time, the surface of the film can again change its electrical properties due to the oxidation. The next feature of the volt-ampere characteristic of the nanostructured film is the decrease in current strength with an increase in voltage in several local areas (figure 17). This effect is described by introducing the concept of negative resistance, the physical essence of which is the resonant tunneling of electrons through a potential barrier. In contrast to the results of modern studies of nanostructures [92, 93], several potential barriers are present in porous silicon (of a single substance), resulting in an oscillation of the volt-ampere characteristics [94]. Usually, multi-barrier tunneling of electrons is observed in heterojunctions. The multi-barrier nature of quantum-sized structures disappears after the passage of a significant current, since their structure is somewhat leveled. This result means that potential barriers in quantum wires are formed not by contact transitions, but by non-equilibrium distributions of charge carriers in the wire itself. Indeed, if the current at U0). Some asymmetry when U>0, U>1 (τ is the characteristic relaxation time of the electron pulse in the HEMT channel), and a non-equilibrium mode (ωτ