Semiconducting Chalcogenide Glass II Properties of Chalcogenide Glasses SEMICONDUCTORS AND SEMIMETALS Volume 79
Semiconductors and Semimetals A Treatise
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Semiconducting Chalcogenide Glass II Properties of Chalcogenide Glasses SEMICONDUCTORS AND SEMIMETALS Volume 79 ROBERT FAIRMAN B e a v e r t o n , OR, U S A
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Contents LIST OF CONTRIBUTORS PREFACE
Chapter 1 Information Capacity of Condensed Systems M. D. Bal'makov 1.
EXACT COPY
2
2.
DESCRIPTION IN THE FRAMEWORK OF THE ADIABATIC APPROXIMATION
5
3.
ESTIMATIONOF THE NUMBER OF DIFFERENT QUASICLOSED ENSEMBLES
4.
DEFINITION OF A QUASICLOSED ENSEMBLE
10
5.
CONCLUSION
11
REFERENCES
13
Chapter 2
8
Charge Carrier Transfer at High Electric Fields in Noncrystalline Semiconductors
A. Cesnys, G. Ju~ka a n d E. M o n t r i m a s 1.
INTRODUCTION
15
2.
CHARGETRANSFER IN NONCRYSTALLINESELENIUM AND A s - S e SYSTEM THIN FILMS
17 17
2.1. Amorphous Selenium Electrical Conduction Dependence on Impurities 2.2. Temperature and Electric Field Dependencies of Charge Carrier Drift and Micromobility 2.3. Multiplication Effect in Amorphous Selenium 2.4. Influence of Chemical Composition on Charge Transfer in As-Se System Thin Films 2.5. Space Charge Formation and Distribution in As-Se System Thin Films
3.
ELECTRICALCHARGE TRANSPORT IN NONCRYSTALLINEGa(OR I n ) - T e SYSTEMS STRUCTURES
19 20 24 30
3.1. A Variety of Electrical Conductivity in Barrier-less Structures 3.2. Nonactivated Electrical Conduction State 3.3. Electrical Characteristics of Barrier Structures
39 39 46 50
REFERENCES
52
Contents
vi
Chapter 3
The Nature of the Current Instability in Chalcogenide Vitreous Semiconductors
57
Anclrey S. G l e b o v 1.
INTRODUCTION
57
2.
CURRENT CHANNELS IN CVS-BASED SWITCHES
58
2.1. Models of Generation of Current Channels at Presence of Drift Barriers in CVS 2.2. Dimensional Effects in CVS-based Switches
71
3.
THE KINETIC MODEL OF THE CURRENT INSTABILITY AT THE PRESENCE OF THE CURRENT CHANNEL
77
4.
EXPERIMENTALCONFIRMATION OF THE KINETIC MODEL OF THE SWITCHING EFFECT
85
4.1. Influence of CVS Composition on Functional Characteristics of Switches 4.2. Dependence of Electro-physical Parameters of Switches from Temperature and Pressure 4.3. Influence of Synthesis and Thermal Treatment Conditions on Physical-Chemical Properties of Glasses and Electrical Parameters of Mono-stable Switches
85 97 105
REFERENCES
109
Chapter 4
Optical and Photoelectrical Properties of Chalcogenide Glasses
67
115
A. M. Andriesh, M. S. Iovu a n d S. D. S h u t o v 1.
OPTICAL PROPERTIES OF CHALCOGENIDE GLASSES
1.1. The Reflectivity Spectra of Chalcogenide Crystals and Glasses: Electron States
1.2. The Absorption Edge in Amorphous Chalcogenides 1.3. Photo-induced Absorption 2.
PHOTOELECTRICALPROPERTIES OF AMORPHOUS CHALCOGENIDES
2.1. Steady-state Photoconductivity 2.2. Transient Photoconductivity 3.
115 116 121 138 149 149 168
3.1. Chalcogenide Glasses for Integrated and Fiber Optics Application
179 179
REFERENCES
193
CHALCOGENIDE GLASSES IN PHOTOELECTRIC INFORMATION RECORDING SYSTEMS
Chapter 5
Optical Spectra of Arsenic Chalcogenides in a Wide Energy Range of Fundamental Absorption
201
V. Val. S o b o l e v a n d V. V. S o b o l e v 1.
INTRODUCTION
201
2.
THE GENERAL CONSIDERATION OF OPTICAL SPECTRA AND ELECTRONIC STRUCTURE THEORY
202
3.
MEASUREMENTTECHNIQUES AND DETERMINATION OF SPECTRA OF OPTICAL
FUNCTIONS AND DENSITY OF STATES DISTRIBUTIONN(E)
204
4.
OPTICAL SPECTRA OF oL-As2S3
205 205
4.1. Calculations of Sets of Optical Functions 4.2. Decomposition of Dielectric Function Spectra and Characteristic Electron Loss Spectra
into Elementary Components 5.
OPTICAL SPECTRA OF g-As2Se3 5.1. Calculations of Sets of Optical Functions 5.2. Decomposition of Dielectric Function Spectra and Characteristic Electron Loss Spectra
6.
OPTICAL SPECTRA OF g-AsxSe~-x (x = 0.5, 0.36) 6.1. Calculations of Sets of Optical Functions
into Elementary Components
208 212 212 217 219 219
Contents
vii
6.2. Decomposition of Dielectric Function Spectra and Characteristic Electron Loss Spectra
into Elementary Components
7.
OPTICALSPECTRA OF g-AszTe3
7.1. Calculations of Sets of Optical Functions 7.2. Decomposition of Dielectric Function Spectra and Characteristic Electron Loss Spectra into Elementary Components 8.
222 224 224 226
CONCLUSION
227
REFERENCES
227
Chapter 6 Magnetic Properties of Chalcogenide Glasses
229
Yu. S. Tver'yanovich 1.
MAGNETISMOF CHALCOGENIDE GLASSES NOT CONTAINING TRANSITIONAL METALS 1.1. Problems of Physicochemical Analysis of Glassy Systems 1.2. Dorfman's Method
2.
MAGNETISMOF GLASS-FORMING MELTS
1.3. Application of Magneto-chemistry for PCA 2.1. Magnetism of Chalcogenide Glasses at Heating 2.2. Melts 2.3. Magnetism of Melts with Low Conductivity 2.4. Semiconductor-Metal Transition in Chalcogenide Melts 2.5. Metallized State 2.6. Dependencies of Magnetic Susceptibility of Chalcogenide Melts on Composition and Temperature 2.7. Semiconductor-Metal Transition and Glass-Forming Ability of Chalcogenide Melts 3.
CHALCOGENIDEGLASSES CONTAINING TRANSITIONAL METALS
3.1. The Degree of Oxidizing of Transitional Metals in Chalcogenide Glasses 3.2. The Model of Magnetism of Glasses Containing Transitional Metals 3.3. The Results of the Investigations of Magnetic Properties of Chalcogenide Glasses, Containing Transitional Metals 3.4. Using of the Result of Magneto-chemical Investigations at the Modeling of Electrical Properties of Chalcogenide Glasses, Doped with Transitional Metals 4.
MAGNETICPROPERTIES OF GLASS-FORMING CHALCOGENIDE ALLOYS AT MELTING
4.1. Equation Using Results of Magnetic Experience for the Calculation of Liquidus 4.2. System AseSe3-MnSe 4.3. Liquidus for Other Chalcogenide Systems Doped with Transitional Metals
229 229 230 231 232 232 235 235 238 243 244 247 248 249 249 257 265 266 266 269 270
REFERENCES
274
INDEX
277
CONTENTS OF VOLUMES IN THIS SERIES
285
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List of Contributors
A. M. ANDRIESH (115), Center of Optoelectronics of the Institute of Applied Physics,
Academy of Sciences of Moldova, Str. Academiei 1, MD-2028 Chisinau, Republic of Moldova M. D. BAL'MAKOV (1), Chemistry Department, St. Petersburg State University, Universitetskii pr. 26, 198904, St. Petersburg, Russia A. CESNYS (15), Vilnius Gediminas Technical University, LT-10223, Vilnius, Lithuania ANDREY S. GLEBOV (57), Riazan State Radiotechnology Academy (RSRTA)
Center of Optoelectronics of the Institute of Applied Physics, Academy of Sciences of Moldova, Str. Academiei 1, MD-2028 Chisinau, Republic of Moldova G. JUSKA (15), Vilnius University, LT-O1513 Vilnius, Lithuania
M. S. Iovu (115),
E. MONTRIMAS (15), Vilnius University, LT-O1513 Vilnius, Lithuania
Center of Optoelectronics of the Institute of Applied Physics, Academy of Sciences of Moldova, Str. Academiei 1, MD-2028 Chisinau, Republic of Moldova V. V. SOBOLEV (201), Udmurt State University, 426034 Izhevsk, Russia V. VAL. SOBOLEV (201), Udmurt State University, 426034 Izhevsk, Russia Yu. S. TVER'YANOVICH(229), Department of Chemistry, St. Petersburg State University, Petrodvorets, Universitetsky pr. 26, 198504 St. Petersburg, Russia S. D. SHUTOV (115),
ix
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Preface
Volume 79, "Semiconducting Chalcogenide Glass II" of the series Semiconductors and Semimetals, follows up on the topics raised in Volume 78, "Semiconducting Chalcogenide Glass I," including the problems of glass formation, chalcogenide vitreous semiconductor structures, as well as the structural impacts caused by external conditions. With the help of chalcogenide glasses, optical information recording, storage, and reproduction have found widespread use. Progress in this field has resulted from experimental studies and theoretical comprehension of microscopic mechanisms of information copying and recording. In Chapter I of this volume, the information capacity of condensed systems of semiconducting chalcogenide glasses is considered in non-equilibrium states, both in bulk or thin-film form, and as obtained by evaporation or chemical deposition methods. This chapter is a significant contribution to the theoretical research of informational aspects of non-crystalline substances' structures, including their relaxation in the processes of external impacts and in the storage and reproduction of information with the assistance of non-equilibrium systems, particularly in chalcogenide glass systems. The theory of disordered systems, to which glasses belong, remains uncompleted. Further progress in this field appears to be impossible without the use of radically new approaches such as information theory methods. Special attention is concentrated in glass physics on the glass transition process, which is a non-equilibrium process and is still incompletely studied; information plays an important role in physical non-equilibrium processes, and further attention would benefit our understanding. The data presented in this chapter illustrates the promise of further research of the informational aspect of the formation mechanism of nonequilibrium structures for the further development of vitreous matter physics, and condensed matter physics in general. One of the most important properties for semiconductor materials in general, and chalcogenide vitreous semiconductors in particular, is the characteristic of the charge carrier transfer in strong electric fields. The contributors of Chapter 2 have reviewed the theoretical and experimental data and they describe the results of experimental xi
xii
Preface
investigations and theoretical comprehension of vitreous selenium, materials of the A s - S e systems, and the significantly less-studied Ga-Te and In-Te systems. The materials' electrical properties are examined under the influence of chemical composition, degree of impurity, and electric field strength. The contributors' interpretations are provided with a particular focus on the multiplication effect, nonactivated conductivity, and space charge formation. The above problems are physically connected with the problem of the current instability in semiconducting chalcogenide glasses, which are described in Chapter 3. This problem is especially important due to the direct relationship between the creation of electrical switches and re-programmed memory devices based on semiconducting chalcogenide glasses. On the basis of the fundamental experimental investigations, the contributor criticizes the static approach that is typical for the thermal and electrothermal models of current instability. Proposed instead is a kinetic model, in which positive current feedback, which is required for the development of the current instability process, is created by two sources of increasing electrical conductivity: the thermal heating in the strong field and the formation of conducting areas in the semiconductor during the formation of quasi-molecular and quasi-atomic defects. The kinetic model of current instability connects threshold characteristics of semiconducting chalcogenide glasses with their electrical parameters, and provides for the role of thermal and field effects during switching. From a physical standpoint, there is no doubt that the most important and interesting properties of chalcogenide glasses are their optical and photoelectrical properties. Experimental investigations and theoretical comprehension of these properties have led to the use of chalcogenide glasses in such systems of the optical information registration as vidicon devices, electrophotography, photothermography, space-time light modulation, and liquid crystal systems, as well as optical fibers and thin-film waveguides. Investigations of optical properties near the absorption edge are of a special interest. The absorption edge is sensitive to the chemical composition and the material structure, as well as to external factors such as electric and magnetic fields, the thermal, optical, electronic and other radiations. Under the influence of these factors, optical parameters of semiconducting chalcogenide glasses get changed reversibly or irreversibly. All these issues are described in Chapter 4. Special attention is concentrated on problems of the steady state and transient photoconductivity, as well as on physical processes that take place in the photoelectric information recording systems that are based on chalcogenide glasses. Problems regarding the usage of the unique properties of chalcogenide glasses in integrated and fiber optics are also analyzed in this chapter. Addressed here are the properties of chalcogenide glasses to combine unique capabilities of the optical images' phase recording, including holograms, with a high-resolution capability to create strip waveguides based on thin-film waveguides, as well as grating structures and other functional elements of integrated optics. In Chapter 5, the optical spectra of arsenic chalcogenides, which are widely used in electronics, are reviewed in detail. The reflectivity and the optical spectra of glasses in a wide energy range are considered simultaneously with the electronic structures of semiconducting glasses, which are themselves one of the most fundamental problems of the non-crystalline state. The goal of this chapter is to review new information on
Preface
xiii
the complete set of the fundamental optical parameters of chalcogenide glasses in the range of the most intensive transitions, 0 - 3 5 eV. Chapter 6 reviews the magnetic properties of chalcogenide glasses and their melts, both with and without transitional metals. Several fundamental scientific problems which emerged during investigations of vitreous semiconductors are considered here. The significant contribution to solve these problems has been made by magneto-chemical methods of investigations, as proposed by N.S. Kurnakov. These methods are aimed to determine the relationship between physical-chemical properties of systems, in this case, the chalcogenide glass-forming systems, as well as the systems' chemical compositions and structures. These methods have been a significant contribution in the efforts to resolve the fundamental problems discussed above. V.S. Minaev Editor-compiler
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CHAPTER 1 INFORMATION CAPACITY OF C O N D E N S E D SYSTEMS M. D. B a l ' m a k o v CHEMISTY DEPARTMENT,ST. PETERSBURGSTATE UNIVERSITY,UNIVERSITETSKIIPR.26, 198904, ST. PETERSBURG, RUSSIA
Informational aspects of physical processes are now becoming a subject of basic research (Kadomtsev, 1994, 1995, 1997/1999; Kadomtsev and Kadomtsev, 1996). Many of these are based on ideal imaginary experiments with a single particle which may be a particle of an ideal gas, a Brownian particle, etc. Naturally, condensed systems are equally interesting. The practical side of this problem is associated with the urgent necessity to develop the scientific basis of nanotechnology (Yoffe, 1993; The 2nd International Conference on Chemistry of Highly Organized Substances and Scientific Principles of Nanotechnology, 1998), which would specifically make it possible to obtain functional elements of microelectronics of nanometer scale. In principle, investigation of the informational aspect of the formation mechanism of nonequilibrium structures is a logically unavoidable stage in the further development of condensed matter physics. The problem of copying acquires a special significance because of the necessity to prepare numerous identical nanostructures. Its essence consists in the development of processes capable of yielding systems that would be exact copies of the initial system (Bal' makov, 1996). The informational aspect of the copying problem is closely related to the task of determining the maximum large amount of information that could be recorded and preserved over a long time interval tma x in a system containing M atoms. One can easily become convinced that the copying is a specific case of information recording. It may be argued a priori that if M is finite the amount of recorded information, I is also finite. Furthermore, all other conditions being equal, the numerical value of I increases linearly with respect to M. The amount of information increases in an analogous manner as the number of printed characters in the text grows (Kadomtsev, 1994). Therefore, the value of I is enclosed in the interval 0 <-- I <-- Mfi(tma• n)/ln 2,
(1)
where/3(trnax, n) is the specific informational capacity; the components of the vector n are the relative concentrations nl of atoms of each species which form the system under consideration, Y'l n l - 1; the amount of information I and /3(tmax,n) are expressed in E-mail address:
[email protected] Copyright 9 2004 Elsevier Inc. All rights reserved. ISBN 0-12-752188-7 ISSN 0080-8784
2
M.D. Bal'makov
bytes and nats, respectively (Kadomtsev, 1994); the transition from one type of unit to another is done using the factor In 2. The magnitude I is taken to mean the amount of memorized information which is also called macroinformation. It is this term that is meant in information science, usually omitting the prefix 'macro'. An alternative is microinformation, which is the choice of one of the possible variants which is in principle not memorized by the system. Apparently, an ideal gas does not 'remember' the choice of one of the microstates because of the permanent chaotic motion of its constituent particles. The numerical values of I from interval (1) may be varied using definite technical means. In contrast, the upper limit of Mj3(tmax, n ) / l n 2 of this interval is independent of such means, since the function ~(tmax, n) is determined by fundamental equations of quantum theory. But by which equations and how? What is the precise upper limit L(I)(tmax) = sup ]3(tmax, n)
(2)
n
of values of the function fl(tmax,n ) for condensed systems of possible chemical compositions n? By how much will the time tmax of information preservation be reduced upon action of the external perturbation W? Hereafter, l}" is considered to mean the perturbation operator used in conventional quantum mechanics (Landau and Lifshitz, 1977). It can also be the 'measurement' operator in the generalized Schr6dinger equation that considers the informational connection of the system with the outer world (Kadomtsev, 1994). In the general case, the operator is random (Kadomtsev, 1994), and this should be borne in mind when trying to answer the questions listed above. The macroinformation I (Eq. (1)) memorized by the system is a macroscopic concept. However, its maximum possible amount proportional to/3(tmax, n) (Eqs. (1) and (2)) is determined by microscopic parameters. This is not surprising because a sufficiently large number of microscopic states correspond to each macroscopic state. They form a quasiclosed ensemble which is given a mathematical definition in Section 4.
1. Exact Copy All elementary particles of the same kind (e.g., all electrons) are indiscernible in view of the principle of identity of microparticles (Blokhintsev, 1961). The same may also be said about isotopes of the same kind. It is not problematic to make protium isotopes form hydrogen molecules which are exact copies of each other. ~ The situation is radically changed as the number M of atoms forming the system increases. As a rule, it is impossible to get an exact copy of a macroscopic [M >> 104 (Kittel, 1977)] system using conventional physical and chemical methods. Glasses of ~Evidently, exact copies are systems whose wave functions are identical. However, the identity of wave functions is a very rigorous requirement. Their collapse is induced even by a minor interaction (Kadomtsev, 1994). For this reason, it is advisable to take exact copies to mean systems whose dynamics, including collapses, are described in the framework of the same quasiclosed ensemble. In this case, two hydrogen molecules will be regarded as exact copies even when, for example, their rotatory wave functions (Landau and Lifshitz, 1977) are different.
Information Capacity of Condensed Systems
3
the same chemical composition synthesized in absolutely identical conditions of heating and nonequilibrium cooling of the melt have virtually the same macroscopic properties but they are not exact copies of each other. The point is that it is rather difficult to repeat absolutely exactly the specific mutual disposition of structural fluctuations fixed upon glass transition. Indeed, as a result of each glass transition, which is a nonequilibrium transition from the liquid to the vitreous state, one of the structural modifications realized in the liquid is frozen (memorized by the system). Let it be the i-th modification (Fig. 1). Certainly, next time this will be another, e.g., the k-th modification, but again it is the only one. Despite the identity of their macroscopic properties (internal energy, refractive index, density, etc.), these modifications are not exact copies of each other since, as seen from Figure 1, it is impossible to make the coincident superimposition of the disordered ith atomic network on the kth one. If one bears in mind that a virtually infinite number of such modifications exist, then each time the process of glass transition will most probably result in structural modifications different from the preceding ones. Consequently, nonequilibrium cooling of the melt cannot yield even two macrosamples of glass which are exact copies of each other. Thus, in order to perform copying, it is not sufficient to have the required elements of the Mendeleev periodic table. This process also requires the information which was memorized by the initial system and is indispensable for the purpose of copying. Such situations are considered in relation to so-called chemical-informational synthesis (Aleskovski, 1996). When solving the problem of copying, it is necessary in the first place to reproduce the required structure because the information about individual features of a polyatomic system is eventually stored in the mutual disposition of its atomic nuclei. In the framework of classical physics each structural modification (see Fig. 1) is set by the vector R = ( r l , r2, . . . r i , . . . r M ) ,
(3)
'where ri are the radius vectors of all atomic nuclei of the system. But the atomic nucleus is not a mathematical point whose position is unambiguously determined by the vector ri.The motion of microparticles is not characterized by the trajectory ri(t) (Landau and Lifshitz, 1977). One can speak solely about the sites of their localization. In the case of 0
0 0
9
9 0
0
0
9
0
0 0
9 0
i-th modification
0
0 9
0
0
0
0
9
0 9
9
0 9
0
0
9
9
9 0
k-th modification
FIG. 1. Disordered atomic networks (structural modifications i and k) which are not exact copies of each other. The sites of localization of atomic nuclei of different species are denoted by 0 and O, respectively.
4
M.D. Bal'makov
condensed systems the size of the sites of atomic nucleus localization is much smaller than the interatomic distances and is a tenth-hundredth of an angstrom (Vainshtein, 1956). Therefore, one of the ways to make a brief (Bal'makov, 1996) quantum-mechanical description of the structure R consists in setting the coordinates ri (Eq. (3)) of the centers of these sites. As a rule, numerous quantum states forming a quasiclosed ensemble correspond to each memorized macrostate (to each structural modification of R~; see Fig. 1). This raises the question about the number G of different quasiclosed ensembles. It is useful to know G not only in relation to the copying problem. It is the magnitude of (lhG)/ln 2 that determines the exact upper limit of possible values of the amount of information I (Eq. (1)) since the recording of information consists in its essence in realization of the memorized choice of a single variant of the G possible ones. In order to find the numerical value of G, it is necessary to consider primarily the problem of distribution of quantum states over different quasiclosed ensembles. Some of these are formed by the microstates corresponding to one of the free energy minima. The latter holds only for stable and metastable systems (Bazarov, 1983). In the overwhelming majority of cases, however, we are dealing with nonequilibrium systems, the thermodynamic potentials of which are far from being extreme. Thus, structural modifications of the vitreous state (see Fig. 1) are not characterized by the Gibbs energy minimum. Each of them is described by its intrinsic quasiclosed ensemble. Their macroscopic properties are invariable because a quite definite structural modification corresponds to each ensemble. It is for this reason that glasses are kinetically frozen nonequilibrium systems, the properties of which virtually do not change over the long time interval tmax (Eq. (1)). The same may also be said about the overwhelming majority of noncrystalline substances, many of which are already widely used for recording information (Andriesh et al., 1988). Thus, the class of various quasiclosed ensembles (different macrostates memorized by the system with a fixed chemical composition) is extraordinarily broad. Their number is substantially larger than the number of Gibbs energy minima. The magnitude of G cannot be evaluated without application of quantum-mechanical methods. The point is that the components ri of the vector R (Eq. (3)) can vary continuously, i.e., there exists a continuum of various structures (different vectors R~), which cannot even be numbered with the help of the index k, if it has solely integer values. This hampers the determination of the number G of different structural modifications. In a quantum-mechanical description (Landau and Lifshitz, 1977) of a structure, the superfluous detailing is useless because quantum mechanics dictates that a system is usually localized not at one point R~ but in a certain volume (cell ~k). The set of all cells ~k is countable. It is this circumstance that allows one to speak about the number G of different structural modifications of the condensed system with a fixed (M -- const, n = const) chemical composition. All atomic configurations R~ (Eq. (3)) of an ideal monatomic gas are equiprobable. Condensed systems are characterized by the totally opposite situation. Therefore, it is not surprising that some of their structural modifications may be frozen (memorized) for a long time interval tmax (Eq. (1)). Let us illustrate what has been said above in the framework of the adiabatic approximation.
Information Capacity of Condensed Systems 2.
5
Description in the Framework of the Adiabatic Approximation
The adiabatic approximation (Born and Oppenheimer, 1927) is based on the considerable differences in the masses of electrons and nuclei, which makes it possible to describe their motions separately well. Being light particles, the electrons 'succeed' in adapting themselves to the instantaneous configuration R (Eq. (3)) of the atomic nuclei, the latter in turn 'notice' only the averaged disposition of electrons. In the zero approximation the atomic nuclei are regarded to be at rest [R = const, Eq. (3)]. In this case, the wave function q~j(R, X) of the j-th stationary quantum state of the electron subsystem satisfies the equation (Nikitin, 1970) H~j(R, X ) = U~j)(R)~j(R, X),
(4)
where H is the Hamiltonian of electrons at fixed nuclei, which represents the sum of the total Coulomb energy of the interaction of atomic nuclei and electrons, the operator of the spin-orbital interaction of electrons and the operator of the kinetic energy of electrons; X is the sum of spatial and spin variables of all electrons of the system under consideration; U:~)(R) is the adiabatic electron term, which in the case of a polyatomic system (M ~ 1) usually has a great number of different physically nonequivalent minima R~ (Bal'makov, 1987, 1996). The Hamiltonian H does not contain any operator of the kinetic energy of atomic nuclei and, consequently, is the operator of the energy of the system under consideration for the fixed atomic configuration R. When the motion of atomic nuclei does not induce any transitions between different electronic states, the function f[(j)(R) (Eq. (4)) may be interpreted as the potential energy '-'M of the nuclei corresponding to the j-th electronic state. In this case their motion takes place in the potential field of U~)(R). Therefore, the nuclear wave function xj(R,E) satisfies the Schr6dinger equation (Nikitin, 1970)
(? + U~)(R))xj(R, E) = Exj(R, E),
(5)
in which in contrast to Eq. (4), there is no variable X corresponding to the electron subsystem. Here, 7"is the operator of the kinetic energy of atomic nuclei; E is the energy of the stationary quantum state. The chemical composition determines unequivocally the explicit form of Eqs. (4) and (5). Their different solutions describe various modifications of a substance with a fixed composition. This can serve as the basis for classification of these solutions. Thus, in the case of selenium some solutions may be attributed to the fluid state, others to definite crystalline modifications, to amorphous modifications, to the vitreous state, to films, etc. However, it is most advisable to base the discussed classification of solutions of Eqs. (4) and (5) on the structure R (Eq. (3)) because, as noted above, the information about individual peculiarities of a polyatomic system is eventually stored in the mutual disposition of its atomic nuclei. Any structural modification (e.g., the k-th modification, see Fig. 1), which is preserved at least over the time interval tmax (Eq. (1)) is described by the wave functions qbj(R, X) (Eq. (4)) and xj(R, E) (Eq. (5)) localized near the point Rk. The diversity of the latter actually determines all the states belonging to the kth quasi-ensemble. Usually one or a series of potential R~ minima correspond to the points U~)(R), near which the motion of one or other structural modification takes place. In order to estimate
6
M.D. Bal'makov
the number of such points (the number G of different quasiclosed ensembles), it is, as a rule, sufficient to consider only the minima of the adiabatic electron term U~)(R) corresponding to the ground (j = 0) state of the electron subsystem. 2 The point is that the lifetimes re of most excited states of the electron subsystem are relatively short (re << tmax). Therefore, these states alone cannot form a quasiclosed ensemble, in the framework of which the kth structural modification can be described over a long time interval tma x (see Fig. 1). Its preservation is favored by the potential barriers surrounding the minimum R1, of the adiabatic electron term U~)(R) (Fig. 2). If they are sufficiently high, then even the low-energy quasi-steady (Landau and Lifshitz, 1977) states localized in the potential well R~ under consideration have larger [compared t o tma x Eq. (1)] lifetimes ~'l which satisfy the inequalities rr << tmax << Z~
(6)
where Zr is the relaxation time of the phonon subsystem, which is usually appreciably shorter than the time tmax required for the preservation of information. Consequently, quasiclosed ensembles may be formed by the stationary and quasisteady (Landau and Lifshitz, 1977) states with large lifetimes rl (Eq. (6)). Usually these are low-energy states, which describe vibrational motion of atomic nuclei near one of the minima of the adiabatic electron term U~)(R) (see Fig. 2). Transitions between these states are not accompanied by any substantial changes in the R~ structure. The k-th structural modification is preserved when only such transitions take place (see Fig. 1). The same may also be said about the macroinformation I (Eq. (1)) which is the choice of a quasiclosed ensemble memorized by the system. This information is preserved as long as all changes occurring spontaneously or owing to the action of the external perturbation if" are described in the framework of the same quasiclosed ensemble. This means that with the probability P(t) close to unity
P(t)> 1-e
at 0 - < t - < t m a x
and 0 < e < < l ,
(7)
the system 'stays' in this quasiclosed ensemble during the long time interval tmax and, consequently, the transition from the ensemble under consideration to other ensembles may be disregarded. Relations (7) are in full agreement with the definition of a quasiclosed ensemble given below. The same ensemble of quantum states may be quasiclosed relative to a single quite definite operator if" or a group of operators and, generally speaking, they are not be quasiclosed relative to other operators. The latter include the recording operator ~/]/(mk) which brings about the transition to the preset k-th quasiclosed ensemble. Therefore, the ensembles under consideration are usually 'closed' only during the storage and 2 Each minimum of the function U~)(R). sets one of the equilibrium configurations R~. Crystals correspond to the deepest minima (potential wells). Most minima correspond to different noncrystalline structures. Transition from one potential well to another (Ri ~ Rk) means in the general case the rearrangement of all of the M atomic nuclei of the system since the components of the vector R = ( r l , r2, ...rj, ...rm) are radius vectors rj of these nuclei (Eq. (3)). Each point in Figure 2 sets the internal energy E of the system and the coordinates of all its nuclei. In the framework of classical physics the translocation of this point can characterize various processes occurring in the system. The adiabatic electron term U~)(R) does not depend either on temperature or on the thermal prehistory, etc. According to Eq. (4), it is unequivocally determined only by the chemical composition. Various scenarios of the system behavior consist in the sequence of passage over potential wells [the minima of the function U~)(R)].
Information Capacity of Condensed Systems
u(0) M (R)
7
f
R1
R2
Rk
FIG. 2. Adiabatic electron term U~)(R). The rectangles A, Bi, Ci and Di indicate the potential wells corresponding to the Rk structures (quasi-closed ensembles) of liquid, glass, amorphous substance and crystal. The segments of horizontal straight lines set the values of energies of quantum states. This figure is rather conditional because for polyatomic systems (M >> 1) the function U~)(R) is set, in conformity with Eq. (3), in the multidimensional space. reading of information. It is this circumstance that determines the choice of the term quasiclosed. Measurement is performed in the course of information reading. It is known (Kadomtsev, 1994) that any measurement is an irreversible process fixing one of the possible states. The measurement process proper, which in principle permits an extremely small energy exchange between the system and the measuring instrument, exerts nonetheless a substantial effect on the dynamics of the quantum system. The initial state of the system 'is broken, i.e., it is transformed into something that cannot be regarded as a pure state or into another pure state which differs explicitly from the initial one' (Kadomtsev, 1994, p. 472). To preserve the information recorded previously, it is necessary that during the reading this 'something' does not go beyond the frames of the initial quasiclosed ensemble. This condition is met in many cases. Indeed, let us assume that the nuclear wave function x0(R, El) (Eq. (5)) describes the low-energy vibrational motion of atomic nuclei in the potential well R~ (see Fig. 2). Reading (measurement) is done by the collapse x0(R, El)---+ x0(R, E2). If the energy variation I E 1 - E21 is much smaller than the magnitudes of most potential barriers separating the R~ minimum from other minima of the potential U~)(R), there is overwhelming probability of localization of the wave x0(R, E2) of the final state in the initial potential well R~. This can be easily seen since in this case, when applying the theory of perturbations (Blokhintsev, 1961; Landau and Lifshitz, 1977), it is sufficient to take into consideration only the matrix elements (Xo(R, E1)I~v(r)Ixo(R, Es)) of the reading operator 3 ~/]/(r) for the wave functions x0(R, Es) localized in the same potential Rk well 4 Rk. 3 Strictly speaking, the reduction (collapse) is not described by the Schrrdinger equation (Kadomtsev and Kadomtsev, 1996). Nonetheless, approaches are known which allow a highly accurate interpretation of the measurement in terms of quantum-mechanical interaction of the system with an instrument (environment) (Mensky, 1998). This makes it possible to introduce the operator of interaction of the two subsystems ~]/(r) and then to use the Schrrdinger equation. 4 Since the wave functions localized in different potential wells virtually do not overlap, all other matrix elements may be neglected.
8
M.D. Bal'makov
Thus, in order to preserve a polyatomic system, an exact copy and also the recorded information, it is sufficient that all changes occurring in the system do not extend outside the limits of one and the same quasiclosed ensemble. It is this ensemble that characterizes the properties of the system displayed during informational interaction. In fact, the behavior of a quantum system can be interpreted in classical terms with an accuracy up to its belonging to a definite quasiclosed ensemble. It is for this reason that I (Eq. (1)) is regarded as macroinformation. The amount of information I (s) indicating that the state of the system belongs to a given quasiclosed ensemble is equal to i(s) _ In G In 2 '
(8)
where G is the number of quasiclosed ensembles. Naturally, the magnitude of G(tma• e, W, n, M) is a function of many arguments. Its explicit form is unknown and this impedes the direct application of Eq. (8) for calculating the numerical value of I (S). The magnitude of G(tmax, e, ~z, n,M) can be estimated proceeding from the number J(n, M) of different minima of the potential U(M~ This approach allows a relatively simple derivation of numerical estimates as the function J(n, M) depends on only two arguments and, in addition, its determination is actually based on Eq. (4) when j - 0. This unambiguous mathematical definition is useful not only for the problem of information copying and recording but also for considering a wide range of other issues (Bal' makov, 1996). 3.
Estimation of the N u m b e r of Different Quasiclosed Ensembles
For the number J(n,M) of different physically nonequivalent local minima of the adiabatic electron term rr(~ which corresponds to the ground electronic state of the vm electroneutral system consisting of M atoms, the following asymptotic formula (Bal'makov, 1996) is valid as M ~ oo 1 - - In J(n, M) --- an,
M
(9)
where a n is the positive parameter dependent solely on the chemical composition n (Eq. (1)). It follows from Eq. (9) that J(n, M) -- exp(anM + o(M)),
(10)
the function o(M) satisfying the condition limM-.oo o(M)/M = 0. In other words, the number J(n, M) of different physically nonequivalent minima of the U~)(R) potential exhibits a rapid exponential growth with the increasing number M of atoms forming the system with a fixed (n = const) chemical composition. This fact is not surprising because the magnitude J(n, M) (Eq. (10)) takes into account all potentially possible structural modifications Rk (Eq. (3)) of a polyatomic system. These are structures of liquid, glass, perfect crystal, crystals with different concentrations of particular defects, polycrystals, amorphous substances, amorphous and vitreous films, glass-ceramics and many others, including the structures of microheterogeneous materials storing the recorded information. The diversity of minima of the function U~ )(R) makes it possible to explain the possibility to vary properties of a material of the
Information Capacity of Condensed Systems
9
same chemical composition through preparation of its various modifications described by different quasiclosed ensembles. Thus, glass fits not one but many physically nonequivalent quasiclosed ensembles B1,B2,...Bi, .... (see Fig. 2). Therefore, the properties of glasses vary depending on the cooling rate of the glass-forming melt (Bal'makov, 1996). In practice, technical limitations allow, as a rule, the use of only some quasiclosed ensembles. For this reason, the amount of recorded information I (Eq. (1)) is usually smaller than the maximum possible i~s) value (Eq. (8)): I --< {ln G(tmax, ~, W, n , M ) } / l n 2.
(11)
The right side of inequality (11) is simple to estimate, if one takes into account only the quasiclosed ensembles which fit the ground state of the electron subsystem. Indeed, when there are G ~0~ of them the following relations are satisfied: lnG(~
e , W , n , M ) <- l n J ( n , M ) - - ( a n M + o ( M ) )
<-- ( B M + o ( M ) ) ,
(12)
where constant B is determined by the identity B --= sup an.
(13)
n
Let us demonstrate the validity of transformations (12). At low temperatures the motion of atomic nuclei takes place in the proximity of one or a series of minima (potential wells) of the adiabatic electron term U(M~ (see Fig. 2). If all low-energy states ~0(R, X)x0(R, Es) localized in each potential well are stationary or quasi steady and have long lifetimes ~l satisfying inequality (6), then such states seem to form one of the quasiclosed ensembles. In this case, their number is equal to the number J(n,M) (Eq. (10)) of potential wells. In all other cases when a part of the quasiclosed ensembles describe the motion of atomic nuclei near a series of potential U(M ~ minima, the strict inequality G (~ < J(n, M) is satisfied. We have thereby demonstrated the validity of the inequality G (~ --< J(n, M) which in combination with Eqs. (10) and (13) directly yields relations (12) which allow the estimation of G (o~ from above, if one proceeds from the numerical values of ce~ or B. It would not be particularly difficult to find the exact value of constant B (Eq. (13)) if the solutions of Eq. (4) at j = 0 were known for the systems of various chemical compositions. Since this is not the case, one has to use model approaches (Bal'makov, 1996). In their frameworks it is possible to calculate numerical values of the parameter an (Eqs. (9) and (13)) for specific systems. The results of such computations (Bal'makov, 1987, 1996) support the following estimate: B ~ 3.
(14)
The constant B is also useful for the estimation of the upper limit of the specific information capacity/3(tmax, n) (Eqs. (1) and (2)): 0 -
(15)
Tr<
Indeed, in contrast to B (Eq. (13)), the calculation of B ;i~ (Eq. (15)) requires consideration not only of the minima of the adiabatic electron term U~ ~(R) corresponding to the ground
10
M. D. Bal'makov
state of the electron subsystem but also, generally speaking, of the minima of all other potentials UM (J)(R) (Eq. (4)). However, as noted above, the lifetimes % of most excited states of the electron subsystem are relatively short (% << tmax). States of this kind are unsuitable for information storage. The potentials corresponding to them may be neglected. Then the estimate (15) is derived directly from Eqs. (10)-(13). Until now no strict definition of the notion 'quasiclosed ensemble' has been given. It was believed that each structural modification (see Fig. 1) of the system with a fixed chemical composition has an intrinsic set of microscopic states, which form one of the quasiclosed ensembles. This is an illustrative, though somewhat simplified interpretation. It is possible to carry out a more strict consideration based on the definition of a quasiclosed ensemble outside the framework of the adiabatic approximation. This approach requires consideration of many important nuances which were not discussed here. For this reason, it appears advisable to give a definition of a quasiclosed ensemble. 4.
Definition of a Quasiclosed Ensemble
Any state of a system is described by the corresponding statistical operator [density matrix (Landau and Lifshitz, 1977)] 13(0 in the Hilbert space F. A quasiclosed ensemble is perceived as a nonempty set of system states meeting the two following conditions. 1. It is possible to establish a one-to-one correspondence between the elements of this set and various statistical operators /~(U) for a certain subspace N of the Hilbert space F. Each state of the quasiclosed ensemble is set by a single operator fi(N) and, conversely, each operator fi(U) of the subspace N sets a single state from this ensemble. 2. Any state of t3(t) of the system, which belongs initially (t = 0) to the quasiclosed ensemble [(t3(0) -/3(U))], is described in the e-approximation in the subspace N even in the presence of the external perturbation W. This means that the inequalities 0 --< t -< /max are satisfied Sp(fi(t)fi)- SpN(/3(t)~)l < Cle,
l = 1,2, ....
(16)
where fi are the operators of physical quantities; SpN(t3(t)fi) is the sum of the diagonal matrix elements of the operator/3(t)~ in an arbitrary orthonormal basis of the subspace N; Sp(/3(t)fi) is an analogous sum for the Hilbert space F; Cl are constants. In addition, it is assumed that at t > tmax at least one of the inequalities (16) is not respected. It is known that these definitions are not proven. Let us give a number of arguments in favor of the quasiclosed ensemble definition formulated above. The advisability of setting a given ensemble in the corresponding subspace N of the Hilbert space F follows from the superposition principle (Landau and Lifshitz, 1977). In full agreement with this principle, all the solutions of the Schr6dinger equation form a linear manifold with time (Landau and Lifshitz, 1977). If we are interested in only some of these solutions, then again bearing in mind the superimposition principle, it is convenient that these represent a closed linear manifold. The latter is called a subspace (Kolmogorov and Fomin, 1981).
Information Capacity of Condensed Systems
11
The satisfaction of inequalities (16) means that in order to calculate (with the arbitrarily small error Cle) the mean values ~(t) -- Sp(/5(t)~), 1 -- 1,2, ....
(17)
of physical quantities ~ that are of interest to us, it is sufficient to know the corresponding matrix elements only for the subspace N. This is not surprising because the probability P(t) of the system staying in any state of the quasiclosed ensemble is close to unity, or more precisely
P(t) > 1 - e at 0 --< t --< tmax.
(18)
Inequality (18) follows directly from relations (16) and (17), if we assume in the latter that~ -- C1 -- 1 and take also into account that P(t) -- SpN(/3(t)). Relations (18) virtually coincide with inequalities (7), which were used for substantiating the advisability of introducing the concept of a 'quasiclosed ensemble'.
5.
Conclusion
Of course, the investigation of the informational aspect of the behavior of condensed systems is still in its infancy. The development of the macroscopic theory of information copying and recording is restricted by many factors, which include a number of unsolved problems in natural sciences. Let us list some of them. Until now 'the problem of the relationship between the quantum and classical descriptions of physical processes' remains open to debate (Mensky, 1998, p. 1018). There is no consensus regarding fundamental concepts, such as the wave function, reduction (collapse), etc. (Klyshko, 1998). Finally, the subject of discussions continues to be 'the question about irreversibility at the boundary between classical and quantum systems, in particular when measuring quantum systems' (Kadomtsev, 1995, p. 973). The latter circumstance is of prime importance for dissipative and temporally irreversible processes, such as information recording and reading. If the above-listed problems remain unsolved, it would hardly be possible to answer exhaustively all of the questions formulated in this work. It centered attention on the estimation of the number G of different quasiclosed ensembles [various structural modifications (see Fig. 1) preserved over the long time interval tmax Eq. (1)]. As long as their dynamics, including collapses, is described by different quasiclosed ensembles, these modifications do not pass one into another even under the action of the unfavorable external perturbation W. Therefore, there is the potential to use them for the recording and storage of information. Indeed, there are no basic restrictions as to the practical realization of any state described by fundamental equations of quantum mechanics. 5 The same may be argued in 5 Quantum mechanics (Landau and Lifshitz, 1977) admits even the possibility of realization of a coherent superposition of any two states. Naturally, this is also valid for any two structural modifications (Fig. 1). However, due to the ever-occurring weak interaction with the environment their superimposition is rapidly transformed into one of the stable structural modifications. States of this kind are called incoherent (Mensky, 1998).
12
M. D. Bal'makov
respect of various structural modifications (see Fig. 1) of the system with a fixed chemical composition. 6 They can be distinguished using a macroscopic instrument. 7 Naturally, in the course of information measuring (reading) the initial state of the system is obligatorily changed, whereas the structural modification (a quasiclosed ensemble) remains, generally speaking, invariable. The latter circumstance is important for the preservation of the information recorded earlier during its reading because it represents the choice of one of the possible quasi-ensembles memorized by the system. The development of a microscopic theory of information copying and recording stands in need of various model systems. To this end, an ideal glass may prove to be useful (Bal' makov, 1996). It has already been used as a model in the analysis of peculiarities of the operation of neuronal networks (Nemilov, 1998) and in the description of cosmic objects known as black holes (Nieuwenhuizen, 1998). Naturally, an ideal glass is not yet used in theoretical studies as widely as the concept of an ideal gas. The main reason consists in that the development of theory of disordered systems, to which glasses are referred, is still far from completion (Mott and Davis, 1979). Further progress in this field appears to be impossible without radically new approaches, in particular without using the methods of information theory (Stratonovich, 1975; Kadomtsev, 1994, 1995, 1997/1999; Kadomtsev and Kadomtsev, 1996). Indeed, the glass transition involves the internal measurement (self-measurement) and realization of one structural modification memorized by the system (see Fig. 1) of the G possible modifications. As noted above, it is this that is meant when the macroinformation I is discussed (Eq. (1)). It is essential that the memorized choice cannot be realized using an ideal gas or liquid because of their lability. Furthermore, a glass transition is a nonequilibrium process, while information 'plays an important role in physical nonequilibrium processes' (Aleskovski, 1996, p. 451). It appears that the ideology of the vitreous state will henceforward serve as the base for constructing various models for the investigation of the informational aspect of the behavior of polyatomic systems. Liquid is 'a stochastised system with zero information and maximum entropy, i.e., the system of the C type' (Aleskovski, 1996, p. 474). Glass is precisely its antipode. Each glass macrosample memorizes the information indispensable for copying, it whereas the entropy of glass is substantially smaller than that of liquid (Bal'makov, 1996; Bal'makov, Blinov and Pocheptsova, 1998). Liquids are not used for recording information. In contrast, glasses, incidentally like many other disordered systems, are well suited for this purpose (Andriesh et al., 1988). The microscopic mechanism of information copying and recording is determined by elementary processes occurring in small-size fragments. These may be elementary structural transformations, elementary chemical transformations, etc. In their description, it is necessary to take into consideration primarily the potential barriers surrounding each minimum of the adiabatic electron term U ~ ( R ) (see Fig. 2), or more precisely, the coefficients of passage through these barriers (Tveryanovich, Bal'makov and Tveryanovich, 1998). 6 In its practical aspect, the task of obtaining a preset structural modificationis considered in the framework of so-called chemical-informationsynthesis (Aleskovski, 1996). 7 This is also evidenced by the impressiveprogress, e.g., in the developmentof diffraction methods for studying disordered structures, made over the last 70 years (Wright, 1998).
Information Capacity of Condensed Systems
13
Most elementary processes occur in the nanometer-range fragments containing tens to hundreds of atoms (Bal'makov, Tver'yanovich and Tver'yanovich, 1994). Therefore, these processes are in particular responsible for the formation of condensed media-based nanostructures, the diversity of which virtually determines the level of specific information capacity/3(tmax, n) (Eqs. (1) and (15)). The task of the targeted synthesis of individual nanostructures (Kadomtsev, 1994) dictates the need for developing the microscopic theory of information copying and recording. The solution of this particular problem is impossible without such a fundamental characteristic of any material object as information, without which it is in turn impossible to get an exact copy. In this field, studies of an applied character are moving ahead of basic research and stimulating its progress. We witnessed something similar in the middle of this century when information theory was taking shape (Shannon, 1993). This work was supported by the Russian Foundation for Basic Research (project 04-03-33049).
References Aleskovski, V.B. (1996) Khimiya Nadmolekulyarnykh Soedineni (Chemistry of Supramolecular Compounds), Izd. St. Petersb. un-ta, St. Petersburg. Andriesh, A.M., Bivol, V.V., Buzdugan, A.I., Iovu, M.S., Panasuk, L.M., Triduh, G.M., Fulga, V.I. and Shutov, S.D. (1988) Stekloobraznye Poluprovodniki v Fotoelektri-cheskikh Sistemakh Zapisi Opticheskoi Informatsii (Glassy Semiconductors in Photoelectric Systems of Optical Information Recording), Shtiintsa, Kishinev. Bal' makov, M.D. (1987) J. Non-Cryst. Solids, 90, 69. Bal'makov, M.D. (1996) Stekloobraznoe Sostoyanie Veshchestva (The Vitreous State of Matter), Izd. St. Petersb. un-ta, St. Petersburg. Bal'makov, M.D. (1996) Glass Phys. Chem., 22, 344. Bal'makov, M.D., Blinov, L.N. and Pocheptsova, N.S. (1998) Tech. Phys. Lett., 24, 86. Bal'makov, M.D., Tver'yanovich, Yu.S. and Tver'yanovich, A.S. (1994) Glass Phys. Chem., 20, 381. Bazarov, I.P. (1983) Termodinamika (Thermodynamics), Vys-shaya shkola, Moscow, (see also: Thermodynamics, Pergamon Press, Oxford, 1964). Blokhintsev, D.I. (1961) Osnovy Kvantovoi Mekhaniki (Fundamentals of Quantum Mechanics), Vysshaya shkola, Moscow. Born, M. and Oppenheimer, J.R. (1927) Ann. Phys. (Leipzig), 84, 457. Kadomtsev, B.B. (1994) Usp. Fiz. Nauk, 164, 449 [Phys. Usp. 37, 425 (1994)]. Kadomtsev, B.B. (1995) Usp. Fiz. Nauk, 165, 967 [Phys. Usp. 38, 923 (1995)]. Kadomtsev, B.B. (1997/1999) Dinamika i Informatsiya (Dynamics and Information), Red. Zhurn. Usp. Fiz. Nauk, Moscow. Kadomtsev, B.B. and Kadomtsev, M.B. (1996) Usp. Fiz. Nauk, 166, 651 [Phys. Usp. 39, 609 (1996)]. Kittel, C.h. (1977) Thermal Physics, Wiley, New York, [Translated into Russian (Nauka, Moscow, 1977)]. Klyshko, D.N. (1998) Usp. Fiz. Nauk, 168, 975 [Phys. Usp. 41,885 (1998)]. Kolmogorov, A.N. and Fomin, S.V. (1981) Elementy Teorii Funktsii i Funktsio-nalnogo Analiza (Elements of the Theory of Functions and Functional Analysis), Nauka, Moscow. Landau, L.D. and Lifshitz, E.M. (1977) Quantum Mechanics, Pergamon Press, Oxford. Mensky, M.B. (1998) Usp. Fiz. Nauk, 168, 1017 [Phys. Usp. 41,923 (1998)]. Mott, N.F. and Davis, E.A. (1979) Electron Processes in Non-crystalline Materials, Clarendon Press, Oxford. Nemilov, S.V. (1998) Dokl. Akad. Nauk, 359, 554. Nieuwenhuizen, Th.M. (1998) Phys. Rev. Lett., 81, 2201. Nikitin, E.E. (1970) Teoriya Elementarnykh Atomno-Moleculyarnykh Protsessov v Gazakh (Theory of Elementary Atomic-Molecular Processes in Gases), Khimiya, Moscow.
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Shannon, K. (1993) In Raboty po Teorii Informatsii i Kibernetike (Works on Information Theory and Cybernetics) (Eds., Sloane, W.J.A. and Wyner, A.D.) IL, Moscow, [see: Claude Ewood Shannon Collected Papers (Eds, Sloane, W.J.A. and Wyner, A.D.) IEEE Press, New York, 1993]. Stratonovich, R.L. (1975) Teoriya Informatsii (Information Theory), Sov. Radio, Moscow. Aleskovski V.B. (1998) The 2nd International Conference on Chemistry of Highly Organized Substances and Scientific Principles of Nanotechnology (Abstracts of Papers), Izd. UNTsKh St. Petersb. un-ta, St. Petersburg, p. 5. Tveryanovich, A., Bal'makov, M.D. and Tveryanovich, Yu.S. (1998) Extended abstracts of 1 lth International Symposium non-oxide and new optical glasses, Sheffield, UK, September 6-10, p. 334. Vainshtein, B.K. (1956) Strukturnaya Elektronografiya (Structure Analysis by Electron Diffraction), Izd. AN SSSR, Moscow, [Translated into English (Pergamon Press, Oxford, 1964)]. Wright, A.C. (1998) Glass Phys. Chem., 24, 148. Yoffe, A.D. (1993) Adv. Phys., 42, 173.
CHAPTER
2
CHARGE CARRIER TRANSFER AT HIGH ELECTRIC FIELDS IN NONCRYSTALLINE SEMICONDUCTORS A. Cesnys VILNIUS GEDIMINAS TECHNICALUNIVERSITY,LT-10223, VILNIUS, LITHUANIA
G. Ju~ka and E. Montrimas VILNIUS UNIVERSITYLT-01513, VILNIUS, LITHUANIA
1. Introduction Transport phenomena in noncrystalline semiconductors under strong electric fields were analyzed in a number of publications, including several reviews (Owen and Robertson, 1973; Fritzshe, 1974; Sandomirskii and Sukhanov, 1976; Kostylev and Shkut, 1978; Mott and Davis, 1979; Feltz, 1983; Kvaskov, 1988; Cendin, 1996). These works present not only the most typical results of the experimental investigation, but also consider the main theoretical models. In this chapter, we will consider results of the change of electrical features in the electric fields of amorphous selenium (a-Se) and noncrystalline semiconductor A s - S e and Ga (or In)-Te-based structures. The features of these compounds will be exposed under the influence of various parameters, including chemical composition of noncrystalline material, lattice temperature, regime of heat treatment, and doping impurity. We will give special emphasis on the multiplication effect, nonactivated conductivity, formation of space charge and influence of potential barrier on the strong-field conductivity. Before proceeding to the detailed description of the physical phenomena, we will mention briefly the main features of the materials under investigation. Amorphous selenium is a mono-component material, the features of which are similar to features of other chalcogenide glasses (such as AsSe, AsTe, etc.). Thus, a-Se may be used as a model material for the interpretation of properties of other chalcogenide glasses. The photoconductivity effect was obtained in selenium in 1872. For a long time, it was the only material for photosensitive xerographic layers, and its electric and optical properties were investigated extensively. However, the experimental results and their interpretation were ambiguous. This is caused both by the peculiarities of a-Se structure itself, and by the indirect influence of impurities upon it. 15
Copyright 9 2004 Elsevier Inc. All rights reserved. ISBN 0-12-752188-7 ISSN 0080-8784
16
A. Cesnys et al.
The structure of a-Se is sensitive to preparations conditions: while in the form of evaporated layers it depends on substrate temperature, in the form of overcooled liquid it is sensitive to the initial temperature (quenching temperature) of liquid Se. The ratio of Se8 tings and Se~ chains has been estimated using the properties of partial solubility of a-Se: monoclinic Se consisting of corrugated Se8 rings dissolves well, while trigonal Se (which consists of spiral Se~o chains) is insoluble in CS2, (Eisenberg and Tobolsky, 1960). Further investigation by combination scattering and IR spectra demonstrated the absence of Se8 rings. Moreover, a large number of modeling results demonstrated a lack of a consistent fit with the experimentally estimated radial distribution curve (Mott and Davis, 1979; Adler, Fritzsche and Ovshinsky, 1985). Compounds and alloys of As with Se, S and Te make up a large group of the system of glassy chalcogenides. An important contribution to the discovery and investigation of semiconductors in this group came from the works of Kolomietz and collaborators (Goriunova and Kolomietz, 1956; Kolomietz, 1963). Double, triple and even quadruple systems of As chalcogenides exist. Below, special attention is devoted to electric properties of arsenic-selenium compounds and alloys. As and Se form an extensive part of glassy alloys with up to 60 at.% of As. Several chemical compounds exist in that region: AszSe3, As2Se5, AsSe, etc. When the amount of As in a alloy increases, density of covalent bonds also increases, whereas density of Se-Se bonds decreases (Borisova and Bobrov, 1962). Due to the maximum density of covalent bonds achieved in the AszSe3 compound, AszSe3 is characterized by a high value of micro-hardness, high temperature of softening and high stability of properties. Arsenic-selenium compounds have high thermal stability (Hartke, 1962; Kolomietz, 1963). Noticeable crystallization of those compounds is observed at temperatures higher than 200 ~ (Dembovskii, 1964; Muller, E1 Mosli and Borisova, 1964). The change of the forbidden energy gap of arsenic selenide, as well as of arsenic sulfide and arsenic telluride, during a transition from crystalline to glassy state and vice versa (Kolomietz and Pavlov, 1967) is caused by widening of allowed energy bands and disappearance of long-range order (Gubanov, 1963). It follows that electric, optical and photoelectric properties of glassy chalcogenides may be described using the energy band model of a semiconductor. As shown by Kolomietz (1963) and Borisova (1964), electric conductivity of massive AszSe3 samples is of the order of 1 0 - 1 2 10-13 ~ - 1 cm-1. Any deviation of Se content from that composition causes a decrease in electric conductivity (Muller et al., 1964). A small amount of impurities (< 1 at.%) have little influence on electric conductivity of AszSe3, but larger concentration of impurities can cause an increase of conductivity by several orders of magnitude (Danilov and Muller, 1962; Borisova, 1964). Activation energy of electric conductivity changes smoothly with changing chalcogenide composition. This indicates that electric conductivity of chalcogenide glasses is intrinsic (and not caused by impurities), and it is determined by the gap width. Atomic and electronic structure, optical, electrical, photoelectrical properties, also various electronic and other physical phenomena of chalcogenide glass semiconductors (CGS) have been widely discussed in the monograph 'Electronic phenomena in chalcogenide glass semiconductors', edited by Cendin (1996). Semiconductor systems based on Ga (or In)-Te display a huge variety of attractive physical properties. They exhibit photo- and electroluminescence, induced and stimulated
Charge Carrier Transfer at High Electric Fields in Noncrystalline Semiconductors
17
radiation under affection of hot electrons, effects of electrical memory and the possibility on recording of optical information was revealed as well. All these features serve as a strong basis for direct application. For instance, they are very promising for manufacturing of thin-film negistor structures operating in the microwave range (Balevi6ius, Deksnys, Dobrovolskis, Krotkus, Lisauskas, Tolutis and (~esnys, 1978; Balevi6ius, (~esnys, Oginskas, Po~kus and Ga~ka, 1984). This stimulates an interest to physical processes taking place in films made of the given materials, in high electric fields. The specifics of these materials relies on the co-existence of either two congruent (GaTe, InTe, GazTe3, InzTe3) or peritectical phases. The most interesting are thin-films of Ga~-xTex and Inl_xTex, where x - - 0 . 5 , 0.6, 0.75, 0.8. The compounds GaTe, InTe, GazTe3 and InzTe3 (x = 0.5, 0.6) are perspective for manufacturing of negistor structures which do not require preliminary electric formation. The alloys with x = 0.75, 0.8 ensures the fastest and the greatest stability of the characteristics. The specific feature of the thinfilm with x = 0.75 is cluster structure. Short-range order in the structures, according to the data (Lisauskas, Tolutis and Sheremet, 1986), is the same as in crystalline phases of GazTe3 and Te, the distinguishing feature of which is electroconductivity. These microinhomogeneities cause nonuniform distribution of the electric field within film resulting thus into transport features. Therefore, in this review we will discuss and compare two types of these thin films having different levels of homogeneity.
2. Charge Transfer in Noncrystalline Selenium and As-Se System Thin Films 2.1.
AMORPHOUS SELENIUM ELECTRICAL CONDUCTION DEPENDENCE ON IMPURITIES
The interpretation of the electric features of a-Se is ambiguous. For example, the dependence of electric conductivity on quenching temperature was interpreted by some authors as structural change, while others considered it to be the influence of impurities, especially oxygen. Such a discrepancy in interpretation is caused by several factors. One of these is methodical, because the conductivity value and its dependence on electric field significantly differs when measurements were made by using evaporated metallic electrodes from results obtained by thermally infused wire electrodes. This difference is caused by the formation of pre-surface layers. The determinant surface influence was proved by unlimited surface recombination estimated from quantum efficiency dependence on electric field and by much lower quantum efficiency in case of planar rather than sandwich electrodes (Ju~ka and Vengris, 1976). Additionally, in the case of aSe, the classical semiconductor-metal contact theory is invalid because the high chemical activity of Se causes the formation of a metal-selenide sublayer. Moreover, due to the indirect influence of impurities, the classical model of doping is invalid in this material as well. In respect that ESR signal demonstrated low density of localized states, Anderson (1975) proposed the valence alternation pair (VAP) model, according to which the broken bond of chain connects to a nearby chain, and, due to negative correlation energy, it recharges, creating a nonparamagnetic pair (Mott and Davis, 1979; Maden and Shaw, 1988): 2C ~ ~ C o § C o ---, C~- § C1.
18
A. (;esnys et al. 10-2
0
10-3 ~p a~ 10-4
0
~n
,..r rJl
10-5
10-6
0
9
10-7 10-14
10-13
10-12
10-11
10-10
10-9
o (S/cm) FIG. 1. Dependencies of lifetime of holes rp, electrons rn, bulk photogeneration efficiency and absorption coefficient product/3K at hv = 1.5 eV on electrical conductivity of a-Se.
Their concentration
[C 1].[C~-]
-
-
[Nse]2 exp -
EVAP ) kT*
'
(1)
where T * = T, when T > Tg; and r * = Tg, when T < Tg, where Tg is vitrification temperature (305 K), and EVAP VAP formation energy (0.8 eV). The VAP model has been used to explain some of a-Se electrical features. When, according to the condition of charge neutrality, doping by electronegative impurity [N-] takes place (by oxygen, for example), it follows that [C~-] decreases, while [C~-] increases. The latter causes equilibrium hole concentration and, as a result, electric conductivity increases, as well as a longer photogenerated hole lifetime ('rp ~ [C~-]-1); increased photoconductivity at 1.5 eV in photoconductivity spectral dependence; and a decrease of electron lifetime (Zn "~ [C+] -1) occur (Fig. 1). The conclusion that VAP states predetermine charge carrier lifetime also follows from Eq. (1), and, experimentally, it is proved by the insignificant/zz dependence on temperature at T < Tg with transition to activated character at T > Tg (0.86 eV). The latter results demonstrate that by doping with different impurities it is impossible to infinitely increase lifetime of both sign carriers because, as follows from Eq. (1), rn'~'p --< const. Since the influence of impurities upon the transport features of a-Se are widely described by Mott and Davis (1979) and Maden and Shaw (1988), here we will discuss only the features which are also characteristics of other chalcogenide glasses: the effect of deactivation of charge carrier drift mobility with electric field, and the phenomenon of charge carrier heating by electric field and band-to-band impact ionization in high electric field regions.
Charge Carrier Transfer at High Electric Fields in Noncrystalline Semiconductors 2.2.
19
TEMPERATURE AND ELECTRIC FIELD DEPENDENCIES OF CHARGE CARRIER DRIFT AND MICROMOBILITY
In low-conductivity materials of disordered structure, the charge carrier drift mobility usually is investigated by conventional time-of-flight (TOF) method. In a-Se electron hole mobility demonstrates the following typical features: (a) the drift mobility values are independent on technology (~p 0.13-0.15 c m 2 V -1 s -1 , /.Ln ~ ( 5 - 8 ) X 10 - 3 c m 2 V -1 s - 1 , at T - 300 K); (b) ~(T) dependence typically demonstrates activation behavior, and activation energy increases when temperature decreases (Fig. 2); (c) in the vicinity of vitrification temperature (Tg - 305 K) temperature dependencies of/.Lp,/.Ln and o- demonstrate hysteresis, which well correlates with hysteresis of sample volume change with temperature; (d) in the low-temperature region the charge carrier package drifting through the inter-electrode distance demonstrates anomalous dispersion, which increases when temperature decreases. The above-mentioned features had been explained by stochastic transport caused by multiple trapping of charge carriers to energetically distributed localized states of intrastructural nature. Such charge carrier transport model qualitatively explained electric field dependencies on electric field and inter-electrode distance. However, the stochastic transport model is insufficient for the interpretation of experimentally obtained electric field dependencies of mobility (Fig. 2) and mobility activation energy (Fig. 3), which vanishes in high electric field regions (F > 0.5 MV cm- 1). To find out the nature of these
1 /
lO-I
r
E r
10-2
m
10-3 -
g 10-4 0.0
i
166K I
0.5
i
[
1.0
F (MV/cm) FIG. 2. Electric field dependencies of hole drift mobility /LLp and micromobility/x0 at different temperatures in a-Se.
20
A. Cesnys et al. 0.4
0.3
0.2
'-"
-
0.1
0"00.0
I
I
0.5
I
~'~)1
1.0
I
F (MV/cm) FIG. 3. Electricfield dependence of drift mobility activation energy E~ of electrons and holes in a-Se. dependencies, research has taken place using subnanosecond TOF and picosecond Austin switch arrangement, micromobility, transients of charge carrier trapping, and impact ionization in high electric fields. 2.3.
M U L T I P L I C A T I O N E F F E C T IN A M O R P H O U S S E L E N I U M
In order to avoid possible injection from electrodes in very high electric field regions, aSe layer was placed in between two insulating layers. The experimental quantum efficiency /3 has been estimated to be significantly higher than one (Fig. 4) and exponentially dependent on thickness of a-Se layer (Fig. 5). These results point that charge carrier multiplication is caused by impact ionization. More careful investigations demonstrated that densities of generated by electric field holes and electrons are equal. This result pointed to band-to-band impact ionization (Ju~ka and Arlauskas, 1983). The latter effect, together with an increase of nonactivated micromobility with electric fields, showed that charge carrier heating by electric field proceeds, and this is a factor of the/z0 increase with electric field. It is interesting to note that in crystals and in other disordered materials, the mobility of hot charge carriers decreases with electric field due to intensification of scattering, while in a-Se, the charge carrier micromobility increases with energy, as predicted by Mott and Davis (1979). Obtained experimental results allowed the plotting of the mobility band; i.e.,/~n, /-/'p dependencies on charge carrier energy (Ju~ka, 1991), which explained a very unexpected result: band-to-band impact ionization in materials with such low micromobility. Later investigations, as well as the application of this effect in an enhanced sensitivity camera (Tsuji, Takashi, Hirai and Taketoshi, 1989), confirmed this model. Archipov and Kasap (2000) have also proposed a model, which facilitates probability of impact ionization through intermediate localized states.
Charge Carrier Transfer at High Electric Fields in Noncrystalline Semiconductors italy2
.
.
21
.
10 e~
1
I
0.0
0.4
0.8
1.2
F (MV/cm) FIG. 4. Electric field dependencies of quantum efficiencies/3 of holes (thickness of a-Se layers: O, 103/.~m; 77, 33 ~m; +, 7/xm; u 4/xm) and electrons ( • 59/xm; 9 5 / x m ; . , 4/xm).
Experimental estimation of impact ionization coefficient allowed evaluation of the mean kinetic energy E and the distance of energy dissipation distance Ae of both sign charge carriers as
/3 =/30 exp(ad),
where the impact ionization coefficient a is
1 ( Ei )
o l - -~-E-eexp Ei
eFAe
(2)
'
is impact ionization energy (2.3 eV). The electric field and temperatures dependencies of Ae are shown in Figures 6 and 7.
9 MV/cm 0,8
10
0,7 0
50
100
d (~tm) FIG. 5. Dependence of quantum efficiency on thickness of a-Se layers at different electric field.
22
A. Cesnys et al.
~Ep
2
~En
00.6
,
I 0.8
,
I 1.0
,
1.2
F (MV/cm) FIG. 6. Electric field dependencies of energy dissipation distance of electrons
AEnand
of holes
AEpin
a-Se.
These AE values and their temperature dependencies are close to values and temperature dependence of thermalization distance, which has been estimated in terms of quantum efficiency according to Onsager's model (Pai and Enck, 1975). That AE is shorter than Coulomb radius (rc--e2/4"rmeokT) also follows from experimentally obtained Langevin's recombination at high exciting light intensity in a-Se (Jugka, 1991). The impact ionization of electrons, due to their lower mobility, appears in electric fields higher than that of holes. In very high electric fields (> 1 MV cm-1), it has shown the electron impact ionization, which caused avalanche formation with following limitation of maximal electric field Fm. The Fm was calculated from the partial capacitance of the system (insulating layer/a-Se/insulating layer), subtracting the part of the field which was produced by the free carriers in the polarized sample. This part of the electric field was
1.5
- 7.5
~hot >
1.0
5.0 ~Ep
~5 0.5
2.5
la0
0.0 200
I
,
250
I
300
,
0.0 350
T (K) FIG. 7. Temperature dependencies of equilibrium hole micromobility/-to, hot hole mobility/-/.hot (F -- 0.9 X M V c m - 1 ) and energy dissipation distance of holes (F = 1 MV cm -1) in a-Se.
Charge Carrier Transfer at High Electric Fields in Noncrystalline Semiconductors
23
1.5
1.0
0.5
0.0
. . . .
'
'
I
l0
i
i
i
i
. . . .
I
10 2
d (~tm)
FIG. 8. Dependence of avalanche limited maximal electric field Fm on thickness of a-Se layer.
determined from the transit time, when the system is short-circuited immediately after switching-off the voltage. It is necessary to emphasize that the electric field sharply saturates at Fro, and higher electric fields could not be achieved. Figure 8 shows the Fm estimated from the experiment accounting for theoretically calculated condition of avalanche formations: Ynd((exp(Ynd))- 1 ) / ( y p d - 1 ) - 1.
(3)
The Yn and yp is impact ionization coefficients of electrons and holes correspondingly estimated in before-avalanche electric field. Another unexpected experimental result was the abrupt vanishing of drift mobility activation energy (E~) in very high electric fields. In subnanosecond time scale the TOF measurements demonstrated that vanishing of E~ is caused by trapping time (~'c) dependence on the electric field but not by electric field stimulated release time (ZR) as it has been expected (Jugka, Arlauskas and Montrimas, 1987). This conclusion follows from measured trapping to drift states time with trapping factor estimated as micromobility and drift mobility ratio ( f -- ((~0//~) - 1) -1) (see Fig. 9). The experimentally obtained low micromobility values, even at high charge carrier energy, do not support the description of charge carrier transport, either by effective mass or polaron models. In disordered structures, the very strong scattering causes charge carrier transport, and the micromobility may be described as ~o = --~ vh exp - - ~ -
,
(4)
where A is mean free path of charge carriers. Since the charge carrier scattering on randomly distributed atoms is elastic, the A must be shorter than AE ~ 2 nm (obtained by extrapolating to low electric field) but not shorter than inter-atomic distance a ~ 0.26 nm. Thus, the evaluation of charge carrier thermal velocity gives v ~ 3X 105 c m s -1, which is much lower than that become accustomed of semiconductors, while free path duration has been estimated of the order of 10 -13 s (Jugka and Arlauskas, 1995).
24
A. Cesnys et al.
40
20 0
x 20
0
10
i
0.0
0.5 F (MV/cm)
0
,
1.0
FIG. 9. Electricfield dependence of energy E of hot hole, time of capture to drift states ~'c and trapping factor f in a-Se. 2.4.
INFLUENCE OF CHEMICAL COMPOSITION ON CHARGE TRANSFER IN A s - S e SYSTEM THIN FILMS
Chalcogenide glasses, especially compounds and alloys belonging to the A s - S e system, are usually applied in practice in the form of layers. A s - S e layers are prepared by thermal evaporation of A s - S e alloy in vacuum upon metallic or metallized substrates heated up to 1 0 0 - 1 8 0 ~ The initial material for sputtering is usually prepared by heating the Se and As mixture in a vacuum of 10 - 4 - 1 0 -5 Torr at a temperature of 700 ~ during 5 - 7 h. Chemical composition of the layers may be different from composition of the initial material, because partial separation of the components may occur during evaporation (Dembovskii, 1964). It was found that during sputtering of As2Se3, AsSe, and As2Se5 upon substrates at a temperature lower than 200 ~ layer composition is the same as that of the initial material (see Table I). Composition of layers prepared from A s - S e alloys is changed in the direction of the nearest of the compounds As2Se3, As2Ses, AsSe. Composition of layers obtained from alloys with high Se content, which are a mixture of chemical compounds and free Se, is quite different from composition of the
TABLE I Initial compound
a
As2Se3 AsSe As2Se5 AsSe4 AsSe9 AsSe20 aSynthesized 4 h at 700 ~
Chemical composition of layers at substrate temperature, ~ 100
150
200
240
AsSe1.5 AsSel.05 AsSe2.44
AsSe1.47 AsSeo.96 AsSe2.46 AsSe3.87 AsSe5.81 -
AsSe1.55 AsSel.o7 AsSe2.38 AsSe3.57 AsSe5.6 -
AsSe1.63 AsSe1.30 AsSe2.30 AsSe3.46 AsSe4.8 AsSe12.7
--
AsSe7.6 AsSe15.9
Charge Carrier Transfer at High Electric Fields in Noncrystalline Semiconductors
25
initial material (see Table I). The differences between layer composition and the composition of the initial material also increase with temperature of the substrate. Enrichment of layers with As is probably caused by evaporation of Se by way of sublimation from the substrate. Investigation of small-charge drift (SCD) current in selenium-arsenic layers is complicated by the fact that electrical properties of those layers, as well as properties of the SCD current, depend on preliminary illumination, duration of voltage application and electric field strength (Montrimas, Pa~6ra, Tauraitien6 and Tauraitis 1969a; Montrimas, Pa~6ra, Tauraitiene and Tauraitis, 1969b; Dienys, Kalad6, Montrimas and Pa~6ra, 1971; Kalad6, Montrimas and Pa~6ra, 1972; Montrimas, Pa~6ra and Vi~6akas, 1976). The curves of transient SCD photocurrent in selenium-arsenic layers usually have a characteristic break point, which denotes the transit time of charge carriers across the layer (see Fig. 10). This break point becomes more distinct when the voltage pulse is applied almost simultaneously with a short pulse of light. However, if voltage is applied (a) 0.8 1
0.4
o.o
|
t (ms)
2
(b) 1/
0.8
06 0.4
0.0
0.0
i
0.2
,
t(ms)
0.4
i
FIG. 10. ElectronSCD current kinetics in As-Se layers under exposure to a 10-7 Spulse of strongly absorbed light. Curves 1-3 correspond to AsSe2o layer with thickness l = 16/xm. (1) U -- 516 V, (2) U = 460 V, (3) U = 370 V; (1/ to 3/) layer AsSe~2, l -- 12/zm, (1/) U = 360 V, (2/) U -- 272 V, (3/) U = 173 V. Prior to the measurements, the layer has been exposed to white light.
A. Cesnys et al.
26
much earlier than the pulse of light, or charge carrier transit time is measured in electrographic mode (Gaidelis, Montrimas, Pa~6ra and Vi~6akas, 1972), the mentioned break point on the curves of transient SCD photocurrent is quite weakly pronounced, or even absent (see Fig. 10). This fact indicates that the action of electric field causes a significant change of transfer of charge carriers in selenium-arsenic layers. Even small amounts of arsenic, only several percent, cause significant decrease of drift mobility of electrons and holes in comparison with a-Se, as well as a change of curves of SCD current kinetics. As is evident from the kinetics of electron SCD current in selenium-arsenic layers (Fig. 10b), there is an increase of electron SCD current before the characteristic break point, especially in the case of prior exposure of the layer to white light. Clearly, this is a result of inhomogeneous distribution of electric field strength in the layer. An external electric field removes quasi-free holes from the layer, so that negative bulk charge forms in the layer. When negative voltage is applied to the free surface of the layer, or the layer is charged negatively, then a charge of the same polarity as on the layer surface forms in the bulk of the layer. Thus, electric field strength and SCD photocurrent increases the further one gets from the surface (cathode) into the layer. When electrons reach the opposite electrode, an abrupt break appears on the curve of transient SCD photocurrent. This break marks the effective time of electron transit through the layer. However, when the free surface of the s e l e n i u m - a r s e n i c layer has been charged positively, then the highest electric field strength is achieved near the layer surface, and it decreases the further one gets from the surface into the layer according to distribution of negative charge in the bulk of the layer. Such distribution of electric field causes a decrease of transient SCD photocurrent with an insignificant bend on the SCD curve, or current decreases monotonically to zero (Fig. 11, curves 1 and 3) (Montrimas and Pa~6ra, 1968" Dienys et al., 1971). If, however, during exposure to a short pulse of light, the layer is additionally exposed to a semi-infinite pulse of strongly absorbed 1.0
0.5 EL ,,,-~
5 0.0 0.0
|
0.4
0.8
t(ms) FIG. 11. Hole SCD photocurrent kinetics in As2Se3 layers under exposure to a | 0 - 7 s pulse of strongly absorbed light. Curves 1 and 2 correspond to layer thickness 1 -- 11/~m, initial charging potential U -- 140 V. Curves 3 - 5 : l = 12/~m, U -- 292 V. Curves 1 and 3: no illumination; Curves 2 and 4: under weak illumination with strongly absorbed light; Curve 5" intense illumination.
Charge Carrier Transfer at High Electric Fields in Noncrystalline Semiconductors
27
light, then the break on the curve of SCD photocurrent kinetics appears as a small and wide maximum (Fig. 11, curves 2, 4 and 5). As intensity of illumination increases, another small and wide maximum appears on SCD kinetics curves. This maximum has a tendency to shift to longer periods. Strongly absorbed light injects holes into the layer. These holes recombine with trapped electrons and thus decrease their density in the bulk of the layer. In addition, holes are trapped near the cathode, because the electric field is weakest in that region of the layer (Montrimas et al., 1969a,b; Vi~6akas, Gaidelis, Lazovskis, Montrimas, and Pa~6ra, 1969a; Vi~akas, Montrimas and Pa~6ra, 1969b). Electron drift mobility ~ r at electric field strength 105V cm -1 decreases with increasing content of arsenic in selenium-arsenic layers (Fig. 12, curve 1). Already at 1 at.% of As in the layer, ~dr is more than 10 times lower than that in amorphous Se. When the content of As in a selenium-arsenic layer exceeds As amount in AsSe4, electrons become practically immobile (i.e., /.Zdr < 10 - 8 cm 2 V -1 s-l). Electrons are also immobile in layers of compounds AsSe and AszSe3 as well (Montrimas et al., 1969a,b, 1976). When the amount of As in selenium-arsenic layer is increased from 0.3 to 3 at.%, hole drift mobility decreases from 10 -1 to 10 -5 cm 2 V -1 s -1. Hole drift mobility in AszSe3 layers equals (2-3) x 10 -5 cm 2 V -1 s -1 (Fig. 12, curve 2). Hole and electron drift mobilities are strongly dependent on electric field strength (Fig. 13). Increase of electron and hole mobilities in selenium-arsenic layers of various chemical composition with increasing applied voltage is caused by a stronger modulation of potential wells that capture charge carriers during their drift through the layer. Temperature dependence of hole and electron mobility in selenium-arsenic layers is exponential (Fig. 14). Assuming that charge carrier drift mobility in A s - S e layers is determined by trap levels, hole activation energy in AszSe3 layers is 0.5 + 0.05 eV. An increase of As concentration from 0.2 to 8 - 1 0 at.% causes an increase of electron activation energy from 0.36 to 0.51 eV.
-2
lO
2 I
r v
1= ra
1
-8,
:::L zl.
16 6
0.3
3
C (at % As)
30
FIG. 12. Dependenceof electron drift mobility (curve 1) and hole drift mobility (curve 2) on composition of selenium-arsenic layers.
A. Cesnys et al.
28
lj
10 -4
2
E ,,9,o ::L
10
-5
'
200
400
'
600
u(v)
FIG. 13. Dependence of drift mobility on charging potential for holes (curve 1) and electrons (curves 2, 3). Curve 1" AszSe3 layer, l = 15/~m; Curve 2" AsSel2, l -- 16/~m; Curve 3: AsSe4, l -- 18/~m.
10 .3
|
|
!
1 0 .4
::k
"x
1 0 .5
1 0 .6
3.0
3.2 103/T
3.4 ( K -1)
Fxa. 14. Temperature dependence of drift mobility for electrons (curves 1 - 5 ) and holes (curve 6). Curve 1: Se + 2 at.%As, 1 = 16 txm, U = 116 V, AE H = 0.36 eV; Curve 2: Se + 3 at.%As, l = 12 txm, U = 272 V, AEH = 0.42 eV; Curve 3: AsSe9, l = 16 txm, U -- 460 V, AEH = 0.51 eV; Curve 4: AsSel2, l = 16 txm, U = 515 V, AER = 0 . 5 1 eV; Curve 5: AsSe4, l = 18 ~m, U = 4 6 0 V , AEH = 0.5 eV; Curve 6: AszSe3, l = 13 txm, U = 140 V, AEH = 0.5 eV.
Charge Carrier Transfer at High Electric Fields in Noncrystalline Semiconductors
29
Unlike in a-Se layers, for which extensive information concerning the lifetimes of electrons and holes is available (Kalade et al., 1972; Montrimas and Jankauskas, 1985; Kalad6, Montrimas and Jankauskas, 1991, 1999), investigation of the lifetimes of charge carriers in layers of the A s - S e system is complicated by the fact that electric field strength in those layers is sometimes strongly coordinate-dependent. Electric field inhomogenity in Se-As layers decreases after keeping the layer in the dark for a long time. Lifetimes of holes and electrons in layers of the A s - S e system increases with As concentration. Hole lifetime in layers with 2at.% As is as high as 10 -3 s. For comparison, hole lifetime in a-Se layers is only several microseconds. Hole lifetime in A s z S e 3 layers is (2-4) • 10 -3 s. When As concentration increases from 1 to 20 at.%, electron lifetime increases from ( 2 - 3 ) • 10 - 4 t o ( 7 - 1 0 ) • 10 -3 s (Montrimas et al., 1969a,b, 1976). Layers of the a - S e - P - T e three-component system, prepared by the method of discrete evaporation, are important for the needs of electrophotography. Several per cent of Te increase layer photosensitivity significantly in comparison with photosensitivity of a-Se layers. However, Te also facilitates crystallization. The P component increases resistance to crystallization significantly (Montrimas, Jankauskas and Rink~nas, 1997). Depending on concentrations of P and Te components in the three-component system, charge carrier transport microparameters can vary in a wide range (Kalade, Montrimas and Jankauskas, 1994). For example, hole drift mobility in a layer with 5 at.% Te decreases only 15-20 times in comparison with ~h in a-Se, but an increase of P concentration in amorphous Se up to 5 at.% causes a decrease of hole drift mobility from 10 -~ t o 10 - 6 c m 2 V - l s - ] (Fig. 15). Hole drift mobility in threecomponent layers Se0.88P0.02Teo.1 at electric field strength 3 • 105V cm -~ reaches ( 7 - 8 ) • 10 - 5 c m 2 V - ] s -], whereas an increase of P concentration up to 4 at.% causes a decrease of/~h by more than an order of magnitude.
10-' 10 .2
/I / I . / [ Il - i ' - 4 - 1 - - Z
10 -~ ~> e,i
I
d
10-4
E
=L
10 -~
./[,) z_
I zE"_/
5
+
I,," / - T 0 " - "--- ;""-'/1
10 .6 0
7,'3 @." "1~'""~~~
re (at. %)
"
FIG. 15. The hole drift mobility dependence on a composition of layers of a - S e - P - T e system.
30
A. Cesnys et al.
10 .5 A
>
E o
::t.
,~-6
I "~ ~ "~I" ~"
10 .7 10 .8
i(~ s
15
O'
51"10
FIG. 16. The hole (squares) and electron (circles) free path length (~z) dependence on a composition of layers of a-Se-P-Te system.
Hole and electron free paths with respect to trapping into deep traps in layers of a-SeP - T e system have been calculated using the formula UR _ 1-- d--W-
Uo
1-exp
/.z'rUo
(5)
where UR is the residual potential, U0 initial charging potential, d layer thickness, ~ drift mobility and ~-is the lifetime with respect to trapping into deep traps. Dependences of calculated free path on concentrations of P and Te components are shown in Figure 16. When P concentration is increased from 0 to 4 at.%, the hole free path (/~-)p decreases from 2 • 10 -v to (2-4) x 10 -9 cm 2 V -1. Such significant decrease of (~'/')p indicates that P creates new deep hole traps. When Te component concentration in amorphous selenium is as high as 10 at.%, (/~Z)p is equal to ( 3 - 6 ) x 10- 7 cm 2 V - 1. In layers of Seo.s8Po.ozTe0.1 system, (/~-)p ~ 10 -6 cm 2 V -1 . With increasing concentrations of P and Te components in a - S e - P - T e system, (/~Z)n for electrons decreases faster than (/ZZ)p. An increase of P concentration to 1 at.% causes a decrease of (/.LZ)n to ( 2 - 5 ) X 10 - 9 c m 2 V -1, and electrons become practically immobile.
2.5.
SPACE CHARGE FORMATION AND DISTRIBUTION IN A s - S E SYSTEM THIN FILMS
Preliminary illumination has a strong influence on electric properties of layers of A s - S e system. In contrast to a-Se layers, whose electric properties do not change noticeably after a prior exposure to white light, discharge rate of AszSe3 layers in the dark is significantly affected by prior illumination. In particular, the half life of potential dark decay of AszSe3 layers after a prior exposure of 3 • 10v lx s decreases 10 times (Fig. 17) in comparison with
Charge Carrier Transfer at High Electric Fields in Noncrystalline Semiconductors
31
(a)
800
400
0
|
|
0
|
30
60
90
t (s)
(b)
400
1 200
0
0
|
|
75
|
150
225
t (ms) Fro. 17. Curves of positive potential decay for As2Se3 layer in the dark after prior exposure to white light (a): 1, layer has been kept in the dark for 20 h; 2, after exposure Lt = 5 x 102 lx s; 3, Lt = 5 x 103 lx s; 4, Lt -- 2 X 105 lx s; 5, Lt -- 3 x |07 lx s; after prior exposure to light with energy 5 x 10 -4 erg cm -2 (b). Curve 1, after keeping the layer in the dark; 2, • -- 440 nm; 3, A = 600 nm; 4, A = 660 nm.
the same layer kept in the dark for several hours. Discharge rate of As2Se3 layers also depends on spectra composition of light used for preliminary exposure (Fig. 17). The highest discharge rate is achieved after a prior exposure to weakly absorbed light, i.e., when charge carriers are photogenerated in the whole bulk of the layer. The increase of positive potential decay rate after preliminary exposure of AszSe3 layers is a result of hole excitation from occupied levels in the bulk of the layer. This process is accompanied by formation of negative bulk charge due to immobility of electrons. In order to restore initial properties of layers, they must be kept in darkness for a long period (10-40 h). This indicates that recombination intensity of photogenerated charge carriers is low. The restoration time decreases noticeably when the layer is kept at a heightened temperature. Electric field speeds up restoration process in the initial stage of the fatigued
A. Cesnys et al.
32
layers, although the complete restoration cannot be achieved when the field exists. This is caused by ionization under the action of electric field, i.e., changes of layer electric properties caused by electric field are as long lived as those caused by prior exposure. Formation of negative bulk charge in A s - S e layers is especially obvious when applied voltage gradually increases from zero to a specific value (Gaidelis et al., 1972). In such a case, charging current of the previously exposed AszSe3 layer increases at the moment of voltage switch-on, then grows to a maximum and then starts to decrease (Fig. 18, curve 3). If the layer has been kept in the dark, charging current at first decreases, then starts to increase, passes through a maximum and decreases to zero (Fig. 18, curve, 4). The maximum on the charging curve is caused by formation of negative charge in the layer. The hatched area is proportional to the bulk charge. At low values of applied electric field, charging current in layers that were kept in the dark is determined by geometric capacitance of the layer. At electric field strengths above (3-4) x 104 V c m - 1, charging current is caused by excitation of holes from previously filled states. Dissipation of negative bulk charge does not take place during several seconds after voltage switchoff, as evident from the fact that repeated charging during this period of time causes charging of geometric capacitance only (Fig. 18, curve 7). Noticeable neutralization of the bulk charge occurs several seconds after voltage switch-off (Fig. 18, curves 5 and 6). For a-Se layers, charging current in the dark corresponds to charging of geometric capacitance, i.e., bulk charge does not form. In a-Se layers, bulk charge can only form as a result of injection of holes or electrons from electrodes and trapping of charge carriers (Fig. 18, curves 1 and 2). Distribution and re-distribution of bulk charge in a layer can be investigated using the method of bulk charge neutralization by means of linearly decreasing voltage applied to the electrodes of the layer (Gaidelis et al., 1972; Vi~6akas et al., 1969). Figure 19 shows a model of the layer with negative bulk charge. Linear decrease of applied voltage causes accumulation of positive charge on the bottom electrode. Strongly absorbed light causes
T 0
'~__/I[/Z! 1
tt~
I1/!
1//77 2
FIG. 18. Charging kinetics of As2Se3 layers. Curve 3, As2Se3 layer, l = 18/~m, U = 335 V, after prior exposure; Curves 4 - 7 , AszSe3 layer, l = 60/zm, U = 500 V. Curves 1 and 2 correspond to a-Se layer, l = 3 5 / x m , U = 100V.
Charge Carrier Transfer at High Electric Fields in Noncrystalline Semiconductors
-
!: "+
M
-tCti- s .d --,ira
o(t)
<
+ 44+ + + +
p(x) ,ram
~m
33
I
, hv
4
§ +
..!
11
. m
h._ v
|
!
.
FIG. 19. Model of a parallel-plate layer with negative bulk charge distribution of positive and negative charge after partial layer discharge by linearly decreasing potential; holes are injected into the layer under exposure to strongly absorbed light, whereas zero-field boundary--inversion plane M--shifts into the region of negative bulk charge.
injection of holes from the bottom electrode into the layer. Those holes neutralize negative bulk charge up to the lines of field inversion (M). Thus, time dependence of current flowing through the layer during linear decrease of voltage is determined by geometric distribution of bulk charge. Solution of one-dimensional Poisson equation for a parallel-plate layer with bulk charge yields expressions for time dependences of screening depth L(t) and distribution of bulk charge p(L) (Vi~6akas et al., 1969; Gaidelis et al., 1972): L(t) --
dU eeo dt J ,
p(L) =
j3[ dU
dJ] -1
--d-t- e e o - ~
(6)
1.0 1 -.n
xi o,,,~
O.5
/ 1
t/z-
2
FIG. 20. Change of discharge current of A s - S e layers with linearly decreasing voltage. Curve 1" As2Se3 layer, l = 14/xm, U = 263 V, voltage decrease time zi -- 3.7 x 10 -2 s; Curve 2: AsSe4, l = 18/xm, U -- 220 V, ~'i - 1 x l0 -2 s; Curve 3: Se + 2 at.% As, l -- 17/~m, U = 200 V, zi = 1 x 10 -2 s.
34
A. Cesnys et al. 1017
2O
,.
16
14
10 co !
E v
_
_
____.~
o
~,~ (3.
8
10is
1014
~.....~
O
Cathode
,,....,
5
I(l~m)
10
W
~,,.,._...~ 2
Anode
FIG. 21. B u l k charge distribution in As2Se3 (curves 1 - 5 ) and a-Se (curve 6) layers. Curves 1-5" 1 = 1 4 / ~ m (scale on the left). Curve 1" E = 7.2 x 104 V cm -1 , duration of prior action of electric field tE = 5 S, Curve 2: E -- 7.3 X 104 V cm -1, tE = 7 min; Curve 3: E -- 7.6 x 104 V cm -1, tE = 10 S; Curve 4: E = 11 X 104 V • cm -] , tE = 10 S; Curve 5: E = 1.9 X 105 V c m -1 , tE = 10 s; Curve 6: after prior injection of holes into the a-Se layer from the anode under exposure to strongly absorbed light (scale on the right).
Using time dependence of the current j (Fig. 20), bulk charge distributions inside the layer have been calculated (Fig. 21). If both the applied voltage and the duration of its action have low values, then density of negative bulk charge in the AszSe3 layer is low, and its dependence on coordinate is weak (Fig. 21, curve 1). However, an increase of applied voltage or of its duration causes a decrease of negative bulk charge density near the cathode, and its increase near the anode. Re-distribution of negative bulk charge is a result of increase of electric field strength near the anode. This field excites holes, which drift towards the cathode and recombine with electrons near the cathode. Thus, density of negative bulk charge in AszSe 3 layers reaches (1016-1017) cm -3 near the anode, whereas its value near the cathode is as low a s 1 0 1 4 cm -3. Such strong inhomogenity of distribution of negative bulk charge in AszSe3 layers, as well as in these layers with impurities Sb, Bi, Te, causes an increase of electric field strength near the anode to values exceeding 106V cm-1. This extremely strong electric field caused an interesting phenomenon--impact multiplication of charge carriers in the anode region of the layer of a glassy semiconductor (Montrimas, Tauraitien6 and Tauraitis, 1972; Tauraitien6, Tauraitis and Montrimas, 1970). This has been confirmed experimentally by investigation of photodischarge of AszSe3 layers (including those with additives of Sb, Te, Bi), where quantum yield of photogeneration of charge carriers can be as high as 3 or 4 (Tauraitiene et al., 1970; Montrimas et al., 1972; Montrimas, Bal6ianas, Fung Cho and Do Van An, 1985) (Fig. 22). Bearing in mind the absence of photoelectric amplification in electrographic mode and taking into account the fact that energy of light quanta in the spectral range from 300 to 700 nm is insufficient for photogeneration of more than a single free pair, one can conclude that the effective
Charge Carrier Transfer at High Electric Fields in Noncrystalline Semiconductors
35
3 -
eff
2
1 I,,
|
|
300
|
400
~
500
|
600
|
700
%(nm) FIG. 22. Spectral dependences of effective quantum yield of charge carrier photogeneration in As2Se 3 layers (curves 1-5), AsSel.sTlo.o4 (6) and a-Se layer (7). Curve 1" layer thickness I = 1.1/xm, initial positive charging potential U0 -- 100 V, substrate temperature during layer sputtering tc = 150 ~ Curve 2: l - - 10/xm, Uo = 500 V, tc = 150 ~ Curve 3:1 = 19/xm, U0 = 600 V, tc = 160 ~ Curve 4: l = 9/xm, Uo = 400 V, tc = 140 ~ Curve 5: same as curve 4, but with prior exposure to weakly absorbed light; Curve 7" l = 38/xm, U 0 = 1200V, t c = 8 0 ~
quantum yield (/~eff) of photogeneration of charge carriers is determined by impact ionization of charge carriers in strong electric field. Such a high value of/~eff indicates existence of favorable conditions for heating of a charge carrier during its free flight in a narrow region near the anode due to accumulation of electrons in this region of a layer with the composition discussed above. Multiplication of charge carriers is most efficient in a thin surface region of the layer, and it is little dependent on photon energy of strongly absorbed light. However, if light penetrates into the bulk of the layer, then a part of primary photocarriers are generated in a region of weak electric field, where hole multiplication is unlikely, so that 3eff decreases significantly. In oL-Se layers, when electric field strength is (4-6) x 105 V cm-1, which corresponds to limiting value of charging potential, quantum yield of charge carrier photogeneration approaches unity, but does not exceed it. In other words, multiplication of charge carriers does not occur. Evidently, impact ionization of charge carriers in a-Se layers takes place only at field strengths of the order of 106V cm -1 (Jugka and Arlauskas, 1983). Such a high value of electric field strength in a-Se layer can be only achieved using special blocking barriers, which prevent charge carrier injection from electrodes. Value of/3eft in As2Se3 layers depends significantly on electric field strength. When electric field strength increases, ~eff increases at any value of energy of absorbed light quanta (Fig. 23). It has been found that at strong electric fields temperature dependence of /~eff is weak. However, decrease of/~eff with decreasing electric field is most pronounced at lower temperatures (Fig. 24). Most likely, decrease of temperature causes more favorable conditions for energy accumulation on the free path of holes, but separation of photogenerated pairs becomes more difficult at low temperatures, which causes a decrease of/3.
A. Cesnys et al.
36
101 1 "
~eff
10 ~
2,,
:
o
~-~
4
10-1
10 s
........
10 6
F (V/cm) FIG. 23. D e p e n d e n c e of effective q u a n t u m yield of charge carrier photogeneration in As2Se3 layers on electric field strength. Curve 1: layer thickness I -- 1.1/xm, with exposure to light with w a v e l e n g t h A = 260 nm; Curve 2: l -- 10/xm, A -- 260 nm; Curve 3: l -- 19/xm, A - 260 nm; Curve 4: l = 10/xm, A = 560 nm; Curve 5: l = 19/xm, A = 650 nm; Curve 6: l = 10 ~ m , A = 700 nm.
4
'/ V/
100 8
J]eff
6
10
"1
,5/,
2
4
6
, , lo
'
,;,
'
F (V/cm) FIG. 24. D e p e n d e n c e of effective q u a n t u m yield of charge carrier photogeneration As2Se3 on electric field strength. L a y e r thickness I -- 1 8 / z m , A -- 440 nm. Curve 1" sample temperature T -- 10 ~ Curve 2: T --- 0 ~ C u r v e 3" T = - 9 ~ Curve 4: T . . . . 16 ~ Curve 5: T = - 2 4 ~
Charge Carrier Transfer at High Electric Fields in Noncrystalline Semiconductors
37
Preliminary exposure of a layer to weakly absorbed light facilitates the formation and redistribution of negative bulk charge. This, in its turn, causes narrowing of the strong-field region near the anode, where hole generation in the dark is most efficient. Thus, charging of the layer to a higher limiting potential becomes possible. The highest/3eff is peculiar to thin (-< 1/xm) AszSe3 layers (Fig. 23, curve 1). This is related to the fact that even the average electric field strength for these layers can exceed 106 V cm- 1. Large values of electric field strength are a result of small layer volume, which leads to relatively small number of excited charge carriers that limit the charging potential. Evidently, the process of hole impact multiplication is determined by strong electric field, whereas the influence of temperature and photon energy on ~eff is exerted through the process of photogeneration and separation of primary pairs. A spectrum of hole energy levels is present in As2Se3 layers. Thermal and fieldstimulated thermal generation of holes from those states is responsible for layer discharge in the dark. This is clearly demonstrated by dependences of the initial rate of As2Se3 layer discharge in the dark (dU/dt)t=o on the initial potential (Uo), which are shown in Figure 25. Three regions are present in those dependences (dU/dt)t-o = f(Uo). In the initial region, which corresponds to weak electric fields, discharge rate grows with initial potential. After that, the growth of (dU/dt)t=o with Uo becomes less pronounced. The third region corresponds to rapid growth of (dU/dt)t= 0 at large values of initial potential. An increase of the initial potential (Uo) from zero to a certain value causes an increase of effective thickness of the layer due to hole generation from the most shallow states and their extraction from the layer. Thus, effective thickness of the layer, as well as thickness of the hole thermal generation region, increases up to the geometric thickness of the layer.
4)!,_.l] J
90 !
O II
0 ....
2
-TI
-t:l 30
0
,,I
150
u(v)
300
FIG. 25. Dependence of the initial discharge rate of the layer As2Se 3 in the dark on the magnitude of initial potential after 30 s since preliminary exposure equal to 1.8 x 10 -3 J cm -2. Temperature: 1, 20 ~ 2, 30 ~ 3, 40 ~ 4, 50 ~
38
A. C e s n y s et al.
This is the reason of the increase of (dU/dt)t-o with initial potential U0. After removing the holes localized in shallow traps from the whole bulk of the layer, discharge rate is determined by the rate of thermal-field generation of holes from local levels. The latter rate is strongly dependent on temperature and prior illumination. At high values of charging potential, the strong-field effect is observed. That effect causes a sharp increase of hole generation intensity. Description of the strong-field effect, according to Frenkel, does not predict such a rapid increase of (dU/dt)t=o with the initial potential as observed in practice. Most probably, the sharp increase of (dU/dt)t=o with increasing potential is a result of hole multiplication at strong fields near the anode of the layer. The bend-point on the dependence (dU/dt)t=o = f(Uo) between the first and the second regions has been used to determine density of holes removed by the field in the initial stage of charging, as well as density of the negative bulk charge formed in the process. The latter density is strongly dependent on temperature and on preliminary illumination. In AszSe3 layers, which have been kept in the dark for a prolonged time, an increase of temperature from 20 to 50 ~ causes an increase of the mentioned density from 0.5 • 1014 to 3 x 1014 cm -3. Preliminary illumination causes an increase of the same hole density from 2.9 • 1014 to 9 • 1014 c m - 3 . The second region of the dependence (dU/dt)t=o = f(Uo) has been used to determine hole generation rate in the layer that has been kept in the dark for a long time. The just-mentioned rate was found to be equal to 0.8 • 1013, 1.2 • 1013, 3 x 1013 and 6.3 • 1013 cm -3 s -1 at temperatures 20, 30, 40 and 50 ~ respectively.
b
0 -I
~2
,
0
,,
100
i 2 00
t(s)
3 00
FIG. 26. Time dependence l n ( d U / d t ) f o r the As2Se3 layer. Layer thickness d = 9/~m. Curve 1: layer has been kept in the dark for 24 h; Curve 2: after preliminary exposure; Curve 3: calculated according to formulas (2.13) and (2.14) as shown by Gaidelis et al. (1968) U(t) -- Uo -
edZm~
- exp(- q~t)] 2e0e
U(t) = o ~ { 2eoemo[1 - exp(- q~t)]}-1
when Icrl > Ipdl when Io-I < Ipdl.
Charge Carrier Transfer at High Electric Fields in Noncrystalline Semiconductors
39
Using analytical expressions for potential decrease kinetics in the dark in the case of thermal generation of charge carriers from local levels in the bulk of the layer (Gaidelis, Markevi6 and Montrimas, 1968), it is impossible to describe adequately discharge kinetics of AszSe3 layers by adjusting the initial density of occupied levels m0 and probability of thermal excitation of holes q~ = v e x p ( - E / k T ) from levels of depth E. Such attempts are unsuccessful even at low values of initial potential, when strong field effects are insignificant. Thus, linear dependence ln(dU/dt) = f(t) (Gaidelis et al., 1968) does not exist in the general case. This means that discharge of the AszSe3 layer is caused by hole excitation from a spectrum of energy levels. However, when the AszSe3 layer has been kept in the dark for a prolonged time, the dependence ln(dU/dt) = f(t) becomes linear during discharge of the layer (Fig. 26, curve 1 as shown by Montrimas et al., 1972). This means that the process of discharge of a layer that was previously adapted in the dark is accompanied by complete emptying of shallow levels, so that discharge is caused by hole excitation from the deepest level. By comparing the calculated dependences ln(dU/dt) = f ( t ) with experimental discharge curves at different temperatures, the activation energy of the deepest hole trapping level and trap density have been evaluated. The mentioned activation energy is equal to A E - - 0 . 9 1 eV, whereas trap density is mo = 1.9• -3.
3. Electrical Charge Transport in Noncrystalline Ga(or In)-Te Systems Structures 3.1.
A VARIETY OF ELECTRICAL CONDUCTIVITY IN BARRIER-LESS STRUCTURES
Currently, there is evidence of field dependence of electrical conductivity of barrierless film structures such as C - G a l - x T e x - C (either Me), where x values are of 0.5, 0.6, 0.75, 0.8 and C-Ino.zsTeo.75-C (either Me), where as the metals (Me) Mo, Au, A1 can be chosen ((~esnys, Oginskas, Butinavi6iQt6, Lisauskas and Shiktorov, 1983a; Cesnys, Oginskas, Liberis and Lisauskas, 1983b; Cesnys, Oginskas and Lisauskas, 1992, (~esnys and Oginskas, 1998). Semiconductor films in these structures were prepared by thermal separate evaporation in a high vacuum (of the order of 10 -5 Torr) of a substance containing the corresponding ratio of Te and Ga (either In) with following condensation of its vapor on carbon glass substrates at temperatures not exceeding 340 K. In the case of x = 0.75, the mixture into evaporator was supplied either by small amounts with a frequency of 2 - 3 Hz (so-called GaTe3(I) films) or continuously (GaTe3(II) films). The latter manufacturing process ensures the better uniformity of the films. Three types of field dependence of electrical conductivity of those films were established: the first type is inherent to the GaTe3(I) and InTe3 films; the second, is intrinsic to the films of GaTe3(II), GaTe and GazTe3; and the third one is characteristic to the Gal-xTex films with x = 0.8. The first type of conductivity. The beginning of the nonlinear part of the currentvoltage ( l - V ) characteristic of these chalcogenides can be linearized in the ln(j/F) --F 1/2 scale up to electric field strength F = 2.5-3.0 V cm -1, where j is density of
A. Cesnys et al.
40
electrical current; F = U/d marks the external electric field strength; U is applied voltage and d stands for the distance between electrodes of the sample ((~esnys et al., 1983a,b). The thermal activation energy of the electrical conductivity was found to be the same for both strong and weak fields and amounted to 0.34 + 0.03 and 0.39 _+ 0.02 eV for GaTe3 and InTe3, respectively. These data are in a good agreement with the results reported in Tolutis, Jasutis, Lisauskas, Pauk~t6 and David6nien6 (1978) in which the fourprobe method was used to measure the conductivity in weak fields. The exponential dependence of conductivity on F 1/2 may be a consequence of two possible processes (Johnsher and Hill, 1978), i.e., Schottky emission from an electrode or the P o o l e - F r e n k e l emission. The main feature on the electrical transport in the case discussed is the fact that the field dependence of the conductivity is independent of the material of the electrode or the thickness of the semiconducting film ((~esnys et al., 1983a,b). To verify the agreement between the experimental data and the P o o l e - F r e n k e l theory, we have used Hill's method (Johnsher and Hill, 1978) in which a graph depicts the function lg[jT -4 exp(Ei/kT)]----f(F1/Z/T), where Ei is the ionization energy of the Coulomb center, k Boltzmann's constant, and T temperature. If Ei - - 0 . 3 6 eV, points corresponding to conductivities at different temperatures and electric fields are found to lie on the same curve (Fig. 27). Consequently, it can be assumed that the P o o l e - F r e n k e l effect in responsible for the carrier transport. The above-normalized curves are reasonably described for GaTe3 and InTe3 by the function 72 exp 3/, where 3 / - / 3 1 F 1/2/(kT). We note that when this function is calculated
10-1
m
10-2 I
<
10-3
T (K) i
It
v - 297
~t ~
- 273
10.4 .
9 - 253 x - 233 A
10-5
_
213
m I
0.1
I
1.0
I
10
F1/2T-1 (Vl/2.cm-1/2.K-1) FIG. 27. Normalized current density J = j T -4 exp(O.36/kT) as a function o f F1/2/T for the C-GaTe3(I)-Mo specimen. The solid curve in the graph of 3/2 exp 3/.
Charge Carrier Transfer at High Electric Fields in Noncrystalline Semiconductors
41
for control specimens of C - G a T e 3 - M o and C - I n T e 3 - M o , the coefficient fll was taken to be 1.47 X 10 - 4 and 1.14 x 10 -4 eV V -1/2 c m 1/2, respectively. These values of/31 were determined experimentally for T = 230 K from the slope of the current-voltage characteristic plotted in terms of the Poole-Frenkel coordinates. Consequently, the current density can be described by the classical expression (Johnsher and Hill, 1978) (7)
j -- ATZF e x p ( a / T ) ,
where A is a constant and a = k-l([31F1/2 - Ei). The dependence of d l n j / d F 1/2 on T -1 for these structures is linear. It agrees with the thermo-activation criterion of Poole-Frenkel emission (Johnsher and Hill, 1978) in contrast to multi-component chalcogenides semiconductor glass (Kvaskov, Parolj, Jofis and Gorbachev, 1981). The dependence (7) for the noncrystalline semiconductors is known to change the exponential dependence of electrical conductivity on electric field strength at certain critical values (Kvaskov et al., 1981). The characteristic property of the discussed structures is the dependence I = I0(T)exp C~lF2 (I is the current strength) that takes place between the above-mentioned regions of field dependence of conductivity ((~esnys et al., 1992). The activation nature of the conductivity persists in this electric field range. However, the activation energy AE which can be found from the dependence In I 0 = f ( T -1) depends on temperature and varies from 0.04 to 0.15 eV. These values are less than the value of AE = 0.36 eV which is inherent for the weak electric field range. The factor C~l increases with temperature rise. The electrical conductivity of the type I --~ e x p C~lF2 was observed in the case of liquid selenium (Glazov, Aivazov, Zelenov and Vadov, 1976). However, in the experiments performed in dc regime, thermal effects were observed (Glazov et al., 1976) which could basically change the experimental results. The Joule heating was insufficient to explain the data in the investigated structures: the experimental results did not depend on the pulse duration (2.5-10 ns) and the temperature increase of the samples did not exceed 2 - 3 K ((~esnys, Gagka, Oginskas and Bal~ianas, 1988). The dependence of I on F 2 is inherent to the many-phonon ionization of the local centers (many-phonon tunneling) assisted by electric field (Timashev, 1977; Karpus and Perel, 1985). However, the theory of such ionization predicts the decrease of t~1 with temperature increase as opposed to our experimental results (see Fig. 28). The parameter al can be expressed as follows (Karpus and Perel, 1985): al1/3 -- (2k) -1 (h2eZ/3m) 1/3(A + l / T ) ,
(8)
where h is Planc' s constant, e electron charge, m the effective mass of charge carriers and A is a parameter. Discrepancy between the theoretical and experimental results can be explained (Timashev, 1977) by nonuniform distribution of electric field strength in noncrystalline semiconductor, and by the change of this nonuniformity with temperature change. Taking into account the validity of theory of compensated semiconductors with high doping level (Gulyayev and Plesskii, 1976) the relation between true value of F and the mean value P can then be expressed as F = P~I,
T1 -- 1 - ~T 2,
~-
Al(ek/eZN1/3) 2,
(9)
42
A. Cesnys et al. 12
1.55
1.5o
10
>
e-i
o o
0
1.45
•
8
X
m
i
-
. 1.40 X
/ i
3.0
I
I
3.8
I
1.35
I
4.6
103/T (K -1)
FIG. 28. Temperature dependence of parameter al[I ~ exp(oqF2)] (1) and of product F/[;; see Eq. (9)] (2) for the noncrystalline GaTe3(I) film.
Cel/3T/2/3[where r/is
where A 1 denotes a numerical factor of the order of 1, e dielectric permittivity, and N the density of the centers. This expression is valid in the following temperature range: ( k / m ) l / 3 ( h e / e 2 ~ ) 2/3 =-- T 1 < T < T 2 =-- e k / n l / 3 e 2 ~ < < T3,
(10)
where n is electron density, T3 is the temperature at which the semiconductor become 1/3 intrinsic. Taking into account expression (9) the quantity a 1 in Eq. (8) must be changed to (al T12) 1/3. The quantity (a1~72)1/3, which is extracted from the experimental data, when ~ = 5 • 10 -6 K -2 according to Eq. (8), linearly depends on T -1 (Fig. 28). The slope in Fig. 28 is 1.2 x 10 - 2 V -2/3 c m 2/3 K. This value is in an agreement with the theoretical estimation obtained from Eq. (8) (3.68 x 10 -2 V -2/3 cm2/3 K for m - m0, where m0 is electron mass). It is worth to note that in this case A-1 ,,~ 130 K. On the other hand (Karpus and Perel, 1985), A-1 __ hw/k In C, where o) denotes vibration frequency of impurity center and C the factor of the order of reciprocal constant of electron-phonon interaction. Then, hw/k is equal to 300 K, i.e., it is close to the value of the Debay temperature. The limit T1, calculated from formula (9) for m - m0 and e - 5 - 1 0 , amounts 150-230 K and correlates well with the experiment if T --> T1. The characteristic size of electron drops in a random potential, estimated using formula R T - ( e ~ l / Z / k ) l / 3 ( h Z / m e ) 2/3 (Gulyayev and Plesskii, 1976) at T -- 300 K for the e values given above gives reasonable values of 33.6-16.8 A. On the basis of the findings presented above, one can infer that the dependence of the electrical conductivity on electric field in noncrystalline Gao.z5Teo.75 films reveals signatures of multiphonon ionization of local centers by a nonuniform electric field. In stronger electric fields, this dependence probably could be related to the 'cold' ionization .,
Charge Carrier Transfer at High Electric Fields in Noncrystalline Semiconductors
43
of electrons due to the tunneling effect without participation of phonons. This can be illustrated by the fact ((~esnys et al., 1988) that the conductivity dependence on electric field becomes less pronounced with the change of temperature. The second type of conductivity. Let us consider the properties of GaTe3(II) films as a typical chalcogenide of this type. The nonlinear conductivity of these films is described by the function o- --~ exp(YbF) up to fields of about 5 • 105 V cm-1 ((~esnys et al., 1992). This type of conductivity, as is well known, may be caused by the appearance of space charge limited currents (SCLC) for homogeneous trap distribution in energy scale (Kolomietz, Lebedev and Cendin, 1971a), and by thermal field Poole-Frenkel emission under conditions of screening (Gubanov, 1954) or by overlapping of Coulomb potentials (Johnsher and Hill, 1978). The latter situation takes place at large concentrations of emission centers N ( > 1018 cm-3). Characteristics that do not support SCLC appearance include the independence of the film conductivity on the electrode material and on the distance between contacts d (film thickness), and most importantly, the essential variation of the character of o - - - f ( F ) curves in this field range when forming a heterotransition of the crystallinenoncrystalline semiconductor type (see (~esnys, Oginskas, Butinavi~ifit6, Lisauskas and Shiktorov, 1984a; (~esnys, Oginskas, Lisauskas, Shiktorov and Butinavi6ifit6, 1984b). On the other hand, I - V characteristics are well normalized according to the Hill technique (Johnsher and Hill, 1978) in coordinates lg(I exp A E / k T ) and lg(F/T). The latter is thought to be the main argument in favor of the second conductivity mechanism of this type of chalcogenides mentioned (Johnsher and Hill, 1978). The normalized curve is described by the function y exp 3', where 3' = y l F / k T . Parameter ")/1 in this case, however, is slightly (by 10-12%) less than its values estimated from the slope of the dependences of ln I / U = f ( U ) . For GaTe3(II) films e.g., Yl is found, take (1.31 _+ 0.01) • 1 0 - 7 and (1.47 + 0.02) • 1 0 - 7 e V V - 1 c m - 1 (at T = 293 K), respectively. This difference is understood by an extra manifestation of a process typical for noncrystalline semiconductors; i.e., the delocalization of charge carriers from shallow local states at the tails near energy band edges, which occurs due to the reduction of potential barriers in Coulomb wells (Lebedev and Rogachev, 1981).1 The intersection of the abscissa axis with an extrapolated line Yb = f ( T - l ) at the point T -1 -- Tc 1 # 0 (Fig. 29b) points out to this fact. For the GaTe3(II) films with x -- 0.75, the parameters are Tc -- (1-1.3) • 103 K, A b -- OTb/~)T -1 -- (2.0 + 0.1) • 10 -3 V -1 cm -1 K -1, r0 e-1 = 1.2 • 10 -7 cm (i.e., r0 ~ 100 A). These values are close to the corresponding data for multicomponent chalcogenides glasses (Lebedev and Rogachev, 1981). In the case considered, the AE value coincides with AE in low fields and is approximately equal to the half of the mobility bandgap (Tolutis et al., 1978). The conductivity curve is normalized with respect to electric field strength F and T (for AE determined from the temperature dependence of o-), when the argument is the quantity lg[F(T-1 _ Tcl)] which coincides with the one computed using experimentally
l Account of this process transforms the classical dependence Yb= AbT-1 for the thermal field ionization screening of the Coulomb potential (Tj) into Yb= Ab( T - I -- Te l) (Lebedev and Rogachev, 1981), where A b - - 3ero/2ek; Tc is the parameter of state distribution in a mobility gap described by the dependence g(E) --~ exp[-(Ep - E)/kTc]; E is energy, Ep the energy level of percolation and r0 the screening radius.
A. C'esnys et al.
44
4.5
"7~ 3 >
103/T (K-~) 4 5
"
6
c5 "~ 3.5
10-4
.
10-6
.
10-8
b
8 "
.
c
1
4
T (K) o
-
169
I
_
178
,t
_
194
m
10-1o
0
2
4
103/T ( K
6
V-
-1)
209
9 - 267 A-
103/Tc
272
9 - 290
2.5
I--
322
I
I
I
I
2
2.5
3
3.5
lg[f(T-1-Tcl)] FIG. 29. Investigation results of the field dependence of electroconductivity of noncrystalline film G a l - x T e x ( I I ) (x -- 0.75): the dependence of the normalized conductivity Gn = (I/U)exp(O.42/T) (in 12-l) upon F(T -I Tc l) (in V cm -1 K -1) (solid curve presents the plot of the f u n c t i o n exp[AbF(T - 1 - Tel)], where A b = 2.1 x 10-3 V -1 cm -1 K -I , Tc -- 1125 K; points denote the experiment) (a); the dependence Yb =f(T) (b); the temperature dependence of the pre-exponential multiplier Ro 1 in the expression I/U = Ro 1 exp ybF (c).
o b t a i n e d Tc and A b values (Fig. 29a). C o n s e q u e n t l y , in this case o- = f ( F , T) is described by the expression o - = o0 exp[Ab(T -1 - T c l ) F - A E / k T ) ] , w h e r e o0 = const. T h e field d e p e n d e n c e of the c o n d u c t i v i t y of GaTe3 and GazTe3 films b e c o m e s m o r e p r o n o u n c e d than described above, starting f r o m F ~ 7 X 105 and ~ 5 x 1 0 5 V c m - 1 , respectively. H o w e v e r , reliable i n f o r m a t i o n on the m e c h a n i s m of charge transport of these films does not exist. The third type o f conductivity. This kind of c o n d u c t i v i t y m e a n s that for n e w l y m a n u f a c t u r e d samples up to F = ( 4 . 8 - 5 . 0 ) x 105 V c m -1 (deviation f r o m the O h m ' s law starts here at F ~ ( 2 . 0 - 2 . 5 ) x 1 0 4 V c m -1) I - V characteristics are described by the function I = I0 e x p ( / 3 1 F 1 / 2 - A E / k T ) (I0 = const). (After the t h e r m a l t r e a t m e n t in an inert a t m o s p h e r e at 3 6 0 - 3 7 0 K, I - V characteristics are better linearized in coordinates lg I / U and F l/Z). A w e a k t e m p e r a t u r e d e p e n d e n c e of/31 in a wide t e m p e r a t u r e range is appropriate in this case (Fig. 30). At T = 2 3 0 - 2 5 0 K, 131 b e c o m e s m i n i m a l value and equals to ( 0 . 8 - 1 . 2 ) x 10 -2 V -1/2 cm-1/2. C o n d u c t i v i t y is i n d e p e n d e n t of the electrode m a t e r i a l and on the distance d b e t w e e n electrodes. It d e m o n s t r a t e s an activation character with AE = 0.37 _+ 0.1 eV, which, similarly to the previous case, coincides with A E in low electric fields.
Charge Carrier Transfer at High Electric Fields in Noncrystalline Semiconductors
45
7 3" r
-150
.
3
",
100 /
"7. m-1
5/
./"
I
\X.~<
- 1020
I
[ I"
.4
12.~"
,*
I
~ ~ ~ I
0
I
I
200
E
31 I
-50
1019 ~.
-
,~1
l
I
I
.
1018
1017
400
T(K)
FIG. 30. The temperature dependence of the parameter/31 for the noncrystalline film Gal-xTex (x = 0.8) (1) and computed curves /31//301 =f(T) (2-4), and T1 = f ( N ) (5). Dashed for e = 5, dot-dashed for e = 10. N, cm-3:1018 (2), 2.5 x 1018 (3), 5 x 1018 (4). In computing T1, m = 0.8m0 was assumed (Kvaskov, 1988).
Contrary to the temperature anomaly of I - V characteristics of this type in chalcogenides glasses (Kvaskov, 1988), /31 is not constant at low temperatures in the considered case, and at high temperature its dependence on temperature is not so pronounced. This anomaly was treated by Cesnys et al. (1992) similarly to Kvaskov (1988), assuming that the theory of highly doped compensated semiconductors is applicable to the noncrystalline semiconductor under study. This theory was developed for nondegenerate electron gas, in the case when inhomogenity of the field distribution, as well as the thermal expansion of nondegenerate electron, drops inside the accounted-for fluctuation potential wells (Gulyayev and Plesskii, 1976). In this analysis, additional attention has been paid to the above-mentioned delocalization of carriers from shallow states (in the region of) thermal field emission due to the reduction of potential barriers. In this case, these processes are revealed in a uniform field,/31 = (/901/k) • (T -1 - Tcl), where/301 = ( e 3 / ' n ' e ) 1/2 (Johnsher and Hill, 1978", Lebedev and Rogachev, 1981). After substituting in this expression 131"01/3 for/31 (taking into account Eq. (9)), the dependence/~1//301 - - f ( T ) was computed for T -> T1 (10), ~0 < T-2 (11), e -- 5 and 10, Tc - 1100 K and N ranging from 1018 to 1019 c m - 3 . Results of the calculation are presented in Figure 30. It was found that the given temperature dependences depend strongly on N. The temperature T1 of origination of the anomaly effect increases noticeably with increasing N. Computed curves ]31--f(T) as well as experimental ones, have a minimum with its broadening (with respect to temperature) and position also dependent on N. Their best fit is observed at N 1018cm -3 e - - 5 ( o r N - - 9 x 1 0 1 8 c m -3 -- 10). The qualitative agreement between experimental and calculation results is better in the considered case than in Kvaskov (1988). The results of this experiment are interpreted using the Gulyayev-Plesskii model (Gulyayev and Plesskii, 1976; Timashev, 1977)
46
A. Cesnys et al.
in the whole temperature range considered. (The low temperature part of the curve /31 = f ( T ) for chalcogenide glasses is interpreted in Kvaskov (1988) by hopping conductivity.) In higher fields (F = (3.2-7.8) • 105 V cm-1; T = 295 K), the conductivity of the films with x -- 0.8 (analogous to the case of GaTe3(I) films considered above) obeys the law I -~ exp CelF2 with the anomalous dependence a 1 = f(T). However, this dependence is linear in (a1772)1/3 a n d T -1 coordinates only at T --> 270 K, when ~: ~ 8.5 • 10 -6 K -2. The slope of this line is (8.6 + 0.5)x 10 -2 V -2/3 cm -2/3 K -1, which agrees satisfactorily with the theoretical value of 3.68 x 10 -2 V -2/3 cm -2/3 K -1 (if m - - m0) determined using the dependence (air/z) 1/3= (2k)-1(hZeZ/3m)1/3(A + I/T) (A is a parameter). The latter is valid for multi-phonon tunneling under conditions of inhomogeneous field distribution (Karpus and Perel, 1985; (~esnys et al., 1988). From the experiment it follows that A- 1 ~ 360 K. A typical dimension of electron drops inside fluctuation potential wells was estimated using the formula RT = ( e~ 1/2/ k) 1/3( h2 / em)2/3 (Gulyayev and Plesskii, 1976) and equals to 36.7-18.3 ,~ (e - 5-10, T - 300 K). This parameter is close to RT for GaTe3(I) films ((~esnys et al., 1988) and to mean dimensions (11 A) of inhomogeneities in these film as well estimated from electron diffraction (Tolutis et al., 1978). The trend towards the stronger field dependence of conductivity above the region of I--~ exp eelF2 in these films was observed only at T--< 270 K (contrary to the films considered in (~esnys et al. (1988)). Generalizing the above-mentioned investigation results, it is possible to conclude that in the field and temperature dependences of conductivity of noncrystalline films of G a - T e systems in high (pre-breakdown) fields, there appears the features of the Poole-Frenkel effect in the case of isolated and screened impurity centers, as well as the delocalization of shallow local states that are typical of structures based on chalcogenides glasses. There are also signs of multi-phonon tunneling under conditions of nonuniform field distribution.
3.2.
NONACTIVATED ELECTRICAL CONDUCTION STATE
Chalcogenide noncrystalline semiconductors in the low-resistance state (LRS) which appear due to the high-field electric instability (the monostable switching effect) possess conduction either slightly dependent on temperature or totally nonactivated (Vezzoli et al., 1975; Oginskas and (~esnys, 1984). Both these conduction types were first observed in chalcogenides glasses of complicated chemical composition, and they are associated with the monopolar injection effect and a Mott-type phase transition (Vezzoli, Doremus, Tirellis and Walsh, 1975; Vezzoli, 1980). However, such interpretation is in hard agreement with the results of Kolomietz, Lebedev and Cinman (197 lb) that point out to possible heating of charge carriers by the electric field in LRS of such a kind of semiconductors. Nonactivated conduction has also been found in noncrystalline G a - T e films ((~esnys and Oginskis, 1998). The distinguishing property of these films is a low level of microwave noise in their LRS which characterizes only heating efficiency of the region of higher density of electrical current (current filament). However, this type of electrical conduction of these films manifests itself only at the currents of low-resistance state ILRS
Charge Carrier Transfer at High Electric Fields in Noncrystalline Semiconductors (a)
40
~
47
8967
30 10
< E 20
0 . _
i
0
1
2 u (v)
3
10
"-- - - r',,2 ~Q
0.5 U (V)
(b) 200
A
A
A
A
A
lO
100 ~
|
'-
I
200
m
"-
12
~
I
250
I
300
350
TO(K)
(c) 150 o
o
o
100
~
"
,w
a
~
.
,qw
.
~,~,-
o
~ .
.
,w
w
-
m
A -
11
15 -v
lq AL,~'
50
I 10-9
I 10-7
I
I 10-5
~d(s) FIG. 31. Measurement results of electric characteristics of the structures carbon glass-noncrystalline Gal-xTex film-carbon glass in the low-resistance state. (a) Transient (solid lines) and static (dash-dotted lines) I - V characteristics (x = 0.75; stationary LRS). ILRS in mA: 2.3 (curves 1, 6 and 7); 5.2 (2, 8 and 9); 12.9 (3); 20(4); 28,4 (5). To, in K: 293 ( 1 - 6 and 8); 205 (7 and 9). Curves 6 and 7 (8 and 9, respectively) were recorded at the same magnitude of ILRsULRs- (b,c) The dependence of the electric resistance determined from the slope of linear transient I - V characteristics upon the environment temperature (b) and switching delay time in LRS at To = 293 K (c). x is 0.6 (curves 10 and 11); 0.75 (12 and 13); 0.8 (14 and 15). The values of ILRS and distance between electrodes for different curves 10-15 do not coincide and are scattered within the range from 10 to 20 mA and from 0.65 to 1.0/xm, respectively.
48
A. Cesnys et al.
exceeding some critical value Ic (Fig. 31). Ic is close to the upper limit of currents at which the structure possesses negative differential resistance and, it is this current at which the current density saturation takes place in the filament ((~esnys, Oginskas, Ga~ka and Lisauskas, 1987; (~esnys and Oginskis, 1998). At ILRS < Ic, transient I - V characteristics which represent the conductivity of current filament are nonlinear, and the conductivity, though of a semiconductor type, depends upon temperature much more weakly than a similar dependence in the high-resistance state. The results on transient I - V characteristics nonlinearity are considered in Cesnys and Oginskis (1994). The straight linearity of transient I - V characteristics and nonactivated electric conduction of the structures on the base of Ga-Te films take place not only in the stationary LRS at ILRS > Ic, but also in the nonstationary LRS, including the mode of the so-called nanosecond monostable switching (nonstationary LRS means that during the action of the pulse applied a constant current across the structure has still not been achieved (Oginskas, Gagka, l~lesnys, 1986)). These phenomena were also observed in barrier-less crystalline structures of Ga2Te3 films. The latter fact demonstrates that the given type of conduction is not associated with the disorder of structure of the active layer. The resistance of the structures RLRS (transient I - V characteristics slope RLds = dlmp/dUmp where Umpand Imp are the voltage drop across the structure and the current in it during the action of the measuring pulse) in the case of stationary LRS at the same ILRS > Ic is independent of the switching pulse amplitude Us (Fig. 31c) (~'d --f(Us); ~'d varied from 2 - 5 ns to 6 - 2 0 ~s). Consequently, RLRS and simultaneously the state of the structures after switching are independent of the processes determining electric charge transport in pre-breakdown fields region ((~esnys et al., 1992) and is responsible for the initial stage of the electric instability development. The noise temperature (Tn) of the structures at ILRS is close, e.g., to the threshold (minimum) current of LRS maintenance and did not exceed 400 K, which is by one or two orders of magnitude below the high-frequency Tn in chalcogenides glass (Kolomietz et al., 1971b) and amorphous selenium (Prikhod'ko, (~esnys and Bareikis, 1981) films. Noise temperature at ILRS- const, is also independent of Us which points to the absence of hot charge carriers in LRS in all the monostable switching modes (Tn was measured at ~'d ranging from 10 ns to 50/xs (Cesnys and Oginskis, 1998)), and the microwave noise level (heating degree) increases only with increasing ILRS up to Ic. When electric current strength reaches the critical value of Ic its growth gradually retards and the dependence Tn--f(ILRs) afterwards tends to saturation at ILRS > Ic (Fig. 32). Such a behavior of Tn remains within the entire environment temperature range from 200 up to 350 K. Temperature in the center of the filament (Tz=0) , current density in filament (j0 and electroconductivity in the range of current filament (o-f) are proportional to the values of ATn, ATn/ULRS and ATn/U2Rs, respectively ((~esnys and Oginskis, 1998). (Here A T n - - T n - TO; TO is the ambient temperature.) One may deduce from the characteristics in Figure 32 that the filament parameters jr, o-f, and Tz=o in the nonactivated conduction state of the films (ILRs > Ic) are virtually constant and current filament radius varies linearly with i1/2 "LRS"Independence of ATn/UZRs on temperature (Fig. 32) is consistent with the suggestion of o-f independence on
Charge Carrier Transfer at High Electric Fields in Noncrystalline Semiconductors
4
~ff-"
ATn ' -
-
U
--
49
"6
,v
-
<1
ATn U-2LRs( I O2 K.V -2) 0
I
0
,,
7!
i- !
I
I
8
I
Ic
u --
I
220 I
16
I
260 I
'
9 ,,
-2
'
--
300 '
24
-
'
T 0(K) i
i
~< < 0
32
ILRS (mA) FIG. 32.
The results of microwave noise temperature measurements in the low-resistance state of the structure
carbon glass-Gao.25Teo.75 f i l m - c a r b o n glass.
temperature in LRS as it was made in the study of transient I - V characteristics ((~esnys and Oginskis, 1998). The temperature in the center of the filament at ILRS > Ic was measured by microwave noise technique (Cesnys and Oginskis, 1998). In GaTe3 film, it was found to be equal to 720-730 K. However, such a heating does not explain the increase of the film conductivity up to 4.5-11.1 f~-~ cm-1; i.e., up to levels suitable for filament formation ((~esnys and Oginskis, 1998). Consequently, on the basis of the classical electrothermal model which explains the development onset of threshold electric instability (switching) in the Gal-xTex films ((~esnys et al., 1983a,b, 1992), it is worth to stress that this approach is insufficient to explain the formation of nonactivated conductance in their LRS. For this purpose one should assume additional influence of electronic processes for which insignificance of hot charge carrier effects is a principal feature. Among such processes involved in explaining the LRS formation in noncrystalline semiconductors, nonactivated conductance would be provided by a phenomenon such as electronic phase transition (Sandomirskii, Sukhanov and Zhdan, 1970; Sandomirskii and Sukhanov, 1976; Kostylev and Shkut, 1978). One of its modifications (Sandomirskii et al., 1970) interpreting the results in the nonlinear electric conductivity of the films of Gal-x-Tex and In~_xTex under study in LRS and the decay process of such a state was earlier successfully used (Oginskas and (~esnys, 1984; (~esnys, Oginskas, Ga~ka and Lisauskas, 1986; (~esnys and Oginskis, 1994). It is distinguished by the fact that by increasing the free charge carrier concentration, gradual 'metallization' of the current filamentation area takes place, which is caused by restructuring of the energy spectrum of levels in the mobility gap of the semiconductor. Any process increasing the free charge carrier concentration in the current filamentation area, including Joule heating, would stimulate this transition. It should be pointed out that with the exception of the above concentrational model, none of the familiar electronic LRS models (Sandomirskii and Sukhanov, 1976; Kostylev
50
A. Cesnys et al.
and Shkut, 1978) is able to explain the formation of near-contact areas with residual weakly expressed semiconductor conduction (t~esnys and Oginskis, 1994) and smooth demetallization at the current filament region during its decay in these films at ILRS < Ic ((~esnys et al., 1986). This is an additional, and at the same time decisive, argument for choosing the electronic phase transition of the above type of the chalcogenides to interpret the described investigation results. On the basis of the experimental findings given above and the results presented in (~esnys et al. (1983a,b, 1986, 1992) and (~esnys and Oginskis (1994), one may thus suppose that the nonactivated conduction state formation in the analyzed chalcogenide films is determined by both thermal and electronic (like electronic phase transition) processes. The former ones are responsible for the onset of this process, or for the classical electrothermal instability arising in the films. The latter ones play the basic role during LRS formation after reaching a seed concentration of charge carriers (Sandomirskii et al., 1970) in it mainly due to Joule heating of the current filamentation region.
3.3.
ELECTRICAL CHARACTERISTICS OF BARRIER STRUCTURES
The field dependencies of carrier transport in noncrystalline semiconducting films can be essentially modified by usage of crystal-semiconductor as an electrode evaporated on the substrate. The key point of this idea is connected with the fact that the concentration of the main carriers in crystalline semiconductor is several orders of magnitude higher than the relevant value in noncrystalline one. Thus, the crystalline semiconductor can serve as a huge reservoir of free carriers which can be injected into noncrystalline material (Dunn and Mackenzie, 1976; Ciulianu, Andriesh and Kolomeiko, 1978). The case of current injection can be realized in materials with heterostructure barrier, for instance, in GaTe3 film evaporated on silicon substrate (t~esnys et al., 1984a,b). Two phenomena can be responsible for a situation that can occur in the GaTe3-Si heterostructures (HS): (1) a change from an exponential I - V curves of the GaTe3 layer, due to bulk effects, to a power-law relationship upon formation of a contact between it and nondegenerate Si (Fig. 33, curve 1) and (2) the presence of a quadratic segment that is similar to heterostructure chalcogenides glass/single crystal HS (Ciulianu et al., 1978) in the forward branches of the I - V curves. As we know, such a segment is one of the primary indicators of space-charge limitation of injection current (SCLC conditions). The strong temperature dependence of the current on these I - V curves can be accounted for by the appearance of a process of 'sticking' of injected carriers on discrete layers (Lampert and Mark, 1973; Ciulianu et al., 1978). In case of electron injection, the activation energy of this layer is 0.36 _+ 0.01 eV as determined from the abovementioned temperature dependence of conductivity. The superquadratic I - V characteristic segment that precedes the quadratic segment in chalcogenides glass/single crystal HS is usually accounted for in terms of the effect on SCLC of capture of the injected carriers by traps that are exponentially distributed in the mobility gap of the glass (Lampert and Mark, 1973; Dunn and Mackenzie, 1976; Ciulianu et al., 1978). In case of noncrystalline GaTe3-nSi HS, however, this
Charge Carrier Transfer at High Electric Fields in Noncrystalline Semiconductors
51
l0 ~ 103
10-2 1 102 < 10-4 101
10-6 10o 0.1
1.0
10
u (v) FIG. 33. Electrical characteristics of noncrystalline GaTe3-nSi barrier heterostructure in the conducting direction: 1, I - V characteristics; 2, the dependence of the ratio of barrier (Rb) and nonbarrier (r) region resistance upon voltage.
part of the characteristic could be interpreted in terms of redistribution of the voltage drop across the amorphous semiconductor and across the barrier region of the single crystal (Cesnys et al., 1984a,b; (~esnys and Urbelis, 2001). Two other facts also argue against the above interpretation based on the assumption regarding SCLC. First, the activation energy AEe of the conduction, as determined from the temperature dependence of the current at the point of transition to the quadratic segment of the I - V characteristic, is less than the value AEa obtained at voltages corresponding to this quadratic segment. (As we know (Ciulianu et al., 1978), AEe can be taken as the distance of the Fermi quasi-level from the edge of the corresponding energy band, when it corresponds to the end of the energy interval in the mobility gap with the above exponential trap distribution. According to the relative position of the quadratic and superquadratic portions of the segments, filling of these traps should occur earlier, and, therefore, the upper edge of this distribution should be at a greater distance from the edge of the band than the discrete level, i.e., we should have AEe > AEa, which is inconsistent with experiment.) Secondly, the characteristic parameter Tt of the presumed exponential distribution of the traps (Lampert and Mark, 1973), as determined from the slope of the I - V lines in l o g / - l o g U coordinates, is temperature-dependent in our case. It is worthwhile to note that in certain cases, the change of character of the field dependence of electrical conductivity cannot be observed. This situation was determined in the study of GazTe3 and SiTe3 ((~esnys et al., 1984a,b).
52
A. Cesnys et al.
References Adler, D., Fritzsche, M. and Ovshinsky, S.K. (Eds.) (1985) Physics of Disordered Materials, Plenum Press, New York. Anderson, P.W. (1975) Model for electronic structure of amorphous semiconductors, Phys. Rev. Lett., 34, 953. Archipov, V. and Kasap, S.J. (2000) Is there avalanche multiplication in amorphous semiconductors?, Non-Cryst. Solids, 266-269, 959. Balevi~ius, S., Cesnys, A., Oginskas, A., Pogkus, A. and Coagka,K. (1984). The negistor structure for formulators of subnanosecond electric voltage drops. In Ways of Enhancing the Stability and Reliability of Microelements and Microschemes. Abstracts of reports of All-Union Scientific Technical Seminar, Moscow, p. 150. Balevi~ius, S., Deksnys A., Dobrovolskis, Z., Krotkus, A., Lisauskas, V., Tolutis, V. and (~esnys A. Material for manufacturing of nanosecond electric pulse former, USSR Author's Certificate No. 736806, H01L (1978) 28/60. Borisova, Z.U. (1964) Influence of some elements on conductivity and micro-hardness of glassy AsSe, Izv. AN SSSR, 28(8), 1293 (in Russian). Borisova, Z.U. and Bobrov, A.I. (1962) Conductivity of system of glasses As-Se-Ga, Vestnik LGU, Ser. Phys. Chem., 22(4), 159 (in Russian). Cendin, K. (Ed.) (1996) Electronic Phenomena in Chalcogenide Glass Semiconductors, Nauka, St Peterburgh, (in Russian). (~esnys, A., Gagka, K., Oginskas, A. and Bal~iQnas, V. (1988) On signs of manifestation of multi-phonon ionization of local centers in non-crystalline GaTe3, Fiz. Tekh. Poluprovodn. [Soy. Phys.-Semicond.], 22(6), 1132 (in Russian). (~esnys, A. and Oginskis, A.K. (1994) Nonlinear electrical conductivity of chalcogenides negistor structures in the low-resistance state, Lithuan. Phys. J., 34(3), 237. (~esnys, A. and Oginskis, A.K. (1998) The state of nonactivated electric conduction of chalcogenide films from microwave noise investigation data, Lithuan. Phys. J., 38(4), 324. Cesnys, A., Oginskas, A., Butinavi~ifit6, E., Lisauskas, V. and Shiktorov, N. (1983) Breakdown in amorphous GaTe3 and InTe3 films in a pulsed electric field, Lietuvos Fizikos Rinkinys [Sov. Phys.-Collect.], 23(2), 46 (in Russian). (~esnys, A., Oginskas, A., Butinavi~iQte, E., Lisauskas, V. and Shiktorov, N. (1984a) Electrical transport and breakdown processes in amorphous GaTe3/monocrystalline Si heterostructures, Lietuvos Fizikos Rinkinys [Sov. Phys.-Collect.], 24(3), 83 (in Russian). (~esnys, A., Oginskas, A., Gagka, K. and Lisauskas, V. (1986) Peculiarities of the decay process of nonstationary low-resistance state in the switching structure based on GaTe3, Lietuvos Fizikos Rinkinys [Sov. Phys.Collect.], 26(5), 589 (in Russian). (~esnys, A., Oginskas, A., Gagka, K. and Lisauskas, V. (1987) Microwave noise and transient on-characteristics as an efficient source of information in investigating the on-state of the switching structures, J. Non-Cryst. Solids., 90, 609. (~esnys, A., Oginskas, A., Liberis, J. and Lisauskas, V. (1983) The role of Joule heating at monostable switching of amorphous GaTe3 and InTe3 films, Lietuvos Fizikos Rinkinys [Soy. Phys.-Collect.], 23(6), 75 (in Russian). (~esnys, A., Oginskas, A. and Lisauskas, V. (1992) Field dependence of electroconductivity and pulsed breakdown in noncrystalline films of Ga-Te system, Lithuan. Phys. J., 32(5), 345. Cesnys, A., Oginskas, A., Lisauskas, V., Shiktorov, N. and Butinavi~il]t6, E. (1984b) Two kinds of electric transfer in heterostructures of amorphous (GaTes, Ga2Te3 or SiTe3)-crystalline (Si) semiconductors, Proceedings of the International Conference on 'Amorphous Semiconductors-84' Coabrovo, Bulgaria, pp. 16-18 (in Russian). (~esnys, A. and Urbelis, A. (2001) On electrical conduction of crystalline-noncrystalline semiconductor barrier structures, Lithuan. Phys. J., 41(4-6), 283. Ciulianu, D.I., Andriesh, A.M. and Kolomeiko, E.M. (1978) Injection currents in vitreous chalcogenides semiconductors of the As2S3-Ge system, Vol. 1 Proceedings of the Conference on 'Amorphous Semiconductors-78', Pardubice, (in Russian). Danilov, A. and Muller, R.L. (1962) J. Non-Organ. Chem, 35(9), 2012 (in Russian). Dembovskii, S.A. (1964) Crystallization of glass system Se-As2Se3, J. Non-Organic Chem, 9(2), 389 (in Russian).
Charge Carrier Transfer at High Electric Fields in Noncrystalline Semiconductors
53
Dienys, R., Kalad6, J., Montrimas, E. and Pa~6ra, A. (1971) Investigation of effective lifetime of charge carriers in Se and As-Se amorphous layers, Sov. Phys.-Collect., 11(4), 666. Dunn, B. and Mackenzie, J.D. (1976) Transport properties of glass-silicon heterojunctions, J. Appl. Phys., 47(3), 1010. Eisenberg, A. and Tobolsky, A.J. (1960) Polym. Sci., 44, 19. Feltz, A. (1983) Amorphe und Glasartige Anorganische Festk6rper, Academie-Verlag, Berlin. Fritzshe, H. (1974) Electronic Properties of Amorphous Semiconductors, Plenum Press, London. Gaidelis, V., Markevifi, N. and Montrimas, E. (1968) Physical Processes in Electrophotographic Layers, Mintis, Vilnius, p. 92 (in Russian). Gaidelis, V., Montrimas, E., Pa~6ra, A. and Vi~6akas, J. (1972) Investigation of space charge formation and Its distribution in electrophotographic layers, Current Problems in Electrophotography, Walter de Gruyter, Berlin, pp. 126-132. Glazov, V.M., Aivazov, A.A., Zelenov, A.V. and Vadov, G. (1976) Investigation of switching effect in liquid selenium, Fiz. Tekh. Poluprovodn. (Soy. Phys.-Semicond.), 10(4), 636 (in Russian). Goriunova, N.A. and Kolomietz, B.T. (1956) New glassy semiconductors, Izvestiya AN SSSR, Ser. Phys., 20(12), 1496. Gubanov, A.I. (1954) To the theory of the high field effect in Semiconductors, Zh. Tekhn. Fiz., 24(2), 308 (in Russian). Gubanov, A.I. (1963) Quantum-electron theory of amorphous semiconductors, Acad. Sci. USSR, MoscowLeningrad (in Russian). Gulyayev, J.V. and Plesskii, V.P. (1976) On electronic properties of non-degenerate highly doped compensated semiconductors, Zh. Eksp. Teor. Fiz., 71(4(10)), 1475 (in Russsian). Hartke, J.L. (1962) Drift mobilities of electrons and holes and space-charge-limited-currents in amorphous selenium films, Phys. Rev., 125(4), 1177. Johnsher, A.K. and Hill, R.M. (1978) Electrical conductivity of unordered nonmetallic films, In Physics of Thin Films, Vol. 8 Mir, Moscow, p. 180 (Russian translation). Ju~ka, G. (1991) Properties of free-carrier transport in a-Se and a-Si:H, J. Non-Cryst. Solids, 137-138, 401. Ju~ka, G. and Arlauskas, K. (1983) Features of hot carriers in amorphous selenium, Phys. Stat. Sol. (a), 77, 387. Ju~ka, G. and Arlauskas, K. (1995) Properties of hot carriers in a-Si:H in comparison to a-Se, Solid State Phenom., 44-46, 551. Ju~ka, G., Arlauskas, K. and Montrimas, E. (1987) Features of carriers at very high electric fields in a-Se and a-Si:H, J. Non-Cryst. Solids, 97-98, 559. Ju~ka, G. and Vengris, S. (1976) Hole photogeneration in amorphous selenium at low electric fields, Phys. Stat. Sol. (a), 35, 339. Kalade, J., Montrimas, E. and Jankauskas, V. (1991) Determination of the carrier drift mobility and lifetime in the semiconductive layers in electrographic regime: two trap model, Lithuan. Phys. J., 31(4), 207 (in Russian). Kalad6, J., Montrimas, E. and Jankauskas, V. (1994) Investigation of Charge Carrier Transfer in Electrophotographic Layers of Chalcogenide Glasses, Vol. 2 Proceedings of ICPS'94 Rochester, New York, pp. 747-752. Kalade, J., Montrimas, E. and Jankauskas, V. (1999) Investigation of charge carrier lifetime in high resistivity semiconductor layers by the method of small charge photocurrent, J. Non-Cryst. Solids, 243, 158-167. Kalad6, J., Montrimas, E. and Pa~6ra, A. (1972) Kinetics of drift current of small charge and determination of lifetime of charge carriers, Phys. Stat. Sol. (a), 13, 187. Karpus, V. and Perel, V.I. (1985) Thermal ionization of deep centers in semiconductors in electric field, Pis'ma V ZcETF, 42(10), 403 (in Russian). Kolomietz, B.T. (1963) Glassy Semiconductors, Nauka, Leningrad (in Russian). Kolomietz, B.T. and Pavlov, B.V. (1967) The change offorbidden energy gap in arsenicum chalcogenides in case of transition from glass to crystal, Fiz. Tekh. Poluprovodn. [Sov. Phys.-Semicond.], 1(3), 246 (in Russian). Kolomietz, B.T., Lebedev, E.A. and Cendin, K.D. (1971 a) The influence of currents limited by the space charge on the thermal breakdown, Fiz. Tekh. Poluprovodn. [Soy. Phys.-Semicond.], 5(8), 1568 (in Russian). Kolomietz, B.T., Lebedev, E.A. and Cinman, E.A. (1971b) Investigation of noises during switching in chalcogenides glasses, Fiz. Tekh. Poluprovodn. [Sov. Phys.-Semicond], 5(12), 2390 (in Russian). Kostylev, S.A. and Shkut, V.A. (1978) Electronic Switching in Amorphous Semiconductors, Naukova Dumka, Kiyev (in Russian).
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Kvaskov, V.B. (1988) Semiconducting Devices with Bipolar Conductivity, Energoatomizdat, Moscow (in Russian). Kvaskov, V.B., Parolj, N.V., Jofis, N.A. and Gorbachev, V.V. (1981). The Electrical Properties and Applications of Chalcogenide Semiconductor Glass. CNII 'Electronica', Moscow (in Russian). Lampert, M. and Mark, P. (1973) Injection Currents in Solids, Mir, Moscow (Russian translation). Lebedev, E.A. and Rogachev, A.N. (1981) Conductivity of chalcogenide glass-like semiconductors in high electric fields, Fiz. Tekhn. Poluprovodn. [Sov. Phys.-Semicond.], 15(8), 1511 (in Russian). Lisauskas, V., Tolutis, V. and Sheremet, G. (1986) The ordering of the Ga-Te system amorphous layered structure during annealing in vacuum, Lietuvos Fizikos Rinkinys [Sov. Phys.-Collect.], 26(6), 740 (in Russian). Maden, A. and Shaw, M.P. (1988) The Physics and Applications of Amorphous Semiconductors, Academic Press, New York. Montrimas, E. (1976) Investigation of Electric and Photoelectric Properties of Amorphous Semiconductors in Ionic Contact Regime, Amorphous Semiconductors'76 Publishing House of the Hungarian Academy of Sciences, Budapest, pp. 281-294. Montrimas, E., Bal~i0nas, J., Fung Cho and Do Van An (1985) The photodischarge mechanism for multicomponent electrophotographic chalcogenide films based in arsenic sesquiselenide, Sov. Phys.Collect., 25(2), 49. Montrimas, E. and Jankauskas, V. (1985) The charge transfer in the system of amorphous layers of seleniumphosphorus-tellurium, Sov. Phys.-Collect., 25(4), 30. Montrimas, E., Jankauskas, V. and Rink~nas, R. (1997) Influence of Te and P sublayers on properties of amorphous Se layers, Lithuan. Phys. J., 37(5), 352. Montrimas, E. and Pa~6ra, A. (1968) The space charge effects on the fast photoinduced discharge of selenium electrophotgraphic layers, Sov. Phys.-Collect., 8(5-6), 865. Montrimas, E., Pa~6ra, A., Tauraitien6, S. and Tauraitis, A. (1969a) Drift mobility of charge carriers in As-Se layers, Soy. Phys.-Collect., 9(5), 963. Montrimas, E., Pa~era, A., Tauraitien6, S. and Tauraitis, A. (1969b) On longitudinal photoconductivity kinetics of AszSe3 layers, Sov. Phys.-Collect., 9(2), 353. Montrimas, E., Pa~6ra, A. and Vi~6akas, J. (1976) The drift of charge carriers in As-Se layers, Phys. Stat. Sol. (a), 3, K199. Montrimas, E., Tauraitien6, S. and Tauraitis, A. (1972) Latent image formation mechanism in AszSe3 electrophotographic layers, Current Problems in Electrophotography, Walter de Gruyter, Berlin, pp. 139-145. Montrimas, E. and Vi~akas, J. (1974) Charge carrier photogeneration and photodischarge in electrophotographic layers of disordered structures. In Proceedings of the Second International Conference on Electrophototgraphy, (Ed., Deane White), Columbia, USA, pp. 220-224. Mott, N.F. and Davis, E.A. (1979) Electron Processes in Non-crystalline Materials, Clarendon Press, Oxford. Muller, R.L., Mosli, E. and Borisova, Z.U. (1964) Influence of thermal treatment on conductivity and microhardness of glassy As-Se, Vestnik LGU, Ser. Phys. Chem., 22(4), 94 (in Russian). Oginskas, A. and (~esnys, A. (1984) Transient I - V characteristics of a switching structure based on amorphous GaTe3 in the initial stage of high-resistance state recovery, Fiz. Tekh. Poluprovodn. [Sov. Phys.-Semicond. ], 18(8), 1511 (in Russian). Oginskas, A., Ga~ka, K. and (~esnys, A. (1986) Electric resistance relaxation of a monostable switching structure in the low-resistance state, Fiz. Tekh. Poluprovodn. [Sov. Phys.-Semicond.], 20(4), 734 (in Russian). Owen, A.E. and Robertson, J.M. (1973) Electronic conduction and switching in chalcogenide glasses, IEEE Trans. Electron Devices, ED-20(2), 105. Pai, D.M. and Enck, R.C. (1975) Onsager mechanism of photogeneration in amorphous selenium, Phys. Rev. B, 11, 5163. Prikhod'ko, A.V., (~esnys, A.A. and Bareikis, V.A. (1981) Investigation of microwave noise in amorphous selenium films in the monostable switching mode, Fiz. Tekh. Poluprovodn. [Sov. Phys.-Semicond.], 15(3), 536 (in Russian). Sandomirskii, V.B. and Sukhanov, A.A. (1976) Electric instability phenomena (switching) in glass-like semiconductors, Zarubezhn. Radioelektron., 9, 68-101 (in Russian). Sandomirskii, V.B., Sukhanov, A.A. and Zhdan, A.G. (1970) Phenomenological theory of concentrational instability in semiconductors, Zh. Eksp. Teor. Fiz., 58(5), 1683 (in Russian).
Charge Carrier Transfer at High Electric Fields in Noncrystalline Semiconductors
33
Tauraitien6, S., Tauraitis, A. and Montrimas, E. (1970) Electrographic Layers of As-Se. Non-silver and Unconventional Photographic Processes, Papers, Section E, Moscow, p. 244 (in Russian). Timashev, S.F. (1977) On temperature dependences of switching effect, Fiz. Tekh. Poluprovodn. [Sov. Phys.Semicond.], 11(7), 1437 (in Russian). Tolutis, V., Jasutis, V., Lisauskas, V., Pauk~t6, J. and David6nien6, D. (1978) Amorphous state of thin films of Ga-Te and In-Te systems, Lietuvos Fizikos Rinkinys [Lithuan. Phys.-Collect.], 18(1 ), 29 (in Russian). Tsuji, K., Takashi, Y., Hirai, T. and Taketoshi, K.J. (1989) Impact ionization process in amorphous selenium, Non-Cryst. Solids, 114, 94. Vezzoli, G.C. (1980) Interpretation of amorphous semiconductor threshold switching based on new decay-time data, Phys. Rev. B, 2(4), 2025. Vezzoli, G.C., Doremus, L.W., Tirellis, G.G. and Walsh, P.J. (1975) Amorphous semiconductor threshold onstate properties as functions of decay time, ambient temperature and polarity, Appl. Phys. Lett., 26(5), 234. Vi~fiakas, J., Gaidelis, V., Lazovskis, T., Montrimas, E. and Pa~6ra, A. (1969) Method of estimation of space charge in semiconductors, Sov. Phys.-Collect., 9(6), 1102. Vi~fiakas, J., Montrimas, E. and Pa~era, A. (1969) Fast photodischarge of selenium electrophotographic layers, Appl. Optics Suppl., 3, 79.
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CHAPTER
3
THE NATURE OF THE CURRENT INSTABILITY IN CHALCOGENIDE VITREOUS SEMICONDUCTORS Andrey S. Glebov RIAZAN STATE RADIOTECHNOLOGYACADEMY (RSRTA)
1. Introduction There are several reviews of experimental and theoretical works (Kostylev and Shkut, 1978; Maden and Sho, 1991) where recent achievements in the field of investigations and practical applications of the switching effect in vitreous materials have been described. It follows from the literature analysis that the switching effect in glassy films of chalcogenide alloys is studied sufficiently to start creation of active elements and devices on their bases but not enough to understand the switching nature (Kostylev and Shkut, 1978). The overwhelming majority of works connected with considerations of physical models of the current instability phenomena in chalcogenide vitreous semiconductors (CVS) is based on the 'threshold' approach where the jump transition from the high-resistance state to the low-resistance one at application of the electrical field is considered to be related either with reaching of the critical value of the electric field, and this mechanism is referred to as the electronic mechanism, or with reaching of the critical temperature (the thermal power), and this mechanism is referred to as the thermal mechanism. However, as experimental data were accumulated, it has been clarified that these 'threshold' parameters are unstable and their values depend on measurement conditions and the design of devices. Switching parameters measured in the wide range of electrical fields and temperatures values have indicated ambiguity of the critical (threshold) character of switching and, therefore, illegality of the static approach to the problem of the current instability in chalcogenide glasses. Existing theories of the current instability are based, as a rule, on models developed for solids irrespective of their structure, composition, energy spectrum features and capability of their transformation under the influence of external conditions, methods of the thin film preparation, material composition, the contact phenomena and other properties that make vitreous semiconductors different from crystalline ones. In these models a number of switching effect features have not found any explanation. In this chapter an attempt is made to propose the so-called 'kinetic' concept of the current instability development that is based on generalization of published experimental data and theories and proposed for the first time in works of 57
Copyright 9 2004 Elsevier Inc. All rights reserved. ISBN 0-12-752188-7 ISSN 0080-8784
58
A. S. Glebov
Glebov (1987, 1988) as an analogy of the kinetic theory of destruction of solids under mechanical loading. At the approach to the problem of current instability from the point of view of the 'kinetic' model the jump transition of a vitreous material from the low-conductivity state to the high-conductivity state is considered as the process developing actually in time. At that, the main fundamental characteristics are not the electric field and temperature but the switching delay time, i.e., the time of the sample being in high-resistance state after a voltage pulse is applied till the moment of switching. It is clear that it is prematurely to consider the kinetic theory of the current instability in chalcogenide glass as completed. There are many unclear and disputable questions left which to the great extent determine ways of further development of the physics of glass and the kinetic concept of switching. However, as it is shown in this chapter, now the possibility has already appeared to formulate main concepts determining development of the kinetic theory of switching, to classify existing experimental data, the recent information on structure and the configuration of chalcogenide glass in the framework of the unified concept of switching indicating the role of both thermal and electronic processes in it. The most essential features of chalcogenide glass, in our opinion, lying in the base of the switching phenomena, are the existence of charged broken bonds in them which are able to transform from one type to another under external influence leading to appearance of new structural units, and therefore to transformation of the energy spectrum of charge carriers in glass.
2.
Current Channels in CVS-based Switches
In numerous experimental investigations (Kostylev and Shkut, 1978) it has been established that at development of the current instability in vitreous semiconductors the high-resistance region of the current-voltage diagram is determined by the current transfer through the whole area of the inter-electrode gap, and the low-resistance one is characterized by the current in a local area of the inter-electrode gap (the current filament). It is possible to understand the nature of the current filament (generation of current channels) at development of the S-type current instability in vitreous semiconductors taking into account structural features of real vitreous materials. We have proposed for the first time in Oreshkin, Glebov, Oreshkin, Beliaev and Mikhaylichenko (1969) to take into account the influence of material heterogeneities in vitreous semiconductors where the suggestion has been proposed that CVS can be considered as a complex structure containing several immiscible phases at which borders chains of micro-diodes of physical potential junctions like, for example, the Schottky diode, can originate. Reasoning from the statistically random distribution of such diodes in glass volume, it can be assumed that a way can be found between electrodes, which has the minimal number of barrier layers (a 'weak area'). This 'weak area' becomes a cause of the switching channel origination. Physical barriers in non-crystalline semiconductors can be of various natures. In particular, in complex structures, like selenium, inter-molecular barriers originate. Grain boundaries, dislocations are the cause of the potential barriers origination like Schottky diodes, homo- and hetero-junctions. Besides, non-electrical potential barriers can
The Nature of the Current Instability in Chalcogenide Vitreous Semiconductors
59
originate due to density fluctuations of material or the different saturation of chemical bonds. In Phillips (1979a,b; 1980) it has been shown that due to accumulation of the deformation energy the vitreous semiconductor should consist of clusters whose borders are layers of broken chemical bonds. While determining the role of barriers in processes of the charge carriers transition it is necessary to take into account effects related with the ratio of dimensions of heterogeneities and geometrical parameters of the sample (Kostylev and Shkut, 1978). The heterogeneity, like grains in the case whose size is less than the cross-section of the sample and completely blocked by the matrix of the basic material, would not necessary change the charge carriers transfer mechanism. Charge carriers can pass around the heterogeneity that just changes the geometrical distance between electrodes. These features can be specified more accurately by the percolation theory of heterogeneous medium (Shklovsky and Efros, 1975a). In the case dimensions of heterogeneities are comparable with the sample cross-section it is necessary to take into account their blocking influence on the process of the carriers transfer in investigated materials. At the present time a large number of experimental data is collected which confirm the presence of various heterogeneities and potential barriers in vitreous semiconductors. For example, in Goryanova, Ryvkin, Shpenikov, Tichina and Fedotov (1968) and Minaev, Aliev and Schelokov (1986) it has been shown that the vitreous state of AzB4CStype compounds, like CdGeP2, is characterized by the presence of local heterogeneities revealed by electron microscopy investigations. In Abalmazova, Demidov and Ivanov (1970) and Ivanov and Abalmazova (1971) local heterogeneities in amorphous film structures, vitreous materials included, have been investigated by the method of the electronic mirror. It has been shown by studying of compensation and photomechanical effects and from the dielectric dispersion data that there are local heterogeneities in CVS (Kasharin, 1972). In works of Philips (1983) the cluster structure in vitreous films of AszSe3 has been revealed. The size of clusters was 1000 .A. Investigating the process of the current filament formation in Ge~oSi~zAs3oTe4o-based and Ge~sTes~Asa-based glasses by the mirror microscopy method, it has been shown that electrical heterogeneities with large potential fluctuations are observed in the interelectrode space even before the external electric field is applied. When the electric field is applied, re-distribution of the surface potential occurs. This process is terminated by the transition of the structure from the high-resistance state to the low-resistance one (Oreshkin, Vikhrov, Glebov, Mal'chenko, Petrov, Andreev and Sazhin, 1974). Using high-speed filming, it has been shown that at stresses close to the threshold the local reconstruction takes place in the inter-electrode gap of planar elements of multicomponent CVS (Oreshkin et al., 1974). Dimensions of such local regions are 10 -5 cm that coincide with dimensions of Schottky barrier layers whose theoretically evaluated thickness is presented in Oreshkin, Petrov and Glebov (1972). Investigations of CVSs using the positron spectroscopy method based on the positron annihilation in CVS have been carried out under the direction of Kobrin, Kupriyanova, Minaev, Prokopiev and Shantarovich (1983) and Kobrin (1985) and have shown that the microstructure of Ge-Te, Si-Te, G e - S e and more complex glass systems presents either a glass-crystallite material with the 1015 cm -3 crystallite density or it consists of clusters of Phillips structural type with the characteristic cluster's size of 2000 A.
60
A. S. Glebov
Low values of mobility and the frequency dependence of conductivity in Mott (1969) can be explained by the presence of potential drift barriers. It is known (Stratton, 1973) that, depending on the hetero-junction width, the mechanisms of charge carriers transfer through reverse-biased Schottky-type barriers can be the thermo-electrical emission (TEE) through barriers (wide barriers, high temperatures), the thermal-stimulated cold emission (TSE) (intermediate thickness and temperature), the tunneling through barriers for thin barriers and low temperatures (CE). Possible mechanisms of the carriers transfer through potential barriers of the 'collector' junction are presented in Figure 1. In fact, in works under the direction of Dovgoshey, Savchenko, Zolotun, Baran, Firtsak, Chepur and Mitsa (1975) and Dovgosheyi, Savchenko, Zolotun, Nechiporenko, Firtsak and Luksha (1980) it is shown that in many vitreous semiconductors the current-voltage diagram is described by the j--exp(AV) expression that can evidence, in the authors' opinion, in favor of the barrier's mechanism of conductivity. It is indicated in Dovgoshey et al. (1975) that the barrier's mechanism of the carriers transfer is also confirmed by the conductivity temperature dependence in accordance with the/x --~ exp(Aq~/kT) law as well as by the conductivity activation energy dependence on the applied voltage V which is expressed by/lEo- = (7 + 2) x 10 -2 V. The presence of the polarization emf (Ryvkin, 1972) indicates, in authors' opinion, the presence of interface barriers. It is necessary to note, however, that current transfer mechanisms indicated are typical not for all structures but for bulk samples and thick film structures where effects of highvoltage fields are expressed weakly. In particular, in thin film vitreous semiconductor samples in the region of high-voltage fields the current-voltage dependence is described by the Frenkel-Pool's law of thermal-electronic ionization (Dovgoshey et al., 1975) where the theoretical current-voltage dependence looks like: (1)
j .-. exp(AV1/2).
In thin film samples the prevailing role in the current transfer mechanism is played by effects of high-voltage fields which can lead not only to the lowering of potential barriers
TEE TSE ECK
EFK
I eV
!I @ EFAM T
FIG. 1. The band diagram of the reverse-biased hetero-junction 'glass-crystal' and possible channels of carriers transfer through it.
The Nature of the Current Instability in Chalcogenide Vitreous Semiconductors
61
but to the participation in structural re-construction, in defect generation in particular. It should be in its turn followed by the appearance of new features of conductance of glass that are not laid in the frameworks of known mechanisms developed for crystalline semiconductors. As a matter of fact, the character of conductivity of CVS in strong electrical fields has a complex appearance. According to Marshall, Fisher and Owen (1973) and Kazakova, Lebedev and Rogachev (1975)), we have for chalcogenide glass: ~r--~ exp(E/Eo),
(2)
where Eo = A + BT, at T > 300 K; A and B are constants. In the authors' opinion (Kazakova et al., 1975), such character of electrical conductivity can be conditioned by the process of delocalization of levels in the bandgap at decreasing of their screen potential. The process of delocalization of energy levels at the presence of barriers can be readily presented as a process where under the electrical field effect the potential drift barriers for current carriers get lower and the carriers are converted from the state of low mobility to the state of high mobility. In other words, the transition of carriers through interface potential barriers can be considered as the effect of the disappearance of local levels at screening of free carriers. Let us now turn to another group of facts confirming the correctness of the model of the current channels presented as a chain of gate layers. We bring some considerations that come out from this model and can be verified experimentally. 1. The current-voltage diagram in the case of the tunnel mechanism of carrier transition through a barrier can be written as (Nadkarni, Sankavraman and Radhakshan, 1983): J - A e ~v,
(3)
where A is the equivalent to the initial value of the current flowing through structures" B-
m/Ad,
(4)
where m is the factor accounting for heterogeneity of the field and the nonequilibrium of the barrier; d, the film thickness; Ad = n, the number of gate layers and A is the proportionality coefficient. From expression (4) the B value must decrease when the film thickness increases. Besides, the B coefficient must increase with the temperature increase due to the parameter (m) increase, because the field inhomogeneity and the increase of the potential barriers height should be expected at the temperature increase. 2. The equivalent circuit of the M e - C V S - M e structure for low frequencies can be presented as shown in Figure 2. For such circuit (Nadkarni et al., 1983) the capacitance at low temperatures is equal to the geometrical capacitance and it decreases with the film thickness increase. The sample capacitance will increase with the temperature increase due to the resistance and the cluster's material capacitance decrease. 3. When the applied voltage increases, the structure's capacitance must decrease because reverse-biased gate layers get expanded under the influence of field.
62
A. S. Glebov Rb!
B
Rk
Ck
Ckl
Cbl
Rkl
Rb
C
Cb
Rb2
Cb2 Ckr
Ukr
Rkr
Cbr
FIG. 2. The equivalent circuit diagram of the Me/Glass/Me structure: A, the general circuit diagram; B, the reduced circuit diagram; Rb, Cb, the resistivity and the capacitance of the junction; Rk, Ck, the resistivity and capacitance of the cluster.
Besides, in the case of the 'short circuit' of barriers leading to the decrease of the number of RC circuits, the sample must show the inductive character. 4. According to the generalized barrier model of the non-homogenous semiconductor constructed on the base of the equivalent circuit shown in Figure 2, the logarithm of the difference of resistivities of the sample at high and low frequencies must be a linear dependence of the reversed frequency 1/f (Oreshkin, 1977), i.e. lg(pl - p ) = B - ( ( 0 . 4 3 / 1 0 5 4 " r ) l O S / f ) ,
(5)
where B = d n o ~ o / 2 a e i ~ n l n ; ~o, the constant; no, the bulk concentration of carriers; n, the carrier concentration in the depleted layer; nl, the carrier concentration at low frequency;/z, the carrier mobility; T0, the relaxation time of gate layers. The above considerations following from the barrier model of the current channel have been confirmed experimentally. In Figure 3 the dependence of lg I as a function of the applied voltage iSoPresented for structures Me-GelsTeslSb2S2 film-Me. The film thickness is 2100 A (Nadkarni et al., 1983), C - V characteristic has been obtained at different environment temperatures. It can be seen that the slope of straight lines increases as temperature increases that evidences the B coefficient increase in expression (3) and agrees with predictions following from the proposed model of the current channel. Figure 4 shows similar dependencies for film-planar structures based on CVS of Ga12Si6.sGe6.sAs25Teso whose inter-electrode gaps are different. It can be seen that the slope of curves decreases when the inter-electrode gap increases. The change of the capacitance of film structures based on GelsTeslSb2S2 depending on temperature and the applied voltage has been investigated in Nadkarni et al. (1983). These dependencies are presented in Figures 5 and 6. As it can be seen from the figures, the experimental results confirm the theoretical conclusions based on the barrier model rather well. The presence of inductive properties, so-called 'negative' capacitance phenomena, has been investigated comprehensively in Gasanov, Deshevoyi and Petrovskiy (1971) and Shklovsky, Schur and Efros (1971). It has been shown that at
The Nature of the Current Instability in Chalcogenide Vitreous Semiconductors
63
lgI,A II
-2
P
4
9
D
3
-3
,J "
1
-4
-5
-6 3
6
U,
V
Fio. 3. The voltage-current characteristic of the Me/Ge~sTes~SbzSz/Me structure possessing the switching effect: 1-205 K; 2-220 K; 3-245 K; 4-282 K; 5-298 K.
lgI,A
r 1
I
-5 r"
x~
r"
x
c x
3
-6
-7 0
50
100
U, V
FIG. 4. The voltage-current characteristics of film-planar structures based on CVS of the Gal2Si6.sGe6.5 As25Teso composition with different inter-electrode gaps: 1-30 txm; 2 - 2 2 Ixm; 3-10 p~m.
64
A. S. Glebov
C, pF
80
40
180
260
340
T,K
FIG. 5. The temperature dependence of the low-frequency capacitance of the Me/GelsTe81Sb2S2/Me structure.
voltages close to threshold ones the reactive character of conductivity changes its impedance from capacitance to inductive. As for experimental verification of the dependence (5), it has also been made in the work of Kasharin (1972) for various compositions of chalcogenide semiconductors. One of typical dependencies obtained in our works for samples based on CVS of the GalzSi6.sGe6.sAszsTe5o composition is shown in Figure 7. Based on formula (5) and Figure 7, vitreous semiconductors can be considered as a composition of local barriers of Schottky type divided by homogenous material (bases) whose conductivity o - = l i p determines the Maxwell's relaxation time in the base zM -- eeop. At that, impurity energy levels determining conductivity are not completely exhausted (Oreshkin, 1977).
C, pF
/
,// 4
6
8
d-1, pm-1
FIG. 6. The dependence of the low-temperaturecapacitance vs. the glass oxide thickness.
The Nature of the Current Instability in Chalcogenide Vitreous Semiconductors
65
lg (rl-r), Ohm.cm
0
100
200
103/f, Hzu -1
FIG. 7. The dependence of lg(rl - r) vs. the reciprocal frequency for the Me/Ga12Si6.sGe6.sAs25Tes0/Me structure.
Therefore, experimental data indicate the presence of the drift barriers in vitreous materials. Drift potential barriers can be formed not only in technologically imperfect materials having large amount of non-homogeneities but also in materials with covalentcoordinated, polymer-crystallite or only in pure polymer structures, all bonds of which are saturated. In Shklovsky (1971) and Shklovsky et al. (1971) it has been shown that blocking barrier layers in disordered semiconductors may arise due to the random character of distribution of the carriers' potential energy leading to different values of the border energy of the continuous spectrum in various parts of the sample. Such drift barriers can be a cause of the leak channel appearance. At low temperatures electrons join in metal drops divided by wide potential barriers (Fig. 8). Conductivity in such system can be performed either by electron tunneling through the barrier or as a result of the electron bypass of the barriers whose potential energy is higher than the percolation energy. Presence of potential energy fluctuations can lead to appearance in vitreous semiconductors of regions with bipolar conductivity, such system can be considered as quasi-multi-layered structures of the dinistor type (Ryvkin, 1972) (Fig. 9). In Oreshkin, Glebov, Andreev, Vihrov, Glebov, Borschevsky, Minaev and Petrechenko (1977)
E_pe . . . . . . . . . . . . .
~
......
Ie
FIG. 8. The band diagram of the disordered semiconductor: ~p, the passage level for electrons; level for holes.
h Ep, the passage
66
A. S. Glebov
/
B
FIG. 9. The energy band diagram of the n - p - n - p structure: A, at equilibrium conditions; B, after the electrical field is applied.
it is indicated that the presence of structural units with different rupture energy of individual chemical bonds in semiconductor glass can complicate significantly the energy bands with ruptures and lead to noticeable blocking of carriers in locations where one structural unit borders another. In other words, along with smooth curvature of energy bands or large-scale fluctuations of potential energy in glass with strongly pronounced hetero-bonds there may arise chains of hetero-junctions without chemical bond ruptures. The qualitative energy diagram of disordered vitreous semiconductors consisting of two groups of structural units is shown in Figure 10. Conductivity of such structures cannot be described only by conductivity activation energy because relatively high conductivity of structural units with small ionization energy will be suppressed by the blocking network of structural units with higher ionization energy of chemical bonds
FIG. 10. The spatial structural network of glass: A, for two structural units; B, the qualitative energy diagram.
The Nature of the Current Instability in Chalcogenide Vitreous Semiconductors
67
(Muller, 1964). It is obvious that this condition will be satisfied under a certain ratio of concentrations of both structural units. Glass conductivity in this case will be determined by a small number of carriers which are able to pass from one electron drop to another by tunneling or by the Schottky-type over-barrier thermoelectronic emission as it is shown in Figure 10B. Similar hetero-junctions can also arise between structural fragments of vitreous semiconductors consisting of different number of atoms (Balmakov, 1985). In this case energy fluctuations may reach several electron volts that is determined not by chemical bonds ruptures and other radical changes of the structure but by small structural transformations realized by coordinated re-grouping of many atoms on distances less than inter-atomic ones. The possibility of appearance of a potential barrier between structural units as well as between hetero-bonds is confirmed by numerical calculations carried out by Gubanov (1984) for a simple model of polymeric semiconductor. It has been shown that for potential barriers of 1 eV height, 10 A width, the transmittance at the electrical field intensity of 10 - 4 Vcm -1 turns to be 2.1 • 10 -4. At such barrier transmittance the flow of electrons through it is very insignificant. The transmittance rises sharply with the electrical field and temperature increase. The list of works where presence of potential barriers in non-crystalline materials is stated can be continued but, obviously, the above mentioned has proved to be unbiased enough. Therefore, at considering the physical mechanism of current instability in vitreous semiconductors local inhomogeneities leading to the gate layers formation must be taken into account.
2.1.
MODELS OF GENERATION OF CURRENT CHANNELS AT PRESENCE OF DRIFT BARRIERS IN C V S
In Shklovsky et al. (1971) and Nadkarni et al. (1983) it has been shown that presence of drift barriers in non-crystalline materials can lead to formation of increased conductivity channels comparing with the integral conductivity of the sample. First of all, it is possible due to the sharp increase of current in strong fields when tunneling of carriers through the potential barrier takes place (Shklovsky et al., 1971) or as a result of Zener's transition 'band-band' at sharp curvature of energy bands of the reverse-biased gate layer in strong fields (Nadkarni et al., 1983). The authors (Oreshkin et al., 1969) have proposed the model of the current channel consisting of alternate layers of crystalline and glassy materials (Fig. 11) (Oreshkin, Glebov, Petrov and Beliavsky, 1974). Isotype hetero-junctions appear on boundaries of different phases. When the field is applied a part of junctions becomes reverse biased and they are 'collectors', the other part is direct biased and they are 'emitter' junctions. In certain electrical fields applied to the structure the band curvature in 'emitter' junctions decreases and becomes flat that corresponds to 'emitter' junction's short circuit. Because of that the main influence on current flow is exerted by reverse-biased 'collector' junctions. The mechanism of conductivity increase of the channel is Joule's heating by the current flow which has been created by carriers which come to the percolation level due to, for example, Schottky's over-barrier emission. Besides, temperature in the current
A. S. Glebov
68 EC 1
CS 1 CF
J
EC 2 AF
X
CF
The vacuum level Q
•"" t / eV ~ _/
CS 2
""~176176176176176 Qq?l~ EFA
~02
y Q ~176176 EFK """" /
g Fla. 11. The model of the current channel (A) and its band diagram for the case of j2 > Jl in the external electrical field.
channel may arise due to phonon's excitation as a result of electron transition from the percolation level to electron localized states in the amorphous phase (Fig. 11B). Calculations of temperature delivered by electrons passing from the Ec level of the free band of crystallite to the EL level of the localized state in the vitreous phase in accordance with formula (6) show that the temperature change near the 'collector junction' will be about 300 ~ AT = ((Ec - EL)I'r)/LCVI<,
(6)
where VK is the volume of the region where the heat emitted at one barrier is distributed and equal to 10 -~3 cm3; I, the average current for the delay time, equal to 10 -5 A; L, the thickness of the CVS film equal to 10 -5 cm and C is the specific thermal capacity J cm -3 degree. The temperature value near the gate layer may reach, therefore, the temperature of softening of the vitreous semiconductor at which phase transformation of conductivity ' s e m i c o n d u c t o r - m e t a l ' is possible that is well correlated with calculated and experimental data (Oreshkin et al., 1974). The model shown in Figure 11 is, of course, a rough approximation and can be used when crystalline inclusions are present in the vitreous matrix. The most realistic model is presented in Nadkarni et al. (1983) where gate layers are localized on cluster boundaries. The potential barrier is created due to the presence of negatively charged ruptured bonds at the boundary (Fig. 12). Such structure is characteristic for all vitreous materials to a certain extent. It is important to underline that the replacement of one type of potential barrier to another does not lead to the replacement of mechanisms of current channels formation. At strong electrical fields ( 106 V c m - l) the band energy diagram of the system can be presented in the form shown in Figure 12B. In this case the tunnel conductivity of the ' b a n d - b a n d ' type is added to the band conductivity. At that, the current increases uncontrollably that creates heating of the conductivity channel and can lead to structural rearrangements in vitreous semiconductor.
The Nature of the Current Instability in Chalcogenide Vitreous Semiconductors
5/
"
69
v
B
Er
eV
EF Ev FIG. 12. The energy band diagram of the Me/Glass/Me structure in equilibrium conditions: A, and after the electric field is applied B.
It is shown in Vikhrov (1977) and Glebov (1980) that a prerequisite of increased conductivity channels formation in vitreous materials is a topology of the vitreous matrix region formed by different structural units. Let us consider a spatial network consisting of nodes connected by bonds through which the current can flow. The nodes of the network can be of two types: (a) open nodes, i.e., nodes letting the current to flow to neighboring nodes, (b) close nodes, i.e., nodes not letting the current to flow to neighboring nodes. Let us designate the part of open nodes as X. According to the percolation theory, a critical part of open nodes Xs exists so that for X < Xs there is not a continuous infinite way along open nodes, and for X --> X s there is such way (or, in terms of the percolation theory) the infinite cluster of connected open nodes (IC) appears. Appearance of conducting channels can be explained if in vitreous material the structure consisting of open and closed nodes is disclosed and a dependence of the part of open nodes from the field is determined. In Shklovsky and Efros (1979) the Xs value for various types of space lattices has been calculated. Depending on the lattice type (tetragonal, cubic, etc.) this value changes from 0.26 to 0.5 and in average it is equal to 0.3. This Xs value will be used for further numerical estimations. Let us consider the simple binary S i - T e system in which the switching effect is observed (Prihod'ko, Deksnis and Chesnis, 1979). To be concrete, we select the composition of 14.29% Si and 85.71% Te. In this case the ratio Si : Te is equal to 1 : 6, i.e., SiTe tetrahedrons are connected via additional Te atoms. Energy of covalent bonds T e - T e and S i - T e is different (Ovshinsky, 1975): EO'Te-Te = 4.5 eV; E O r T e _ S i - - 5.2 eV. We assume that the type of conductivity is a hole one. Holes can travel along bonds under
70
A . S . Glebov Te
\/ /\
T e - T e - Te
Si
Te
B
\/ /\
Te
Si
Te-Te-Te
ESi_Te
Te
C
ETe-Te -
-
FIG. 13. The fragment of the glass structure of the S i - T e system A. The potential barrier for the hole in absence B, and presence C, of the electrical field.
the action of field without energy consumption but, having come to the S i - T e bond, they meet the rectangular barrier A E = E O ' T e _ S i - EO'Te_Te --- 0 . 7 eV. When the field is applied the barrier shape becomes triangular. With certain probability the holes coming to the barrier can tunnel through it (Fig. 13). Let us establish the following relationship between concepts of the percolation theory and structural elements of glass: nodes in the percolation theory correspond to Si atoms together with their bonds Si-Te. These nodes are connected by T e - T e bonds. A node (Si atom) will be open if a hole coming to the barrier corresponding to this node tunnels through it, and it will be close otherwise. Then, the fraction of open nodes is equal to the probability (w) of the tunneling through the barrier (the barrier' s transparency). If the fraction of open nodes exceeds the critical value Xs there is a through way from one electrode to another. It corresponds to the switching into the high-conductivity state where conductivity changes O'Te_Te/O'Te_Si = exp((EO'Te_Te -- EO'Te_Si)/2kT ) ~
10 3.
(7)
Probability of the tunneling through a barrier is calculated according to the formula of the inter-band tunneling in strong fields (Oreshkin, 1977). Making this probability equal to the critical part of open nodes Xs = 0.3, the value of the field Ecr at which IC appears in the first time, and therefore a conducting channel, can be determined *
3/2
0.3 -- exp(('n'/enE)2mpAE c )
(8)
assuming A E = 0.7 eV and mp--mn, we obtain the field value in the barrier region Ecr = 4 • 107 V cm -1 . Because the whole voltage drop occurs in the barrier regions, the average field in the sample will be several times less than the above value that corresponds to experimental data. It is known that the tunneling effect itself cannot lead to the S-ODC appearance because it does not provide conditions for the positive current feedback appearance. At that, however, according to Eq. (7), the conductivity can vary several orders of value. The presented models of the current channels appearance are constructed taking into account the presence of potential barriers in vitreous
The Nature of the Current Instability in Chalcogenide Vitreous Semiconductors
71
semiconductors. Appearance of high-conductivity channels under electrical field influence is the first stage of the current instability development in non-crystalline semiconductors, hence the local current instability is not present in material beforehand but is acquired owing to thermal-field effects in the process of the current instability development. This is probably one of the reasons of the appearance of those local inhomogeneities in glass which have been described in works of Kolomiets, Smorgonskaya and Shpunt (1978), Sukhanov, (1978a), Kolomiets, Smorgonskaya and Shpunt (1980), Kalmykova, Smorgonskaya and Shpunt (1982), Smorgonskaya and Shpunt (1982) and Kolomiets, Lebedev, Taksami and Tsendin (1983) for coordination of experimental and theoretical data in the framework of the single so-called 'inhomogenous' model of switching. As a matter of fact, the assumption that before the switching moment there is a 'weak point' in the active region of the diode structure with increased conductivity comparing with the rest of the sample can explain some peculiarities of the switching process. They are, for example, reduced temperatures of the active region of the diode structure in the moment of switching compared with the conclusions of the thermo-electronic model (Sukhanov, 1978a), frequency dependencies of the current on the close part of the current-voltage diagram (Kolomiets et al., 1980), the dynamics of recovery of the low-conductivity state at different temperatures and the character of the current filament radiation (Kolomiets et al., 1983) as well as the switching in CVS at ultra-short (nanoseconds) pulses. According to the 'inhomogenous' theory, the electron-thermal instability starts to develop first of all in the region with maximum conductivity of the channel, being 'secretive' at the background of the large current of the wide surrounding area, and at the latest stage of this self-accelerating process of instability the current of the switching channel exceeds the current of surrounding background area that is manifested as a sharp raise of the diode structure currentmthe switching. The additional experimental proof of inhomogenous character of the current instability development is dimensional effects in CVS switches investigated by the authors.
2.2.
DIMENSIONAL EFFECTS IN CVS-BASED SWITCHES
If the conception that the switching occurs under the condition of the current value in the channel being comparable with the background current value (Sukhanov, 1978b; Smorgonskaya and Shpunt, 1982) is considered to be true, i.e., Isw = Ich--Ibg, the diameter of the switching channel and the moment of transition of the diode structure from the low-conductivity state to the high-conductivity state can be theoretically calculated. From the expression dsw -- 2x/O'bgA/TrO'bg it can be seen that the switching channel diameter is related with electro-physical parameters of CVS (o0, AE) as well as with geometrical dimensions of the working area of the diode structure and environment temperature (Glebov, Petrov and Sazhin, 1984a). To investigate the dependence of the switching channel diameter from the working area of the diode structure, the film-planar structure based on the Ca12Si6.sGe6.sAsesTeso composition CVS with different electrode widths has been used. The inter-electrode gap was constant and equal to 10 txm.
72
A. S. Glebov
d.106, M 0.8
0.4 S 0
I
..,o
"" 20
40
S.10,12M2
FIc. 14. The dependence of the channel diameter vs. the active area of the switch: 1-the experimentalcurve; 2-the calculated curve. It can be seen from Figure 14 that there is a good coincidence of experimental and calculated values. The dependence of the channel diameter from the current in the open state taken from Petersen and Adler (1979) confirms quantitatively our results. Some concepts of the inhomogenous switching model are confirmed by investigations of quasi-static current-voltage diagrams of film-planar switches with different electrode widths (Fig. 15, Table I). The test structures were made on glass-ceramic substrates, molybdenum was used as the electrode material. The film of In4Ge~6Tes0 composition was made by the thermal vacuum evaporation method. It can be seen from Figure 16 that both threshold characteristics of switching (Itr, Utr) and the character of ODC region on current-voltage diagrams are changing depending on electrode widths. In the case of relatively narrow electrodes (b < 100 txm) the ODC region of current-voltage diagrams can be practically passed by points of the current generator mode, and the value of the threshold current is much lower than that of wider electrodes. The increasing of electrodes width more 100 p~m leads to changing of the switching character: there is practically no ODC region and the switching occurs with the sharp raise of voltage. As the current-voltage diagrams were obtained at the same regime (duration of the rise-up and fall-down portions is equal to 25 s) and the constant inter-electrode gap, the character of current-voltage diagrams can be related with changes of the mechanism of the device's switching process. The explanation of the effect observed is in good fit within the framework of the inhomogenous model of switching. If electrodes are narrow,
FIG. 15. The topology of the test structure.
73
The Nature of the Current Instability in Chalcogenide Vitreous Semiconductors TABLE I (A) AND INTERELECTRODE'S GAP (B) OF THE TEST STRUCTURES
WIDTH OF ELECTRODES
No.
1
B(~m) 490 A (p~m) 22
2 310 22
3
4
5
100 50 22 22
20 22
6
7
8
9
10
11
12
12.5 17 12.5 900 900 900 22 22 22 147 122 50
900 40
13
14
15
16
900 900 10 26
900 30
900 30
the ODC region is likely to be related with the appearance of the conducting switching channel whose nature can be explained by the dependence of the film conductivity on temperature and electrical field intensity at all stages of the instability development. Devices with such character of the positive feedback are known to be controlled in the current generator mode. So, with narrow electrodes the current-voltage diagram of the inhomogeneity is observed which has the ODC region. In this case the ODC region in the generator mode can be passed by points. The current-voltage diagram's appearance indicates that the inhomogeneity appears in the process of voltage increase on the structure and has not existed beforehand as it has been interpreted in some works of Glebov and Sazhin (1983) and Glebov et al. (1984a). With narrow electrodes, conditions are likely created where inhomogeneity's dimensions are comparable with electrodes' widths. In this case the switching model can be apparently considered as homogenous and therefore limits of the inhomogeneity model's application can be found. Electrodes' width increase leads to background currents starting to play a greater role. At that, the switching mechanism will be related not with electro-conductivity of
1.103, A
Illllll
0.8
i
0.6
/ ~._~~]~
i//__._~/.
15 /
16 _
2
0.4
0.2
0
10
20
30
40
u, v
FIG. 16. The CCM switches based on CVS of the Ga12Ge6.sSi25As25Tesocomposition (the numeration of curves corresponds to Table I).
74
A. S. Glebov
material (glass) change but with the process of the high-conductivity channel expansion after the critical conductivity in it is reached (Petersen and Adler, 1979; Glebov and Sazhin, 1983; Glebov et al., 1984a). Despite the switching channel formation is followed by the ODC region formation on the current-voltage diagram, at this stage the instability develops secretly against the background of the large current of the wide surrounding area, and when at the final stage of the switching the channel's current exceeds the current of the surrounding background area, the sharp raise of voltage will be observed on the current-voltage diagram. The sharp voltage raise in the current generator mode in this case can be explained by the channel diameter increase under limitation of the current flowing through the sample must be followed by the sharp voltage decrease on the structure. The dependence of the breakdown current on electrodes widths as well as a change of ODC's character on the currentvoltage diagram indicates that the influence of background currents must be taken into account when analyzing the switching process. Based on the 'inhomogenous' model of switching, the character of dependences of the threshold current (Fig. 17) and the temperature coefficient of the threshold current TCIthr (Fig. 18) on electrodes widths can also be explained. With narrow electrodes the whole active area works and the homogenous distribution in the working area takes place. When the electrodes width increases, homogeneity of the current distribution gets broken, formation of current channels is observed where current instability of S-type develops. At that, the current value of the background area becomes very important. The relationship between the channel current and the background area current is determined by the electrodes width, and with broad electrodes (more than 100 txm) the background current determines the character of the switching process and therefore the regime of their operation. For example, the switching effect is observed only with electrodes widths which are not more than 20 Ixm. With electrodes widths of about 100 Ixm both the switching effect and thermistor effects are observed depending on the environmental temperature increase rate. Increase of electrodes widths to more than 500 txm leads to such increase of the background current at which the switching effect disappears and the diode structure operates as a thermistor.
Ith r. 10 6, A
40
f
30
20
e
,,
3
J~
\
z
3 lg l(gm)
FI6. 17. The dependence of the threshold current vs. the electrode width: 1-90 ~ 2-50 ~ 3-30 ~
The Nature of the Current Instability in Chalcogenide Vitreous Semiconductors
75
TCC.10-2, 1/K
2
1
2
7
1
0
2.5
5
lg l([.tm)
FIG. 18. The dependence of the threshold current temperature coefficient on the electrode width: 1-90 ~ 2-50 ~ 3-30 ~
Besides, in Glebov, Petrov and Sazhin (1984b) the effect of the 'reverse' switching has been revealed and investigated which allows to convert the CVS-based switch from the low-conductivity state to the high-conductivity state with the help of light. The p h e n o m e n o n of the 'reverse' switching is illustrated in Figure 19 where c u r r e n t - v o l t a g e diagrams obtained in darkness (1) and under incandescent lamp illumination (2) are presented. If the switch is illuminated from the amorphous film side, the switch current value I 1 becomes larger than its dark current value I2. To convert the switch in high-conductivity state it is necessary either to exceed the 11 current value or to let the I current (11 > I > I2) pass through the switch and eliminate the illumination. In other words, in the latter case the switch can be converted from the low-conductivity state to the high-conductivity state not by the illumination but, on the contrary, by elimination of the illumination. It has been noticed that control of the switch characteristics in such a way can be succeeded if its electrodes width exceeds 10 txm. The process of switching of the threshold switch after
1.10-3, A 4.5
12
3.5 0
50
100Uthr, V
FIG. 19. The CVC of the switch measured in darkness 1, and at illumination by a incandescent lamp 2.
76
A. S. Glebov
elimination of illumination occurs during a short time, practically without a delay time. Duration of the transient process at switching is determined by the short-time component of the photo-response. The observed effect of 'reverse' switching can be explained based on the 'inhomogenous' model of switching (Sukhanov, 1978b; Smorgonskaya and Shpunt, 1982) according to which the value of the switching current must be determined by the background current value. When the CVS film is illuminated by light, its conductivity increases and consequently the background current value passing through the active region of the threshold switch increases as well. In connection with this, under illumination of the sample by light the switching current increase takes place (Fig. 19). If the current whose value is less than 11 but greater than I2 passes through the switch, the switch will stay in the fixed low-conductivity state. When illumination is eliminated, the switch current value decreases and, because the current passing through the switch is greater than the dark current of switching I2, the conversion of the switch in the high-conductivity state takes place. Thus, the presented data do not contradict to theses of the 'inhomogenous' model of switching which can be formulated in general as follows: 1. The switching process must consist of two stages. The first stage is likely of the electron nature. The proof of the fact that the switching channel appears under the electrical field action and is not inherent may be some experimental data. The electron nature of the switching channel formation can apparently indicate the presence of relaxation vibrations on the close region of the current-voltage diagram which do not connect with circuit-related effects (Kostylev, 1978), existence of the vertical region on the current-voltage diagram when switches work with short current pulses (Kostylev and Shkut, 1978), as well as the fact that the process of current localization starts with some delay time after the control pulse is applied (Kalmykova et al., 1982). The presented data are not, however, enough for the unconditional approval of the thesis discussed. The basis of the switching channel appearance is probably various inhomogeneities in CVS including such blocking factors for charge carriers transfer as potential barriers of the fluctuation character (Ryvkin, 1972), as well as that arising due to different ionization energy of hetero-bonds in the glass network (Glebov, 1980). Since we are discussing the random distribution of potential barriers, so, according to the percolation theory, the formation of a narrow channel of increased conductivity or the infinite cluster is possible between electrodes under the field action (Shklovsky and Efros, 1975b). 2. At the second stage of switching the electro-thermal instability develops leading to the S-ODC appearance in the switching channel before it develops in the rest of the part of sample. Possibility and conditions of such active inhomogeneity have been considered, in particular, in Glebov and Sazhin (1983). Numerous experimental data (Aivazov, 1995) indicate the electro-thermal character of S-ODC. The possible kinetic model of S-ODC has been presented above. 3. In the process of the S-ODC formation, the temperature in the switching channel increases to the critical value at which the material of the filament undergoes the phase transformation of the 'semiconductor-metal' type. At that, the conductivity
The Nature of the Current Instability in Chalcogenide Vitreous Semiconductors
77
reaches the limit value and becomes independent on temperature. Significant influence on the value of the critical temperature is exerted by the electrical field (Kostylev, 1975). The macroscopic nature of the phase transformation is not clarified. One of the possible explanations of this phenomenon is presented in Kolomiets et al. (1983), however additional data are required for complete understanding of these processes. The kinetic model of the current instability allows, in our opinion, to explain the nature of the phase transformation. 4. The process of switching occurs as a result of the high-temperature channel expansion and manifests itself on the current-voltage diagram as the voltage jump in the moment when the channel current becomes comparable with the background area current. The latter thesis is confirmed, in particular, by the results of this work. 5. Application of the inhomogenous model of switching is limited by geometrical dimensions of the working area of the switch. If electrodes diameters or widths become comparable with transversal dimensions of the active inhomogeneity, the switching model must be considered as homogenous. In this case the currentvoltage diagram of the switch will be different from that of the sample with active inhomogeneity.
3.
The Kinetic Model of the Current Instability at the Presence of the Current Channel
The character of dependences shown in Figures 39 and 40 is similar to that of the destruction time of solids on the environmental temperature and mechanical stress value (Regel, Slutsker and Tomashevsky, 1972). Based on the analogy of the switching delay time and the solids destruction time under the external stress (electrical or mechanical) one can assume that during the delay time the relaxation of excess energy of CVS from its maximum to a certain minimum value takes place. The value of the excess energy is determined by synthesis conditions and CVS composition, and its decrease--transformation of the structure from disordered state to more ordered one (Glebov, 1978; Glebov, 1987; Glebov and Rozhkova, 1987). At that, the microscopic mechanism of the switching phenomenon, like the case of solids destruction under mechanical stress, is the chemical bonds rupture. According to expression (25) and Figures 40 and 41, the rupture of chemical bonds is realized at the expense of both thermal energy and electrical field. Depending on experimental conditions (the geometry of the sample and parameters of the control signal), either factor can be determining, i.e., either thermal or electrical switching mechanisms can be observed in the same vitreous material as well as their combination and the smooth transition from one mechanism to another. It is important to underline that the process takes place in a local inhomogeneity area with the increased current density that is the peculiarity of the switching effect in CVS comparing with crystal semiconductor structures where the current inhomogeneity formation takes place on the stage of the ODC region formation. The process of the inter-atomic bonds rupture can be depicted based on published conceptions on defects in vitreous semiconductors.
78
A. S. Glebov
Let us consider one of the possible mechanisms of the formation of conducting channels based on the defect formation process. The attempt to connect the defect formation process and the structural reconstruction with the switching effect has been done in the works of Subhani, Shur, Shaw and Adler (1977) and Kvaskov, Parol and Iofis (1984). In Subhani et al. (1977) the electron model has been proposed based on creation of the large concentration of carriers provided by centers C +3, C ~ C~- as a result of ionization by processes of collision, diffusion and recombination. However, in Kostylev and Shkut (1978) it is indicated that the model does not agree with experiments in the main thesis--the field of low-resistance state retention must linearly decrease with the length of the sample increase that does not correspond to experimental data. In Kvaskov et al. (1984) the low-temperature switching in CVS has been explained based on the reconstruction of valence bonds which are followed by the conversion of C~- and C~centers in C o that was not successful on the base of other models. Valeev and Kvaskov (1983) and Tsendin (1985) are also inclined to admit the idea that the low-resistance state is determined by C o centers and their appearance is related with the pressure increase in the increased conductivity region (Tsendin, 1985). The above-reviewed ideas are, in our opinion, quite fruitful. From the set of experimental and calculated data we are inclined to think that the switching mechanism is based on thermal-electron processes where the reconstruction of chemical bonds under action of the thermal activation of current carriers underlies with the appearance of high-conductivity channels. The electrical field is a stimulator of the process. In Subhani et al. (1977) and Chiang (1984) it is assumed that the increase of the number of chemical bonds owing to the transition of the chalcogen from C o state to C o state in accordance with the mechanism: 0
*
2C ~ ~ 2C3(e ),
(9)
leads to the sharp increase of conductivity because C Ohas the larger number of bonds with other atoms than C Odue to the larger number of conductivity channels for carriers (Fig. 20) (the symbol * in Eq. (9) indicates that C Ohas the excited electron being in the anti-bonding state). The excited electron can pass to the wondering bond with energy release: 2C~ *) ~ 2C + + 2e + energy
(10)
The second possibility of C o to C o transition can take place along the following way: 2C ~ ~ 2C~ *) + C ~
(11)
In this case two neighboring C o can interact forming one C o and one wondering bond (Fig. 20B). The electron in the anti-bonding state can pass to C o and free the energy: C~ *) + C o ---, C~- + C + + energy.
A
B
FIG. 20. The scheme of formation of COcenters from Co.
(12)
The Nature of the Current Instability in Chalcogenide Vitreous Semiconductors
79
9
dO'' Fla. 21. The scheme of transformationof the ruptured bond of Co and Co into the three-coordinatedcenter C~ Thus, if there are defects in glass-like ruptured bonds C o, under action of the thermal heating and the external electric field, the reverse direction of Eqs. (10) and (12) reactions is possible, and also the following reaction can take place at the presence of the ruptured bond between C ~ and C~ 2C o + C o ~ C o(e*) + C o ,
(13)
i.e., the transition of a chalcogen atom from the state of minimum energy C o to an excited state C o (Fig. 21). At the elimination of the external excitation source the chalcogen atom C o may give the excited electron to another C o (e*) causing the rupture of the chemical bond with the formation of defects which were called 'pairs with variable valence' (PVV) (Fig. 22). To explain diamagnetism, an interaction is supposed between PVV pairs, i.e., the appearance of interacting pairs with variable valence (IPVV) (Abalmazova et al., 1970) (Fig. 22C). To make the transition of the chalcogen from C~ state to C~ more energy-efficient, the model of the defect formation proposed in Vikhrov (1985) can be probably used. The process of the single-coordinated defect formation can be energy-wise efficient compared with another defects formation if the gain of energy stored in material as a result of the chemical bonds and valence nodes deformation at the formation of such defect is taken into account. The appearance of the single-coordinated defect leads to decreasing of energy of the atom group that turns to be energy-wise efficient for the system as a whole. Actually, owing to the chemical bonds deformation, their energy can change in a wide range and be much less than the energy of the non-deformed chemical bond. In the result, a spectrum of energy states must appear in the bandgap. Strained chemical bonds are the first to rupture under the action of external energy disturbances. At that, the number of localized states inside permitted bands, which are centers of the electron capture, decreases. The ruptured chemical bond can then pass
C
9
9 9
9
C 1-~C,,)~
FIG. 22. Schemes of formation of the interacting pair of selenium with variable valency.
80
A. S. Glebov
in charged centers C]- and C f which are deep energy centers fixing Fermi levels in the middle of the mobility slit. The appeared C1 and C Ocenters can then pass to C Othat gives an energy benefit, in that way as if seaming ruptured bonds, increasing the coordination number of the chalcogen atom and thereby conductivity of the material. Such transition must be followed by ordering the material in the conductivity channel, by delocalization energy levels in the mobility slit, by the reduction of the activation energy of conductivity, because conductivity takes place along chalcogen bonds, as well as by the sharp increase of the electro-conductivity of the material. Another type of defects which can be formed in the current channel and increase its conductivity under the action of the thermal and electrical field are so-called 'quasimolecular defects' (QMD) formed by orbital-deficit bonds and proposed in Popov (1980, 1981) and Dembovsky and Chechetkina (1984). The author has shown that in CVS there can exist quasi-molecular defects originating due to the formation of multi-center orbitaldeficit bonds similar to xenon fluoride bonds. These quasi-molecules are formed as shown in Figure 23. The possibility of the formation of quasi-molecules under the electrical field action (Popov, 1981) with preferred axis orientation along the field creates preconditions for transition of the material into the high-conductivity state as a result of the integration of quasi-molecules in quasi-polymers. The appearance of OMD explains the phenomenon of photoluminescence and photodarkening. All types of defects are likely to exist in CVS (OMD, PVV, IPVV), OMD being formed probably at first, and at hightemperatures (near Tg), where probability of OMD becomes small, the concentration of quasi-atomic defects being increased (Popov, Mikhalev and Bekicheva, 1984). The formation of the defect leads in the final result to ordering of the CVS material as a whole. Thus, the relaxation of the excess energy is followed by the transition of the material in the switching channel from the state containing C ~ C~-, C + centers in the material containing mainly OMD and C Ocenters. The high-conductivity state will consist mainly of C Ocenters. Stages of the current instability development as well as the energy diagram of the channel materia 1 are schematically shown in Figure 24. The kinetics of the
9
-t-
/
tl
tl tl
tt
tt tt
tl tltl tt tt tt
FIG. 23. The scheme of formation of the quasi-molecule.
The Nature of the Current Instability in Chalcogenide Vitreous Semiconductors
81
4
1
C
1
CMD
2
2
CMD
3
4
3
4
FIG. 24. The current-voltage characteristic;A, and the energy diagramof the current channel; B, on different stages of the current instability development C.
switching process can be different to some extent depending on the device design and material structure, although development stages are the same in all cases that will be discussed later. The longitudinal expansion of the ODC region is indicated by data of Makhinya (1980) and the current filament kinetics. Based on the similarity of the switching process with the process of the solids destruction under the action of the mechanical load, the kinetics of the switching process and the picture of the re-structuring in the inter-electrode space of the switching element can be presented as follows. We assume that the kinetics of accumulation of ruptured molecules under the action of the electric field, like in the case of the mechanical loading, are described by the firstorder chemical reaction equation (Korsukov and Shunkevitch, 1975): Ct = C(I - eKt),
(14)
where Ct is the current concentration; C, the concentration of bonds excited by the electrical field; K, the rate constant of the reaction and t is the time. In its turn, the rate constant (K) is the subject of the Arrhenius equation taking into account the electrical forces action (Regel, Slutsker and Tomashevsky, 1974): K = Koexp(-(Wo - ~ E ) / k T ) ,
(~5)
where K0 is the pre-exponential factor; W0, the effective activation energy at zero voltage; /3, the activation volume of the reaction and E is the intensity of the electrical field.
A. S. Glebov
82
From above equations the expression can be written which characterizes the switching time in CVS as well as conditions of the current instability generation:
~-= l n ( C / ( C -
Ct))l/Koexp((W o - flE)/kT).
(16)
If it is assumed that in strong electrical fields the ionization potential decreases in accordance with the Frenkel's rule (Valeev and Kvaskov, 1983), i.e.
W-
Wo - 2e~/eE/ei.
(17)
and the rate constant of the reaction of chemical bonds rupture is determined by the rate of electrical field expansion in the material, i.e. K o -- I/'rM, where ZM is the Maxwell's relaxation time of vitreous material; E, the intensity of the electrical field; e i -- 47tee0, Eq. (16) can be rewritten as z = ZM(ln C / ( C -
Ct))exp((W0 - 2ex/eE/ei)/kT).
(18)
In the moment of switching when Ct approaches to C, Eq. (17) looks like z = ~'Mexp((W0 -- 2e~/eE/ei)/kT),
(19)
that completely coincides with expression (25) obtained experimentally from the temperature dependence of the switching delay time at different amplitudes of the switching pulses (Fig. 40). The value W0 determined from the temperature dependence of the delay time coincides with the value of the conductivity activation energy of CVS (Fig. 40). The ~- value corresponding to z0 value in the 'pole point' is equal to 10 -8 s that coincides with the value of the Maxwell's relaxation time of carriers for given CVS composition. This value is determined with logarithm accuracy (ln z0 = - 8 + 1). The value /3-0.57 eV/(mV/cm) 1/2 that is close to the value 2ex/eE/ei---- 0.7 eV at ei = 1. The /3 value changes depending on material production regimes and is probably determined by the chemical bond tension. Comparing the conductivity activation energy AEo-with the delay time activation energy W, it can be seen that the switching effect is related in essence with CVS conductivity activated by the electric field. Thermal fluctuations in absence of the electric field cause ruptures of inter-atomic bonds in various parts of solids. But these ruptures are liquidated owing to restoration of ruptured bonds because the fluctuation necessary to restore a bond is not larger than the fluctuation causing its rupture. The electrical field applied decreases the energy of the bond rupture. It means that the bond rupture will be caused by fluctuations of less values which, as it can be seen from expression (19), will 'come' to the atom more frequently, i.e., ruptures of inter-atom bonds will occur more frequently than they had been before the field was applied. But the main thing is that, having made the bond rupture easier theoretically, the external field will make their recombination more difficult, because it leads to the structural reconstruction of material in the filament region. Thus, at the first stage of the current instability development, the process of the thermofield activation of electrons takes place followed by the structural reconstruction. First of
The Nature of the Current Instability in Chalcogenide Vitreous Semiconductors
83
all, electrons in Lp states of chalcogen atoms undergo this process followed by the transition of C o centers in C o centers with the emergence of one free electron in the conduction band and one electron in the excited anti-bonding state (Fig. 20 and formulae (9)). It is obvious that for realization of such reconstruction the energy must be consumed which is equal to the conductivity activation energy because Lp electrons in chalcogenide glasses create the valence band (Chiang, 1984). Therefore, the defect formation in CVS is followed by increase of the electro-conductivity of material and requires overcoming the energy barrier not exceeding the conductivity activation energy. The heating of the current channel due to the electro-conductivity increase at the transition of C o centers in C o centers will lead to the rupture of inter-atomic chemical bonds. In the first place, the strained chemical bonds, carrying the maximal deformation load, will be ruptured. Such process requires higher energy consumption than the transition of C~ centers in C o centers because it is followed by the covalent bond destruction, but it will be energetically efficient for a large atomic system because the outflow of the deformation energy and the reduction of the excess atomic energy in the current channel material take place in this case (Vikhrov, 1985). In addition to defects of OMD, PVV, IPVV types which are formed as a result of the bond reconstruction in chalcogen atoms, the formation of defects on atoms of the V group of the periodic table is possible (Elliott and Davis, 1979). In this case the picture of the defect formation will be more complicated because the hybridization of energy states is required for this. Defects with the smallest energy are, like the case of chalcogens, charged centers with the variable valence PP2 and pP+. In multi-component CVS containing V group elements, defects of both C-centers and P-centers types can be produced. Their concentration will be different due to different formation energies. In Adler (1982) it is indicated that the main negatively charged center will be probably C1, and positively charged centers will be both C~- and SpP +. The defect formation process in the current channel will be continuing until the excess deformation energy in the current channel material will reach its minimal value. At that, all chemical bonds carrying the large deformation load will be ruptured and the process of the bond reconstruction will be completed. The further temperature increase in the current channel will not cause any significant increase of the electroconductivity because, to increase the free carriers concentration, the higher energy equal to the energy of rupture of non-deformed covalent bonds must be consumed that requires significantly higher temperatures than the CVS melting point (Glazov, Chizhevskaya and Glagoleva, 1967). If it is taken into account that current paths of chalcogen atoms have been formed due to the bonds reconstruction in the current channel, it means that the conductivity activation energy of the current channel material will be reduced, i.e., the 'mobility slit' will tend to 'collapse'. From the other side, such ordering of the material in the channel will lead to the delocalization of energy levels, caused by the chemical bonds deformation, that must sharply increase the mobility of electrons for which energy levels, excited by the deformation, are acting as traps (Vikhrov, 1985; Glebov, 1995). From what is said above, it follows that defects formation in the channel followed by the reconstruction and the rupture of deformed chemical bonds must lead to the transition of the conductivity from the semiconductor type to the metal type. Actually, such transition has been found in many works of Cesnis, Ogiskas and Gashka (1985),
84
A. S. Glebov
Lebedev and Tsendin (1986) and Babenkas, Balevicius, Cesnis, Poskus and Siktorov (1987) at temperature of ---500 K. The transition to the metal type conductivity limits further temperature growth. Values of the conductivity transition temperature coincide with the glass softening temperature that also allows to relate the conductivity with structural changes which probably sharply increases at the softening temperature. The value of the transition temperature can be possibly determined using the dependence of the threshold voltage from temperature at different values of the 'inter-electrode' distance (Fig. 39). The 'pole' point of straight lines intersection gives the value of the temperature at which the switching effect will be lacking. It has been noted in Kolomiets, Lebedev and Tsendin (1981) that the transition to the metal type conductivity is inherent to CVSs with relatively high conductivity in which the stable switching and memory effect is observed. In its turn, the stable switching and memory effect is observed in CVS with the certain chalcogen concentration exceeding the certain (percolation) threshold (Bicerano and Ovshinsky, 1985). It confirms the current instability mechanism related with the bond re-switching in chalcogen atoms and the formation of conducting filaments along C o excited centers. The mentioned chain of phenomena leads to the conclusion that processes causing the current instability are determined, like the defect formation process, by the chalcogen concentration in glass and, consequently, the electron concentration of unshared pairs of the chalcogen (Dembovoky and Ilizarov, 1978). The other important consequence of the proposed model is the forecasted inversion of the sign of carriers in the filament. It follows from the mechanism of the sign inversion in the presence of the deformation energy in CVS (Vikhrov, 1985) as well as from the possibility of the appearance of the large carrier concentration at the transition of C o centers in C o centers taking into account that C o centers can be also suppliers of electrons in the conductivity band because they are shallow donor centers. The reduction of the traps concentration at the delocalization of deformation-induced levels will lead to increasing of their mobility comparing with the holes mobility. Actually, in works of Petersen and Adler (1975) the n-type conductivity with 1019 cm -3 carrier concentration has been revealed that is in accord with the C o centers concentration in CVS indicated in Tsendin (1985). According to theoretical and experimental evaluations presented in various works, the current density in the filament after the transition to the metal type of conductivity is j ~ 10 s A m -z, the conductivity is o- ~ 10 - 1 - 1 0 - 2 ~ cm (Oreshkin et al., 1969; Adler, 1977; Babenkas et al., 1987). The transition of the current channel material to the metal type of conductivity, as it has been noted before, takes place in the glass formation temperature range. At that, the ordering of the material takes place that has been indicated in Lizima, Sugi, Kikuchi and Tanaka (1970) where the symbiosis between the changing of the endothermal transition enthalpy and the changing of the conductivity of the G e - A s - T e system glasses depending on time has been established at the glass formation temperature. The other proof of the material ordering is the data of the work of Kotz and Shaw (1984) where higher density of the channel material comparing with the starting material density has been noted. The considered switching mechanism based on the material reconstruction in the switching channel at the action of the thermal heating and the electric field can explain the discord in evaluations of shares of thermal and electric
The Nature of the Current Instability in Chalcogenide Vitreous Semiconductors
85
phenomena in the switching effect observed in published works. If one takes into account that the reduction of the chemical bond strength takes place under the electrical field action equal to the 0.01-0.001 part of its value, the rupture reaction takes place with the noticeable rate even at the room temperature due to the reaction rate constant increase in Eq. (15), the role of thermal and electrical phenomena in the switching effect will be different depending on the inter-electrode distance value, the environmental temperature and the over-voltage.
4. Experimental Confirmation of the Kinetic Model of the Switching Effect 4.1.
INFLUENCE OF C V S COMPOSITION ON FUNCTIONAL CHARACTERISTICS OF SWITCHES
Results of investigations of bulk samples based on G e - T e and A s - T e systems, which possess the largest crystallization rate (Dembovsky, 1969; Zaliva, Kudrina, Minaev and Nekrasov, 1980) and are used for creation of memory elements, are presented in Figure 25, 26 and Table II. Figure 27 shows temperature dependences of specific electro-conductivity of vitreous semiconductor films for constant current. In the investigated temperature range they have several regions divided by points of inflection or jumps. Practically for all investigated films there are two regions on the lg o- vs. lIT dependence at low temperatures with different slope which are approximated by the expression o-= o-nexp(-AE/kT). Temperatures T 1 at which the slopes change are presented in Table II. The second region of this dependence loses its linear character when temperature increases and is terminated with the sharp increase of the electro-conductivity at the temperature T2. The further heating of the film leads to the non-linear change of the electro-conductivity with the tendency of the activation energy E decrease. At the temperature T3 the second sharp change of the electro-conductivity is observed. Values of the activation energy and the preexponential factor E1 and o1 between T2 and T1; E2 and o'2 below T1, as well as temperatures T2 and T3 are given in Table III. Values of the specific electroconductivity at room temperature and the activation energy at high temperatures Ekp (higher than T3), are also shown there, the characteristic temperatures are indicated by arrows in Figure 27. The temperature dependence of the thermo-emf for films of this system (Fig. 28) has rather complicated character, so the determination of the thermo-emf activation energy for these samples is not possible. The thermo-emf coefficient for all films is positive and its value corresponds to the notion of the Fermi level location in the middle of the mobility 'slit' shifted slightly to the ceiling of the valence band (Mott and Davis, 1982). Values of the thermo-emf coefficient at the room temperature Sk are presented in Table III. It is interesting to compare experimental data obtained from investigations of electro-physical properties of glasses with energies of chemical bonds in the system investigated. The integral estimate of all chemical bonds energies can be the atomization enthalpy of the vitreous alloy but there are practically no published works concerning the determination of this value for chalcogenide glasses (Minaev, 1981; Minaev and Aliev, 1986).
86
A. S. Glebov
lgS, Om-1 cm-1
-3
"%%.
-4 -5
--'%<:. x~,:. x-.
-6
-7
lg S, Om-"cm-'
<~...
,,x~
3 -3
lg S, Om-' cm-'
\~... " - ' ~ - .-~. ~. ... ~
=
\ ..
-6 ,,,,....
~ -6 -7
-7
7
=
-4 -5
,<.9
"\,,'"'-. k\ "-.
-S
4/N"x"'''',f 2
3
4
5
103, K_1 T
FIG. 25. The temperature dependences of the electroconductivity of bulk CVS samples of the X4Gel6Te8o system (the curve numbers correspond to composition numbers in Table II).
This is why it is expedient to use close to this value the energy of the chemical or covalence-ion binding of atoms in alloys (Minaev, 1980) as the estimate of the total energy of chemical bonds in the system. The example of calculations of this value is presented in Minaev (1980). The energy of the covalence-ion binding ECIB is the averaged energy of the chemical bond in material (Eav) multiplied by the half-value of the averaged effective coordination number Kav (the number of atoms linked with the given atom by covalence-ion bonds): EcI B -- EavEav/2. The calculation of energies of the covalence-ion binding (EcIB) is based on the analysis of the glass structure. Therefore, it is necessary to construct a structural model of the glass-forming network of the system under investigation which can serve as a basis for calculations required. In Lucovsky and Hase (1982) two models of the glass-forming network are proposed: (a) the network model with random covalence bonds where the distribution of all possible bonds between atoms is the statistical one;
The Nature o f the Current Instability in Chalcogenide Vitreous Semiconductors
S,mW.degree -1
87
6
2.0 . I o *S ~ ~
~ ~ ~
~
J
/ "
/
.,
-
,,,,.,,
1.5
~ ~
~
.I" o
//%
/.If""
/ ~
,'/~t
1.0
,I"
9~
111
.I"
I
"
11
11
~
~I I
I ~ ~I
I I
I
~
I
1 I"N2
~
~
11
.
~.
~_.
1"" ~
,"
. "Y ~
I'~.._
..
~176 ~ o
~
I"
~
..'"" ~,,/ .."'" . " ^ X
o~176
I ~176
~
~ ~
~
~5
<~
8 X
x
i
~
4
o I
0.5 310
315
410
4.;
5.0
10___3, K-1 T
FIG. 26. The temperature dependence of the thermo-emf coefficient of bulk CVS samples of X4Gel6Teso
compositions (numbers correspond to numbers in Table II).
(b) the model with the chemically ordered network which takes into account relative bond energies and is based on the assumption that for all compositions the heteropolar bonds are more beneficial. Models of all glasses considered in this work are constructed in accordance with the latter model taking into account one more initial principle: the ideal glass network must have the maximum number of bonds with maximum energy, the formation of bonds being in the following sequence: heterogeneous bonds followed by homo-polar bonds placed according to the energy decrease (Petrov, Shrainer, Raykin, Glebov, Kozlov and Rotsel, 1985). This postulated rule seems to have some exceptions caused by the formation of complex compositions (Nadkarni et al., 1983) where the important role is played by interaction of various atomic groups, which had been already linked by chemical bonds, that can lead in some cases to the segregation phenomena in glass. It is possible that for non-segregating glasses this rule has no exceptions. Let us consider the application of this method to the glass of the I n - G e - T e system. In accordance with the proposed postulate in this glass the existence of the following chemical bonds is possible: G e - T e (171.5), I n - T e (148.4), I n - G e (128.1), T e - T e (168), G e - G e (157) and I n - I n (97.2). The bond energies in kJ mo1-1 were calculated from Poling' s (1974) formula and are presented in parentheses. The results of such calculations
TABLE I1 PARAMETERS OF ELECTRO-PHYSICAL PROPERTIES OF BULKCVS SAMPLES OF THE SYSTEM X4Ge16Teso The group number of the Periodic Table
CVS composition (bulk)
AEu (eV)
AE, (eV)
The Nature of the Current Instability in Chalcogenide Vitreous Semiconductors
89
lg s, Ohm-lcm-1
~ "m
I i..
',--.. |
lg s, Ohm-lcm-1
-1
Ikl : 1\
-2
!~i I I
"r -
8 x
;\l
' l;
\
-3 -4
",,~ x.. x
"x x "'-
-5 -6 -7
-4
-8
- - -~
::.:......
. - ~
t
T3
t
,T2 3
.-::...
6
T1 4
;
103, K -1
T Fro. 27. The temperature dependence of electroconductivity of amorphous films of the X4Ge16Te8osystem (numbers of curves correspond to numbers of compositions in Table II-III).
for the composition X4Ge16Te8o are presented in Table II. Doing such calculations, one must be especially careful if there are Cu, Ag, Au, T1, Sn, Pb in the system because they may be present in the glass in different valence states (Minaev et al., 1986). The analysis of data presented in Table III suggests that the value of the chemical coordination significantly influences on electro-physical properties of glasses. The higher energy of covalence-ion coordination, the higher the threshold voltage, the higher the activation energy value, and the lesser the conductivity of CVS. However, it does not work to obtain the wide control of parameters by a small quantity of additives. In connection with this, it is interesting to study the influence of the third component on glass properties under the condition of its constant elemental composition. For such experiments three systems I n - G e - T e , G a - G e - T e , P b - S i - T e were selected. The glasses obtained by synthesis have been investigated in the same sequence as glasses in the system X4Cel6Te80 . The results of investigations are presented in Tables IV-VI. Dependences lg o- vs. 1/T and S vs. I//T in the investigated temperature range are described by the same equations as in the system X4Cel6Te80 (Figs. 25 and 26). For all CVS compositions in the investigated systems the value of the chemical binding has been calculated on the base of principles described above. The obtained values are
90
o o o
9
o 9
< >
9
<
9
<
0
0 r.~
z <
0 [..
< .<
I
I
I
I
I
I
0
"~
I
I
> -.1
I
,-.,,
~.~
b~
0
r..) ~=
c~. ~
r".-
I
I
tt"~ c ~
cq
I
I
I
r
I
I
r ~'~ tt'~ r ,,~1- tt3 ["-.- ,-.~ tt') I".-, tt') tt-~
I
tt'~ ~
r
',~- tt'~
o
0 0
t--. ~
~5
C7,~ ,....~ r162
0 0 tt'~ r
r162 ,....~ 0
~'~ tt"~ ~
,....~ r
d
eq
d
r
0 0 r162 0
0
~,--,.--,
0 I"-
0
r
cq
eq
A. S. Glebov
I
tt'~ tt3 0 ,...~ r162 tt~
r
r
eq ~ , . 6
The Nature of the Current Instability in Chalcogenide Vitreous Semiconductors
91
S, gV.degree -1 I I
2
1440
r
1000
,-1' I . / ) ;if-
600 200 /9
S, gV.degree -1 1440
_J'J"
\ 5
1000
600 200 2;6
3;0
312
3;4
10__3, K-1 T Fro. 28. The temperature dependence of the thermo-emf coefficient of amorphous films of the X4Ge16Te80 composition (numbers of curves correspond to numbers of compositions in Table III).
presented in Tables I V - V I from which the relation between the chemical composition and main electro-physical characteristics can be judged. As it can be seen from Figures 29 and 30 for I n - G e - T e and G a - G e - T e systems, such properties as the activation energy of electro-conductivity and the threshold voltage change cymbately in relation with the binding atoms energy. At that, for the I n - G e - T e system the conformity between the composition and properties remains the same for film samples as well. The results of film samples investigations are presented in Table VII (Ampilogov, Vikhrov, Glebov and Minaev, 1982; Vikhrov, Oreshkin, Ampilogov and Glebov, 1982). Similar relation of parameters of vitreous materials with threshold characteristics and the chemical binding energy has been found for systems X8Ce15.64Te76.36, X8As46Te46 and X4As4sTe48. The analysis of data obtained for the XsGea5.64Te76.36 system (Table VIII) shows that EClB, as a rule, correlates with investigated properties of the system. Especially close correlation is observed for AE and Tg 9the AE/EcI B ratio for all compositions lies in the range of 0.0021-0.0029 = 0.0025 _+ 0.0004 (+ 16%), the ratio
TABLE IV PARAMETERS OF TRANSPORT PROPERTIES OF BULKCVS SAMPLES OF In-Ge-Te CVS composition In 12Ge14Te74 InloGe 14Te76 1n10GeI 2Te78 I~ T ~ u o InsGe I 2Texo In4Ge I 6Texo In2Ge I X T ~ X O As4Ge15Te8I
uk
a ' cm-I) 3.2 4.4 8.4 15.0 16.0 9.6 5.6 3.0
SYSTEM
Sk (kV d e g l )
E u l (eV)
Es (eV)
E u - Es (eV)
cro ( 0 ' c m l )
1600 1200 1150 560 850 1100 1060 1670
0.45 0.43 0.41 0.39 0.41 0.42 0.42 0.45
0.26 0.36 0.3
0.19 0.07 0.11
88.6 157.6 88.6 28.3
115 80 65 40
70 110 140 150
126 195.6 192.3 188.7
-
0.07 0.14
-
203.0 86.7 157.0
55 65 80
150 130 80
191.8 198.1 201.3
0.32
0.13
99.8
115
80
-
0.34 0.28
-
U
(V)
I
(A)
EyB (Jlmol)
-
? FO
8
0-
9
The Nature of the Current Instability in Chalcogenide Vitreous Semiconductors
93
TABLE V ELECTRO-PHYSICAL PROPERTIESOF BULK CVS SAMPLESOF S i - P b - T e SYSTEM CVS composition
Pb2Si21Te77 Pb2Si16.66Te81.34 Pb4Si16.32Te79.68 Pb4SilzTe84 PbaSillTes5 Pb6Sils.98Tevs.62 Pb8Si15.64Te76.36 PbloSils.3Te74.7 PbloSi13Tev7
o(106, ~-1 cm-1)
Ek (eV)
o0 (10-3 ~-1 cm-1)
T (~ hump
Uthr (V)
0.67 7.24 6.3 8 28.1 6.3 20 200 141
0.65 0.57 0.66 0.48 0.478 0.54 0.53 0.46 0.42
63 5 19 9.1 4.05 10 29 14 2.27
275 293 253 238 200 254 227 246 235
125 25 33 27 40 43 34 40
EyB
(kJ/mol) 219.72 209.381 198.944 196.528 209.5357 209.69 209.84 204.288
Tg/Eci B 1 . 8 5 - 2 . 1 7 = 2.01 _+ 0.16 (_+8%). For the X8As46Te46 system the ratio Tg/Ecm = 2.16 _+ 0.09 = (_+4.2%), and for the system X4As4sTe4s --- 2.12 + 0.1 =
(_+ 4.5%). Figure 31 shows EcIB and the softening temperature of glasses in the system X8As46Te46 (Minaev, Glebov, Rozhkova, Shrainer and Paykin, 1987a; Minaev, Glebov, Rozhkova, Shrainer and Raykin, 1987b). Similar calculations made by Minaev for glasses of two-component telluride systems with A1, Ag, Ga, Si, Ge, As have shown (Minaev et al., 1986) that the ratio of the softening temperature (Tg) to the energy of the covalence-ion binding (EclB) is 2.075 _+ 0.205 cal J mo1-1 ( + 9.9%). In the same limits there is the ratio Tg/Ecm for 20 arbitrary compositions of glasses of 10 arbitrary triple telluride systems (Minaev et al., 1986). Thus, these investigations confirm conceptions of the model of the current instability that the main parameter determining electrical characteristics of the switching process is the parameter which is close to the total energy of chemical b o n d s - - t h e energy of the chemical or covalence-ion binding of atoms in glass. At that, the activation energy of the intrinsic conductivity can be considered, according to Muller, 'as the measure of the difference of energies of double-electron and single-electron chemical bonds
TABLE VI ELECTRO-PHYSICAL PROPERTIESOF BULK CVS SAMPLES OF G a - G e - T e SYSTEM CVS composition GalGe16.83Te82.17 Ga2Ge16.66Te81.34 Ga6Gels.32Te79.68 Ga4Gels.98Te78.o2 GasGe15.84Tev7.16 GaloGels.3Te74.7 Gal 1Ge15.3Te73.7 Ga14Ge14.62Tevl.38
EyB
tr (105, 12-1 cm -1)
Ek (eV)
tr0 (103, f1-1 cm -1)
S (txV/oc)
Uthr (V)
(kJ/mol)
10 7.95 4 5 4 2.51 1.41 1.26
0.42 0.54 0.48 0.44 0.38 0.48 0.43 0.48
1.2 12.6 5 1.48 0.24 3.1 0.25 1.85
901 1157 1030 1189 992 1081 990 828
38 36 40 48 60 75 80 93
200.05 200.56 201.28 206.35 207 207.46 208.03 210.27
94
A. S. Glebov
Ecib, kJ mole 200
Uthr,
V 100
80 60
195
40 Es, eV 0.46
190 9 /
0.42
.....
// //
.... 9 ~ ..,,..
0.40
///
-.,~F---~N N
0.38 In
2 Ge i8 Te'
1'6
~i
8
1'0
1'0
1'0
1'2
1'4
1'2
1'0
1'2
1'4
1'4
80 8'0 8'0 80 78 76 At.% FIG. 29. The relation between the covalent-ion binding and the chemical composition and electrophysical properties for glasses of the In-Ge-Te system.
b e t w e e n corresponding atoms, as the measure of ionization (Minaev et al., 1987b). The stronger a bond, the less, obviously, conductivity, and the higher the threshold voltage. The same dependences between the switching voltage, the Tg temperature
of the covalent bond' the value of the electroreasons seem to cause and the CVS resistance
Uthr,
V 120
J
60
slO5, Ohm-lcm-1 10 8
100
80 40 20
•
6 4 2 89
4
6
8
1'0
1'2
1'4 Ga,'at. %
FIG. 30. The relation of the chemical binding energy with the chemical composition and electrophysical characteristics of the Ga-Ge-Te glass system.
TABLE VII PARAMETERS OF TRANSPORT PROPERTIES A N D THRESHOLD CHARACTERISTICS OF AMORPHOUS CVS FILMSOF In-Ge-Te Amorphous CVS film composition
4 R-I cm-')
Sk
(kV deg-I)
AEuo (eV)
AEul (eV)
AEu2 (eV)
AEukp(eV) TI first hump
T2 second hump
SYSTEM
no
(TI
02
( K ' cm-I)
( R - ' cm-l)
( 0-' cm-I)
96
A. S. Glebov
TABLE VIII PROPERTIES OF GLASSES OF X8Ge15.64Te76.36 SYSTEM Composition (at.%)
E??? (kJ/mol)
Tg (K)
E (eV)
Uthr (V)
Tg/Eci b
E/Ecib
CusGe15.64Te76.36
191.44 205.33 198.48 215.79 191.69 199.34 206.83 199.18
403 445 413 433 413 430 383 388
0.46 0.59 0.51 0.62 0.42 0.49 0.51 0.51
35 125 63 230 27 40 45 63
2.1 2.17 2.08 2.01 2.15 2.02 1.85 1.95
0.0024 0.0029 0.0026 0.0029 0.0022 0.0025 0.0025 0.0026
CasGe 15.64Te76.36 InsGe 15.64Te76.36
Si8Ge15.64Te76.36 PbsGe 15.64Te76.36
AssGels.64Te76.36 88Ge15.64Te76.36 Se8Ge 15.64Te76.36
which were obtained for the A 1 - A s - T e system in Himenets (1975). These dependences are shown in Figure 32 and Table IX and can be approximated by the following expressions: gth r --
2 lg
7.41 exp(0.02Tg),
(20)
lg R - 2.08.
(21)
gth r --
From the latter expression it follows that the switching power is the same for all compositions: (22)
U 2 r / R -- 0.008 W,
This indicates that the equal energy is required for switching in glasses of the same system. The data obtained, showing the relation between the chemical bond energy, II - bivalent copper
I - univalent copper (a) Tg~ 140
Ecib' kJ
(b) Ecib' [ kJ [
210
210[
200
200[
190
190[
m-bTe
m-;l-e
120
100
As As
"
I
/
i
As As
Cu Ga TI Ti Ge Sb
~ Gesb
~Cu(II) C 9
9 Ga
laO
10
'
Tg,~
FIG. 31. The covalent-ion binding and the softening temperature of glasses in the X8As46Te46 system.
The Nature of the Current Instability in Chalcogenide Vitreous Semiconducto'rs
97
lg Uthr,
v 1000
100
.
.
.
.
I
1
,
,
|
,I
10
.
.
.
.
I
100
.
.
.
.
lg R, M Ohm
FIG. 32. The dependence of the threshold voltage vs. the resistance of the A1-As-Te glass system. the softening temperature Tg, the activation energy of the conductivity and the threshold voltage, confirm the assumption that in the base of the positive current feedback causing occurrence of the current instability there is the structural reconstruction of CVS material in the current channel followed by the re-switching and rupture of chemical bonds.
4.2.
DEPENDENCE OF ELECTRO-PHYSICAL PARAMETERS OF SWITCHES FROM TEMPERATURE AND PRESSURE
In Petrov, Oreshkin, Glebov, Timofeev, Baryshev and Semenov (1971) and Glebov, Vikhrov, Malchenko and Petrov (1975) temperature dependences of main static parameters of switches have been experimentally measured. Figure 33 shows the static CVD of planar switches at various environment temperatures. It can be seen that the dots corresponding to the voltage and current breakdown are well laid on the hyperbola curve that corresponds to the constant power (the energy) required for the development of the current instability at all its stages. At certain temperature the structures lose their switching ability, at that they have the varistor characteristics. With increase of the environment temperature, the switching voltage decreases in accordance with the exponential law. This dependence is shown in Figure 34. At low temperatures
TABLE IX THRESHOLD VOLTAGE,RESISTANCE,TEMPERATURESOF SOFTENINGAND CRYSTALLIZATION OF GLASSESOF A1-As-Te SYSTEM A1 (at.%) 10 10 10 20 20 20 20 23
As (at.%)
Te (at.%)
20 30 40 10 20 30 40 0
70 60 50 70 60 50 40 77
Tg (~
120 137 165 150 175 207 236 150
T s (~
232, 296 244 271
250, 300
Uthr (B)
R (Mf~)
73 117 173 175 292 472 776 144
0.55 1.7 3.6 4.0 10.8 32 80 2.1
98
A. S. Glebov lthr 106, A 300 T=86~ 200
1O0
.
~..._ 41~
50
100
150
Uthr,
V
FIG. 33. The temperature of the static CVC parameters of the planar switch. the exponential dependence of the switching voltage on temperature is upset (Kolomiets, Lebedev and Smorogonskaya, 1972; Adler, 1973). The threshold current increases with the temperature increase (Fig. 35). The diode resistance in the open state at certain current flowing through the diode, for example 400 txA, increases linearly with the environment temperature increase (Fig. 36). It confirms the metallic character of the current filament conductivity. Similar dependences of the threshold voltage have been found in Mott (1974) and Nakashima and Kao (1979). In general case the ratio of the threshold voltage and the absolute temperature can be expressed as (Himenets, 1975): Uth r = CT exp(AEn/2kT), where C is the parameter determined by CVS properties and AEn is the activation energy of switching. In all cases the activation energy of switching En determined from the temperature dependence of the threshold voltage (Fig. 38) turns to be less than the conductivity
Uthr,
300
200
100
-50
0
50
T~
FIG. 34. The temperature dependence of the threshold voltage of the film-planar monostable switch.
The Nature of the Current Instability in Chalcogenide Vitreous Semiconductors
99
Ithr 10 -4, A 300
200
__.j
100
-50
0
50
T,oc
FIG. 35. The temperature dependence of the threshold current of the film-planar monostable switch.
activation energy determined from the temperature dependence of the CVS conductivity. It is well seen from Table IX. The analysis of investigations of the temperature influence on the threshold voltage carried out in the work of Shemetova (1983) shows that the activation energy of switching in CVS is determined by the location of traps in the mobility slit of material and, consequently, the switching effect is related with the electron-phase transition. In our opinion, the above results correspond to the assumption that the activation energy of switching is nothing else than the conductivity activation energy which is facilitated by the electric field and characterizes the strength of chemical bonds. Actually, depending on geometrical dimensions of samples and the electro-conductivity of CVS, the activation energy will have different values and as a result, it is difficult to determine regularities of this value change for CVS of different compositions and for samples of different designs (Shemetova, 1983). Above that, the character of the temperature dependence can be influenced by the inhomogenous current distribution in the interelectrode area. However, for glasses of the same system and structures with the same
Rthrl0 -2, Ohm
/
40
20
/
-50
0
/ Iopen = 400 mA
50
100 T, ~
FIG. 36. The temperature dependence of the switch resistance in the high-conductance state (at the current of 400 ~a).
l O0
A. S. Glebov Uthr/Y,
V.K-1
I
2 1~
"
1
.I'
.1 ~
..>4 .-
~,
"
/
..I""
.I"
0.1
J
I""
i"
3
.
5
,,/
7
..,' .,#
~
.-'>.Ff 06
f" ~176
~
%8
-'" ,~
"-;%-/ 2.6
3.0
3.4
1000/T,Kq
FIG. 37. The temperature dependence of the threshold voltage for bulk diode structures based on CVC systems" 1- AlzoAs4oTe4o; 2- AlzoAs3oTe5o; 3- AlzoAszoTe6o; 4- AlloAS4oTeso; 5- Alz3Tev7" 6- A12oASloTe7o;7- AlloAs3oTe6o;8- AlloAS2oTe7o. inter-electrode gap and point electrodes, this regularity is clearly seen: the activation energy of switching cymbately changes with respect to the conductivity activation energy (Himenets, 1975) (Fig. 37 and Table X). In the presented example a slight dependence of the activation energy from the electric field intensity is observed because bulk samples with the large inter-electrode gap were investigated, so the linear character of the dependence Lg Uthr/T "" I / T does not change, and only the slope of the straight line changes. In the case of decreasing of the inter-electrode gap, the role of the electric field in decreasing of the activation energy of switching will increase that must decrease the activation energy of switching (Table X). It is confirmed by the results of the analysis made in the work of Shemetova (1983) and well illustrated by dependences of the threshold voltage on temperature for samples with different inter-electrode gaps (Fig. 38). With temperature increase, the share of the electric field in decreasing of the chemical bonds strength will be decreasing due to the electro-conductivity increase, and, consequently, the activation energy of switching will be increasing that is also observed in experiments (Shemetova, 1983). TABLE X ELECTROCONDUCTIVITY ACTIVATIONENERGY AND SWITCHINGACTIVATION ENERGY OF GLASSESOF A1-As-Te SYSTEM A1 (at. %) 10 10 10 20 20 20 20 23
As (at. %)
Te (at. %)
ER (eV)
E (eV)
20 30 40 10 20 30 40 0
70 60 50 70 60 50 40 77
0.43 0.44 0.45 0.46 0.42 0.48 0.52 0.46
0.30 0.37 0.42 0.44 0.38 0.44 0.48 0.39
The Nature of the Current Instability in Chalcogenide Vitreous Semiconductors
lg Uthr,
,,I"5
V 2
1
~'...~'.~%
1
lg Ucr, V 0
101
m
..,,,~1 u
m
100
200
/
Tcr
i
I T,~
FIG. 38. The temperature dependence of the threshold voltage of film-planar switches based on CVS of the Ga12Ge6.sSi25Teso system with different inter-electrode distances (1-10 Ixm, 2-17 txm, 3 - 2 2 I.m, 4 - 3 0 ~m, 5 - 4 0 ~m).
Thus, the activation energy of switching can be characterized, like the conductivity activation energy, by the strength of chemical bonds, and the mechanism of the current instability can be explained on the base of the model notions proposed by us. The temperature dependence of the threshold voltage, based on above considerations, can be probably written as gthr
-
-
gthrexp((AE~- A E F ) / 2 k T ) ,
(23)
where Uth r is determined by CVS properties; E~, the conductivity activation energy of CVS and AEF is the reduction of the chemical bonds energy caused by the electrical field effect. The mechanism of the reduction of the chemical bond strength is probably determined by the Pool-Frenkel effect according to which the ionization potential is reduced by the electric field as (Frenkel, 1938): U-
Uo - 2ex/(eF/eoo).
(24)
The assumptions are well confirmed by investigations of the temperature dependence of the delay time obtained at different values of the amplitude of the square pulse. Figures 39 and 40 show dependences of the delay time on temperature and the square pulse amplitude value for film-planar samples of the GalzGe6.sSi6.sAszsTeso glass composition. It can be seen that the delay time obeys the expression: z3 - % e x p ( W / k T ) ,
(25)
where W = W0 - / 3 x / F is the activation energy of switching; f, the electric field intensity and/3 is the coefficient dependent on the initial state of the CVS film. The expression (25) shows that dependences lg r = f ( I / T ) and lg r = f ( I / V ) must form fan-shaped families of straight lines intersecting in one point with the value of r = to, which is observed in the experiment (Figs. 39 and 40). The proportionality of r to the factor eW/~T determines the thermal nature of the switching process facilitated by the electric field. The experiment shows that parameters z0 and W0 are constant values for the given composition of CVS independent on the state of the structure. The value W0 coincides
A. S. Glebov
102
lg t d,
/
-6
1
-7 4
lg td0,
~.~.,,
S
-8 40
80
120
9/
Tkp
o
T, C
FIG. 39. The temperature dependence of the switch delay time at different amplitudes of the control pulse: 1 - 1 4 V ; 2 - 1 6 V; 3-18 V; 4 - 2 0 V.
with the conductivity activation energy value of CVS films and, accordingly, is proportional to the energy of the chemical bond rupture. The value r0 ~ 10 -8 s that coincides with the value of the Maxwell's relaxation time for the material of the filament area. Above that, the physical meaning of W0 and r0 parameters in expression (25) can be clarified taking into account the coincidence of characters of dependences shown in Figures 40 and 41 with characters of dependences describing the kinetics of the solid state destruction (Regel et al., 1972) under the mechanical load action where the time of destruction is described by the expression: (26)
r -- roe w / x r ,
where U~ = U0 - y~ is the activation energy of the process; U0, the initial activation energy of the destruction process, the energy required for the chemical bond rupture; y,
lgt d, s
-6
2
3 -----" ~
K
4 ------~
-7
"%.,
~
\
\ \
lg td0, S
-8 12
16
20
24
28 U, V
FIG. 40. The dependence of the switch delay time vs. the amplitude of the control pulse at different environmental temperature: 1-26 ~ 2 - 4 0 ~ 3-51 ~ 4-81 ~ 5-98 ~
The Nature of the Current Instability in Chalcogenide Vitreous Semiconductors
103
lgR 3
~,~o
-3 ~ o
2
4
OOoooo
6
P, GPa
FIG. 41. The dependence of the electrical resistance of the amorphous Ge2oTe8o sample on pressure.
the parameter characterizing the chemical bond tension and To = 10 -13 C is the average period of thermal vibrations of atoms in condensed matter (however, from the point of view of all said above, it can happen that here To is also the time of the process' s transfer). Based on the analogy of ~'3 and T0 dependences on temperature and tension (or voltage), it can be assumed that in both cases the rupture of chemical bonds occurs causing either the switching or the destruction of samples. In both cases it turns out to be energetically beneficial for the structure. Let us consider limits of the application of kinetic (or activation) notions to the switching process. The switching has the kinetic character when the final rupture of tense inter-atomic bonds occurs due to thermal fluctuations. At that, noticeable time is required for the bond rupture. It is related with the fact that the simultaneous action of both factors (the field and temperature) is required, and, consequently, the re-distribution of the electric field in the inter-electrode gap occurs during the time ~-. If the switching occurs due to the direct action of the electric field or another mechanism of the conductivity increase in conditions of the strong electric field, such switching can be called electronic or non-thermal one (because of its independence on temperature). Such switching is characterized by the absence of dependence of the delay time from voltage and temperature, and the delay time itself is of a small value. The typical demonstration of the kinetic character of switching is the case where the delay time is described by Eq. (18). The Boltzmann's character of the relation of ~'3 with F and T evidences that the determining factor responsible for the switching is thermal fluctuations of thermal energy resources of the body. The external field plays a role of the valve facilitating and directing the switching effect. In the case when the delay time is small and the dependence of the type (18) is not observed, it should be assumed that the switching takes place not according to the kinetic mechanism. Such a case can be observed at supplying the structure with large over-voltage. The main part of the destruction is carried out by the electric field and, if W0 =/3~/F, the complete transition to the electronic mechanism of switching occurs. At that, the re-distribution of the field in the inter-electrode gap is not required, and the delay time can be limited only by the time of thermal fluctuations which is equal to 10 -12 s. It should be noted that it is rather difficult to obtain
104
A. S. Glebov
the pure electronic mechanism of switching because there is a high probability that the bond will be ruptured at approaching of the barrier value W = W0 - / 3 ~ / F with the electrical field increase to the k T value under the action of a small thermal fluctuation without even reaching the limit tension state. Thus, in the range of not very low temperatures the switching is always thermoelectronic one even if the condition (18) is not met. In relation with this, the switching can be performed with short nanosecond pulses at large over-voltage that is observed in experiments (Prikhodko et al., 1979). At W0 >>/3~/F the thermal nature of switching is manifested to a greater extent because the main share of the work for the bond rupture falls on thermal energy. At increasing of/3~/F the switching acquires more of the electronic nature. The approximate condition of the transition from the thermal to the electronic mechanism can be taken as: W0 - / 3 ~ / F ~ (1-5)kT. At temperatures lower than Debye temperatures the switching can have the nonthermal mechanism. At that, quantum-mechanical effects can occur (for example, the tunnel effect) facilitating the switching process. Above that, we can observe a smooth transition of thermal effects into field effects in the process of the current instability development. Such transition has been experimentally confirmed by investigations of non-linearity parameters (Kalmykova, Smorgonskaya and Shpunt, 1986) as well as by the self-accelerating character of the switching process (Makhinya, 1980) because of the increasing share of the electric field in the process of re-construction and rupture of chemical bonds due to the reduction of the effective inter-electrode gap at the longitudinal expansion of ODS (Fig. 18). In Mathur and Arntz (1972), Zamechik, Barik and Shochova (1976), Weinstein, Zalln and Stade (1980), Kolobov, Lyubin and Taguyrdzhanov (1982), Parthasarathy, Rao, Asokan and Gopal (1984a), Parthasarathy, Rao and Gopal (1984b) and Bhatia, Parthasarathy and Gopal (1985) investigations of influence of hydrostatic pressure on electro-physical parameters of chalcogenide glasses and electrical parameters of switches on their basis have been carried out. It turned out that the pressure leads to a sharp change of the optical forbidden bandgap of CVS (Weinstein et al., 1980) and to the increase of the conductivity of vitreous semiconductors (Parthasarathy et al., 1984a,b; Bhatia et al., 1985) as well as to the reduction of the threshold voltage and the delay time of switching (Mathur and Arntz, 1972; Zamechik et al., 1976). The presented data allows to assume that the hydrostatic pressure leads to changing of the chemical bond strength causing the appearance of new localized states in the mobility slit whose nature is determined by the deformation of chemical bonds. At certain values of the applied pressure CVS can undergo the electro-conductivity transition (Parthasarathy et al., 1984a) (Fig. 41) which is indicated by the negative temperature resistance coefficient of CVS at certain values of the hydrostatic pressure (Fig. 42, Bhatia et al., 1985). Such phenomenon is similar to the transition of the current filament material to the metallic conductivity which is observed at the switching. In relation with this, it can be assumed that the pressure effect, like the field effect, influences not only on the chemical bonds strength, reducing its value, but leads to changing of the surplus deformation energy in CVS material. For example, from changing of the resistance value of CVS the conclusion has been made that its increase under the pressure action is connected with the reduction of the electron mobility due to the appearance of new localized states in the mobility slit, and its sharp reductionmwith the reduction of the forbidden gap and the appearance of defects leading to the structural
The Nature of the Current Instability in Chalcogenide Vitreous Semiconductors
105
lg R 12
f/ 5
5.0
7.0
9.0
1000/T, K-1
FIG. 42. The temperature dependencies of the amorphous GeAs3.5 resistance vs. the pressure.
reconstruction and ordering of CVS material. These phenomena depend on rigidity of the glass structural network (Parthasarathy et al., 1984b; Bhatia et al., 1985) that also confirms their deformation nature. Thus, the presented results evidence in favor of the proposed model of the current instability related with the ordering of the current filament material as a result of the defect formation facilitated by the electric field and pressure.
4.3.
INFLUENCE OF SYNTHESIS AND THERMAL TREATMENT CONDITIONS ON PHYSICAL-CHEMICAL PROPERTIES OF GLASSES AND ELECTRICAL PARAMETERS OF MONO-STABLE SWITCHES
In this section results of investigations concerning the influence of chalcogenide glass synthesis conditions and heat treatment on its physical-chemical properties and electrophysical parameters of devices based on it are discussed. Based on differential thermal analysis results, processes leading to the stabilization of material and causing higher reliability and stability of devices made of this material are explained (Glebov, Petrov, Baryshev and Oreshkin, 1972; Oreshkin, Minaev, Skachkov, Petrov and Glebov, 1973; Petrov, Zhivoderov, Glebov and Glebov, 1973). The corresponding ratio of starting materials has been taken for synthesis of chalcogenide glasses of the (Si, 12.64; Ge, 9.76; As, 29.94; Te, 47.7) atomic percent composition. Certified materials have been used (Temspecial purity with the impurity content less than 5 • 10 -5 wt%, Asmspecial purity, Ge~polycrystal of 5 0 f ~ c m resistivity, Si: B-doped, Sb-doped, P-doped). Starting materials in the corresponding ratio were loaded in quartz ampoules which were evacuated and sealed afterwards. The sealed ampoules were placed in the horizontal tube furnace, heated to 1100 ~ and exposed 30 h at this temperature with constant stirring of the melt. After the synthesis was finished the ampoules with the melt were quenched in regimes of the furnace self-cooling (about 3 ~ rain-l), in air and in liquid nitrogen. Annealing of the materials was carried out in vacuum at 240 ~ during 21 h.
106
A. S. Glebov
Switches made by fusion of wire electrodes in chalcogenide glass preforms in accordance with the usual bead technology (Milns) have been used for investigations. Investigations were performed by obtaining of dynamic current-voltage diagrams (CVD) at 400 Hz frequency (Glebov, Vikhrov, Petrov, Oreshkin and Litvak, 1975; Tatarinov, Petrov and Glebov, 1975). It turned out that the voltage of the first switching of devices after they are produced (Uthr) was higher than the subsequent operating switching voltage (Uthr). Uthr The transition from Uthr to Uthr was achieved by the conditioning during a certain time, e.g., 20 h. The value of the conditioning, i.e., the difference between Uthr and Uthr, and the conditioning rate depends on glass synthesis conditions, in particular on glass quenching method after synthesis and the value of the threshold voltage. The time dependence of Uthr is shown in Figure 43. It is seen in Figure 43 that the heat treatment leads to the sharp reduction of the conditioning value. The investigations have shown that the most stable characteristics are possessed by devices made of the glass cooled in the furnace. Figure 43 shows dependence curves of the operating switching voltage vs. the first switching voltage for devices made of glasses undergone different quenching methods. It turned out that devices of the composition cooled in nitrogen (curve 4) are conditioned significantly more intensive than that cooled in air (curve 3) and in the furnace (curve 2). At that, independent on the first switching voltage, practically all devices were conditioned to 70-90 V voltage during a short time (about 30 min). The most stable were devices made of the same composition with the inter-electrode distance not larger than 30 p~m. When inter-electrode distance is increased, the threshold voltage fluctuations are increased as well. So, the value of conditioning depends on the glass-cooling rate after synthesis. The glass cooling rate influences likely on the ordering degree of structural units that affects the time stability of device parameters. To check this assumption, the heat treatment of the glass has been carried out. The curve 1 (Fig. 44) shows the dependence Uth r VS. Uth r for the heattreated composition. The maximum value of the conditioning voltage in this case was not more than 10%. Devices with close and time-stable parameters can be produced from this composition in the case of the accurate fixation of the inter-electrode distance.
3O0
/
200
,7
Uthr.op, V
100
0
100
200
300
Uthrl,V
FIG. 43. The dependence of the operation voltage vs. the voltage of the first switching.
The Nature of the Current Instability in Chalcogenide Vitreous Semiconductors DT,
107
~ 1
~
~ 2 275
200
~
300
3
T, ~
FIG. 44. The DTA curves of glasses with various heat treatments: 1-cooled in liquid nitrogen; 2-cooled at the rate of 3 ~ 3-annealed at 240 ~ during 21 h.
The glass formation processes have been studied experimentally from temperature dependences of physical parameters which are determined by the glass structure. In our case this dependence has been studied with glasses undergone various heat treatment by comparing heating curves of DTA which characterize changes of the enthalpy (AH) or the thermal capacity of the system (AC). The essence of the glass formation process is that with the temperature decrease the structure of liquid undergoes changes caused by re-grouping of kinetic units leading to changing of the short-range order. These re-groupings are caused by the tendency of liquid to pass in the equilibrium state characterized by a certain structure for every certain temperature. In the theory of the structural glass formation the main factor is the rate of the re-grouping, i.e., relaxation processes determining the rate of the structural reconstruction in liquid. Structural units, like atoms, molecules and chains, can participate in the re-groupings. These re-groupings present the activation process. The activation energy of the re-grouping is conditioned by the presence of structural energy barriers dependent on temperature and pressure. It is necessary to note that in complex structures, beside the rupture of bonds between kinetic units, processes of the reversible and irreversible structuring and the inter-molecular interaction are possible leading to the strong temperature dependence of the activation energy and physical properties (Bartenev, 1966; Bal'makov, 1975; Kasatkin and Bal'makov, 1975). The relaxation regularities of any properties are similar because they are described by similar equations, so the application of the DTA method, allowing to analyze changes of the enthalpy (AH) or the thermal capacity of the system (AC), gives the possibility to observe changes of glass properties related with the regrouping of kinetic units. Figure 44 shows DTA heating curves of glasses undergone different heat treatment. The position of the endothermic effect maximum is taken as the glass formation temperature (T -- 275 ~ For the glass obtained by cooling in liquid nitrogen (Fig. 44, curve 1), the heat release is characteristic at reaching 240 ~ because, as a result of the relaxation process, the transition of kinetic units from the state with the internal energy E2 to the state with internal energy E1 (where E2 > EI) is observed. In this case the
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exothermic effect is observed on the DTA heating curve at 240 ~ and the thermal capacity of the system has the minimum value comparing with the equilibrium state. The relaxation process of the re-grouping of kinetic units which leads to the transition of the glass in more ordered equilibrium state conditions is exothermic effect. The endothermic effect at 275 ~ characterizes the thermal absorption by kinetic units and their transition in the state with the internal energy E 2. On the DTA heating curve of the glass obtained by cooling at the 3 ~ min-a rate (Fig. 44, curve 2) there are also two thermal effects. In this case the time lag of the structuring process from the temperature decrease process was significantly lesser and the larger part of the kinetic units had enough time to consume the E 2 energy and transmit from the state E2 in the equilibrium state EI. It is natural that significantly lesser exothermic effect is observed on the DTA heating curve. Subsequent deeper endothermic process characterizes the absorption of the heat required for the transition of the kinetic units from the E1 state to the E 2 state. For the glass that has undergone the heat treatment at 240 ~ during 21 h (Fig. 44, curve 3) the maximum heat absorption is characteristic, i.e., the maximum value of the thermal capacity. It is obvious that in this glass there are few kinetic units possessing the E 2 energy because at the annealing this energy was consumed for the re-grouping of kinetic units, for their ordering in accordance with their tendency to the equilibrium state. Thus, as a result of the heat treatment of the Si12.64Ge9.76As29.9Te47.7 glass, structural changes take place leading to the stabilization of its properties. In the course of the differential thermal analysis of glass the absence of any noticeable thermodynamic phase transition has been determined. All glass samples undergoing different heat treatment were amorphous which was controlled by the X-ray analysis. The data obtained allow to make the assumption that glasses of such composition are not crystallized and melt but just are softened by changing their viscosity. Conditions of glass quenching after synthesis exert great influence on its physicalchemical properties. The lesser the cooling rate of the ampoule with melt, the more ordered material structure is obtained. The degree of the material ordering can be increased by the additional heat treatment at the temperature corresponding to the transition of kinetic units from the state of higher internal energy E 2 in the equilibrium state of the minimum energy of the kinetic units El. The state of glass kinetic units (their energy) exerts great influence on electric parameters of glass-based devices. Thus, the glass quenching regimes, influencing the internal energy of kinetic units, create the different deformation degree of chemical bonds. In fast quenched glass such excessive deformation energy is likely very high. As the cooling rate decreases, their deformation energy value decreases as well, approaching to its minimum value. The presence of the excess deformation energy leads to the metastable state of glass. The transition to the equilibrium glass state with the minimum energy of kinetic units is possible at the formation of defects (single-coordinated), i.e., the rupture of chemical bonds leading to the ordering of a whole group of atoms (Vikhrov, 1985, 1987). In connection with this, the dependence of the conditioning value on glass quenching regimes can be explained by that in the current channel at the transition of the device from the OFF condition to the ON condition the structural reconstruction takes place leading to the reduction of the excess deformation energy. At that, the number of localized states in the mobility slit, which are traps for electrons, decreases that leads to increasing
The Nature o f the Current Instability in Chalcogenide Vitreous Semiconductors
109
of the current carrier mobility and, therefore, to the glass electro-conductivity increase. It, in its turn, is followed by the threshold voltage decrease because certain energy is required for switching and, consequently, lesser switching voltage at the increased value of the switching current is observed. Heat-treated glasses have higher initial switching voltages than that of quenched glasses because there are less numbers of strained deformed bonds that are ruptured and reconstructed in the first place. The results presented are also the evidence of the determining role of the chemical bond energy in the development of the current instability as well as parameters stability of glass-based devices. Thus, the presented kinetic model of the current instability explains published experimental results and allows to determine the role of both thermal and electronic processes in the framework of the unified conception of the switching.
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parameters of S-diodes based on CVS, Physical- Technological Problems of Cybernetics: Proc. AS USR AS USR, Kiev. Oreshkin, P.T., Vikhrov, S.P., Glebov, A.S., Mal'chenko, S.I., Petrov, I.M., Andreev, V.P. and Sazhin, B.N. (1976) Investigations of the filament formation process in semiconductor glass-based elements and development of the programmable ROM matrix, Structure and Properties of Non-crystalline Semiconductors: Proc. VI International Conf. on Amorphous and Liquid Semiconductors, Leningrad, USSR, November, 18-24, 1974 Nauka Publishing House, Leningrad, pp. 470-474. Ovshinsky, S.R. (1975) Amorphous materials as interactive systems. Electrical Phenomena in Non-crystalline Semiconductors: Proc. YI Int. Conf. on Amorphous and Liquid Semiconductors. 18-24 XI, 1975, Leningrad, pp. 426-435. Parthasarathy, G., Rao, K.J., Asokan, S. and Gopal, E.S.R. (1984a) Electrical transport and high pressure studies on bulk Ge2oTeso glass, Pramana, 23(1), 17- 29. Parthasarathy, G., Rao, K.J. and Gopal, E.S.R. (1984b) High pressure studies of Sel00-xTex glasses, Philos. Mag. B, 50(3), 335-346. Petersen, K.E. and Adler, D. (1975) Electronic nature of amorphous threshold switching, Appl. Phys. Lett., 27(11), 625-627. Petersen, K.E. and Adler, D. (1979) Model for the "on"--state of amorphous chalcogenide threshold switches, J. Appl. Phys., 50(2), 925-932. Petrov, I.M., Oreshkin, P.T., Glebov, A.S., Timofeev, V.N., Baryshev, V.G. and Semenov, V.A. (1971) Technology and electrical parameters of negative resistance devices based on chalcogenide glass, PhysicalTechnological Problems of Cybernetics: Proc. AS USSR AS USSR, Kiev, pp. 113-116. Petrov, I.M., Shrainer, Yu.A., Raykin, L.G., Glebov, A.S., Kozlov, V.M. and Rotsel, G.P. (1986) Dimensional effects in CVS-based switching elements. Glassy Semiconductors: Proc. All-Union Conf., Leningrad, October 2-4, 1985. Leningrad, 1986, pp. 52-53. Petrov, I.M., Zhivoderov, A.N., Glebov, A.S. and Glebov, S.S. (1973) Influence of technological factors on parameters of s-diodes based on CVS, Physical-Technical Problems of Cybernetics: Proc. AS USR AS USR, Kiev, pp. 41-48. Philips, J. (1983) Physics of glass, Foreign Physics: Collection of Scientific-Popular Papers Mir Publishing House, Moscow, pp. 154-179. Phillips, J.C. (1979a) Structure of amorphous (GeSi)l_•215 alloys, Phys. Rev. Lett., 42(7), 1151-1154. Phillips, J.C. (1979b) Topology of covalent non-crystalline solids: short-range order in chalcogenide alloys, J. Non-Cryst. Solids, 34, 153-181. Phillips, J.C. (1980) Structural principles of amorphous and glassy semiconductors, J. Non-Cryst. Solids, 35-36, 1157-1165. Poling, L. (1974) General Chemistry, Mir Publishing House, Moscow, 848 pp. Popov, N.A. (1980) New model of chalcogenide glassy semiconductors, Lett. JETP, 31(8), 437-440. Popov, N.A. (1981) Quasi-molecular defects in chalcogenide glassy semiconductors, FTP, 15(2), 369-374. Popov, A.I., Mikhalev, N.I. and Bekicheva, I.V. (1984) Property control of glassy arsenic triselenide by structural modification of material. Amorphous Semiconductors--84: Proc. Conf., Gabrovo, September 17-22, 1984. Vol. 1, pp. 171-173. Prihod'ko, A.V., Deksnis, A.G. and Chesnis, A.A. (1979) Nano-second switching in selenium, Phys. Semicond., 1, 193-195. Regel, V.R., Slutsker, A.I. and Tomashevsky, E.E. (1972) The kinetic nature of the solid state strength, Usp. Phys. Nauk, 106(2), 193-208. Regel, V.R., Slutsker, A.I. and Tomashevsky, E.E. (1974) Kinetic nature of solid state strength, Nauka Publishing House, Moscow, 560 pp. Ryvkin, S.M. (1972) On switching mechanism in amorphous semiconductors, Lett. JETP, 16(10), 632-635. Shemetova, V.K. (1983) Influence of technological factors and external effects on parameters of threshold switches based on chalcogenide glassy semiconductors: Doctor's theses, Moscow Energy Institute, Moscow, 256 pp. Shklovsky, B.I. (1971) Optical and electrical band-gaps of amorphous semiconductor, Lett. JTEP, 13(6), 397 -400. Shklovsky, B.I. and Efros, A.L. (1975a) Percolation theory and conductivity of heavily inhomogenous matter, Usp. Phys. Nauk, 117(3), 401-438.
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Shklovsky, B.I. and Efros, A.L. (1975b) The percolain theory and conductivity of heavily inhomogenous matter, Usp. Phys. Nauk, 117(3), 401-438. Shklovsky, B.I. and Efros, A.L. (1979) Electronic properties of doped semiconductors, Nauka Publishing House, Moscow, 416 pp. Shklovsky, B.I., Schur, M.S. and Efros, A.L. (1971) S-like current-voltage diagram in compensated semiconductor, FTP, 5(10), 1936-1942. Smorgonskaya, E.A. and Shpunt, V.H. (1982) The non-uniformity model of the switching effect in chalcogenide glassy semiconductors, Amorphous Semiconductors-82: Proc. Conf., Bucharest, 30 August-4 September, 1982 Central Physics Institute, Bucharest. Vol. 3P. pp. 25-30. Stratton, R. (1973) Tunneling in Schottky-Barrier rectifiers. In Tunneling Phenomena in Solids (Eds., Burnshtein, E. and Owndkvlet, S.) Mir Publishing House, Moscow, pp. 106-125. Subhani, K., Shur, M.S., Shaw, H.P. and Adler, D. (1977) The mechanism for switching in thin chalcogenidebased amorphous films, Amorphous and Liquid Semiconductors: Proc. 7th Int. Conf., Edinburgh, UK, 1977 CICL University of Edinburgh, Edinburgh, pp. 712- 716. Sukhanov, A.A. (1978a) Properties of diodes with electro-thermal instability in the switching channel, Microelectronics, 7(5), 455-463. Sukhanov, A.A. (1978b) Electro-thermal instability in semiconductors with the switching channel, FTP, 12(12), 2338-2345. Tatarinov, V.G., Petrov, I.M. and Glebov, A.S. (1975) Dynamical memory in switches based on amorphous glasses and some problems of its applications, Optoelectronics and Spectroscopy--Ul'yanovsk, 1, 54-57. Tsendin, K.D. (Ed.) (1966) Electronic Phenomena in Chalcogenide Glassy Semiconductors, Nauka Publishing House, St. Petersburg, pp. 224-279. Tsendin, K.D. (1985) The qualitative microscopic electron-thermal model of the switching effect in chalcogenide glassy semiconductors. Glassy Semiconductors. Proc. All-Union Conf., Leningrad, October 2-4, 1985. Leningrad, 1985, pp. 64-65. Valeev, H.S. and Kvaskov, V.B. (1983) Non-linear metal-oxide semiconductors, Enrgoizdat Publishing House, Moscow, 159 pp. Vikhrov, S.P. (1977) The barrier model of switching phenomenon in glassy semiconductors, Physics of Semiconductors and Microelectronics--Riazan, 4, 11 - 15. Vikhrov, S.P. (1985) Role of deformation energy in generation of n- and p-type conductivity defects in CVS. Ways of Stability and Reliability Increase of Microelements and Microcircuits: Proc. III All-Union Science and Technology Seminar, Riazan, June 14-16, 1984. Riazan, 1985, pp. 139-142. Vikhrov, S.P. (1987) Unordered state and role of excess deformation energy in formation of high-energy defects. New Ideas in Glass Physics: Proc. All-Union Seminar, Moscow, October 9-10, 1987. Vol. 1, pp. 41-49. Vikhrov, S.P., Oreshkin, P.T., Ampilogov, V.N. and Glebov, A.S. (1982) Electro-physical properties of amorphous films of I n - G e - T e system, Amorphous Semiconductors-82: Proc. Conf., Bucharest, 30 August-4 September, Bucharest Central Physics Institute, Bucharest, Vol. 3P. pp. 74-76. Weinstein, B.A., Zalln, R. and Stade, H.L. (1980) The effects of pressure on optical properties of AszS3 glass, J. Non-Cryst. Solids, 35-36, 1235-1259. Zaliva, V.V., Kudrina, A.V., Minaev, V.S. and Nekrasov, D.N. (1980) On the problem of material selection for bi-stable switches using the phenomenon of the "glass-crystal" phase transition, Physical-Technological Problems of Cybernetics IC AS USSR, Kiev, pp. 10-25. Zamechik, J., Batik, J. and Shochova, E. (1976) Influence of the overall pressure on electrical conductivity of the amorphous semiconductors GelsTesISzAs2, Czech. J. Phys., 26(9), 1053-1058.
CHAPTER
4
OPTICAL AND PHOTOELECTRICAL PROPERTIES OF CHALCOGENIDE GLASSES A. M. Andriesh, M. S. Iovu and S. D. Shutov CENTER OF OPTOELECTRONICS OF THE INSTITUTE OF APPLIED PHYSICS, ACADEMY OF SCIENCES OF MOLDOVA, STR. ACADEMIEI 1, MD-2028 CHISINAU, REPUBLIC OF MOLDOVA
1. Optical Properties of Chalcogenide Glasses To understand the nature of electronic processes in non-crystalline semiconductors, it is necessary first of all to investigate their energy spectrum, the phenomena of charge carrier transfer, and the process of radiation interaction with such materials. The energy spectrum of electron states in the range hv > Eg can be studied from the reflectivity spectrum of light in the fundamental absorption band where hu is the energy of quantum and Eg the optical gap. Of special interest is the study of the optical features of noncrystalline semiconductors near the absorption edge. It is known that the absorption edge of non-crystalline materials is sensitive to the composition and the material structure as well as to external factors such as electric and magnetic fields, optical, heat, electronic and other radiations. Under the influence of these factors optical parameters of noncrystalline semiconductors suffer reversible and irreversible changes. The study of such phenomena not only clarifies the mechanisms of light absorption in the matter at significant disorder of its structure, but also suggests all possible practical applications, which are not always peculiar to crystalline semiconductors. However, to understand all these phenomena, it is necessary to know the position of electron states, the position and the nature of the absorption edge, near which the majority of photostimulated phenomena in non-crystalline vitreous semiconductors takes place. The study of optical properties of chalcogenide crystals and glasses is very important from the theoretical point of view because it allows the determination of the energetic appropriateness of the interaction of the optical radiation with ordered and disordered solid-state systems, and to clarify how much the disorder influences the peculiarities of energy spectrum and optical phenomena in the above-mentioned group of materials (Phillips, 1966; Collway, 1969; Tauc, 1972, 1974; Tauc, Abraham, Pajasova, Grigorovici and Vancu, 1974; Taylor, 1984; Popescu, Andriesh, Ciumash, Iovu, Tsiuleanu and Shutov, 1996). Short information concerning optical phenomena in the above-mentioned group of materials will be given in this chapter. The peculiarities of energetic spectrum will also be discussed. 115
Copyright 9 2004 Elsevier Inc. All rights reserved. ISBN 0-12-752188-7 ISSN 0080-8784
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1.1. THE REFLECTIVITYSPECTRA OF CHALCOGENIDE CRYSTALS AND GLASSES: ELECTRON STATES The general method for the investigation of the energy spectrum of electron states in the range hv >> Eg is the study of the reflectivity spectrum of light in the absorption band, of photoemission and energetic losses of the electrons reflected by solids (Phillips, 1966; Collway, 1969; Tauc, 1972, 1974; Tauc et al., 1974; Taylor, 1984; Popescu et al., 1996). The reflectivity spectra of these materials were studied in the large energetic range (1.512.5 eV) that allowed investigating their electronic structure. Reflectivity measurements were performed at room temperature using the cleavage surface of AszS3 natural and artificially obtained single crystals as well as the surface of glasses (Fig. 1). The obtained reflectivity spectra have the following peculiarities: The reflectivity spectrum of AszS3 crystals contains a few maxima. The main maxima is placed at 4.0 eV and others appear in the range of 5-12.5 eV having a doublet form (Table I). The reflectivity spectra of AszSe3 single crystal contains some reflectivity maxima, whose positions are given in Table II. The reflectivity spectra of AszTe3 crystals contains peaks at 3.0, 6.5 and 8.7 eV. Upon the crystal-glass transition only the broadest maxima remain at 3.0 and 8.810.0eV (Belle, Kolomiets and Pavlov, 1968; Bishop and Shevchik, 1975; Sobolev, 1995). The peaks in the reflectivity spectra of glasses are very broad, but in main points the peculiarities of reflectivity spectra of single crystals are repeated; it is especially true for the range of high energies. So, for the 10-eV ranges the peaks of reflectivity are situated at the same energies. In the range of energies 5.5 < hu < 8 eV the reflectivity peaks of glasses are shifted to the longer wavelengths in comparison with reflectivity peaks of crystals, but they have the same shape. The above-mentioned peculiarities were confirmed by many authors. The magnitudes of energy for the peculiarities of optical transitions are given in Table I (Andriesh and Sobolev, 1965; Andriesh and Sobolev, 1966; Andriesh, Sobolev and Lerman, 1967; Belle et al., 1968; Andriesh, Sobolev, Popov and Lerman, 1969; Sobolev, Donetskich and Svorostenco, 1971; Zallen, Drews, Emerald and Siade, 1971a; Drews, Emerald, Siade and Zallen, 1972; Kolomiets, Mazets, Sarsembinov, Efendiev, Lusis and Langsdons, 1972c; Andriesh, Iovu, Tsiuleanu and Shutov, 1981) and they differ only a little although they were obtained by different authors who used, of course, different samples. It is worthy to note that the complexity of chalcogenide glasses band structure in the field of high energies (E >> Eg) was also confirmed by Bobonici, Dovgoshei, Migolinets (a) 8
(b) 8
6 4
._.-
~
2
6
-'"3
)4
,
,
,
,
3
2 1
0 5 4 6 8 10 12 E, eV E, eV FIG. 1. The reflectivityspectrafor crystalline(1, 3) and vitreous (2, 4) As2S3(a) and As2Se3(b), respectively. '
'
TABLE I THEENERGY POSITIONS OF MAXIMA OF REFLECTIVITY AND PHOTOCONDUCTIVITY OF As2S3AND As2Se3COMPOUNDS AT 293 K REFLECTIVITY A N D PHOTOCONDUCTIVITY METHODS (IN
Composition
As2S3
A~~S3
As2S3 As2S3 As2Se3 As2Se3 As~Sei As2Se3
Structure
Light polarization
E
Crystal
Nonpolarized
2.5
El
E2
-
-
E3 -
E4 4
ev)
E5
E6
E7
E8
4.7
5.9
7.0
9.1
Crystal
Nonpolarized
-
-
-
-
-
5.1
6.4
7.6
9.8
Crystal Crystal Crystal Crystal Crystal Crystal Glass
Nonpolarized Nonpolarized Nonpolarized Nonpolarized EIIa EIIc Nonpolarized
2.61 2.67 2.43 2.64
2.83 2.89
3.55
4.27
-
-
-
-
-
-
-
-
-
-
-
6.3
-
3.35
3.9 3.9
-
-
3.03 3.11 3.0 2.94
-
7.1
-
-
-
-
-
-
2.87
-
-
2.0
-
-
3.38 3.5
-
4.68 4.43 4.43 4.8
Glass
Nonpolarized
2.0
-
-
-
3.65
2.2 2.2 1.96 2.03
2.8 2.38
-
-
-
Glass Crystal Crystal Crystal Glass
Nonpolarized Nonpolarized EIIa Elk Nonpolarized
1.77 1.82 1.87 1.87 1.6
-
-
-
5.4
-
10.2 8.7 9.85 9.1 9.5
4.6
5.6
6.4
9.2
-
-
-
2.85
3.9
4.7
5.8 5.7
7.0
9.3 8.6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3.2
-
3.6
5.3
5.3
9.3
6.3
-
MEASURED B Y
References Andriesh and Sobolev (1965, 1966) and Andriesh et al. (1967, 1969, 1981) Andriesh and Sobolev (1965, 1966) and Andriesh et al. (1967, 1969, 1981)
0
2. a, a
R
2 % C
2
I?
-. cr
a, Belle et al. (1968) Sobolev et al. (1971) Zallen et al. (1971b) and Drews et al. (1972) Zallen et al. (1971b) and Drews et al. (1972) Andriesh and Sobolev (1965, 1966) and Andriesh et al. (1967, 1969, 1981) Andriesh and Sobolev (1965, 1966) and Andriesh et al. (1967, 1969, 1981) Belle et al. (1968) Sobolev et al. (1971) Kolomiets et al. (1972~) Kolomiets et al. (1972~) Andriesh and Sobolev (1965, 1966) and Andriesh et al. (1967, 1969, 1981)
b
B3s, 2
e? 9
g-
3
g
Q
$rp 0
118
A. M. Andriesh et al.
and Sarcani (1985) who studied the cathodoluminescence spectra of As2S3 films under the action of electron beam. Accordingly to these authors the cathodoluminescence spectra of AszS3 films contained maxima at 3.81,4.06, 4.28, 4.32, 4.56, 4.81, 5.32 and 5.56 eV. From the comparison of these data with the data indicated in Table I one can see a very good coincidence. This confirms that not only reflectivity spectra but also cathodoluminescence spectra obtained in the conditions of electron beam action can be used for the study of band structures of crystalline and vitreous semiconductors. As shown by Bishop and Shevchik (1975) from the photoemission spectra Nv(E) of these crystals have doublet bands in the range of 0 - 6 and 7 - 1 6 eV and are caused by two groups of occupied states. As far as AszTe3 crystals are concerned, no doublet is observed in the spectral range 7 - 1 6 eV. It is surprising that in the case of AszTe3 compound the crystal-glass transition has no significant effect on the character of photoemission spectra (Bishop and Shevchik, 1975). As indicated by Sobolev (1995), the changes in the short-range order of AszTe3 do not manifest themselves in the optical absorption and photoemission spectra. The reflectivity spectra obtained by Zallen and co-authors (Zallen, Slade and Ward, 1971b; Drews et al., 1972) were used by them for the calculation of e 2 constant in the whole spectral range studied using Kramers-Kronig relations. Having compared the reflectivity spectra with the respective e 2 spectra, the authors observed that the peculiarities of both the spectra were approximately at the same energies. Energy interval for the determination of e2 in the case of AszS3 was enlarged by Perrin, Cazarex and Soukiassien (1974) by measuring the energetic losses of electrons, which have a high maximum at 19.8-20 eV for all crystallographic directions and a maximum at 19.2 eV for AszSe3 glasses. These maxima are due to oscillation of free electron plasma. Less-pronounced maximum of electron energy losses is observed at 7 - 8 eV. In the range 3 - 1 2 eV the spectrum e 2 calculated from these data follows the spectral dependence obtained from the reflectivity spectra. At higher energies up to 35 eV the decrease of e 2 is observed for crystalline as well as for vitreous AszS3. The reflectivity spectrum of amorphous AszS3 films have also been investigated at room temperature in the vacuum ultra-violet light in the region between 35 and 55 eV. As shown by the authors a peak of reflectance was observed in the energy region around 44 eV. This peak in the opinion of Cardona and Lei (1978) corresponds to the 3d core levels of an As atom. As it follows from the theory (Phillips, 1966) in crystals, the positions of maxima of reflectivity and maxima of e 2 at energies E > Eg determine the value of the energies of direct band-band transitions in special points of Brullion zone. The theoretical analysis of the energy spectrum of the AszS3 crystal was made by Gubanov and Dunaevski (1974) using the method of pseudopotential. The analysis was made along the symmetry axis 2, A and along two directions perpendicular to each other in the plane perpendicular to axis A. If one considers the extrema nearest to the forbidden gap then one can observe that the maximum of the valence band in the point (0,0,0,2), which is placed in the symmetry plane, and minimum corresponds almost to the same energy. The difference between the minimum direct transitions and the minimum indirect transitions is less than 0.1 eV. This explains the small difference between the minimum direct and indirect transitions. One can also observe that accordingly with energy model calculated for AszSe3 the energy positions of reflectivity maxima can find correspondence with the values of electron energetic transitions.
Optical and Photoelectrical Properties of Chalcogenide Glasses
119
From the band model calculated for As2Se3 by Gubanov and Dunaevski (1974) the energy distances at point F, between two valance bands and three conductivity bands, permit electron optical transitions at 3.25, 3.96, 4.98, 5.68, 6.96 and 8.68 eV. These data correspond, in many cases, with energy positions of the reflectivity maxima in the framework of fundamental band absorption of AszSe3 (see Table I). This proves the concordance of experimental data with the theoretical model. When reflectivity and e 2 spectra of AszS3 and As2Se3 are compared, it is necessary to take into account that the structure of these crystals has the same structure characterized by the term isomorphism. This can be seen in Figure 2 (Andriesh and Sobolev, 1965) which represents the dependence of energy positions of the reflectivity maxima of crystals As2S3 versus the energy positions of the same values in the crystals AszSe3. The experimental data show a straight line with steepness equal to unity. So, in order to obtain the parameters of AszS3 energetic band-model, it is enough to increase the corresponding parameters of AszSe3 band-model by the magnitude 0.7 eV. The optical transitions of electron in crystals occur under the conditions when the rule of quasi-pulse conservation acts. At the same time Tauc et al. (1974) suggested that at large energetic distances from the margin bands the density of states gc(E~) and gv(Ep) of crystals and of amorphous semiconductors of the same composition do not differ. Therefore e 2 can be determined from formula
e2
1 ~hv-Eg
--~
~
0
P(En, Ep)gc(En)gv(Ep)dEp
(1)
where En = h u - Eg - Ep is a factor of weight, which depends on En and Ep and it is not constant when energy is changed in the wide interval. If the optical properties of crystals are determined by the reduced function of state density in the case of amorphous semiconductors, these properties depend on combination of states density of both bonds taken separately. The integration 10 +
o
<
/ O0
/ ,
I
2
,
I
4
J
I
6
,
I
8
,
l0
EAs~Se3,eV Fro. 2. The reciprocal dependence of the energetical position of reflectivity maxima for crystals As2S3 and As2Se3.
120
A. M. Andriesh et al.
of expression (1) leads to erasing of fine structure, which is contained in gc(En) or gv(Ep). This is why the details of the e 2 spectra of amorphous semiconductors should be erased. This condition permits to determine the type of optical transitions, the energy distances between free and occupied states in different points of K space as well as other peculiarities of the band structure of crystal. In amorphous semiconductors, the processes of optical absorption are possible without taking into account the law of quasi-pulse conservation, which does not take place in such materials. The energetic bands in amorphous semiconductors can be discussed only from the point of view of density of states and not from that of the view energy of electrons in K space. Therefore one cannot expect that the reflectivity spectra of amorphous semiconductors could be characterized by the same energy structures in K space with Van Hove singularities. From the factors mentioned above, it is quite clear why the reflectivity spectra of noncrystalline AszS3 and AszSe3 do not contain fine structure. At the same time in the region of high energies 7 - 1 0 eV reflectivity spectra of corresponding crystals and glasses are very alike. This can be understood if one takes into account that in the region of 7 - 8 eV e 2 increases due to the beginning of a new absorption band. The last is determined by electron transitions from the valence band, which is placed deeper. The lack of order does not significantly influence the structure of this band. Watanabe, Kawazoe and Yamane (1987) have pointed out the important role of intermolecular interaction in chalcogenide glasses, in which very strong dependence of the optical gap on the external pressure was discovered. The inclusion of the intermolecular interaction leads to marked change in the density-of-states spectra of the valence bands, giving smoothing and broadening of the structure. Such kind of alterations has been observed in the reflectivity spectra upon addition of metal impurity to AszS3 (Fig. 3) (Iovu, Shutov, Popescu, Furniss, Kukkonen and Seddon, 1999).
25 2 3
20
4
15
10
5 I
3
I
4
5
6
hv, eV Fro. 3. Reflectancespectra of bulk glasses: AszS3 (1), AsaS3+ 0.1 at.% Dy (2), AszS3 + 0.1 at.% Sm (3), AszS3 + 0.5 at.% Sm (4), AszS3 + 0.1 at.% Mn (5) and AszS3 + 0.5 at.% Mn (6).
Optical and Photoelectrical Properties of Chalcogenide Glasses
121
Introduction of rare earth Sm and Dy ions enlarges the main reflection peak, especially around its high-energy maximum at 3.5 eV. On the contrary, the transient metal Mn being added to the glass decreases the reflectivity in that band. It is seen from Figure 3 that the degree of influence is increased with the impurity content growing from 0.1 to 0.5 at. % in both the cases of Sm and Mn. The observed changes in the shape of the reflectivity spectrum look like the shift of the main peak to lower or to higher energy when the impurity atom of more (Mn) or less (Sin, Dy) electronegativity is introduced into the host glass. In the high-energy range (from 5 to 6 eV) the presence of impurity leads to decrease of reflectivity in the high-energy shoulder of the main peak (5.4-5.6 eV) and --~6 eV. The fall of reflectivity in this energy range may be associated with the effect of impurity on the degree of intermolecular interaction, as the latter significantly influences the density of states in the given energy interval. The changes in the intermolecular interaction have been revealed as increasing (in case of Mn), or decreasing (in case of Sm and Dy), the interlayer distance from X-ray diffraction examination. On the basis of systematization of the theoretical and experimental data of the investigation of optical properties of chalcogenide crystals and glasses, some peculiarities of electron states in these materials were determined. The comparison of the reflectivity spectra of crystals and glasses of same composition allows to clarify to what extent the optical properties are changed. It is shown that in the region near the optical gap single crystalline As2S3 and AszSe3 cannot contain fine structure. At the same time, in the region of high energies (7-10 eV), reflectivity spectra of crystals and glasses are very alike because electron transitions occur with the participation of more deeper valence bands which are less influenced by the lack of order.
1.2.
THE ABSORPTION EDGE IN AMORPHOUS CHALCOGENIDES
1.2.1. The Main Features of the Absorption Edge To elucidate the features of the absorption spectra caused by the losses of the far order, it is suitable to use typical non-crystalline semiconductor materials such as arsenic sulfide and arsenic selenide. These materials possess such important advantages as the fact that they can exist in both amorphous and crystalline states. They are very convenient for optical investigation because their absorption edge is in the visible region of the spectrum. Besides, the vitreous materials can be obtained as bulk and thin film samples as well as in the form of fibers. Moreover, the vitreous state of these materials is preserved at considerable deviation from the stoichiometry as well as at variation of the composition by introducing impurities and additions of other elements and alloys. The structure of the bulk and thin-layer specimens do not differ significantly; consequently, in the wide range of thickness the optical features of specimens slightly depend on thickness. This circumstance is very important for the investigation of the absorption coefficient in a wide spectral range. Many investigators paid attention to the advantages mentioned and devoted many of their works to the study of the absorption edge of vitreous arsenic sulfide and arsenic selenide. The results of the studied absorption edge of vitreous sulfide and arsenic selenide are shown in Figure 4 (Zorina, 1965; Kolomiets, Mazets, Efendiev and Andriesh, 1970; Kosek and Tauc, 1970; Popescu et al., 1996).
122
A. M. Andriesh et al. 6 O0 0 9
im IB go
4
g3o ~
2
~1
2 q 1 0
t '
1.0
.
1.5
2.0
,
I
,
2.5 hv, eV
I
,
3.0
I
3.5
FIG. 4. The absorption edge of vitreous AszS3 (1) and AszSe3 (2). o, our data; 9 (K14); zx, (Z5); v, (K18). It is seen that the results obtained by various authors are in good agreement with each other. There is some discrepancy only in the region of slight absorption (less than 1 cm-1). The analysis of the experimental results shows that the absorption curves of amorphous sulfide and arsenic selenide, as well as of other amorphous materials, can be presented by three portions at high, medium and low absorption coefficient values. As shown in Figure 5, the absorption edge of the amorphous arsenic sulphide in the region of high values of the absorption coefficient (c~ > 104 cm -1) can be described by the square dependence of the type ce - a ( T ) / h u [ h u -
Eg(T)] 2
(2)
Coefficient A(T) does not depend on the photon energy and slightly depends on temperature. Eg is the energy value which, according to Tauc et al. (1974), can be taken as the optical width of the forbidden gap. From the graph, the determined dependence (ceh~) 1/2 o n Eg value for amorphous AszS3 appeared to be 2.35-2.38 eV. In the range of values (1-3) x 103 cm-1, the absorption coefficient depends on the exponential energy and can be described by the following ratio ce0 - ce exp{ - [ E 0 ( T ) - hu]/A},
for hu < E o
(3)
where E0 approximately coincides with Eg value, but A is approximately equal to 0.05 eV. When the temperature decreases, no structure appears, but the absorption edge first moves parallel to itself with the temperature coefficient 1.3 x 10 -3 eV, and then its position remains unchanged (Zakis and Fritzshe, 1974). In the region of weak absorption (ce < 1 cm-1), the absorption coefficient value strongly depends on the synthesis regime. At annealing of vitreous ingots, the absorption edge moves to the area of large energies. However, the exponential dependence of the type c e - exp y h v / A t
Optical and Photoelectrical Properties of Chalcogenide Glasses
123
6 5
4 3 2 1 0 2.0
c~
, 2.5
, 3.0
3.5
hv, eV FIG. 5. The absorption edge for amorphous As2S3.
is also characteristic of this absorption edge section where A t is --~0.3 eV (Wood and Tauc, 1972). Analogous results have been obtained when studying the absorption edge of the vitreous arsenic selenide, and this is indicative of the fact that the features of the absorption edges of vitreous arsenic sulfide and arsenic selenide are common. However, this is not surprising, as these materials are analogous, and they have the same structure both in the crystalline and vitreous states. The absorption edge of other amorphous materials has the same shape as in the case of the sulfide and arsenic selenide. As a rule, however, the steepness of the exponential section edge and its position slightly differ (Lastovickova, 1972). The slope of the edge is probably influenced by the impurity as well as by the technology of amorphous alloys.
1.2.2. The Influence of Doping on the Absorption Edge and Structure of As2Ch3 Glasses Let us consider the influence of doping by different elements of the periodical table on the absorption edge of vitreous AszS3, AzSe3, typical representatives of vitreous semiconductors. From the elements of the first group, silver has been chosen. With the increase in concentration of silver impurities, the absorption edge of the arsenic selenide shifts to the long-wave region and decreases its steepness (Kolomiets, Lebedev and Rogaciov, 1974). According to these authors, the insertion of silver into arsenic selenide with concentration from 8 • 1019 to 5 • 10 21 cm -3 results in the charged centers randomly distributed in the space and to the decrease of the absorption edge steepness from 16.6 to 10.7 eV. The magnitude of energy, which characterizes enlarging absorption edge, is approximately equal to the change of the forbidden gap. This can be explained by enlargment of band edges caused by fluctuation of internal potential, which appears due to chaotic distribution of the charge of doping atoms in space. The introduction of other elements
124
A. M. Andriesh et al.
may lead to the decrease of the gap. For example, the introduction of the second group elements and particularly copper into arsenic sulfide shifts the absorption edge to the side of smaller energies to 0.4 eV (Getov, Kondilarov, Semidceva and Andreicin, 1966). The introduction of copper leads to the decrease of the photo-darkening process at the same time (Liu and Taylor, 1987). Pfister, Liang, Morgan, Taylor, Frieble and Bishop (1978) consider that in AszS3 and AszSe3 compounds copper does not generate deep defects, which could be detected by photoluminescence and EPR measurements. As was established in the case of introduction of copper, no structure modification occurs because the insertion of copper into the glass brings to the satisfaction of all chemical links. In other words, Cu atoms become integral part of the amorphous lattice structure, but they do not have a significant effect on the tunneling systems or the dichroism. This is because the tunneling levels and the dichroism involve only local configurations. In the model proposed by Pfister et al. (1978), it was shown that introduction of copper determines the transition of chalcogen atoms from twofold to fourfold coordination. This leads to the appearance near the top of valence bands of the electron metal-chalcogen states, which result in the decrease of optical gap. It is understandable that this leads to the shift of absorption edge to the smaller values and the disappearance of the photodarkening effect. The influence of the elements of group III on the absorption edge of chalcogenide glasses can be demonstrated with the example of thallium. As against the cases of silver and copper, which can be inserted into chalcogenide glasses only up to a few percent, thallium can be inserted, for example, in AszSe3 glasses in big quantities, because thallium creates weak bonds with selenium. In the systems A s - C h - T e , A s - C h - C h - T 1 (where C h - C h is S - S e or Se-T1), the vitreous state is formed even in the case of large concentrations of thallium. The physical properties of such materials were widely studied by Andriesh and Kolomiets (1963) and Kolomiets, Mamontova and Stepanov (1967). When inserting thallium into the arsenic selenide up to 0.1 at.%, the position of the absorption edge is unaffected; however, the Fermi level shifts to the conduction band because the concentration of negative defects D* is increased (Kitao, Senda, Takano and Yamada, 1991). At the introduction of thallium in large concentrations, the composition of the vitreous material changes, giving rise to the shift of the absorption edge to smaller energies. In this case, a definite number of atoms play the role of impurities manifested by the concentration increase of charged defects and the energy of activation conductivity. Lanthanides belong to the third group of periodic table as well. These elements now play a very important role as luminescent additives in chalcogenide glasses for optoelectronic applications. The optical absorption of chalcogenide glasses is sensitive in the case of their modification with heavy rare-earth metals. Iovu et al. (1999) have shown that the addition of small amounts of dysprosium and samarium (0.1-0.5 at.%) leads to the shift of the absorption edge to longer wavelength and to an increase of the absorption above the edge (Fig. 6), due to defects generated in the process of modification of the glass composition. The influence of the elements of group IV on the absorption edge can be demonstrated with the example of tin and germanium. Even the earliest investigation of the tin influence on electrical and photoelectrical properties of AszS3glasses has shown that elements of the fourth group play a role of active impurity when introduced into gasses. The addition of tin
Optical and Photoelectrical Properties of Chalcogenide Glasses
125
(b) 3
(a) 300
2
~7/
r
200
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~ 1 ,,,
>
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-1
/ / I
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|
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2.5
|
I
2.6
hv, eV
I
2.7
2.8
1.6
1.8
2.0
2.2
Energy E, eV
FIG. 6. (a) Absorption spectra of thin films: As2S3 (1), AszS3 4- 0.1 at.% Dy (2), AszS3 4- 0.1 at.% Sm (3), AszS3 4- 0.5 at.% Sm (4), As2S3 4- 0.1 at.% Mn (5) and AszS3 4- 0.5 at.% Mn (6). (b) The absorption spectra of bulk glasses: AszS3 (1), AszS3 4- 0.1 at.% Sm (2), As2S3 4- 0.5 at.% Sm (3), AszS 3 4- 0.1 at.% Dy (4), AszS3 4- 0.1 at.% Mn (5) and AszS3 4- 0.5 at.% Mn (6).
to 3 at.% decreases the width of the optical gap slightly by the value 0.1 eV, while the steepness of the edge suffers great changes increasing from A -- 0.05 to 0.085 eV, and then decreasing to 0.07 eV (Burdiyan, Gerasimenko, Kovalenko and Torodii, 1988). In correspondence with the M6ssbauer spectra, tin is four-valence (Sn a+) in the arsenic sulfide and arsenic selenide alloys, and all four valence electrons participate in the formation of the lattice (Seregin and Nistiriuc, 1991). However, in the process of crystallization of glasses in the M6ssbauer spectrum, the lines which appear correspond to bivalent tin. In the AszSnx glasses tin atoms are inserted in the atomic network of glass, having the maximum valence 4 + . They do not form the energy levels in the forbidden band of the vitreous semiconductor. Under the influence of light illumination, the appearance of two-valence tin, which is considered to be the recharge of tin centers, was observed. The spectra of edge optical absorption (Fig. 7a) of the AsSe films with various contents of tin impurity are characteristic of amorphous semiconductors. The variation of the F,opt ~g determined from Tauc plot for various tin contents is shown in Figure 7b. It is seen that tin impurity lowers the optical gap, first (to 1 at.%) steeply, and then nearly proportional to the tin concentration. This fact probably indicates that at sufficiently high tin content, new structural units are formed with lower optical threshold energy, the presence of which lowers the mean value of the gap, as with alloys. This type of explanation for the variation of the optical gap upon tin content was suggested by Myuiller, Timofeeva and Borisova (1965) using the following structural units AsSel.5, A s z S e 2 , As2 and SnSe as possible constituents of the ternary chalcogenide glass. A similar consideration in the frame of 'alloy' approximation based on structural units like Se, AsSe, AsSel.5 and SnSe2 has been advanced by Seregin and Nistiriuc (1991).
126
A. M. Andriesh et al. (a) 105
o
104
(b)
§
1.80
1.75 "?~ 103 6 ~ 5~
~
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,,,,~,,
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.
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I.
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0
,
I
2
,
I
,
I
,
I
,
I
4 6 8 10 Concentration at. % Sn
FIG. 7. Edge absorption of AsSe:Sn thin films (a) and optical gap vs. tin content (b). (1) AsSe; (2) AsSe + 1.0 at.% Sn; (3) AsSe + 2.0 at.% Sn; (4) AsSe + 3.0 at.% Sn; (5) AsSe + 7.5 at.% Sn; (6) AsSe + 10 at.% Sn.
At intermediate values of the absorption coefficient in the range hv < Eg, the absorption edge behaves exponentially a h v --~ exp[(hv Egpt)/Eoo] (Fig. 7). The Urbach edge arises from the superposition of electron transitions from the valence band tail to extended states of the conduction band (and vice versa). As a rule, the broader valence band tail is dominant, i.e., the width E00 is characteristic of it. Between the apparent gap Eg and the tail width E00 a simple correlation exists: Eg = Ego - cEoo, where Ego is the limiting value of the gap for a vanishing small tail width and c is constant (c = 5 - 1 0 for a-Si:H) (Cody, Tiedje, Abeles, Brooks and Goldstein, 1981). If the tail width varies with the impurity content (or temperature), the extrapolations of the Urbach edges to higher energies for various impurity concentrations have to cross at a focus, the position of which corresponds to Ego. It is seen from Figure 7 that the slope of the exponential portions decreases with the increase of the tin content, and the largest slope corresponds to undoped AsSe. The above correlation fits to all alloys with the values Ego -- 2.15 eV and c -- 5.2, and the absorption at the end of the exponential tail is increased more than 100 times. The above-described behavior of the spectral dependence of the absorption in the exponential absorption region indicates that tin impurity induces broadening of the band tail states from 0.06 eV for undoped AsSe to 0.15 eV for AsSe:10%Sn. This broadening may be caused by the formation of new Sn-based structural units as well, which add a compositional disorder to the existing structural one. The observed behavior of the Urbach edge is usually ascribed to the variation of the degree of structural disorder, in fact the medium-range ordering, which includes both the thermal and frozen-in disorder. Hosokawa, Sakaguchi, Hiasa and Tamura (1991) observed a fan-like decrease of the Urbach slope of AszS3 and AszSe3 in a wide-range temperature interval 25-900 ~ Ticha, Tichy and Klikorka (1988) obtained similar behavior of spectra of glassy AszSe3 samples under thermal treatment with various quenching rates. The reasons for this behavior and the role of disorder in the formation of the Urbach edge, first stressed by Olley (1973), are still under discussion. Here we wish to notice that the behavior of this type is, for the first time, observed for the case of chalcogenide glass with varying impurity concentration. -
Optical and Photoelectrical Properties of Chalcogenide Glasses
127
As in the case of copper, metal impurities of III and IV group elements effectively reduce the photo-darkening and its relaxation under light exposure in amorphous films of AszSe3:0.5 at.% Me (Me = Sn, Mn, Sm and Dy) and AsSe:Snx (x = 1 - 1 0 at.%) (Iovu, Shutov, Rebeja, Colomeyco and Popescu, 2000). The degree of reduction becomes stronger as the impurity concentration is increased. Thermal treatment of the films at 100 ~ in vacuum reduces the photo-darkening, especially in undoped AsSe films, where there are numerous homopolar bonds. Doping of AsSe films by tin reduces the photodarkening for x -< 2 at.% Sn. Changes in the optical transmission of AsSe:Sn and AszSe3:Me films under illumination may be described by a stretched exponential with the dispersive parameter 0.4-< o~-< 1.0. This fact indicates the presence of strong dispersion in the photodarkening process. In the context of the 'slip-motion' model (Ganjoo and Shimakawa, 2001), this dispersion may be naturally attributed to the multiple trapping of photoinduced holes. The strong effect of metal additives on the photo-darkening kinetics, especially on its response to thermal treatment, is in agreement with the model as well. In particular, with its tetrahedral type of coordination, tin should reduce the flexibility of the layer network, thus retarding the photo-darkening phenomenon. Doping of amorphous chalcogenide films by metals assists in stabilizing the glassy matrix with respect to light exposure and thermal treatment. The influence of the elements of group V will be considered in the example of antimony. The structural pyramidal units ASS3/3 and SBS3/2 are preserved, but length of A s - S bands increases. The last one leads to the shift of the absorption edge to smaller energies and to corresponding change of the optical band from 2.4 eV (for AszS3) to 2.1 eV (for AszS3-Sb2S3). As a result of the introduction in the composition of the As2-xSbxS3 glasses of small quantities of antimony (0 -< x -< 0.1) the modification of refraction index occurs in the range 1.2-2/xm (Cimpl and Kosek, 1986). The same modification takes place in the case of introduction of antimony in Asz-xSbxSe3 the values of antimony concentration (0-< x ~< 0.3) (Cimpl and Kosek, 1986). The modification of refractive index follows the relations nl = n l (0) + (0.08 + 0.01)x
for As2-xSbxS3 system
(4)
n 2 = n2(0 ) -+- (0.22 _+ 0.01)x
for Asz_xSbxSe 3 system
(5)
where nl(0) and n2(0 ) are refractive indexes, respectively, for AszS3 and AszSe3 glasses. According to Andriesh, Gerasimenko, Lyalikova, Iovu, Minaev, Radautsan, Tsiuleanu and Shutov (1976a) and Cimpl and Kosek (1986) in the system AszS3-SbzS3 the substitution of arsenic for antimony does not lead to considerable changes in the glass structure. The lack of the noticeable change of boring order upon arsenic substitution for antimony is the result of the fact that Sb2S3 structure consists of a trigonal pyramid which is similar to AszS3 structure. In the same time, the arsenic atoms substitution for antimony influences the average order, giving rise to gradual transition from layer AszS3 structure to continuous net structure, which according to Cervinka (Cervinka and Hruby, 1982) very much influences absorption in the infrared range. The influence of the element of group VI can be followed in the example of sulfur for selenium and sulfur for tellurium substitution in the AszS3 alloys. The optical features AszS3 and AszSe3 are very similar which follow from their structure. As many authors
128
A. M. Andriesh et al.
have shown upon sulphur substitution for selenium, the absorption edge shifts to the region of smaller energies. Upon the substitution of sulfur for tellurium, the absorption edge also shifts to the side of smaller energies (Tatarinova, 1972; Das, Platakis and Bever, 1974); however, the value of the steepness of the absorption edge increases. Kolomiets and Pavlov (1959) consider that upon the introduction of tellurium in small quantities the tellurium atoms substitute sulphur without changing the glass structure, while the glass structure is deformed in large quantities. The strong influence of tellurium on the absorption edge of the system AszSe3-AszTe3 was observed. Adding tellurium to the alloys AszSe3-AszTe3 leads to the shift of the absorption edge to longer wavelength. If AszSe3 alloys have the maximum transparency at 0.8/~m, then in the case of AszSe34AszTe3, the maximum transparency is in the region of more than 1.4 ~m. The optical gap determined from conductivity and photoconductivity data is also changed when selenium is substituted by tellurium in the system AszSe3-AszTe3 from 1.5 eV (for AszSe3) till 0.9 eV (for AszSe3-4AszTe3). The effect of doping on optical properties of chalcogenide glasses is very intensive in the case of addition of Mn, the transient metal (Fig. 6). The samples with 0.5 at.% Mn are practically opaque in the whole investigated spectral range (0.5-25 ~m). The latter effect suggests the alteration of the macrostructure of the glass material at high Mn content. This suggestion was confirmed by mentioned authors using X-ray diffraction procedure (Iovu et al., 1999). These results indicate a significant modification of the mean distance between the disordered layers, induced by metals. 1.2.3.
Absorption Edge in the Multicomponent Alloys
As it was established from investigation of optical properties of multi-component chalcogenide glasses, the composition of glasses has a slight influence on the general aspects of the absorption edges. In both the cases of binary stoichiometric glasses As2S3 and As2Se3 and non-stoichiometric glasses As-S, As-Se, A s - S - S e , As-Se-Te, AsS-Ge, As-Se-Ge, G e - B i - S , G e - S b - B i - S e and others, the absorption edge is described quite well using only two exponential functions (in the regions of weak absorption and Urbach tail) and by quadratic functions (in the range of high absorption). By changing the composition of glasses the position of absorption edge is also changed due to the change of optical gap. In the range of weak absorption, the steepness of the absorption edge depends not only on the composition of glasses, but also on the technology of preparation, additional components, and on the history of samples. In the higher regions of the absorption edge (1 - 104 cm- 1), the steepness of the absorption edge can manifest a strong alteration, but this happens only in the cases when the changes of the composition of glasses is accompanied by changing glass structure. The glass structure change is directly connected with the absorption edge steepness. For example, upon changing the composition in the As2S3-As2Se3, As2S3-Sb2S3 systems which is considered by many authors to be ideal solid solutions, the steepness of the absorption edge suffers slight changes influencing only its position, i.e., the optical gap. By changing the composition in the system As2Se3-As2T13, the width of the optical gap changes linearly with the composition as follows from the relationship suggested by Shimakawa (1981), the use of which for various glasses was analyzed by Tichy, Triska,
Optical and Photoelectrical Properties of Chalcogenide Glasses
129
Frumar, Ticha and Klikorka (1982) and Yamaguchi (1985) EgAB = Veg A + ( I -
Y)Eg B
(6)
where EgA and EgB are the optical gap components of A and B, Y is the share of element A volume. At the same time in the systems such as Gel-xSx in which the change of the composition leads to the change of the ratio of structural units Ge-S, Ge-Ge, S - S the deviation of the exponential values of the optical gap calculated according to formula (6) is observed. In the systems where there is a change of the composition and in the same time the ratio of the structural units changes as was mentioned above, the change of the steepness of the absorption edge occurs. This can be seen from the data (Andriesh and Tsiuleanu, 1973a,b; Andriesh, Shutov, Tsiuleanu and Iovu, 1974e), where the optical features of the systems AszS3-Ge were investigated. With the enrichment of arsenic sulphide vitreous alloys by germanium, the absorption edge shifts to longer wavelengths, but the steepness of the edge increases rather sharply, to the germanium concentrations of 7 at.%, and then changes more smoothly along the curve with the maximum corresponding to the composition given by formula AsS~.sGeo.73. Andriesh and Tsiuleanu (1973a,b) studied thin films of such compositions of AszS3-Ge, which can be obtained in amorphous state only in the form of thin films, bulk samples having polycrystalline structure. The experimental results of the absorption edge of the materials AszS3-Ge are presented in Figure 8. Increasing germanium in the glass leads to the shift of absorption edge to longer wavelengths. In the range of big absorption coefficients the absorption edge can be described by the formula: cehp--~ ( h p - Eg) 2
(7)
This relation was used for the determination of optical gap (Eg). Obtained values are given in Figure 8b. One can observe that Eg is changed almost proportionally when germanium is introduced into the glass. For all studied compositions AszS3-Ge, the exponential dependence of absorption versus energy of photons is observed for all energies below Eg (see Fig. 8a). The steepness of the absorption edge is changed when the composition of glass is changed. When the concentration of germanium in the As2S3 glass is not too high (0-7 at.%), A is changed drastically, but at higher concentrations the parameter A suffers a small change and A follows a curve with maximum corresponding to the composition AsS1.sGeo.73 (Fig. 8b). As one can note, the absorption edge of AszS3-Ge glasses have the same shape, as in the case of AszCh3 glasses having quadratic and exponential dependence versus energy of photons (see Figs. 7 and 8). With the temperature increase, the optical gap decreases with the temperature coefficient ( 4 - 8 ) x 10 -4 eV per degree, which is typical for vitreous semiconductors (Kolomiets and Raspopova, 1970, 1972). As Andriesh and Tsiuleanu (1987) who carried out complex investigations of the mentioned materials in the form of heterostructures pSi-As2S3-Gex have shown, the diminution of the forbidden gap width with the addition of germanium to As283 is due to the fact that in the process of chalcogen and arsenic substitution by germanium atoms the reorganization of the valence band structure occurs as the edge of valence band moves up (Fig. 9). The influence of the glass structure on the position and steepness of the absorption edge was pointed out by Kosek, Cimpl and Chlebny (1977), who investigated the absorption
130
A. M. A n d r i e s h et al.
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(b)
I
,
2.5
1.4
I
3.0
' ' ' ' ' ' ' ' 0.00 10 20 30 40 50 Concentration, at.% Ge '
0
by, eV
FIG. 8. (a) The dependence of absorption coefficient on photon energy a vs. hv for amorphous AsSi.5-Gex thin films, x: (1) 0; (2) 0.1" (3) 0.19" (4) 0.5" (5) 0.73; (6) 1.7; (7) 2.0. (b) The composition dependence of the band gap E0 (1) and of the parameter of the Urbach edge A for the amorphous AsS ~.5-Gex thin films.
edge in the systems TexAs2-xS3-x, where 0 < x < 1 and in the system As2S3-xTex, where 0 --< x --> 0.015. As has been observed, the addition of tellurium shifted the absorption edge to lower values. At the same time, the steepness of the absorption edge (Zl) increased while tellurium is added. It is thought that adding a small quantity of tellurium into AszS3-xTex glass leads to the substitution of sulphur atoms by tellurium atoms and does not change the structure of the glass. However, at a higher concentration of tellurium the structure of the glass is deformed and the composition of the glass can be regarded as solution of AszS3 a n d A s z T e 3 .
As far as the system A s - S - G e is concerned, the results obtained by Frumar, Kodelka, Ticha, Faimon and Tichy (1977) were confirmed by measurement of the optical spectra of glasses As2S3-GeS 2 (Rosola, Puga, Mita, Cepur, Himinet and Gherasimenko, 1981). According to this data the glass alloy consists of structural units ASS3/2 and GeS4/2. By
(a) 2.5
xx
.
.
.
.
(b) I: (eV),
rid
................
6~
0.2
.
0. 1
~\\\\\\\\\'~.,X\\\\\\\'~, cr
2.0 a
1.5 N
N N
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0
I
20 40 Concentration, at.% Ge
" 0.0
O--
t0
AszS~
~
~0
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~ Asz$sGe 4 ?o a t . G e
FIG. 9. The modification of the valence band edges (a), of the Fermi level (b), and the difference Eg/2 - Eo on doping of AszS3 with Ge.
Optical and Photoelectrical Properties of Chalcogenide Glasses
131
increasing the GeS2, the level of ionicity increases due to the transition from trigonal structural units to tetrahedron ones. It is accompanied by shifting of the absorption edge to lower values, although the shape of the absorption curve remains the same as in the case of other glasses. The absorption edge that is typical for chalcogenide glasses with quadratic and exponential dependence of the absorption coefficient versus the energy of quanta is also observed in the system G e - B i - S (Frumar et al., 1977). The optical gap is decreased approximately linearly when the temperature is increased, having the temperature coefficient (4.6-4.9) x 10 -4 eV K -1. These data correspond with data obtained in the other chalcogenide glasses. It was established that in the case of the system Gez0.Sbzs-xBixSe55 (0 -< x -< 15) during the substitution of Sb by Bi the absorption is displaced to small energies without any changes of steepness. The fact that the optical gap is very sensitive to the structure of glasses makes it impossible to predict the optical data in the complex of multi-component glasses, and many authors have searched supplementary relations between optical gap and the physical-chemical parameters of glasses. For example, Myuiller et al. (1965) considered the correlation between the optical gap and the chemical composition of chalcogenide glasses, taking into account the analysis of the average atomization heat and the average coordination number. It was found that when the atomization heat is increased, the width of the optical gap is also increased for those vitreous materials, which have the same value of the average coordination number. Earlier it was shown that there is a clear dependence between Tg and Eg (Bube, Grove and Murchison, 1967; Kastner, 1972, 1973). On the basis of the investigation of thin films of As2S8, As2S3, AszS 1.sS1.5, AszSel.sTe 1.5, it was found that for the atomization heat the following relation exists: H~(A-B)-
89 A + H~)
(8)
where H A and H B are atomization heat of elements A and B. In the binary alloys the relation gives the average number of coordination: n -- XNA + (1-- X)NB = I (H A + H B)
(9)
where NA and NB are coordination numbers of elements A and B. In the case of chalcogenide glasses having the same number of coordination, the value of Eg also increases. Myuiller et al. (1965) considered the correlation between the optical gap and the chemical composition of chalcogenide glasses proceeding from the analysis of the average atomization heat and the average coordination number. It was found that when the atomization heat increased, the width of the optical gap increased for those vitreous materials which had the same value of the average coordinating number. A good correlation has been found between the width of the forbidden gap of the glasses and the bond length for the characteristic for which the sum of covalent radii in alloys with the coordinating number n - 2.4 was used. For such alloys, the plot of the dependence of Eg from the reverse length of the inter-atomic bonds can be approximated by straight line.
132
A. M. Andriesh et al.
By this means the atomization heat, the coordinating number and the length of the chemical bond are the parameters which coordinate well with the value of the optical forbidden gap of vitreous materials. In this case, it is important to compare the mentioned parameters for the glass characteristics of one and the same coordinating number. The most pervasive impurity in chalcogenide glasses is oxygen. Girlany, Yan and Taylor (1998) established that for oxygen concentration below 1019 c m -3, the conductivity is independent of oxygen, but at concentrations exceeding the 1019 cm -3 oxygen promotes doping by increasing the densities of dangling bond defects at threefold-coordinated chalcogens. To determine this fact, the compositions Cu6As4S 9 and Cu6As4Se 9 were studied because at these compositions the S (or Se) and Cu atoms were all tetrahedral coordinated and there exist only C u - S and A s - S (or Cu-Se and As-Se) bonds. Addition of oxygen to these glasses increased the conductivities by more than three orders of magnitude (Hautala, Moosman and Taylor, 1991). For oxygen concentrations higher than 3 • 1019 c m -3 the absorption increased drastically. By comparison of the last data with the data of conductivity, one can conclude that in this case the energy levels responsible for the impurity absorption could be associated with acceptor levels. In conclusion, we note that the presented data is of great interest for discussing the absorption edge nature in non-crystalline (amorphous) semiconductors, which is detailed in Section 1.2.4. 1.2.4.
The Nature of the Absorption Edge in Non-crystalline (Amorphous) Semiconductors
The nature of the absorption edge in non-crystalline (amorphous) semiconductors has been discussed in the literature for many years. This is caused by the complexity of obtaining the optical characteristics of amorphous semiconductors, due to the complexity of their structure. For this reason, the nature of the absorption edge, even in AszS3 and AszSe3 crystals, is not completely understood. Moreover, there is no unambiguous explanation of the exponential dependence, which is subordinated to the so-called Urbach rule. In conformity with the Urbach rule, the steepness of the absorption edge depends on temperature as 1IT. It is supposed that in crystals Urbach edge may occur as a result of different reasons, e.g., the interaction of coupled excitons with the lattice fluctuations (Toyozawa, 1962), and the widening of the absorption edge by the electric field (Dow and Redfield, 1971). To understand the physical mechanism of the formation of the exponential edge in semiconductors, some theories have been worked out taking into account the defects (Redfield, 1963; Dow and Redfield, 1971). Dexter (Dexter and Knox, 1965) investigated the influence of the lattice deformation arising due to its oscillations on the width of the forbidden gap and the spectrum of the inter-band absorption. The absorption coefficient (c~), calculated by Dexter, corresponds with the Urbach rule, but only in a narrow range of temperatures and c~ values. The exponential dependence of the absorption edge of crystals by Redfield (1963) opinion is connected with the presence of internal electric field caused by the lattice defects. To calculate the absorption coefficient, Redfield used Frantz-Keldish effect caused by the effect of the internal electric fields.
Optical and Photoelectrical Properties of Chalcogenide Glasses
133
Explanation of the absorption edge in amorphous semiconductors creates more difficulties. To interpret the nature of the absorption edge of vitreous semiconductors, it is necessary to take into account that in these materials the law of quasi-momentum preservation is not realized, or is realized in the small regions (Tauc, 1974; Tauc et al., 1974). According to the theoretical notions, in the forbidden gap of amorphous semiconductors are spread so-called tails of the state density, the form of which can be described by Gaussian or exponential function. Thus in the first works on the absorption edge of the amorphous semiconductors, the exponential section of the edge was considered as the result of optical transition between non-localized and localized states. However, such an explanation is not completely adequate. Following Davis and Mott (1970), the main objection against this explanation is the identical steepness of the absorption edge of the great majority of various materials. The authors are inclined to explain the exponential absorption edge in amorphous semiconductors by broadening of exciton line by the internal electric fields, suggesting the presence of excitons and internal electric fields in amorphous semiconductors. There is no doubt about the presence of strong and internal electric micro-fields in them, yet the presence of excitons is problematic. As Bonch-Bruevich and Iscra (1971) showed, there exists a rather appreciable possibility of exciton disintegration in an internal field. At the same time, experimental observation in amorphous materials has been carried out on amorphous analogue of monoclinic selenium. It was reported by Cherkasov and Kreiter (1974). The suggestion that exponential absorption edge of Urbah type can arise from the effect of disorder upon exciton absorption was also experimentally shown by Olley (1973). For the evidence of this suggestion, the author studied the changes of optical absorption of both crystalline and amorphous semiconductors during the introduction of disorder by heavy ion bombardment of crystals PbI2 by helium ions. The author has shown that such process quenches the exciton effects and leads to the appearance of experimental edge which broadens with increasing dose. Olley observed similar broadening after bombardment of thin films of amorphous AszSe3 and amorphous Se at 25 K. It is very important to note that the bombardment-induced changes in absorption edge of the mentioned materials can be annealed merely by warming the films to room temperature, and they can then be rebombarded (Olley, 1973). These results can be regarded as convincing evidence that the Urbach edge observed in amorphous semiconductors arises from inherent structural defects, which are manifested by both broken and strained bonds. From the results discussed above, one can conclude that the thermal treatment influences optical properties of amorphous materials. One can find the evidence of this fact, for example, in Tanaka, Gohda and Odajma (1985), Rosola, Zatsarinaya, Baranova and Khimients (1987) and Ticha et al. (1988). Ticha et al. (1988) studied the temperature dependence of the Urbach edge of glassy AszS3 prepared by slow (--~ 10- 3 K s- 1) cooling and rapid (into cold water) quenching from temperature 600 ~ the slope of Urbach edge decreases for low cooling rate. It was proved by X-ray diffraction, differential scanning calorimetry (DSC) measurements and density determination. It is worthy to note that under slow cooling, the structure of glassy AszS3 is improved. In the opinion of the authors, the structure improvement (under a very slow quenching rate) proceeds because of the decrease of the wrong bonds density and simultaneous increase of the medium range order.
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As shown above, any mechanism of explaining the nature of the absorption edge of amorphous semiconductors should take into account the presence of incidental internal micro-fields, which in these materials can arise as a result of lattice distortion, the freezing of fluctuations in the inter-atomic distance, introduced admixtures and other factors. There is every reason to consider that the nature of the absorption edge in strongly doped semiconductors and in the amorphous ones are alike. The likelihood of a great analogy between the strongly doped crystalline semiconductors with a clustered structure and amorphous semiconductors has been referred to by Ryvkin and collaborators in their works (Ryvkin and Shlimak, 1974). Redfield (1965) associated the nature of the exponential 'tail' absorption in strongly doped semiconductors with Frantz-Keldish effect on the internal electric fields created by ionized impurities. This idea was further developed by Shklovskii and Efros (1972), who proceeded from theoretical consideration and studied strongly doped semiconductors and exponential absorption edge. Some time elapsed before the idea of large-scale fluctuations was used by Fritzsche (1971) for analyzing the discrepancy of concentration values of local states near Fermi level determined by optical and electrical methods. If it is taken into account that part of large-scale fluctuations are caused by deviations in inter-atomic distances which can be considered as frozen phonons of high concentration, then these phonons must not change with temperature (up to Tg) the steepness of the absorption edge (Kolomiets and Raspopova, 1970). Bonch-Bruevich (1969, 1970) proposed the theory of inter-band optical transitions in disorder systems for two extreme cases, when the incidental internal field immediately changes in space and when this condition is not deliberately fulfilled. Examining the optical transitions between the states of the continuous spectrum of the nearly intrinsic semiconductor at low temperatures for the case of slowly changing internal field the following exponential dependence of the absorption coefficient on the quantum energy was also obtained: (10)
ce - e x p ( h v / w )
o9 -
q92)1/3;
--~
q~2
3h
-4mc ((AU))2
(11)
where U is potential energy of electrons in the internal field and tl --~U2). So the steepness of the absorption edge is determined by the average square fluctuation product of the potential electron energy (((AU)2)). The theory of inter-band absorption being applied to the vitreous semiconductors in the system AszS3-Ge allowed obtaining the values of ((AU)2). These data show the value of square average fluctuation of potential energy derivate of electron when germanium is introduced into AszS3. From this point of view the most disordered alloy is AsS1.sGeo.73 or As4S6Ge3. On the basis of analysis of the absorption threshold of amorphous semiconductors the information concerning the distribution of the density of states in band tails was obtained. This was obtained taking into account the following conditions: (a) the law of pulse
Optical and Photoelectrical Properties of Chalcogenide Glasses
135
conservation is not fulfilled and (b) the function of matrix element M(w) does not depend on photon energy h~,. Then the function e2(o) ) can be written in the following way: e2((-O)
---
m(w)Pconv(CO)
(12)
where Pconv( o J ) - f ~ p v ( o J ) p v ( d - k - o J ) d d
(13)
Therefore, for determining the function M(oo) it is necessary to use formulas (12) and (13). At the same time it is known that this above-mentioned spectral function is difficult to calculate from the first principles. Dersch, Overnof and Thomas (1987) make use of the theory developed by Miller and Thomas (1984). They have taken into consideration not only the static disorder, but also the dynamical one conditioned by the phonons. These authors have found that M(oo) has a weak maximum near o)-- ~32 -- ~3v, which is in full agreement with the results of the work (Abe and Toyozawa, 1981). In this case M(w) is changed by approximately two times. Bonch-Bruevich showed that in the case of long-wave fluctuations of the potential, the matrix element strongly depends on the photons energy. Dersch et al. (1987) in collaboration with M. Grunvald calculated M(oJ) on the basis of the accepted Hamilton model for a one-dimensional circuit. As a result, they showed that for the investigated case M(oJ) was a dropping (lowering) function which completely determined the optical spectrum in the tail section. That was in full agreement with Bonch-Bruevich's results. On the basis of ideas developed by Mott et al. (Mott, Davis and Street, 1975; Street and Mott, 1975), Kolobov and Konstantinov (1979) showed in the case of unfigurational coordinate model of amorphous semiconductors Urbach' s law can be obtained only when the maximum of conductivity band corresponds to the maximum of the valence band. As it was shown by many authors, the exponential form of the absorption threshold in amorphous semiconductors is determined by the density of states in the bands tails, the last being connected with disorder induced by impurities. Some authors accepted that logarithm of state density (Halperin and Lax, 1966) In g(E) is proportional to F n, where for the three-dimensional case 1 < n < 2. Exponential index n is a function of correlation length of disorder L and energy E. If the correlation disorder length caused by the j~oint effect of the structural and oscillating distortion lies in the range of L = 2 - 5 A but the potential fluctuation is proportional to (ev) 2, then as Sritrakool, Sa-Yakanit and Glyde (1985) and Sritrakool, Sa-Yakanit and Glyde (1986) showed, the determining function of the absorption edge is the state density. In such a way, the Urbach tail of the absorption edge directly follows from the function form of the state density and the value n(L, E ) = 1. Yet, in these authors' opinion, the above-mentioned arguments may not take place in strongly doped semiconductors where the typical values of L are 2 5 - 5 0 * and the potential fluctuation is evaluated as 0.04 eV 2. In Tauc' s (1987) opinion, two reasons for the formation of states in the band tail should be pointed out. The first is due to the disorder of the lattice structure of the glass as a result of angle fluctuations and band lengths. The states arising as a result of this can be called proper electron states of the bands tails. Parallel with these states in the forbidden gap can arise due to the broken bonds and impurities. However, it should be mentioned that
136
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the electron states could be caused by the fundamental characteristics of non-crystalline solid bodies, i.e., by the structure disorder. Since the absorption edge of amorphous semiconductors is caused by the structure disorder, there arises a question whether it is possible to get some information about the glass structure investigating the form of the absorption edge. The answer to this question was obtained by Busse and Nagel (1981) in which the author analyzed the absorption edge of the vitreous As2S3, taking into consideration the thesis that two types of disorders are additively created in non-crystalline semiconductors. One of them has a thermal nature that is a pure form which exists in crystals, and the other type is a structure disorder, which together with the thermal disorder is present in amorphous semiconductors. This thesis was used as the basis for interpreting the power index o-in the expression for the absorption coefficient: a = a0 e x p [ ( h v - E0)/o-]
(14)
where a0 and E0 are the material constants, o-is the reverse value of the absorption edge slope, which, in the author's opinion, expresses the disorder degree. In crystals: ~r = AkT*
(15)
where A is the constant, k Boltzmann invariable and T* the efficient temperature making a contribution to the fluctuating atom shift. In non-crystalline materials: cr = AkT* + Os ce = AkT*
(16)
where 0s is the contribution of the structural disorder. The interpreted analytical expression of parameters T* and 0s, and taking into account that the electron capture brings additional disorder, the authors obtained the following expression for o-: c r = a k [ ( O 1 / 2 ) c o t h ( O 1 / 2 T ) - f ( O z / 2 ) t a n h ( O z / 2 T ) ] + gTf
(17)
where 01 -- 4o9/k, o9 is the frequency of the fluctuating atom shift, kO2 the energy of the electron excitation and 0 the contribution of the structures disorder, which takes into account the glass prehistory: 03 = gTf + h
(18)
Experimentally measured d e / d T in the region T > Tg it is possible to evaluate gf and by adjusting the expression for o~T) with the experiment f and 02 values are obtained. Using the above-given procedure Ihm (1985) has found the value for o-in the case of glasses like AsSe2 to be equal 56 meV at 77 K, while the experimental value constitutes 52 meV, which shows a surprisingly good coincidence. From this analysis one more conclusion can be drawn: as in the expression for o-the first term AkT* depends on temperature, then for o-to be independent of temperature it is necessary the second term 0 to be also dependent on temperature and in such a way to compensate the first term of A K T * . This means that with the increase of temperature on the glass-like AszSe3 the structure must change. It is surprising that, Busse and Nagel (1981) carrying out
Optical and Photoelectrical Properties of Chalcogenide Glasses
137
X-ray diffraction of the glass-like arsenic selenide really found that the intensity of the first peak in the roentgen graph of the glass-like arsenic selenide is supposedly connected with the correlation between the layers, which indeed increases with temperature following the model described by Ihm (1985). In such a way, the exponential of the absorption edge in amorphous or so-called Urbach rule in amorphous semiconductors was subjected to a thorough analysis by many investigations. At the same time it should be underlined: the last investigation connecting the nature of Urbach absorption edge in amorphous semiconductors with their structure for the first time allows not only to bring arguments for the explanation of the absorption edge form but also to use the experiments for investigating the absorption edge to obtain information about the structure of glass-like materials (Ihm, 1985). If Urbach absorption edge in amorphous semiconductors arouse a great discussion, the area of weak absorption has received a more unambiguous explanation. The absorption edge of glass-like semiconductors in the area of weak absorption (a < 1 cm-1), as been already shown, strongly depends on the synthesis regimes and can be described by the exponential function of the type described by formula (14). Taking into consideration the structural sensitivity of this section of the absorption edge it is possible to suppose that it is connected with the optical transitions with the participation of non-localized and localized states found deep in the forbidden gap. Wood and Tauc (1972) consider that the section of weak absorption is connected with the deep fluctuations potential which can arise because of the loss of distant long-range order, defects or impurities. They counted the concentrations of local states making contribution to absorption. The calculation value of the general concentration of local states turned out to be equal to 1016-1017 cm -3. Such an order of concentrations of local states (N) in the forbidden gap of the glass-like arsenic sulfide was also found in other experiments. However, the experiments on magnetic susceptibility give greater values of the order 6 x 1017 cm -3 for N. The problem of the nature of the weak-absorption tail was studied recently using the constant photocurrent method (CPM) (Tanaka and Nakayama, 1999). It was established that the weak-absorption tail detected by CPM is substantially smaller than that evaluated from transmission measurements (Nishii and Yamashita, 1998). In the same time the steepness of the weak-absorption tail in AszS3 determined from CPM measurements is equal to 80 meV instead of 300 meV, as found by the utilization of optical method. Also, at low temperatures, the Urbach tail detected by the CPM appears to be blue shift. In As2S3 and GeSe at 10-150 and 150-400 K, respectively, spectral features are qualitatively similar to those in AszS3; i.e., the weak-absorption tail is substantially redressed and the non-photoconduction spectral gaps appear (Tanaka and Nakayama, 1999). That means that the thermal excitation of holes from the gap states is nearly impossible in the weak absorption region. In the opinion of Halperin and Lax (1966) the value of energy excitation for holes is so much that it leads to large time constant ~"and small rate constant ~.-1_ ~2exp(-E/kt), where ~2 is the vibrational frequency (--~ 1012 s -1) and E is the energy difference between the localized state and the mobility edge of the valence band. For the observed experimental result, one can give another explanation in the case when the weak-absorption tail arises from conduction-band tail. In this case, geminate recombination can occur before thermal excitation (Pfister and Scher, 1978) at higher temperatures, and thermally activated separation
138
A. M. Andriesh et al.
of photogenerated electron-hole pairs overcome germinate recombination and the nonphotoconducting spectral gap width decreases. This fact has been experimentally established by Tanaka and Nakayama (1999) for many studied glasses (n-a-Se, GeS2, GeSe2, AszS3, AszSe3).
1.3. PHOTO-INDUCEDABSORPTION The interaction of radiation with vitreous materials provokes irreversible and reversible changes of atomic and electronic structure. Under radiation influence the structure of vitreous materials change, new defects appear, film crystallization or amorphization take place, and phase transition or transition from one unstable state to another unstable state occurs (Popescu et al., 1996). All these phenomena and some others will be discussed in Chapter 5. In this chapter attention will be paid only to reversible phenomena due to interaction of light with non-equilibrium excited carries and phonons. Different models of photo-induced absorption will be discussed: the model on the basis of interaction of light with multiple trapped carriers in localized states, the model of photo-induced non-linear absorption due to interaction of light with non-equilibrium localized phonons, the cooperation model on the basis of the coherent generation of the non-equilibrium phonons, and the model of two-photon and two-step absorption. 1.3.1.
Photo-induced Absorption on the Basis of the Model with Multiple Trapped Carriers in Localized States
Many authors have found that transport phenomena in non-crystalline semiconductors including chalcogenide glasses are conditioned by interaction of excited non-equilibrium carriers with traps distributed quasi-continuously in the forbidden gap (Pfister and Scher, 1978; Toth, 1979; Arkhipov and Rudenko, 1982; Arhipov, Rudenko, Andriesh, Iovu and ~utov, 1983; Yuska, 1991). However, the excitation of non-equilibrium carriers in such systems also leads to many peculiarities of optical properties and mainly to photoinduced optical absorption. It is important to note that in the specific conditions of experiment, photo-induced changes in chalcogenide glasses are observed at very small levels of light excitation as high as 10 - 6 - 1 0 -2 W cm -2 (Andriesh, Culeac and Loghin, 1992c). Such optical changes hardly may be explained by photostructural transformations. They can be interpreted using electron transitions in the framework of electron and phonon systems of chalcogenide samples, taking into account the existence of high concentration of localized states distributed quasi-continuosly in the forbidden gap of these materials. While chalcogenide glass samples are excited by the light with energy of hu >- Eg non-equilibrium carriers appear in free bands (Fig. 10). Very quickly they are captured by the tail states proportional to their density, since the capture coefficient is supposed to be the same for different values of trap energy E0. The probing light with energy hv < Eg excites the trapped carriers in the band of localized states, leading to an additional optical absorption in a wide range of energy that results in photo-induced absorption due to pure electron processes (Fig. 11). As shown by Arkhipov and Rudenko (1982), Arhipov et al. (1983), Andriesh, Culeac and Loghin
Optical and Photoelectrical Properties of Chalcogenide Glasses
139
g(E)
Ec
N~ /
i/ i!V / R2
~r
Fro. 10. The model of localized states in the forbidden gap of amorphous materials. (1989b), Andriesh, Arhipov, Culeac and Rudenko (1989a) and Andriesh et al. (1992c), who had developed the model with carriers multiple trapping in localized states, the distribution of carriers trapped on the localized states in the gap can be determined by several processes. These processes are the capture of charge carriers on the traps, their subsequent thermal activation, followed by their repeated trapping. In the case of continuous illumination, the equations representing the generation of carriers, multiple trapping of excess carriers on localized states and their thermal activation and recombination may be written as follows:
d p ( t ) / d t - G - Rpo(t)p(t) (a)
4
(b)
(19)
2
o ~-2
~-2 .a -4
"~ -4
-6 016 '018' 1'.0' 112' 114' 116" 118 hm, eV
-6
0'.6'0'.8"1'.0"1'.2"1'.4"1'.6'1'.8 hm, eV
FIG. 11. The spectral distribution of photoabsorption steady state coefficient Aa in As2S3 (a) and As-S-Se (b) fiber at T -- 300 K (1) and T = 77 K (2) for illumination with an Ar-laser at P = 10 -2 W / c m 2.
140
A. M . A n d r i e s h et al.
dp(t, E ) / d t = (1/ooNt)[g(E) - p(t, E)]p~(t) - Vo e x p ( - E / k T ) p ( t , E)
~
(20)
oo
p(t) -- pc(t) +
o
(21)
dE p(t, E)
where p is the full density of excess holes, Pc the density of mobile holes, E the energy of a localized state, p(t, E)dE the density of holes localized in the energy range from E to E + dE, t the time interval after switching on the illumination (t > 0), G is the generation rate of the carriers, o-0 is the time of life of carriers between captures, g(E) is the energy distribution of localized states, v0 is the attempt-to-escape frequency, T is the temperature and k is the Boltzmann constant. Eqs. (19) and (21) are written for holes, but they can easily be rewritten for electrons. Eq. (19) represents the generation and recombination of excess carriers; Eq. (20) the kinetics of carriers trapping and their thermal activation, and finally Eq. (21) gives the ratio of mobile and trapped carrier numbers. Eqs. (19)-(21) take into account the recombination of delocalized holes with localized electrons and do not take into consideration the recombination of mobile electrons with trapped holes. The photo-induced absorption coefficient Ace for probing light frequency a~ is determined by the density of excess charge carriers localized in the energy range 0 < E > hw (Andriesh et al., 1992c): Ace(~, t ) -
,zr-lC
dEp(t,E)
(22)
where C is a constant which is inversely proportional to the refractive index (for not too large a frequency range one can assume C to be a constant). In the case of exponential distribution of localized states, which is the most frequently used model for trap distribution in chalcogenide glasses, we can write: (23)
g(E) = ( N t / E o ) e x p ( - E / E o )
where Nt is the total density of traps and E 0 is the characteristic energy of distribution. The photo-induced absorption stationary state coefficient Ac~ for the case of sufficiently long exposure time can be written as follows: Ao~st(Oo ) -- o9- 1 C N t ( k T / E 0 ) ( G / R N 2 0 " 0 p 0 ) I / ( I + y ) x
exp[(h~o/kT) - (hw/Eo)]
(24)
and Ao~st(Og) -- o ) - l C N t [ ( G / R N 2 o . o P o )
y/(I+y) -
exp(-hw/Eo) ]
for hoo > E
(25)
where E is the energy of the quasi-Fermi level determined as E -- kT(1 + y ) - ~ ln(RN2o-o Vo/ G) and y is the dispersion parameter, y = kT/Eo.
(26)
Optical and Photoelectrical Properties of Chalcogenide Glasses
141
The solutions for photo-induced absorption time dependences after switching of the exciting light were presented in Andriesh et al. (1992c). The maximum on photo-induced absorption kinetics curves observed for small photon energy can be explained as a result of excess carrier redistribution on shallow states. At the first moment after switching on the illumination the main part of the excess carriers is trapped in the shallow states at the bottom of the conduction band. However, as time goes on because of the thermal release of the carriers and their multiple trapping, an increasing number of excess carriers are trapped on the deep states. The ratio of the number of excess carriers localized on shallow states to the number of excess carriers localized on deep states changes with time. This process leads to the appearance of a maximum on the PA time dependence curve. The intensity dependence on the photo-induced absorption coefficient, as follows from analytical solutions of (19)-(21), has a power-law character. The following causes the increase of the photo-induced absorption coefficient with decreasing temperature. When the temperature decreases the probability of thermal activation of the trapped carriers also decreases, leading to an increase in density of localized carriers and, respectively, to an increase in PA. The proposed model is in good correlation with experimental results (Pfister and Scher, 1978; Toth, 1979; Arkhipov and Rudenko, 1982; Arhipov et al., 1983; Andriesh, Culeac, Ponomari and Canciev, 1987; Andriesh et al., 1989a,b, 1992c; Yuska, 1991) although this component of photo-induced absorption is not too high because the concentration of localized states quasi-continuously distributed in the forbidden gap with small exceptions is less than 1018 cm -3. So the photo-induced absorption controlled by optical transitions from localized states to free bands will be 104 times less than the absorption due to the contribution of optical transitions between free bands. Usually the experiments for study of photo-induced absorption are undertaken on thin films. This means that the number of absorbed photons, which is proportional to the thickness of the sample, is very low, because the thickness of films is as a rule of the order of 0.5-10/zm. The measured optical signal of probe light can be increased if the thickness of the sample is increased. Experiments on fiber samples of chalcogenide glassy semiconductors give especially good results. Investigation of the interaction of light radiation with fiber samples of ChG leads to the possibility of studying many peculiarities of photo-induced absorption in ChG. Indeed, the use of optical fibers rather than thin films or bulk samples enabled us to better observe small changes in the optical absorption caused by lateral excitation by light from the region hv > Eg and even in the case of hu < Eg. This takes place because of longer optical path in the fibers. Besides, the use of fibers instead of bulk samples allows for a decrease in the thresholds of power needed for developing non-linear optical processes (Dianov, Momishev and Prohorov, 1988). As shown in our previous papers (Andriesh et al., 1989b, 1992c), when chalcogenide glass fibers are excited by the light with the energy of hv > Eg, their optical losses are increased. The latter is observed using the probing light with the energy hv < Eg. In this experiment the probing light with a photon energy hu < Eg was launched into the input face of the fiber. The intensity of the probing light, transmitted through the fiber, was measured at the output of the fiber. When illuminating the fiber lateral surface with a continuous band gap light, the intensity of the probing light at the output of the fiber
142
A. M. Andriesh et al.
decreased from its initial value (in the dark) because of the manifestation of the photoinduced absorption. A rather low intensity of the exciting light was employed in the experiments; therefore, no structural photo-induced changes occurred. The absence of the structural changes was confirmed by a complete restoration of the initial optical transmittance of the fibers after the cessation of the exciting light. The restoration rate depended on the illumination conditions and on the glass composition. The spectral distribution of the photo-induced absorption coefficient measured in the energy range of the probing light 0.6-1.6 eV is presented in Figure 11 for the A s - S - S e fibers. Similar dependencies were observed for A s - G e - S e fibers. We note the exponential character of the spectral dependence at Aa for a rather large energy range is in good agreement with the analytical solution given above. The illumination of the fiber at a lower temperature (77 K) leads to a significant increase of photo-induced absorption with respect to the room temperature illumination. The intensity dependence of the photo-induced absorption coefficient exhibits a powerlaw behavior, Aa --~ P", when the intensity of the exciting light (P is varied by about four orders of magnitude (Fig. 12a). The value of n changes with the probing light photon energy in the range 0.3-0.5. The photo-induced absorption kinetics measurements were carried out in a time interval of 10 -2-104 s after switching on the exciting light for the AszS3, A s - S - S e and A s - G e - S e fibers. The typical curves for A s - G e - S e fibers are shown in Figure 12b. The character of the photo-induced absorption kinetics depends on the illumination conditions, such as the temperature, the probing light photon energy and the power of the exciting light (Fig. 13). Experimental results confirm the model with carriers multiple trapping in localized states, distributed continuously in the gap (Andriesh, Culeac, Ewen and Owen, 2001). The qualitative analysis of experimental results in terms of the multiple trapping enables us to evaluate some parameters of localized states distribution and carriers transport. For example, the temperature dependence of the photo-induced absorption coefficient can be used to determine the characteristic energy of localized states distribution E0. Taking into account that in real conditions the dispersion parameter y < I, and the second term in the right side of Eq. (26) is less than the first one, we can
(a) 2 ~" ~i
1
(b) 4
4
~'." 2
3
5 o -2 5
6 "7 8 Ln (Pexc, a.u.)
9
-2
2
4
; Ln (Pexc, a.u.)
FIG. 12. The dependenceof Ac~steady-statevalueuponlight intensityfor As2S3(a) and As-Se-Ge (b) fibersat T = 300 K. The photonenergyof probinglight (eV): (1) 0.7; (2) 0.8; (3) 0.95; (4) 0.98; (5) 1.08; (6) 1.2; (7) 1.3.
Optical and Photoelectrical Properties of Chalcogenide Glasses
143
4
-1 -2 -'-3
3
5-4 <1
2 1
-5 -6 -7 -8
I
-2
,
I
I
0
~
I
i
2 4 Ln(t, s)
I
,
6
I
8
FIG. 13. The photoinduced absorption kinetics Ac~ vs. t curves for As2S3 fibers during the illumination in the spectral range 0.35-0.75 eV and intensity Pe• -- 10-3 W/cm2. The photon energy of probing light (eV): (1) 0.75" (2) 1.08; (3) 1.2; (4) 1.5.
a p p r o x i m a t e the t e m p e r a t u r e d e p e n d e n c e o f the P A coefficient as f o l l o w s : ln(Ac~) -- In C1 - ( k T / E o ) l n A - S
(27)
wlCN1, A - RNZtouo/G > 1 and S is the a d d i t i o n a l n e g a t i v e t e r m w h i c h
w h e r e C1 -
d e p e n d s w e a k l y on t e m p e r a t u r e :
S-
e x p ( - h w / E o ) A kt/E~
(28)
F i g u r e 14b s h o w s h o w the v a l u e o f the S t e r m for different t e m p e r a t u r e can be d e t e r m i n e d f r o m e x p e r i m e n t a l c u r v e Ac~(T).
(a)
2
(b)
_,-., t
0
:21L ,a
d -6
~
0 /
100 I
i
200..,,~/)~0 t ~
;~
-1
8
-10
1;0
'
2;0
'
3;0
'
T,K FIG. 14. (a) The temperature dependence of the steady-state absorption coefficient in As2S3fibers. (b) The plot of Ln S vs. T.
144
A. M. Andriesh et al.
The linear approximation ln(Ac~) against T must be a tangent to the experimental curve ln(Acr) against T at low temperatures, i.e., where the magnitude of term S is negligible (see Eq. (28)). The temperature dependence of the term ln(S) obtained from Figure 14 must exhibit a linear behavior when it is represented as a function of T: In S - - h w / E o + (kT/Eo)ln A
(29)
Therefore, by plotting the magnitude of term In S against T and extrapolating it to T = 0 (Fig. 14b) one can find the magnitude of the characteristic energy of the distribution of traps E0. Note that both the linear functions in Figure 14 must have the same slope, i.e., (1/Eo)lnA. In this way, the magnitude of E0 obtained from the PA temperature dependence is about 0.26 eV, and is therefore in good agreement with the value 0.3 eV given in the literature for E0 in the field of weak absorption (recall that the measurements were undertaken with the light hv < Eg (Ihm, 1985)). The fact that the dependence of photo-induced absorption has a power law character following a square-root function confirms that carriers excited in the process of photoabsorption as well as carriers participating in photoconductivity recombine according to the bimolecular mechanism (O'Oconnor and Tauc, 1982). This can be used for determining the magnitude of drift mobility. Orenstein and Kastner (Orenstein and Kastner, 1979; Orenstein, Kastner and Monroe, 1980) have shown that photo-absorption and carriers mobility are governed by the same localized carriers. For low-mobility semiconductors the diffusion-limited recombination can be presented by the Langevin equation: b = (e/eeo)(tx u + tXp)
(30)
01 = 4 w / k
(31)
In the case/x. <
(32)
where cr is the absorption coefficient for excitation light, F the incident photon flux, y the quantum efficiency and R the reflectivity for excitation light. From the temperature dependence of steady-state photo-induced absorption measurements O'Oconnor and Tauc (1982) found the temperature dependence of the bimolecular rate coefficient b in AszS3 glass which was used for determining the temperature dependence of the timeaveraged drift mobility in AszS3 glass (Fig. 15). The temperature hole drift mobility in AszS3 was found to be temperature activated at high temperatures, and almost temperature independent below approximately 130 K. The hole mobility at room temperature was found to be of the order of 10 -l~ cm 2 V s -1, which correlates with the results obtained from electrical measurements. The recombination radius R0 was estimated to be about 20,4,, which is quite close to the value of the recombination radius, obtained for AszS3 by Orenstein and Kastner (Orenstein et al., 1980).
Optical and Photoelectrical Properties of Chalcogenide Glasses
145
-8
-9
;> r
('4
E r
=1.
-10
9
-11
-12
2
,
i , i , i , i , ll2 , 4 6 8 l0 14 1000/T, K -1
FIG. 15. The temperature dependence of the time-averaged drift mobility in As2S3glass.
1.3.2.
Photo-induced Non-linear Absorption in ChG with the Participation of Non-equilibrium Localized Phonons
The excitation of the non-equilibrium carriers with the energy hu > Eg photons leads to the appearance of hot electrons and holes. Their thermalization in the non-crystalline systems is accompanied by the generation of the non-equilibrium localized phonons (fractons) (Andriesh, Enaki, Cojocaru, Ostafeichuc, Cerbari and Chumash, 1988b; Andriesh, Bogdan, Enaki, Cojocaru and Chumash, 1992a; Chumash, Cojocaru, Fazio, Michelotti and Bertolotti, 1996; Popescu et al., 1996). The phonons with the wavelength of the order of the magnitude modulation length of the random potential in the ChG drastically change the form of the potential, which modulates the bottom of the conductive band and the top of the valence band of the ChG. In this way non-equilibrium localized phonons open a new channel of the interband light absorption. For this reason the absorption coefficient increases with the increasing light intensity and the phenomenon can be explained by means of photo-induced light absorption in ChG with the participation of the fractons (Andriesh et al., 1988b, 1992a; Chumash et al., 1996; Andriesh and Chumash, 1998; Andriesh, Enaki, Karoli, Culeac and Ciornea, 2000). In fact, the coefficient of the interband light absorption can be represented as ce sum of two parts (Andriesh et al., 2000): c e - ce0 + / 3 , n
(33)
where ce0 is the part of the absorption coefficient, which does not depend on the temperature and/3, is the part of the absorption coefficient, which depends on the mean number of the localized phonons n. Thus, in the process of the interband light absorption the transitions with the simultaneous participation of light quanta and localized phonons play an essential role. The second part of the absorption coefficient in Eq. (33) essentially changes in the process of relaxation of the excited electrons into the localized states
146
A. M. Andriesh et al.
in the optical gap of ChG. This relaxation is accompanied by the coherent generation of the non-equilibrium phonons An = n - no, where no is the mean number of the equilibrium localized phonons (Andriesh et al., 2000). Andriesh et al. (1992b, 2000, 1988b), Andriesh, Chumash, Cojocaru, Bertolotti, Fazio, Michelotti and Hulin (1992c), Chumash et al. (1996) and Andriesh and Chumash (1998) studied the non-linear absorption by laser pulses in thin film samples of chalcogenide glasses As-S, As-Se, Ge-Se, A s - S - G e and others (0.2-5.0/.~m thickness). It was shown that when the input light pulse (with hu >- Eg) intensity was relatively low, the transmission of thin ChG films did not manifest the non-linear effect. However, increasing the incident light intensity over some threshold values (I0) leads to a non-linear character of the light transmission by ChG films (Andriesh et al., 1992a, 1988b; Chumash et al., 1996; Popescu et al., 1996; Andriesh and Chumash, 1998). The characteristic value of the threshold light intensity depends on the ChG film composition, wavelength of excitation, temperature and the laser pulse duration (Fig. 16). As a result of the non-linear light absorption a change of time profile of the laser pulses is observed which leads to a hysteresis-like dependence of the output light intensity on the corresponding value of the input intensity (Fig. 17). Andriesh et al. (2000) have shown that a contribution to non-linear absorption in ChG can have cooperative phenomena in the process of the generation of coherent phonon pulses by hot electrons. Among randomly distributed quantum wells of quasi-electrons one can always pick out the quasi-equidistant subgroups of two-level states in such randomly distributed states. For example, if we consider a single localized electron with the transition energy h,o~ = E 2 c ~ - El~ one can always find the large number of other localized electrons with the same transition energy between the ground and excited states. Therefore, let us introduce the subgroup distribution function p~ of the electron states in the quantum wells with the same energy distance ho~. Every subgroup c~ of coupled electrons generates localized phonons with the proper frequency ho~,~. The certain quasi-equidistant subgroup can generate a coherent Dicke pulse of the non-equilibrium localized phonons. The localized phonons decay into the acoustic phonons. Anderson, Halperin, Varma, Baranovskii, Fuhs, Jansen and Oktii (1972) proposed the analogous
1.5 As2S 3 300K
1.0 .o
. I9 I I I I
e~r~
0.5
0.0
0
20
9
40
Io, ( kW/cm 2 )
FIG. 16. Intensitydependence of the light transmission of a-As2S3.
Optical and Photoelectrical Properties of Chalcogenide Glasses
As2S 3
k
147
"*
A
Eo
4>
0
0
9
50
100
150
Io, ( kW/cm 2) FIG. 17. The dependence of the output light intensity of the corresponding value of the input intensity for a-As2S3.
two-level systems. Such two-level systems occur when certain numbers of excited atoms (or group of atoms) have two equilibrium positions. The mechanism of the excitation of the localized kinetics is given in Andriesh et al. (2000). Solving this equation in the stationary conditions the authors obtained for the nonlinear absorption coefficient a(Is) = dls(z)/l~ dz the following expression: c e - a 0 +/3n
(34)
n -- no + An
(35)
where coefficients/3 and a 0 do not depend on light intensity. It is clear that with increasing light intensity the absorption coefficient increases. As mentioned above such increase was experimentally observed. When the time duration of the excitation pulse is shorter than the decay times of the localized electrons, for the relaxation of the non-linear absorption coefficient after the passage of the short-pulse through the sample of ChG in the quasi-stationary case Andriesh et al. (2000) obtained the following expression:
where t '~ is the delay time of the subgroup ce. From this expression one can see that the relaxation depends on the cooperation law between the localized electrons. Every function sech 2 in the last equation has the maximum, when t - t0~. The sum on a takes into account all subgroups of the equidistant two-level states, which have different delay times. In this case relaxation law of the absorption coefficient can be more broadened than that in the case of single group of the equidistant two-level states. The broadening depends on the explicit form of the subgroup distribution function pa (Andriesh et al., 2000). As established by Andriesh et al. (1992a, 1988b), Fazio, Hulin, Chumash, Michelotti, Andriesh and Bertolotti (1993), Chumash et al. (1996) and Popescu et al. (1996) such delay of photo-induced absorption was observed experimentally.
A. M. Andriesh et al.
148
1.3.3.
Photo-induced Non-linear Absorption Due to Two-photon and Two-step Absorption
The first investigations of the non-linear absorption of nanosecond laser pulses with h ve < Eg in ChG were reported by Lisitsa, Nasyrov and Fekeshgazi (1977) and Nasyrov, Svechnikov and Fekeshgazi (1980). The dynamics of such induced absorption with subpicosecond and picosecond time resolution have been investigated by Fork, Shank, Migus, Bosh and Shah (1979) and Ackley, Tauc and Paul (1979). These authors showed that as a result of ChG strong excitation with huex < Eg, an additional induced absorption appears, which exhibits maximum amplitude during the excitation pulse and relaxes with several time constants. This kind of photo-induced absorption (when h Vex is far from the absorption edge Eg) appears only at strong laser excitation of ChG. The mechanisms of two-photon (or two-step) absorption and of the carrier localization and redistribution on states in the gap were proposed to explain the photo-induced absorption in ChG. For intraband excitation of AszS3 thin films (Eg = 2.4 eV) Lisitsa et al. (1977) and Nasyrov et al. (1980) utilized 100 fs laser pulses (pumping at 2.0 eV, and probing at 2.14 and 1.4 eV). The dynamics of the induced absorption relaxation is shown in Figure 18 (Fazio et al., 1993) which is composed of two parts: a first one, coherent, shaping as the crosscorrelation of the pump and probe pulses, followed by a second less intense and slower component. From the slower component fitting parameters, using the model of a nondegenerate two-photon absorption process, followed by a direct absorption of the probe pulse by carriers in localized states (two-step absorption), the measured depletion time (from 54 to 61 ps) depends on the pumping rate (from 1.5 to 0.75/zJ pumping, respectively) (Fazio et al., 1993). In such a way Fazio et al. (1993) observed a competition between two-photon and two-step absorption. It is for this reason that the pump pulse energy is lower than the gap. In this case the excitation
0.022 0.02 0.018
.~ 0 . 0 1 6 c
@
0.014
-~ o . 0 1 2 0
0. o
0.01
A
0.0O8
~" 0 0.006 e-
"-
.
.
, 5 ~ J ~
r,
0.004
0.002 o -0.002
~
.... i
i i
I
''
l
" .
.
.
.
delay time [ps]
FIG. 18. The photoinduced absorption relaxation in a-As2S3for 0.75 and 1.5/zJ pumping.
Optical and Photoelectrical Properties of Chalcogenide Glasses
149
can excite carriers into localized states in the gap by one-photon processes or into delocalized states by two-photon transition. A probe pulse can be absorbed by twophoton transitions and by transition of carriers in localized states, which are directly pumped by one-photon processes. Besides that, there is a possibility of excitation of non-equilibrium carriers excited into extended states. So the theoretical and experimental researches of the photo-induced absorption phenomena provide the information concerning possible mechanisms of photo-induced absorption which include many models described above. The realization of one or another model depends on concrete experimental conditions: composition of glass, the wavelength and intensity of pump and probe light, temperature, etc.
2. Photoelectrical Properties of Amorphous Chalcogenides 2.1. 2.1.1.
STEADY-STATEPHOTOCONDUCTIVITY L u x - A m p e r e Characteristics
We call the lux-ampere characteristics the dependence of the photocurrent upon the excitation light intensity. The photoconductivity O'ph can be expressed by the product of photogenerated free carrier concentration p and their mobility ~0 O'ph = e l~oP = e lxo ~oG
(37)
where G is the generation rate and T0 = p / G is the free carrier lifetime. Instead of using /x0 and ~'0 the experimentally measured drift mobility of carriers/L/,d (measured from timeof-flight experiments, for example) and photoresponse time ~'d, the photoconductivity may be written as Orph ---
elJ,d'rdG
(38)
One can measure the photoresponse time from the initial decay of photoconductivity after switching off the exciting light:
d/ h
1 'i'd
Iph
--d~- It=0
(39)
Under the condition that the equilibrium between free and trapped charge carriers was established long before the onset of recombination, the photoresponse time represents the recombination lifetime ~'r of excess photogenerated carriers, both free (p) and trapped (Pt): 'rd ='rr = (P + P t ) / G . That condition should be verified in each special case (Adriaenssens, Baranovskii, Fuhs, Jansen and Oktii, 1995; Adriaenssens, 1996). The recombination lifetime 7r is the characteristic of the recombination process, which determines the photoconductivity in a given material at a certain temperature and generation rate of excess carriers. Some most common recombination mechanisms were analyzed by Zeldov, Viturro and Weiser. The general dependence of photoconductivity
150
A. M. Andriesh et al.
on light intensity is usually expressed as a power law O'ph =
A.G ~
(40)
where the power y lies between 0.5 and 1.0 and A the proportionality factor. The linear dependence of the photoconductivity on the generation rate corresponds to monomolecular recombination (MR) process at low light intensity, while at high intensities the square root dependence trph oc G ~ complies with the bimolecular recombination (BR) process. The intermediate values 0.5 -< 3' -< 1.0 indicate the case of trap-controlled recombination by localized states distributed in the gap in energy. We refer to the well-known result of Rose (1963) trph oc G 1/(l+a) for the important case when the quasi-Fermi level moves through the exponential section of localized states energy distribution g(E) = No e x p ( - E / k T * ) with the characteristic energy E0 = kT*, and a = k T / E o. At the early stage, the photoconductivity of amorphous AszS3 and AszSe3 was examined at exposure to continuous or pulsed light (Kolomiets and Lyubin, 1973; Hammam and Adriaenssens, 1983; Popescu et al., 1996). Usually the dependence of the photoconductivity upon the light intensity of the type (39) was observed with A constant weakly dependent on the temperature and the power y between 0.5 -< y-< 1.0. At the same time some deviations from the common behavior were reported with respect to the exponent y. In thin AszS3 films the value of 3/= 0.73 was obtained in the region of high light intensity (P6) while at low light intensity a superlinear dependence of the photoconductivity upon the light intensity with the power index y = 1.38 (Kolomiets, Lyubin, Mostovski and Fedorova, 1965) and 3/-- 1.7 (Kolomiets and Lyubin, 1973) was observed. For arsenic sulfide in the case of excitation with ruby laser pulses ( h u = 1.78 eV = 0.74 Eg), the dependence was linear in a wide range of light intensities. Even at the highest intensities, which caused the sample surface erosion, no tendency to saturation, or, conversely, any transit to superlinearity, was observed. This fact indicates the existence of high localized state density in the range of the laser photon energy, and on the other hand, the absence of two-photon excitation processes. In the later study of the photoconductivity of bulk arsenic sulphide samples performed at various temperatures under high-intensity pulsed excitation (No = 1014-3 x 1017 x cm -2 s -1) (Fig. 19) the lux-ampere characteristics were described by the expression (40) with the power index y, the value of which changed from 1.0 at room temperature to 0.7 for the temperature T = 440 K for all light intensities. It follows from Rose's definition of y = 1/(1 + a) = T*/(T + T*) that at increasing temperature T the power index y decreases in such a way that 1/ 3/oc T. From the linear dependence 1 / 3 / = 1 + T/T* the parameter of the density-of-states distribution T* may be determined (Fig. 19b). For amorphous AszS3, the parameter T ~ 600 K thus correspond to the value/3 = 1/kT* = 19.6 eV measured from the slope of the tail optical absorption. Although the qualitative behavior of the dependence of the photoconductivity upon the light intensity corresponds to Rose's definition, the quantitative values of the parameter 3' obtained experimentally are sometimes different from those calculated for T* = 600 K. The discrepancy may be removed if one takes into account that we actually do not measure the concentration of free carriers p but the value of the photoconductivity trph, which also includes the temperature dependence of drift mobility ~d (I7).
Optical and Photoelectrical Properties of Chalcogenide Glasses (a)
~"
4
Temperature T, K: 1234-
3
151
(b)
|
,
293 343 398 440
|
,
e
~
~
1.2
1.1 9
2 1.0 1
-3
|
i
-2 -1 Log (F, a.u.)
|
i
0
0.9
.
. . . 350 400 Temperature, K
450
FIG. 19. The lux-ampere characteristics of photoconductivity for the vitreous As2S3 (a) and the power index y dependence vs. temperature T (b).
In order to extend the interval of light intensities, the lux-ampere characteristics of the vitreous alloys in the system ( A s z S 3 ) x : ( S b z S 3 ) l - x (0 > x - - 1.0) were investigated in two regimes: with the stationary excitation from an incandescent lamp (light intensity N o --1015-1017 cm -2 s -1) and with the pulsed excitation from a flash-lamp ( N o 1017-1019 cm -2 s -1) by illumination of the sample in the range of the spectral maximum of photoconductivity. For all bulk samples ( A s z S 3 ) x ( S b z S 3 ) l - x the lux-ampere characteristics could be described by Eq. (40), with different y values for 'high' and 'low' excitation levels. For the 'low' levels of excitation, the power index 3' of the stationary lux-ampere characteristics of the alloys was close to unity at room temperature, and with increase in temperature, it initially decreased to 0.7 and then increased again with a tendency to reach unity. For various glassy alloys this minimal value of the power index 3' occurred between 370 and 420 K. For 'high' levels of pulsed excitation the power index 3' monotonously decreased when the temperature increased with no minimum in the y(T) dependence. The specific feature of this type of excitation was superlinear lux-ampere characteristics with the power index y = 1.2-1.4, which was observed for the AszS3-rich compositions in the temperature range 300-350 K. For highest levels of excitation, especially at high temperatures for the ( A s z S 3 ) x ( S b z S 3 ) l - x alloys, a portion with the power index y = 0.5 was observed. A superlinear lux-ampere characteristic with the power index y = 1.0-1.4 was observed in the case of thin films of ( A s z S 3 ) x ( S b z S 3 ) l - x for 'low' levels of excitation (Andriesh et al., 1981) and for thin films AsS1.sGex (Andriesh, Iovu, Tsiuleanu and Shutov, 1975). For the majority of compositions of the system AsS1.sGex the power index 3' of the lux-ampere characteristic takes the values from 0.51 for AsS1.sGel.0 up to 0.74 for the composition AsS1.sGe0.73. The temperature dependence of the power index 3' for the AsS1.sGex alloys is strongly influenced by the composition and the deviation from the Rose theory becomes greater when germanium content increases. This fact indicates significant modification of the energy distribution of traps which appear as the result of Ge doping as it is clearly seen for the composition AsS1.sGeo.73 (Andriesh et al., 1975). The lux-ampere characteristics were also studied for A s - S e chalcogenide glasses (Kolomiets and Lyubin, 1973; Fuhs and Meyer, 1974; Hammam and Adriaenssens, 1983;
152
A. M. Andriesh et al.
Hammam, Adriaenssens and Grevendonk, 1985). For both bulk compositions and thin films, the dependence of the photoconductivity upon light intensity was described by the relationship (40). For the composition AsSe4, a non-monotonous dependence of the power index y with the temperature was observed. For the bulk AszSe3 at 'high' levels of excitation the maximal value of y - 0.36-0.40 was obtained for the positive polarity at the illuminated electrode. At the negative polarity on the illuminated electrode the luxampere characteristics showed a classical behavior. Low values of the exponentials of the lux-ampere characteristic y < 0.5 ( y - 0.35-0.40) with non-standard temperature dependence were also observed by Hammam and Adriaenssens (1983) in a-AszSe3 for excitation at wavelength 0.8/xm. Such type of behavior is associated with light absorption near the contact in the depletion layer. The fact that y < 0.5 means that illumination under these specific conditions creates an additional recombination channel. 2.1.2.
Temperature Dependence of Photoconductivity
With increasing temperature, the photoconductivity rises typically exponentially at low temperatures when O'ph > O'dark, then passes through a maximum when O'ph = O'dark and after that, decreases with O'ph < O'dark (Arnoldussen, Bube, Fagen and Holmberg, 1972; Simmons and Taylor, 1972a). The temperature of the maximum Tmax in the O'ph = f(103/T) dependence is determined by the expression: Tmax __
O'ph EF - Ev
Ordark
2k
(41)
When the light intensity is increased, the value of Tmax shifts to higher temperature. The appearance of the maximum in the temperature dependence of photoconductivity is explained by the transition from the high to low level of excitation, in correlation with the behavior of the lux-ampere characteristics (Arnoldussen et al., 1972). In the range of the temperatures T < Trnax(Crph > O'dark) the photocurrent is proportional to the square root of the light intensity ( y - - 0 . 5 ) for the high excitation level, and is proportional to light intensity (y = 1.0) for low levels of excitation. In the range of high temperatures T > Tmax(O'ph < O'dark), the photoconductivity is proportional to the light intensity ( y - - 1.0) and decreases when the temperature increases. In Figure 20 the temperature dependences of photoconductivity for some compositions of (As2S3)x: (Sb2g3)l-x glasses for both stationary (a,c) and for pulsed excitation (b,d) are shown. For comparison the dependence of dark conductivity O'dark versus temperature T is also shown. It is remarkable that in the case of intense pulsed excitation the temperature dependence of photoconductivity has higher values of photoconductivity in comparison to the dark conductivity (Oph >> O'dark), with the absence of a tendency to reach the maximum. In the Eq. (41) EF - Ev corresponds to the position of the equilibrium Fermi level, which may be evaluated as an activation energy of the temperature dependence of the dark conductivity. The values of Tmax calculated for various (As2S3)x:Sb2S3)I_ x glasses are situated around T ~ 400 K and correspond to the experimentally determined values (Tmax = 450 K for x = 0.75 and Tmax = 370 K for x = 0.25, respectively). When the light
Optical and Photoelectrical Properties of Chalcogenide Glasses '
(a)
I
'
i
'
i
'
x = 1.0
(c)
10_12
~
i
'
i
'
I
'
O.35
X
[*~'~--o
~
~=~
10-12 b
~I'\ . , ,"
\'.
~'=~ 10-14 10-16
,
' 2.5
' 3:0 103]y,
,--
10-8
'
,o,o I ' - ' \ k ' "
10_14
(b)
i
--
153
'
10-1o
'
'
'
4
~
10-16 /
% ,
3
' 3.5
' 4.0
2.;
/'\\5
Sdark ON ' 2.'5 ' 3.; ' 3.; ' 4.0
K -1 '
103/T, '
'
x=l.O
-
~.1-
10-12
2
'
(d)
I
'
K -1 i
'
i ~-
' .
10-8
~
lO-1~
7 10-12
,x=
9
_
10-14 10-14 10-16
,
-
2.5
i
3.0 103/T,
3.5 K -1
4.0
2.0
I
2.5
,
Sd
3.0 103/T,
3.5
4.0
K -1
FIG. 20. The temperature dependence of the stationary (a, c) and pulsed (b, d) photoconductivity for As2S3 (a, b) and (AszS2)o.35:(SbzS3)o.65 (c, d). Light intensity F (%): (1) 100; (2) 10; (3) 1.0; (4) 0.1" (5) 0.01.
intensity increases, the position of the maximum is shifted to higher temperatures in agreement with the expectation. In the range of the intermediate temperatures the photoconductivity has a temperature-activated character with the activation energy about 0.3-0.4 eV (Hammam et al., 1985). Similar dependence was found for the (AszS3)x:Sb2S3)l_x thin films. If we suppose, following Simmons and Taylor (1972a), that two types of states are localized in the gap of an amorphous semiconductor, one donor-like set in the upper half and another acceptor-like set in the lower half of the gap, then, with account for conduction and valence bands, a basic four-level energy system is obtained. The Fermi-level is positioned between the two groups of states, or slightly nearer to the valence band to explain the p-type conduction (this condition is not really necessary).
154
A. M. Andriesh et al.
For this four-level system, it is supposed that the recombination of photoexcited excess charge carriers occurs between the carriers trapped in the localized states and those in the conductive bands. The analysis of this recombination model provides the temperature dependence of photocurrent with the maximum at Tmax, which corresponds to transition from MR at T < Tmax to BR at T > Tmax. The corresponding activation energies of the temperature dependence of photocurrent take the values: EMR = (ED -- Ev) - E o-
(42)
EBR = (EA -- Ev)/2
(43)
where EA and ED are the energies of the donor-like and acceptor-like states, respectively, Ev the energy of the valence band edge and E~ the activation energy of dark conductivity. With these relations one can evaluate the energies EA and ED from the temperature dependence of photocurrent. For a-AszSe3 these evaluations provide values of about 1.0 and 0.6 eV for ED and EA, respectively, measured from the valence band edge.
2.1.3.
Spectral Distribution o f Photoconductivity
The spectral distribution is an important characteristic of photoconductivity as it expresses the dependence of the basic processes of generation, transport and recombination of excess charge carriers (photocarriers) on the excitation photon energy. The photoconductivity spectra are sensitive to the composition and conditions of preparation of the initial material, to the temperature, the strength and polarity of the applied electric field; they are dependent on the electrode material, the intensity of excitation light or the additional bias illumination, etc. (Kolomiets and Lyubin, 1973; Hammam et al., 1985; Popescu et al., 1996). If we take into account that the generation rate G of photocarriers is proportional to the number of absorbed photons then the photoconductivity in Eq. (37) may be expressed as O'ph
-
-
-
(1/L)etzd'rd rlFo[1 - exp(-kL)]
(44)
Here F0 is the photon flux, L the sample thickness, and rt describes the generation efficiency. The exponential describes the light absorption in the sample as a function of the absorption coefficient k. The conductivity is supposed to be monopolar. The spectral interval of the photosensitivity therefore falls into the region of fundamental edge absorption of the photoconductor and the absorption coefficient varies in this region by 4 - 5 orders of magnitude. It is then convenient to distinguish the regions of strong and weak absorption. In the region of strong absorption exp(-kL) << 1 the light is absorbed near the sample surface and O'h = (1/L)etXdrr~qNo
(45)
If there is no strong surface recombination affecting the photocarrier lifetime then the photoconductivity in this region is weakly dependent on the photon excitation energy,
Optical and Photoelectrical Properties of Chalcogenide Glasses
155
thus giving the opportunity to find the product r//Xdrr. This value characterizes the photosensitivity of the photoconductor. In the weak absorption region e x p ( - k L ) ~ 1 - k L and from Eq. (44) we have: (46)
O'ph - - e/XdT"r rlkNo
It follows from Andriesh, Shutov, Abashkin, Iovu, Kolomeyko and Chernii (1974c) that in this region the spectral dependence of the photoconductivity is governed by the absorption coefficient, because the rltXard product weakly depends on energy in this spectral range. As a typical example, in accordance with the Eq. (44) the normalized photoconductivity spectra of bulk samples of the system (As2S3)x(Sb2S3)~-x are shown in Figure 21 in the full interval of composition variation including both the glassy alloys x = 1.0-0.25 and polycrystalline samples of x = 0 . 2 5 - 0 , as well as the spectrum of the Sb2S3 single crystal (Andriesh, Iovu and Shutov, 1974a). It is seen that the shape of the photoconductivity spectra is in many respects similar: nearly constant sensitivity at photon energies greater than the optical gap Eg, a maximum at the absorption edge particularly clearly defined in crystalline samples, more or less pronounced shoulder at about 1.3 eV, after which the photoconductivity rapidly decreases down to the level 10 .3 of the maximal value at about 1.0 eV. The shoulder at 1.3 eV is characteristic of the antimony-containing alloys. The photon energies corresponding to the above-mentioned peculiarities as well as the optical gap Eg values are listed in Table II for various compositions. The position of the photoconductivity peak clearly follows the optical gap Eg. The photosensitivity increases with the Sb2S3 content and then leaps up at about five orders of magnitude when passing to the crystalline alloys. Passage to the crystalline samples is followed by the shift of the photoconductivity to lower energies in accordance with the known differences in
I
'
I
'
,*/'\ s
~,~ / ?" ~: / :
-9 o -10
-12
I
'
I
I
Ib'.IH~.#''I~"
o~.O..~..o
,.%~%o ..............
.
,
.,#,4~.-.-+~ 6- -3
/
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/
-4
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"~ ~)- 1[ A,~,A,R,~,a,A.a.a.aa 4 "" - "3 / r ~" .,. '~" ~ ' '. 2. .t.~ I ' ' ~ 1 - 6 ;
,9"
r
,
,,g'%
-7
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I t
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""
/~
.,-
:~ "
.
9
/
~/ff
2
- -7
i , i , i , i , i , i 0.8 1.2 1.6 2.0 2.4 2.8 hv, eV
FIG. 21. The normalized spectra of photoconductivity for the (As2S3)x:(Sb2S3)l-x.x: (1) 1.0; (2) 0.85" (3) 0.75; (4) 0.45" (5) 0.15; (6) 0 (polycrystalline); (7) 0 (single-crystalline).
A. M. Andriesh et al.
156
TABLE II ENERGY CHARACTERISTICS OF PHOTOCONDUCTIVITY SPECTRA OF (AszS3)x(SbzS3),-x ALLOYS
Content, x Optical gap, Locationof PC Locationof PC Locationof PC edge eV peak for bulk peakfor films 'shoulder'in energy (at 10-3 samples, eV (L = 1 ~m), eV PC spectra of levelfrom the bulk samples, peak),eV eV 1.0 0.85 0.75 0.65 0.55 0.45 0.35 0.25 0.15 0
2.40 2.26 2.16 2.10 2.06 1.96 1.92 1.88 1.80 1.73
2.07 1.94 1.97 1.88 1.88 1.80 1.76 1.70 -
2.50 2.45 2.28 2.25 2.16 2.11 2.08 2.06 1.95 1.93
1.34 1.39 1.28 1.31 1.30 1.20 1.32 -
1.45 0.98 1.03 1.02 0.98 1.04 1.02 1.04 -
parameter, eV
0.043 0.058 0.052 0.051 0.041 0.040 0.040 0.040 0.035 0.035
absorption spectra of crystalline and amorphous arsenic and antimony chalcogenides (Andriesh et al., 1969). The spectral distribution of photoconductivity of the vitreous semiconductors presents a special interest in the range where the energies of photons of the light excitation are less than the band gap Eg. In that range of energies the photoconductivity may provide important information about the weak absorption region, i.e., about the energy distribution of gap states, especially in thin-film samples. Thin films are photosensitive in a wide range of photon energies ( 1 - 4 eV). The photoconductivity spectra in this region show some peculiarities characteristic for amorphous materials (Hammam et al., 1985). In Figure 22 the spectral distribution of photoconductivity of amorphous films of arsenic sulfide is presented. As in many photoconductors the maximum of photosensitivity is situated near Eg at 2 . 4 - 2 . 8 eV and is conditioned by the band-to-band optical transitions. Qualitatively the photoconductivity edge corresponds to the form and position of the absorption edge. The maximum of photoconductivity is rather wide (the half-width of the maximum is about 0.7 eV). An important aspect of the photoconductivity spectra is connected with the photoconductivity at energies much lower than Eg, for the first time observed for TlzSe.As2Te3 (Andriesh and Kolomiets, 1963). According to the specific energy spectra of localized states in amorphous materials, a continuous transition from intrinsic photoconductivity to that of impurities is expected. The analysis of the photoconductivity spectra of amorphous AszS3 thin films makes evident the presence of a wide photoactive absorption band in the range of 1.3-1.9 eV with the maximum located at about 1.3 eV (Fig. 22). The existence of a group of localized states of high concentration in the indicated energy range is confirmed by the experimental study of thermostimulated depolarization and photoresponse decay. These results are in agreement with the data of Kolomiets (1969), who experimentally established the presence of fluctuation levels in amorphous semiconductors. The probable generation mechanism of the non-equilibrium charge carriers in non-crystalline semiconductors is the thermo-optic mechanism (Kolomiets and Lyubin, 1973; Andriesh, Iovu, Kolomeyko,
Optical and Photoelectrical Properties of Chalcogenide Glasses 100
,
i
,
i
,
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i
80
.~.
o
6O
40
20
0 ~ 0.8
2,"
I
/
-
,, ,."" " ,,it tit
1.2
1.6
t 2.0
,
2.4
hv, eV FIG. 22. The photoconductivity spectra for amorphous AszS3 thin films without illumination (1) and with bias illumination.
Chernii and Shutov, 1977). Under bias illumination (Fig. 22, curve 2) the photoconductivity in the weak absorption region is strongly increased as a result of photo-induced absorption. The existence of photo-induced phenomena in amorphous chalcogenides were clearly demonstrated by observations in optical fibers (see Section 1.1). The photoconductivity spectra of thin films of several alloys of the system AszS 3Sb2S3 are given in Figure 23 (Iovu, Iovu and Shutov, 1979). The most interesting peculiarity of the spectra is the photosensitivity at energies much lower than the optical gap energy. This evidence indicates the existence of optical absorption with the participation of wide spectrum of localized states (Andriesh, Shutov, Iovu, Colomeico and Lerman, 1972b; Andriesh, Shutov, Colomeico and Lerman, 1973). In a wide range, the photocurrent exponentially decreases with the energy indicating the decrease of the absorption coefficient with the photon energy in accordance with Eq. (46). Assuming this decreasing is described as kc~exp(hv/A) (Wood and Tauc, 1972), from the slope of the exponential portion of the photoconductivity spectrum the value of the A parameter can be found (see Table II). The existence of deep photoactive centers in arsenic trisulphide is verified by experimental data of thermostimulated depolarization and photoconductivity relaxation (Andriesh et al., 1974c). In Figure 24, the photoconductivity spectra are presented for thin films of the AsxSe~_x chalcogenide system obtained by thermal deposition technique. Photoconductivity spectral distribution of thin films is typical for disordered materials as well. The spectra to a considerable extent depend on the parameters of the deposition technique. The slope
158
A. M. Andriesh et al.
10-6
5
10-7
10-8
z e..,
10-9
/
10-1o
10-11 10-12
I
i
1.0
I
I
1.5
2.0
~
I
~
I
2.5
3.0
hv, eV FIG. 23. Photoconductivity spectra of thin amorphous films of the system (As2S3)x - (Sb2S3)l-x. x: (1) 1.0; (2) 0.75" (3) 0.55; (4) 0.35.
4
10-6
1
3 10-7 2 10-8 o
Z .=
10-9
10-10
10-11
10-12
I
1.0
i
I
1.5
~
I
2.0
~
I
2.5
~
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3.0
hv, eV FIG. 24. Photoconductivity spectra of thin thermally deposited amorphous films of the system AsxSej_x. x: (1)
0.28; (2) o.4o; (3) o.5o; (4) o.6o.
Optical and Photoelectrical Properties of Chalcogenide Glasses
139
of the photoconductivity edge is sensitive to the modification of the glass composition and to the conditions of preparation of amorphous thin films. For the A s - Se system it was found that when the contents of arsenic increases, the value of the slope decreases from 16.7 eV-1 for AszSe5 to 14.3 eV-1 for AszSe3 for thin films prepared by deposition from vapor phase and from 16.2 eV to 11.8 eV-1 for thin films obtained by laser evaporation and may be connected with the specific structure of these layers (Iovu, Iovu, Mironos and Shutov, 1985). For the films obtained by laser deposition the energy of spectral distribution maximum corresponding to the fundamental optical absorption edge is higher for all compositions than that for the thermally deposited samples. The position of the spectral maximum of photoconductivity in the latter slightly depends on the composition and has minimum in the region of stoichiometry. This is in accordance with measurements of the optical gap variation in bulk samples of As-Se (Street, Nemanich and Connell, 1978). On the contrary, in the laser deposited films the photoconductivity peak energy reaches maximum for AszSe5 composition. The extreme values of the parameters are observed as well for other characteristics of this composition obtained by laser deposition: the lowest slope of optical edge, maximal photosensitivity, and drift mobility. For these films greater scatter of the parameters is observed, as opposed to the small difference in parameters of thermally deposited films. For example, the photosensitivity of laser deposited films is three orders of magnitude varied with the composition from x -- 0.07 to 0.28. These peculiarities of the photoelectrical properties indicate structural specificity of the laser deposited films, as for more equilibrated thermally deposited films the composition variation affects the photoconductivity to a much lesser degree. Higher optical gap energies of the laser deposited films compared to those for thermally deposited films indicate higher degree of structural disorder (Pfister and Morgan, 1980). Greater rate of vapor condensation and quenching at laser deposition stipulate for molecular character of the freshly deposited film prone to polymerization. Strong effect of the composition on the photoconductivity spectra was observed in the A s - S - G e amorphous alloy system. Introduction of germanium up to 7 at.% in arsenic sulfide determines the displacement of the maximum of photoconductivity to the red side of the spectrum. Further increase of germanium content shifts the photoconductivity spectrum towards longer wavelength proportionally to the atomic content of Ge. The non-monotonous movement of the photoconductivity spectrum in the case of doping of arsenic sulfide with germanium is probably connected with the appearance of some new structural units in the material such as GeS4/2, GeS2/2, and AsAs3/3, which lead to the radical reconstruction of the atomic structure and energy spectrum of the chalcogenide glass (see Section 1, Figs. 11 and 12). The magnitude and polarity of the applied field affects the form of the photoconductivity spectra of the chalcogenide glasses. If, in the case of negative polarity applied to the illuminated electrode, a clear maximum is seen in the photoconductivity spectra, at positive electrode polarity the maximum is weakly pronounced and the photocurrent rises monotonously in the energy range hv > Eg (Fig. 25). With negative polarity applied to the illuminated electrode the photoconductivity sharply decreases in the energy range h~, > Eg. This behavior may be explained by the monopolarity of the conductivity of the amorphous binary chalcogenides. When a negative voltage is applied to the illuminated electrode the holes generated at the electrode do not penetrate in the bulk of the specimen and the photocurrent falls down due to polarization of the sample.
160
A. M. Andriesh et al.
10-8
10-9
<
10-10
tl.) 9 9 10-11
10-12
10-13 1.2
1.4
1.6 hv, eV
1.8
FIG. 25. The spectral distribution of photoconductivity of AsS1.5Geo.125 thin films for positive (1, 2) and negative (3, 4) polarity at the illuminated electrode. The applied voltage U (V): (1) 1.0; (2) 4.0.
For GeSe and GeTe amorphous thin films, when the applied field increases, the photoconductivity edge is shifted towards the longer wavelength and Stiles, Chang, Esaki and Tsu (1970) suggest that the effect is not caused by the phenomena at the metalsemiconductor interface but by the bulk phenomena. Another situation is found in the ( A s z S 3 ) x : ( S b z S 3 ) l - x system (Fig. 21), for which the type of structural units of arsenic sulfide and antimony sulfide is similar. The same photosensitivity is observed in the range hv > Eg, a maximum in the range of the absorption edge, which is very clear in the crystalline alloys (x --< 0.15), and the plateau in the energy range of 1.3 eV, after which a sharp drop of photoconductivity of about 10- 3 of magnitude at about 1.0 eV is observed. The existence of the shoulder in the photoconductivity spectra of the glasses which contain Sb2S3 is determined by new localized states which are introduced by Sb atoms in the AszS3 matrix. In the (AszS3)x:(Sb2S3)l-x amorphous thin films, when the content of Sb2S3 is increased, the maximum of photoconductivity also shifts to longer wavelengths from 2.5 eV for the AszS3 to 1.85 eV for the Sb2S3, respectively, in accordance with the widening of the optical band gap Eg (Andriesh et al., 1981). Contrary to the bulk glasses, the photoconductivity maximum in amorphous thin films is situated at higher energies (hv > Eg), which correspond to the highest values of the absorption coefficient. The photoconductivity beyond the fundamental absorption edge may be associated with foreign impurities even at very low concentrations. The impurity photoconductivity was studied in the case of amorphous Se doped by oxygen, and in the opposite case, doped both with the oxygen and compensating arsenic impurity (McMillan and Shutov, 1977). The experiment was carried out with Se of high purity (contamination
Optical and Photoelectrical Properties of Chalcogenide Glasses
161
less than 10-4%), to which 0.025 wt.% of oxygen in the form of SeO2 or both oxygen and arsenic (0.025 wt.%) were introduced under pure nitrogen atmosphere. The photoconductivity spectra of these species are shown in Figure 26 along with the quantum efficiency distribution of a-Se. It is seen from the results that at addition of the impurity the main alterations of the spectra appear just at the long-wavelength side of the absorption edge. The spectrum takes the form of a peak at 1.55-1.60 eV, which grows with the oxygen content or rapidly decreases when the compensating arsenic impurity is added. It was found from the IR spectral analysis of the samples that the oxygen content decreased in succession from Se:O (curve 1) through 'pure' Se (curve 2) to Se:O:As (curve 3) indicating that the photoresponse peak at low energies may be associated with the centers introduced by the addition of oxygen. This type of behavior is typical for impurity photoconductivity in crystalline semiconductors. The photoconductivity spectra can provide additional information concerning the optical transitions involving gap states; as in the low-absorption region they are determined mainly by the absorption coefficient. In the case of thin films the measurements of photocurrent provide better sensitivity in the low-absorption region than optical transmission measurements. The photoconductivity spectra of AsSe:Sn films normalized per incident photon are presented in Figure 27. The gap width Eph(A1/2) determined from the photoconductivity spectra as the energy where the photocurrent falls down to half the maximum value (so called Moss criterion) is listed in Table I for various tin concentrations. Incorporation of tin is followed by the shift of the photoconductivity spectra to lower energy exceeding the decreasing optical gap (the shift of Egpt is about 0.18 eV (see Fig. 7), while the shift of the photoconductivity edge Eph is 0.3 eV for 10 at.% Sn. The spectra show nearly exponential dependence of the long-wavelength edge on the photon energy, which extends much deeper into the gap than it follows from ,
l
,
i
,
'
1
10-4 10_5
10-1
Z~ 10-6
10-2
"~ 10-7 10-3 10 -8
10 -4
10 -9 ,
1.2
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1.6
,
I
i
I
2.0 2.4 hv, eV
,
I
2.8
FIG. 26. Photoconductivity spectra of doped Se samples Se:O (1), Se (2), Se:O:As (3). Dashed line: the spectrum of quantum efficiency of a-Se according to data [M5].
162
A. M. Andriesh et al. I
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-4
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1.2
,
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hv, e V FIG. 27.
The photoconductivity spectra for AsSe:Sn thin films.
the optical data (hu < 1.5 eV). The characteristic energy of the slopes is slightly greater than E00 and is weakly dependent on the tin content. An exception is the composition with the highest tin concentration of 10 at.% Sn. After addition of tin the photocurrent increases (more than 250 times for 10 at.% Sn). The above peculiarities indicate that the photoconductivity is determined not only by the band tail absorption but also by absorption at deep defect states in the weak absorption region. 2.1.4.
Photoresponse at the Amorphous Semiconductor-Metal Contact
At the metal-amorphous semiconductor contact surface, a contact barrier is formed. When illuminated, this barrier provides an injection photocurrent, if the photon energy is greater than the barrier height. Determination of the photoemission threshold provides the measurement of the barrier height, which is an important characteristic of the contact. The technique is based on measurement of the spectral characteristic of the emission photocurrent at photon energy less than the optical gap Eg. The spectral distribution of the injection current is described as a square dependence on the photon energy in the interval of few tenth of electron-volt over the injection barrier %. The experimental photocurrent spectrum presented in 11/2 "ph versus hv coordinates gives a straight line (Fowler's graph), whose intersection with the energy axis determines the barrier height. This technique has been frequently applied for numerous semiconductor materials. Sandwich-type chalcogenide glass thin-film samples (0.2-3.0/~m) deposited in vacuum onto conducting glass substrate were supplied with the upper electrode of the investigated metal. The metal-chalcogenide glass pairs are listed in Table III.
Optical and Photoelectrical Properties of Chalcogenide Glasses
163
TABLE III ENERGY PARAMETERS OF METAL -- CHALCOGENIDE GLASSY SEMICONDUCTOR CONTACT
Semiconductor
Electrode
~v~ (eV)
q~ (eV)
Dv (eV)
q~sc(eV)
A1 Ni Sb Bi Au Cr Pt Te A1 Ni Bi Au A1 Sb
4.35 4.36 4.38 4.40 4.56 4.58 4.71 4.73 4.35 4.36 4.40 4.56 4.35 4.38
1.23 1.32 1.27 1.26 1.13 1.30 1.03 1.14 1.62 1.74 1.55 1.25 1.16 0.75
0.41 0.50 0.45 0.44 0.31 0.48 0.21 0.32 0.65 0.77 0.58 0.28 0.35 0.06
4.76 4.86 4.83 4.84 4.87 5.06 4.94 5.05 5.00 5.13 4.98 4.84 4.70 4.32
Sb2S 3
AszS 3
As2Se3
The samples were illuminated by m o n o c h r o m a t i c light from the transparent substrate side. The photoresponse was m e a s u r e d at r o o m temperature at a bias of both polarities or without applied voltage. As in the range hu < Eg, the excitation in the chalcogenide layer is uniform and the transparent electrode does not absorb, because the cause for the p h o t o r e s p o n s e at the absence of the external voltage is the contact field at the metal electrode. The photocurrent corresponds to the m o v e m e n t of holes from the electrode into the c h a l c o g e n i d e layer and is about 20 times greater than the current at the opposite polarity. S h o w n in Figure 28a are the e x p e r i m e n t a l F o w l e r ' s graphs of the photoresponse n o r m a l i z e d per incident photon for Sb2S3 samples with A1, Te, Au and Pt electrodes with
(a)
~,
~
(b)
5
3 d -~ 2
0
1.0
I'/)
d
hv, eV
//
./
9
2 1
I,/11, 1.2
3
r
/
1.4
0
1.2
1.4 hv, eV
FIG. 28. Spectral distribution of photocurrent for Sb2S3 film (a) with electrode of A1 (1), Te (2), Au (3) and Pt (4) without applied voltage and (b) with A1 electrode under voltage (V): (1) 0; (2) 2; (3) 4.
164
A. M. Andriesh et al.
and without bias voltage dragging injected holes from the illuminated electrode. Same graphs for AszS3 are shown in Figure 28b. It is seen that 11/2 -ph is proportional to the photon energy in rather wide energy interval. This fact allows to find the barrier height % (as shown by dashed lines) for various pairs of metal-chalcogenide semiconductors listed in Table III. The values of the metal work functions in Table III are given on the basis of the work by Geppert, Cowley and Doge (1966), where the data for thin metal films used as contacts to semiconductors have been analyzed. It is seen from Table III that the threshold energy values fall in the interval 1.0-1.7 eV varying with the electrode or semiconductor material. With increase in the work function of metal the barrier is getting lower, the highest barriers develop for A1, Cr and Ni, the lowest ones for Pt and Au. Assuming the simple energy scheme shown in the the insert of Figure 28b one can evaluate the band bending Dv at the contact using reduced thermal activation energy of conductivity as the Fermi energy: 0.97 eV for AszS3, 0.86 eV for Sb2S3, 0.81 eV for AszSe3 and 0.91 eV for AsSbS3. The barrier height weakly depends on the applied field slightly decreasing with the field growth. Estimation of the Schottky barrier lowering in the field E = 105 V cm -1, A% = (1/2)(eE/Treeo) = 0.05 eV is in the limits of experimental error (Iovu, Iovu and Shutov, 1978). 2.1.5.
Thermostimulated Photoconductivity
An effective method of localized states investigations is the study of thermostimulated depolarization (TSD) of samples pre-charged by field, which basically corresponds to the method of stimulated polarization currents (SPC) proposed by Simmons and Taylor (1972b,c). According to this method the population of the localized states by charged carriers under illumination by light of corresponding photon energy takes place at sufficiently low temperatures when the thermally induced escape transitions of the electrons from localized states to the conduction band is practically absent. Then the sample is heated in the presence or absence of an external electric field. As a result, the captured charge carriers are released step by step from the traps, and in the external electrical circuit the current i appears, which is changed with the temperature T and presents a curve i = f ( T ) with a maximum. The SPC method permits distinguishing single levels which are closely situated on the energy scale. For example, the experiments carried out on 8b283 crystals permitted to reveal three groups of localized levels situated at 0.19, 0.30, and 0.41 eV, respectively. By the TSD experiments in vitreous alloys based on arsenic sulfide (Andriesh, Shutov, Abashkin and Chernii, 1974b; Andriesh et al., 1974c) a rich structure in the localized spectra was discovered. Further, the experimental results obtained on amorphous AszS3 thin films will be discussed and interpreted in frame of the theory of charge relaxation in high-resistivity dielectrics and semiconductors. The temperature dependence of depolarization current (Fig. 29) for A1-AszS3-A1 thin film structures exhibits a structure containing five peaks positioned in different temperature range presented in Table IV. The peak E1 dominates in TSDC spectrum and was studied in more detail. When the charging temperature is raised from 300 to 390 K, the position of maximum E 1 is unchanged but its amplitude first abruptly increases and then saturates around T -- 365-390 K. The position of peak E1 is independent of the applied voltage (Figs. 30 and 31).
165
Optical and Photoelectrical Properties of Chalcogenide Glasses
I,A 2 t I L I
/,
4.1(~12
',
/
'~
',
t
,
3.o-IO
i[
2.1(~12
I I.A
E2
/
E1
.lo-lO
/,-_._
-.,
-"
190 230 270
:
,
310
a
,
3,50
"
390 T,*K
FIG. 29. TSD curves in thin films of vitreous As2S 3" experiment (solid line) and calculation (dashed line).
The experimental results of TSDC measurements in amorphous semiconductors were interpreted on the basis of the theoretical model developed by Simmons and Taylor (1972b,c). The theory supposes the current flow through metal-dielectric-metal structure with blocking Shottky contacts for the case of compensated dielectric which contains deep localized traps. T A B L E IV EVALUATION OF THE PARAMETERS OF THE ENERGY LEVELS WHICH DETERMINE THE MAXIMUM OF THE T S D CURVES FOR THE AMORPHOUS As2S 3 No. 1
2
Parameter Temperature range of peak maximum (K) Energy depth (eV)
Method of determination
4
Trap density (cm-3)
E3
E4
360-390
275-285
245-260
205-230
Et = 25kTm
0.79 + 0.03
0.59 _+ 0.01
0.53 + 0.01
0.48 _+ 0.05
0.81
•
-
0.70
+ 0.1
-
E t --
Peak broadening (eV*) Cross-section (cm 2)
E2
TSDC curves
Et --
3
E1
In/31Tern2
kTml Tm~2 Tm--r*
~2T21
1.51kTmT* TIn-T*
TZm 1 lg--~- VS. Tm
0.77 + 0.08
-
Comparison of experimental and calculated TSDC-curves*
0.75
0.65-0.7
0.5-0.6
0.3-0.4
0.12-0.16
0.03
0.05
0.08
5 X 10 -19
10 --18
10 -18
10 -19
1016
1013_1014
1013_1014
1013
E = kTmln
NcSvkTm ~-
Magnitude of released charge
166
A. M. Andriesh et al.
(a)
I(A)
(c)
I
I(A)
I" fO -9
4 'i0-" 6.|0 -~o
2.~0m ~. ~0-10
3ZO (b)
I
~
I(A)
400 T(K)
l _
i
!
......
i,.
I
4~o
;370
~
|
T(K)
I
5.~0-11 2,5 "I0-~I
~I0
. . . . . . . . . . . . .
~0
~
400 T(K)
FIG. 30. TSDC curves of the maximum El at different conditions: (a) charging temperature T (K): (1) 387; (2) 367; (3) 347; (4) 331" (5) 310; (6) 298; (b) charging voltage U (V): (1) 200; (2) 100; (3) 50; (4) 25; (c) heating rate v (deg/s): (1) 0.98" (2) 0.85; (3) 0.61; (4) 0.49; (5) 0.35; (6) 0.21" (7) 0.13.
We obtained a family of TSDC curves which may be compared with the experimental curve. The values of the energy Et which have the best agreement between the theoretical and experimental curves and characterize the energy position and the depth of the localized states are presented in Table IV for A s z S 3 amorphous thin films. In Table IV
5•
-11
3X10 -11
1•
-11
1
2
i
200
240 T,K
280
320
FIG. 31. The DSTC curves in the range of the maximums E 2 - E5 obtained at the repetition of five cycles in the same conditions with the interval between cycles of 30 min.
Optical and Photoelectrical Properties of Chalcogenide Glasses
167
along with the depth of localized levels, the estimations of other parameters as well as the trap cross-section, the trap density and the peak broadening are presented. From Table IV it follows that for vitreous AszS3 in the energy range 0.35-0.80 eV from the valence band edge there exist four groups of localized levels. The presence of some groups of localized levels in the energy range 0.3-0.7 eV was also noticed for other amorphous semiconductors (Averjanov, Kolomiets and Lyubin, 1970; Kolomiets, Lyubin, Shilo and Averjanov, 1972b). The most broadened level is E 1 of about ~E = 0.12-0.16 eV, the levels E3 and E4 are less broadened and the level E 2 should probably treated as discrete. The cross-section of the centers is relatively small. For E 1 levels it is of order 5 • 10 -19 cm 2, and for other centers it is somewhat greater, remaining significantly less than 10-15 cm 2. These cross-section values suggests that the centers under considerations are neutral atoms, in agreement with the known fact of low activity of impurities in glasses. The greatest concentration of order 1016 cm -3 was found for the level group El, while the other shallower levels (Ez-E4) have less density (1013-1014 cm-3). An analysis of the energy diagram of the forbidden gap of vitreous As2S3 shows that the obtained experimental results do not frame in a simple model with energy tails of the bands for amorphous semiconductors, but according to theoretical considerations of Bonch-Bruevich (1971), in non-crystalline semiconductors there is a possibility of existence of some discrete levels. These results show that the theory of the amorphous semiconductors has to take into account the superposition of the quasi-continuous distribution of traps of some groups of localized states and some of them may be discrete. The influence of composition and doping with germanium, iodine and copper up to 2 at.% on the TSDC curves of vitreous AszSe3 were studied by Kolomiets et al. (1972b). It is remarkable that for pure AszSe3 on the TSDC curves two groups of localized levels situated at 0.31 and 0.62 eV appeared. Doping with germanium practically did not change the energy position of the spectrum of traps with the exception that the effective center of shallow traps shifted from 0.31 to 0.34 eV. By doping with copper on the TSDC curves besides the maximum situated at T - 295 K which is characteristic for pure AszSe3 an additional high and wide maximum situated at T = 340 K appeared. Doping with iodine leads to the apparition of a narrow maximum of highest intensity at T - 325 K and diminishing maximum situated at T = 295 K. The appearance of new localized states with the effective center situated at 0.68-0.72 eV as a result of doping with iodine and copper may be caused by the formation of some additional polymeric links in vitreous AszSe3. The investigation of the influence of the excess and deficit of selenium in the stoichiometric composition of the glasses A s - S e show that the introduction of the excess selenium determines the appearance of an additional weak maximum at T = 320 K which corresponds to the energy of 0.68 eV and the deficit of selenium leads to the appearance of a maximum of high intensity at T = 330 K which corresponds to the trap energy of 0.7 eV. The low-temperature maximum situated in the temperature range T = 130-140 K is changed very weakly by doping of AszSe3 and with deviation from the stoichiometric composition. The TSDC method, one of the more effective methods for studying the spectrum of localized states was also applied for other vitreous chalcogenide semiconductors. For
168
A. M. Andriesh et al.
example, doping the glass Ge3S2 up to 1 at.% Te leads to increase of the conductivity and the maximum of the TSDC curve is slightly shifted to the lowest temperatures. The multiple trapping model was involved for interpretation of the TSDC spectrum (Benyuan, Zhengyi and B izhen, 1987). In this case in the calculation of the TSDC curves the thermal emission of the captured carriers from the localized states into the conduction band, as well as the trapping and recombination processes were taken into account. It was shown that the structure of TSDC curves exactly reflects the particularities of the spectrum of localized states. The calculation of the TSDC spectrum in frame of the multiple trapping model for oL-Si:H is in good agreement with the experimental results.
2.2.
TRANSIENTPHOTOCONDUCTIVITY
2.2.1. Experimental Evidence Transient photoconductivity in amorphous semiconductors has received much attention because of its specific behavior determined by the wide distribution of the time constants controlling the photocurrent transients. Multiple trapping of charge carriers by localized states, which are quasi-continuously distributed in the gap, leads to well-known prolonged non-stationary processes such as dispersive transport and photoinduced transient optical absorption. One may expect that a similar non-equilibrium relation between the fractions of filled and empty gap states governs the photoconductivity kinetics by affecting trap-controlled recombination rates. For the vitreous semiconductors with low conductivity (101~ 12-1 cm -1) the transient photoconductivity in the long-time domain is determined not only by the activity of deep levels of the semiconductor but also by the current relaxation processes. These latter processes depend on the particularities of the carriers distributed and accumulated in the volume and in the vicinity of the contacts and play an important role, especially at low levels of the non-equilibrium conductivity. For this reason the photoconductivity relaxation is usually determined not only by the factors typical for photoconductivity (photon energy, light intensity, temperature) but also by the nature of the contacts, the strength and direction of the external electric field, etc. (Andriesh et al., 1977). At the beginning of the study of transient photoconductivity usually pulse light excitation by pulse lasers and flash-lamps were used. As most of the researchers noted, the form of the photocurrent transients was non-exponential and consisted at least of fast (10-3-10 -4 s)and subsequent slower (1-100 s)components. The fraction of the slow components decreased with increasing light intensity and temperature (Kolomiets and Lyubin, 1973). These experimental data indicated the existence of a wide distribution of relaxation times caused by multiple trapping of extra carriers in widely distributed gap localized states. As a typical example of such kind of photocurrent transients in Figure 32 a fast photoresponse decay in a-As2S3 is shown for flash-lamp pulse excitation (pulse duration 5 • 10 -4 s). The decay curve is normalized to the initial maximal value of the photocurrent. The dashed line indicates the exponential version of the photocurrent decay. The photoconductivity decay curves are typical for glasses and have a fast
Optical and Photoelectrical Properties of Chalcogenide Glasses '
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'
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0
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Time, s 0.0
0.5
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2.5
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3.5
FIG. 32. Fast photoresponse decay in vitreous AszS3. F --- 1017 c m - 2 s - l ; A -- 0 . 4 2 - 0 . 5 5 / , m . T = 409 K (1) and T = 380 K (2). Dashed curve (3) indicates the exponential version of photocurrent decay.
component of 1 or 2 ms in duration followed by a much slower portion. The initial fast portion of the decay has nearly exponential form with a photoresponse time Zd, determined as a logarithmic derivative of the decay (see Eq. (39)). Under simple assumption that this parameter characterizes the photoresponse time delay due to trapping (Adriaenssens, 1996) the initial portion of the decay may be used for probing the density of states in the gap. Measuring the photoresponse time in As283 at various light intensities (5 • 1014-1017 cm -2 s -1) in the temperature interval from 289 to 448 K Andriesh, Shutov and Iovu (1972a) found that in the interval from 0.3 to 0.75 eV from the valence band top the localized states are distributed exponentially p t ( E ) - - P 0 x exp(-E/A), wherep0 = 3.4 x 1019 cm -3 eV -1 and A = 0.052 eV. For different samples the values of P0 and A lay between 8 x 10 is and 102~ cm -3 eV -1 and 0.052 and 0.047 eV, respectively. For the related materials, for example, non-crystalline AszSe3 a quasi-continuous distribution of localized states was found between 0.4 and 0.75 eV (Kolomiets, 1969). Later Monroe and Kastner (1986) found in amorphous AszSe3 a power law decay Iph(t) oc t -~ extending over nine decades of time at T - 259 K. This result leads to the existence of an exponential density-of-states distribution extending from 0.3 to 0 . 8 6 e V above the valence band mobility edge. The exponential 1 - a = 0.48
170
A. M. Andriesh et al.
corresponds to the characteristic energy of the exponential density of states equal to 49 meV. This value is in close accordance with the slope of Urbach edge in amorphous AszSe3, supporting the interpretation as the distribution of states of the valence band tail. The study of the decay of photoconductivity in vitreous arsenic sulfide in the case of excitation with the light pulse of the ruby laser (hv = 1.78 eV -- 0.74 Eg) showed that the recombination of non-equilibrium carriers in As2S3 is characterized by the times of order 1 0 - 6 - 1 0 -5 s, which correlates with the values of ~---~ (1-2) x 10 -5 s determined from the kinetics of the photoluminescence (Shutov and Iovu, 1975). Typical examples of photoconductivity relaxation curves are presented in Figures 33 and 34 for vitreous AszS3 and AsSe depending on excitation wavelength, light intensity and temperature. The rise and decay rates increase when the photon energy of excitation and/or the temperature is raised. The photoconductivity relaxation in the long-time domain was described in detail for AszS3 by Andriesh, Shutov and Iovu (1974d) and Andriesh et al. (1977), for AszSe3Ge by Tsiuleanu and Tridukh (1980) and for AszSe3 by Arnoldussen et al. (1972), Kolomiets and Lyubin (1973) and Fuhs and Meyer (1974). The dependence of long-time photoconductivity kinetics on excitation wavelength and temperature in vitreous AszS3 and AszSe3 may be interpreted in frame of the model with participation of thermo-optical transitions. It was clearly demonstrated with the example of photoelectrical characteristics of the A s - S e system. The conclusion concerning participation of thermo-optical transitions in photoelectrical phenomena was made on the basis of analyzing the experimental results of photoconductivity spectra at different ,
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FIG. 33. The relaxation curves of photoconductivity for As2S3: (a) wavelength h (~m): (1) 0.5" (2) 0.548; (3) 0.6; (4) 0.645" (5) 0.702; (b) temperature T (~ (1) 72; (2) 98" (3) 136; (4) 172.
171
Optical and Photoelectrical Properties of Chalcogenide Glasses
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Time, s Time, s FIG. 34. Photoconductivityrelaxationin the As5oSe5ofilms at various intensities F (a) and temperatures T (b). Light is switchedon at t = 0 s and off at t = 26 s. (a)F (cm -2 s-l): (1)5.3 x 1011; (2)2.4 x 1012; (3) 1.5 x 1013; (4) 6.5 x 10 ~4. (b) T (K): (1) 289; (2) 341; (3) 393. frequencies by interrupting the incident light of excitation and also from the results of the kinetics of photoconductivity at different wavelength in the range 1.2-1.8 eV. The most peculiar feature of the photocurrent rise portion is the anomalous spike character of relaxation observed at certain conditions, when the steady state is reached after going over a maximum (Figs. 33 and 34). Time and again the overshot in the photoconductivity kinetics of chalcogenide glasses attracted attention of researchers and was observed in many materials (Kolomiets and Lyubin, 1973; Andriesh et al., 1977; Tsiuleanu and Tridukh, 1980; Andriesh, Arkhipov, Iovu, Rudenko and Shutov, 1983; Ganjoo and Shimakawa, 2001), AszS3 thin films (Andriesh et al., 1977; Andriesh, Arkhipov, Iovu, Rudenko and Shutov, 1983), AsSel.5Gex (Tsiuleanu and Tridukh, 1980), and AszSe3 (Andriesh et al., 1983). It was shown that the overshot amplitude increased relative to steady-state value as the excitation energy grew approaching the absorption edge and then reduced. In AszS3 the overshot appears when the excitation photon energy exceeds the optical gap. Sumrov (1978) used the spectral dependence of the overshot to determine the optical gap of the material (2.6 eV for AszS3 thin films). In most of the works the relation of the overshot with electrode effects was pointed out, i.e., the dependence of the behavior on the electrode material, on the value of the applied voltage and its polarity on the illuminated electrode, on the time storage of the sample in dark, etc. These observations indicate that some effects of charge accumulation and redistribution near the electrodes significantly affect the photoconductivity kinetics. The analysis of the overshot-type transient photoconductivity from this point of view is given in more detail in Kolomiets and Lyubin (1973), Andriesh et al. (1977, 1981) and Tsiuleanu and Tridukh (1980). Here we show that overshot behavior of the transient photoconductivity naturally follows from the trap-controlled recombination approach (Arkhipov, Popova and Rudenko, 1983) with no assumptions about existence of inhomogeneities in the bulk or at the contacts.
2.2.2. Theoretical Background Photoelectrical phenomena in chalcogenide glasses are traditionally considered in terms of charged-defect model (Mott et al., 1975), in which recombination is described as a tunneling process between metastable defect states.
172
A. M. Andriesh et al.
The kinetics of photocarrier generation and trap-controlled recombination is described by the following equation (Arkhipov et al., 1983; Arkhipov, Iovu, Rudenko and Shutov, 1985):
dp(t) pe(t) - G(t) - RPe(t)p(t ) dt ~1~
(47)
where t is the time, p the total carrier density, Pe the density of carriers in extended states, G(t) the generation rate, ~'R the lifetime of carriers in extended states before monomolecular recombination (MR), and R the constant of BR. Eq. (1) should be supplemented with the relation between the total charge carrier density and the density of carriers in extended states. Under the non-equilibrium (dispersive) transport conditions this relation takes the form (Arkhipov and Rudenko, 1982): d Pe(t) -- -~ ['r(t)p(t)]
(48)
where -r(t) is the lifetime of carriers in extended states before capture into the fraction of currently deep gap states located below the demarcation energy Ed(t):
= YONtLdEa(t) dE g(E)
r(t)
]1
(49)
where To is the free-carrier lifetime before capture by gap states, Nt the total density of localized states, and g(E) the density-of-states (DOS) energy distribution. The demarcation energy is defined as the energy of a localized state for which the carrier release time, (1/vo)exp(Ed/kT), is equal to the current time t, with v0 being the attemptto-escape frequency, T the temperature, and k the Boltzmann constant. This leads to the following expression for Ed(t): Ed(t) = kT ln(t0t )
(50)
Eqs. (48) and (49) combination kinetics is essentially controlled by the density-of-states distribution. It is generally believed that the energy distribution of shallow band-tail states in amorphous semiconductors features an exponential density-of-states function as,
Nt exp(- E
g (E ) - ~
(51)
-E-~o)
Solving Eqs. (47)-(50) with the density-of-states function given by Eq. (51) for a rectangular photoexcitation pulse of the duration To,
G(t) = 0,
-c~ < t < 0,
t > Tph,
G(t) = Go,
0 < t < Tph
(52)
yields formulae for rising, quasi-steady-state, and decreasing regimes of the free carrier density which are summarized in Table V where c~ = kT/Eo is the dispersion parameter. The transition from the recombination-free to MR-controlled photocurrent occurs at the time t = t R determined as, tR
=
1
- -
v0
- -
~'0
(53)
173
Optical and Photoelectrical Properties o f Chalcogenide Glasses
TABLE V EXPRESSIONS FOR THE DENSITY OF DELOCALIZEDCARRIERSpc(t) Trapping
MR regime
BR regime
Rise Steady-state
G0r0(v0t)~ -
G0ZR
( voroGo /R) l /2 ( pot) -(l-a)~2 N t ru, 9 ~a/(l+a)rG /RN2) 1/(1+~) ~. 0 0 ) I, 0 / t
Decay
poa(VoZo)~(t/Zo)-(1-~)
poa(VOrO)~(ZR/zo)Z(t/Zo)-(l+~)
a/Rt
-
Since the photocurrent is proportional to the free carrier density, iph "~ p c ( t ) , every equation listed in Table V corresponds to a specific time domain revealed in transient photocurrent curves. 2.2.3.
Comparison
to the E x p e r i m e n t
Photoconductivity kinetics was studied in AsSe, As2Se3 and As2Se3:Sn films deposited onto glass substrates by thermal flash-evaporation. The photocurrent was generated in a step-function mode by H e - N e laser light and was registered by an oscilloscope and a chart-recorder. A typical picture of the photocurrent transients is shown in Figure 34 for various intensities (a) and temperatures (b). In Figure 35 the rise and decay curves of Figure 34a are replotted in double-logarithmic scale to visualize the power-law portions of the transients discussed below. The characteristic time dependencies listed in Table V are seen in the growth and decay kinetics of the photocurrent transients shown in Figure 35a,b. P h o t o c u r r e n t rise (Fig. 35a). At short times, t < tR, the photocurrent rise is fully controlled by carrier trapping while recombination that is so far not significant yields iph-~ Go t~. At longer times, the rise depends on the excitation intensity. At low intensities, MR always predominates over B R such that the photocurrent monotonously increases and saturates on a steady-state level. At higher light intensities, a quasistationary portion of the photocurrent is observed after saturation followed by a 9 . (71/2t-(1-a)/2 decreasing portion of the transient, tph "-'0 , within which the BR mechanism (a) -8 < ~-9
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FIG. 35. Double-logarithmicplot of photocurrent rise (a) and decay (b) in the AssoSeso film at various light intensities F (cm -2 s-l): (1) 5.3 X 1011; (2) 2.4 x 1012; (3) 6.6 x 1012; (4) 1.5 x 1013; (5) 6.5 x 10 TM. Straight line portions are calculated with a - 0.67 (see text for details).
174
A. M. Andriesh et al.
is dominant. At even higher excitation levels the rise is entirely controlled by BR and the quasi-stationary portion of photocurrent is missing. At such levels of excitation, the photocurrent exhibits an overshoot (Figs. 33 and 34). A remarkable feature of the observed photocurrent transients is the overshoot, which, in terms of the multiple-trapping model, is due to non-equilibrium BR recombination whose intensity increases with the total carrier density. If this recombination mode is dominant the rate of recombination eventually gets high enough and, together with carrier trapping by states below the demarcation level, provides conditions for decreasing density of free carriers. Photocurrent decay (Fig. 35b). The decay kinetics depends on the density of photogenerated carriers at the end of the photogeneration pulse. If the total filling of gap states below the demarcation energy is not achieved, an initial portion of the decay will 9 -(1-~ where iph0 is the still be controlled by trapping. Within this portion, / p9h " ~ tph0t photocurrent at t = ~'ph.If the BR regime was not established during the generation pulse, i.e., at low excitation intensities, the starting portion turns into final decay along which iph "~ iph0t-(l+~). If the generation rate provided an intermediate for the BR regime, /ph" " ~ tph0t" - 1 , portion of the relaxation curve exists. The above-described kinetics is in good agreement with the experimental photocurrent transients shown in Figure 35a,b. Fitting these data yields the dispersion parameter ce = 0.67 for AsSe that leads to the characteristic energy of the density-of-states distribution E0 of 0.037 eV (Arkhipov et al., 1985). For As2Se3 and As2Se3:Sn the values of ce are 0.54 and 0.70, respectively (Arkhipov et al., 1983). The power-law photocurrent asymptotes calculated with ce = 0.67 are plotted in Figure 35a,b. The fact that the complex picture of the photocurrent kinetics can be described by a single parameter supports the model of trap-controlled recombination. The temperature dependence of the photocurrent kinetics also obeys the model predictions. Enhanced carrier trapping in amorphous semiconductors delays the onset of recombination and increases the time tR. Since the carrier release time exponentially decreases with temperature, the transition time tR exponentially shifts to shorter times. The smallest value of t R = 10 -2 S was observed in the stoichiometry composition As2Se3. This time is about 3.3 s in AsSe films containing excess As atoms and becomes even longer (up to 10-15 s) in As2Se3:1 at.% Sn films. In contrast to the prominent insensitivity of glassy semiconductors to doping, tin impurity strongly affects the dispersive transient photoconductivity due to the enhancement of carrier trapping by deep localized states. 2.2.4.
Effect of Impurity and Composition
It is known that impurities weakly affect electrical characteristics of chalcogenide glassy semiconductors (GCS) if they are introduced in the course of thermal synthesis. However, 'cold' modification of CGS by some impurities in the absence of thermal equilibrium creates electrically active centers (Kolomiets and Averjanov, 1985). Tin impurity, introduced into GCS during thermal synthesis, was found to have strong effect on the transient photoconductivity characteristics of thermally deposited a-AszS% and a-AsSe films although the equilibrium photoconductivity remained almost unchanged. This effect is caused by enhanced carrier trapping by relatively deep-localized states that
Optical and Photoelectrical Properties of Chalcogenide Glasses
175
are apparently created in GCS upon tin doping. Enhanced trapping leads to slower photocurrent rise, delays the onset of recombination in doped samples, and increases the lifetime of the photoexcited state after the inducing light is switched off. Tin was introduced in an amount (x) of 0.1-3.5 at.% into AszSe3 and of 1-10 at.% into AsSe during standard thermal synthesis of the materials prior to sputtering. Thin film (1.0-10.0/xm) samples of sandwich configuration were obtained by flash evaporation in vacuum on glass substrates held at 100 ~ Photocurrent excited by a H e - N e laser was recorded with a time constant not exceeding 0.3 s. The light intensity, typically of F0 = 1015 cm -2 s-l~ could be decreased with calibrated filters. A remarkable feature of the photocurrent transients, the overshoot, is absent in the increasing section of Sn-doped CGS, which, in terms of the multiple-trapping model, indicates that the trapping and MR are strongly enhanced, and solely those processes balance carrier generation. Tin doping also slows the photocurrent decay after switching off the inducing illumination as shown in Figure 36. While the decay pattern in undoped materials strongly depends upon the photogeneration intensity, this dependence is weak in tin-doped samples (curves 1-3). A faster relaxation of charge carrier density in an undoped sample in the interval 1-10 s can again be explained by more efficient MR, at low-excitation intensities, or B R, at higher intensities. This is also in agreement with photocurrent rise kinetics with the current overshoot disappearing at lower photogeneration intensities. The curves plotted in Figure 37 reveal an opposite effect of changing temperature on the photocurrent decay kinetics. Increasing temperature gives rise to a substantial increase of the decay rate in the tin-containing films (curves 1- 3) while the temperature effect on the decay in undoped samples is comparatively weak (curve 4-6). Increasing temperature eliminates the effect of tin impurity. Constant bias illumination, acting even after the main excitation is removed, has a similar effect. Prolonged hyperbolic photocurrent decay as well as a weak light-intensity and quite strong temperature dependencies indicate that trapping by deep states dominates tindoped samples. Since enhanced trapping suppresses recombination, the time domain of
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FIG. 36. Photocurrent decay in As2Se3:1 at.% Sn (1-3) and As2Se3 (4-6) samples after photoexcitation with different inducing light intensities F, cm -2 s-l: 1,4-1015; 2,5-1014; 3,6-1013. T = 290 K.
176
A. M. Andriesh et al.
0.1
i9:i'
9
0.01
\
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|
|
50
5
Log (t, s) FIG. 37. Photocurrent decay in As2Se3:l at.% Sn (1-3) and As2Se3 (4-6) samples at different temperatures T, K: 1-290; 2-313; 3-345; 4-288" 5-304; 6-341. The excitation intensity F = 1015 cm -2 s -1.
relaxation is extended in tin-doped films. From the kink on curves 1-3 (Fig. 36) one can estimate the demarcation energy at the time tR and the total density of trapping states in doped materials. For ~'0 = 10-12 s and v0 = 1012 s -1 Eq. (50) yields the demarcation energy Ed ~ 0.85 eV and a very high density of localized states Nt ~ 10-2Nc, where Nc is the density of extended states. The effect of constant bias illumination also supports the concept of delayed recombination in AszSe3:Sn samples as additional illumination facilitates the decay by accelerating photoionization and recombination of localized carriers. The increase of the lifetime of non-equilibrium holes for AszSe3 samples with small additions of tin also follows from transient photocurrent measurements in the 'time-of-flight' configuration. Some useful information about possible nature of localized states created in AszSe3 upon tin doping can be obtained by the M6ssbauer spectroscopy (Seregin and Nistiriuc, 1991). Embedded in the AszSe3 glass matrix tin is tetravalent, Sn 4+. All four valence electrons of tin participate in chemical bonds with the matrix atoms and do not affect electrical properties. However, in unannealed films some tin atoms are present in the form of divalent tin, S n 2+ and only 5p electrons participate in the formation of chemical bonds while 5s electrons can play the role of deep donors. Another possibility is photo-induced charge exchange in tin impurities Sn 4+ ~ Sn 2+ with electron trapping by tin-induced centers. Since tin doping suppresses carrier recombination over several seconds or even several tens of seconds, the doping can be an effective tool for increasing the photoconductivity of GCS-based electrographic devices for recording optical information. Differences concerning the form of the decay curves of photoconductivity were also observed for the (AszS3)x-(SbzS3)l_x system, which are significantly different from those for As2S3. In general, on the decay curves of alloys a specific slower hyperbolic portion appeared, which has strong dependence upon the light intensity and temperature and is absent in AszS3. This peculiarity is attributed to the group of localized centers of high density caused by introducing Sb2S3. This group of localized states is revealed in the form of a shoulder around 1.3 eV in the spectra of photoconductivity and in the decay curves of photoconductivity of the vitreous alloys. In the chalcogenide alloy system
Optical and Photoelectrical Properties of Chalcogenide Glasses
177
As2S3:Ge the photoconductivity decay rate was found dependent on the composition as well, this time determined by the variation structure ordering due to the change of structural units. The effect of retarding decay rate was observed as a result of ~/ irradiation of AszS3 (Andriesh et al., 1981). 2.2.5.
Negative Transient Photocurrents in Amorphous Semiconductors
As the charge transport in amorphous materials is controlled by traps, at any moment a significant fraction of the carriers is trapped. The dipole moments of the filled traps may be considerably different from those of empty traps. As a result, the dielectric permittivity of the material becomes dependent on the density of trapped carriers. In a time-of-flight experiment, during the packet movement, the trapped-carrier density is changed, and as a result, the dependence of the dielectric permittivity on time and coordinate appears. The transient dielectric constant causes an additional displacement current, which may be negative relative to the electric field direction (Arkhipov and Rudenko, 1978). In a certain time interval, this additional current can dominate, and as a result, the total current in the sample becomes negative. Note that the polarization current may be due both to traps distributed in the volume and to surface traps. The results of negative current observation in time-of flight experiments on amorphous 0.55AszS3:0.45SbzS3 is presented. The experiments are carried out under the conditions of the dispersive transport regime (see Arkhipov, Iovu, Rudenko and Shutov, 1979). It is shown that the polarization of volume traps alone is unable to describe the observed values and the behavior of the negative transient current. This fact shows the significant role of surface traps in the mechanism of negative current generation. Consider a sample of thickness L, sandwiched between two electrodes, which build up an electric field F in the bulk of it. At a moment t -- 0 near the anode (x -- 0) a sheet of holes is injected by light with the surface density tr. Owing to the electric field the carriers drift to the cathode at x -- L. During the drift, the carriers take part in trapping processes and change the dipole moments of the traps. This leads to the time-dependent local variation of the dielectric constant of the material e(x, t) -- eo + 4~rKo
o
O(x, t, E)dE
(54)
where x is the coordinate, t the time, E the trap energy, e0 the equilibrium dielectric constant, p dE is the density of carriers trapped in the traps within the energy interval from E to E + dE, and K0 is the coefficient characterizing the change of the dipole moment of the traps due to capture of carriers in them. The detailed theoretical description of the effect of the polarization effect on the transient current is given in Arkhipov, Iovu, Iovu, Rudenko and Shutov (1981). The experimental dependence j versus t is presented in Figure 38. As it can be seen from the figure, the negative current portion occurs at t >> tT, where tT is the transit time. In this time domain the distribution of carriers in the sample is nearly uniform (Arkhipov et al., 1979), and in this case the transient current, with account of the polarization effect, takes the form: j(t) = [(eLl2) - KoF][-dp(0 , t)/dt]
(55)
178
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A. M. A n d r i e s h et al.
102
100 ",-~
100
102
10-3
10-2
10-1
10~
Time, s FIG. 38. Transient negative photocurrents for Al-(As2S3)o.55-(SbzS3)o.45-A1, E -- 4.55 x 105 V/cm. Temperature, K: 1-293, 2-328, 3-343, 4-373, 5-403.
where p(x, t) is the total density of carriers in localized and extended states. It is seen from Arkhipov et al. (1985) that the appearance of the negative current in a sample should require the existence of the dipole moments •0 F of the length comparable to L. The observation of negative current may be due to the polarization of the surface traps, located near the rear contact x - L. The negative transient currents have been obtained in amorphous films 0 . 5 5 A s 2 8 3 : 0.45Sb2S3 in time-of-flight experimental arrangement. Thin-film samples (L-- 3.3/~m) obtained by vacuum deposition and supplied with aluminum contacts were used. The transient current was excited by a short (1.5 ~s) pulse of strongly absorbed light. The measurements were made in the temperature interval from 20 to 130 ~ with electric fields from 9 x 106 to 6 x 107 V m-1. A typical experimental time dependencies of the transit currents are shown in Figure 38. Over the interval t << t T the usual curve for the dispersive transport currentj(t) is seen (see, for example, Arkhipov et al., 1979)" over the initial interval t << t T the current decays as j oct -1+~, and over the 'final' interval tT << t << to it decreases asj oct -1-~, where a i s the dispersive parameter. But subsequently the current drops faster and changes sign at t - to. Over the negative current portion a minimum j - j, is observed at t - t,, after which the current decreases in value, remaining negative. The theoretical results are in good agreement with the experimental data (including temperature and electric field dependence) at Es - 0.77 eV, where Es is the characteristic depth of the trap energy in the layer of traps near the rear sample surface x - L. To give rise to negative current, the surface traps should lie deeper than that of the bulk traps. The condition to >> tT is provided
Optical and Photoelectrical Properties of Chalcogenide Glasses
179
by the small value of the parameter (KoF/eL), which presents the ratio of the trap dipole length to the sample thickness. The energy Es controls the decrease in absolute value of the negative transient current after t = t, by the lawj cc t-l-~v/Es ~ (see Fig. 38).
3. Chalcogenide Glasses in Photoelectric Information Recording Systems 3.1.
CHALCOGENIDEGLASSES FOR INTEGRATED AND FIBER OPTICS APPLICATION
It is quite clear that multifunctional optical integrated devices can be fabricated on the basis of monocrystalline semiconductor hetero-junctions. Such devices require planar waveguides for connection of different integrated elements of devices. Among the large groups of materials chalcogenide glasses have many properties which make them absolutely suitable for realization of such role. The thin-film waveguides (TFW) are known to be one of the important elements in the integrated optical circuits, meant to accomplish the optical signals transmission without losses and also perform the wavelength division, multiplexing and de-multiplexing of optical channels, the optical switching, deflection and adulation, as well as the connection of optoelectronic and microelectronic circuits. The materials for the TFW should meet the following requirements: high optical transparency, excellent boundaries and high refractive index magnitudes. Although there are many materials with the above-mentioned properties, the chalcogenide glasses present a special interest as a new and promising material for TFW production. These materials are known to possess large refractive index magnitudes (n = 2.5-3.0) and high transparency in a wide spectral range from 0.6 to 14/~m. Chalcogenide glasses are also characterized by a significant acousto-optical factor and by relatively small acousto-optical attenuation. Especially important for integrated optics is the fact that chalcogenide glass properties mentioned above are well combined with the unique possibilities of the optical images phase recording, including the holograms with a high resolution capability. This fact creates favorable premises for constructing strip waveguides on the basis of TFW, as well as for constructing grating structures and other integrated optics functional elements (Andriesh, Ponomari, Smirnov and Mironos, 1986). The first utilization of chalcogenide thin-films as planar waveguards show very high optical losses. Later research and more successful choices in the composition of waveguides materials offered the possibility to obtain thin-films waveguides with relatively small optical losses good enough for their utilization in integrated optics. The arsenic selenide and the alloys on their base, as well as the germinate glasses are thought to be the most suitable materials for such waveguides fabrication. The optical losses in TFW based on As2S3 have been estimated to be 3 - 5 db cm-~ at 0.63 m wavelength and less than 1 db cm-~ at 1.15 m wavelength. The optical losses depend not only on the kind of material and substrates but also on used technology, wavelength range, and number of modes. The last dependence is presented in Figure 39a. The investigation of AszS3 TFW optical properties using waveguide method allowed for the first time revealing of refractive index anisotropy in amorphous arsenic sulfide
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FiG. 39. (a) The dependence of absorption coefficient versus mode number; (b) dependence of AoLversus irradiating light intensity for different mode numbers. films. This conclusion was made on the basis of TE and TM spectra measurements at 0.63 ~m wavelength. The difference (n 1 - - n 2 ) was about 10 -2 for samples with waveguide thickness less than 1/.tm. We believe that this optical anisotropy is caused by a substrate orientation effect during the film deposition process that leads to the appearance of strained regions in the vicinity of the substrate surface. As mentioned above, the optical losses of waveguides may be changed by lateral illumination. The effect depends on the intensity of the lateral light, as shown in Figure 39b. Of course, the dependence is different for different mode numbers. The mechanism of the light-induced effect can be understood in terms of the electron rearrangement on the trap levels and photostructural phenomena. Structural changes are very expressive when chalcogenide thin films are exposed by CO2 laser irradiation. The experimental investigation was performed by A. Popesku together with the Italian scientists M. Bertolotti, A. Ferrari and others (Andriesh, Bulgaru, Malkov and Verlan, 1993a). The chalcogenide glasses' peculiar ability to change their refractive index under the influence of external factors (optical and X-ray radiation, electron beam) can be used in producing the reflective grating filters, the information optical channels, multipliers and demultipliers with various channel frequency (Fig. 40). By means of the chalcogenide glass TFW, one can accomplish the electro-optical, acousto-optical, and photo-optical modulation of light. The electro-optical modulation
FIG. 40. Schematicillustration of diffraction gratings (a) and channel frequencies mixers (b) in waveguides.
Optical and Photoelectrical Properties of Chalcogenide Glasses
181
in chalcogenide glass TFW relies on the ray double refraction phenomenon noticed in the arsenic sulphide bulk samples. The acousto-optical modulator is fabricated on the basis of TFW, the AszS3 layer of which is deposited on the Li NbO3 substrate. The chalcogenide glass-based TFW can be used for the construction of light-guided switching modulators. These waveguides can also have an application in the optical radiation recording. The waveguide photodetectors, for instance, are made by depositing onto glass substrates the chalcogenide glass layers of two different compositions, one of them being fitted with an electrode. Especially interesting is the case when films are irradiated by short light pulses with hu > Eg. The optical hysteric's phenomenon has been observed under interband excitation of thin films of the compounds As-Se, A s - G e - S e , and As-Ge-S. The chalcogenide glasses' peculiar ability to change their refractive index under the influence of external factors (optical and X-ray radiation, electron beam) can be used in producing the reflective grating filters, the information optical channels multipliers and demultipliers with various carrier frequency. At last, let us note that the chalcogenide glass TFW can find an application in the bulk waveguide hologram recording by using the superficial light waves. The most prospective applications of the chalcogenide fibers rely on their potentially low optical losses in the middle and far-IR wavelength region. The chalcogenide glass waveguide-associated transmission of IR radiation might become useful for optical communication systems, particularly for detection devices registration systems; for energy supply to cooling detectors; for welding and soldering; for local heating of materials, and for surgery purposes. Lightguides on base of chalcogenide glasses are thought perspective for the development of highly sensitive pressure and temperature sensors, for the production of coupling assemblies and, particularly, for the fabrication of planar and cylindrical waveguides matching devices. In order to demonstrate how large the possibilities of application of Chg glasses fibers are afferent in different optical devices we will take two examples: (a) fiber optic displacement sensor with modified configuration and (b) variable fiber optic attenuator controlled by light. (a) Fiber optic displacement sensor. Fiber optic technology offers the possibility for developing a variety of physical sensors for a wide range of physical parameters. Employment of optical fiber samples for development of optical fiber sensors allows obtaining very high performance in their response to many physical parameters (displacement, pressure, temperature, electric field, etc.) in comparison with conventional transducers. The main advantages of fiber optic sensors lie in their full dielectric construction, giving electrical isolation, immunity against electromagnetic fields, small dimensions, and compatibility with optical fiber technology. Novel approaches based on sensor-oriented technology are very promising for development of high-performance fiber sensors. Depending on the deformer design and materials, it is possible to make acoustic, magnetic, electric, temperature, acceleration, displacement sensors, etc. Fiber optic displacement sensors may have different important uses which exploit their nonelectrical nature. For example, as vibration monitors in generators, the fiber sensors guard against damage of expensive equipments, and they are immune to the high electrical noise that plagues piezoelectric vibration sensors. Also, in explosive atmosphere media (e.g., in mines) fiber sensors could safely monitor the vibration of equipments.
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It is well known that when an optical fiber is bent, its transmission loss increases as some of the light propagating along the fiber is radiated out. Microbending along the axis of the fiber causes mode changing. Periodic perturbations of the fiber axis result in strong intermodal power transfer when the period of perturbation corresponds to the difference in propagation constants of interacting modes. Consequently, the power lost at the propagation of radiation modes is at a maximum when the fiber spatial bent frequency equals the difference of propagation constants between the propagation and radiation modes. Authors have proposed a modified sensor configuration based on clad modes detection. The compact model of fiber-optic displacement sensor was developed. Its schematic illustration is presented in Figure 41. It consists of a diode laser, a photodiode, an electronic package and a plate. A diode laser is coupled to a multimode transmitting fiber through a standard optical connector. The transmitting fiber, of about 10 m long, is connected to a segment of the sensor fiber. The electronic package includes the power supply, the preamplifier, an A/D converter, and a digital display. (b) Fiber optic attenuator. A novel type of variable fiber-optic attenuator utilizing photo-induced absorption effect in chalcogenide glass fibers has been fabricated. Attenuation is controlled by the level of lateral light illumination of the fiber. Optimal composition of glass material and empirical relations were found. The optical transmission of the fiber was controlled by a weak flux of lateral light over a wide dynamic range. The attenuating light with photon energy corresponding to midgap energy range of ChG was launched into the input face of ChG fiber (Fig. 42). When illuminating the fiber literal surface with band gap light the intensity of attenuating light at the output end of the fiber decreases from its initial value I0 (in the dark) to a new one (I). The photo-induced absorption coefficient (PA) Ac~ (cm -1) was determined as follows: Ac~ = L-1 In I o/I, where L (cm) is the length of illuminated segment of the fiber with diameter d.
FIG. 41. The performances of the fiber-optic displacement sensor. (1) Range of displacement amplitudes: 0-60 ~m; (2) sensitivity: 0.1 mV/~m; (3) dynamic range: --~55 dB; (4) resolution: 0.1 ~m; (5) deviation from linearity: --~6%;(6) error 2.8%.
Optical and Photoelectrical Properties of Chalcogenide Glasses
183
FI6. 42. The model and some specifications of the fiber optic attenuator. Wavelength range (As-Ge-Se fiber): NIR (0.8-1.8 txm); Safe energy level: 1 kW/cm2 CW; Aperture (green-lens): O 1.5 mm; Attenuation range: -20 dB; Attenuation resolution: ~--1dB; Insertion loss (without AR coating): 40%; Polarization light: non-polarized; Time change of attenuation coefficient: --~3 s; Dimensions: 5 x 2 • 2 cm2; Weight: - 30 g.
3.1.1.
High-resolution Solid-state Image Devices Based on the M e - C h G S - S i 0 2 - S i Structures
The optoelectronic methods of the processing of information in the form of images, holograms and bits are of great interest due to their application in development of the new generation equipment of computers with high-speed processing of information and in other fields of techniques such as TV, etc. The chalcogenide glass semiconductors thin films possessing the properties such as high sensitivity, low conductivity, wide range of spectral sensitivity, homogeneity, and high resolution are promising for applications such as active elements for optoelectronic information processing. The reversible optoelectronic devices based on metal (Me)-chalcogenide glass semiconductors (ChGS)dielectric (D)- semiconductor (S)-(MeChDS) structures were developed and used for writing and readout of the optical images, as a new type sensor of radiation in wide range of energy, and as X-ray solid state image devices (Andriesh et al., 1981, 1993b; Andriesh, Malkov and Verlan, 1993a, 1994; Andriesh, 1998). The semiconductor structures Me-Asz(S,Se)3:Sn-SiO2-Si were used for writing and readout processes of the optical images with high resolution. The above-mentioned structures make the positive and negative image possible. The devices work in regimes of both accumulation of the small signal and real time. It was found that the quantity of accumulated charge versus light intensity has a linear dependence, Q = Qmax(Ce-k- flD) where D = It is the dose of radiation. Some type of signal recording were studied and developed by measuring the photo-emf, displacement photocurrents and accumulated charge, which allow proposing different type of sensors of radiation. The space functional separation of the recording and readout allows to carry out undestroyed repetition readout of the image and other operations (Fig. 43). During projecting the object image on the surface of the structure under simultaneous action of the voltage, the charging of ChGS by positive or negative charge exists. The maximum accumulation of charge occurs at the SiO2-ChGS interface. Its quantity depends on absorption light dose. In this way, the light image is memorized by the structure in a relief charge kind. This relief of captured charge induces, in Si substratum through dielectric SiO2, the same charge relief of opposite signals in ChGS or otherwise the relief of the surface potential. By connecting the top and down contacts by electric circuit
184
A. M. A n d r i e s h et al.
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FIG. 43. The schematic energy-band diagram of Me-ChGDS structure during the positive charge writing process and the scheme of writing and readout of the image. (1) He-Ne laser (A = 0.6328 Ixm); (2) Modulator; (3) Condensers; (4) First galvanometer mirror; (5) Second galvanometer mirror; (6) The object; (7) Source of illumination; (8) Me-ChDS structure: (a) semitransparent Al-electrode; (b) AszS3(AszSe3) layer; (c) SiO2 layer; (d) Si wafer.
and scanning the surface from top electrode side by laser beam with energy of the quanta
Egl < h~, < Eg2, where EgX and Eg2 are the values ofthe forbidden gap ofthe Si and ChGS, respectively, we obtain the electric impulses, whose amplitude depends on quantity of the charge that is accumulated in ChGS layer. In this way we obtain the invisible image that is written through charge relief. The space separation of the writing and readout processes of the visible light permits us to provide the repeated readout of one image. Schematic energy band diagram of Me-ChDS structure during the positive writing are shown in Figure 39. In positive charging case the volume of AszS3 near the AszS3-SiO2 interface has positive charge and induces the negative charge in Si through SiO2. As a result the band profile bends down until they attain the surface inversion state of conductivity, the creation of p - n junction. The creating of the p - n junction in Si determines the photo-emf saturation. The readout of the relief image is measured by two photoelectric methods, namely: 1. The method of measuring the photoelectromotive force (photo-emf) under illumination of the structure with light from the energy range described above. 2. The method of the observation of the recharging photocurrents under illumination of the structure in case 1.
Optical and Photoelectrical Properties of Chalcogenide Glasses
185
The readout of the information about the optical image by photo-emf method carried out by optical scan system is depicted in Figure 39. The impulse signal of the photo-emf (Ui) generated by the carrier photoexcited in the space charge range of Si were obtained with the help of point scan of the H e - N e laser (A = 6328 A) and consequently were registered. Regarding charge in ChGS, one can make the same conclusions from the flat bands shift but in this case one cannot carry out the local readout when we use the whole electrode on the area of the structure. If in the structure the big electric charge is memorized, which causes depletion of the Si surfaces, the Ui signal is observed without external potential. The value of the maximum signal was equal to 0.3 V. The ratio Uimax/Uiminis about 100. The complete cycle of the writing and readout of the image is necessary to illuminate the whole surface of the top semitransparent electrode with uniform integral light. This procedure leads to the complete erasing of information. Then the polarity of the external voltage source is changed to opposite and by illumination through object the image writing takes place. The device permits to obtain either the positive or negative image. The readout by measuring the recharging photocurrents is more promising for practical applications as compared with photo-emf. The photocurrent readout consists of applying the depletion voltage impulses and illuminating the light impulses. The maximum frequency of readout in this method is limited by the time of transition of the depletion voltage to a steady state in semiconductors and we attain some MHz. The spatial resolution is limited by the laser scan beam diameter of used scan system (in our case it was 30/,m). It is assumed that the resolution of Me-ChDS structures is analogous to one of the optoelectronic memory element which is more than 108 bit cm -2. The use of well-focusing laser beam and more fast and precise electrooptic or acousto-optic scanning deflectors makes this possible. Experimentally obtained parameters of the writing, the storage and readout of the Me-ChDS structure can be improved by selection of amorphous semiconductor with more dark resistivity and photosensitivity. For above-mentioned effects of the writing and readout of the information we can propose the following application: 9 The writing of the low intensity signal in time of the accumulation; 9 the processing of the images in the real time regimes of the observation under normal and big light intensities; 9 for carrying out practical work in the wide range of the radiation spectrum as the visible, UV- and X-ray ranges; 9 the realization of the bit regime processing of information; 9 for carrying out different operations under image as the making of positive or negative images, the measuring of sum and difference of the image and their areas, the recognition of the image and other operations such as the formation of the contour of the object, the obtaining of the moving object trajectories, etc.
3.1.2. Registration Media and Holographic Information Technologies The progress of science and engineering presents new requirements to holographic recording media: reduction of recording time, high stability, and possibility of recording over large areas. These requirements are partially satisfied by registration media based
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on CHGS. At the same time the modem development of the holographic techniques require recording holograms and reconstruction of image in real time. Because were proposed new recording structures based on ChGS and new methods of holographic recording. The change of the surface relief in the 'sandwich' amorphous thin film structures under simultaneous action of the illumination and applied electric field was established by Andriesh and Tsiuleanu, (1976), Andriesh, Shutov and Tsiuleanu (1976b) and Andriesh, Iovu, Bivol and Khanchevskaya (1995). The nature of the electrostimulated and photo-induced surface microdeformations in M e - C h G S - M e thin film structures is explained by a sharp increase in density of the photocurrent in the illuminated portions of the specimen and a strong heating of the ChGS up to the Tg temperature. As a result the viscose forces in the illuminated areas are relaxed and under the action of the electrostatic forces the optical properties (reflectance and transmission) of the recording structure are changed yielding the effect of an optical image recording. Because the deformation grains lie strictly along the illuminated bands of the interference picture, we may also record holographic information. For storage and treatment of massive information (image analysis and transformations, search information in data banks, multichannel signal treatment, etc.) the holographic methods are most promising. Use of the laser beams gives the possibility to record the information on very small areas of memory media. The sizes of these areas are limited by the light diffraction. These methods provide density storage of information up to 1012 bit cm -2 and a high velocity of informative treatment. The structure of recording media based on M e - C h G S - M e structures and the setup of the recording procedure are shown in the Figure 44. The microholograms were registered on the recording structures by means of interference of two H e - N e laser beams 1 (A -- 6328 nm) with a power of 10 mWt when the electric field 2 is applied. As recording media we elaborate new M e - C h G S - A 1 structures and heterostructures based on amorphous thin films. The latter are more effective, because they exhibit low conductivity in darkness and high photoconductivity due to barrier effects and has a larger spectral sensitivity range as compared with single layer structures. The proposed recording structure consists of a transparent isolator substrate 3 (glass or polymer), first -~ .___.___ E\ - . I
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Optical and Photoelectrical Properties of Chalcogenide Glasses
187
semitransparent electrode 4 (ITO, SnO2, In203), the photosensitive layer from an amorphous chalcogenide semiconductor 5 (AszSe3, AsSe, etc., or a heterostructure such as InP/AszSe3, GaP/AszSe3, Si/AszSe3, Ge/AszSe3, SbzSe3/AszSe3, T1SbSeffAszSe3 InzS3/AszSe3, InzSe3/AszSe3, Se/AszSe3, etc.), and the second top semitransparent electrode 6 from A1, Au, Sn, Ni, etc. The sensitivity of the recording structures and the diffraction efficiency of elementary holograms depend on the strength and polarity of the electric field, light intensity, electrode material and density of the recorded information. The microscopic studies of the dynamics of the microdeformations development show that applied electrical field under exposure leads to appearance of the first sign of deformations. The size of the deformations depends on the strength of the electric field, spatial resolution and light intensity. Figure 45 shows the dependence of the grain size of the microdeformations versus the spatial resolution of the diffraction gratings recorded on the photosensitive structure p-InP/AszSe3-A1. The deformation grains which appear as a result of an interferential picture lies strictly along the illuminated bands. Its dimensions depend on the stretch of the electrical field, as well as on the density of recording information. Increasing the capacity of the recording optical information logarithmically decrease the sizes of the mechanical deformations. The diameter of the mechanical deformations d depends on the spatial frequency of the diffraction grating u according to the expression d--~ A u -1, where A is a coefficient depending on the stretch of the electric field E, light intensity W and recording time t: A = f ( E , W,t). Increasing the spatial resolution v from v = 1000 to 16 mm -1 also increases the size of the microdeformation grains from 0.65/xm up to 35/xm, respectively (E = 4 x 105 V cm -1, W = 0.32 Wt cm -2, t = 3.5 s). So far as the microdeformations appear on the surface portion of the specimen with high photoconductivity and mainly when negative polarity is applied to the top aluminum electrode, its evolution may be controlled by both the electric field and light intensity. In order to determine the possibility of the hologram recording in the real time scale on the structure Me-InzS3/AszSe3-A1, growth of the diffraction efficiency versus the exposure to monochromatic irradiation at various values and polarity of the applied field was investigated. In general, the kinetics of the diffraction efficiency presents an S-like curve, the form of which is determined by the electrical and photoelectric characteristics of the investigated heterostructures. Because the maximal values of the photocurrent are reached in the time interval At = 0.001-0.1 s, in order to reach the maximal deformation velocity it is necessary to apply an electric field pulse after illumination in this time interval.
FIG. 45. The picture of the surface of the registration structure with the diffraction grating: (a) v -- 20 mm-1, d = 30 Ixm; (b) v = 200 mm-1, d = 3 jxm.
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In fact, the microscopic investigation of the dynamic evolution of the microdeformation allows one to conclude that the first sign of microdeformation appears with some time delay as soon as the electric field and illumination are applied. The time delay may be reduced if during the exposure a series of voltage pulses of the electric field E 1 and E2 of different amplitude (E2 > El) are applied with the time interval At. It was also found that the time delay may be essentially reduced, and the sensitivity and the diffraction efficiency of microholograms can be increased if, during the recording time, an additional incoherent light of definite value is applied on the surface of the specimen. In the case when the light intensity F of the structure surface increases from F -- 0 up to F = 900 Lx, the recording time of the elementary holograms may be reduced from 0.9 to 0.5 s, respectively (Fig. 46). This effect may be explained by the increase in photoelectric sensitivity of the recording structure because the current density increases and an additional stimulation of microdeformations evolution of the exposed areas take place. The current density increases as a result of sharp increase in the drift mobility and of reduction of its activation energy because the deep localized states are occupied as a result of an additional illumination. For example, in the AszS3 thin layers it was found that the additional illumination increases the conductivity and the drift mobility by a factor of about two. A considerable increase of the diffraction efficiency and sensibility has been reached in the experiments when a series of the applied field pulses of different polarity were applied to the recording structure. The recording process of the elementary holograms was performed on the A1-AszSe3-A1 and AI-InzS3/AszSe3-A1 recording structures by a successive applying of negative voltage pulse to the top aluminum electrode, and a positive polarity pulse of the duration At -- 0 . 0 1 - 1 0 . 0 s during the continuous projection of the image. Figure 47 shows the dynamics of the diffraction efficiency in the case when some successive negative and positive voltage pulses (U -- 30 V, At = 1 s) were applied to the AI-InzS3/AszSe3-A1 heterostructure.
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Optical and Photoelectrical Properties of Chalcogenide Glasses -~
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It is seen that at the negative polarity on the top Al-electrode, when the optical information is recorded as a result of the effect of the electrostimulated deformation of the surface of the specimen, the recording rate is low and the m a x i m a l value of the diffraction efficiency is about r / = 1.5%. The increase in the recording rate when the polarity of the applied field is switched (tsw) leads to the general growth of sensitivity up to S = 5 x 103 cm 2 J-1 and of the diffraction efficiency up to r / = 6% as a result of an additional electrostimulated chemical interaction of the top Al-electrode with the AszSe3 thin film. The sharpest diffraction efficiency growth takes place after the voltage at the top a l u m i n u m electrode is switched from negative to positive polarity. If during the first cycle of voltage pulses the m a x i m a l value of the diffraction efficiency is not reached, then this procedure of the holographic information recording may be p r o l o n g e d by applying a new series of the v o l t a g e pulses of a l t e r n a t i v e polarity. S o m e p a r a m e t e r s of the electrocontrolled registration m e d i a are presented in Table VI.
TABLE VI THE PARAMETERS OF THE HOLOGRAPHIC RECORDING STRUCTURES 1.
2. 3. 4. 5. 6. 7. 8. 9. 10.
Spatial resolution Recording wavelength Reading wavelength Writing time Diffraction efficiency Sensibility Storage time Size of one hologramme Capacity of one hologramme Processor speed (R-R type operation)
> 1000 mm -~ 0.48-0.63 ~m 0.63-0.87/~m 40-100 ms 5- 6% 6 x 103 c m 2 J- 1 Unlimited 0.8 mm 5000 bit 6 x 105 op/s
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An analysis of the electrical and photoelectric characteristics of the p-InP/As2Se3-Me and Me-InzS3/AszSe3-A1 heterostructures show, they also strongly depend on the electrode material and allow us to conclude that the recording process of the optical information is determined by both, electrode and volume properties of the chalcogenide thin film. These results may be confirmed by the experiments where different materials of A s - S e system were used as amorphous layers including alloyed materials with Sn and Ge impurities, changing in the Tg value in a wide range. The results of the currentvoltage, lux-ampere and photoelectric characteristics of the recording structures with different electrodes allow one to state that the structures with the bottom electrode of SnO2, Cr and Ni are more effective for the recording process. The increase in recording rate of microhologram when the polarity of voltage pulse is switching correlates with the photoconductivity characteristics of the investigated structures. In particular it was shown that for the Me-AszSe3-A1 and M e InzS3/As2Se3-A1 structures the photoconductivity is more than one order of magnitude greater in the case when the positive voltage is applied to the top aluminum electrode, in comparison with the case when a negative voltage polarity is applied. We must also remark that in that energy region at the negative polarity of the aluminum top illuminated electrode, the surface recombination rate increases and the photoconductivity sharply falls down. It is evident that an increase in the recording rate and the diffraction efficiency at switching the polarity of the applied field is due to increase in the photocurrent density. Reversing the pulse polarity probably stimulates additional chemical interaction of the top aluminum electrode with the AszSe3 thin film and led to stronger changes in optical characteristics of the holography registering media. Moreover, the photocurrent in heterostructure is several times more than that in onelayer structures due to the sensibilized effect, leading to increase in the recording rate for the Me-InzS3/AszSe3-A1 heterostructures. Thus, in the Me-InzSe3/AszSe3-A1 heterostructure in the long-wave spectrum region the photocurrent reverses the sign. This effect also may be used in the field control registered processes which gives us new possibilities for utilization of this heterostructure. The effect gives the possibility to record the information in two-light-wave regime (• --- 1.55-0.83, and 0.83-0.50 p~m) (Iovu and Khancevskaya, 1996). The experimental results show that the holograms recorded on such media have the spatial resolution no less than 10,000 mm-1. The maximum diffraction efficiency of the holograms measured in the reflection mode is about 7%. The following chemical treatment in some alkaline solution allows to increase the diffraction efficiency up to 70%. Investigation of the exposition characteristics of the amorphous electrocontrolled registration media allows us to construct the characteristic curves. These curves determine an optimum recording process. Frequency-contrast characteristics of the electrocontrolled media indicate the possibility of the effective recording of the microholograms, which have a capacity of 3 x 103 bit with the size of one hologram about 0.8 mm in diameter. Studying the dynamics and recording regimes of the microholograms at different conditions it is possible to stabilize the diffraction efficiency value at ~ = 5% level with the recording time of about t = 10 -2 s. The photosensitivity of the proposed recording media is around S = 1 0 - 4 j cm -2. The time-dependent characteristics of the electrocontrolled registration media shows that the storage time of
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the microholograms is unlimited at insignificant primary decreasing of their initial value up to 10%. The proposed recording media permit the control and monitoring of the holographic parameters during the recording process. New holographic information technologies for creating data banks and information storage systems of a constant type with great and supergreat capacity based on holographic memory modules and devices compatible with PC were proposed. The software for an automation system of holographic memory by 'page-to-page' reading and handling of binary information from the holographic carrier with a mobile plan was developed (Andriesh, Bivol, Iovu and Prisacari, 1999; Andriesh, Bivol and Iovu, 2002). In amorphous films of chalcogenide glasses electron irradiation produces structure transformations followed by changes in the chemical dissolution rate and index of refraction (the effect resembles the photostructural transformations). These two effects may be used for electron-beam recording of relief and planar phase diffraction elements, respectively (Handa, Suhara, Nishihara and Koyama, 1980). In both the cases the diffraction efficiency is sensitive to the shape of the grating profile. The spatial distribution of the etching rate as well as of the refraction index n(x) are of the same basic nature, namely, the distribution of transformations in chemical bonds induced by electron irradiation. Experimental dependencies of the grating diffraction efficiency on the recording electron-beam current usually show sublinear behavior due to dose widening of the area of electron beam interaction with the chalcogenide resist material. The interdependence between the diffraction grating properties and the parameters of the recorded line (linewidth to period (w/A) ratios) is determined by the operating conditions of electron-beam recording (Sergeev and Shutov, 1995).
3.1.3. Wide-gap ChS in Xerographic and Photothermoplastic Systems of Information Storage Xerography is one of most effective and widely dispersed means of optical information recording on silverless media. Usage of thermoplastics for visualization of the latent electrostatic image increases the recording efficiency, minimizing the delay between the exposure and image processing. The main part of the xerographic or thermoplastic media is the photosensitive layer with high dark resistivity. Several semiconductor materials such as amorphous Se, AszS3 and AszSe3 and alloys on its base, some organic semiconductors and other photoconductors like a-Si, ZnO, CdS, dispersed in a binder are used for these layers. The advantage of amorphous materials for registration media is the ultimate resolution, which is not limited by the grain size. High resolution is a key important requirement for holography and some other applications. In this section some properties of ChG will be considered from the position of application of them as a photosensitive unit of xerographic or photothermoplastic information recording techniques. The set of requirements for the photoconductor is rather wide and contradictory. It includes high dark specific resistance, high photosensitivity with quantum efficiency approaching unity in a wide spectral range, absence of surface charge leakage and electrode injection, high uniformity of properties
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over large areas, mechanical strength, stability at cyclic processing and some other issues. In the case of photothermoplastic media thermal stability during heating for the development of the image is added. a-Se layers have received wide applications in xerographic techniques. Though highly sensitive, these layers have narrow spectral range 300-550 nm, which should be broadened by sensibilization additives. The drawback of Se is low temperature stability and tendency to crystallize. The AsSe layers have better photosensitivity spectra (400-750 nm) with quantum efficiency approaching unity, but the dark storage time of latent image is much shorter. Further broadening of the spectral range of sensitivity is achieved by addition of sensibilisators and amorphous alloys of arsenic and antimony sulphides. High sensitivity was obtained for Se-Te alloys, which is difficult to produce with high uniformity over large area. The study of electrical and photoelectrical properties of chalcogenide amorphous system (AszS3)x(SbzS3)I-x shows perspectivity of its application as a photosensitive layer of xerographic and photothermoplastic media. Increase of Sb2S3 content raises the sensitivity in the red section of the spectrum, significantly increases drift mobility and thermal stability. The examination of the layers of the system in xerographic mode suggests the possibility of chemical sensibilization of As2S3 layers by alloying with Sb2S3 with the good opportunity of smooth adjusting of characteristics (0.2-0.5 lx -1 s -1) (Andriesh, Bivol, Buzdugan, Iovu, Panasyuk, Tridukh, Fulga, Tsiuleanu and Shutov, 1988a). The more effective approach is to use multilayer structures with function sharing between the layers. A separated function of the layers opens fertile resources for optimization of media characteristics. Heterostructures give the possibility to use photoinjection to increase the integral photosensitivity in comparison with the monolayer film. We refer here the results of the study of two-layer chalcogenide structure, obtained by successive vacuum deposition of Sb2S3 and AszS3 layers (thickness 0.2-4.0/~m). Both the layers with different optical gap (2.4 eV for AszS3 and 1.73 eV for Sb2S3) took part in photoresponse. Sensibilizing layers of the amorphous system AszS3Gex (x -- 0.38, 1.0, 1.46, 2.0, 3.0) were used as well. From the study of heterostructures it follows that using them makes it possible to obtain a series of advantages against monolayers. First, the photogeneration spectrum of the heterostructure is much wider than that of the monolayer (between 0.45 and 0.9 eV). The enhancement of the range is achieved not only at the expense of the additive contribution of both layers but also due to generation at the boundary between the layers, which generates an additional sensitivity in the intermediate energy range. Due to broadening of the photosensitivity and injection, the integral sensibility of the heterostructure increases and in xerographic regime reaches 5 - 1 0 lx -1 s -1. Second, the layer of As2S3 is an effective blocking element and provides dark conductivity of the structure less than 10-15 ~ - ~ cm-~ and prolonged storage of surface charge. Third, due to the bottom Sb2S3 layer the dark and injection characteristics of the heterostructure are independent of the bottom electrode. Fourth, the capacitance of the heterostructure is several times less than the monolayer structure, thus lowering the time of transient processes. Finally, the passivating action of the upper layer of AszS3 enhances the thermal stability of the structure ( l l 0 ~ (Buzdugan, Zelenina, Postnikov, Subbotin and Shutov, 1983).
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CHAPTER
5
OPTICAL SPECTRA OF ARSENIC CHALCOGENIDES IN A WIDE ENERGY RANGE OF F U N D A M E N T A L ABSORPTION V. Val. Sobolev and V. V. Sobolev UDMURT STATE UNIVERSITY, 426034 [ZHEVSK, RUSSIA
1. Introduction The current state of science and technology depends on both the practical applications of microscopic and the quantum mechanical properties of condensed systems. The solution of one of the main challenges, the possibility of obtaining solids with predefined properties, also depends on contributions from theoretical research. A great revolution in natural sciences and engineering has been spurred by research in optical properties, and also in energy levels of atoms and crystals. Further investigations of their energy spectra, binding regularities based on the nature of components and chemical bonds, as well as the structure of the short-range order of glasses, should spur additional advances. The electronic structure of semiconductor glasses presents one of the most fundamental problems of non-crystalline materials. It is mostly studied in a narrow energy range near the long-wavelength edge of intrinsic absorption. Compared to crystals, the studies of electronic structure of glasses are still in a very early stage. The lack of long-range order does not allow us to use the theoretical methods well developed for crystals. The experimental reflectivity and absorption spectra of glasses in a wide energy range are very diffuse, and they do not allow the necessary reference parameters to be obtained. In comparison to crystals, the theory of the electronic structure of glasses is more qualitative and often uses rather ambiguous models. Successful experimental and theoretical researches of the optical properties and electronic structure have been carried out (see, for example, Sobolev, Alekseeva and Donetskich, 1976; Lazarev, Shevchenko, Grinberg and Sobolev, 1978; Sobolev, 1978-1984, 1986, 1987; Lazarev, Sobolev and Shaplygin, 1983; Sobolev and Nemoshkalenko, 1988, 1989, 1992; Sobolev and Shirokov, 1988). Nevertheless, some principal problems have not been solved: there is no unified theory that combines the band theory and that of metastable excitons; therefore, there is no unified theory of dielectric function, which would allow unambiguous determination of the nature of the maxima of optical spectra (Sobolev, 1999). 201
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V. Val. Sobolev and V.V. Sobolev
In the case of glasses, there are similar problems which are much more complicated (Sobolev, 1995). In order to discuss their peculiarities, one should collect a considerably larger amount of information on their properties. A comprehensive research of optical properties of glasses in a wide energy range of intrinsic absorption is of special importance to understanding these materials. This chapter is aimed at obtaining new information on the spectra of complete sets of the fundamental optical functions of arsenic chalcogenide glasses in the range 0 - 3 5 eV, concerning their most intensive transitions and the main parameters of these transitions.
2. The General Consideration of Optical Spectra and Electronic Structure Theory One of the fundamental peculiarities of the crystal theory is based on the necessity to take into account both the long-range and the short-range order. However, for a long time it was not clear, which type of order is more important. Ioffe and Regel (1959) studied the electrical conductivity and the structure of many amorphous and liquid semiconductors. They put forward a fundamental hypothesis that the electronic structure of condensed materials in the region of minimum energy gap is determined by the short-range order. The hypothesis was developed further in many theoretical models of glasses (Gubanov, 1963; Mott and Davis, 1979; Tsendin, 1996). The conservation of energy law holds in glasses. But the selection rules for quasimomentum do not hold. In a wide energy regime, the intensity of transition between an occupied and an unoccupied state is determined, aside from the transition probability, by the joint density of states in crystals or by the product of densities of both states in glasses. After the crystal-glass phase transition, the intensity of indirect optical transitions becomes comparable to those of direct transitions and the their localization in the Brillouin zone is smeared. Therefore, optical spectra of glasses are expected to be strongly broadened and without any complex fine structure, which is specific to the spectra of crystals. Much depends on the nature of excitations and the role of excitons, as well as on the variations of the density of states. In Sobolev et al. (1976), Lazarev et al. (1978, 1983), Sobolev (1978-1984, 1986, 1987), Sobolev and Nemoshkalenko (1988, 1989, 1992) and Sobolev and Shirokov (1988) optical spectra of many crystals and glasses are considered, including the spectra of dielectric function, reflectivity and absorption coefficients in a wide energy range. One can distinguish several typical cases. At the crystal-glass transition the spectra lose their fine structure and the band maximum is shifted strongly to the lower energy. This is characteristic of A 4 and A3B 5 compounds. The optical spectra of crystals, belonging to some other groups (As2X3; S, Se, AzB4C52), contain two or three separate bands. In glasses, they keep the positions of the band maxima and the remains of the previous structure, where the fine structure maxima are transformed into the steps of the broad resulting band. The third group of materials (SiO2, GeO2) is characterized by the very weak effect of losing of the long-range order upon the complex structure of optical spectra. Usually, this fact is explained in the following way: all the maxima of transition bands are due to the small radius excitons. The exciton spectra of glasses have not yet been studied theoretically. Many maxima of optical spectra of crystals, including AszX 3
Optical Spectra of Arsenic Chalcogenides
203
group, can be explained qualitatively by the metastable exciton model (Sobolev et al., 1976; Lazarev et al., 1978, 1983; Sobolev, 1978-1984, 1986, 1987, 1995, 1999; Sobolev and Nemoshkalenko, 1988, 1989, 1992; Sobolev and Shirokov, 1988). A very strong smearing of the bands of optical transitions of semiconductor glasses makes it much more difficult to consider the competition between the exciton model and the usual model of electronic transitions. Let us consider briefly the main results of some theoretical calculations of energy levels and densities of states N(E) of molecular clusters AsxXy (Salaneck, Liang, Paton and Lipari, 1975; Babic and Rabii, 1988; Babic, Rabii and Bernholc, 1988; Strujkin, 1989; Schunin and Schwarz, 1989). In Salaneck et al. (1975) the molecules As4S4 and As4Se4 are studied, using the simplest method of self-consistent field molecular orbitals (SCFMO) in the complete neglect of differential overlap (CNDO) approximation. The lined spectrum was broadened by Gaussians with the half-width at half maximum (HWHM) of 1 eV. The N(E) spectra of both molecules consist of three bands in the ranges 0 to - 4 (I), - 4 to - 8 (II), - 8 to - 13 (III), and - 13 to - 19 eV (IV) for As484, and in the ranges 0 to - 4 (I), - 4 to - 7.5 (II), - 7.5 to - 11.5 (III), and - 11.5 to - 16 eV (IV) for As4Se4. They are mostly due to p-states of As and S, Se (I, II), s-states of As (III), and s-states of S, Se (IV). Later the N(E) spectra and the joint density of states (I(E)) spectra of molecules As484, As4Se4, and As4S6 were calculated by the XoL-method of scattering waves (Babic and Rabii, 1988), and the N(E) spectra of the same molecules--by the cluster pseudopotential method in the local density approximation (Babic et al., 1988). All the calculations of N(E) proved to be in good agreement with the experimental data (Bishop and Shevchik, 1975; Salaneck and Zallen, 1976). In Babic and Rabii (1988) the theoretical I(E) spectra of three different molecules were compared in the range 2 - 1 2 eV to the known ez(E) spectra. The calculated joint density of states spectra contain a band with very complex fine structure in the range 2 - 8 eV, while the experimental ez(E ) spectra consist of two strongly overlapping bands with the maxima at 4 and 9 eV. The main fault of the theoretical calculations of I(E) is the absolute absence of the second band in the energy range E > 8 eV. In Strujkin (1989) the R(E) and ez(E ) spectra of AszS3 were calculated in the range 1 - 1 4 eV using the quantum defect method. By fitting the adjustable parameters the author managed to obtain both of the transition bands in good agreement with the experimental results. This method is used for the calculation of photoionization crosssections of impurities. It has not become clear, whether it is valid for the calculations of electronic structure in a wide energy range. In Schunin and Schwarz (1989) the dependence of the band-gap energy Eg on the arrangement of clusters in AsxSe~-x (x = 0-0.75, Eg = 1.15-1.70 eV) was determined. The calculations were performed on the basis of the cluster model in the coherent potential approximation. With the increase in the parameter x, the energy Eg decreases almost monotonously with a wide maximum Eg -- 1.45 eV at x = 0.50. Thus, the theoretical calculations of the N(E) of the occupied states of molecules As4X4 (XmS, Se) are in good agreement with the experimental results of photoemission. However, the theoretical optical spectra show only one of the two known experimental bands. This is, likely, due to strong imperfections of the calculational methods used for unoccupied states. The problem remains to what extent the model of molecular levels of As4X4 reflects the main features of AszX3 glasses.
204
V. Val. Sobolev and V.V. Sobolev
3. Measurement Techniques and Determination of Spectra of Optical Functions and Density of States Distribution N(E) Processes of interaction between the light and the matter are very complicated. They manifest themselves through a large set of optical functions, connected with each other by the integral and relatively simple relations. In order to obtain the most complete information on these processes and the electronic structure of a material, it is necessary to analyze all or most of the functions in a wide energy range of fundamental absorption. This set includes the reflectivity (R) and the absorption (~) coefficients; the refraction (n) and the absorption (k) indices; the imaginary (/32) and real (/31) parts of the dielectric function/3; the characteristic bulk (-Im/3-1) and surface (-Im(1 +/3)-1) electron loss functions; the effective number nef(E) of the valence electrons, participating in the transitions up to the given energy E; the effective dielectric function/3ef; the integral function of density of states (I) multiplied by transition probability, and the optical conductivity (o-), which are equal to /32E2 and /32E, respectively, except for constant factors; the phase 0 of the reflected light; and well-known differential optical functions ce and/3, which are widely used in the analysis of modulation spectra and connected by the analytic formulae with/31 and/32, or n and k (Sobolev and Nemoshkalenko, 1988). In experiment in a wide energy range only the R(E) spectrum at normal incidence of light is measured directly. The characteristic losses of high-energy electrons are studied much rarely. After performing a thorough analysis of these losses and using several normalization and approximation methods, one obtains the loss function -Im/3-1. Sometimes, /32(E) and /31(E) are determined by ellipsometric methods, but only in a relatively narrow energy interval 1-5 eV. It is common to calculate a complete set of optical functions on the basis of the available R(E) or -Im/3-1 spectra in a wide energy range, and/32(E) and/31(E)--in the narrow range 1-5 eV by means of special programs involving the integral KramersKronig relations and the analytic formulae between the functions. In the general case, which occurs in glasses, transition bands are strongly overlapped resulting in the extreme case in complete disappearance of some of the features in the total spectral curve of an optical function. The fundamental problem of determination of the three main transition parameters (the total number N of the most intensive transitions, the transition energies Ei and the intensities, or the oscillator strengths f (the band areas Si), as well as the band HWHMs Hi and the peak heights Ii) is usually solved with one of the two following methods: (1) the method of reproduction of the integral R(E) or/32(E) curve with a set of N Lorentz oscillators with a large amount (3N) of adjustment parameters (up to 30, when N - 10) and (2) the method of combined Argand diagrams within the same Lorentz oscillator model, but without adjustment parameters, which consists in simultaneous analysis of the/32 and/31 spectra. Any optical transition can have two components: the transverse and the longitudinal. The transverse component manifests itself in ordinary optical spectra, while the longitudinal onemonly in the characteristic loss spectrum (Pines, 1966). The complete sets of optical functions of arsenic chalcogenides were calculated by us on the basis of the known experimental R(E) (or -Im/3-1) spectra with the help of the integral Kramers-Kronig relations. The decomposition of the/32 and -Im/3-1 spectra
Optical Spectra of Arsenic Chalcogenides
205
into the elementary transverse and longitudinal components was made on the basis of combined Argand diagrams. This method has been described in detail in Sobolev and Nemoshkalenko (1988) and Sobolev (1996) and applied to many crystals (Sobolev et al., 1976; Lazarev et al., 1978, 1983; Sobolev, 1978-1984, 1986, 1987, 1999; Sobolev and Nemoshkalenko, 1988, 1989, 1992; Sobolev and Shirokov, 1988). The crystal lattice of A s z X 3 compounds has a very complex layered and chained structure. Its unit cell contains a large number of valence electrons (20 atoms, which give 112 valence electrons) (Hullinger, 1976). The calculations of its complex band structure are therefore rather difficult. The shift from a crystal to a glass even more complicates the problem of determining the structure of energy levels and optical spectra of g-AszX3 in a wide energy range of intrinsic absorption. For g-AszX3 the experimental reflectivity spectra in the range 1-12 eV and characteristic electron loss spectra in the range 1-35 eV are known. From these one can directly obtain only very scarce information on the electronic structure of the material. It is no mere chance that the majority of monographs and reviews ignores this problem, particularly in the case of g-AszX3.
4. Optical Spectra of o~-As2S3 4.1.
CALCULATIONS OF SETS OF OPTICAL FUNCTIONS
For g-As2S3, the reflectivity spectra of polished bulk samples in the ranges 112.5 eV (Andriesh and Sobolev, 1965, 1966; Andriesh, Sobolev and Popov, 1967; Sobolev, 1967; Belle, Kolomietsh and Pavlov, 1968) and 2 - 1 4 eV (Zallen, Drews, Emerald and Slade, 1971) are known. The results of Andriesh and Sobolev (1965, 1966), Andriesh et al. (1967), Sobolev (1967) and Belle et al. (1968) are in good agreement with each other. In Zallen et al. (1971), the structures of the R(E) spectrum are seen less clear than in Andriesh and Sobolev (1965, 1966), Andriesh et al. (1967), Sobolev (1967) and Belle et al. (1968), and the values of R(E) in the energy range E > 6 eV seem to be overestimated. Therefore, we used the R(E) spectrum from Sobolev (1967) in the calculations. On the basis of this spectrum, a complete set of the fundamental optical functions of g-AszS3 was calculated in the range 0-12.5 eV (Fig. 1). In Table I (Column 1) the maxima energies values of the resultant optical functions are given. The experimental reflectivity spectrum R(E) consists of a very broad and intensive band in the range 2 - 5 eV with a maximum at 3.6 eV and weak side maxima at 2.9 and 4.5 eV. Besides this band, the broad bands are seen in the ranges 5 - 8 and 8 - 1 2 eV with the maxima at - 6.0 and 10.4 eV. The long-wavelength maximum of the calculated spectra almost coincides in energy with the maximum No. 1 of R(E) for el (el "~" 9) and n (n --~ 3), and maximum No. 2 of R(E) for e 2 (e 2 -~ 5.8), or is shifted into the higher energy range by --~0.4-0.6 eV for k, ~, n, and E2e2 (k = 0 . 9 , / z = 2.4 • 105 cm-1). The maximum of the electron loss -Im e-1 is shifted by 1.3 eV. The energy values of the shifts of the analogs of two other reflectivity bands in the spectra of the optical functions are approximately the same.
V. Val. Sobolev and V.V. Sobolev
206 ,,
(a)
0.3
,-
8
- 3.0
g -A 6
" ""
S2 S 3
R
~0"2 - 2.5
,'.n
4
- 2.0
~.,,...
0.1
~ I
0
5
. -.-.- ' . ~
I
10
15
1.5
210
25
E, eV (b)
6
.
I.~ . +"4
If" "
:-
'.
,.
..//E2E2 "
"
",
~:~"
0
\
g " ,
A s 2 S 3 0.9
"'\
/
,,'~'~.,, , X ." .
t 5,
10
~
.".,
k
.
,, "
.
*
15
~"
0.6
" "\
.
2
l /
",
i
V" l"/ . / '
j.
.
i
.'i "
',
/a~2
1.2-
, .\
--~ !
/q
/
20
25
E, eV
(c)
2.5
15
__ ........
F_,e"f.,..," 12
2.0
1.5
"..."
.
-Ime-
). /
.~
rt~ 0.2
.
6
3 ~
.;~
/"
3 Z f ~ 0 -
7 +
A s2 S 3
9
5
'. / ,~"
',.
-Im(l+e) -1 ,
,
10
15
..
.
"'.,.
.
0.1 ~ "7 -.
"i 20
25
E, eV Fro. 1. Experimental spectrum of R and the calculated spectra of n, /31 (a), k, /x, 82, E2/32 (b), - I m / 3 - 1 - I m ( 1 +/3)-1, nef,/3ef (c) for g-AszS3 in the energy range 0 - 2 2 eV.
ENERGIES (ev) O F T H E MAXIMA A N D SHOULDERS FOR R
No.
1 2 3 4 5 6 7 8 9 10 11 12 13
1
2
2.9 3.6 4.5
3.1 4.1 4.4 5.3 6.3 9.4 11.0
-
6.0 -
10.4 -
-
n
EI
-
12.5
1
2
2.9
2.7 3.9
-
-
6.0
-
-
-
10.0 -
-
-
-
-
14.5 -
-
10.4 11.7
2
3.1
2.9 3.9
1
3.1 4.0 -
-
-
-
-
-
-
5.8 -
10.6
5.8 -
10.6
5.2 6.1 8.5 10.4
1 -
4.0 -
-
6.0 -
10.8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
14.0 -
-
5.7 8.0 10.4 11.7
2
3.6
-
-
14.0 -
-
TABLE I VARIANTS (1
k
82
1
-
TWO
13.0 -
-
AND
2) IN THE SPECTRA OF OPTICAL
F2 3.1 4.1 4.6 5.3 6.5 7.8 9.2 10.7 12.4 13.0 13.7 14.6 16.5
1 -
4.1 -
6.1 -
11.2 -
-
-
E
2 3.1 4.1 4.6 5.2 6.2 7.9 9.4 10.7 12.4 13.0 13.7 14.6 16.5
~
E
~
-1m
FUNCTIONS OF
Im(1
E-'
2
1
-
-
-
-
-
4.2
4.9
-
4.8
-
4.2 4.4
-
-
-
-
-
-
-
-
6.9
-
6.6
-
7.8 9.9
-
11.2
-
-
6.2 -
11.3
-
9.0 10.5
12.0
-
-
-
-
-
-
-
13.2 13.8 14.6 16.6
-
-
2
1
1
12.0 -
14.0 15.0 16.4
-
-
g-As2S3
+ E)-' 2 3.1 4.2 4.8 5.5 -
7.6 10.0 -
0
En
A
2. B
-
-
3.0 5.8
4.2
-
6.3 6.9; 7.5 11.5
-
-
6.4 12.0
-
-
-
-
-
-
-
-
-
-
-
-
12.7
14.6 -
16.0
15.0
f?.
?I? 3
B b
3
3.
9
5
3
3. f$
208
V. Val. Sobolev and V.V. Sobolev
The two weak reflectivity bands in the range E > 5 eV manifest themselves as very intensive in the absorption (/x(E)) and the joint density of states (EZez(E)) spectra. A remarkable feature of the ez(E) spectrum of many materials, including g-AszS3 is the presence of only one very intensive maximum, the rest of the maxima being usually very weak. Unlike the e 2 spectrum, in the spectra of R, k,/x, and E 2e 2 one can see many maxima of comparable intensity. For A 4 (Sobolev, 1978), A3B 5 (Sobolev, 1979), and AZB 6 (Sobolev, 1980) crystals, good agreement between the theory and the experiment is found only for ez(E), while for other optical functions, there are significant contradictions between them (Sobolev, 1999). An agreement between the theory and the experiment only for the ez(E) spectrum, which is commonly considered, does not affirm the validity of theory. Consequently, research data from the spectra of other optical functions are of increased importance. The experimental electron loss spectrum - I m e-1 of g-AszS3, given in Perrin, Cazaux and Soukiassian (1974) is interesting mostly because of its large measured energy region (0-35 eV). On this basis, we also calculated a complete set of fundamental optical functions (Fig. 2). In Table I (Column 2) the energies of maxima of some optical functions are given. The spectra of the second group of calculations contain a much larger number of weak maxima. Unfortunately, a half of them exceed the calculation error. To determine the fine structure of the optical with greater certainty, much more precise measurements of the characteristic loss spectrum in intensity and spectral resolution are necessary. It follows from the photoemission spectra (XPS) of Bishop and Shevchik (1975) that the occupied states of oL-AszS3 consist of two very broad doublet bands in the ranges 0-7.5 and 7.5-17 eV with the maxima at --~2.2, 4.4, 10.0, and 13.2 eV. According to the results of Salaneck and Zallen (1976), they have more complex structure of seven maxima at --~ 1.0, 3.8, 4.3, 4.9, 5.5, 9.5, and 14.0 eV. The differences in the locations of maxima in the XPS spectra of these papers are due to the differences in the preparation technologies of the two samples, the peculiarities of the applied XPS measurement techniques, and the errors in their normalization to the maximum height of the occupied states. It is interesting to note that the XPS spectra of crystals and glasses in both papers differ very little. Theoretically, the maxima of optical transitions in glasses are mostly determined by the relative energy locations of the maxima of density of the occupied and the unoccupied states. Therefore, with the value Eg--~ 2.0 eV and the XPS photoemission results for g-AszS3 from Bishop and Shevchik (1975) and Salaneck and Zallen (1976), four or seven optical bands can be expected; their energy values are given in Columns B and A of Table I. They are due to the transitions from the maxima of the occupied states to the lowest unoccupied states. These bands are possible due to the transitions to higher unoccupied states. This extremely simplified model can give only the qualitative evaluation of the energy values of the expected maxima of optical spectra. Nevertheless, it is in good agreement with our calculated spectra.
4.2.
DECOMPOSITION OF DIELECTRIC FUNCTION SPECTRA AND CHARACTERISTIC ELECTRON LOSS SPECTRA INTO ELEMENTARY COMPONENTS
The experimental reflectivity spectrum, as well as other functions calculated from it, collects all the individual transitions from occupied to unoccupied states. For glassy
209
Optical Spectra of Arsenic Chalcogenides
J
10
8-
4
0.4--
i i
g-As2S 3 i.
6
.
3
0.2
2
0.1
1
R
".
4
0.3
,
2
. ..--~---
i;
0 Ix -
.......
I
10
I
30
20
40
E, eV ~, ' , :"
(b) 12
I
]
"*
.'* ,'-:'\ ;- , , , x
/"
.
.
x
'~
,', ,
.
,
'
.
g - A s2 S 3
"''"
',
132 E 2
." . . . . . . . . . . .
d~
', ",k ", E2
(c)
ll0
25 -
- I m (1WE)-1
"'""'"
,.~
".g
3
0
/q
r 3 1.5J
"
J!"/
"~6
1.8
"
J
" 1
0.6 " ' .........
0.3
0 --
1 ~ .
" -- ..
20 E, eV
30
40
30~
,,/"",
.
" -Imc-Z
0.6
!
;i
20 -
"~.i
i 15
_
"
:
g - A s 2 S~ ~
0.4
1.0
,
7
-7
.
I
10
.'
"
,
.
9
,
.~ . . . . . . . .
5
'''"
,Y
Eef
\"
0.2
0.5
9
-\-
"~
I
I
I
10
20
30
t
40
E, eV FIG. 2. Calculated spectra of R, n, el (a), k,/x, 82, E2E:2 (b), - I m e -1 , - I m ( 1 + e) -], nef, 8ef (C) for g-As2S3 in the energy range 0 - 4 0 eV.
210
V. Val. Sobolev and V.V. Sobolev
compounds, it is important to solve the inverse problem" having an integral curve, one has to restore the contributions of elementary transitions and determine the parameters of each (the maximum energy Ei, its half-width Hi and height Ii and the area Si of the transition bands, and oscillator strength). It is possible by the method of joined (combined) Argand diagrams ez(E ) - f l (el (E)). On the basis of the obtained ez(E) and el (E) spectra, a joined (combined) associated Argand diagram is plotted. Then, starting with the most intensive maximum of ez(E), the individual bands are successively extracted, with subsequent optimization of the decomposition. In electron loss spectra, the analogs of e 2 and el functions are - I m e-1 and - R e e-1 functions. Therefore, the calculation of a spectrum of elementary longitudinal components and the determination of their parameters are performed similarly to those of transverse components, using the method of joined (combined) Argand diagrams for - I m e -1 - f z ( - R e e - 1 ) . Theoretically, the energy of the longitudinal component is always somewhat larger than the energy of its transverse analog. Quantitative evaluations of this shift AE are known only for free excitons (Sobolev and Nemoshkalenko, 1992). The electron loss function depends on el and 82: - I m e -1 - 8 2 ( 8 2 + e2) -1 . From the analysis of this formula and the loss spectra of some studied materials (Pines, 1966), it follows that the intensity of the long-wavelength part in a loss spectrum is always much lower (compared to the short-wavelength one) than in a e 2 spectrum. The main calculation parameters of the transverse (1) and longitudinal (2) components are given in Table II. Nine transverse (Nos. 1-9) and eight longitudinal (Nos. 3 - 9 and 6~) components were found in the transitions of g-AszS3. The small values of the loss functions in the range E < 4 eV made it impossible to extract weak bands Nos. 1 and 2. The integral curves of the optical spectra contain only three maxima (ez,R) with the weak triplet fine structure of the most long-wavelength reflectivity maximum. The half-widths H i of the majority of the spectra decomposition components are in the interval 1-2 eV. This makes it considerably more difficult to extract weak longwavelength bands of the loss spectrum and to determine the energy values of the shifts AE between both transition components. The long-wavelength components (Nos. 1-3) are mostly 1.5-2 times narrower than the other ones. The band areas Si (and the transition probabilities) of the transverse components are larger than the Si values of the longitudinal ones 10-20 times (Nos. 3 - 5 and 8) and 3 - 5 times (Nos. 6 and 7). This does not only confirm the theoretical qualitative evaluations on larger intensity of the transverse components (Pines, 1966; Sobolev and Nemoshkalenko, 1988), but it also quantitatively establishes that the transverse components are very much larger in intensity than the longitudinal ones for the majority of the transition bands. In the above discussion of the interpretation of maxima of the integral spectra of the g-AszS3 optical functions, the energy values En of possible transitions were evaluated (Table I) on the basis of XPS data on the density of occupied states (Bishop and Shevchik, 1975; Salaneck and Zallen, 1976) and the value of Eg. According to these evaluations, the most intensive components extracted by us can be due to the transitions to lower unoccupied states from the maxima of bands of occupied states (values En in Table II). The rest components are due to the transitions from the maxima of the XPS spectra to
Optical Spectra of Arsenic Chalcogenides TABLE
211
II
ENERGIES ( e V ) E i OF THE MAXIMA, H A L F - W I D T H H i , AND AREAS S i OF THE BAND COMPONENTS FOR TWO VARIANTS (1 AND 2) OF THE DECOMPOSITION OF THE SPECTRA 8 2 AND - I m 8 -~ AND POSSIBLE ENERGIES E. OF OPTICAL TRANSITIONS (VARIANTS A AND B) OF g - A s 2 S 3 No.
Ei
Hi
e2
-
1
2
-
Im e- 1
1
Si
82
2
82
1
2
En
-- I m e - 1
1
2
1
82
2
A
1
1
3.2
3.2
-
-
0.4
0.9
-
-
0.8
6.4
-
2
3.7
3.6
-
-
0.7
1.0
-
-
2.3
2.5
.
B
2
-
3.0
.
.
-
.
3
4.2
4.1
4.2
-
1.2
0.9
4.2
-
3.8
6.8
0.1
-
-
4.2
3/
-
4.6
4.9
-
-
1.0
1.0
-
-
3.3
0.2
-
-
-
4
5.2
5.2
4.9
-
2.0
1.1
1.0
-
1.8
5.6
0.2
-
5.8
-
5
6.0
-
5.9
-
2.0
-
1.2
-
2.4
-
0.2
-
6.3
6.4
5/
-
6.4
-
-
-
1.3
-
-
-
6.2
.
6/
7.2
-
7.1
6.7
2.1
-
1.6
3.0
1.8
-
0.4
6.9
-
6
-
7.8
-
-
-
1.6
-
-
-
7.0
.
7/
9.0
-
8.3
-
1.6
-
1.2
-
0.4
-
0.2
-
-
-
7
-
9.4
9.4
9.7
-
1.6
1.0
1.6
-
5.9
0.1
0.2
7.5
-
-
3.0
1.3
1.1
-
4.4
3.3
0.2
-
1.0
1.4
1.4
2.3
0.7
2.2
0.4
0.5
8
10.7
10.8
10.5
9
12.0
12.3
11.8
11.9
10
-
13.8
-
13.7
-
11 /
-
-
-
15.9
-
11
-
16.8
-
-
-
12
-
19.2
-
18.9
13
-
-
-
21.8
14
-
-
-
32.2
15
-
-
-
38.0
higher
unoccupied
states,
bands
of the
spectra
XPS
agreement
between
the results
of decomposition
Salaneck
and
valence
band
Zallen
dielectric into
function
have
been
the model
-
0.8
-
1.8
-
-
-
-
1.9
-
7.0
-
-
-
6.3
-
-
-
-
-
-
from
on
states
obtained and
and
of transitions
states.
These
results
substantially
and
electronic
structure
They
in
absorption. electronic
structure
lay,
bulk
0.2
-
-
2.0
-
-
16.0
-
15.2
12.9
-
-
-
5.5
-
-
6.1
-
-
-
1.6
-
-
2.3
-
-
-
0.9
-
-
of the
very
wide
A
good
transitions
and
structure and
Zallen
(1976).
of possible
complex
confirms
the results
structure
The
new
0-35
the in
eV,
loss function main
of
a wide
foundation
of
the
of
higher
of
spectra
of
been
decomposed components
proposed
states
information range
theoretical
functions
of the
has been
energy for
integral
have
of occupied
amount
optical
their
parameters
interpretation
of densities
g-AszS3
materials.
of the fundamental
electron
enlarge of
principle,
of glassy
-
-
and
of their
the maxima
spectra
12.0
1.4
more
0-12
components.
the scheme
from
11.5
-
into components
sets of spectra
characteristic
and
.
-
the spectrum
or
.
of g-AszS3.
in the range
longitudinal
determined,
quintet
0.5 .
-
in Salaneck
concerning
.
-
of the finer
obtained
the
2.2 -
.
1.6
the maxima
was
of the e 2 spectrum
the complete
been
transverse
1.2
-
than
(1976)
of occupied
have
-
our evaluations
For the first time, g-AszS3
and
1.6 -
.
within
to unoccupied on of
the
optical
fundamental
calculations
of
212
V. Val. Sobolev and V.V. Sobolev
5. Optical Spectra of g-As2Ses 5.1.
CALCULATIONS OF SETS OF OPTICAL FUNCTIONS
For g-As2Se3, the reflectivity spectra of polished bulk samples have been obtained in the ranges 1-12.5 eV (Andriesh and Sobolev, 1965, 1966; Andriesh et al., 1967; Sobolev, 1967; Belle et al., 1968) and 2 - 1 4 eV (Zallen et al., 1971). The results of Andriesh and Sobolev (1965, 1966), Andriesh et al. (1967), Sobolev (1967) and Belle et al. (1968) are in good agreement with each other. In Zallen et al. (1971), the structures of the R(E) spectrum are seen less clear than in Andriesh and Sobolev (1965, 1966), Andriesh et al. (1967), Sobolev (1967) and Belle et al. (1968), and the values of R(E) in the energy range E > 8 eV seem to be overestimated. Thus, we used the R(E) spectrum from Sobolev (1967) in the calculations. On the basis of this spectrum, a complete set of the fundamental optical functions of g-AszSe3 was calculated in the range 0-12.5 eV (Fig. 3). In Table III (Column 1) the maxima energies of the obtained optical functions are presented. The experimental reflectivity spectrum R(E) consists of a very broad and intensive band in the range 2 - 5 eV with a maximum at 2.9 eV and weak side maxima at 2.4 and 4.1 eV. Besides, the broad bands can be seen in the ranges 5-7.5 and 7.5-12 eV with the maxima at --~5.7 and 9.6 eV. The long-wavelength maximum No. 1 of the calculated spectra is shifted relative to the maximum of R(E) to the lower energy range by --~0.6 (el), 0.4 eV (n), or to the higher energy range by --~0.4 eV (e2). In the spectra of other functions it is relatively weak. The analog of short-wavelength maximum No. 2 of the first reflectivity band is seen to be shifted slightly to the higher energy range for k and/x, while the shift to the higher energy range for EZe2, - I m e -1, and - I m ( 1 + e) -1 is quite noticeable (up to ---0.4 eV). The analogs of two other maxima (Nos. 3 and 5) are shifted to the lower (el, n, e2) or higher (e2, k,/x, E2~:2, - I m e - 1 , - I m ( 1 + e) -1) energy ranges by --~0.3-0.5 eV. Besides the reflectivity spectrum, the characteristic bulk electron loss spectra - Im -1 are also known, which have been measured on thin films of g-AszSe3 in the ranges 0 - 4 0 eV (Perrin, 1973) and 0 - 1 0 0 eV (Rechtin and Averbach, 1974). On the basis of these spectra, we also calculated the set of optical functions (Figs. 4 and 5). In Table III (Columns 2 and 3) the energy values of some of their maxima are shown. The spectra of optical functions, calculated on the basis of the - I m e-1 spectrum from Perrin (1973) (Column 2 in Table III), contain the largest number of maxima. In the reflectivity spectrum R(E) one can see, besides the experimentally known maxima (Nos. 1, 2, and 5), also the maxima No. 4/, 5 ~, 6 ~, 6, 7, and 8. Bands No. 3 and 4 manifested themselves more clearly in the k(E), tx(E), and EZez(E) spectra. The calculated reflectivity spectrum of the third group contains the maxima No. 1, 2, 3~, 4, and 6 (Column 3 in Table III). Their analogs exist in the spectra of other optical functions with a shift up to 0.5 eV. In a reflectivity spectrum of any material, the long-wavelength bands are usually the most intensive in the range E < 6 eV, while for E > 6 eV the values of R(E) are strongly decreased. On the contrary, in electron loss spectra the most intensive are the short-wavelength bands, while the long-wavelength parts of these spectra are very
Optical Spectra o f Arsenic Chalcogenides
213
(a)
-
3.5
-
3.0
-
2.5
100.3
g - A S2 Se 3
8 -
6
-
0.2-
-
'fn
4 -
R
2.0 0.1
-
1.5
2 I
ll5
lo
5
20
25
E, eV (b)
15
8 ..,.~. . . . . ~.,,,.\
g -A
f ""E2E 2 l
7
f
"~v(. "
r tt~
~ , i ,
4 \
=:1.
&
.t/" "
/'\
~
Se 2
S2
\
f
tI
x. N 9
\
,
~
"
"
"
,, 1.0
" ,
k
I f"
9
\ ~
7z
\
.
~9
"
I
I
I
5
10
15
~D
0.5
I
25
20
E, eV
(c)
,, 15
3
_
! i
_.' .i
/ !
~ " ~
Eef
"''"
, - .......
-Imc-1
" ,"~ .''.. / 12 ; r ..,. //. , \./ ',,/ i ! .~ .,," /x. i'. ~/ / ". 9 ~;,'. " / ".,
~!,.
2
/
~ef
~'"
/
;/
6;.."
,,r ~
0
i/
~
/
g-As2Se3
0.2
""
.
.
,
9
9
9
\.
-Im (l+r
-
...........
"
~ '~
0.2-
~
I
7 + 0.1 " I
-.,:
\'".,,. " . .O.1-
I
I
I
I
5
10
15
20
, 25
E, eV FIG. 3. Experimental spectrum of R and the calculated spectra of n, el (a), k, /.t, /32, E2e2 (b), - I m e -1 - I m ( 1 + e) -1 t / e f ~ 8 e l (c) for g-As2Se3 in the energy range 0 - 2 2 eV.
ENERGIES (eV) R
No.
1
2
2 . 4 1 2.9 2 4.1 3 ' 3 5.7 41 4 -
5,
OF THE
-
2.8 3.9
TABLE I11 MAXIMA AND SHOULDERS FOR THREE VARIANTS (1,2 A N D 3) IN THE SPECTRA OF OPTICAL FUNCTIONS A N D POSSIBLE ENERGIES E, OF OPTICAL TRANSITIONS (VARIANTSA A N D B ) OF g-As2Se3 n
EI
1
2
1
2
-
-
-
-
-
2.9 2.3 3.5 4.6-
-
-
5.2
4.7
6.7
-
-
-
-
8.0-
8.8
-
-
2.7 4.5
1
2
-
-
-
2.7 3.9
2.9 3.3 2.7 3.4 3.8 4.35.4-
-
2.9 2.5 3.4 4.2-
-
-
5.2 6.6-
-
7.8-
-
-
1
2 -
5.8 6.9-
-
7.8-
k
"2
-
-
1 -
2
CL
1
2
-
-
-
-
3.2
-
-
3.9 4.5
4.0 4 . 6 -
-
5.7
-
-
-
8.2
8.0
-
-
4.4
1
-
-
-
4.0 -
-
6.0
5.7
-
6.0
-
-
-
-
-
8.5
-
-
8.2 -
2
-
-
-
4.4 -
5.8 -
8.5 -
E
1 -
2 -
3.2 3.9 4.2 4 . 6 -
8.0 -
6.0 -
~
1 -
4.4 -
5.8 -
E
2 -
1
-
3.2 4.0 4.5 4 . 6 5.6 -
8.8
8.5
-
-
6.2
-
+
-Im(l
I m E-'
~
2
1
2
-
-
-
-
-
-
4.6
-
4.3
2.8 4.6
-
-
-
-
s
En
8)-'
2
1
-
1
-
-
-
2.9
2.8 4.3 5.0
-
3 0-
3 e
5
6.0
6.0
6.0
6.0
5.7
5.7
-
-
-
-
-
-
-
5
-
-
-
-
8.5
-
-
-
-
-
3 J-
-
6.4
-
s
Optical Spectra of Arsenic Chalcogenides (a)
215 0.4
4
0.3
3
i
i,
12-
g - A s2Se 3 9
=
','.
~o 6
R
3
.........
'
ii:
0.2
2
Q.L
1
........ 20
10
30
40
E, eV
(b)
15
i'-; . i t~
, ,
,_,
"
'
i.
"
1.8-
, "
,-~l o
~~ 9
-3
\
i.
' ,
12
. \
i.
-x.
t,l ""-
..
-2% r
,, "~
g - A s 2Se.3
",-
"x . , .
. ...
6
E2 E 2 "" . . . . . .
s
",,
tl}!~ k "
3
o0
".
.,,..,.
""'"'"'"'"
r
" . .}.t ",k
~o
"~ 0.6-
'''.
2o
j.~)
........
~o
40
E, eV
(c)
30
.
-Im ( l +eO-1 i" ",
25
2. -- 0.8
"'" "
"
i ~ ' . i ~ ;/):
20
oa
9
~15
"
//
10
i"
_ 0
,
[
~
/';7." ." " , ~
" "
9
10
1.5--0.6
".
:
g-As2Se 3
" "" -Ime-11
_- '.
I I"
\
~
"
~.
-?
~o
+
~r
~1.0
0.4 ,~ !
~
\.
~176
0.2
\
,
,. ".
20
-,..
,
,
,
. . . .
"---,_'_21_:_i_'_ 30
40
E, eV Fro. 4. Calculated spectra of R, n, el (a),k,/.t, 82, E 28 2 ( b ) , - I m 8-1 , - I m ( 1 + 8 ) - 1,nef, eef (c) for g-As2Se3 in the energy range 0 - 4 0 eV.
216
V. Val. Sobolev and V. V. Sobolev (a) 12
It
0"414 g - A $40 Se60
9
6 3
_'_'_' .....
0.3
3
0.2
2
0".1_.-L1
0 110
RI0
30
40
E, eV
(b)
/~.
12
6 IA Ill
'i- ',',
t
i I~ "
~ "\
]i l , "i"
9
4 ]: \ ~ x I' \l .
.
12-
"
, ,,.,, ..
',
\
i
g- A $40 Sea0
x.
,
0.8-
""--.... E2 E 2
~
"
"'..
,,
3
IJ
-,
j
0 Calculated spectra of
.. -,-..
/
FIG. 5.
-3
~
-----A-
04
,., ~
~
",-
,'
9._.
10
20 30 40 E, eV R, n, el (a), k,/x,/32, E2e2 (b) for g-As4oSe6o in the energy
range
0-40 eV.
weak and measured with large errors. This can explain the differences in the locations of the maxima, obtained by us after the calculations of three sets of optical functions on the basis of the experimental R(E) and - I m e - 1 spectra. Disagreement in the results of the two calculations from loss spectra of Perrin (1973) and Rechtin and Averbach (1974) seems to be mostly due to the differences in the preparation modes of g-AszS3 samples and in the measurement techniques of loss spectra used in both papers. In Table III, only those of the maxima of the three calculated sets of optical functions are given. The experimental - I m e -1 spectra of Perrin (1973) and Rechtin and Averbach (1974) are interesting mostly because of their large measured energy regions ( 0 - 4 0 eV (Perrin, 1973), 0 - 1 0 0 eV (Rechtin and Averbach, 1974)). This made it possible to substantially broaden the energy interval of the calculated optical functions. To determine the complex fine structure of the optical spectra with certitude, it is necessary to perform considerably
Optical Spectra of Arsenic Chalcogenides
217
more accurate measurements of the characteristic loss spectra in intensity and spectral resolution. It follows from the photoemission spectra of Bishop and Shevchik (1975) that the occupied states of AszSe3 consist of two very broad doublet bands in the ranges 0 - 7 and 7 - 1 7 eV, below the top of the occupied states, with the maxima at --~ 1.5, 4.3, 10.5, and 13.3 eV. The differences between the XPS spectra of the crystalline and those of glass samples are quite insignificant. In Hayashi, Sato and Taniguchi (1999), densities of occupied states in the range 0 - 1 3 eV and densities of unoccupied states in the range 0 - 1 0 eV were studied. The following maxima were found: three maxima of densities of occupied states at --~ 1.4, 2.9, and 4.9 eV, and two maxima of densities of unoccupied states at --~3.6 and 8.0 eV. According to the general theory of the optical properties of glasses, the maxima of the optical transitions in glasses are mostly determined by their relative positions in the energy scale of densities of occupied and unoccupied states. Therefore, taking into account the value Eg ~ 1.4 eV and the positions of the maxima of densities of states for g-AszSe3, one can expect four (Bishop and Shevchik, 1975) and eight (Hayashi et al., 1999) maxima of transition bands (the data in Columns B and A in Table III). They are due to transitions from the maxima of densities of occupied states into the lowest and higher maxima of densities of free states. This rather simplified model can give only the evaluations of the energy values of the expected maxima of the optical spectra of g-AszSe3. Nevertheless, it is in good agreement with our calculated spectra.
5.2.
DECOMPOSITION OF DIELECTRIC FUNCTION SPECTRA AND CHARACTERISTIC ELECTRON LOSS SPECTRA INTO ELEMENTARY COMPONENTS
For g-As2Se3, three sets of fundamental optical functions were calculated on the basis of the experimental R(E) spectra (Sobolev, 1967--No. 3) and characteristic bulk electron loss - I m - 1 spectra (Perrin, 1973mNo. 1; Rechtin and Averbach, 1974mNo. 2). As in the case of g-AszS3, the dielectric function spectra and electron loss spectra of these three sets were decomposed into elementary components, and their main parameters (Ei, Hi, Si, f~, li) were determined. Three of the obtained parameters (Ei, Hi, and Si) of decomposition of the functions of the three sets are given in Table IV. On the whole, 11 (No. 3), 7 (No. 2), and 8 (No. 1) transverse components and 7 longitudinal ones were found. The largest numbers of the transverse components were found from the ez(E ) spectrum, calculated on the basis of R(E). The longitudinal components in the energy range E > 14 eV were determined only from the experimental loss spectra. These and other characteristic features of the components of the spectrum curves' decomposition are connected with the properties of processes of optical and electronic excitation of transitions. The most intensive bands are located in the long-wavelength (shortwavelength) part of the e 2 ( - I m e -1) spectrum. Moreover, when moving from the bands maxima to the higher (lower) energy range, the values of e 2 ( - I m e -1) are not merely decreasing, but drop sharply to very small values, which are recorded with relatively large errors. Hence, the transverse components are determined most reliably in the energy range E < 12 eV, while the longitudinal o n e s ~ i n the energy range E > 12 eV. Characteristic bulk loss spectra are affected by the samples preparation
TABLE IV ENERGIES (eV) EiOF THE MAXIMA, HALF-WIDTH Hi, A N D AREASSi OF THE BANDCOMPONENTS FOR THREE VARIANTS ( 1 , 2 A N D 3) OF THE DECOMPOSITION OF THE SPECTRA E2 AND -1m E - ' AND POSSIBLE ENERGIES En OF OPTICAL TRANSITIONS (VARIANTS A AND B) OF g-As2Ses NO.
Ei
-1m
&2
1
2
3
Si
Hi
1
2
-1m
&I
E-'
3
1
2
3
1
-Im
&2
&-'
2
En
3
1
2
3
1
B
E-'
2
3
A
Optical Spectra of Arsenic Chalcogenides
219
technology and the methods of obtaining the - I m e-1 function from the experimentally measured electron loss curves (Pines, 1966). These features of e 2 and - I m e -1 can explain certain differences in the values of the components' parameters in the three calculations (Nos. 1- 3). In the above consideration of the integral spectra of the optical spectra of gAszSe3, a simplified model of their interpretation was proposed, based on the experimental spectra of distribution of densities of occupied and unoccupied states (two right columns A and B in Table III). This model can also be applied to the components of decomposition of the e 2 and - I m e -1 spectra (two right columns A and B in Table IV). Thus, the complete sets of spectra of the fundamental optical functions of g-AszSe3 have been obtained for the first time in the range 0 - 1 2 and 0 - 3 5 eV, their integral spectra of dielectric function and characteristic bulk electron loss function have been decomposed into transverse and longitudinal components, the main parameters of the components have been determined, the scheme of their interpretation has been proposed within the model of transitions from the maxima of densities of occupied states to free states. These results substantially enlarge the amount of information on the optical spectra and electronic structure of g-AszSe3 in a wide energy range of fundamental absorption. They create a conceptually new foundation for theoretical calculations of electronic structure of vitreous arsenic chalcogenides.
6. Optical Spectra of g-AsxSel-x (x = 0.5, 0.36) 6.1.
CALCULATIONS OF SETS OF OPTICAL FUNCTIONS
The glasses of A s - S e system can have continuous composition. They were modeled theoretically in Schunin and Schwarz (1989) with clusters AsxSel-x of various compositions. The value of Eg of many of them lies in the small energy interval 1.4-1.6 eV. In Rechtin and Averbach (1974), the loss spectra - I m - 1 of two phases of such system ( x - 0.50 and 0.36) in the range 3 - 1 0 0 eV are given. On the basis of these spectra, we calculated the sets of optical functions (Figs. 6 and 7). The experimental - I m e -1 spectrum of thin layers of AssoSeso contains intensive maxima No. 1, 3, 5, and 8 (Table V). The most intensive and broad maximum No. 8 is due to bulk ( - I m e - 1 , E p v - 18.8 eV) and surface ( - I m ( 1 + e) -1, E p s - 14.6 eV) plasmons. The value of parameter p - Epv/Eps- 1.3 is close to the theoretical one (p - 1.4) (Pines, 1966) for free electrons. In the calculated spectra of many functions, maxima No. 3, 5, 6, and 9 can be seen. Other maxima manifest themselves with various intensities, reflecting the character of their dependencies on energy. Usually, as is the case with AssoSeso, the most long-wavelength maximum can be seen more clearly in the R, n, and /31 spectra, while in the 82, k,/z, and E 282 spectra, one sees more clearly the next one or two maxima. The experimental - Im e -1 spectrum of As36Se64 films contains maxima No. 3 - 5 , 7, and 9 (Table VI). The most intensive and broad of them--maximum No. 7--is due to
V.
220
Val.
Sobolev
and
Sobolev
V.V.
(a) o
7 ,.I
|~ t'
,I
6--
.iI i't
0.2
g-As5o Seso
2
!
J
4
, ,
.
". ... 9 9
~
R ~ R
0.1 1
2 9
l I
,
~
~
o
,
'
,
.
'
'
'
'
'
'
'
'
'
0
i
i
10 (b)
- 5
12-
9
/~ I~
I
\**
rio
4 ~
~
~
' \" ,.
g-As5~176
.
',\'\
" ~
".
0.8." /
"\'.
~
9\ :
E2 E 2
'~.
~
0
..,......""
,.~
09
" k " ,~ ,,
o1 .," 9
%
..." ,"
~ ............
eq
2 o
/
~ 2
40
.
,,x
"~6
30
"~r
.
~,.
Ii 7 /
i
r,
1.2-
,.,,, ~.
I/I,~\~"'"Il i "
3
20
I
I
10
20
.
.
.
.
.
.
.
0.4.
I
E, eV
30
40
FIG. 6. Calculated spectra of R, n,/31 (a), k,/x,/32, E2e2 (b) for g-AssoSeso in the energy range 0-40 eV.
bulk (Epv -- 19.0 eV) and surface (gps -- 11.3 eV) plasmons. Parameter p - Epv/Eps -1.7 noticeably exceeds the theoretical value for free electrons. In the calculated spectra of many optical functions, maxima No. 4 - 6 can be seen. In the case of As36Se64, the most intensive maxima are No. 3 (R, n, el) or No. 4 (e2, k,/~, E 2e2). All the maxima of the set functions' spectra, except for maxima No. 8 (AssoSeso) and No. 7 (As36Se64), are due to transitions from occupied states into free ones. In Hayashi et al. (1999), it is found from the photoemission spectra that the maxima N ( E ) of free states of many phases of g - A s - S e system are at energy values 4.0 and
Optical Spectra of Arsenic Chalcogenides
221 0.4 m 4
(a)
I I
9-
~, i"
g-As36 8e64
0.3 m 3
.I
6
tl
0.2 m 2
3
,......
,'
.....
.
-,-
...........
0 10
(b)
20
30
E, eV
40
. I ~" ,'iL!
" -
~'i!.
9
s
"
9
-
I
g-As36 Se64
. / 1.6-
"~
~
,\ "'\ ~ \'xe2E2
"
,,idI . .
2
9
\x
I I
3
/ /
~ ri i! i Ii I ~ 1 ' t'l t/
~z~ 6
./ 9
-
~'/-'!I..
2.0"~ ~ *
"
\
\x\
~
"" ""
/"
"
t"q
eq
./ 0.8-
'-"
.
1.2-
9/
.
1
, . . 0.4-
E2 ~ "/
0
.
~
I
I
10
20
I
E, eV
30
40
FIG. 7. Calculated spectra of R, n, el (a), k,/z, e2, E2e2 (b) for g-As36Se64 in the energy range 0 - 4 0 eV.
9.0 eV, above the top of occupied states, while the maxima N(E) of their occupied states are below their top by 1.3, 2.8, 5.0, and 10.0 eV. On the basis of the results for N(E) from Hayashi et al. (1999), we evaluated the energy values En of the maxima of possible transitions of both phases g-AsxSey (right columns of Tables V and VI). These evaluations are mostly in good agreement with the energy values of the maxima of many optical f u n c t i o n s (/32,/.s k).
V. Val. Sobolev and V.V. Sobolev
222
TABLE V ENERGIES (eV) OF THE MAXIMA AND SHOULDERS IN THE SPECTRA OF OPTICAL FUNCTIONS AND POSSIBLE ENERGIES E n OF OPTICAL TRANSITIONS (VARIANTS A AND B) OF g-AssoSeso No.
R . 2.7 3.7 . 9.2 12.3 . . 27.0 .
1 2
3 4 5 6 7 8 9 10
6.2.
/31
n
132
. 3.0 . . 7.5 11.0 . . . . . .
. 3.0 -
. . 4.0
7.8 11.0 . . 30.0 .
8.8 12.8
.
/x
k .
. .
.
3.8 5.5 9.3 12.8
.
.
. 3.6 5.6 9.3 12.8 18.0
. . -
E2/32
. 3.6 5.6 9.3 12.8 18.0
. 27.0 32.0
. .
. .
- h n / 3 -1
-Im(1 +/3) -1
2.1 . 3.5 10.0 18.8
2.1
. .
3.5 10.0 14.6 . .
En -
2.7 4.2 5.3 10.3 11.4 19.0 -
. .
DECOMPOSITION OF DIELECTRIC FUNCTION SPECTRA AND CHARACTERISTIC ELECTRON LOSS SPECTRA INTO ELEMENTARY COMPONENTS
T h e e x p e r i m e n t a l loss s p e c t r a - I m e - 1 o f g - A s s o S e s o a n d g-As36Se64 f i l m s a n d t h e spectra, calculated from them, were decomposed
82
into elementary components. The most
intensive transverse and longitudinal components of the transitions and their parameters were determined. In Tables VII and VIII, numbering
of the components
is g i v e n o n
the a s s u m p t i o n of the s a m e nature o f the s a m e n u m b e r c o m p o n e n t s of both phases, their d i f f e r e n c e s in e n e r g y c o n s t i t u t i n g o n l y a s m a l l p a r t o f t h e i r h a l f - w i d t h s . C o m p o n e n t s N o . 1, 4 ( A s s o S e s o ) a n d N o . 7, 10, 11 (As36Se64) w e r e n o t d e t e c t e d , p r o b a b l y b e c a u s e o f t h e i r small intensity. After d e c o m p o s i t i o n of the - I m e -1 spectra into c o m p o n e n t s , i m p r o v e d values of bulk plasmon
energy were obtained: Epv-
18.7 e V ( A s s o S e s o ) a n d 18.6 e V
(As36Se64). T h e s e v a l u e s a r e s m a l l e r t h a n Epv o f A s z S e 3 ( T a b l e I V ) o n l y b y 0.7 e V . Our evaluations of energy values of the maxima
of the bands of possible transitions
b e t w e e n t h e m a x i m a o f d e n s i t i e s o f s t a t e s f r o m H a y a s h i et al. ( 1 9 9 9 ) o f b o t h g - A s x S e l - x
T A B L E VI ENERGIES (eV) OF THE MAXIMA AND SHOULDERS IN THE SPECTRA OF OPTICAL FUNCTIONS AND POSSIBLE ENERGIES En OF OPTICAL TRANSITIONS (VARIANTS A AND B) OF g-As36Se64 No. 1
2 3 4 5 6 7 8 9
R . . 3.7 5.5 8.2 9.9 . 19.0 28.5
el
n
. .
. . 3.7 7.2 -
.
k
. .
. .
. .
.
. 5.3 8.1 . . .
3.7 5.1 7.2 . 20.0
. 20.0 .
/32
.
.
/x . . .
. 5.7 8.4 10.5 .
E2/32
- I m e -1
. . 5.7 8.4 10.6
5.5 8.2 11.0
. . .
. .
.
.
4.5 6.8 9.5 19.0 . 29.5
-Im(1 +/3) -1 1.4 2.4 4.5 6.8 9.5 11.3 29.5
En
2.7 4.4 5.3 7.0 10.3 19.0 -
223
Optical Spectra of Arsenic Chalcogenides TABLE ENERGIES FOR TWO
( e V ) Ei O F T H E M A X I M A , VARIANTS
Hi,
AND AREAS
(1 A N D 2 ) O F T H E D E C O M P O S I T I O N
POSSIBLE No.
VII
HALF-WIDTH
ENERGIES
E n OF OPTICAL TRANSITIONS
Ei 82
S i OF THE BAND
OF THE SPECTRA
-
Im e- 1
Si
82
-
-
Im e- 1
-1
AND
OF g-As5oS%0
Hi
-
COMPONENTS
e 2 AND --Ime
132
En
-
Im e- 1
-
2
3.5
-
1
-
2
-
2.7
3
4.3
-
1.9
-
8.6
-
4.2
5
5.9
6.7
2.2
3.5
7.0
0.4
5.3
6
7.5
6.7
1.7
3.5
2.5
0.4
-
7
8.8
-
2.3
-
6.8
-
8
9.8
-
2.5
-
2.9
-
10.3
9
10.9
-
2.3
-
4.7
-
11.4
10
13.3
14.8
2.3
8.0
3.1
2.0
-
11
15.9
14.8
2.9
8.0
3.3
2.0
-
18.7
-
8.1
-
21
2.3
5.5
12 13
20.9
-
11.5 1.4
-
3.1
19
14
-
25.9
-
3.9
-
1.8
-
15
-
31.5
-
5.3
-
1.5
-
16
-
38.0
-
3.0
-
2.4
-
phases are in good agreement with the energy values of many decomposition components of the e 2 spectra (energy values En in the right columns of Tables VII and VIII). The obtained results prove the strong similarity between the structures of the optical functions' spectra and the electronic structure of the three g-AsxSel-x phases (x - 0.40,
0.50, 0.36). TABLE
VIII
(eV) E i OF THE MAXIMA, HALF-WIDTHS Hi, AND AREAS S i OF THE BAND COMPONENTS F O R T W O V A R I A N T S (1 AND 2 ) O F T H E D E C O M P O S I T I O N OF THE SPECTRA e 2 AND --Im e -1 AND
ENERGIES
POSSIBLE No.
ENERGIES
En O F O P T I C A L T R A N S I T I O N S
No. e2
OF g-As36Se64
Ei - Im e- 1
/32
Hi
-
-
Im e- 1
82
En
-
-
Im e- 1
1
2.2
-
1.4
-
2.5
-
2
3.6
-
1.6
-
5.4
-
2.7
3
4.5
-
1.5
-
6.0
-
4.4
4
5.4
-
1.5
-
10.8
-
5.3
5
6.0
-
1.4
-
4.7
-
-
6/
6.6
7.1
1.5
2.0
0.3
7.0
6
8.2
-
1.3
-
3.7
-
7.0
8
10.3
-
1.7
-
2.8
-
10.3
9
11.5
1.1
5.0
12
-
13 15
11.1
1.0
1.7
2.7
3.4
-
7.3
-
18.6
-
2.6
-
-
20.3
-
77.0
-
5.7
-
29.0
-
8.6
-
0.9
19.0 -
224
V. Val. Sobolev and V.V. Sobolev
7. Optical Spectra of g-As2Te3 7.1.
CALCULATIONS OF SETS OF OPTICAL FUNCTIONS
For g-As2Te3, the reflectivity spectra of p o l i s h e d bulk sampl es in the ranges 0 . 5 - 2 5 eV (Andriesh and Sobolev, 1965, 1966; A n d r i e s h et al., 1967; Sobolev, 1967; B e l l e et al., 1968) and 0 . 5 - 1 4 eV (Velicky, Z a v e t o v a and Pajasova, 1975) are k n o w n . T h e results of these papers are in g o o d a g r e e m e n t with each other. Thus, we used the
(a) 4 - -0.4
15 ifg-As 2 Te 3
12
.
~
I
3 -0.3
9 2 -0.2
6
,:-,
..
.
3 ,
_
-0.1
i
~ E 1 ~
0
||
,
,
o
|
,
,
o
|
,
~
I
10
5
E, eV
I
I
15
20
25
(b)
2
i ., . i "~" "
d"
I
I
~
~
,c--6
/
"
~
4~ ::t.
1 2
I
0
5
10
E, eV
15
20
25
FIG. 8. Experimental spectrum of R and the calculated spectra of n, el (a), k, tx, e2, EZe2 (b), - I m e -l, -Im(1 + e) -I , nef , eef (C) for g-As2Te3 in the energy range 0-25 eV.
Optical Spectra of Arsenic Chalcogenides
225
(c) o
0.5
*
20
0.4 I oD -t-
15 ~D
0.3 f
10
x I'~.x_im(l+~)_s t" /
.........
" " ._
":' ="~...- . . . . . . . . . . . . . . . . . . . . . . .
I / !
" " " " "' .' - "." -. ' . . . .
# jlnef ##?f/ 9
I
0.2
I
I
"-........
--
0.1
I
FI6. 8 (continued)
R(E) spectrum from Sobolev (1967) in the calculations. On the basis of this spectrum, a complete set of the fundamental optical functions of g-AszTe3 was calculated in the range 0 - 2 5 eV (Fig. 8). The experimental reflectivity spectrum R(E) contains a very intensive and asymmetric broad band in the range 0 - 5 eV with the main maximum at ---2.0 eV and very weak side maxima at --- 1.3 and 3.2 eV. It is strongly overlapped with a band in the range 5-7.5 eV with the maximum at ---6.3 eV. The main band of R(E) in the calculated spectra of other optical functions is transformed into narrow (el, n, e2) o r broad (k,/~, EZe2) maxima at --- 1.14 (el), 1.20 (n), 1.97 ( e 2 ) , 2.63 (k), 3 . 3 5 (EZe2), and 4.0 (/.~). The analog of the second band of R(E) is shifted into the lower energy range by ---0.3 eV (e 1, n, e2), stays where it is (k), or is shifted into the higher energy range by --~0.5 eV (~, E 2e2). The values of g-AszTe3 optical functions at the long-wavelength maximum come very quickly to very large values: ---18 (el), 4.25 (n), 13.5 ( e 2 ) , and 1.4 • 107 cm-1 (1~). The characteristic bulk electron loss spectrum contains the main doublet band with maxima at ---7.9 and 9.5 eV and a maximum at ~-5.3 eV. Their analogs in the surface loss spectrum are shifted into the lower energy range to locations ~--5.1, 7.1, and 8.7 eV. From the photoemission spectra (XPS) of Bishop and Shevchik (1975), it was found that the distribution of density of occupied states N(E) in g-AszTe3 consists of two bands in the ranges 0 - 7 and 7 - 1 5 eV. The first band has doublet structure with the maxima at 1.6 and 4.5 eV. The maximum of the second band is very broad and lies in the interval 9.8-12.3 eV. For g-AszTe3, Eg is equal to ---0.8 eV (Mott and Davis, 1979; Tsendin, 1996). On the basis of these results, one can evaluate the energy values of possible transitions from occupied states to the lowest free states. One can also expect bands in the range 0.8-7.8 eV with the maxima at --~2.4 and 5.3 eV and a very broad band in the range 10.6-13.1 eV. These bands will be strongly overlapped with the bands of transitions from occupied states to higher free states.
226
V. Val. Sobolev and V.V. Sobolev
7.2.
D E C O M P O S I T I O N OF D I E L E C T R I C F U N C T I O N S P E C T R A A N D C H A R A C T E R I S T I C E L E C T R O N LOSS S P E C T R A I N T O E L E M E N T A R Y C O M P O N E N T S
The
dielectric
AszTe3 and
were
longitudinal
Altogether, intensive
16
spectra
components
and very broad
and
characteristic
into elementary
transverse
bulk plasmons. bound
function
decomposed
and
and
24
their
parameters
longitudinal
longitudinal
The rest components
bulk
components.
electron
The
most
were
spectra
determined
components
components
loss
intensive
were
of g-
transverse (Table
IX).
The
most
found.
N o . 131 a n d 1 4 1 / a r e a p p a r e n t l y
are connected
with the electronic
due to
transitions
from
states to free levels.
According longitudinal
to
the
transitions
general
transition
theory
are larger than the energy
(Pines, values
1966),
the
energy
of their transverse
values
of
analogs
by
TABLE IX ENERGIES ( e V ) E i OF THE MAXIMA, HALF-WIDTHS Hi, AND AREAS Si, AND AMPLITUDES I i OF THE BAND COMPONENTS OF THE DECOMPOSITION THE SPECTRA •2 AND - - I m e -1 AND POSSIBLE ENERGIES En OF OPTICAL TRANSITIONS (VARIANTS A AND B) OF g - A s 2 Z e 3 No.
Ei /32
1 2 3 4 5 6 7 8 9 10 10 /
-
Hi -
Im e - 1
/32
1.22 1.46 1.66 1.98 2.32 2.68 3.06 3.50 3.96 4.4 -
1.58 1.84 2.38 2.90 3.32 3.84 4.08 4.56 4.94
11
5.5
5.24
1.0
1 l/
_
5.66
-
12
6.3
6.46
1.7
12 /
-
6.96
13
7.2
13 /
-
14 14 / 14"
15 151 15" 16 16 / 16"
-
Im e - ~
-
-
Im e - 1 0.00 0.01 0.03 0.02 0.02 0.12 0.01 0.09 0.02
1.0
0.73
0.8
-
1.7
-
0.46
7.26
0.7
7.9
-
8.7
8.6
-
12.7 -
/32
-
En -
Im e - 1
2.00 4.30 3.20 8.20 2.40 6.75 1.30 3.74 0.53 2.00 -
0.01 0.01 0.02 0.02 0.02 0.06 0.02 0.07 0.02
2.4 2.4 2.4 5.3 5.3 5.3 5.3 5.3
0.25
0.50
0.17
5.3
0.08
-
0.06
5.3
3.87
0.42
1.57
0.17
-
0.02
-
0.03
10.6-13.1
0.6
0.50
0.04
0.47
0.05
10.6-13.1
2.1
-
0.92
-
0.30
10.6-13.1
2.5
1.2
3.24
0.05
0.90
0.03
10.6-13.1
9.0
-
1.5
-
0.19
-
0.09
10.6-13.1
9.9
-
2.5
-
0.88
-
0.24
10.6-13.1
11.7
1.9 -
1.7 1.5
1.30 -
0.24 0.36
0.46 -
0.10 0.16
10.6-13.1 10.6-13.1
12.2
-
0.40
-
0.02
-
0.04
10.6-13.1
12.6 13.0
2.50 -
0.8 0.49
2.70 -
0.11 0.04
0.73 -
0.09 0.05
10.6-13.1 10.6-13.1
13.9
-
2.2
-
0.95
-
0.29
10.6-13.1
10.7
0.65 1.1 0.30 1.3 -
0.25 0.35 0.8 0.54 0.6 1.4 0.42 0.8 0.6
/32
li
1.20 2.49 1.87 8.13 1.63 9.50 1.25 5.90 0.24 3.74 -
10.6 -
0.43 0.40 0.40 0.70 0.46 1.0
-
Si
5.3
Optical Spectra of Arsenic Chalcogenides
227
0.1-0.2 eV (Nos. 4, 11, 14, 16). This difference constitutes only a small part of their halfwidths Hi, and is within the accuracy of decomposition. In the spectrum of transverse components, one can distinguish three groups of most intensive bands: Nos. 4, 6, 8, 10, 12 and Nos. 14, 15, 16. They can be due to transitions En from the three bands of N(E) occupied states to the lowest free states (the rightmost column in Table IX). For g-As2S3 and g-AszSe3, considerably more complex structures of N(E) occupied states are known (Bishop and Shevchik, 1975; Salaneck and Zallen, 1976; Hayashi et al., 1999), as well as a complex structure of N(E) free states of the phases of g-As-Se system (Hayashi et al., 1999). Improvement of the XPS registration technique will undoubtedly allow observing more complex N(E) structures in g-AszTe3 and explain in more detail the nature of the determined transition components of g-AszTe3 in a wide energy range.
8.
Conclusion
Complete sets of the spectra of the fundamental optical functions of three glassy arsenic chalcogenides As2S3, AszSe3, AszTe3, and two phases of AsxSel-x system (x -- 0.50, 0.36) in a wide energy range of intrinsic absorption have been obtained for the first time. In another first, their integral dielectric function and characteristic bulk loss spectra have been decomposed into the elementary transverse and longitudinal components. The main parameters of components have been determined, including the transitions energies and probabilities. The schemes of interpretation of the components have been proposed in the model of transitions occurring from the maximum densities of the occupied states to the unoccupied states. The obtained results substantially enlarge the amount of information about the optical spectra and electronic structure of AszX3 glasses in a wide energy range of fundamental absorption. In addition, they lay a new principal foundation for the consideration of g-AszX3 properties, and provide a basis for future theoretical calculations of their electronic structure and optical spectra.
References Andriesh, A.M. and Sobolev, V.V. (1965) Thesises of of 3rd Conference "Chemical Bond in Semiconductors", CSU BSSR, Minsk, p. 48. Andriesh, A.M. and Sobolev, V.V. (1966) Chemical Bond in Semiconductors (Proceedings of the 3rd Conference "Chemical Bond in Semiconductors"), Science and Technics, Minsk, 212 pp. Andriesh, A.M., Sobolev, V.V. and Popov, Yu.V. (1967) Thesises of 4th International Conference "Glassy Semiconducting Chalcogenides", Nauka, Leningrad, p. 5. Babic, D. and Rabii, S. (1988) Phys. Rev. B, 38, 10490. Babic, D., Rabii, S. and Bernholc, J. (1988) Phys. Rev. B, 39, 10831. Belle, M.L., Kolomietsh, B.T. and Pavlov, B.V. (1968) Phys. Tech. Semicond., 2, 1448. Bishop, S.G. and Shevchik, N.J. (1975) Phys. Rev. B, 12, 1567. Gubanov, A.I. (1963) Quantum Electronic Theory of the Glass Semiconductors, AN USSR, Moscow, 250 pp. (in Russian). Hayashi, J., Sato, H. and Taniguchi, M. (1999) J. Electron Spectrosc. Relat. Phenom., 101-103, 681. Hullinger, F. (1976) Structural Chemistry of Laser-Type Phases, D. Reidel, Dordrecht. Ioffe, A.F. and Regel, A.R. (1959) Prog. Semicond., 4, 238.
228
V. Val. Sobolev and V.V. Sobolev
Lazarev, V.B., Shevchenko, V.Yu., Grinberg, Yu.Ch. and Sobolev, V.V. (1978) Semiconductors ofA2B 5 Group, Nauka, Moscow, 256 pp. (in Russian). Lazarev, V.B., Sobolev, V.V. and Shaplygin, I.S. (1983) Chemical and Physical Properties of the Simple Metal Oxides, Nauka, Moscow, 239 pp. (in Russian). Mott, N.F. and Davis, E.A. (1979) Electron Processes in Non-crystalline Materials, Clarendon Press, Oxford, 656 pp. Perrin, J. (1973) These: Contribution a l'etude des Transitions Interbandes et des Plasmons de Trisulfure d'arsenic, Universite de Reims, Reims, 82 pp.. Perrin, J., Cazaux, J. and Soukiassian, P. (1974) Phys. Stat. Sol. (b), 62, 343. Pines, D. (1966) Elementary Excitations in Solids, W.A. Benjamin, New York, 305 pp.. Rechtin, M.D. and Averbach, B.L. (1974) Phys. Rev. B, 9, 3464. Salaneck, W.R., Liang, K.S., Paton, A. and Lipari, N.O. (1975) Phys. Rev. B, 12, 725. Salaneck, W.R. and Zallen, R. (1976) Solid State Commun., 20, 793. Schunin, Yu.N. and Schwarz, K.K. (1989) Phys. Tech. Semicond., 23, 1049. Sobolev, V.V. (1967) Thesis of Dissertation "Spectroscopy of the Solid State Energy Bands and Excitons", Institute of Appl. Phys. of AN MSSR, Kishinev, 564 pp.. Sobolev, V.V. (1978) The Energy Bands ofA 4 Group, Shtiinza, Kishinev, 207 pp. (in Russian). Sobolev, V.V. (1979) The Optical Fundamental Spectra ofA3B 5 Compounds, Shtiinza, Kishinev, 287 pp. (in Russian). Sobolev, V.V. (1980) Bands and Excitons ofA2B 6 Compounds, Shtiinza, Kishinev, 255 pp. (in Russian). Sobolev, V.V. (1981) The Energy Bands of A4B 6 Compounds, Shtiinza, Kishinev, 284 pp. (in Russian). Sobolev, V.V. (1982) Bands and Excitons of Ga, In and Tl Chalcogenides, Shtiinza, Kishinev, 272 pp. (in Russian). Sobolev, V.V. (1983) The Energy Structure of the Low Energy-Bands Semiconductors, Shtiinza, Kishinev, 287 pp. (in Russian). Sobolev, V.V. (1984) Excitons and Bands of the A1B 7 Compounds, Shtiinza, Kishinev, 302 pp. (in Russian). Sobolev, V.V. (1986) Bands and Excitons of Cryocrystals, Shtiinza, Kishinev, 206 pp. (in Russian). Sobolev, V.V. (1987) Bands and Excitons of the Metal Chalcogenides, Shtiinza, Kishinev, 284 pp. (in Russian). Sobolev, V.V. (1995) Fiz. Khim. Stekla, 21, 3. Sobolev, V.V. (1996) J. Appl. Spectrosc., 63, 143. Sobolev, V.V. (1999) J. Appl. Spectrosc., 66, 299. Sobolev, V.V., Alekseeva, S.A. and Donetskich, V.I. (1976) The Calculations of the Semiconductor Optical Functions by Kramers-Kronig Correlation, Shtiinza, Kishinev, 123 pp. (in Russian). Sobolev, V.V. and Nemoshkalenko, V.V. (1988) Electronic Structure of Semiconductors, Naukova Dumka, Kiev, 423 pp. (in Russian). Sobolev, V.V. and Nemoshkalenko, V.V. (1989) The Band Structure of Rare Metal Dichalcogenides, Naukova Dumka, Kiev, 296 pp. (in Russian). Sobolev, V.V. and Nemoshkalenko, V.V. (1992) Solid State Electronic Structure (Introduction to the Theory), Naukova Dumka, Kiev, 566 pp. (in Russian). Sobolev, V.V. and Shirokov, A.M. (1988) Electronic Structure of Chalcogens (S, Se, Te), Nauka, Moscow, 224 pp. (in Russian). Strujkin, V.V. (1989) Solid State Phys., 31, 261. Tsendin, K.D. (Ed.) (1996) Electron Processes in Chalcogenide Glassy Semiconductors, Nauka, SanctPeterburgh, 486 pp. (in Russian). Velicky, B., Zavetova, M. and Pajasova, L. (1975) Proceedings of the 6th International Conference on Amorphous and Liquid Semiconductors, Nauka, Leningrad, p. 273. Zallen, R., Drews, R.E., Emerald, R.L. and Slade, M.L. (1971) Phys. Rev. Lett., 26, 1564.
CHAPTER
6
MAGNETIC PROPERTIES OF CHALCOGENIDE GLASSES Yu. S. Tver'yanovich DEPARTMENTOF CHEMISTRY,ST. PETERSBURGSTATEUNIVERSITY,PETRODVORETS,UNIVERSITETSKYPR. 26, 198504 ST. PETERSBURG,RUSSIA
1. Magnetism of Chalcogenide Glasses Not Containing Transitional Metals There is a continuous network built into the glass that has geometrical order irregular in comparison with that of the crystal. It is impossible to account for this network without taking into account various crystalline defects and the discontinuity of chemical bonds involved. The latter should have the uncompensated magnetic moment. Therefore, it was necessary to expect the existence of the Curie paramagnetism for glassy semiconductors. However, the careful measurements of the magnetic susceptibility (X) of glassy semiconductors (which do not contain any impurities) at low temperatures, as well as the investigations of ESR, showed that the concentration of paramagnetic centers in these materials is below that was expected in some orders. The detection of this inconsistency gave a strong impulse to the development of the theory of the structure of glassy semiconductors and has reduced to origin of the series of models for the structure of chalcogenide glasses, based on Anderson's idea about the energy preferability of the existence of the charged breakaways of bonds in comparison to the neutral ones (Anderson, 1975; Mott, Davis and Street, 1975; Kastner, Adler and Fritzsche, 1976).
1.1.
PROBLEMS
OF PHYSICOCHEMICAL
ANALYSIS OF GLASSY SYSTEMS
One of the major directions of the investigations of chalcogenide glasses is the study of their chemical structure. The research in this field may be carried out using the magnetochemical method within the framework of the physicochemical analysis (PCA). The following definition of the PCA was denoted by N.S. Kurnakov: 'The physicochemical analysis is aimed at detecting the correlation between composition x and properties e of the equilibrium systems, and its outcome is the pictorial build-up of the diagram composition-property.' He also noted that the PCA methods can be applied to the equilibrium systems only: 'The common principle of the physicochemical analysis is the quantitative study of the properties of equilibrium systems consisting of two or more 229
Copyright 9 2004 Elsevier Inc. All rights reserved. ISBN 0-12-752188-7 ISSN 0080-8784
Yu. S. Tver' yanovich
230
components, depending on their composition.' However, the glassy state is not in thermodynamical equilibrium. The analysis of this problem was carried out by Gutenev (Tver'yanovich and Gutenev, 1997). As a result, the following requirements of applicability of original principles of PCA for the glassy systems were formulated: 1. The system A - B belongs to the class of the chemically rational ones, i.e., only one chemical transmutation or series of sequential transmutations may take place in it. 2. All the glasses of the system are obtained by cooling of melts reduced to the state of the chemical equilibrium, at the same cooling rate. 3. Tg for the system is constant. If Tg depends on composition and varies in gap Tg +_ 0.1Tg, the enthalpy of the reaction nA + mB ,--, A n B m should be outside of the interval - 4 R T g <-- A H ~ <- -0.7RTg provided that its entropy is close to zero.
1.2.
DORFMAN'SMETHOD
The magnetic susceptibility of chalcogenide glasses does not contain the contribution from free carriers (see later) and consists of Langeven's diamagnetic susceptibility and van-Vleck's paramagnetic susceptibility (1)
X = Xd -+- Xp.
van-Vleck' s paramagnetic susceptibility, as it is known, is determined by the deviation of the valent electronic shell from a spherical symmetry. Therefore, this component of X is the most responsive to the modification of the chemical bonds, and consequently the usage of Xp for PCA is the most productive. But the dividing of X on Xd and Xp is experimentally impossible, as neither of them depends on the magnetic field and temperature. One of the most simple and reliable methods of separation X on components is Dorfman's method (Dorfman, 1961), which implies the following. The quantummechanical expression for optical (electronic) polarizability (c~o) of Z-electronic atom has the following aspect: 4 ceoo -- -~ ZaB
(k]r 2 k)
,
(2)
i=1
where aB is the Bohr radius. The total area of all the electronic orbits (in a plane, perpendicular axis of a field) is placed in round brackets. The expression for Langeven's diamagnetism can be noted as follows: NA e2
~ . (k r2i [k), Xa = - 6mc------~i=1
(3)
where NA is the Avogadro number, e is the electron charge, m is the electron mass and c is the light velocity. From these two expressions, we discover that NAe2 (ceoaBZ) 1/2. Xd = -- 4mc-------g
(4)
Magnetic Properties of Chalcogenide Glasses The value of a~ is determined by Lorentz-Lorentz's formula: 2 4 7rNoa~o noo - 1 = 3 n2+2 '
231
(5)
where No is the number of atoms in m 3 and n~ is the static value of the refraction index ( n ( h ) - n~o-k-a/A2). Thus, we can discover Xp using Eq. (1) and calculating Xd according to Eq. (4). 1.3.
APPLICATIONOF MAGNETO-CHEMISTRY FOR PCA
1.3.1.
System PxS l - x
It is necessary to take into account the following experimental facts at the model operation of the chemical structure of glasses network for this system. At first, phosphorus in the glass network is fourfold coordinated. Secondly, the inconvertible chemical compound P4Slo ( x - - 0 . 2 8 6 ) exists in the system. This compound melts congruently and cannot be transformed into glassy state. The region of glass formation in the system PxSl-x is the following 0.02 --< x -< 0.24. Thus, the atoms of phosphorus are fourfold coordinated by sulfur. One of the atoms of sulfur is non-bridge, and is bonded with the atom of phosphorus only; each bridge sulfur atom is coordinated by 0, 1 or 2 of phosphorus. Therefore, three variants of the allocation of the states of the twofold coordinated atoms of sulfur in glassy matrix are possible. Three different types of isotherms of Xp correspond to each of these variants. 1. Thus, the structure of the glass with x -- 0.20 is chemically ranked (atoms of sulfur have the coordination number on phosphorus equal to 1) and consists of structural units SPS3/1. The formation of such structure should be accompanied by occurrence of any singular point in the diagram Xp(X) (the fracture most probable). 2. The second correlated variant of the allocation is characterized by the presence in the glassy network of sulfur atoms having the coordination number (by phosphorus) equal to 0 and 2. This variant corresponds to the association of the same type structural units $82/2 and units SPS3/2 separately in the interval 0 < x < 0.286 (quasi-eutectic or microemulsion structure). The dependence Xp(X) must be linear in this case. 3. The smooth non-linear dependence Xp(X) corresponds to the uncorrelated (statistical) variant of the allocation of all the three states of sulfur atoms on volume of a glass. The presence of a fracture in the dependence Xp(X) at x - - 0 . 2 0 corresponds to the model (1). This means that the glass at x - 0.20 has a chemically ranked structure and a structural unit SPS3/1 is its basic element. 1.3.2.
Systems GexSl-x and GexSel-x
For these systems the compositions of chemically regular structures are characterized by values x - ZCh(Ce~/(Zch(~e)+ ZCe(Ch~), where ZA(B) are the possible
232
Yu. S. Tver'yanovich
9t
(a)
-,.,.
7t
(b)
o11
o12
m
_/w e.,
Q.
'
0:2
'
014
(c) 18
16 I
014 x FIc. 1. Dependencies of a polarization paramagnetism on composition for the systems PxSl_x (a), GexSl_ x (b) and GexSe1 - - x ( C ) " 0.2
coordination numbers of A atoms by B atoms. So, x accepts values 0.20, 0.33, 0.40, 0.50 and 0.67. The dependencies of Xp on the composition (see Fig. lb) have singularities at x -- 0.33 and 0.40. Apparently it testifies that the chemically regular structures are formed and structural units GeCh4/2 and GezCh6/2 serve as the elements of the chemical reproducibility of the structures. 1.3.3.
Systems (GeSe2)l-x(GeS2)x and (GeSel.5)l-x(GeS1.5)x
The sleek shape of dependencies of Xp on the composition for these systems and considerable positive deviations from additive dependencies (Fig. 2) specify a mainly statistical substitution of selenium atoms by sulfur atoms. However, the asymmetry of concentration dependence of a polarization paramagnetism for the dichalcogenide system (see Fig. 2a) is stipulated by the tendency to dimensional segregation of structural units GeSe4/2 and GeS4/2 in the compositions region near GeS2.
2. Magnetism of Glass-forming Melts 2.1.
MAGNETISM OF CHALCOGENIDE GLASSES AT HEATING
Numerous measurements (Figs. 3 and 4) showed that magnetic susceptibility (X) of chalcogenide glasses at heating up to softening point does not vary. The correlation
Magnetic Properties of Chalcogenide Glasses
233
(a) 16~
m
E 12 e~
E
!
(b)
12
10
0.2
0.4
0.6
S, at. part. FIG. 2. Dependencies of a polarization paramagnetism on composition for the systems (GeSe2)l-x(GeS2)x (a) and (GeSel.5)l-x(GeS1.5)x (b).
energy of states D + and D - in two or three times is less than the bandgap. Therefore, it is expected that at the raise of temperature, a considerable part of these states will get a magnetic moment and will lose electric charge before the noticeable thermal generation of carriers where the mobility gap begins. This process, however, cannot have an effect on X, as the common concentration of such states does not exceed 1018 cm -3, and the magnitude of the Curie paramagnetism fast impinges at propagation of temperature. Therefore, by the moment when a noticeable concentration of the localized breakaways
As 2 S3 3,4
(GeS2)0,2 (As2 S3)0,8
3,0 o
2,6 eAsS
v~
I
2,2 .
i
500
, .
!
Se . Se'~
I
,
1000
T,K FIG. 3. Dependencies of magnetic susceptibility of different alloys in glassy and liquid state on temperature.
234
Yu. S. Tver'yanovich
.~
2-
i
o [\~
/ b
S2 S e 3
1 !
-.
\
0
500
1000
1500
T,K FIG. 4. Dependencies of magnetic susceptibility on temperature: (a) magnetic susceptibility of glassy As2Te3. Temperature dependencies of X for crystalline As2Te3 and Te were depicted by horizontal solid lines. (b) Temperature dependencies of X for liquid AszTe3 and Te, including supercooled state. Melting and crystallization of the supercooled melts AszTe3, Te and glassy AszTe3 are shown by verticals. AX is the difference between magnetic susceptibility of alloy in glassy and liquid state.
of chemical bonds or carriers appears as a result of temperature rise, all of them have magnetic moments. Let us estimate the maximal of the energy gap, at which it is possible to guess the detection of the magnetism of carriers. The length of free-run for carriers in chalcogenide glasses and in their melts is commensurable with interatomic distance. Therefore, the carriers cannot have Landau's diamagnetisms and have only Curie paramagnetism. Therefore, calculation of their concentration with the help of the Curie equation gives the correct result (within a factor about one) irrespective of the degree of localization of carriers (this calculation is valid also for the localized paramagnetic breakaways of bonds, as will be utilized below). It allows us to estimate the concentration of the magnetic centers without the detailed analysis of their nature. Let us consider that the softening point of a glass is equal to 500 K; the minimum magnetic susceptibility of carriers which can expected to be measured at this temperature is equal to 4rr x 10 -~1 m 3 kg -~. Then the concentration of carriers should be n >- 101910 20 cm -3. This concentration corresponds to the energy gap equals 0.5 eV. Thus, though the magnetism of carriers in chalcogenide glasses is not detected, the numerical estimations show that searches of this effect should have a positive outcome in glasses with a small energy gap and high crystallization temperature. The modification of magnetic susceptibility was not revealed at glass transition. The modification of a magnetic susceptibility at the crystallization of some glasses is
Magnetic Properties of Chalcogenide Glasses
235
observed. However, a systematic study of this effect was not carried out. The magnetic susceptibility varies at the crystallization of some glass-forming melts (melting of crystals). But these modifications are not always interlinked with the transformation order-disorder, and are stipulated by the processes happening in supercooled melts. It is visible from the temperature dependencies of the magnetic susceptibility for AszTe3 and Te in the supercooled state (see Fig. 4).
2.2.
MELTS
In reviewing the process of melting and the properties of glassy semiconductors melts, it is possible to tell that they occupy an intermediate position between melts of crystalline semiconductors and oxide glasses. The transforming of crystalline semiconductors in a metal state at melting dramatically changes their structure. The structure of oxide glassforming melts, especially in the first coordination sphere, does not differ practically from the structure of the relevant glasses. The structure of glassy semiconductors at the transition through the liquidus temperature also practically does not vary. The lowtemperature melts maintain semiconductor properties (in this respect glassy semiconductors are semiconductors in a greater degree than crystalline semiconductors). However, at further heating the structure of the melts of glassy semiconductors undergoes major modifications down to passage (for some compositions) in a metal state. So it is clear that the nature of the magnetism of glass-forming chalcogenide melts depends on their conductivity. Let us consider the diagram linking the magnetic susceptibility of melts with their conductivity (Fig. 5). It is known, from the X-ray investigations of high-resistance chalcogenide melts (Poltavcev, 1984), that their structure does not undergo essential modifications in a wide temperature range above liquidus temperature. Therefore, we have no foundation to guess the modification of a Langeven' s diamagnetism or of van-Vleck' s paramagnetism. Noticeable modifications of magnetic susceptibility can occur at small modification of structure only in the case of a magnetism having much more magnitude than diamagnetism per one electron. So, it can be either the paramagnetism of localized electrons (breakaways of chemical bonds), or the paramagnetism of carriers in a conduction band. In the case of low-conductive melts, it is more preferable to speak about the breakaways of chemical bonds. In the case of semiconductor melts with high conductivity, it is more correct to speak about the paramagnetism of carriers. The boundary between these two cases is conditional, though it can seem strange. In the case of the former, the activation energy of formation of paramagnetic centers corresponds to the energies of the rupture of chemical bonds; in the latter case, it corresponds to the energy gap. It visually demonstrates genetic connection of the energy of chemical bonds with the energy gap.
2.3.
MAGNETISM OF MELTS WITH Low CONDUCTIVITY
First of all, the melts of selenium and of arsenic sulfide should be surveyed. The structure of the melt of selenium is investigated with the help of direct methods
236
Yu. S. Tver' yanovich (~min
Te
3-
~
2.
e3
<1 1-
10 -3
10 -2
10 1
1
101
10 2
10 3
~ , O m ' l . c m "1 Fro. 5. Interrelation between conductivity of melts and the difference between magnetic susceptibility of alloy in glassy and liquid state (Ax). For melts, situated to the left from dotted line, p-AT = const; to the right - p AT ~ const (A is the constant). Dashed line separates metal and semiconductor melts.
(Poltavcev, 1984) and indirect methods (Briegleb, 1929; Chistov, Chernov and Dembovskiy, 1968). The temperature of transformation from the structure derived by the rings Se8 to chain structure is below the melting point, as against sulfur. Therefore, when in flux, Se has mainly chain structure, and at the raising of temperature there is a further step-by-step diminution of the part of ring structures and cutting of average length of selenium chain. Magnetic susceptibility of Se on temperature was investigated up to 1200 K (Fig. 3) (Tver'yanovich and Borisova, 1979). The dropping of diamagnetic susceptibility at the temperatures higher than 700 K is the result of the formation of localized paramagnetic centers connected with the breakaways of selenium chains. The number of paramagnetic centers per gram of melt (n), average number of Se atoms in one chain (1), enthalpy and entropy of chain breaking (AH and AS) can be calculated using the following equations:
AX
n(T)tx2 3k~
'
l-
2NAq)c
asen(T)'
n(T)- 2
NA (AH-TAS) exp ~Se 2RT
'
(6)
where AX is the difference between the magnetic susceptibility of melt and the magnetic susceptibility of glass, /x is the magnetic moment of electron, NA is the Avogadro number, Ase is the selenium atomic mass and qSc is the atomic fraction of chain molecules. The dependence of qSc on temperature was investigated in Briegleb (1929). So, it was obtained from the magnetic susceptibility (Tver'yanovich, Borisova and Funtikov, 1986) that A H - 33 kcal mo1-1 and AS = 13.2 cal mo1-1 deg -1. Using
Magnetic Properties of Chalcogenide Glasses
237
phenomenological description of chain decay process (Misawa and Suzuki, 1978), it was calculated that l - 0.11 q5c exp(AH/2RT).
(7)
The comparison of the results obtained regarding magnetic susceptibility and Eq. (7) was carried out in Figure 6. Near the critical temperature, the structures of saturated vapor and of melt became similar. The critical temperature of Se is 1770 K, and the average length of chain molecules is lgl = 0.4 (Rau, 1974). This result was obtained from the extrapolation of the properties of saturated vapor to the critical point. The extrapolation of the temperature dependence of 1for melt state to the critical temperature leads to lgl - 0.8. The proximity of both values means that the mechanism of the decay of chains in Se melt does not change up to the critical temperature. All mentioned above is true if the melt is under saturated vapor pressure. Other chalcogenide glass-forming melts with low conductivity have similar magnetic properties (see, for example, As283): (AxT) is the exponential function of T -1. But structural interpretation of the process of temperature-stimulated decay of covalent network is not simple because the chemical composition is more complex. For all these melts n(T) ---, 1024 cm -3 at T ~ oo. This value seems to be real particularly if we take into account that the limited number of magnetic moments per atom may be equal to the number of valence bonds. It should be mentioned that the vapor of chalcogenide melts is paramagnetic. First of all, it is significant for the melts containing S and Se, melts with low conductivity. This phenomenon must be taken into account at the measurement of magnetic susceptibility of melt placed into sealed quartz tube. Furthermore, if we measure the temperature dependencies of magnetic susceptibility for a set of samples (quartz ampoules with
T m
/ 4-
/
T cryt.
//
40/ /
/ A3
I
/
i g
/I
|
I
/
m
2
./.. I
I
I
I
0.5
1.0
1.5
2.0
1000/T, K 4 FIG. 6. Dependencies of average number of atoms in Se chains on temperature. Solid line is calculated from magnetic susceptibility, dashed lines are calculated using Eq. (7) (corresponding values of AH are pointed out by numbers in kcal mol-~).
238
Yu. S. Tver' yanovich
l \
10
\
\
\
\
"
0.5
~.~ 0 . 0 -0.5
As2Se3 ~~\
-1.0-
0.6
'
0~8
~~
" li0 1 0 0 0 / T , K -1
"
FIG. 7. Dependencies of paramagnetic molecules vapor pressure on temperature. (1) Dependence of total vapor pressure for AszSe3.
the same substance but with different ratio of substance volume and of free volume), we can calculate the temperature dependence of paramagnetic molecules vapor pressure (Fig. 7).
2.4.
SEMICONDUCTOR--METAL TRANSITION IN CHALCOGENIDE MELTS
While arranging investigated substances in the ascending order of their conductivity (see Fig. 5), the common dependence of the magnetic susceptibility on temperature appears (Fig. 8). It consists of low-temperature linear range (I), transitional range (II) and high-temperature linear range (III). More high-temperature site of this common dependence corresponds to substance with higher conductance. The indicated regularity allows us to state that the process of a drop of a diamagnetism at the rising of temperature is intimately interdependent with the process of magnification of conductance.
T
P
FIG. 8. Generalized dependencies of a magnetic susceptibility and density of melts on temperature: (1) semiconductor state; (2) transition region; (3) metal state.
Magnetic Properties of Chalcogenide Glasses
239
The modification of a magnetic susceptibility at the semiconductor-metal transition (SMT) is determined by the modification of the magnetic susceptibility of the atomic network as a result of delocalization of a part of valence electrons and formation of the degenerated gas of free carriers.
x(T)
:
Xa~ - (Xa~ - Xion)cP(T) -t- Xel(T),
(8)
where )(~t is the magnetic susceptibility of semiconductor melt with negligible concentration of paramagnetic centers and free carriers (or the magnetic susceptibility of the glass), )(ion is the magnetic susceptibility of ions skeleton without the valence electrons which became free at metal state (the values of magnetic susceptibility of ions are calculated for all elements; most reliable results were calculated using the HartreeFock model (Mendelson, Beggs and Mann, 1970)) and q~(T) is the fraction of valence electron which became free at the temperature equal to T (0 < q~ < 1). Cohen and Jortner (1978) assumed that at SMT the melt consists of semiconductor and metal microregions, volumetric shares of which vary according to the temperature. Mott (1978) believed that melts at SMT are microscopically homogeneous. The question of the microscopic nature of SMT becomes important in connection with the development of the concept of medium-range order in glasses and melts. The magnetic susceptibility of degenerated electron gas Xel(T) can be calculated by means of three methods. Conductivity at SMT, according to Mott, is proportional to the square of gl factor; magnetic susceptibility of the degenerated electronic gas is proportional g. Therefore, )(el(T) - ~elet(T)
o.met(T).
(9)
o-(T) and o'met(T) are real conductivity and the result of extrapolation of conductivity of a melt at metal state accordingly; ~elet(T) is the magnetic susceptibility of the degenerated electronic gas for a melt at metal state. The second method of calculation Xel(T) used Eq. (10) for the degenerated electronic gas, which takes into account the influence of electron-electron correlation effects on a Pauli paramagnetism and on a Landau diamagnetism (Kojima and Isihara, 1979): Xp • 106 -- [(2.5886/rs)m* + 0 . 4 2 9 3 4 - 0.071123r s + 0.0356rs In rs]r -1 --Xd • 106 -- [(0.8629/rs)m* + 0.05984 + 0.02385 In rs -- 0.02459r~
(10)
+ 0.01269rs In rs]r -1. rs was calculated using (3/47r)(rsrB)-3= n, where n is the concentration of free electrons, rB is the Bohr radius and m* is the effective mass of carriers. Mott' s model and Eq. (10) suppose the homogeneity of a melt at SMT. The third mode of calculation of the susceptibility of mobile electrons is based on the supposition that the melt consists of metallized and semiconductor microregions nanometer of a scale. Then Xe -- ~(T))(meet(T)
and
X - Xg[ 1 - qg(T)] + Xi qg(T) + ~e et(T) q~(T).
( 11 )
i g __ NF/N~ where NF is the density of states for Fermi level for the melt and No is the density of states for Fermi level according to the model of free electron gas.
Yu. S. Tver'yanovich
240
Let us explain the basic thesis of non-homogeneous model of the SMT in melts. At SMT a change of different electronic properties takes place, including conductivity and electro-moving force (Shmuratov et al., 1977). But not only electronic properties change. The rise of the density of melts (Fig. 9), coordination number (Cabane and Friedel, 1971), compressibility (Tsuchiya, 1993) and heat capacity (Fig. 9) can all be observed. Furthermore, the changing of the nature of chemical bonds from covalent to metallic takes place. Directed covalent chemical bonds with low coordination number are substituted by the density packing of the spherically symmetric ions in the degenerated electronic gas. As a result, we observe the rise of the melt density. The pressure favors SMT and, therefore, the rising of density. So, the compressibility maximum is observed. (A)
Pm(T)
I ....~
5.6. 5.4.
AI:)
3
'6
O
Z
, ~ ' ........ '""
4
,~,,
5.2. 2
7~
~o
"
~.
60
/gA~ 40
5
/
\
4-
20 0
400
'
6[)0
' 8130 T,K
'
10'00
(B)
-0 G -1
As2Te3 ~ ' ~
-2
..J_M
/"
c
460 ' 800 ' 12'00 ' T,K FIG. 9. Dependencies on temperature of different properties of melts at semiconductor-metal transition. (A) Properties of the GelsTe85 melt: ( 1) density; (2) expansion factor; (3) excess heat capacity; (4) compressibility (Tsuchiya, 1993). For curves 1-3 points and the broad line mark the experimental data, narrow lines mark the result of fitting by Eqs. (13) and (15). (B) Magnetic susceptibility of AszTe3 melt: (a) total susceptibility; (b) free electrons input in total susceptibility; (c) atoms input in total susceptibility.
241
Magnetic Properties of Chalcogenide Glasses / /
lgq 12
/
s S
sS
s S s S
s
s
s
ss~
///
s s
s
s ~
s S
s
/
SS
/
/
/
/
//
/
SSS" /
s
.. -..
s
OguTg/T
-4
0.0
'
I
0.2
'
I
0.4
'
I
0.6
'
[
0.8
'
I
1.0
FIc. 10. Dependence of viscosity on reciprocal temperature for As2Te3 melt (Tver'yanovich and Kasatkina, 1992). Tg is the glass-forming temperature for As2Te3. Arrow marks the temperature of semiconductor-metal transition for AszTe3.
The decreasing of the melt viscosity at SMT is the result of not only the activation of atoms moving at constant chemical structure, but also of the breaking of covalent bonds. So, the character of viscosity dropping (Tver'yanovich and Kasatkina, 1992) is similar to the same for the fragile melts according to the classification of Angel (Fig. 10). All these phenomena are reversible on temperature. Thus, reversal on temperature SMT in the melts is accompanied by the endothermic effect, by the change in the nature of chemical bonds and by the change of chemical structure. All mentioned above testifies that this effect should be attributed to phase transitions. At the same time, it cannot be considered a classical phase transition occurring under isothermal conditions, because SMT occurs in a wide temperature range. So, it is necessary to attribute the SMT to the so-called smeared phase transitions. The presence of the maximum Cp = f ( T ) (endothermic effect) is an attribute of the first-order smeared phase transition. The smeared phase transition consists of numerous elementary acts every one of which covers a miserable part of substance only--a microregion of co-operative structural transformations (RCST). The size of such RCST is very important for the explanation of the degree of smearing of the phase transition. Two possible mechanisms of smearing exist in the case of inhomogeneous model. 2.4.1.
Non-uniform RCST
The internal parameters of the microregions (including Ttr) differ from each other as a result of the statistical deviations of their composition and size. The smaller the RCST are, the greater the deviation of the local parameters' values of various microregions from the average value. Therefore, the appropriate phase transition is more smeared. The degree of smearing of the phase transition decreases with the growth in size of RCST. Finally, when the
242
Yu. S. Tver'yanovich
volume becomes equal to the total volume of the system under consideration, the classical, isothermal phase transition is observed. The nature of the smearing of phase transition in this case was described in Bal' makov, Tver'yanovich and Tver'yanovich (1994). 2.4.2.
Uniform R C S T
If RCST are small, the heat of the elementary acts of transformation is of approximately the same value as the heat of thermal fluctuation and this would also cause the smearing of the phase transition. In this case, even if all the elementary regions were identical, the smearing of the phase transition would be caused by the thermal fluctuation. At any temperature, the probability that part of the RCST is in non-ground state exists. If the size of RCST is small, the nature of a smeared phase transition becomes close to the nature of the chemical equilibrium, because at every temperature the equilibrium of the transitions in both directions exists. Let us estimate the size of RCST on the basis of this idea. It is possible to take into consideration the constant of equilibrium of the transition K = go/(1 - go), where go is the part of the RCST in the metal state and ( 1 - go) in the semiconductor state. - R T In K = AF = H - TAS, where H is the enthalpy of SMT for the Avogadro number of RCST. The following equations take place at the transition temperature (Ttr): Klrt~ -- 1,
H ~ AS -- , 7 . rtt
AFITtr -- O,
(12)
According to Tver'yanovich et al. (1986) p(T) = (1 - r + gopm(T), where ps(T) and pro(T) are linear temperature dependencies of density for the melt in the semiconductor state and metal state, respectively (Fig. 9). Thus, the following equations can be written for p(T) and for excess heat capacity ACp(T) (it is a part of the total heat capacity, which is connected with SMT): H 1 go(T)--{I+exP[R-(T-
d9
_
ZXCp
[,,(, 1)]
_
Otr air
p(T) =
QtrH exp ~-
R T 2 1 + exp ~-
ps(T)+
p ( T ) -- p ~
1 -1 Ttr)]} '
goAp,
-~ - Ttr T
(13)
Ttr
ps(T) = p~
- ozT),
(14)
Ap
- o~T) +
H
+
1
1
-
'
(15)
tr)]
where Ap is the increase of the density of melt as a result of SMT (Fig. 9), Qtr = f A Cp dT is the total heat of transition for the Avogadro number of atoms and a is the thermal expansion factor which is supposed to be the same for the semiconductor melt and for the metal melt.
Magnetic Properties of Chalcogenide Glasses
243
The equation for Aa(T) (excess thermal expansion factor) is the same as for ZXCp,but Qtr must be replaced by zXp. The number of atoms involved in one RCST (N) is equal to H N -. (16)
Qtr
The following assumptions are used for Eqs. (13) and (15): (i)
(ii)
The semiconductor and metal states have the same values of Cp and of c~. In other words, SMT is the first-order smeared phase transition without any involvement of the second-order smeared phase transition. All RCST are identical and have a size, independent from temperature.
The calculations of dependencies of the magnetic susceptibility of melts on temperature with usage of models both homogeneous and micrononuniform melt give very close outcomes. Therefore, a special examination (Tver'yanovich and Ugolkov, 2004) was devoted to the study of the microscopic nature of SMT. It was allowed to prefer micrononuniform model. 2 The boundedness of the volume of the book does not allow us to give a complete account of this examination. Here is its essence. When the composition of the single-phase melt comes nearer to the boundary of the liquation field, the concentration fluctuations appear and their sizes grow. So, according to the non-homogeneous model, we must observe the rising of the number of atoms, which are involved in every RCST, and therefore the decreasing of the width of transition. On the other hand, the growth of the size of RCST leads to the appearing of additional differences in their local chemical composition, therefore--to the additional differences in their ability of transforming in metallic state. Therefore, according to the homogeneous model, we should expect the magnification of the temperature width of SMT. The investigation of SMT for GelsTess-xSex melt demonstrates that the temperature width of SMT decreases when the composition of melts comes nearer to the boundary of the liquation region which is located at x = 14.
2.5. METALLIZED STATE The magnetic susceptibility of the completely metallized melts is a linear function of temperature. It consists of a magnetic susceptibility of ions and magnetic susceptibility of the degenerated electronic gas. The raise of temperature of melts and diminution of their density can affect properties of electronic gas and, in much smaller degree, on a configuration of ions screened from each other by electronic gas. Therefore, the observable changing of the magnetic susceptibility should be assigned to the magnetism of the degenerated electronic gas. Such strong dependence of the magnetic susceptibility on temperature cannot be explained by magnification of correlation radius rs (see Eq. (10)) as a result of thermal expansion of a melt. It forces us to assume the magnification of the effective mass of free carriers at the propagation of temperature. A similar phenomenon is observed at high temperatures even for the melt of such a classical metal as 2 The absence of the taking into account of mutual influence of microregions with different nature is the basic shortage of the micrononuniform model of SMT.
244
Yu. S. Tver' yanovich
sodium. Therefore, it is possible, for example, for As2Te3 to find the temperature dependence of an effective mass with the help of Eq. (10): 2.06(m*) 2 + (0.017 - 1.2T X 10-3)m * - 0.688 = 0.
(17)
For example, at 1100 K m* = 0.97, and at 1400 K m* -- 1.09. The calculation of the effective mass of free carriers for the melt of tellurium from its magnetic susceptibility at completely metallized state gives the following values: m* = 0.96 at 1000 K and m* = 1.17 at 1400 K. These outcomes are close to similar outcomes for AszTe3. q~ = 0.5 at the temperature of SMT (according to the definition of the temperature of SMT). Parameter g at this temperature is equal to 0.3 (according to Mott). Therefore, Eq. (8,9) can be rewritten:
X-
0"5(Xat -it- )(ion) -Jr-0.3fie et.
(18)
Using this equation for the melt As=Se3, we can calculate ~ e et and find the magnitude of an effective mass m*, which is equal to 1.75. The obtained outcome is rather interesting. It gives the foundation to suppose that the melts, possessing initially by greater electrical resistance, even after metallization, differ from metallized melts, possessing initially by higher conductivity; namely, carriers in first melts are exposed to more strong scattering. In Figure 5 it is visible that the melt AszSe3 comes to the field of the metal state, but does not achieve such high conductance as the melts AszTe3 or Te do. Figure 5 visually demonstrates the behavior of melts in a wide interval of temperatures. Some melts, such as tellurium, fast achieve the metallized state at a rise of temperature. Thus, the propagation of paramagnetism is observed, the reasons of which were already considered. The further increase of temperature, especially at the approach to critical temperature, would reduce in reverse: localizations of electrons on separate atoms and lowering of conductance. Unlike the conductance, the magnetic susceptibility, apparently, will grow. Precisely the same arc in this figure would be described also for melts with higher electrical resistance, but they would not reach the field of metallized state.
2.6.
DEPENDENCIES OF MAGNETIC SUSCEPTIBILITY OF CHALCOGENIDE MELTS ON COMPOSITION AND TEMPERATURE
We have considered by examples in a list of substances, the variation of the magnetizability of semiconductor melts. An interesting illustration of all above circumscribed regularities of the modification of properties of melts is the system S e - T e (Gardner and Cutler, 1977). It is visible from the temperature dependencies of the magnetic susceptibility (Fig. 11) that the passage from melts with the localized paramagnetic centers and non-degenerate free carriers, to melts with the degenerated electronic gas, and then to the metallized state, occurs at replacement of selenium by tellurium. Let us assume that the binary system is composited by components largely metallized at melting. In this case the maximums of diamagnetism observed for isotherm of the magnetic susceptibility (Fig. 12) are determined by localization of electrons as the outcome of formation of stable heteroatomic structural units. Naturally, the most intensive maximums correspond to congruent compounds: GazTe3, InzTe3, AlzTe3, Ag2Te (Fischer and
Magnetic Properties of Chalcogenide Glasses i
"
"•
.10
'
i
o
x=
[]
x = 0.I0
o
x = 0.20
~
I
i
i
i
I
245
0.0
,a
x = 0.40
v
x = 0.50
6
-
i/
-20
-30
200
400
i
I
600
800
1000
T, ~ 30 20
o
x = 1.00
[]
x = 0.90
o
x = 0.80
9
x = 0.60
v
x = 0.50
x = 0.70 10 m. @
6
e~
~4 ~
,:1
0.8
1.0
1.2 1000/T,
FIG.
11.
1.4
1.6
K -I
D e p e n d e n c i e s of a m a g n e t i c susceptibility on t e m p e r a t u r e for melts in the s y s t e m s e l e n i u m - t e l l u r i u m
( G a r d n e r and Cutler, 1977).
246
Yu. S. Tver'yanovich +1o I
,
,
,
,
!
t
i
!
] I
I
l
"~L, -10
_ "-'e..,...
-20 -
-
r,
800 or
-30 -
-40
Ga
+20
1
20
I
:....
I
I
60
80
I
I
I
Te, at.%
Te I n
I
700 ~
J
i
i
i
I
20
40
60
80
"""'".-.
-
1
.....................
o
I
T
=
I
!
/
I
J
1000 ~
it,
~
-1o
<
-30
AI
Te
Te, at.%
T = 1000 ~
"
~
I
t
40
I
W
<
20
40
60
Te, at.%
80
Te 1 1
i Ag
I 20
i
4o
l
i
6o 8o Te, at.%
Te
FIG. 12. Dependencies of a magnetic susceptibility on temperature for different binary systems (Fischer and Guntherodt, 1977). Letters sign temperature (~
Guntherodt, 1977). At the rise of temperature of melts, the smearing of maximums of diamagnetism is observed, which indicates the thermal decomposition of compounds. In this case, the process of thermal decomposition of the compounds has the nature of SMT. The structural modifications at SMT are not only the rise of a medial coordination number. This passage indicates the decomposition of the metallized compounds. If AszTe3 is at the semiconductor state of a melt, for example, the atoms of arsenic are surrounded by atoms of tellurium; but at the metallized state the allocation of atoms on volume is mainly statistical, with a slight deviation to the direction of formation of heteroatomic bonds.
Magnetic Properties of Chalcogenide Glasses 2.7.
247
SEMICONDUCTOR--METAL TRANSITION AND GLASS-FORMING ABILITY OF CHALCOGENIDE MELTS
As has been already mentioned, the destruction of a system of covalent bonds occurs as a result of a melt metallization at increased temperature. At the same time, it is known that the glass-formation phenomenon is conditional on the presence of directional covalent bonds. This leads us to assume that there is a correlation between formation of glass-forming fields and the thermal dissociation of the semiconductor state. In Figure 13, a comparison of the phase diagrams of systems A s - T e and G e - T e with the concentration dependencies of temperature of SMT is carried out. It is visible that the concentration intervals for glass formation and of the semiconductor state of melts coincide. For the systems AszTe3-T1AsTe2 and T1AsTez-T1AsSe2 the temperatures of SMT are placed above the liquidus line for all concentration interval, and glasses can also be obtained at all concentration intervals. The metallization of a melt restricts the glass formation not only in telluride systems. It is possible to mention many sulfides and selenides, the melts of which have
700
[-.., 500
"
%
GeTe
60
300
~
!
14
t
t
70
80
t
90
Te, at.%
~4
600
,+. - + o - - /
,U *
s00
/
/ 400
/ i
Te
9
20
[
"
40 60 As, at. %
FIG. 13. Comparison of the phase diagrams for systems As-Te and Ge-Te with dependencies of temperature of SMT on composition. Temperature of SMT calculated from measurements of (1) density, (2) magnetic susceptibility, (3) conductivity and (4) the regions of glass formation.
248
Yu. S. Tver'yanovich
a metallic conduction, such as PbS. Such compounds have no ability to form glasses. But the metallization of melts is not the only reason for the lack of ability to form glasses. Therefore, fields of glass formation can exist that do not submit to the regularity remarked above. For example, if the system of covalent bonds in a melt is insufficiently complex (chain structure in the melt of selenium), even partial metallization can delete the ability to form glasses. Another example is melt TlzS, which even in the case of complete localization of valence electrons, does not form a network of covalent bonds. SMT restricts the expansion of field of glass formation not only in concentration of components, but also in structural temperature. In other words, it is difficult to obtain, for example, the glass with composition As3Te7 and with structural temperature higher than 800 K with usually used speed of cooling of a melt (-< 100 K c -1) (see Fig. 13). Its experimental evidence will be demonstrated in Chapter 4 devoted to glasses, containing transitional metals. Let us assume that utilizing superfast cooling of melts gives a possibility to receive an alloy As3Te7 with structure relevant to the metallized state. It means that the possibility would be presented to compare physicochemical properties of two glasses with different structure, but having the same composition. Such an experiment would help to understand the degree of distinction between metal glasses and glasses possessing a network of covalent bonds.
3. Chalcogenide Glasses Containing Transitional Metals The problem of introduction of transitional metals in glassy semiconductors (GS) is interesting in connection with searching of a possibility of modification of GS electrical properties, making the ion-selective electrodes responsive to these metals, doping the luminescent materials with lanthanides. The problem of allocation of atoms of transitional metal on volume of a glass is of great importance at the introduction of transitional metals in GS: 9 What is the composition of structural units containing the atoms of transitional metal? 9 Are structural units distributed on volume of a glass statistically or do they form accumulations? 9 Do these structural units form a microphase of any compound or not? The understanding of reasons of sharp increase of crystallizing ability of chalcogenide alloys at introduction in their composition even of an inappreciable amount of transitional metal is also of great importance. The magneto-chemical method allows us to solve not only the above-mentioned problems, but also allows us to determine the degree of oxidizing of transitional metal and, in some cases, its coordination. However, the usage of this method is more fruitful in the case of GS doped with 3d transitional metals. The reason is that the indirect exchange interaction is an important radiant of information. But indirect exchange interaction, as a rule, is not enough for 4f transitional metals. Many outcomes reported in this part of chapter can be used not only for chalcogenide, but also for other groups of glasses and for crystalline solid solutions.
Magnetic Properties of Chalcogenide Glasses 3.1.
249
THE DEGREE OF OXIDIZING OF TRANSITIONAL METALS IN CHALCOGENIDE GLASSES
It is possible to make opinions about the degree of oxidizing of transitional metals by utilizing the magnitude of their magnetic moment. The examinations of the magnetic susceptibility of various GS containing copper and silver have shown that all these materials are diamagnets and their magnetic susceptibility does not depend on temperature. It means that copper and silver in GS have only the degree of oxidizing of + 1. Moreover, the region of glass formation for the system AszSe3-CuO was investigated. The copper was put in composition of fusion mixture as the compound CoO. The region of glass formation for this system reaches up to 40 mol% of CuO. (The glasses were synthesized in the pumped out and soldered quartz ampoules.) These glasses also have the diamagnetic susceptibility independent of temperature. Therefore, the degree of oxidizing of copper at synthesis of glasses varies from + 2 up to + 1; the structuralchemical composition of glasses contains the structural units AsO3/2 and 8e2/2 (Shkol'nokov, D'yachenko and Shkol'nikova, 1995). Utilizing the observed value of magnetic moments of manganese and iron ions, it was established that the manganese, incorporated in composition of telluride, selenide and sulfide glasses, has a degree of oxidizing of § 2. The atoms of iron in GS also have the main degree of oxidizing of § 2. (With the help of Mossbauer spectroscopy, it was established that only inappreciable amount of them, in two or three order smaller than their common concentration, has the degree of oxidizing of + 3.)
3.2.
THE MODEL OF MAGNETISM OF GLASSES CONTAINING TRANSITIONAL METALS
In the present chapter we shall be restricted to the review of glasses, in which the indirect exchange interaction between atoms of transitional metals through an anionic sublattice is carried out. The cases of the direct exchange interaction between atoms of transitional metal, indirect exchange interaction through atoms of diamagnetic metals and exchange interactions through the degenerated electronic gas are not considered here, as they do not correspond to the nature of the glassy state and are not met, as a rule, neither in halide, nor in oxide glasses. For embodying such mechanisms of exchanging in chalcogenide glasses, it is necessary to create a strong deficit of chalcogen. Such glasses were not studied except cases mentioned specially. At a solution of a problem about character of allocation of atoms of transitional metal in volume of a glass, the fact of existence or absence of the microphase of its compound is the most rough answer. It seemed easy to judge, for example, about the presence of antiferromagnetic phase by the presence of Neel phase transitions. But, at first, this test allows us to do only quality, generalized opinions. Secondly, these opinions are not always correct. If the concentration of atoms of transitional metal is low, for occurrence of a microphase of the compound of transitional metal, which can be described by a Neel transition, the existence of very strong deviations from a statistically uniform distribution of transitional metal in glass volume is necessary. In the case of high concentration of transitional metal, even the homogeneous glass has the effect of freezing of a spin subsystem, which can be confused with the Neel transition. Thus, it is necessary to take
250
Yu. S. Tver'yanovich
into account that when the crystals of compound of transitional metal have a mesh size, the temperature of magnetic-phase transition depends on its size and does not coincide with corresponding temperature for the macroscopic phase. The formation of accumulations of structural units containing atoms of transitional metals and microcrystals of the corresponding compounds leads to increase of the quantity of bonds with the indirect exchange interaction (n) per atom of transitional metal and to increase of an absolute value of Weiss constant in the Curie-Weiss equation. By assuming that the energy of the exchange interaction per bond does not depend on n (correctness of this supposition will be discussed later), the authors (Bal'makov and Stepanov, 1976) have obtained the equation:
O= Opn/Z,
(19)
where 0 is the Weiss constant for investigated glass, 0p is the Weiss constant for the compound corresponding to the structural units of glass containing transitional metal and z is the number of bonds with exchange interaction per atom of transitional metal in this compound. The obtained outcome is extremely important. However, it remains vague, where the value of 0 corresponds to the case of the statistically uniform distribution of structural units in glass. Let us consider the alloys of a quasi-binary system A - B with statistically uniform distribution of structural units A and B. The magnetic susceptibility of the compound B is governed by Curie-Weiss law with Weiss constant equal to 0p. The compound A does not contain any transitional metal. Let us enter an autocorrelation function
P(r) = (bRbR+r)/b.
(20)
Here ( ) means the average in volume of a sample; bR is the local parameter of filling up of a point with coordinate R by structural unit, adequate to the compound B (BSU). Parameter bR can be equal to 0 or 1, and
O - K~'[I(r,b)P(r,b)],
(21)
where K is the constant defined by the magnetic moment of transitional metal atom and I(r, b) is the exchange integral. The summarizing is done in all spaces except the first coordination sphere of transitional metal atom, which is completed by anions. In the case of statistically uniform distribution of A and B the value P(r, b) is constant for any point of space, i.e., P(r, b) = P(b), and P(b) = b. Let us suppose that l(r, b) does not depend on the relation of concentrations of A and B, it is defined by the distance between the interacting atoms of transitional metal only (the correctness of this supposition will be discussed later), i.e., I(r, b) = I(r). Besides, the magnetic moment of atom of transitional metal is a constant value. Then
0- bK~I(r).
(22)
By entering a label 0p = Ky'I(r), finally we shall receive
0 = bop.
(23)
Magnetic Properties of Chalcogenide Glasses
251
The linear relation O(b) in the case of statistical distribution of builders can be obtained also by the following less strict reasoning. According to Eq. (19) 0 is proportional to the quantity of bonds with exchange interactions per atom of transitional metal. The full quantity of such bonds at statistically uniform distribution of A and B is proportional to the probability of the formation of bonds B - B , i.e., is proportional to b 2. By dividing this value per concentration of transitional metal and taking into account boundary conditions, 0 b-0 - 0 and 0]b=l 0p, we shall again receive the formula (23). Thus, for the solution of the problem of presence in an alloy of the tendency to association of structural units containing atoms of transitional metal, it is enough to clarify, whether there are any positive deviations of i01 from the linear dependence on concentration. The obtained outcome is equally applicable to melts, glasses and crystalline solid solutions. However, it is necessary to take into account that the magnitude of 0p is known, as a rule, for some crystalline substances only. Furthermore, the dependence O(b) for the case of glasses and solid solutions often cannot be investigated for full concentration range. At the same time, the accumulations of B structural units in glass at early stages of its formation can have amorphous structure, and they should be characterized not by 0p, but by the magnitude of 0p~ (Weiss constant of the compound B in amorphous state). According to the concept of Gubanov (1963), the amorphization reduces in diminution of absolute value 0p, i.e., 10p] > ]0pl]. In this case, the melt of compound B or the melts of the system A - B (if they are uniform certainly) can be used for estimation of magnitude 0p~ (if the chemical structure and the mechanism of exchange interaction do not vary at melting). If in the alloy of the system A - B the concentration of pairs of type AB is higher than it is predicted by statistical distribution, it means that there exists the tendency of formation of structural units of composite compound with the formula A m B I _ m. For such a system the negative deviations from the linear dependence 10i on a molecular part of B will be observed. If the structural units of the compound A m B I _ m are absolutely stable, the dependence of i01 on concentration would break up to two linear ranges located below the linear dependence for the whole system (Fig. 14) and intersected at composition A m B I _ m. -
l
A
IOiI
Am BI_ m
B
FIG. 14. Dependencies of average Weiss constant on composition: (1) statistically uniform distribution of components; (2) formation of stable compound AmBl_m; (3) total phase separation.
Yu. S. Tver'yanovich
252
So far for the discussion of magnetic properties of a glass, we used the parameters which are averaged on whole sample volume. But the glass has a fluctuation nature. Whether it is always correct to substitute the band of parameters describing each microarea by its medial magnitude? What happens to the losses of the information? Let us make four suppositions: (1) (2)
(3)
(4)
There exists strong short-range order in the glass. All the metal cations are connected with anions only, and vice versa. The glass contains only one type of anions A and only one type of transition metal cations B with the magnetic moment independent of temperature. But the glass contains one or more types of diamagnetic metal cations D. The coordination number of cations B is equal to Z. The energy of indirect exchange interaction steeply decreases with increasing distance and with deviation of the angle of the bond from the straight direction. Therefore, there exist Z cation sites in the second coordination sphere, which allow formation of strong indirect exchange interactions with the energy significantly larger than those with all other cation sites. The cation B is marked as Bi if it has i cations B and (Z - i) cations D which are located in these Z sites, b is the mole fraction of B among all cations B and D. b i is the mole fraction o f Bi among all cations B and D. 01 is the Weiss constant, which describes the behavior of the magnetic moment of cations B1 in exchangeable pairs B - A - B . Oi is equal to 01 multiplied by i. 0 i ---
i01,
i = 0, 1,2,...,Z.
(24)
The energy of the exchange interaction (k 0) is smaller than that of any chemical bond. Therefore, the arrangement of electron density around B i does not depend on the presence or absence of exchange interaction or, in other words, it does not depend on i. Thus, Eq. (24) is correct. However, it may be possible that the electronegativity of B strongly differs from the electronegativity of D. In this case, the replacement of a part of B cations in the second coordination sphere of the central cation B by D cations can lead to the redistribution of the electron density and the change of the energy of single exchange interaction of the central cation B. Thus, Oi is not a linear function of i. For the glasses studied, the electronegativity of B is close to the electronegativity of D, and therefore, we can use Eq. (24). The maximum absolute value of Oi (IZOil) can differ from the Weiss constant of the crystalline compound in the A - B system, in which cations B form Z exchange interaction bonds (0ph). The absolute value of Oz is likely to be a little smaller than 0pn due to the distortion of the angles and lengths of the bonds, typical of the vitreous state. Thus, the expression for the temperature dependence of the magnetic susceptibility (X) is z bi gi (T > Oi) gi, ~ ' . g i - 1, (25) X - - C ~ (T - Oi) ' Zbi i=o
where T is the temperature, C is the Curie constant and gi is the fraction of Bi among all cations B. Function /1 may be introduced as follows: z
i=0 ( T -
Oi)
0 -~ ~ . giOi, i=0
(26)
Magnetic Properties of Chalcogenide Glasses
253
where 0 is the average Weiss constant. Then Eq. (25) can be rewritten as C - t ~ ) ( ' T (1 + A). ~
XWe can submit 1 in function (26) by
Y.gi.
So, we would obtain"
giOi
, 5 - 1~. T -
(27)
gi
0i
(28)
ZgiOiZ T - 0----~"
-
If we repeat the submission of 1 by ~.gi and then multiply the sums, we would obtain:
a
gigj
Yij v -
oi
(0 i _
oj~
_
yi>j.
gigj( Oi-- OJ ~
v-
oi
Oj- Oi ). v-
(29)
oj
The latter expression can be transformed in the following way:
,5
(0 i -- Oj) 2
/-. gigJ ~ j>i
(30)
o i ~ v - oj)
It can be concluded that function (30) has the following properties:
(1)/t > 0; (31)
(2) A ---, 0 at T ---, co; (3) A ----, co at T ~ max
Oi (max Oi =
0 at 0 < 0 and max
Oi = ZO1 at
0 > 0).
Therefore, the temperature dependencies of the reciprocal magnetic susceptibility are as presented in Figure 15. In the absence of correlation between the type of the central cation and the composition of its second coordination sphere, the weight factors gi can be calculated using the combinatorial relation:
gi-
Tibi( 1 - b) z-i,
1
/ ~-
(32)
2
/ O?=o ~3+
oW
FIG. 15. Theoretical dependencies of reciprocal value of paramagnetic susceptibility of glasses on temperature for the case of negative (1) and positive (2) exchange interaction.
254
Yu. S. Tver' yanovich
where b is the mole fraction of B among all cations B and D and Yi is the number of possible arrangements of i cations B and (Z - i) cations D in Z positions. For the case of Z = 6 : 3/0=3/6=1; y~=ys=6; 3 ' 2 = 3 / 4 = 15; Y 3 = 2 0 . This is the case of a statistically uniform distribution of different structural units throughout the bulk of the glass. If we introduce expressions (24) and (32) into the definition of 0 (Eq. (26)), we would again obtain an equation similar to Eq. (23): (33)
O= b(ZO~).
But the sense of the left part of Eq. (33) differs from Eq. (23) and is more correct. The equation log(g0) = Z log(1 - b) (34) follows from Eq. (32) for i = 0. This equation makes it possible to calculate the coordination number of transitional metal for solid solution with statistically uniform distribution of transitional metal atoms on metal sites, go can be easily calculated from the temperature dependence of magnetic susceptibility using the following method:
go
lim x--~cO lim T-*co
d(x -1) dT d(x-1) ' dT
or for the case of negative exchange interaction and for 00 = 0
go --
lim r---*0 lim r-"~co
d(x -1) dT d(x_l)
9
(35)
dT
For statistically uniform distribution the ratio (P) between the probability of a vacant cation site being occupied by B or by any D cation is given by P = b/(1 - b ) . The existence of the correlation in distribution of different cations among the cation sites is taken into consideration using the segregation factor S: P = S[b/(1 - b)]. If S is larger than unity, there is a tendency for association of structural units containing cation B. If S is smaller than unity, there is a tendency for formation of complex structural units containing both B and D cations. In order to take into consideration S ~ 1 in, for example, Eq. (33) we replace real concentration b with effective concentration b *: b S- 1-b
-
b* l-b*
(36)
When the concentration of B is equal to b * and statistically uniform distribution takes place, all parameters gi are the same as for the glass under study, in which the concentration of B is equal to b and there exists the deviation from statistically uniform distribution. As it was mentioned above, the energy of indirect exchange interaction steeply decreases with the increase of distance. This means that the exchange interactions with other B cations, apart from those Z cations which were considered above, can be neglected compared to 01 and, so, 0 0 - - 0 . However, if the exchange interaction is
Magnetic Properties of Chalcogenide Glasses
255
negative and the temperature of measurements is much lower than - 01, the value of 0o is not negligible compared to the temperature of measurements, and it is necessary to introduce 00 ~ 0. Thus, the following equation can be used for the magnetic susceptibility:
x-
C
T-
Oo
]
gi = Ti(b*)i( 1 - b*) z-i,
'
i=1T-i01
(37)
where b *, 0o and 01 are free parameters. According to the model, 01 is the same for all glasses with the same A, B and Z. The formation of stable intermediate compound AmB 1--m is the limit of the case of the preferential interaction of different structural units. The shape of concentration dependence of 101 for this case was already considered (see Fig. 14). The phase separation is the limit of the case of the preferential interaction between similar structural units. This case requires a detailed review. Let us make it with the example of a liquid system A - B with the liquation range extended at temperature T (T is so high that A = 0 in Eq. (27)) from composition A1-LBL up to composition A1-L-dBL+d (Fig. 16a). Taking into account the assumption about unchanging of a magnetic moment of atom of transitional metal, we can use the following equality 0 = T - ( C / x ) (where X is the paramagnetic susceptibility of glass per mole of compound B; C is the Curie constant). It can be written for composition AaBb at temperature T: (1
-
(38)
6)L + 6(L + d) = b,
where 6 is the fraction of the phase with the content of compound B equal to (L + d) (the right border of the liquation region); 0 -< 6 -< 1. Then
X-
C
L(1 - 6) b(T 0plL ) -
-
+
b(T
-
-
0pl(L -+- d))
.
(39)
The latter equation was written with the supposition that for the outside of the liquation region and for borders of the liquation region the relation (0) = bOpl is correct. At the same time it is possible to write the formal equality, which follows from the definition of Weiss constant, mentioned above: C X= ~ . T - 0eff
(40)
If we designate 0eff - [0pl(L + 6d) + 0"] and use Eq. (39), we would discover:
C __ b(T - OplL)(T - 0pl(L + d)) = T - [0pl(L + 6d) + 0"] X (6dT + L(T - 0pl(L + d)))
(41)
or 0"=
Opld2(1 - r
6d+L[1-
--T-Opl(L + d) ]"
(42)
Yu. S. Tver'yanovich
256
T
(a)
~--L A
B
(b)
- O p'pll -'~r162162
..-2,2"
II
~.fL
."
d
A
B
FIa. 16. (a) Schematic view ofcalotte of liquation and labels used at a deduction of Eq. (42). (b) Dependencies of 0 on composition at different values of the parameter L for system with the region of immiscibility.
The dependencies of O(b) for different L and d = 0.4 are depicted in Figure 16b. It can be seen that 10"1 rises at the moving of the liquation region to the diamagnetic component A. It means that the magneto-chemical method is very sensitive for early stages of separation of paramagnetic phase from the alloy at the low content of the latter. The specificity of liquid state was not utilized anywhere at the deduction of Eq. (42). Therefore, it is possible to apply this equation to the exposition of the process of separation of a crystalline phase of compound of transitional metal from the matrix of a glass. Let us suppose that at the rising of a molecular ratio of the compound of transitional metal (B) more than L, the separation of its crystalline phase begins. Thus, the content of B in glass remains constant value, which is equal to L. Then, L + d = 1, and in Eq. (42) it is necessary to write 0p instead of 0pl. And by designating the molecular ratio of B as x, we obtain:
O* =
Op(x - L)(1 - x) (x - L) --I-L ( 1 -
--~ )
(43)
Magnetic Properties of Chalcogenide Glasses 3.3.
257
THE RESULTS OF THE INVESTIGATIONS OF MAGNETIC PROPERTIES OF CHALCOGENIDE GLASSES, CONTAINING TRANSITIONAL METALS
The results of the usage of model of the low-temperature paramagnetism of glasses (Eq. (37)) at the study of glasses GeSz-GazS3(PbS, AszS3)-MnS are discussed in Tver'yanovich and Murin (1999) and Tver'yanovich, Vilminot, Degtyaryev and Derory (2000). The restricted volume of the book does not allow us to discuss them in complete volume. So, Figure 17 demonstrates the satisfactory description of the experimental results with the help of Eq. (37). In Table I the values of parameters describing the investigated system are listed. The sense of effective concentration b * is explained in Figure 18. In the overwhelming majority of cases the limit of content of 3d transitional metals in chalcogenide glasses does not exceed one or two atomic percents. The exceeding of this limit leads to the segregation of the crystalline phase of the compound of transitional metal. Usually, it is desirable to know the concentration of transitional metal at which the formation of a crystalline phase begins, and at which crystalline phase appears. Let us consider some concrete systems. The concentration dependence of the average value of Weiss constant for glassy and glassy-crystalline alloys (1 - x)(0.3CuzSe-0.7AszSe3)-xMnSe, obtained in the condition of cooling the quartz ampoules in water, was investigated (Fig. 19). The calculation of this dependence by using Eq. (43) is carried out. In this calculation the following values of parameters were utilized: L -- 4.3 tool% of MnSe (1 at.% ofMn); 0ph -- -- 420 K. Thus
s~ 40
O
E
20
,7
0
rI
~
i
5O
i
T,K Fro. !7. Dependencies of reciprocal value of paramagnetic part of magnetic susceptibility per mole of Mn on temperature. Points are the experimental values and results of simulations (Eq. (37)) are unbroken lines. The numbers indicate the compositions given in Table 1.
258
Yu. S. Tver' yanovich
TABLE COMPOSITIONS
I
GLASSESA N D RESULTS OF T H E
OF THE STUDIED
FRACTION
b*; WEISS CONSTANTS
APPROXIMATION"
EFFECTIVE
MOLE
0 0 A N D 01
N
MnS (b) (mole fraction)
GeS2 (mole fraction)
GAS1.5 (mole fraction)
b* (mole fraction)
00 (K)
1 2 3 4 5
0.0384 0.0632 0.0873 0.1225 0.2308
0.6674 0.6215 0.5759 0.5102 0.3077
0.2942 0.3158 0.3368 0.3674 0.4615
0.074 +__0.001 0.126 _+ 0.002 0.151 +_ 0.002 0.189 +_ 0.002 0.329 + 0.01
-0.95 + 0.03 -0.74 _+ 0.07 - 1.05 +_ 0.09 - 1.21 +_ 0.08 1.17 +_ 0.3
-01 (K) 46 39 59 61 50
_+ 1.4 _+ 1.5 +_ 2.3 _+ 1.6 +_ 2.6
calculated, the limit of the content of m a n g a n e s e in glasses coincides well with the outcomes of m e a s u r e m e n t of this parameter with the help of ESR. The E S R spectrum of m a n g a n e s e in investigated glasses consists of two lines: the first has g = 2 and superfine structure (SFS) with bad resolution; another has g = 4.3 and SFS with good resolution. The degree of resolution of SFS is the ratio between the amplitude of single c o m p o n e n t of SFS and the amplitude of full sextet. The curves of dependencies of degree of resolution of SFS with g = 4.3 and of half-width for line with g = 2 on m a n g a n e s e content have the m a x i m u m s at 1 at.% M n (Fig. 20). The rising of half-width and the decreasing of degree of resolution of SFS at the growth of the content of m a n g a n e s e up to 1 at.% are the result of the magnification of the casual d i p o l e - d i p o l e interaction between Mn ions. W h e n the content of m a n g a n e s e b e c a m e larger than 1 at.%, the formation of microcrystals of antiferromagnetic c o m p o u n d of Mn begins. A more detailed discussion of these results (Fig. 20) was carried out in C h e p e l e v a and T v e r ' y a n o v i c h (1987) and T v e r ' y a n o v i c h and Gutenev (1997). m
.
1.5
-0 (K)
""~ ~
"~
...........
1.0
300
~
3
.....:.-
200
1
0.5
0.0
100
Z" b-.i i/b*
"-
0.0
9
,
0.2
.
,~-
.7
I
,
I
0.4 0.6 0.8 b (tool f r a c t i o n )
,
0
1.0
FIG. 18. Concentration dependencies of average Weiss constant (1) and segregation factor (2) for glasses GazS3-GeSz-MnS. (3) The concentration dependence of average Weiss constant for model glasses with statistically uniform distribution.
Magnetic Properties of Chalcogenide Glasses
259
400-
I
200-
2/ 40 8
1'2
Mn,at.%
1'6
20
FIG. 19. Dependence of average Weiss constant of alloys ( 1 - x)(0.3Cu2Se.0.7As2Se3)-xMnSe on composition. Points mark the experimental datum; solid line is the result of calculation with Eq. (43).
But even 1 at.% of transitional metal has not always manage to be entered into the composition of chalcogenide glasses. W h e n glassy AszSe3 is doped with manganese, the appearing of a crystalline phase begins, as it was shown with the help of the magnetochemical method, at concentration which is not exceeding 0.05 at.% of Mn. Such concentration is far from being the limit of the ability of the m a g n e t o - c h e m i c a l m e t h o d to detect the inserts of paramagnetic crystals in v o l u m e of glass.
0.12 -200 0.08
.150
r
;
'4P
i
-3
0.04
100 ~
50
[~__0. ~ 0!5~_~i~0
1.15 210
Mn, at.%
FIG. 20. Alloys (1 - x)(0.3Cu2Se.0.7As2Se3)-xMnSe. Dependencies on concentration of: (1) average Weiss constant (0); (2) the degree of resolution (R) of SFS for line of ESR with g = 4.3 at 77 K; half-width (614)of line with g = 2 at 77 K (3) and at 300 K (4).
260
Yu. S. Tver' yanovich (a)
t, min 100
I
I
200
I
I
11. 10. (b)
"~ 2
y .= ~'
3 0.5
I
1.0
I
1.5
!
2.0
Co, at.% FIG. 21. (a) Changing of magnetic susceptibility of alloy 0.3CuzSe-0.7AszSe3 with 1 at.% Mn during the annealing at 185 ~ (b) Dependence of magnetic susceptibility of alloys (1 -x)GezzSb19Se59-xCoSe on concentration.
The magneto-chemical method allows us to explore thermo-stimulated crystallization of glasses also. At the crystallization of glasses CuzSe-AszSe3, in opposite to glassy AszSe3, the noticeable diminution of diamagnetism takes place. Therefore, the modification of the magnetic susceptibility during annealing glass 0.3CuzSe.0.7AszSe3 containing 1 at.% of manganese has a rather composite nature (Fig. 21). At the first stage the formation of the antiferromagnetic crystalline phase of the compound of manganese takes place and, as a result, the falling of paramagnetism takes place. At the second stage the crystallization of matrix of a glass and magnification of paramagnetism takes place. Thus, the first phase, appeared at crystallization, is the compound of transitional metal. The magnetic susceptibility of glassy and of glassy-crystalline alloys doped with cobalt, which are obtained by sharp cooling of a melt in the air, slowly grows at the growth of cobalt content (Fig. 21b) and, as it seems, does not contain the information on crystalline phases containing cobalt. The dependence of magnetic susceptibility on temperature (in the range of low temperature) (Fig. 22a) shows that modifications of magnetic susceptibility are stipulated by temperature-independent paramagnetism of the order 2 x 4~r • 10 -9 m 3 kg -1 per compound of Co. The crystalline chalcogenides of cobalt in degree of oxidizing of + 2 have just the same susceptibility. The d-electrons in them form a conduction band and have, therefore, Pauli paramagnetism, which is characteristic for the degenerated electronic gas. The Curie paramagnetism, dependent on temperature and increased at magnification content of cobalt, is also observed at low temperatures. However, the concentration of paramagnetic centers is less (in two or three orders) than the concentration of cobalt atoms. Therefore, they are either the states being unrepresentative for a groundmass of atoms of cobalt, or an impurity of other transitional metal, which is the satellite of cobalt. As we will see in the following part, the magnetic susceptibility of alloys grows sharply at melting (Fig. 22b). It grows out because the phase of the cobalt compound 'is dissolved' in melt of
Magnetic Properties of Chalcogenide Glasses a
3
o
9
2
261
o
9
o3
TK ooo
~
2 ~
~, 0
~ 1.0
-1
50
lOO
15o
200
~
250
T,K FIG. 22. Dependencies of magnetic susceptibility of alloys (1 - x)Ge22Sb19Se59-xCoSe on temperature: at low temperatures (a) and at high temperatures (b). The numbers are the value of x.
glass and the d-electrons are localized on ions of cobalt. The passage from the Pauli paramagnetism to the Curie paramagnetism takes place. Told means that the introduction of already 0.01 at.% of cobalt in glass reduces the formation of microphase of its compound. It is shown by Mossbauer spectroscopy (Kudoyarova, Nasredinov and Seregin, 1982) that the introduction of 10 - 4 at.% of cobalt in glassy A s 2 8 3 as a result of synthesis at 550 ~ and slow cooling reduces the formation of crystalline microphase of its compound. Chalcogenide glasses doped with nickel have similar magnetic properties. The dependencies of average Weiss constant on Mn content for alloys 6(GeS).4(AsS)Mn and Si12Ge~oAs3oTe48-Mn have extreme character (Fig. 23). In these glasses along with bonds metalloid-chalcogen there are also bonds metal-metalloid (the amount of chalcogen is not enough for saturation of all valence needs of metalloids). Therefore, when the particular content of manganese is obtained, except formation of a phase of its chalcogenides with a negative exchange interaction (sites II in a Figure 23), the formation of its compounds with Ge and As takes place. The latter compounds have positive exchange interaction (sites III). For sulfide system it is terminated by the formation of alloys at 3.9 at.% of Mn with a ferromagnetic component of magnetization. Glassy alloys of the system CrzSe3-CuzSe-AszSe3 demonstrate the most composite behavior of magnetic properties at passage from glassy state to glassy crystal. The crystalline phase CrSe is formed at once by the introduction of CrzSe3 (less than 0.1 at.% of Cr) into AszSe3. This crystalline phase is identified at 5 and 10 at.% of Cr with the help of RPA, and at 0.5 and 5 at.% of Cr with the help of the magnetic analysis. (The temperature of antiferromagnetic transformation for CrSe is equal to 47 ~ and Weiss constant - 2 0 0 K.) The effects of antiferromagnetic transformation for both alloys take place at indicated temperature, and the Weiss constant is equal to - 217 and - 187 K for alloys with 0.5 and 5 at.% of Cr, respectively. The ferromagnetic phase of CuCrzSe4 is formed by the introduction of CrzSe3 into alloys 0.1CuzSe.0.9AszSe3 and 0.2CuzSe.0.8AszSe3 (slits I and II accordingly). It was
262
Yu. S. Tver' yanovich Mn, at.% 2
|
r,
50
!
/
b
I/ a
1, t , 0
2
4 Mn, at.%
FIc. 23. Dependencies of average Weiss constant of alloys ( 1 - x)(GeS)o.6.(AsS)o.4-xMn (a) and (1 - x)Si12GeloAs3oTea8-xMn (b) on concentration of Mn.
identified with the help of the RPA at the concentration of chrome higher than 2 at.%, at lower concentrations--by the magnetic method (using the magnitude of the Curie temperature). Thus, at the introduction of CuzSe into the alloys of the system A s - C r - S e the modification of sign of the exchange interaction between chrome atoms and also of degree of its oxidizing happens. In the system C u - C r - S e except CuCrzSe4 there exists one more triple compound CuCrSe2. It is an antiferromagnet. During the interaction of CuCrzSe4 with CuCrSe2 the formation of solid solutions based on CuCrzSe4 takes place (Cu 1+xCrzSe4, where 0 -< x -< 1) (Babicyna, Emel'yanova and Kudryashova, 1980). And the size of a unit cell at the introduction up to 15 mol% of CuCrSe2 remains practically invariable (a - 10.335-10.348 A). At the same time the Curie temperature is reduced to 75 K, already at x = 0.05. The influence of the size of microcrystals of a ferromagnetic compound on its magnetic properties should be observed, except the influence of the modification of composition of solid solutions. It can be stipulated by two reasons. At first, the energy of the exchange interaction linking surface atoms of transitional metal with its neighbors is less than for the atoms placed in the volume of a crystal. Secondly, the exchange interaction for some ferromagnets (for example, CuCrzSe4 in the ferromagnetic state) is carried out through the degenerated electronic gas. The requirements of its quantization depend on the size of a microcrystal. Therefore, it is important to divide the total magnetization of a sample on two components: paramagnetic (xooH) and ferromagnetic (YF). The latter does not depend on the magnetic field, and the common magnetic susceptibility of the sample can be written as X = Xoo + (YF/H). Therefore, to determine the paramagnetic contribution in the magnetic
Magnetic Properties of Chalcogenide Glasses
263
susceptibility of a sample, it is necessary to study its linear dependence on the reciprocal value of the magnetic field. Xoo is the outcome of extrapolation of this dependence to H-1 = 0. The magnitude of YF can be calculated from the slope of this dependence 9 The concentration dependencies of Xoo for slits 1 and 2 have a maximum (Fig. 24). It is stipulated by the following 9 At the rising of chrome content and the appearing of the crystalline phase containing chrome, the transformation from a paramagnetic material to a superparamagnetic one takes place 9 This transformation is accompanied by the magnification of Xoo. This magnification is so large that the experimental values of Xoo exceed the value obtained by calculation with the Curie equation for non-interacting magnetic moments, in some tens of times. This outcome gives the foundation to speak about superparamagnetism. Then the ferromagnetic microcrystals begin to appear 9They do not give the major contribution to Xoo. They determine the magnitude of a ferromagnetic saturation magnetization (YF). The Yv rises with the magnification of content of chrome only up to particular concentration of the latter (see Fig. 24), as the deficit of selenium appears according to (44)
Cu2Se -k 2Cr2Se3 ~ 2CuCr2Se4-Se.
/
160.
/
\
I
260
\4
.L
k \
o 120
180
\
\ ,.. 80 8
8O
\3
40
0
~
C 0.2
\
\
40
r 0.4
N
, 0.6
aT. % 0.8
Cr, at.% FIG. 24. Dependenciesof magnetic susceptibilityat H---- oo (Xoo) and of ferromagnetic magnetization(Yv)on concentration for alloys (1 - x)0.1CuzSe.0.9As2Se3-xCrzSe3(1), (3) and (1 - x)0.2Cu2Se.0.8AszSe3-xCr2Se3 (2), (4).
264
Yu. S. Tver'yanovich
The deficit of selenium, in its turn, leads to the formation of solid solutions CuCr2Se4CuCrSe2 based on CuCr2Se4. As it was mentioned, the Curie temperature for these solid solutions is reduced up to temperature below the room temperature. It was proved by the following: the addition of about 0.3 at.% of Se into the composition of alloys results in increase of a magnetization in twice or more. The rigidity of bonds between magnetic moments in superparamagnetic and ferromagnetic particles, as it was mentioned, depends not only on temperature, but also on its size. Therefore, the boundaries between the ensembles of the paramagnetic, superparamagnetic and ferromagnetic particles in the same sample move and depend on many conditions including temperature. This fact results in the existence of maximum for the dependencies of Xoo on temperature (Fig. 25). A part of incidentally ferromagnetic particles became superparamagnetic at the rising of temperature. In some temperature range this process dominates over the decreasing of paramagnetism according to Curie-Weiss law. A more detailed discussion including the dependencies of lie on concentration and temperature was carried out in Tver'yanovich and Gutenev (1997). The investigation of ferromagnetic microcrystals with the size corresponding to the conception of 'quantum dot' and with exchange interaction through degenerated electron
3.~1 36~
/~\
\17
140
~100
\ 6o
2o --_20
40
60
80
100
r--120
l
140
T,~ FIG. 25. Dependencies of magnetic susceptibility at H ~ oo (Xoo) on temperature for alloys (1 - x)0.1Cu2_ Se-0.9AszSe3-xCrzSe3 (curves 1-4) and (1 - x)0.2CuzSe.0.8AszSe3-xCrzSe3 (curves 5-7). Content of Cr is equal: (1) 0.1 at.%; (2) (5) 0.2 at.%; (3) (6) 0.4 at.%; (4) (7) 0.9 at.%.
Magnetic Properties of Chalcogenide Glasses
265
gas would be very fruitful. These materials can have unusual magnetic properties (Yarmak, Tver'yanovich and Gitsovich, 1990).
3.4.
USING OF THE RESULT OF MAGNETO-CHEMICAL INVESTIGATIONS AT THE MODELING OF ELECTRICAL PROPERTIES OF CHALCOGENIDE GLASSES, DOPED WITH TRANSITIONAL METALS
Electrical properties of glassy semiconductors, as it is known, are not sensitive to impurities. But some ideas allow us to suppose that a small amount of transitional metals would change the electrical properties of chalcogenide glasses. Really, the appearing of fractures of the dependence In o-(1/T) was observed as a result of the doping of chalcogenide glasses with transitional metals (Popova, Tver'yanovich and Borisova, 1984; Aver'yanov and Cendin, 1985; Belyakova, Borisova, Bychkov, Zhilinskaya and Tver'yanovich, 1985). Does magneto-chemical investigations can say anything about that? The analysis of results of magneto-chemical investigations of the borders of glassformation regions for chalcogenide systems, containing transitional metals, demonstrates that the glass-formation regions are either absent absolutely (the formation of microcrystals begins at the content of transitional metals less than 0.05 at.%), or they are very small. In such conditions of the formation of crystalline phase of the compound of transitional metal, when the concentration of its structural units is low and when the cooling ratio of viscous melt is high the diffusion processes are suppressed and the formed crystalline phase has high degree of dispersibility. Even if a glass does not contain any microcrystals, the distribution of transitional metal throughout the glass volume is not uniform (see above). Furthermore, in some cases it was demonstrated that the 'doped' breaking of the dependence In o-(1 IT) coincides with the appearing of microcrystals of compounds of transitional metals (Popova et al., 1984; Belyakova et al., 1985). All the above mentioned is the reason for the model of 'pseudo-doping conductivity' in chalcogenide glasses (Tver'yanovich and Borisova, 1987). The contact potential difference appears on the border of microcrystal and glass. 3 Shielding distance for chalcogenide glasses, according to various authors, is more than some hundreds of A. Chalcogenide compounds of transitional metals have, as a rule, metallic conductivity or the conductivity of degenerated semiconductors. Furthermore, the microcrystals of these compounds are selected from alloys, possessing composite chemical composition, and as a result, contain high concentration of impurities. Therefore, unlike the chalcogenide glasses, the shielding distance in them is significantly less. Due to this the space charge covers only the part of a microcrystal and does not completely exhaust its store of free carriers. The realization of the following inequality testifies this:
2 rre2Nk r2 >- 1, eU
(45)
3 After some modification this model can be used for description of conductivity of a glass containing amorphous clusters of structural units with transitional metal atoms.
Yu. S. Tver'yanovich
266
where Ark is the concentration of free carriers in microcrystal, r is its radii, e is its dielectric constant and U is the contact potential difference. Assuming that U ~ 0.5 eV, e -~ 10, r ~ 10- 8 m and Ark ~ 102~c m - 3, we conclude that this inequality is true. Therefore, we can use the following equation for the calculation of radii of space charge around microcrystal:
3eU ) R - r 1 + 4 ~reNc '
(46)
where Nc is the concentration of charge states in glass. The volume fraction of the regions of space charge in glass, at such conditions, is larger in 1.5 orders than the volume fraction of microcrystals. Therefore, the addition into the glass composition less than 1 at.% of transitional metal is enough for the formation of the infinite cluster of a space charge. The distortion of zone structure of the semiconductor happens, as is known, in the field of a space charge. It reduces (the Fermi level is located in the middle of the energy gap for chalcogenide glasses) in magnification of conductance and diminution of its activation energy. Thus, a microcrystal is 'a collective impurity', injecting the carriers in a matrix of a glass. The size of space charge will be shortened as a result of the increasing concentration of free carrier at increasing temperature. As temperature reaches the critical value, the infinite cluster of space charge will disappear and the transposition of a charge will happen again through the matrix of a glass with undisturbed zonal structure. So, the fracture of the dependence In tr (1 IT), which is typical for an 'impurity conductivity' of semiconductors, will form. The model of 'pseudo-impurity conductivity' also predicts the effect of sharp increase of dielectric constant at origin in volume of a glass of microcrystals of composition of transitional metal. This effect was experimentally observed in Tver'yanovich, Gutenev and Borisova (1987) and Gutenev, Tver'yanovich, Krasil'nikova and Kochemirovski (1989). The equations, circumscribing this effect, are explained in Gutenev et al. (1989) and Tver'yanovich and Gutenev (1997).
4. Magnetic Properties of Glass-forming Chalcogenide Alloys at Melting 4.1.
EQUATION USING RESULTS OF MAGNETIC EXPERIENCE FOR THE CALCULATION OF LIQUIDUS
The majority of the phase diagrams of quasi-binary systems consists of one or several eutectic diagrams. Therefore we shall consider the eutectic diagram derived by diamagnetic compound A and paramagnetic compound B. We shall make the same assumptions, as at the deduction of the Eq. (23). These assumptions are simultaneously applied to both solid and melted phases. X is the paramagnetic contribution to the magnetic susceptibility of an alloy, reduced to 1 tool of transitional metal. ~ is Weiss constant for a single-phase melt with composition AaBb (~ - b0pl). For alloys placed between A and eutectic composition at temperatures lower than the eutectic temperature, and for all other alloys as well, the dependence X-1 (T) should coincide with the similar dependence for compound B in the solid state, as the alloys have microheterogeneous structure. At the eutectic temperature the component B fully
Magnetic Properties of Chalcogenide Glasses
267
FIG. 26. Generalized aspect of dependencies of paramagnetic susceptibility per mole of transitional metal on temperature for alloys A - B with different relation between A and B content (see the text): (1) for component B in crystalline state; (2) for melt with eutectic composition; (3) for atoms of transitional metal not connected by exchange interaction.
passes in the fluid phase. As a result of B's dissolution into some part of component A (which also passes partially into the fluid phase) the absolute value of the Weiss constant falls sharply. This effect is amplified by the transformation from crystalline structure to liquid. The further magnification of temperature up to the temperature of liquidus leads to magnification of the fraction of the component A in a melt, i.e., to dilution of the solution B in A. Therefore, further lowering of the absolute value of the Weiss constant occurs (Fig. 26, curve a). Immediately after exceeding of the eutectic temperature the magnitude of X is identical for all compositions, placed between a eutectic alloy and a compound A. The smooth varying of a Weiss constant (in a melt state) is absent for eutectic compositions, as all substances pass at once into melt state (curve b). For compositions placed between the eutectic and the component B at the eutectic temperature, only a part of the component B transforms in a melt. Therefore the jump of Weiss constant, at the eutectic temperature, is rather small. The magnitude of this jump depends on the content of components A and B, as it is determined by the part of component B that is transformed in a melt at this temperature. With a further rise of temperature, the part of B (which has remained in the solid state) gradually transforms to a melt up to the liquidus temperature. This process is accompanied by step-by-step decreases in the module of Weiss constant (curve c), as in the melt the component B is mixed with the component A. If the eutectic composition coincides with the diamagnetic component A (degenerated eutectic), then B does not change its state at the eutectic temperature. Therefore, the jump of the magnetic susceptibility and Weiss constant at the eutectic temperature is absent (curve d in Fig. 26). Let us consider an alloy placed between the eutectic alloy and the component A, for which the molecular fraction of the component B is equal to b, and the molecular fraction of the component A is equal to a (a + b - - 1). Let us vary the temperature
Yu. S. Tver'yanovich
268
from the eutectic temperature up to liquidus temperature. The concentration position of liquidus at some temperature T differs from the concentration position of the investigated alloy on the value ce. Then, using the relation (23), we can write for the magnetic susceptibility: X-
C T-
0
-
C T-
0 p l ( b + o/)
(47)
or
b + ce(T) -
O(T)
(48)
0pl
Thus it is possible to find the line of liquidus in the interval of compositions between the eutectic composition and the alloy AaBb from the dependence of the magnetic susceptibility of the mentioned alloy on temperature. In the case of the melting of eutectic composition, for which the molecular fractions of components are equal to a0 and b0 correspondingly, the jump of Weiss constant is equal to (49)
A0 = 0 p h - 0plb 0
This relation gives us a means to calculate the eutectic composition. It is possible to describe the composition of an alloy, located between the eutectic composition and the component B, at some temperature T situated between the solidus and the liquidus, as [(1 - c)(Bb_~A 1-b+/3)lliq
-Jr-[cB]so I
(50)
where c is the mole part of alloy in crystal state and /3 the difference between concentration position of liquidus at temperature T and concentration position of investigated alloy. Moreover
(1-c)(b-~)+c=b
or ( 1 - c ) ( 1 - b + / 3 ) = ( 1 - b )
(51)
from which we obtain c = / 3 / ( 1 - b +/3) = fl/(a + fl)
(52)
The magnetic susceptibility divided on Curie constant is equal to X
c
-
( b - / 3 ) ( 1 - c)
b i t - 0pl(b-/3)]
+
c
b ( r - 0ph)
(53)
On the other hand x / C = (T - 0) -1 . Then using Eq. (53) and defining (b - / 3 ) as x, we finally obtain
x 2 O p l [ ( T - O) - b ( T -
0ph)] nt- x [ b O ( T -
0ph ) -- 0 p h ( T - 0) -- bOpl(Oph -- 0)1
+ bT(Oph - 0) = 0 So, from Eq. (54) we can find the dependence x(T), which is liquidus.
(54)
269
Magnetic Properties of Chalcogenide Glasses 4.2.
SYSTEMAs2Se3-MnSe
The shape of dependencies of paramagnetic input in magnetic susceptibility of alloys AszSe3-MnSe per mole of Mn (Fig. 27) corresponds to the case of degenerated eutectic (Fig. 26). The dependence of Weiss constant for melts on its composition is linear (Fig. 28) (6/(b)). So, the liquation region is absent. The extrapolation of this dependence up to MnS (b -- 1) gives 0pl ~ - 350 K. The intervals of the liquidus line, calculated with the help of the Eq. (54) from the dependencies of the magnetic susceptibility on temperature for alloys with various chemical compositions, satisfactorily coincide with each other. The resulting liquidus is depicted in Figure 28. It can be seen that the phase diagram of the system is characterized by degenerated eutectic near AszSe3 with an extremely fast uprise of temperature of liquidus with a small addition of MnSe. Thus, in a melt containing only 0.2 at.% Mn (1 mol% of MnSe) at cooling, the crystalline phase of MnSe is formed almost 300 K above the melting point of AszSe3. Such a melt is insufficiently viscous for passage into the glassy state. This also explains the sharp decrease of the glass-forming ability of AszSe3, even with the addition of an inappreciable amount of manganese. It is clear that DTA would not provide an explanation for the interval of the diagrams placed so carefully close to AszSe3. Furthermore, as opposed to DTA, the discussed method allows us to
o 1
.2
.•370 -! 3s0
~
0 0 : ~
-~ 330 37~
./ ,.r
_~~
~.~
x=50,0 j
~,e~"n~"
o""
/'/
.
.
.
/
330
q
-I 350
330
-I
50 33"
.-
/ _.~"/ --I350 ~:o--~i~,~..,,.~./ ~ 330
x=30,O ~
/
j.---
o.4 t
"~/
~
//-
x=15,0/"
/-/
--I310 ~
~~~N
X=5'~"~"r
~
.
.or
,.,g
./~
./
.
x=40,O /
-~350
/0-/:(~P. ~~''8~ /
,o-" .,6 ~
/
~=0
j/
-13oo
~280 4
-t 260
x=2,5 ,
I
800
,
I
1000
I
T,K
I
1200
i
I
,,,
1400
F~G. 27. Dependencies of paramagnetic susceptibility per tool of Mn on temperature for alloys AseSe3-MnSe. The numbers mark the content of MnSe (tool%): (1) measurements were carded out at cooling; (2) measurements were carried out at hitting.
Yu. S. Tver'yanovich
270
0
0.5 |
Mn Se, mol.% 1.0 1.5 ,
.
2.0 .
~Q
,ooo/. ~ N
-
,200 + 100 0 As 2 Se 3 10
20
30 Mn Se, mol.%
40
FIG. 28. Liquidus for the system As2Se3-MnSe, constructed using magnetic measurements (1) and dependence of average Weiss constant of melt on concentration (2).
construct a liquidus in some concentration interval, using the results of the investigation of an alloy of single composition only.
4.3.
LIQUIDUS FOR OTHER CHALCOGENIDE SYSTEMS DOPED WITH TRANSITIONAL METALS
Let us consider two other magneto-chemical experiments. The first confirms that the sharp rise of the liquidus temperature is a reason of propagation of crystallizing ability of alloys; the second confirms that the temperature of the yield of dependence X-I(T) in a hightemperature linear range really corresponds to the transfer through the liquidus temperature. In Figure 29 the dependencies of the paramagnetic susceptibility of alloys AszSe3 and 0.7AszSe3.0.3CuzSe, containing an identical amount of manganese (2 at.%), on temperature are given. From the figure it is visible that the introduction of CuzSe in AszSe3 results in a drop of the liquidus temperature (the maximal temperature of existence of crystalline phase of compound of manganese). Due to these outcomes it becomes clear why in glassy As2Se3 no more than --~ 0.05 at.% of manganese can be entered, and the glass of composition 0.7AszSe3.0.3CuzSe can contain up to --~ 1 at.% of Mn (see previous section). The second experiment is the following: the evacuated thin-walled quartz ampoule containing an alloy 0.7AszSe3.0.3CuzSe with 2 at.% of Mn (total load is about 0.1 g)
Magnetic Properties of Chalcogenide Glasses
271
T, K 600 a
i
800 i
1000 i
i
I0
7"
f
~0~00
v
o/o
~o
I
7;0 8;0 9;0 l;oo T,K
FIG. 29. Dependencies of paramagnetic susceptibility on temperature for alloys As2Se3 (1) and 0.7As2Se3. 0.3CuzSe (2), contained of 2 at.% of Mn, and dependence of magnetic susceptibility (at room temperature) of alloy 0.7AszSe3.0.3CuzSe with 2 at.% Mn on temperature of melt from which the sharp quenching was began (3). Arrows mark the liquid temperature for AszSe3 and 0.7AszSe3.0.3CuzSe without Mn.
was hung in the vertical furnace which was closed from above, but did not have a bottom. At first, the furnace temperature is raised higher than liquidus, then lowered to the temperature of the experiment, at which the sample is allowed to stand for some minutes. Then the sample is dropped in a glass with a cooling fluid placed under the furnace. The magnetic susceptibility of the sample is then measured, and the experiment is repeated at other temperatures. The outcome of one trial is submitted in Figure 29 (curve 3). The sign of the indirect exchange interaction is negative. Therefore the magnification of the magnetic susceptibility corresponds to the more homogeneous distribution of manganese on the volume of the sample. From the comparison of curves 2 and 3, it is visible that the maximal degree of homogeneity of glass is achieved at quenching from the temperature of completion of the transformation to a homogeneous melt (temperature of liquidus). The microcrystals of the compound of transitional metal already exist at quenching from lower temperatures. At quenching from higher temperatures the heat content of the sample is incremented, so the effectiveness of quenching decreases. The sharp rise of the liquidus temperature at the introduction of chalcogenide compounds of transitional metals in glassy chalcogenide alloys is a common phenomenon. The outcomes of magneto-chemical experiences with a lot of chalcogenide glass-forming systems doped with chalcogenide of iron, cobalt, manganese demonstrate this. A similar pattern is observed for the system AszTe3-MnTe (Figs. 30 and 31). The latter example differs from the previous trials. At the deduction of Eq. (54), the invariance of the mechanism of the exchange interaction at transformation from the solid state to liquid was supposed. This supposition was omitted in the case of cobalt alloys for reasons that were analysed in the previous section. The dependencies of their magnetic susceptibility on temperature differ cardinally from the dependencies of the magnetic susceptibility on temperature for alloys AszSe3-MnSe. The dependencies of the magnetic
272
Yu. S. Tver'yanovich
500
10 20
~300,..~
I
100
I
I
I
600
I
800
I
I
1000
T, K FIG. 30. Dependencies of reciprocal value of paramagnetic susceptibility per mole of Mn on temperature for As2Te3-MnTe alloys. The numbers correspond to MnTe content (mol%).
susceptibility on temperature for alloys As2Te3-MnTe appear at first view to have no essential differences (see Fig. 30). But the magnetic moment of atoms of manganese for liquid alloys of this system, unlike solid state, does not correspond to the oxidation state + 2 (5.92 mB), and it varies in limits 4.0-4.7 mB. The Weiss constant changes the sign from negative to positive on transformation of the substance from solid to the melt state. The Weiss constant of the substance in melt state is not a linear function of the concentration of transitional metal compound, as Eq. 5 of Chapter 4 predicts (Fig. 31). The reason for these essential modifications is that in AszTe3, unlike AszSe3, the degenerate electronic gas already exists at the melting point
900
a
30
/I
9
0
700-It
10
40
. . . . . mol.%
20 MnTe,
mol.%
Fro. 31. (a) Different lines of liquidus (for system As2Te3-MnTe), constructed from datum of magnetic susceptibility measurements of alloys with different MnTe content (it was marked by numbers corresponded to tool% of MnTe). Two bold points are the result of DTA. (b) Dependence of average Weiss constant of melts on composition (system AszTe3-MnTe).
Magnetic Properties of Chalcogenide Glasses
273
(see above). Therefore the atoms of manganese realize the exchange interaction not through the localized electrons of anions, but through the degenerate electronic gas. The substances with such type of the exchange interaction are well known, e.g., the so-called Gaisler alloys in which the magnetic moments of manganese atoms vary in limits 3.964.4 roB. The magnitude and even the sign of Weiss constant at the exchange interaction through mobile electrons are non-monotone functions of the concentration of manganese and of mobile electrons. The approximate equations for magneto-chemical method of build-up of liquidus line can be offered and in the case of modification of the exchange interaction mechanism at melting [4]. The established fact of sharp increases of liquidus at the introduction of transitional metal in the composition of glass alloy allows testing of the statement made earlier. The semiconductor-metal transition restricts the expansion of the field of glassformation on the concentration of components and on structural temperature. As a result of the introduction of a small amount of transitional metal in the composition of a glassforming alloy, the temperature of a liquidus increases so considerably that it was higher than a semiconductor-metal transition temperature. Under these conditions, production of homogeneous glass from such alloy by the usual methods of quenching of a melt becomes impossible. For the system M n - G e - T e (in the neighbourhood of a binary eutectic GelsTeg2), the liquidus was constructed using the dependencies of magnetic susceptibility on temperature and the fast quenching method (similar to the curves given in Fig. 29). Having compared liquidus with the dependence of the temperature of semiconductor-metal transition on concentration (see Fig. 13), it is possible to come to the conclusion that they are intersected at the concentration of manganese of about 0.50.9 at.%. The samples with composition Ge~sTes2, containing 0.4, 0.6, 0.8 and 1.0 at.% of manganese, were obtained in the condition of sharp quenching. The dependence of Weiss constant of obtained alloys testifies that the boundary of glass-forming range is very close to 0.7 at.% of Mn (Fig. 32). It is shown that crystallization of glassy semiconductors at the introduction of transitional metals in their composition is stimulated by a sharp rise of the liquidus temperature. The existence of degenerate eutectics coinciding with a sharp increase of liquidus temperature is peculiar for systems with positive enthalpy of component mixture. To derive glasses with a supplemented content of transitional metals, it is necessary to find systems with negative enthalpy of mixture of glass-forming
400
of ~ o
I 200
. _ . o , - - - ? ~ ,~ 0
!
0,4 0,8 Mn, at.%
FIG. 32. Dependence of average Weiss constant of alloys Gel8Te82-Mn on Mn content.
274
Yu. S. Tver'yanovich
chalcogenides with chalcogenides of transitional metals. The limit of the diminution of mixing enthalpy is the formation of intermediate multicomponent compound. Indeed, in the already mentioned system MnS-GazS3-GeS2, the triple compounds MnzGeS4, MnGazS4 and MnzGazS5 exist, and as a result, glasses containing up to 30 mol% of MnS can be obtained.
References Anderson, P.W. (1975) Model for the electronic structure of amorphous semiconductors, Phys. Rev. Lett., 34(15), 953-955. Aver'yanov, V.L. and Cendin, K.D. (1985) Doped Glassy and Amorphous Semiconductors, Preprint N928 Physical-Technical Institute, Leningrad, 24 pp. Babicyna, A.A., Emel'yanova, T.A. and Kudryashova, T.I. (1980) J. Non-Org. Chem. (Russian), 25(4), 1084-1087. Bal'makov, M.D. and Stepanov, S.A. (1976) Phys. Chem. Glasses (Russian), 2(3), 238-241. Bal'makov, M.D., Tver'yanovich, Yu.S. and Tver'yanovich, A.S. (1994) Glass Phys. Chem. (Russian), 20, 381. Belyakova, N.V., Borisova, Z.U., Bychkov, E.A., Zhilinskaya, E.A. and Tver'yanovich, Yu.S. (1985) Phys. Chem. Glasses (Russian), 11(5), 573-577. Briegleb, G. (1929) Diedynamischen-Allotropen Zustande des Selens, Phys. Chem. A, 144(5-6), 321-358. Cabane, B. and Friedel, J. (1971) J. de Physique, 32, 73. Chepeleva, I.V. and Tver'yanovich, Yu.S. (1987) Phys. Chem. Glasses (Russian), 13(5), 747-751. Chistov, S.F., Chernov, A.P. and Dembovskiy, S.A. (1968) Non-Org. Mater. (Russian), 4(12), 2085-2088. Cohen, M.H. and Jortner, J. (1978) Electronic structure and transport in liquid Te, Phys. Rev. B, 13(13), 5255-5260. Dorfman, Ya.G. (1961) Diamagnetism and Chemical Bond, State Publisher for Physical-Mathematical Literature, Moscow, 232 pp. (in Russian). Fischer, M. and Guntherodt H.-T. (1977) Proceedings of the 7th International Conference on Amorphous and Liquid Semiconductors, Edinburg, pp. 859-864. Gardner, T.A. and Cutler, M. (1977) Proceedings of the 7th International Conference on Amorphous and Liquid Semiconductors, Edinburg, pp. 838-842. Gubanov, A.I. (1963) Quantum-Electronic Theory of Amorphous Semiconductors, Russian Academy of Science, Moscow, 250 pp. (in Russian). Gutenev, M.S., Tver'yanovich, Yu.S., Krasil'nikova, A.P. and Kochemirovski, V.A. (1989) Phys. Chem. Glasses (Russian), 15(1), 84-90. Kastner, M., Adler, D. and Fritzsche, H. (1976) Valence--alternation model for localized gap states in lone pair semiconductors, Phys. Rev. Lett., 37, 1504-1507. Kojima, D.Y. and Isihara, A. (1979) Density dependence of the magnetic susceptibilities of metals, Phys. Rev. B, 20(2), 489-500. Kudoyarova, V.H., Nasredinov, F.S. and Seregin, P.P. (1982) Phys. Chem. Glasses (Russian), 8(3), 350-352. Mendelson, L.B., Beggs, F. and Mann, J.B. (1970) Hartree-Fock diamagnetic susceptibilities, Phys. Rev. A, 2(4), 1130-1134. Misawa, M. and Suzuki, K. (1978) Ring-chain transition in liquid selenium by a disordered chain model, J. Phys. Soc. Jpn, 44(5), 1612-1618. Mott, N.F. (1978) Phil. Mag. B, 37, 377. Mott, N.F., Davis, E.A. and Street, R.A. (1975) States in the gap and recombination in amorphous semiconductors, Phil. Mag., 32(5), 961-996. Poltavcev, Yu.G. (1984) Structure of Semiconductor Melts, Metallurgy, Moscow, 176 pp. (in Russian). Popova, T.K., Tver'yanovich, Yu.S. and Borisova, Z.U. (1984) Phys. Chem. Glasses (Russian), 10(3), 374-377. Rau, H. (1974) Vapour composition and critical constants of selenium, J. Chem. Thermodyn., 6(6), 525-535. Shkol'nokov, E.V., D'yachenko, Yu.I. and Shkol'nikova, A.M. (1995) J. Appl. Chem. (Russian), 68(9), 1437 - 1444.
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Shmuratov, E.A., Andreev, A.A., Prohorenko, V.Ya., Sokolovskiy, B.I., Bal'makov, M.D. (1977) Solid State Phys. (Russian), 19(13), 927-928. Tsuchiya, Y. (1993) J. Non-Cryst. Solids, 156-158, 704. Tver'yanovich, Yu.S. and Borisova, Z.U. (1979) Non-Org. Mater. (Russian), 15(12), 2117- 2121. Tver'yanovich, Yu.S. and Borisova, Z.U. (1987) J. Non-Cryst. Solids V, 90(1-3), 405-412. Tver'yanovich, Yu.S., Borisova, Z.U. and Funtikov, V.A. (1986) Non-Org. Mater. (Russian), 22(9), 1546-1551. Tver'yanovich, Yu.S. and Gutenev, M.S. (1997) Magneto-chemistry of Glassy Semiconductors, St. Petersburg State University, St. Petersburg, 149 pp. (in Russian). Tver'yanovich, Yu.S., Gutenev, M.S. and Borisova, Z.U. (1987) Non-Org. Mater. (Russian), 23(10), 1749-1750. Tver'yanovich, A.S. and Kasatkina, E.B. (1992) Glass Phys. Chem. (Russian), 18, 86. Tver'yanovich, Yu.S. and Murin, I.V. (1999) J. Non-Cryst. Solids, 256&257, 100-104. Tver'yanovich, Yu.S. and Ugolkov, V.L. (2002) Smeared first-order phase transition in melts. In New Kinds of Phase Transitions: Transformations in Disordered Substances (Ed., Brazhkin, V.V.) Kluwer Academic Publishers, Printed in the Netherlands, pp. 209-222. Tver'yanovich, Yu.S., Vilminot, S., Degtyaryev, S.V. and Derory, A. (2000) J. Solid State Chem., 152, 388-391. Yarmak, E.V., Tver'yanovich, Yu.S. and Gitsovich, V.N. (1990) Phys. Chem. Glasses (Russian), 16(6), 884-888.
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Index noncrystalline semiconductors 15- 39 optical spectra 212- 23 reflectivity spectra 116- 21 solid-state image devices 183-5 space charge 30-9 steady-state photo-conductivity 157-9 thin films 17-39 transient photo-conductivity 169-77 arsenic sulfide absorption edge 121 - 38 germanium alloys 129-31, 159-60 magnetism 235-8 optical spectra 205-11 photo-conductivity 150-3, 155-62, 168-9 reflectivity spectra 116-18 selenium fibers 142 solid-state image devices 183-5 thermostimulated photo-conductivity 167 thin-film waveguides 179-80 arsenic tellurium magnetic susceptibility 232-4, 241,271-2 manganese tellurium alloys 271-2 optical spectra 224-7 reflectivity spectra 116 atomic configurations 4-10 attenuators 182-3
absorption coefficient 122-3, 129, 134, 140-1,145-8 edge 121-38 energy range 201 - 27 photo-induced 138-49 threshold 134- 5 acousto-optical modulation 180-1 activation energy A1-As-Te systems 100 amorphous selenium 19-20, 23 barrier-less structures 40-1 current instability 82 photo-conductivity 152-4 adiabatic approximation 5 - 8 aluminum alloys 96-7, 100, 244, 246 amorphous arsenic selenide 169-77 amorphous arsenic sulfide 168-9, 205-11 amorphous selenium 15-39 amorphous semiconductor-metal contacts 162-4 antimony doping influences 127 antimony sulfide 155-6, 158, 160, 163-4 arsenic chalcogenide optical spectra 201-27 arsenic selenide absorption edge 121-38 charge carrier density 15- 39 charge carrier transfer 17- 39 chemical composition 24- 30 copper selenium alloys 270-1 energy spectra 117- 21 magnetic properties 269-71 manganese selenium alloys 269-71
band diagrams 65-9, 203 band-to-band ionization 18 barriers barrier-less structures 39-46 CVS-based switches 59-60, 65, 67-71 277
278 electrical characteristics 50-1 photoresponse 162-4 bimolecular regime 150, 172-3 binary Si-Te systems 69-71 binary stoichiometric glasses 128-32 bombardment-induced changes 133 bond lengths 131-2 bond rigidity 264 bulk charge films 32-5 calotte of liquidation 255-6 capacitance 62-5 carriers s e e charge... cation magnetic susceptibility 253-4 chain decay processes 236-7 chalcogenide systems absorption energy range 201 - 27 charge carrier transport 15- 51 current instability 57-109 magnetic properties 229-74 optical properties 115-49 optical spectra 201-27 photo-electrical properties 149-79 photoelectric information recording systems 179-92 vitreous semiconductors (CVS) 57-109 charge carriers arsenic selenide thin films 17- 39 chemical composition selenide 24-30 CVS-based switches 60-7 drift 19- 20 effective mass 244 excess 139, 154-62 heating 18 multiple trapping 138-45, 168 optical properties 115 paramagnetic susceptibility 235 photo-conductivity 154-62, 168 photo-induced absorption 138-45 thin film arsenic selenide 17- 39 transfer 15-51, 60-7, 115, 138-45 charge-defect model 171 - 3 chemical analysis 105-9, 229-32, 248, 260, 265 - 6 chemical bonds 79-80, 89-97, 100-1,235 chemical composition influence 24-30 chromium doping 261-2 cobalt doping 260-1 coherent generation 138, 148-9 combination kinetics 172- 3
Index
composition dependence magnetic susceptibility 244-8 photo-conductivity 159, 174-7 switch functional characteristics 85-97 compressibility 240-1 concentration dependency 263-4 condensed matter systems 1-13 conditioning values 106 conducting channel formation 78-84 conductivity activation energy 82 barrier-less structures 39-46 electrical 16-18, 39-50, 60-7 magnetism 235-8 magneto-chemical investigations 265-6 s e e a l s o photo... contact potentials 265 cooperation model 138, 148-9 coordination numbers 131,240 copper doping influence 124, 167, 260-2 copying, information capacity 1-4 covalence-ion binding 86-7, 93-7 Curie paramagnetism 229, 233 current channels 58-77 current density 40-1 current injection 50 current instability 57-109 kinetic concept 57-8, 77-109 switching effect 85-109 current-voltage (I-V) characteristics barrier-less structures 39-40, 43 current instability 80-1 CVS-based switches 60-3, 72-3, 75 nonactivated electrical conduction 48 CVS s e e chalcogenide vitreous semiconductors dark conductivity 152 decomposition 208-11, 217-19, 222- 3, 226-7 defect formation process 78-84 degenerated electron gas 239, 243-4 delay time 82, 101 - 2 density of states spectra 203-5 destruction process 102-4 diamagnetic susceptibility 230-1,235 dielectric constants 177 dielectric function spectra 208-11,217-19, 222- 3, 226- 7 diffraction efficiency 188- 91
279
Index
dimensional effects 71-7 displacement sensors 181 - 2 doping influences absorption edge 123-30, 132 magnetic susceptibility 258-66 photo-conductivity 160-2, 167, 173, 175-6 Dorfman's method 230-1 drift barriers 65, 67-71 drift mobility 18-20, 23, 25-8, 144-5 DTA curves 107-8, 269-70 effective mass 244 effective quantum yield films 34-6 electric field dependence 19-22, 39-46, 50 electrical characteristics 15-39, 5 0 - 1 , 1 0 5 - 9 electrical conductivity 16-18, 39-50, 60-7 electrical property modeling 265-6 electro-optical modulation 180-1 electro-physical properties 91, 93-4, 97-105 electrode widths 73-5 electron states 116-21 electronic structure theory 202-3 electrons drift mobility 25-8 loss spectra 208-12, 217 - 19, 222- 3, 225-7 magnetic susceptibility 239 photo-induced absorption 138-9, 145-6 energy dissipation distances 21-3 energy distances 21 - 3, 119 energy levels 65-9, 203 energy spectra arsenic selenide 117-21,212-17, 219-22 arsenic sulfides 205-11 arsenic tellurium 224-7 optical properties 115 enthalpy 236 entropy 236 equilibrium holes 18, 21 - 3, 176 equivalent circuits 61-2 ESR signals 17-18, 229-32 eutectic diagrams 266-8 exact copies 2 - 4 excess charge carriers 139, 154-62 excess energy relaxation 77, 80-1 exchange interaction 248-50, 252-5 excitons 133 exponential dependence 40, 132-8
Fermi levels 152-4 fiber optics 141-2, 179-92 field effect magnitudes 159-60 fluctuation nature 252 forbidden gap widths 131-2 free carriers 244 Frenkel-Pool 60 fundamental absorption energy range 201-27 gallium sulfide 257-8 gallium tellurium charge carrier transfer 15-17, 39-51 germanium systems 91, 93-4 magnetic susceptibility 244, 246 gap state optical transitions 161 - 2 germanium doping influence 124-5, 129-30, 167 selenium systems 231-3, 257-8 sulfur systems 231 - 3 tellurium systems 87, 89-92 glass formation 107-8, 232-48, 266-74 forming alloys at melting 266-74 forming melts 232-48 physical-chemical properties 105-9 prehistory 136-8 quenching 108- 9 transition energy 131 transition temperatures 94-7, 131 grating filters 180-1 half-widths 210-11 heat capacity 240 heating effects 232-48 heterogeneities 59 high electric field charge carrier transfer 15-51 high-resolution solid-state image devices 183-5 holes 21-4, 26-9, 144-6 holography 179, 185- 91 hot electrons 145-6 hot holes 21-4, 145-6 hydrostatic pressure 104-5 hyperbolic photocurrent decay 175-6 I - V s e e current-voltage impurity effects 17-18, 160-1, 174-7
280 indirect exchange interaction 248-50, 252-5 indium tellurium charge carrier transfer 15-17, 39-51 germanium systems 87, 89-92, 94-7 magnetic susceptibility 244, 246 information technology 1- 13, 179- 92 inhomogeneous switching model 72-5 integrated devices 179-92 Intensity dependence 141 inter-atomic bond rupturing 77-83 inter-band absorption 134, 145 interacting pairs with variable valence (IPVV) 79 intermediate compound formation 255-6 intermolecular interaction 120-1 iodine doping influence 167 ions 121,243-4 IPVV s e e interacting pairs with variable valence joint density of states spectra 203 jump transitions 58 kinetics current instability 57-8, 77-109 photo-induced absorption 141, 143 switching effect 85-109 transient photo-conductivity 172-4 Langeven's diamagnetic susceptibility 23O- 1,235 lanthanide doping 124 laser pulses 146 lattices 132, 135-6, 205 lifetimes 6, 29 limited currents 43 liquidus calculations 266-74 localized states 138-45, 168 long-wave fluctuations 135 longitudinal optical transitions 204-5 low conductivity melts 235-8 low-resistance states (LRS) 46-50 lux-ampere characteristics 149-52 macroinformations 6 magnetism 229-74 alloys at melting 266-74 glasses 232-48, 252-74
Index
ions 243-4 low conductivity melts 235-8 magnetic susceptibility 229-48, 252-66, 268-74 melts 232-48 metallized states 243-4 non transitional metals 229-32 transitional metals 248-66 magneto-chemico method 248, 260, 265-6 manganese 128, 258-62, 273 melting magnetic properties, glass-forming alloys 266-74 melts, magnetic susceptibility 232-48 memory elements 85 metal doping influences 123- 7 metal-As(S,Se3):Sn- SiO2- Si structures 183-5 metal-chalcogenide glass pairs 162-4 metal-CVS-metal structures 61-2, 68-9 metallized states, magnetism 243-4 microcrystal sizes 262-5 microdeformations 187-8 micromobility 19- 23 microregion of co-operative structural transformations (RCST) 241 - 3 microwave noise 46-9 mobile electrons 239 monomolecular recombination (MR) 172-3 monostable switches 105-9 M6ssbauer spectra 125 MR s e e monomolecular recombination multicomponent alloys 128-32 multifunctional optical integrated devices 179-92 multiphonon ionization 42-3 multiple trapped carriers 138-45, 168 multiplication effect 20-4 Neel phase transitions 249 negative bulk charge formation 32-5 negative capacitance 62, 64-5 negative transient photocurrents 177-9 noise temperatures 48-9 non-activated electrical conduction states 46-50 non-crystalline semiconductors 15- 51, 132-8 non-equilibrium carriers 138- 9 non-equilibrium phonons 138, 145-8
281
Index
non-linear absorption 138 non-linear photo-induced absorption 138, 145-8 non-transitional metals 229- 32 non-uniform microregion of co-operative structural transformations 241-2 number of coordination 131,240 ODC regions 70, 72-4, 76-7, 81 optical absorption 120 optical anisotropy 179-80 optical fibers 141 - 2 optical integrated devices 179-92 optical losses 181 optical properties 115-49 optical spectra amorphous arsenic sulfide 205-11 arsenic chalcogenides 201 - 27 arsenic tellurium 224-7 arsenic-selenides 212- 23 optical transitions 161 - 2 overshoot 175 oxidizing degree 249 oxygen doping influences 132, 160-1 pairs with variable valence (PVV) 79 paramagnetism 230-1,235,269-70 PCA s e e physicochemical analysis peak energy 159 phase recording 179 phase transition smearing 241-3 phosphorus 29- 30, 231 photo-carrier generation 172 photo-conductivity arsenic selenide 116-18 arsenic sulfide 116-18 doping influences 160-2, 167, 173, 175-6 selenium 15 photo-current dependence 149, 173-6 photo-electric information recording systems 179-92 photo-electrical properties 149-79 steady-state photo-conductivity 149-68 transient photo-conductivity 168-79 photo-generation films 34-7 photo-induced absorption 138-49 photo-optical modulation 180-1 photo-response 162-4
photo-thermoplastic systems 191 - 2 photon energy 129-30, 135, 154-62 physicochemical analysis (PCA) 105-9, 229-32 planar waveguides 179 polarity 159-60 polarization 164-8, 231 - 3 Poole-Frenkel emission 40-1 potential barriers 65, 67-71 potential dark decay 30-2, 37 potential energy 65-7 power index 136-8, 150-1 power laws 144, 150-1, 174 pressure 97-105, 240 pseudo-impurity conductivity 266 PVV s e e pairs with variable valence quantum efficiency 20-1 quantum energy 134 quantum mechanics 4 quantum states 4, 6-7 quantum yield 34-6 quasi-closed ensembles 4-13 quasi-equidistant subgroups 146-7 quasi-molecular defects 80-1 quasi-static current-voltage characteristics 72-3 quenching 17-18, 108-9 radiation interaction 115 rare earth ions 121 RCST s e e microregion of co-operative structural transformations reading 7 recorded information 9-10 recording media 185- 7 reflectivity spectra 116-21,203-8, 212-22, 224-7 refractive index anisotropy 179-80 registration media 185- 91 relaxation 77, 80-1,170-1 resistance 94-5 reverse switching 75-6 reverse-current heterojunctions 60 reversible phenomena 138-49 rupturing 77, 79-84, 102-3 SCD s e e small-charge drift Schottky's over-barrier emission 67
282 SCLC s e e space charge limited currents selenium magnetism 235-8 tellurium alloys 244-5 s e e a l s o arsenic... semiconductor-metal transitions (SMT) 238-43, 247-8 sensibility 188- 9 SFS s e e superfine structure sign inversion, current instability 84 silicon lead systems 91, 93 oxides 183-5 solid-state image devices 183-5 tellurium systems 69-71, 91, 93 silver 123-4, 244, 246 small-charge drift (SCD) current 25-7 smearing 241 - 3 SMT s e e semiconductor-metal transitions softening temperature 94-7, 234 space charge 30-9, 43 space charge limited currents (SCLC) 43 spectra distribution 154-62 state coefficients 140 state density 135-6 stationary state coefficient 140 steady-state photo-conductivity 149-68 stimulated polarization currents 164-8 strained chemical bonds 79-80 structure absorption edge 136-8 doping influences 123-8 magneto-chemical investigations 266 units 160 sulfur s e e arsenic sulfide superfine structure (SFS) 258-60 switches current channels 58-77 CVS-based 65, 67-71 electro-physical parameters 97-105 switching activation energy 98-101 channel diameter 71-2 effect 69-71, 85-109 functional characteristics 85-97 resistance 99, 102- 3 time 82 voltages 94-5, 106 synthesis influence 105-9
Index
tail widths 126, 133, 136-7 TEE s e e thermo-electrical emission tellurium absorption edge 127-8, 130 charge transfer 29-30 current instability 87, 89-92 magnetic susceptibility 232-4, 244-8 s e e a l s o arsenic... temperature dependence absorption edge 129-30, 133-4, 136-8 barrier-less structures 41-2 charge carrier drift 19- 20 CVS-based switches 62-5, 68, 74-5 drift mobility films 27-9 equilibrium holes 21 - 3 magnetic susceptibility 232-48, 252-5 photo-conductivity 150-4, 170-1, 175-6 photo-induced absorption 141-4 switch electro-physical parameters 97-105 thermo-electromotive force films 85-8 T F W s e e thin-film waveguides thallium doping 124 thermal activation 40-1, 139 thermal fluctuations 82-3 thermal stimulated cold emission (TSE) 60 thermal treatments 105-9, 133-4 thermo-electrical emission (TEE) 60 thermo-electromotive force films 85-8 thermo-plastic systems 191 - 2 thermo-stimulated crystallization 260 thermo-stimulated depolarization (TSD) 164-8 thermo-stimulated photo-conductivity 164-8 thickness effects 20-1 thin film arsenic selenide 17-39, 157-9 thin-film waveguides (TFW) 179-81 threshold currents 74-5, 98-9 threshold energy 164 threshold voltage 98-9 time delay 188, 190-1 time dependence 37-8, 141, 178-9 tin doping influences absorption edge 124-7 solid-state image devices 183-5 steady-state photo-conductivity 161-2 transient photo-conductivity 173, 175-6 transformation validity 9-10 transient photo-conductivity 168-79 transitional metals, magnetism 248-66
283
Index
transport charge carriers 15- 51 properties 92- 3 transverse optical transitions 204-5 trapping factor 23-4 TSD s e e thermo-stimulated depolarization TSE s e e thermal stimulated cold emission tunneling 70-1, 1 7 1 - 3 two-photon model 138, 148-9 two-step absorption 138, 148-9 uniform microregion of co-operative structural transformations 242- 3 Urbach edges 126, 132-4 Urbach rule 132, 135 valence alternation pairs (VAP) 17-18 validity of transformations 9 - l 0 van-Vleck paramagnetic susceptibility 230-1,235
VAP s e e valence alternation pairs vapor, magnetism 237-8 variable fiber optic attenuators 182-3 variable valence 79 viscosity 241 vitreous chalcogenide semiconductors 57-109 vitreous sulfide 121-8 voltage pulse polarity 190 wave functions 5, 7 waveguides 179-81 wavelength dependence 170-1 weight factors 253-4 Weiss constant 250-2, 256-9, 261-2, 267-8, 272-4 wide-gap chalcogenides 191 - 2 xerography 191 - 2
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Contents of Volumes in This Series
Volume 1
Physics o f l l l - V Compounds
C. Hilsum, Some Key Features of III-V Compounds F. Bassani, Methods of Band Calculations Applicable to III-V Compounds E. O. Kane, The k-p Method V. L. Bonch-Bruevich, Effect of Heavy Doping on the Semiconductor Band Structure
D. Long, Energy Band Structures of Mixed Crystals of III-V Compounds L. M. Roth and P. N. Argyres, Magnetic Quantum Effects S. M. Puri and T. H. Geballe, Thermomagnetic Effects in the Quantum Region W. M. Becket, Band Characteristics near Principal Minima from Magnetoresistance E. H. Putley, Freeze-Out Effects, Hot Electron Effects, and Submillimeter Photoconductivity in InSb H. Weiss, Magnetoresistance B. Ancker-Johnson, Plasma in Semiconductors and Semimetals
Volume 2
Physics o f l l l - V Compounds
M. G. Holland, Thermal Conductivity S. I. Novkova, Thermal Expansion U. Piesbergen, Heat Capacity and Debye Temperatures G. Giesecke, Lattice Constants J. R. Drabble, Elastic Properties A. U. Mac Rae and G. W. Gobeli, Low Energy Electron Diffraction Studies R. Lee Mieher, Nuclear Magnetic Resonance B. Goldstein, Electron Paramagnetic Resonance T. S. Moss, Photoconduction in III-V Compounds E. Antoncik and J. Tauc, Quantum Efficiency of the Internal Photoelectric Effect in InSb G. W. Gobeli and L G. Allen, Photoelectric Threshold and Work Function P. S. Pershan, Nonlinear Optics in III-V Compounds
285
286
Contents o f Volumes in This Series
M. Gershenzon, Radiative Recombination in the III-V Compounds F. Stern, Stimulated Emission in Semiconductors
Optical Properties o f l l l - V Compounds
Volume 3 M. Hass, Lattice Reflection
W. G. Spitzer, Multiphonon Lattice Absorption D. L. Stierwalt and R. F. Potter, Emittance Studies H. R. Philipp and H. Ehrenveich, Ultraviolet Optical Properties M. Cardona, Optical Absorption Above the Fundamental Edge E. J. Johnson, Absorption Near the Fundamental Edge J. O. Dimmock, Introduction to the Theory of Exciton States in Semiconductors B. Lax and J. G. Mavroides, Interband Magnetooptical Effects H. Y. Fan, Effects of Free Carries on Optical Properties E. D. Palik and G. B. Wright, Free-Carrier Magnetooptical Effects R. H. Bube, Photoelectronic Analysis B. O. Seraphin and H. E. Benett, Optical Constants
Volume 4
Physics of III-V Compounds
N. A. Goryunova, A. S. Borchevskii and D. N. Tretiakov, Hardness N. N. Sirota, Heats of Formation and Temperatures and Heats of Fusion of Compounds of AIIIBv D. L. Kendall, Diffusion A. G. Chynoweth, Charge Multiplication Phenomena R. W. Keyes, The Effects of Hydrostatic Pressure on the Properties of III-V Semiconductors L. W. Aukerman, Radiation Effects N. A. Goryunova, F. P. Kesamanly, and D. N. Nasledov, Phenomena in Solid Solutions R. T. Bate, Electrical Properties of Nonuniform Crystals
Volume 5
Infrared Detectors
H. Levinstein, Characterization of Infrared Detectors P. W. Kruse, Indium Antimonide Photoconductive and Photoelectromagnetic Detectors M. B. Prince, Narrowband Self-Filtering Detectors I. Melngalis and T. C. Harman, Single-Crystal Lead-Tin Chalcogenides D. Long and J. L. Schmidt, Mercury-Cadmium Telluride and Closely Related Alloys E. H. Putley, The Pyroelectric Detector N. B. Stevens, Radiation Thermopiles R. J. Keyes and T. M. Quist, Low Level Coherent and Incoherent Detection in the Infrared M. C. Teich, Coherent Detection in the Infrared F. R. Arams, E. W. Sard, B. J. Peyton and F. P. Pace, Infrared Heterodyne Detection with Gigahertz
IF Response H. S. Sommers, Jr., Macrowave-Based Photoconductive Detector R. Sehr and R. Zuleeg, Imaging and Display
Contents o f Volumes in This Series
Injection Phenomena
Volume 6
M. A. Lampert and R. B. Schilling, Current Injection in Solids: The Regional Approximation Method R. Williams, Injection by Internal Photoemission A. M. Barnett, Current Filament Formation R. Baron and J. W. Mayer, Double Injection in Semiconductors W. Ruppel, The Photoconductor-Metal Contact
Volume 7
Application and Devices
Part A J. A. Copeland and S. Knight, Applications Utilizing Bulk Negative Resistance F. A. Padovani, The Voltage-Current Characteristics of Metal-Semiconductor Contacts P. L. Hower, W. W. Hooper, B. R. Cairns, R. D. Fairman, and D. A. Tremere, The GaAs
Field-Effect Transistor M. H. White, MOS Transistors G. R. Antell, Gallium Arsenide Transistors T. L. Tansley, Heterojunction Properties
Part
B
T. Misawa, IMPATT Diodes H. C. Okean, Tunnel Diodes R. B. Campbell and Hung-Chi Chang, Silicon Junction Carbide Devices R. E. Enstrom, H. Kressel, and L. Krassner, High-Temperature Power Rectifiers of GaAsl-x Px
Volume 8
Transport and Optical Phenomena
R. J. Stirn, Band Structure and Galvanomagnetic Effects in III-V Compounds with Indirect Band Gaps R. W. Ure, Jr., Thermoelectric Effects in III-V Compounds H. Piller, Faraday Rotation H. Barry Bebb and E. W. Williams, Photoluminescence I: Theory E. W. Williams and H. Barry Bebb, Photoluminescence II: Gallium Arsenide
Volume
9
Modulation Techniques
B. O. Seraphin, Electroreflectance R. L. Aggarwal, Modulated Interband Magnetooptics D. F. Blossey and Paul Handler, Electroabsorption B. Batz, Thermal and Wavelength Modulation Spectroscopy I. Balslev, Piezooptical Effects D. E. Aspnes and N. Bottka, Electric-Field Effects on the Dielectric Function of Semiconductors
and Insulators
287
288
Contents o f Volumes in This Series
Volume
10
Transport Phenomena
R. L. Rhode, Low-Field Electron Transport J. D. Wiley, Mobility of Holes in III-V Compounds C. M. Wolfe and G. E. Stillman, Apparent Mobility Enhancement in Inhomogeneous Crystals R. L. Petersen, The Magnetophonon Effect
Volume
11
Solar Cells
H. J. Hovel, Introduction; Carrier Collection, Spectral Response, and Photocurrent; Solar Cell Electrical
Characteristics; Efficiency; Thickness; Other Solar Cell Devices; Radiation Effects; Temperature and Intensity; Solar Cell Technology
Volume 12
Infrared Detectors (II)
w. L. Eiseman, J. D. Merriam, and 17. F. Potter, Operational Characteristics of Infrared Photodetectors P. R. Bratt, Impurity Germanium and Silicon Infrared Detectors E. H. Putley, InSb Submillimeter Photoconductive Detectors G. E. Stillman, C. M. Wolfe, and J. 0. Dimmock, Far-Infrared Photoconductivity in High Purity GaAs G. E. Stillman and C. M. Wolfe, Avalanche Photodiodes P. L. Richards, The Josephson Junction as a Detector of Microwave and Far-Infrared Radiation E. H. Putley, The Pyroelectric Detector - An Update
Volume
13
Cadmium Telluride
K. Zanio, Materials Preparations; Physics; Defects; Applications
Volume
14
Lasers, Junctions, Transport
N. Holonyak, Jr., and M. H. Lee, Photopumped III-V Semiconductor Lasers H. Kressel and J. K. Butler, Heterojunction Laser Diodes A. Van der Ziel, Space-Charge-Limited Solid-State Diodes P. J. Price, Monte Carlo Calculation of Electron Transport in Solids
Volume
15
Contacts, Junctions, Emitters
B. L. Sharma, Ohmic Contacts to III-V Compounds Semiconductors A. Nussbaum, The Theory of Semiconducting Junctions J. S. Escher, NEA Semiconductor Photoemitters
V o l u m e 16
Defects, (HgCd)Se, (HgCd)Te
H. Kressel, The Effect of Crystal Defects on Optoelectronic Devices C. R. Whitsett, J. G. Broerman, and C. J. Summers, Crystal Growth and Properties of Hgl-x Cdx Se Alloys
Contents o f Volumes in This Series
289
M. H. Weiler, Magnetooptical Properties of Hgl-x Cdx Te Alloys P. W. Kruse and J. G. Ready, Nonlinear Optical Effects in Hgl-x Cdx Te
Volume 17
CW Processing of Silicon and Other Semiconductors
J. F. Gibbons, Beam Processing of Silicon A. Lietoila, R. B. Gold, J. F. Gibbons, and L. A. Christel, Temperature Distributions and Solid Phase Reaction
Rates Produced by Scanning CW Beams A. Leitoila and J. F. Gibbons, Applications of CW Beam Processing to Ion Implanted Crystalline Silicon N. M. Johnson, Electronic Defects in CW Transient Thermal Processed Silicon K. F. Lee, T. J. Stultz, and J.F. Gibbons, Beam Recrystallized Polycrystalline Silicon: Properties, Applications,
and Techniques T. Shibata, A. Wakita, T. W. Sigmon and J. F. Gibbons, Metal-Silicon Reactions and Silicide Y. I. Nissim and J. F. Gibbons, CW Beam Processing of Gallium Arsenide
Volume 18
Mercury Cadmium Telluride
P. W. Kruse, The Emergence of (Hgl-x Cdx)Te as a Modern Infrared Sensitive Material 14. E. Hirsch, S. C. Liang, and A. G. White, Preparation of High-Purity Cadmium, Mercury, and Tellurium W. F. H. Micklethwaite, The Crystal Growth of Cadmium Mercury Telluride P. E. Petersen, Auger Recombination in Mercury Cadmium Telluride R. M. Broudy and V. J. Mazurczyck, (HgCd)Te Photoconductive Detectors M. B. Reine, A. If. Soad, and T. J. Tredwell, Photovoltaic Infrared Detectors M. A. Kinch, Metal-Insulator-Semiconductor Infrared Detectors
Volume 19
Deep Levels, GaAs, Alloys, Photochemistry
G. F. Neumark and K. Kosai, Deep Levels in Wide Band-Gap III-V Semiconductors D. C. Look, The Electrical and Photoelectronic Properties of Semi-Insulating GaAs R. F. Brebrick, Ching-Hua Su, and Pok-Kai Liao, Associated Solution Model for Ga-In-Sb and Hg-Cd-Te Y. Ya. Gurevich and Y. V. Pleskon, Photoelectrochemistry of Semiconductors
Volume 20
Semi-Insulating GaAs
R. N. Thomas, H. M. Hobgood, G. W. Eldridge, D. L. Barrett, T. T. Braggins, L. B. Ta, and S. K. Wang,
High-Purity LEC Growth and Direct Implantation of GaAs for Monolithic Microwave Circuits C. A. Stolte, Ion Implantation and Materials for GaAs Integrated Circuits C. (7,. Kirkpatrick, R. T. Chen, D. E. Holmes, P. M. Asbeck, K. R. Elliott, R. D. Fairman, and J. R. Oliver~ I~EC GaAs for Integrated Circuit Applications J. S. Blakemore and S. Rahimi, Models for Mid-Gap Centers in Gallium Arsenide
Volume 21 Part A J. I. Pankove, Introduction
Hydrogenated Amorphous Silicon
290
Contents o f Volumes in This Series
M. Hirose, Glow Discharge; Chemical Vapor Deposition Y. Uchida, di Glow Discharge T. D. Moustakas, Sputtering I. Yamada, Ionized-Cluster Beam Deposition B. A. Scott, Homogeneous Chemical Vapor Deposition F. J. Kampas, Chemical Reactions in Plasma Deposition P. A. Longeway, Plasma Kinetics H. A. Weakliem, Diagnostics of Silane Glow Discharges Using Probes and Mass Spectroscopy L. Gluttman, Relation between the Atomic and the Electronic Structures A. Chenevas-Paule, Experiment Determination of Structure S. Minomura, Pressure Effects on the Local Atomic Structure D. Adler, Defects and Density of Localized States
Part B J. i. Pankove, Introduction G. D. Cody, The Optical Absorption Edge of a-Si: H N. M. Amer and W. B. Jackson, Optical Properties of Defect States in a-Si: H P. J. Zanzucchi, The Vibrational Spectra of a-Si: H F. Hamakawa, Electroreflectance and Electroabsorption J. S. Lannin, Raman Scattering of Amorphous Si, Ge, and Their Alloys R. A. Street, Luminescence in a-Si: H R. S. Crandall, Photoconductivity J. Tauc, Time-Resolved Spectroscopy of Electronic Relaxation Processes P. E. Vanier, IR-Induced Quenching and Enhancement of Photoconductivity and Photoluminescence H. Schade, Irradiation-Induced Metastable Effects L. Ley, Photoelectron Emission Studies
Part C J. I. Pankove, Introduction J. D. Cohen, Density of States from Junction Measurements in Hydrogenated Amorphous Silicon P. C. Taylor, Magnetic Resonance Measurements in a-Si: H K. Morigaki, Optically Detected Magnetic Resonance J. Dresner, Carrier Mobility in a-Si: H T. Tiedje, Information About Band-Tail States from Time-of-Flight Experiments A. R. Moore, Diffusion Length in Undoped a-S: H W. Beyer and J. Overhof, Doping Effects in a-Si: H H. Fritzche, Electronic Properties of Surfaces in a-Si: H C. R. Wronski, The Staebler-Wronski Effect R. J. Nemanich, Schottky Barriers on a-Si: H B. Abeles and T. Tiedje, Amorphous Semiconductor Superlattices
Part D J. i. Pankove, Introduction D. E. Carlson, Solar Cells
Contents o f Volumes in This Series
291
G. A. Swartz, Closed-Form Solution of I - V Characteristic for a s-Si: H Solar Cells I. Shimizu, Electrophotography S. Ishioka, Image Pickup Tubes P. G. Lecomber and W. E. Spear, The Development of the a-Si: H Field-Effect Transistor and its Possible
Applications D. G. Ast, a-Si:H FET-Addressed LCD Panel S. Kaneko, Solid-State Image Sensor M. Matsumura, Charge-Coupled Devices M. A. Bosch, Optical Recording A. D'Amico and G. Fortunato, Ambient Sensors H. Kulkimoto, Amorphous Light-Emitting Devices R. J. Phelan, Jr., Fast Decorators and Modulators J. I. Pankove, Hybrid Structures P. G. LeComber, A. E. Owen, W. E. Spear, J. Hajto, and W. K. Choi, Electronic Switching in Amorphous
Silicon Junction Devices
Volume 22
Lightwave Communications Technology
Part A K. Nakajima, The Liquid-Phase Epitaxial Growth of InGaAsP W. T. Tsang, Molecular Beam Epitaxy for III-V Compound Semiconductors G. B. Stringfellow, Organometallic Vapor-Phase Epitaxial Growth of III-V Semiconductors G. Beuchet, Halide and Chloride Transport Vapor-Phase Deposition of InGaAsP and GaAs M. Razeghi, Low-Pressure, Metallo-Organic Chemical Vapor Deposition of GaxInl-xAsP~-y Alloys P. M. Petroff, Defects in III-V Compound Semiconductors
Part B J. P. van der Ziel, Mode Locking of Semiconductor Lasers K. Y. Lau and A. Yariv, High-Frequency Current Modulation of Semiconductor Injection Lasers C. H. Henry, Special Properties of Semi Conductor Lasers Y. Suematsu, K. Kishino, S. Arai, and F. Koyama, Dynamic Single-Mode Semiconductor Lasers with a
Distributed Reflector W. T. Tsang, The Cleaved-Coupled-Cavity (C 3) Laser
Part C R. J. Nelson and N. K. Dutta, Review of InGaAsP InP Laser Structures and Comparison of
Their Performance N. Chinone and M. Nakamura, Mode-Stabilized Semiconductor Lasers for 0.7-0.8- and 1.1-1.6-~m Regions Y. Horikoshi, Semiconductor Lasers with Wavelengths Exceeding 2 ~m B. A. Dean and M. Dixon, The Functional Reliability of Semiconductor Lasers as Optical Transmitters R. H. Saul, T. P. Lee, and C. A. Burus, Light-Emitting Device Design C. L. Zipfel, Light-Emitting Diode-Reliability T. P. Lee and T. Li, LED-Based Multimode Lightwave Systems K. Ogawa, Semiconductor Noise-Mode Partition Noise
292
Contents o f Volumes in This Series
Part D F. Capasso, The Physics of Avalanche Photodiodes T. P. Pearsall and M. A. Pollack, Compound Semiconductor Photodiodes T. Kaneda, Silicon and Germanium Avalanche Photodiodes S. R. Forrest, Sensitivity of Avalanche Photodetector Receivers for High-Bit-Rate Long-Wavelength
Optical Communication Systems J. C. Campbell, Phototransistors for Lightwave Communications
Part E s. Wang, Principles and Characteristics of Integrable Active and Passive Optical Devices S. Margalit and A. Yariv, Integrated Electronic and Photonic Devices T. Mukai, E Yamamoto, and T. Kimura, Optical Amplification by Semiconductor Lasers
Volume 23
Pulsed Laser Processing of Semiconductors
R. F. Wood, C W. White and R. T. Young, Laser Processing of Semiconductors: An Overview C. W. White, Segregation, Solute Trapping and Supersaturated Alloys G. E. Jellison, Jr., Optical and Electrical Properties of Pulsed Laser-Annealed Silicon R. F. Wood and G. E. Jellison, Jr., Melting Model of Pulsed Laser Processing R. F. Wood and F. W. Young, Jr., Nonequilibrium Solidification Following Pulsed Laser Melting D. H. Lowndes and G. E. Jell&on, Jr., Time-Resolved Measurement During Pulsed Laser Irradiation of Silicon D. M. Zebner, Surface Studies of Pulsed Laser Irradiated Semiconductors D. H. Lowndes, Pulsed Beam Processing of Gallium Arsenide R. B. James, Pulsed CO2 Laser Annealing of Semiconductors R. T. Young and R. F. Wood, Applications of Pulsed Laser Processing
Volume 24
Applications of Multiquantum Wells, Selective Doping, and Superlattices
c. Weisbuch, Fundamental Properties of III-V Semiconductor Two-Dimensional Quantized Structures: The
Basis for Optical and Electronic Device Applications H. Morkof and H. Unlu, Factors Affecting the Performance of (A1,Ga)As/GaAs and (A1,Ga)As/InGaAs
Modulation-Doped Field-Effect Transistors: Microwave and Digital Applications N. T. Linh, Two-Dimensional Electron Gas FETs: Microwave Applications M. Abe et al., Ultra-High-Speed HEMT Integrated Circuits D. S. Chemla, D. A. B. Miller and P. W. Smith, Nonlinear Optical Properties of Multiple Quantum Well
Structures for Optical Signal Processing F. Capasso, Graded-Gap and Superlattice Devices by Band-Gap Engineering W. T. Tsang, Quantum Confinement Heterostructure Semiconductor Lasers G. C. Osbourn et al., Principles and Applications of Semiconductor Strained-Layer Superlattices
Volume 25
Diluted Magnetic Semiconductors
w. Giriat and J. K. Furdyna, Crystal Structure, Composition, and Materials Preparation of Diluted Magnetic
Semiconductors W. M. Becker, Band Structure and Optical Properties of Wide-Gap A~ixMnxBiv Alloys at Zero Magnetic Field
Contents o f Volumes in This Series
293
S. Oseroff and P. H. Keesom, Magnetic Properties: Macroscopic Studies T. Giebultowicz and T. M. Holden, Neutron Scattering Studies of the Magnetic Structure and Dynamics of
Diluted Magnetic Semiconductors J. Kossut, Band Structure and Quantum Transport Phenomena in Narrow-Gap Diluted Magnetic
Semiconductors C. Riquaux, Magnetooptical Properties of Large-Gap Diluted Magnetic Semiconductors J. A. Gaj, Magnetooptical Properties of Large-Gap Diluted Magnetic Semiconductors J. Mycielski, Shallow Acceptors in Diluted Magnetic Semiconductors: Splitting, Boil-off, Giant Negative
Magnetoresistance A. K. Ramadas and R. Rodriquez, Raman Scattering in Diluted Magnetic Semiconductors P. A. Wolff, Theory of Bound Magnetic Polarons in Semimagnetic Semiconductors
V o l u m e 26
Compound Semiconductors and Semiconductor Properties of Superionic Materials
III-V
z. Yuanxi, III-V Compounds H. V. Winston, A. T. Hunter, H. Kimura, and R. E. Lee, InAs-Alloyed GaAs Substrates for Direct Implantation P. K. Bhattacharya and S. Dhar, Deep Levels in III-V Compound Semiconductors Grown by MBE F. Ya. Gurevich and A. K. Ivanov-Shits, Semiconductor Properties of Supersonic Materials
V o l u m e 27
High Conducting Quasi-One-Dimensional Organic Crystals
E. M. Conwell, Introduction to Highly Conducting Quasi-One-Dimensional Organic Crystals I. A. Howard, A Reference Guide to the Conducting Quasi-One-Dimensional Organic Molecular Crystals J. P. Pouquet, Structural Instabilities E. M. Conwell, Transport Properties C. S. Jacobsen, Optical Properties J. C. Scott, Magnetic Properties L. Zuppiroli, Irradiation Effects: Perfect Crystals and Real Crystals
V o l u m e 28
Measurement
of
High-Speed Signals in Solid State Devices
J. Frey and D. Ioannou, Materials and Devices for High-Speed and Optoelectronic Applications H. Schumacher and E. Strid, Electronic Wafer Probing Techniques D. H. Auston, Picosecond Photoconductivity: High-Speed Measurements of Devices and Materials J. A. Valdmanis, Electro-Optic Measurement Techniques for Picosecond Materials, Devices and Integrated
Circuits J. M. Wiesenfeld and R. K. Jain, Direct Optical Probing of Integrated Circuits and High-Speed Devices G. Plows, Electron-Beam Probing A. M. Weiner and R. B. Marcus, Photoemissive Probing
V o l u m e 29
Very High Speed Integrated Circuits: Gallium Arsenide LSI
M. Kuzuhara and T. Nazaki, Active Layer Formation by Ion Implantation H. Hasimoto, Focused Ion Beam Implantation Technology T. Nozaki and A. Higashisaka, Device Fabrication Process Technology
294
Contents o f Volumes in This Series
M. Ino and T. Takada, GaAs LSI Circuit Design M. Hirayama, M. Ohmori, and K. Yamasaki, GaAs LSI Fabrication and Performance
Volume 30
Very High Speed Integrated Circuits: Heterostructure
H. Watanabe, T. Mizutani, and A. Usui, Fundamentals of Epitaxial Growth and Atomic Layer Epitaxy S. Hiyamizu, Characteristics of Two-Dimensional Electron Gas in III-V Compound Heterostructures Grown by
MBE T. Nakanisi, Metalorganic Vapor Phase Epitaxy for High-Quality Active Layers T. Nimura, High Electron Mobility Transistor and LSI Applications T. Sugeta and T. Ishibashi, Hetero-Bipolar Transistor and LSI Application H. Matsuedo, T. Tanaka, and M. Nakamura, Optoelectronic Integrated Circuits
Volume 31
Indium Phosphide: Crystal Growth and Characterization
J. P. Farges, Growth of Discoloration-Free InP M. J. McCollum and G. E. Stillman, High Purity InP Grown by Hydride Vapor Phase Epitaxy I. Inada and T. Fukuda, Direct Synthesis and Growth of Indium Phosphide by the Liquid Phosphorous
Encapsulated Czochralski Method O. Oda, K. Katagiri, K. Shinohara, S. Katsura, Y. Takahashi, K. Kainosho, K. Kohiro, and R. Hirano, InP
Crystal Growth, Substrate Preparation and Evaluation K. Tada, M. Tatsumi, M. Morioka, T. Araki, and T. Kawase, InP Substrates: Production and Quality Control M. Razeghi, LP-MOCVD Growth, Characterization, and Application of InP Material T. A. Kennedy and P. J. Lin-Chung, Stoichiometric Defects in InP
Volume 32
Strained-Layer Superlattices: Physics
T. P. Pearsall, Strained-Layer Superlattices F. H. Pollack, Effects of Homogeneous Strain on the Electronic and Vibrational Levels in Semiconductors J. Y. Marzin, J. M. Ger~rd, P. Voisin, and J. A. Bruin, Optical Studies of Strained III-V Heterolayers R. People and S. A. Jackson, Structurally Induced States from Strain and Confinement M. Jaros, Microscopic Phenomena in Ordered Superlattices
Volume 33
Strained-Layer Superlattices: Material Science and Technology
R. Hull and J. C. Bean, Principles and Concepts of Strained-Layer Epitaxy W. J. Shaft, P. J. Tasker, M. C. Foisy, and L. F. Eastman, Device Applications of Strained-Layer Epitaxy S. T. Picraux, B. L. Doyle, and J. Y. Tsao, Structure and Characterization of Strained-Layer Superlattices E. Kasper and F. Schaffer, Group IV Compounds D. L. Martin, Molecular Beam Epitaxy of IV-VI Compounds Heterojunction R. L. Gunshot, L. A. Kolodziejski, A. V. Nurmikko, and N. Otsuka, Molecular Beam Epitaxy of I-VI
Semiconductor Microstructures
Contents o f Volumes in This Series
Volume 34
295
Hydrogen in Semiconductors
J. I. Pankove and N. M. Johnson, Introduction to Hydrogen in Semiconductors C. H. Seager, Hydrogenation Methods J. I. Pankove, Hydrogenation of Defects in Crystalline Silicon J. W. Corbett, P. Deilk, U. V. Desnica, and S. J. Pearton, Hydrogen Passivation of Damage Centers in
Semiconductors S. J. Pearton, Neutralization of Deep Levels in Silicon J. I. Pankove, Neutralization of Shallow Acceptors in Silicon N. M. Johnson, Neutralization of Donor Dopants and Formation of Hydrogen-Induced Defects in n-Type Silicon M. Stavola and S. J. Pearton, Vibrational Spectroscopy of Hydrogen-Related Defects in Silicon A. D. Marwick, Hydrogen in Semiconductors: Ion Beam Techniques C. Herring and N. M. Johnson, Hydrogen Migration and Solubility in Silicon E. E. Haller, Hydrogen-Related Phenomena in Crystalline Germanium J. Kakalios, Hydrogen Diffusion in Amorphous Silicon J. Chevalier, B. Clerjaud, and B. Pajot, Neutralization of Defects and Dopants in III-V Semiconductors G. G. DeLeo and W. B. Fowler, Computational Studies of Hydrogen-Containing Complexes in Semiconductors R. F. Kiefl and T. L. Estle, Muonium in Semiconductors C. G. Van de Walle, Theory of Isolated Interstitial Hydrogen and Muonium in Crystalline Semiconductors
V o l u m e 35
Nanostructured Systems
M. Reed, Introduction H. van Houten, C. W. J. Beenakker, and B. J. Wees, Quantum Point Contacts G. Timp, When Does a Wire Become an Electron Waveguide? M. Bitttiker, The Quantum Hall Effects in Open Conductors W. Hansen, J. P. Kotthaus, and U. Merkt, Electrons in Laterally Periodic Nanostructures
V o l u m e 36
The Spectroscopy of Semiconductors
D. Heiman, Spectroscopy of Semiconductors at Low Temperatures and High Magnetic Fields A. V. Nurmikko, Transient Spectroscopy by Ultrashort Laser Pulse Techniques A. K. Ramdas and S. Rodriguez, Piezospectroscopy of Semiconductors 0. J. Glembocki and B. V. Shanabrook, Photorefiectance Spectroscopy of Microstructures D. G. Seiler, C. L. Littler, and M. H. Wiler, One- and Two-Photon Magneto-Optical Spectroscopy of InSb and
Hgl-xCdxTe
V o l u m e 37
The Mechanical Properties of Semiconductors
A.-B. Chen, A. Sher, and W. T. Yost, Elastic Constants and Related Properties of Semiconductor Compounds and
Their Alloys D. R. Clarke, Fracture of Silicon and Other Semiconductors H. Siethoff, The Plasticity of Elemental and Compound Semiconductors S. Guruswamy, K. T. Faber, and J. P. Hirth, Mechanical Behavior of Compound Semiconductors S. Mahajan, Deformation Behavior of Compound Semiconductors J. P. Hirth, Injection of Dislocations into Strained Multilayer Structures
296
Contents o f Volumes in This Series
D. Kendall, C. B. Fleddermann, and K. J. Malloy, Critical Technologies for the Micromatching of Silicon I. Matsuba and K. Mokuya, Processing and Semiconductor Thermoelastic Behavior
Volume 38
Imperfections in III/V Materials
U. Scherz and M. Scheffier, Density-Functional Theory of sp-Bonded Defects in III/V Semiconductors M. Kaminska and E. R. Weber, El2 Defect in GaAs D. C. Look, Defects Relevant for Compensation in Semi-Insulating GaAs R. C. Newman, Local Vibrational Mode Spectroscopy of Defects in III/V Compounds A. M. Hennel, Transition Metals in III/V Compounds K. J. Malloy and K. Khachaturyan, DX and Related Defects in Semiconductors V. Swaminathan and A. S. Jordan, Dislocations in III/V Compounds K. W. Nauka, Deep Level Defects in the Epitaxial III/V Materials
Volume 39
Minority Carriers in III-V Semiconductors: Physics and Applications
N. K. Dutta, Radiative Transition in GaAs and Other III-V Compounds R. K. Ahrenkiel, Minority-Carrier Lifetime in III-V Semiconductors T. Furuta, High Field Minority Electron Transport in p-GaAs M. S. Lundstrom, Minority-Carrier Transport in III-V Semiconductors R. A. Abram, Effects of Heavy Doping and High Excitation on the Band Structure of GaAs D. Yevick and W. Bardyszewski, An Introduction to Non-Equilibrium Many-Body Analyses of Optical Processes
in III-V Semiconductors
Volume 40
Epitaxial Microstructures
E. F. Schubert, Delta-Doping of Semiconductors: Electronic, Optical and Structural Properties of Materials and
Devices A. Gossard, M. Sundaram, and P. Hopkins, Wide Graded Potential Wells P. Petroff, Direct Growth of Nanometer-Size Quantum Wire Superlattices E. Kapon, Lateral Patterning of Quantum Well Heterostructures by Growth of Nonplanar Substrates H. Temkin, D. Gershoni, and M. Panish, Optical Properties of Gal-x InxAs/InP Quantum Wells
Volume
41
High Speed Heterostructure Devices
F. Capasso, F. Beltram, S. Sen, A. Pahlevi, and A. Y. Cho, Quantum Electron Devices: Physics
and Applications P. Solomon, D. J. Frank, S. L. Wright and F. Canora, GaAs-Gate Semiconductor-Insulator- Semiconductor FET M. H. Hashemi and U. K. Mishra, Unipolar InP-Based Transistors R. Kiehl, Complementary Heterostructure FET Integrated Circuits T. lshibashi, GaAs-Based and InP-Based Heterostructure Bipolar-Transistors H. C. Liu and T. C. L. G. Sollner, High-Frequency-Tunneling Devices H. Ohnishi, T. More, M. Takatsu, K. Imamura, and N. Yokoyama, Resonant-Tunneling Hot-Electron Transistors
and Circuits
Contents o f Volumes in This Series
V o l u m e 42
Oxygen in Silicon
F. Shimura, Introduction to Oxygen in Silicon W. Lin, The Incorporation of Oxygen into Silicon Crystals T. J. Schaffner and D. K. Schroder, Characterization Techniques for Oxygen in Silicon W. M. Bullis, Oxygen Concentration Measurement S. M. Hu, Intrinsic Point Defects in Silicon B. Pajot, Some Atomic Configuration of Oxygen J. Michel and L. C. Kimerling, Electrical Properties of Oxygen in Silicon R. C. Newman and R. Jones, Diffusion of Oxygen in Silicon T. Y. Tan and W. J. Taylor, Mechanisms of Oxygen Precipitation: Some Quantitative Aspects M. Schrems, Simulation of Oxygen Precipitation K. Simino and L Yonenaga, Oxygen Effect on Mechanical Properties W. Bergholz, Grown-in and Process-Induced Effects F. Shimura, Intrinsic/Internal Gettering H. Tsuya, Oxygen Effect on Electronic Device Performance
Volume 43
Semiconductors for Room Temperature Nuclear Detector Applications
R. B. James and T. E. Schlesinger, Introduction and Overview L. S. Darken and C E. Cox, High-Purity Germanium Detectors A. Burger, D. Nason, L. Van den Berg, and M. Schieber, Growth of Mercuric Iodide X. J. Bao, T. E. Schlesinger, and R. B. James, Electrical Properties of Mercuric Iodide X. J. Bao, R. B. James, and T. E. Schlesinger, Optical Properties of Red Mercuric Iodide M. Hage-Ali and P. Siffert, Growth Methods of CdTe Nuclear Detector Materials M. Hage-Ali and P. Siffert, Characterization of CdTe Nuclear Detector Materials M. Hage-Ali and P. Siffert, CdTe Nuclear Detectors and Applications R. B. James, T. E. Schlesinger, J. Lund, and M. Schieber, Cdl-x Znx Te Spectrometers for Gamma
and X-Ray Applications D. S. McGregor, J. E. Kammeraad, Gallium Arsenide Radiation Detectors and Spectrometers J. C. Lund, F. Olschner, and A. Burger, Lead Iodide M. R. Squillante and K. S. Shah, Other Materials: Status and Prospects V. M. Gerrish, Characterization and Quantification of Detector Performance J. S. Iwanczyk and B. E. Patt, Electronics for X-ray and Gamma Ray Spectrometers M. Schieber, R. B. James and T. E. Schlesinger, Summary and Remaining Issues for Room Temperature
Radiation Spectrometers
Volume 44
II-IV Blue/Green Light Emitters: Device Physics and Epitaxial Growth
J. Han and R. L. Gunshor, MBE Growth and Electrical Properties of Wide Bandgap ZnSe-based II-VI
Semiconductors S. Fujita and S. Fujita, Growth and Characterization of ZnSe-based II-VI Semiconductors by MOVPE E. Ho and L. A. Kolodziejski, Gaseous Source UHV Epitaxy Technologies for Wide Bandgap II-VI
Semiconductors
297
298
Contents o f Volumes in This Series
C. G. Van de Walle, Doping of Wide-Band-Gap II-VI Compounds - Theory R. Cingolani, Optical Properties of Excitons in ZnSe-Based Quantum Well Heterostructures A. Ishibashi and A. V. Nurmikko, II-VI Diode Lasers: A Current View of Device Performance and Issues S. Guha and J. Petruzello, Defects and Degradation in Wide-Gap II-VI-based Structure and Light Emitting
Devices
V o l u m e 45
Effect of Disorder and Defects in Ion-Implanted Semiconductors: Electrical and Physiochemical Characterization
H. Ryssel, Ion Implantation into Semiconductors: Historical Perspectives You-Nian Wang and Teng-Cai Ma, Electronic Stopping Power for Energetic Ions in Solids S. T. Nakagawa, Solid Effect on the Electronic Stopping of Crystalline Target and Application to Range
Estimation G. Miller, S. Kalbitzer, and G. N. Greaves, Ion Beams in Amorphous Semiconductor Research J. Boussey-Said, Sheet and Spreading Resistance Analysis of Ion Implanted and Annealed Semiconductors M. L. Polignano and G. Queirolo, Studies of the Stripping Hall Effect in Ion-Implanted Silicon J. Stoemenos, Transmission Electron Microscopy Analyses R. Nipoti and M. Servidori, Rutherford Backscattering Studies of Ion Implanted Semiconductors P. Zaumseil, X-ray Diffraction Techniques
V o l u m e 46
Effect of Disorder and Defects in Ion-Implanted Semiconductors: Optical and Photothermal Characterization
M. Fried, T. Lohner, and J. Gyulai, Ellipsometric Analysis A. Seas and C. Christofides, Transmission and Reflection Spectroscopy on Ion Implanted Semiconductors A. Othonos and C. Christofides, Photoluminescence and Raman Scattering of Ion Implanted Semiconductors.
Influence of Annealing C. Christofides, Photomodulated Thermoreflectance Investigation of Implanted Wafers. Annealing Kinetics
of Defects U. Zammit, Photothermal Deflection Spectroscopy Characterization of Ion-Implanted and Annealed Silicon
Films A. Mandelis, A. Budiman, and M. Vargas, Photothermal Deep-Level Transient Spectroscopy of Impurities
and Defects in Semiconductors R. Kalish and S. Charbonneau, Ion Implantation into Quantum-Well Structures A. M. Myasnikov and N. N. Gerasimenko, Ion Implantation and Thermal Annealing of III-V Compound
Semiconducting Systems: Some Problems of III-V Narrow Gap Semiconductors
Volume 47
Uncooled Infrared Imaging Arrays and Systems
R. G. Buser and M. P. Tompsett, Historical Overview P. W. Kruse, Principles of Uncooled Infrared Focal Plane Arrays R. A. Wood, Monolithic Silicon Microbolometer Arrays C. M. Hanson, Hybrid Pyroelectric-Ferroelectric Bolometer Arrays D. L. Polla and J. R. Choi, Monolithic Pyroelectric Bolometer Arrays
Contents o f Volumes in This Series
299
N. Teranishi, Thermoelectric Uncooled Infrared Focal Plane Arrays M. F. Tompsett, Pyroelectric Vidicon T. W. Kenny, Tunneling Infrared Sensors J. R. Vig, R. L. Filler, and Y. Kim, Application of Quartz Microresonators to Uncooled Infrared Imaging Arrays P. W. Kruse, Application of Uncooled Monolithic Thermoelectric Linear Arrays to Imaging Radiometers
Volume 48
High Brightness Light Emitting Diodes
G. B. Stringfellow, Materials Issues in High-Brightness Light-Emitting Diodes M.G. Craford, Overview of Device Issues in High-Brightness Light-Emitting Diodes F. M. Steranka, A1GaAs Red Light Emitting Diodes C. H. Chert, S. A. Stockman, M. J. Peanasky, and C. P. Kuo, OMVPE Growth of A1GaInP for High Efficiency
Visible Light-Emitting Diodes F. A. Kish and R. M. Fletcher, A1GaInP Light-Emitting Diodes M. W. Hodapp, Applications for High Brightness Light-Emitting Diodes I. Akasaki and H. Amano, Organometallic Vapor Epitaxy of GaN for High Brightness Blue Light Emitting
Diodes S. Nakamura, Group III-V Nitride Based Ultraviolet-Blue-Green-Yellow Light-Emitting Diodes and Laser
Diodes
V o l u m e 49
Light Emission in Silicon: from Physics to Devices
D. J. Lockwood, Light Emission in Silicon G. Abstreiter, Band Gaps and Light Emission in Si/SiGe Atomic Layer Structures T. G. Brown and D. G. Hall, Radiative Isoelectronic Impurities in Silicon and Silicon-Germanium Alloys
and Superlattices J. Michel, L. V. C. Assali, M. T. Morse, and L. C. Kimerling, Erbium in Silicon Y. Kanemitsu, Silicon and Germanium Nanoparticles P. M. Fauchet, Porous Silicon: Photoluminescence and Electroluminescent Devices C. Delerue, G. Allan, and M. Lannoo, Theory of Radiative and Nonradiative Processes in Silicon
Nanocrystallites L. Brus, Silicon Polymers and Nanocrystals
V o l u m e 50
Gallium Nitride (GaN)
J. I. Pankove and T. D. Moustakas, Introduction S. P. DenBaars and S. Keller, Metalorganic Chemical Vapor Deposition (MOCVD) of Group III Nitrides W. A. Bryden and T. J. Kistenmacher, Growth of Group III-A Nitrides by Reactive Sputtering N. Newman, Thermochemistry of III-N Semiconductors S. J. Pearton and R. J. Shul, Etching of III Nitrides S. M. Bedair, Indium-based Nitride Compounds A. Trampert, O. Brandt, and K. H. Ploog, Crystal Structure of Group III Nitrides H. Morkog, F. Hamdani, and A. Salvador, Electronic and Optical Properties of III-V Nitride based Quantum
Wells and Superlattices K. Doverspike and J. I. Pankove, Doping in the III-Nitrides T. Suski and P. Perlin, High Pressure Studies of Defects and Impurities in Gallium Nitride
300
Contents o f Volumes in This Series
B. Monemar, Optical Properties of GaN W. R. L. Lambrecht, Band Structure of the Group III Nitrides N. E. Christensen and P. Perlin, Phonons and Phase Transitions in GaN S. Nakamura, Applications of LEDs and LDs L Akasaki and H. Amano, Lasers J. A. Cooper, Jr., Nonvolatile Random Access Memories in Wide Bandgap Semiconductors
Identification of Defects in Semiconductors
Volume 51A
G. D. Watkins, EPR and ENDOR Studies of Defects in Semiconductors J.-M. Spaeth, Magneto-Optical and Electrical Detection of Paramagnetic Resonance in Semiconductors T. A. Kennedy and E. R. Glaser, Magnetic Resonance of Epitaxial Layers Detected by Photoluminescence K. H. Chow, B. Hitti, and R. F. Kiefl, IxSR on Muonium in Semiconductors and Its Relation to Hydrogen K. Saarinen, P. Hautojiirvi, and C. Corbel, Positron Annihilation Spectroscopy of Defects in Semiconductors R. Jones and P. R. Briddon, The Ab Initio Cluster Method and the Dynamics of Defects in Semiconductors
Identification Defects in Semiconductors
Volume 51B
G. Davies, Optical Measurements of Point Defects P. M. Mooney, Defect Identification Using Capacitance Spectroscopy M. Stavola, Vibrational Spectroscopy of Light Element Impurities in Semiconductors P. Schwander, W. D. Rau, C. Kisielowski, M. Gribelyuk, and A. Ourmazd, Defect Processes in Semiconductors
Studied at the Atomic Level by Transmission Electron Microscopy N. D. Jager and E. R. Weber, Scanning Tunneling Microscopy of Defects in Semiconductors
Volume 52
SiC Materials and Devices
K. Jiirrendahl and R. F. Davis, Materials Properties and Characterization of SiC V. A. Dmitiriev and M. G. Spencer, SiC Fabrication Technology: Growth and Doping V. Saxena and A. J. Steckl, Building Blocks for SiC Devices: Ohmic Contacts, Schottky Contacts, and p-n Junctions M. S. Shur, SiC Transistors C. D. Brandt, R. C. Clarke, R. R. Siergiej, J. B. Casady, A. W. Morse, S. Sriram, and A. K. Agarwal, SiC for
Applications in High-Power Electronics R. J. Trew, SiC Microwave Devices J. Edmond, H. Kong, G. Negley, M. Leonard, K. Doverspike, W. Weeks, A. Suvorov, D. Waltz, and C. Carter, Jr.,
SiC-Based UV Photodiodes and Light-Emitting Diodes H. Morko9, Beyond Silicon Carbide! III-V Nitride-Based Heterostructures and Devices
V o l u m e 53 Cumulative Subjects and Author Index Including T a b l e s of Contents for Volumes 1 - 5 0
V o l u m e 54
High Pressure in Semiconductor Physics I
w. Paul, High Pressure in Semiconductor Physics: A Historical Overview N. E. Christensen, Electronic Structure Calculations for Semiconductors Under Pressure
Contents o f Volumes in This Series
301
R. J. Neimes and M. L McMahon, Structural Transitions in the Group IV, III-V and II-VI Semiconductors
Under Pressure A. R. Goni and K. Syassen, Optical Properties of Semiconductors Under Pressure P. Trautman, M. Baj, and J. M. Baranowski, Hydrostatic Pressure and Uniaxial Stress in Investigations of the
EL2 Defect in GaAs M. Li and P. Y. Yu, High-Pressure Study of DX Centers Using Capacitance Techniques T. Suski, Spatial Correlations of Impurity Charges in Doped Semiconductors N. Kuroda, Pressure Effects on the Electronic Properties of Diluted Magnetic Semiconductors
V o l u m e 55
High Pressure in Semiconductor Physics I I
D. K. Maude and J. C. Portal, Parallel Transport in Low-Dimensional Semiconductor Structures P. C. Klipstein, Tunneling Under Pressure: High-Pressure Studies of Vertical Transport in Semiconductor
Heterostructures E. Anastassakis and M. Cardona, Phonons, Strains, and Pressure in Semiconductors F. H. Pollak, Effects of External Uniaxial Stress on the Optical Properties of Semiconductors and
Semiconductor Microstructures A. R. Adams, M. Silver, and J. Allam, Semiconductor Optoelectronic Devices S. Porowski and L Grzegory, The Application of High Nitrogen Pressure in the Physics and Technology of
III-N Compounds M. Yousuf, Diamond Anvil Cells in High Pressure Studies of Semiconductors
Volume 56
Germanium Silicon: Physics and Materials
J. c. Bean, Growth Techniques and Procedures D. E. Savage, F. Liu, V. Zielasek, and M. G. Lagally, Fundamental Crystal Growth Mechanisms R. Hull, Misfit Strain Accommodation in SiGe Heterostructures M. J. Shaw and M. Jaros, Fundamental Physics of Strained Layer GeSi: Quo Vadis? F. Cerdeira, Optical Properties S. A. Ringel and P. N. Grillot, Electronic Properties and Deep Levels in Germanium-Silicon J. C. Campbell, Optoelectronics in Silicon and Germanium Silicon K. Eberl, K. Brunner, and O. G. Schmidt, Sil-yCy and Sil-x-yGe2Cy Alloy Layers
Volume
57
Gallium Nitride (GaN) I I
R. J. Molnar, Hydride Vapor Phase Epitaxial Growth of III-V Nitrides T. D. Moustakas, Growth of III-V Nitrides by Molecular Beam Epitaxy Z. Liliental-Weber, Defects in Bulk GaN and Homoepitaxial Layers C. G. Van de Walle and N. M. Johnson, Hydrogen in III-V Nitrides W. G6tz and N. M. Johnson, Characterization of Dopants and Deep Level Defects in Gallium Nitride B. Gil, Stress Effects on Optical Properties C. Kisielowski, Strain in GaN Thin Films and Heterostructures J. A. Miragliotta and D. K. Wickenden, Nonlinear Optical Properties of Gallium Nitride B. K. Meyer, Magnetic Resonance Investigations on Group III-Nitrides M. S. Shur and M. Asif Khan, GaN and AIGaN Ultraviolet Detectors C. H. Qiu, J. I. Pankove and C. Rossington, I I - V Nitride-Based X-ray Detectors
302
Contents o f Volumes in This Series
V o l u m e 58
Nonlinear Optics in Semiconductors I
A. Kost, Resonant Optical Nonlinearities in Semiconductors E. Garmire, Optical Nonlinearities in Semiconductors Enhanced by Carrier Transport D. S. Chemla, Ultrafast Transient Nonlinear Optical Processes in Semiconductors M. Sheik-Bahae and E. W. Van Stryland, Optical Nonlinearities in the Transparency Region of Bulk
Semiconductors J. E. Millerd, M. Ziari, and A. Partovi, Photorefractivity in Semiconductors
V o l u m e 59
Nonlinear Optics in Semiconductors II
J. B. Khurgin, Second Order Nonlinearities and Optical Rectification K. L. Hall, E. R. Thoen, and E. P. Ippen, Nonlinearities in Active Media E. Hanamura, Optical Responses of Quantum Wires/Dots and Microcavities U. Keller, Semiconductor Nonlinearities for Solid-State Laser Modelocking and Q-Switching A. Miller, Transient Grating Studies of Carrier Diffusion and Mobility in Semiconductors
Volume 60
Self-Assembled InGaAs/GaAs Quantum Dots
Mitsuru Sugawara, Theoretical Bases of the Optical Properties of Semiconductor Quantum Nano-Structures Yoshiaki Nakata, Yoshihiro Sugiyama, and Mitsuru Sugawara, Molecular Beam Epitaxial Growth of
Self-Assembled InAs/GaAs Quantum Dots Kohki Mukai, Mitsuru Sugawara, Mitsuru Egawa, and Nobuyuki Ohtsuka, Metalorganic Vapor Phase Epitaxial
Growth of Self-Assembled InGaAs/GaAs Quantum Dots Emitting at 1.3 ~m Kohki Mukai and Mitsuru Sugawara, Optical Characterization of Quantum Dots Kohki Mukai and Mitsuru Sugawara, The Photon Bottleneck Effect in Quantum Dots Hajime Shoji, Self-Assembled Quantum Dot Lasers Hiroshi Ishikawa, Applications of Quantum Dot to Optical Devices Mitsuru Sugawara, Kohki Mukai, Hiroshi Ishikawa, Koji Otsubo, and Yoshiaki Nakata, The Latest News
V o l u m e 61
Hydrogen in Semiconductors II
Norbert H. Nickel, Introduction to Hydrogen in Semiconductors II Noble M. Johnson and Chris G. Van de Walle, Isolated Monatomic Hydrogen in Silicon Yurij V. Gorelkinskii, Electron Paramagnetic Resonance Studies of Hydrogen and Hydrogen-Related Defects in
Crystalline Silicon Norbert 14. Nickel, Hydrogen in Polycrystalline Silicon Wolfhard Beyer, Hydrogen Phenomena in Hydrogenated Amorphous Silicon Chris G. Van de Walle, Hydrogen Interactions with Polycrystalline and Amorphous Silicon-Theory Karen M. McManus Rutledge, Hydrogen in Polycrystalline CVD Diamond Roger L. Lichti, Dynamics of Muonium Diffusion, Site Changes and Charge-State Transitions Matthew D. McCluskey and Eugene E. Haller, Hydrogen in III-V and II-VI Semiconductors S. J. Pearton and J. W. Lee, The Properties of Hydrogen in GaN and Related Alloys J6rg Neugebauer and Chris G. Van de Walle, Theory of Hydrogen in GaN
Contents o f Volumes in This Series
Volume 62
303
Intersubband Transitions in Quantum Wells: Physics and Device Applications I
Manfred Helm, The Basic Physics of Intersubband Transitions Jerome Faist, Carlo Sirtori, Federico Capasso, Loren N. Pfeiffer, Ken W. West, Deborah L. Sivco, and Alfred Y. Cho, Quantum Interference Effects in Intersubband Transitions H. C. Liu, Quantum Well Infrared Photodetector Physics and Novel Devices S. D. Gunapala and S. V. Bandara, Quantum Well Infrared Photodetector (QWIP) Focal Plane Arrays
Volume 63
Chemical Mechanical Polishing in Si Processing
Frank B. Kaufman, Introduction Thomas Bibby and Karey Holland, Equipment John P. Bare, Facilitization Duane S. Boning and Okumu Ouma, Modeling and Simulation Shin Hwa Li, Bruce Tredinnick, and Mel Hoffman, Consumables I: Slurry Lee M. Cook, CMP Consumables II: Pad Franfois Tardif Post-CMP Clean Shin Hwa Li, Tara Chhatpar, and Frederic Robert, CMP Metrology Shin Hwa Li, Visun Bucha, and Kyle Wooldridge, Applications and CMP-Related Process Problems
Volume 64
Electroluminescence I
M. G. Craford, S. A. Stockman, M. J. Peansky, and F. A. Kish, Visible Light-Emitting Diodes H. Chui, N. F. Gardner, P. N. Grillot, J. W. Huang, M. R. Krames, and S. A. Maranowski, High-Efficiency
AIGaInP Light-Emitting Diodes R. S. Kern, W. Gbtz, C. H. Chen, H. Liu, R. M. Fletcher, and C. P. Kuo, High-Brightness Nitride-Based
Visible-Light-Emitting Diodes Yoshiharu Sato, Organic LED System Considerations V. Bulovi~, P. E. Burrows, and S. R. Forrest, Molecular Organic Light-Emitting Devices
Volume 65
Electroluminescence II
V. Bulovi~ and S. R. Forrest, Polymeric and Molecular Organic Light Emitting Devices: A Comparison Regina Mueller-Mach and Gerd O. Mueller, Thin Film Electroluminescence Markku Leskel~, Wei-Min Li, and Mikko Ritala, Materials in Thin Film Electroluminescent Devices Kristiaan Neyts, Microcavities for Electroluminescent Devices
Volume 66
Intersubband Transitions in Quantum Wells: Physics and Device Applications II
Jerome Faist, Federico Capasso, Carlo Sirtori, Deborah L. Sivco, and Alfred Y. Cho, Quantum Cascade Lasers Federico Capasso, Carlo Sirtori, D. L. Sivco, and A. Y. Cho, Nonlinear Optics in Coupled-Quantum- Well
Quasi-Molecules Karl Unterrainer, Photon-Assisted Tunneling in Semiconductor Quantum Structures P. Haring Bolivar, T. Dekorsy, and H. Kurz, Optically Excited Bloch Oscillations-Fundamentals and
Application Perspectives
304
Contents o f Volumes in This Series
Volume 67
Ultrafast Physical Processes in Semiconductors
Alfred Leitenstorfer and Alfred Laubereau, Ultrafast Electron-Phonon Interactions in Semiconductors:
Quantum Kinetic Memory Effects Christoph Lienau and Thomas Elsaesser, Spatially and Temporally Resolved Near-Field Scanning Optical
Microscopy Studies of Semiconductor Quantum Wires K. T. Tsen, Ultrafast Dynamics in Wide Bandgap Wurtzite GaN J. Paul Callan, Albert M.-T. Kim, Christopher A. D. Roeser, and Eriz Mazur, Ultrafast Dynamics and Phase
Changes in Highly Excited GaAs Hartmut Haug, Quantum Kinetics for Femtosecond Spectroscopy in Semiconductors T. Meier and S. W. Koch, Coulomb Correlation Signatures in the Excitonic Optical Nonlinearities of
Semiconductors Roland E. Allen, Traian Dumitricd, and Ben Torralva, Electronic and Structural Response of Materials to Fast,
Intense Laser Pulses E. Gornik and R. Kersting, Coherent THz Emission in Semiconductors
Volume 68
Isotope Effects in Solid State Physics
Vladimir G. Plekhanov, Elastic Properties; Thermal Properties; Vibrational Properties; Raman Spectra of
Isotopically Mixed Crystals; Excitons in LiH Crystals; Exciton-Phonon Interaction; Isotopic Effect in the Emission Spectrum of Polaritons; Isotopic Disordering of Crystal Lattices; Future Developments and Applications; Conclusions
V o l u m e 69
Recent Trends in Thermoelectric Materials Research I
H. Julian Goldsmid, Introduction Terry M. Tritt and Valerie M. Browning, Overview of Measurement and Characterization Techniques for
Thermoelectric Materials Mercouri G. Kanatzidis, The Role of Solid-State Chemistry in the Discovery of New Thermoelectric Materials B. Lenoir, H. Scherrer, and T. Caillat, An Overview of Recent Developments for BiSb Alloys Citrad Uher, Skutterudities: Prospective Novel Thermoelectrics George S. Nolas, Glen A. Slack, and Sandra B. Schujman, Semiconductor Clathrates: A Phonon Glass Electron
Crystal Material with Potential for Thermoelectric Applications
Volume 70
Recent Trends in Thermoelectric Materials Research II
Brian C. Sales, David G. Mandrus, and Bryan C. Chakoumakos, Use of Atomic Displacement Parameters in
Thermoelectric Materials Research S. Joseph Pooh, Electronic and Thermoelectric Properties of Half-Heusler Alloys Terry M. Tritt, A. L. Pope, and J. W. Kolis, Overview of the Thermoelectric Properties of Quasicrystalline
Materials and Their Potential for Thermoelectric Applications Alexander C. Ehrlich and Stuart A. Wolf, Military Applications of Enhanced Thermoelectrics David J. Singh, Theoretical and Computational Approaches for Identifying and Optimizing Novel
Thermoelectric Materials Terry M. Tritt and R. T. Littleton, IV, Thermoelectric Properties of the Transition Metal Pentatellurides:
Potential Low-Temperature Thermoelectric Materials
Contents o f Volumes in This Series
305
Franz Freibert, Timothy W. Darling, Albert Miglori, and Stuart A. Trugman, Thermomagnetic Effects and
Measurements M. Bartkowiak and G. D. Mahan, Heat and Electricity Transport Through Interfaces
V o l u m e 71
Recent Trends in Thermoelectric Materials Research I I I
M. S. Dresselhaus, Y.-M. Lin, T. Koga, S. B. Cronin, O. Rabin, M. R. Black, and G. Dresselhaus, Quantum Wells
and Quantum Wires for Potential Thermoelectric Applications D. A. Broido and T. L. Reinecke, Thermoelectric Transport in Quantum Well and Quantum
Wire Superlattices G. D. Mahan, Thermionic Refrigeration Rama Venkatasubramanian, Phonon Blocking Electron Transmitting Superlattice Structures as Advanced Thin
Film Thermoelectric Materials G. Chen, Phonon Transport in Low-Dimensional Structures
V o l u m e 72
Silicon Epitaxy
s. Acerboni, ST Microelectronics, CFM-AGI Department, Agrate Brianza, Italy V.-M. Airaksinen, Okmetic Oyj R&D Department, Vantaa, Finland G. Beretta, ST Microelectronics, DSG Epitaxy Catania Department, Catania, Italy C. Cavallotti, Dipartimento di Chimica Fisica Applicata, Politecnico di Milano, Milano, Italy D. Crippa, MEMC Electronic Materials, Epitaxial and CVD Department, Operations Technology Division,
Novara, Italy D. Dutartre, ST Microelectronics, Central R&D, Crolles, France Srikanth Kommu, MEMC Electronic Materials inc., EPI Technology Group, St. Peters, Missouri M. Masi, Dipartimento di Chimica Fisica Applicata, Politecnico di Milano, Milano, Italy D. J. Meyer, ASM Epitaxy, Phoenix, Arizona J. Murota, Research Institute of Electrical Communication, Laboratory for Electronic Intelligent Systems,
Tohoku University, Sendai, Japan V. Pozzetti, LPE Epitaxial Technologies, Bollate, Italy A. M. Rinaldi, MEMC Electronic Materials, Epitaxial and CVD Department, Operations Technology Division,
Novara, Italy Y. Shiraki, Research Center for Advanced Science and Technology (RCAST), University of Tokyo, Tokyo,
Japan
V o l u m e 73
Processing and Properties of Compound Semiconductors
s. J. Pearton, Introduction Eric Donkor, Gallium Arsenide Heterostructures Annamraju Kasi Viswanath, Growth and Optical Properties of GaN D. Y. C. Lie and K. L. Wang, SiGe/Si Processing S. Kim and M. Razeghi, Advances in Quantum Dot Structures Walter P. Gomes, Wet Etching of III-V Semiconductors
306
Contents o f Volumes in This Series
Volume 74
Silicon-Germanium Strained Layers and Heterostructures
s. c. Jain and M. Willander, Introduction; Strain, Stability, Reliability and Growth; Mechanism of Strain Relaxation; Strain, Growth, and TED in SiGeC Layers; Bandstructure and Related Properties; Heterostructure Bipolar Transistors; FETs and Other Devices
Volume 75
Laser Crystallization of Silicon
Norbert H. Nickel, Introduction to Laser Crystallization of Silicon Costas P. Grigoropoulos, Seung-Jae Moon and Ming-Hong Lee, Heat Transfer and Phase Transformations in Laser Melting and Recrystallization of Amorphous Thin Si Films Robert Cer@ and Petr P?ikryl, Modeling Laser-Induced Phase-Change Processes: Theory and Computation Paulo V. Santos, Laser Interference Crystallization of Amorphous Films Philipp Lengsfeld and Norbert H. Nickel, Structural and Electronic Properties of Laser-Crystallized Poly-Si
Thin-Film Diamond I
V o l u m e 76
x. Jiang, Textured and Heteroepitaxial CVD Diamond Films Eberhard Blank, Structural Imperfections in CVD Diamond Films R. Kalish, Doping Diamond by Ion-Implantation A. Deneuville, Boron Doping of Diamond Films from the Gas Phase S. Koizumi, n-Type Diamond Growth C. E. Nebel, Transport and Defect Properties of Intrinsic and Boron-Doped Diamond Milo~ Neslddek, Ken Haenen and Milan Van~ek, Optical Properties of CVD Diamond RolfSauer, Luminescence from Optical Defects and Impurities in CVD Diamond
V o l u m e 77
Thin-Film Diamond I I
Jacques Chevallier, Hydrogen Diffusion and Acceptor Passivation in Diamond Ji~rgen Ristein, Structural and Electronic Properties of Diamond Surfaces John C. Angus, Yuri II. Pleskov and Sally C. Eaton, Electrochemistry of Diamond Greg M. Swain, Electroanalytical Applications of Diamond Electrodes Werner Haenni, Philippe Rychen, Matthyas Fryda and Christos Comninellis, Industrial Applications of Diamond Electrodes Philippe Bergonzo and Richard B Jaclonan, Diamond-Based Radiation and Photon Detectors Hiroshi Kawarada, Diamond Field Effect Transistors Using H-Terminated Surfaces Shinichi Shikata and Hideaki Nakahata, Diamond Surface Acoustic Wave Device
V o l u m e 78
Semiconducting Chalcogenide Glass I
K S. Minaev and S. P. Timoshenkov, Glass-Formation in Chalcogenide Systems and Periodic System A. Popov, Atomic Structure and Structural Modification of Glass V. A. Funtikov, Eutectoidal Concept of Glass Structure and Its Application in Chalcogenide Semiconductor Glasses V. S. Minaev, Concept of Polymeric Polymorphous-Crystalloid Structure of Glass and Chalcogenide Systems: Structure and Relaxation of Liquid and Glass
307
Contents o f Volumes in This Series Mihai Popescu, Photo-Induced Transformations in Glass Oleg I. Shpotyuk, Radiation-Induced Effects in Chalcogenide Vitreous Semiconductors
Volume
79
Semiconducting Chalcogenide Glass
II
M. D. Bal'makov, Information Capacity of Condensed Systems A. Cesnys, G. Ju~ka and E. Montrimas, Charge Carrier Transfer at High Electric Fields in Noncrystalline
Semiconductors Andrey S. Glebov, The Nature of the Current Instability in Chalcogenide Vitreous Semiconductors A. M. Andriesh, M. S. Iovu and S. D. Shutov, Optical and Photoelectrical Properties of Chalcogenide Glasses V. Val. Sobolev and V. V. Sobolev, Optical Spectra of Arsenic Chalcogenides in a Wide Energy Range of
Fundamental Absorption Yu. S. Tver'yanovich, Magnetic Properties of Chalcogenide Glasses
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