Semiconducting Chalcogenide Glass II, Volume 79: Properties of Chalcogenide Glasses (Semiconductors and Semimetals)

Semiconducting Chalcogenide Glass II Properties of Chalcogenide Glasses SEMICONDUCTORS AND SEMIMETALS Volume 79

Semiconductors and Semimetals A Treatise

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Eicke R. Weber DEPARTMENT OF MATERIALS SCIENCE AND MINERAL ENGINEERING UNIVERSITY OF CALIFORNIA AT BERKELEY BERKELEY, CA 94720

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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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2004 0

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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 > 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 ) 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)

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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

-

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 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


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

1.0 " ~ - " - - - - - ~ . ~ b |

0

I

20 40 Concentration, at.% Ge

" 0.0

O--

t0

AszS~

~

~0

40

~ 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.

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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

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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

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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

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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

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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)

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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 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) 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


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

I

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

'

I

'

I

e.e ~ e

-3

0.0 4

o,o.O"~ 0.0"

-4

0000" o o

z

/

-5

O

~'-6 0.0 0

-7

JtYt

"

1 - AsSe 2 - A s S e + 2 . 0 at.% Sn 3 - A s S e + 3 . 0 at.% Sn

-8

-9t,

_

4 - A s S e + 5 . 0 at.% Sn

3

5 - A s S e + 7 . 5 at.% Sn 6 - A s S e + 1 0 . 0 at.% Sn I

1.2

,

I

,

1.6

I

2.0

~

_

I

2.4

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 '

I

'

I

'

I

'

I

'

I

'

I

169

'

\ \

o

10-1

~0\

,.d 10-2

O 9 \ 9 0 O O 0 0 \0

I I

I3

10-3

I

I

10 -4

,

I

,

1

10-3

,

I

~

I

10-2

,

1

0 I

0

2

10-1

Time, s 0.0

0.5

1.0

1.5

2.0

2.5

3.0

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 ,

, 1.0 "

,,,/" . . . .

,

.

.

.

.

zl

_Z_S_:

; * "

---*--- - 4

0.8 0.6 0.4 0.2 0.0

0

2

4

6

8 10 Time, s

12

14

(b10.81"0 r~.~-~-~-~-****-

16

i

1 341 3 04t 0.0 0

.,,

2

4

6

l! zzSzz ....... N2"--...,

8 l0 Time, s

12

14

16

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

..~

~0.5 do o.5

0.0

9

0

1'0

20

30

1

".

-,~

~

40

50

0

10

20

30

40

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

~ f

-IO -ii

"

.....

: ........

.....-

~

'

9 oooo,

' ~j,~,l.====

9"

4

9 9" " " " - - 3 9

9

9

9

9

9 9=.

===.-='-"

i

.

l

~ -10

.~oo

9 9

9= = =

i..---

-1.0

,

i

-0.5

,

i

,

0.0 0.5 Log (t, s)

i

1.0

-11

,

i

,

i

-1.5 -1.0 -0.5 0.0 0.5 Log (t, s)

,

i" i~

1.0

1.5

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

.

~

.

.

.

.

.

.

.

;"% " " " ' %

5

,,,. \

,z 0.1 9

i

.

i

.

.

.

'.

2~e-,,~

~4 i

1

,

,

i

,

,

,

li

i

|

,

,

10 Log (t, s)

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

\

I

1

|

|

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

104!

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 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" "

:-

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,.

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~:~"

0

\

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A s 2 S 3 0.9

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/

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10

~

.".,

k

.

,, "

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*

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j.

.

i

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, .\

--~ !

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/

20

25

E, eV

(c)

2.5

15

__ ........

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1.5

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.

-Ime-

). /

.~

rt~ 0.2

.

6

3 ~

.;~

/"

3 Z f ~ 0 -

7 +

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5

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-Im(l+e) -1 ,

,

10

15

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.

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.

0.1 ~ "7 -.

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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 - 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

]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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