Amorphous Chalcogenide Semiconductors and Related Materials

Amorphous Chalcogenide Semiconductors and Related Materials Keiji Tanaka · Koichi Shimakawa Amorphous Chalcogenide S...

Author: Keiji Tanaka | Koichi Shimakawa

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Amorphous Chalcogenide Semiconductors and Related Materials

Keiji Tanaka · Koichi Shimakawa

Amorphous Chalcogenide Semiconductors and Related Materials

123

Keiji Tanaka Graduate School of Engineering Department of Applied Physics Hokkaido University Kita-ku Sapporo 060-8628, Japan [email protected]

Koichi Shimakawa Faculty of Engineering Gifu University Yanaido Gifu 501-1193, Japan and Nagoya Industrial Science Institute Nagoya 460-0008, Japan [email protected]

ISBN 978-1-4419-9509-4 e-ISBN 978-1-4419-9510-0 DOI 10.1007/978-1-4419-9510-0 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2011926594 © Springer Science+Business Media, LLC 2011 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

Preface

Photonic, electronic, and photo-electric applications of non-crystalline1 solids are rapidly growing in recent years. Such growth seems to synchronize with the development of oxide glass1 fibers and related devices for optical communications, which started near the end of the last century. Otherwise, we can trace its growth back to the use of amorphous1 Se films at around 1950 as xerographic photoreceptors in copying machines. In addition, recent applications of thin films, including Ge–Sb–Te to digital versatile disks (DVDs) and amorphous hydrogenated Si (a-Si:H) to solar cells and thin-film transistors (TFTs), are remarkable. On the other hand, we also know that fundamental studies on amorphous chalcogenide semiconductor have yielded several universal and revolutionary concepts such as “mobility edge” and “magic coordination number,” and some of these concepts have been applied to other materials. The authors therefore believe that, to study fundamentals and applications of non-crystalline insulators and semiconductors, amorphous chalcogenides2 such as Se, As2 S3 , and Ge–Sb–Te continue to be instructive and valuable substances. The aim of this monograph is to be an introductory textbook in amorphous chalcogenide and related materials. This text will be suitable for graduate students. Actually, KT has used this text (unpublished versions) in seminars for graduate students, who start to study amorphous materials in the departments of applied physics, inorganic chemistry, and electronics. The present text will also be valuable to researchers working on related materials such as oxides, a-Si:H films, and organic semiconductors. This book also serves in comparative understandings of amorphous and crystalline semiconductors. The readers will see that, for such purposes, chalcogenide could be a good bridging material, since some simple compounds can be obtained in both crystalline and non-crystalline forms. Of course, for materials and topics dealt with in this book, several excellent books, listed at the end of the Preface, are already available. However, those are more or less difficult or detailed for students and research beginners. Zallen’s book (1983) gives a good introduction

1 These

terminologies are defined in Section 1.1. English Dictionary defines “chalco” as a stem, which is a combining form of Greek χαλκóς (copper and brass), and “gen” as an adjective suffix giving the sense “born in a certain place or condition.” We know that minerals such as Cu2 S may be an origin of “chalcogen.” 2 Oxford

v

vi

Preface

for students and researchers, while the content is focused on some fundamental subjects. The authors, therefore, have tried to write a book on glassy semiconductor on the level of the book Introduction to Solid State Physics by Kittel. The present book treats disordered solids, exemplified in Fig. 1, and its related applications in Table 1. To keep the total page into an appropriate length, we will proceed as follows: Experimental methods may be briefly sketched. We then look at fundamental observations, trying to grasp their interpretations from unified standpoints and to draw simple pictures as possible. We will try to bridge atomic structures and physical properties (Fig. 2). In such ways, relationships among different macroscopic properties can be understood. The authors have also tried to point out the remaining and controversial problems. We will consider the amorphous chalcogenide material from two standpoints: One is as a kind of glass. At present, we utilize at least three kinds of photonic (highly pure) glasses, which are the oxide, chalcogenide, and halide, all these being treated as (semi-)transparent insulators. In these three kinds of glasses, both

Si(Ge) Si(Ge)O2 – As2O3 GeS(Se)2 – As2S(Se,Te)3 – S(Se,Te) Ge-Sb-Te, Ag(Cu)-As-S(Se)

Fig. 1 Relationships between materials of interest. Si(Ge) is tetrahedrally coordinated, producing three-dimensional networks. Inserting O to ≡Si−Si≡ bonds produces ≡Si−O−Si≡ connections, giving three-dimensional continuous random SiO2 networks. GeO2 has structures similar to that in SiO2 . O can be changed to S, Se, and Te, producing GeS(Se,Te)2 . With a change in the cation from Ge to As, the atomic coordination number decreases from 4 to 3, giving As2 O(S,Se,Te)3 . And, in pure S(Se,Te), the structure is molecular as rings and polymeric chains Table 1 Typical materials and related applications described in this text. For abbreviations, see the text Film

Bulk

Insulator Semiconductor

Density

SiO2 (fiber) Se (vidicon, x-ray imager) Ge2 Sb2 Te5 (DVD) a-Si:H (solar cell, TFT)

Elastic

Electrical

Optical

constant

conductivity

transparency

ATOMIC STRUCTURE

Fig. 2 A goal of solid-state science, which intends to give universal understandings of macroscopic properties through simple theories on the basis of known atomic structures

Preface

vii

oxygen (O) and chalcogens (S, Se, and Te) belong to the group VIb (16) atoms in the periodic table. Accordingly, the oxide and chalcogenide glasses possess many common features, which will be understood from a unified point of view. In addition, in these glasses, simple compositions such as SiO2 and As2 Se3 , which also solidify into crystals, are available. And, for the crystal we have had firmer scientific knowledge. Therefore, the group VIb glass can be an interesting target for understanding the glass property through comparisons with that of the corresponding crystal. We also mention here that the chalcogenide glass containing group I (1 and 11) atoms such as Li and Ag also exhibits (super)ionic conduction. The other aspect of chalcogenide is as a kind of amorphous semiconductor. As an amorphous semiconductor (or photoconductor), we had utilized a-Se photoreceptors in copying machines, although it has now been taken over by organic photoconductors. We have also developed phase-change memories using Ge–Sb–Te films. In fundamentals, a lot of concepts such as the mobility edge, charged defects, and Phillip’s magic number have been proposed. Applications of these concepts to other materials will extend our total understanding of the solid-state science. Nevertheless, amorphous semiconductor physics has remained far behind that of crystalline. Actually, famous texts on solid-state physics, by Kittel for example, deal mostly with single crystals. The reader may notice that the first (glass) and the second (amorphous semiconductor) standpoints mentioned above have been taken mainly by chemists and physicists, respectively. They also tend to employ different words for pointing nearly the same concepts, e.g., LUMO (lowest unoccupied molecular orbital)–HOMO (highest occupied molecular orbital) in molecular chemistry and conduction– valence bands in physics. However, an important fact here is the interplay between bond and band, developed by Phillips in the famous book, Bonds and Bands in Semiconductors. We will try to take such an approach in the present text. We list several books published in the present and related fields. Written by Physicists J. Tauc, Amorphous and Liquid Semiconductors (Plenum, London, 1974). N.F. Mott and E.A. Davis, Electronic Processes in Non-Crystalline Materials, 2nd Ed. (Clarendon, Oxford, 1979). J.M. Ziman, Models of Disorder (Cambridge University Press, Oxford, 1979). R. Zallen, The Physics of Amorphous Solids (Wiley, New York, NY, 1983). S.R. Elliott, Physics of Amorphous Materials, 2nd Ed. (Longman Scientific & Technical, Essex, 1990). K. Morigaki, Physics of Amorphous Semiconductors (World Scientific, Singapore, 1999). M.A. Popescu, Non-Crystalline Chalcogenides (Kluwer, Dordrecht, 2000). J. Singh and K. Shimakawa, Advances in Amorphous Semiconductors (Taylor & Francis, London, 2003).

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Preface

Written by Chemists Z.U. Borisova, Glassy Semiconductors (Plenum, New York, NY, 1981). A. Feltz, Amorphe und Glasartige Anorganische Festkrper (Akademie-Verlag, Berlin, 1983). R.H. Doremus, Glass Science, 2nd Ed. (Wiley, New York, NY, 1994). V.F. Kokorina, Glasses for Infrared Optics (CRC, Boca Raton, FL, 1996). M. Yamane and Y. Asahara, Glasses for Photonics (Cambridge University Press, Cambridge, 2000). Edited Volumes J. Zarzycki (Ed.), Materials Science and Technology Vol. 9, Glasses and Amorphous Materials (VCH, Weinheim, 1991). G. Pacchioni, L. Skuja, and D.L. Griscom (Eds.), Defects in SiO2 and Related Dielectrics: Science and Technology (Kluwer, Dordrecht, 2000). H.S. Nalwa (Ed.), Handbook of Advanced Electronic and Photonic Materials and Devices Vol. 5 (Academic, San Diego, CA, 2001). A.V. Kolobov (Ed.), Photo-Induced Metastability in Amorphous Semiconductors (Wiley-VCH, Weinheim, 2003). G. Lucovsky and M. Popescu (Eds.), Non-Crystalline Materials for Optoelectronics Vol. 1 (INOE, Bucharest, 2004). R. Fairman and B. Ushkov (Eds.), Semiconducting Chalcogenide Glass (Elsevier, Amsterdam, 2004). I (Glass Formation, Structure, and Stimulated Transformations in C.G.), II (Properties of Chalcogenide Glasses), and III (Applications of Chalcogenide Glasses).

Acknowledgements Finally, we are particularly grateful to M. Mikami and N. Terakado for preparing many illustrations. Discussions with S. Nonomura, A. Saitoh, Y. Shinozuka, M. Tatsumisago, and T. Uchino were extremely valuable to write this book. Last but not least, we are thankful to Kazunobu Tanaka, who had led us to the research on chalcogenide glasses, and to Safa Kasap, without whom this text could not have been published. Sapporo, Japan Gifu, Japan

Keiji Tanaka Koichi Shimakawa

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Non-crystalline, Amorphous, and Glassy . . . . . . . 1.2 Crystalline Versus Non-crystalline . . . . . . . . . . 1.3 Characteristic Feature . . . . . . . . . . . . . . . . . 1.3.1 Amorphous Material . . . . . . . . . . . . . 1.3.2 Amorphous Chalcogenide . . . . . . . . . . . 1.4 Historical Background: Chalcogenide and Oxide . . . 1.5 Atomic and Electron Configurations . . . . . . . . . 1.6 Ionicity, Covalency, and Metallicity of Atomic Bonds 1.7 Variety in Chalcogenides . . . . . . . . . . . . . . . 1.7.1 Elemental . . . . . . . . . . . . . . . . . . . 1.7.2 Binary . . . . . . . . . . . . . . . . . . . . . 1.7.3 Ternary and More Complicated . . . . . . . . 1.8 Preparation . . . . . . . . . . . . . . . . . . . . . . 1.8.1 Glass (Bulk, Fiber) . . . . . . . . . . . . . . 1.8.2 Film and Others . . . . . . . . . . . . . . . . 1.9 Dependence upon Experimental Variables . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . .

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2 Structure . . . . . . . . . . . . . . . . . . . 2.1 Ideal Structure . . . . . . . . . . . . . . 2.2 Practical Structure . . . . . . . . . . . . 2.3 Short-Range Structure . . . . . . . . . . 2.3.1 Experiments . . . . . . . . . . . 2.3.2 Observations . . . . . . . . . . 2.4 Medium-Range Structure . . . . . . . . 2.4.1 Small Medium-Range Structure 2.4.2 First Sharp Diffraction Peak . . 2.4.3 Boson Peak . . . . . . . . . . . 2.5 Defect . . . . . . . . . . . . . . . . . . 2.6 Computer Simulations . . . . . . . . . 2.7 Homogeneity . . . . . . . . . . . . . . 2.8 Surface and Nano-structures . . . . . . References . . . . . . . . . . . . . . . . . . .

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3 Structural Properties . . . . . . 3.1 Structure and Properties . . . 3.2 Glass Transition . . . . . . . 3.3 Crystallization . . . . . . . . 3.4 Thermal and Other Properties 3.5 Magic Numbers: 2.4 and 2.67 3.6 Ionic Conduction . . . . . . References . . . . . . . . . . . . .

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4 Electronic Properties . . . . . . 4.1 Electronic Structure . . . . . 4.2 Band Structure . . . . . . . 4.3 Bandgap and Mobility Edge 4.4 Gap States . . . . . . . . . . 4.5 Optical Property . . . . . . . 4.6 Optical Absorption . . . . . 4.6.1 Tauc Gap . . . . . . 4.6.2 Urbach Edge . . . . . 4.6.3 Weak Absorption Tail 4.7 Refractive Index . . . . . . . 4.8 Optical Nonlinearity . . . . . 4.9 Electrical Conduction . . . . 4.9.1 Background . . . . . 4.9.2 Carrier Transport . . 4.9.3 Meyer–Neldel Rule . 4.9.4 AC Conductivity . . 4.10 Compositional Variation . . References . . . . . . . . . . . . .

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5 Photo-Electronic Properties . . . . . . . . . . 5.1 Photo-Excitation and Relaxation . . . . . 5.2 Photoluminescence . . . . . . . . . . . . 5.2.1 CW Photoluminescence . . . . . . 5.2.2 Time-Resolved Photoluminescence 5.3 Photo-Voltage . . . . . . . . . . . . . . . 5.4 Photoconduction . . . . . . . . . . . . . 5.4.1 CW Photoconduction . . . . . . . 5.4.2 Time-Resolved Photoconduction . 5.5 Avalanche Breakdown . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . .

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6 Light-Induced Phenomena . . . . . . . . . . 6.1 Overall Features . . . . . . . . . . . . . . 6.2 Thermal Effects in Chalcogenide . . . . . 6.3 Photon Effects in Chalcogenide . . . . . . 6.3.1 Classification and Overall Features 6.3.2 Experimental . . . . . . . . . . .

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6.3.3 Computer Simulation . . . . . . . . . . . . . . . . . . . 6.3.4 Photo-Enhanced Crystallization . . . . . . . . . . . . . . 6.3.5 Photo-Polymerization . . . . . . . . . . . . . . . . . . . 6.3.6 Giant Photo-Contraction . . . . . . . . . . . . . . . . . 6.3.7 Other Irreversible Changes . . . . . . . . . . . . . . . . 6.3.8 Reversible Photodarkening and Refractive Index Increase 6.3.9 Other Reversible Changes . . . . . . . . . . . . . . . . . 6.3.10 Photoinduced Phenomena at Low Temperatures . . . . . 6.3.11 Transitory Changes . . . . . . . . . . . . . . . . . . . . 6.3.12 Vector Effects . . . . . . . . . . . . . . . . . . . . . . . 6.3.13 Photo-Chemical Effects . . . . . . . . . . . . . . . . . . 6.4 Photon Effects in Oxide Glasses . . . . . . . . . . . . . . . . . 6.5 Light-Induced Phenomena in Amorphous Si:H Films . . . . . . 6.5.1 Thermal Effects in Amorphous Si:H Films . . . . . . . . 6.5.2 Photon Effects in Amorphous Si:H Films . . . . . . . . 6.6 Photon Effects in Organic Polymers . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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8 Future Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

229 229 230

Appendix: Publications on Related Crystals . . . . . . . . . . . . . . . .

232

Material Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

237

Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

239

7 Applications . . . . . . . . . . . . . . . . . . 7.1 Overall Features . . . . . . . . . . . . . . 7.2 Optical Device . . . . . . . . . . . . . . 7.2.1 Optical Fiber . . . . . . . . . . . 7.2.2 Metal-Doped Fiber . . . . . . . . 7.2.3 Waveguide . . . . . . . . . . . . . 7.3 Photo-Structural Device . . . . . . . . . . 7.4 Phase Change . . . . . . . . . . . . . . . 7.4.1 Background . . . . . . . . . . . . 7.4.2 Optical Phase Change (DVD) . . . 7.4.3 Electrical Phase Change (PRAM) . 7.5 Electrical Device . . . . . . . . . . . . . 7.6 Photo-Electric Device . . . . . . . . . . . 7.6.1 Copying Photoreceptor . . . . . . 7.6.2 Vidicon and X-Ray Imager . . . . 7.6.3 Solar Cell . . . . . . . . . . . . . 7.7 Ionic Device and Others . . . . . . . . . . 7.7.1 Ionic Memories . . . . . . . . . . 7.7.2 Ion Sensor . . . . . . . . . . . . . 7.7.3 Battery . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . .

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List of Abbreviations

DOS D(E) DVD ESR EXAFS FSDP HOMO LUMO MD RDF TFT TOF

density of state density of state digital versatile disk electron spin resonance extended x-ray absorption fine spectroscopy first sharp diffraction peak highest occupied molecular orbital lowest unoccupied molecular orbital molecular dynamics radial distribution function thin-film transistor time of flight

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List of Acronyms

a c g t τ T Tc Tg Tm Z

amorphous crystalline glassy time characteristic time temperature crystallization temperature glass transition temperature melting temperature coordination number

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Chapter 1

Introduction

Abstract We begin with the terminology and definition of several words, which may be somewhat confusing. Comparison of crystal and amorphous materials is made from physical standpoints. Among many non-crystalline solids, we shed light on oxide and chalcogenide glasses with brief histories. The readers will see how glass has made an impact on the present society. We also see the importance of unified understanding of glasses containing VIb elements in the periodic table. There are many kinds of chalcogenide glasses, which will be discussed in terms of atomic elements. Keywords Crystal · Amorphous material · Disorder · Quasi-equilibrium · VIb glass · Obsidian · Preparation dependence · Pressure dependence

1.1 Non-crystalline, Amorphous, and Glassy At the outset, it may be valuable to define the terminology. We divide the condensed matter, which includes liquids and solids, into two: crystal and non-crystal. As imagined from external shapes with flat and conchoidal faces in Fig. 1.1, the crystal has periodically positioned atomic structures, and in non-crystals the atomic structure is disordered. As examples, most of the stones and rocks on the earth are crystalline,1 and liquids are non-crystalline, with a known exception being liquid crystals. However, there exist non-crystalline solids, which are synonymous with amorphous materials in the book by Mott and Davis (1979). Mott and Davis (1979) have defined glass, among amorphous materials, as the one which can be solidified into a non-crystal from the melt. Glassy and vitreous, the words being derived from an Indo-European root and Latin (Doremus 1994), may be synonymously used. Their definitions can be expressed using a mathematical set notation as non-crystalline (disordered) ⊃ amorphous ⊃ glassy ≈ vitreous.

1 It is mentioned that glassy substances on the earth are limited to obsidian, etc., while those seem rather common on the moon (Saal et al. 2008).

1 K. Tanaka, K. Shimakawa, Amorphous Chalcogenide Semiconductors and Related C Springer Science+Business Media, LLC 2011 Materials, DOI 10.1007/978-1-4419-9510-0_1,

2

1

Introduction

Fig. 1.1 Quartz (left), crystalline SiO2 with a melting temperature of 1730◦ C and fused silica (right) SiO2 glass with a glass transition temperature of ∼1500◦ C (http://geology.com/minerals/ quartz.shtml, © Geology.com, reprinted with permission). Quartz cleaves, while the glass cracks conchoidally

Fig. 1.2 GENESIS (Global Energy Network Equipped with Solar cells and International Superconductor grids) project using a-Si:H solar cells and superconductor cables, announced from Sanyo Electric Co., Ltd., in 2001 (© Tokyu Construction Co., Ltd., reprinted with permission)

An amorphous hydrogenated Si (a-Si:H) film (Fig. 1.2) is “amorphous,” but not glassy, because the film is produced from vapor or plasma phases. The film cannot be prepared through the conventional melt quenching of liquid Si (Bhat et al. 2007). On the other hand, the window glass is a typical oxide glass, since it is prepared through the quenching of melts. Phillips (1980) and Elliott (1990) may prefer a different definition. The noncrystalline solid is divided into amorphous and glassy, which does not and does exhibit the glass transition, respectively, i.e., a gradual transition between a glassy

1.2

Crystalline Versus Non-crystalline

3

and the supercooled liquidus state (see Section 3.2). In their definition, the amorphous and the glassy seem to be incompatible: amorphous ∩ glassy (vitreous) = ø (empty set). In this definition, films such as a-Si:H are amorphous, since the film, when heated, crystallizes without showing glass transition. Very thin (∼10 nm) SiO2 films in MOS (metal–oxide–semiconductor) structures may be amorphous in both definitions, while melt-quenched SiO2 is clearly a typical glass. In short, the definition by Mott–Davis depends upon the preparation method and that by Phillips and Elliott depends upon the property. We then see that vacuumevaporated As2 S3 films are amorphous in Mott’s definition because it is not melt quenched, but it is glassy in Phillips’ sense because it exhibits a glassy nature. We will follow in principle the definition by Mott and Davis.

1.2 Crystalline Versus Non-crystalline Crystalline and non-crystalline materials can be defined as the condensed matters which have periodic and non-periodic atomic structures. To make the contrast clearer, let the crystal be a single crystal in the following. In many cases, a polycrystal may possess intermediate properties between the single crystal and the amorphous material. The crystal and the amorphous material may be distinguished from external shapes (Fig. 1.1). Non-metallic crystals tend to exhibit regular anisotropic shapes such as the cubic form of NaCl and the hexagonal form of quartz crystals, the latter giving rise to useful non-centrosymmetric properties such as optical birefringence, piezo-electricity, and optical second-harmonic generation. The cleaved surfaces (cleavage) may be atomically flat. We can prepare such ultimately flat surfaces also by using sophisticated vacuum techniques like molecular beam epitaxy. In addition, we can now pick up and put a single atom from and on the surface (Fishlock et al. 2000). In contrast, the glass breaks conchoidally, which reflects disordered atomic structures. For such fractured surfaces, atomic manipulation is practically impossible. Very roughly, a single crystal is more difficult to prepare than a glass. For preparing a single crystal, e.g., c-Si wafers, the purity must be very high (∼ten 9’s), since impurities tend to destroy the atomic periodicity, as illustrated in Fig. 1.3 (left).

Fig. 1.3 An impurity atom, which is substitutional and interstitial, in crystal (left) and non-crystal (right)

4

1

Introduction

In addition, since most of the crystals are in thermal equilibrium state,2 cooling of the melt from high temperatures needs a long duration (>days). As exemplified in Fig. 1.3 (right), the glass can contain foreign atoms, due to flexible disordered structures. Actually, the purity of silica glass fibers, the purest glass available at present, may be on ppm (∼six 9’s) levels. The disordered atomic structure is more flexible and has lower density, and accordingly, an included ion may move smoothly, which is promising for applications to solid-state batteries. In addition, glass having a quasi-equilibrium state must be prepared through rapid quenching within a short (millisecond to hours, depending upon the material) duration. Owing to this feature, we can prepare wide glass plates, utilized for windows, etc., and long optical fibers within commercially feasible times. Naturally, the price per unit scale (volume, area, length) can become cheaper than that of the crystal. Shapes of wavefunctions in a crystal and a non-crystal are contrastive. As illustrated in Fig. 1.4, in a single crystal all the electron wavefunctions are extended, but in a non-crystal the wavefunction of electrons and holes at band edges and mid-gaps is localized. In consequence, the electron (hole) mobility in a non-crystal becomes smaller than that in the corresponding crystal, since the localized electron (hole) in band edges governs the mobility. On the other hand, in optical absorption, the difference between these two materials appears to be smaller than that in the electron transport, since the localized state gives just a small contribution to the optical absorption. Note that similar situations apply to lattice vibrations. The lattice

Fig. 1.4 Electron wavefunctions and band structures in (a) an ideal crystal, (b) a disordered network with a dangling bond, and (c) a fully connected strained network

2 A known exception is the diamond, which is a non-equilibrium phase of carbon on the earth’s surface. The equilibrium phase is semi-metallic graphite.

1.2

Crystalline Versus Non-crystalline

5

Table 1.1 Comparison of crystal and amorphous material

Atom position Homogeneity Isotropy Structure controllability Sample dimension Stability (equilibrium) Wavefunctions Ion mobility (cm2 /Vs) (in AgAsS2 ) Electron (hole) mobility (cm2 /Vs) Electron–lattice interaction

Crystal

Amorphous material

Periodic Yes No Atomic Small Yes Extend 10−12 ∼103 Small

Short (medium) range order Macroscopically yes Yes Nano-scale Large Meta- (quasi-) Localize 10−10 100 Large

vibrations are also extended and localized in crystals and non-crystals, which provide higher and lower thermal conductivities. But, no big difference exists between heat capacities in a crystal and its corresponding non-crystal. Table 1.1 lists other contrastive features in crystals and amorphous materials. It should be noted that the understanding of properties in non-crystals, specifically the amorphous material, in terms of solid-state science remains far behind that in the crystal. Why has the amorphous material science been immature? The reason is simple. Fundamental physics on single crystals treats one (a few)-particle problems, but the non-crystalline physics must deal with many-particle problems. In crystalline physics, we first determine the atomic structure using diffraction experiments, defining the unit cell, and then try to connect observed macroscopic properties with the structure using the periodicity principle. In many cases, the one-electron approximation or the harmonic vibration approximation can provide basic and firm insights (Kittel 2005). But, for a non-crystalline material we cannot define the unit cell. We must consider the whole lattice structure including 1022−23 atoms/cm3 , which is in principle impossible. In addition, we cannot yet identify the disordered structure. Necessarily, we must follow some approximations, but for the approximation, no principal methods (such as the one-electron approximation and Bloch function formalism) have been available. Instead, we may employ computer simulations, which are not straightforward. Despite the immature science mentioned above, as exemplified in Table 1.2, applications of amorphous materials to photonic and electronic devices are growing, the details being described in Chapter 7. The best known may be the optical fiber of silica glasses and peripheral devices such as optical amplifiers and wavelength filters. Such optical components are more or less difficult to prepare using crystals. In addition, photoconducting devices, specifically large area (∼m2 size) films, have been developed. An invaluable material may be a-Si:H films, which are indispensable to large area solar cells (Fig. 1.2). Also, tellurides are employed as DVD (digital versatile disk) films, which undergo the so-called optical phase change between crystalline and amorphous states. We should note, however, that in many of these applications the inorganic non-crystalline material is in competition with organic polymers.

6

1

Introduction

Table 1.2 Comparison of applications in crystalline and amorphous non-metals Applications

Crystalline

Amorphous

Photonic Electronic Photo-electronic

SHG IC Laser, photodiode, CCD

Fiber, optical amplifier, DVD Flexible film devices, TFT Solar cell, vidicon, x-ray detector

SHG stands for second-harmonic generation, DVD digital versatile disk, IC integrated circuits, TFT thin-film transistor, and CCD charge-coupled device

1.3 Characteristic Feature 1.3.1 Amorphous Material The non-crystalline solid, i.e., amorphous material, possesses two characteristic features. One is structural disorder and the other is quasi-equilibriumness (see Table 1.3). These features yield a wide variety of materials and also pose difficult problems. The disorder affords infinite (∼1050 ) numbers of materials with arbitrary combinations of atoms, or atomic units, with continuously varied compositions (Zanotto and Coutinho 2004). The disordered structure may be continuous, without containing grain boundaries and distinct heterogeneities. For instance, the composition of window glass is 74SiO2 ·16Na2 O·10CaO, which may be selected after balancing properties and production cost. In addition, the disordered structure can be a matrix which incorporates exotic elements such as transition metals and rare earth atoms. Nevertheless, insensitivity or tolerance to included atoms causes lower efficiencies in atomic doping effects. We know as an example that for the p–n type control of semiconductors, ppm-level dopants may be sufficient in c-Si, while percent-order dopants are needed for a-Si:H films. On the other hand, the amorphous material, including glasses, lies in quasiequilibrium states. In other words, its property cannot be uniquely determined by temperature and pressure. The property gradually changes with time. Because of

Table 1.3 A general view on structures and thermodynamic equilibrium of crystal, liquid, gas, and glass

Atomic structure Crystal Liquid Gas Glass

Periodic Disordered Random Disordered

Thermodynamical state Equilibrium Equilibrium Equilibrium Quasi-equilibrium (meta-stable)

1.3

Characteristic Feature

7

this quasi-equilibriumness, we can and must prepare a sample within short duration, which affords to produce wide and long samples. As a consequence, however, sample properties depend upon its preparation methods, conditions, and prehistory. The sample properties can also be modified by electronic excitation, e.g., light illumination, as will be described in Chapter 6. We therefore face not only a variety of compositions but also a variety of modified properties for a fixed composition. This feature can be a merit or demerit in applications. Note that biological substances such as proteins also exhibit quasi-equilibrium properties (Stec 2004).

1.3.2 Amorphous Chalcogenide Glassy chalcogenides can be characterized by the structure and the energy gap. The material can also be compared with other materials such as an amorphous material and a semiconductor. Figure 1.5 locates several amorphous materials as functions of optical gap Eg and atomic structure. Organic polymers and inorganic glasses including oxides and halides are, in general, insulators and are transparent having energy gaps of 5–10 eV. On the other hand, amorphous chalcogenide and tetrahedral materials such as a-Si:H are semiconductors with energy gaps of 1–3 eV. Structurally, a-Se and polymers such as polyethylene (–CH2 –) are characterized by one-dimensional chains, i.e., the network dimension is one (Zallen 1983). Chalcogenide glasses such as As2 S(Se)3 and GeS(Se)2 are assumed to have two-dimensional (distorted layers as crumpled paper) structures, though there may be some controversy, as described in Chapter 2. And, oxide glasses and tetrahedral materials have three-dimensional network structures. Figure 1.6 characterizes chalcogenide as a glass (horizontal) and a semiconductor (vertical). As a glass, the structure becomes more rigid in the order of polymer, chalcogenide, and oxide. On the other hand, semiconductor properties, e.g., carrier mobility, and also material price per unit area become better and higher in the order of organic, chalcogenide, tetrahedral (a-Si:H), and crystalline. This price order

Eg(eV)

Fig. 1.5 Characterization of typical disordered solids in scales of the optical gap Eg and the network dimension (see Section 2.4). The black horizontal band denotes the photon energy of visible light

10 polymer

oxide/ halide

5 chalcogenide 0

1

tetrahedral

2 3 Network dimension

8

1

Introduction

Fig. 1.6 Characterization of typical disordered solids in scales of glass and semiconductor

may be governed by preparation procedures of these materials: coating, vacuum evaporation, glow discharge deposition, and epitaxial growth, respectively.

1.4 Historical Background: Chalcogenide and Oxide The chalcogenide glass has a markedly different history from that of the oxide. As shown in Fig. 1.7, the oxide glass has a history longer than 5000 years, while the chalcogenide has so to say just a half-century history.

Fig. 1.7 History of glasses, including oxide, chalcogenide, and fluoride. The pictures on the righthand side show, from the top to the bottom, obsidian arrows, a floating method for producing window glasses, and an Er-doped fiber amplifier (EDFA)

1.4

Historical Background: Chalcogenide and Oxide

9

A brief historical view of the oxide glass may be the following (Doremus 1994): The first use of the oxide glass by mankind seemed to start with natural glasses such as obsidian, a kind of alumino-silicate (SiO2 –Al2 O3 ) glasses containing crystalline particles such as Fe2 O3 . The black and hard glass was utilized as knives and arrowheads at stone ages (Fig. 1.7, top). About 5000 years ago, people at Mesopotamia might have accidentally discovered a production method of artificial glasses using sand (SiO2 ) and salt (NaCl), which could yield soda-silicate glasses (SiO2 –Na2 O) in charcoal fires (Breinder 2005). Because of unavoidable metallic impurities such as Fe, glasses at that era were necessarily colored, which might make the glass as ornaments. In the Roman age (1st century B.C.–A.D. 5th century), however, transparent wine glasses became available. Later, in the 17th century, Galilei and Newton employed transparent glasses as optical components, e.g., lenses and prisms. Optical instruments such as eyeglasses, telescopes, microscopes, and prism monochromators were devised. Gradually, wider and flatter glass plates became available, which were employed as stained glasses in churches. Glass plates could also be coated with silver, producing mirrors, which replaced polished metal mirrors. However, the glass might have been very expensive till the 19th century. Around 1955, Pilkington and coworkers developed the so-called floating method (Fig. 1.7, middle) for commercial production of large glass plates, which became to be widely utilized as windows. And, at the end of the 20th century, researchers in Corning devised a preparation method, called outside vapor deposition, which can produce ultimately-transparent and long (∼100 km) glass fibers, a kind of photonics glasses, in which the purity (better than ppm) is a determinative factor as that in many crystalline semiconductors. In addition, functional devices as fiber amplifiers (Fig. 1.7, bottom) have been produced. On the other hand, notable studies on the chalcogenide glass started at ∼1950 in Russia and the USA as materials featuring four different properties. Those are semiconductor, ion conductor, infrared transmitting glass, and xerographic photoreceptor. In St. Petersburg in Russia (Leningrad in USSR), Kolomiet’s group in Ioffe Institute (Fig. 1.8) discovered the glassy (vitreous) semiconductor when surveying photoconducting materials (Kolomiets 1964b). They evinced that there exists a material which has disordered atomic structures and bandgap energy of ∼2 eV. At the same time, researchers in Leningrad State University studied the chalcogenide glass from chemical points of view, i.e., as ion-conducting (Borisova 1981) and infrared transmitting materials (Kokorina 1996). It is a surprising coincidence that all the studies started independently from physical and chemical standpoints in the same city. On the other hand, in the USA, As–S glasses were demonstrated to be stable infrared transmitting materials (Frerichs 1953), which might be developed for military purposes as lenses in night goggles. In addition, the glass was revealed to work as a good sealing material (Flaschen et al. 1960). On the other hand, a-Se films were utilized as photoreceptors in xerography, the principle having been patented by Carlson in 1937 (see Chapter 7). Because of these different histories and other factors, the oxide and the chalcogenide glass have been studied in different societies. The oxide has been developed in ceramic industries for a long time and investigated by inorganic

10

1

Introduction

Fig. 1.8 Professor Kolomiets in his office (1987, summer)

chemists more or less empirically. The chalcogenide is studied also by chemists as new glasses and, in addition, as amorphous semiconductors by physicists and as photonics glasses by application-oriented researchers. Such situations tend to limit a unified understanding of these glasses. For instance, similar kinds of neutral dangling bonds are called as an E center and a D0 in the oxide and the chalcogenide society, respectively. Under the circumstances, unified descriptions of physical and chemical ideas will be very important.

1.5 Atomic and Electron Configurations From the top of the group VIb (16) atoms in the periodic table (Fig. 1.9), we see O, S, Se, and Te with a period increase from 2 to 5. The number of valence electrons in these atoms is 6 with a common outer electron configuration of s2 p4 . In the s2 p4 configuration, the p state is responsible for chemical bonding in many cases because, as shown in Fig. 1.10, the energy of the p state lies higher than that of the s state. (As known, the only one exception is the one-electron system H.) The

Group

I(a/b)

IIa

IIIb

IVb

Vb

VIb

VIIb

1,11

2

13

14

15

16

17

VIII

ZERO 18

Period 1

H

2

Li

Be

B

C

N

O

F

He Ne

3

Na

Mg

Al

Si

P

S

Cl

Ar

4

K/Cu

Ge

As

Se

Br

5

/Ag

Sn

Sb

Te

I

6

/Au

Pb

Fe

Fig. 1.9 Chalcogen (S, Se, and Te) and related atoms in the periodic table and sizes of atoms and ions (Pauling 1960). The size, which is assumed to be spherical, is estimated from atomic distances in crystals

1.5

Atomic and Electron Configurations

11

Fig. 1.10 Electron energies of the p and the s state, Ep and Es , in several atoms of interest. The values are obtained from table 2.2 in Harrison (1980). Solid lines connect the values of the group VIb (16) atoms, and dashed lines connect those of the same periods. For Si and Ge, the energies of sp3 states, −8.3 and −8.4 eV, are also plotted by diamonds

p state has three electron lobes, px , py , and pz , each being able to take two electrons with up and down spins. Then, following the so-called Hund rule (Kittel 2005), the four electrons of the p state produce one filled lobe, e.g., pz , and two half-filled lobes, px and py , as illustrated in the upper middle panel in Fig. 1.11. These two kinds of p states take different roles in the solids. The paired pz electrons form a non-bonding state, with the wavefunction being similar to that in an isolated atom. Correspondingly, the energy level is located at the same position as that in an isolated atom, with some broadening arising from interatomic van der Waals-type interaction (the upper right in Fig. 1.11). This state forms the top

Fig. 1.11 Comparison of Se and Si in amorphous structures (left), electron distributions of the atoms in solids (center), and energy levels in the isolated atoms and solids (right). Se and Si have entangled chain structures and cross-linked networks with p4 and sp3 electron distributions. Note that gross features of the electron distributions and energy levels are the same with those in the corresponding crystals. The energy gap appears between LP (lone-pair electron) and σ ∗ in Se and between σ and σ ∗ in Si

12

1

Introduction

of the valence band in solids. Kastner (1972), who emphasized this peculiar nonbonding p electron feature, designated the chalcogenide, e.g., Se and As2 S3 , as a lone-pair electron semiconductor. Needless to say, the idea can be applied to the oxide, e.g., SiO2 , as well. Note that this origin of the valence band is markedly different from that in the conventional semiconductors such as Si and GaAs, in which sp3 hybridization occurs, as illustrated in the lower middle in Fig. 1.11. On the other hand, the electrons in px and py orbitals in the p4 configuration produce covalent bonds with neighboring atoms, giving rise to bonding states σ , which have lower (stabilized) energies than that of the original p state. As a result, the VIb atom can take twofold coordination with neighboring atoms. That is, the coordination number follows the so-called 8−N rule (Mott and Davis 1979), where N = 6 in the present case. The covalent bond accompanies also the anti-bonding state σ ∗ , which forms the conduction band. Note that this p4 bonding scheme is inherent to the covalent group VIb material, irrespective of crystalline or non-crystalline structures. There are, however, at least three notable exceptions from the twofold coordination. The first is tetrahedral coordination in some chalcogenides. It is known that, in crystalline semiconductors such as CdS, S atoms (or S2– ions) are fourfold coordinated, which is ascribed to the sp3 hybridized wavefunction. Such a tetrahedral configuration may be energetically favored in the crystal because of the fairly ionic Cd–S bonds and long-range structural periodicity. A similar situation seems to occur in amorphous In–S, as proposed by Narushima et al. (2004). On the other hand, the tetrahedral configuration of O atoms may be less common (CdO, ZnO), which is probably due to much higher sp3 hybridization energy, arising from a greater energy difference of Ep − Es ≈ 15 eV in O than that (∼10 eV) in S and Se (Fig. 1.10). The second exception can be pointed out for ionic (or ion-conducting) glasses such as Cu(Ag)–As(Sb)–S(Se), in which S and Se are demonstrated to have coordination numbers of 3 – 4 (Simdyankin et al. 2005). Such coordination changes can be understood using a formal valence shell model, proposed by Liu and Taylor (1989), which assumes formal transfer of lone-pair electrons from S(Se) to Cu(Ag). The last exception may be telluride materials such as Ge–Sb–Te, a famous DVD material, in which Te appears to form sixfold coordination with Ge and Sb. This high coordination can be regarded as a manifestation of metallic character of Te (Ep − Es ≈ 8.5 eV), in which the six valence electrons are likely to be mixed up in energy.

1.6 Ionicity, Covalency, and Metallicity of Atomic Bonds Solid has a variety of atomic bonds including ionic, covalent, metallic, and also weaker van der Waals types. In elemental solids such as Si and Se, all the chemical bonds are purely covalent. In multi-component solids, heteropolar bonds are included, which are ionic to some degree. However, as shown in Fig. 1.12a, an ionic degree in As(Si,Ge)–O(S,Se,Te) bonds varies, and it decreases from O to Te. Recalling that the bond ionicity, the difference in electro-negativity of bonding atoms, of Na–Cl is 2.1 (Pauling 1960), we see in Fig. 1.12a that a Si(Ge)–O bond

1.6

Ionicity, Covalency, and Metallicity of Atomic Bonds

13

Fig. 1.12 Comparison of (a) bond ionicity, (b) macroscopic density d, and (c) optical gap Eg in typical binary systems consisting of Si(Ge, As) and group VIb atoms. For instance, the data denoted as Si(Ge) in (a) show, from O to Te, the ionicities of Si(Ge)–O, Si(Ge)–S, Si(Ge)–Se, and Si(Ge)–Te bonds. The data in (b) and (c) show d and Eg in pure chalcogen solids ( with dot-dash lines) and stoichiometric glasses SiO(S, Se, Te)2 ( with dashed lines), GeO(S, Se, Te)2 (× with solid lines), and As2 O(S, Se, Te)3 (◦ with solid lines)

with ∼1.7 is relatively ionic and As–Se with ∼0.4 is mostly covalent. The oxide is much more ionic than the chalcogenide. The ionicity and covalency in the oxide and chalcogenide provide different features in compositional variations. We know that it is difficult to prepare a glass with a composition of, e.g., Si35 O65 , but preparation of As35 S65 glass is straightforward. In the chalcogenide, composition tuning is attained in atomic ratios. On the other hand, in the oxide glass, the compositional variation can be obtained in chemical units, as 74SiO2 ·16NaO2 ·10CaO. Here, the unit may be characterized either as a network former (SiO2 ) or as a network modifier (Na2 O and CaO). We have utilized, for a long time, this kind of compositional tuning in oxide glasses for obtaining

Fig. 1.13 A schematic representation of SiO2 –Na2 O glass. Note that Si is four fold coordinated in a three-dimensional view

14

1

Introduction

selected properties. For instance, thermal shaping of SiO2 glass needs high temperatures (∼1500◦ C), which is inconvenient in mass production. Then, addition of modifier Na2 O to silica networks disrupts firm ≡Si–O– connections to ionic ≡Si–O– –Na+ bonds, as illustrated in Fig. 1.13, which can decrease the shaping temperature. We have discovered also that further addition of CaO is effective for enhancing chemical stability (Doremus 1994).

1.7 Variety in Chalcogenides There exist many kinds of amorphous chalcogenides (Borisova 1981, Popescu 2000), and classification may be valuable. We can classify the amorphous chalcogenide into the elemental, binary, ternary, etc., and the alloys can be divided into stoichiometric (As2 S3 , GeSe2 ) and non-stoichiometric compositions (S–Se, As–Se). Otherwise, we can classify the material with respect to the chalcogen included: sulfide, selenide, and telluride. As illustrated in Fig. 1.14, with an order of O, S, Se, and Te, the bond character changes from ionic, covalent, to metallic. We know that the covalent bond is directional and the ionic and metallic bonds are fairy isotropic. Important defects, such as dangling and wrong bonds, also seem to change with this order. Among many chalcogenide materials, how can we select one composition for a study? To obtain fundamental insights, we may need the simplest, elemental material such as a-Se. However, the non-crystalline solid appears to pose a dilemma to physicists, who prefer simplicity, that is, topological disorder produced only by the twofold coordinated chalcogen is difficult to suppress crystallization. Actually, evaporated a-Se films are likely to crystallize within a few months, depending upon humidity, at room temperature. Compositional disorder is required

O ionic dangling bond

Fig. 1.14 Bond characters and major defects in group VIb glasses such as As2 O(S,Se,Te)3

isotropic wrong bond

metallic

covalent

S directional

Se

Te

1.7

Variety in Chalcogenides

15

for glass stability, and accordingly, multi-component alloys are of major concern. The non-crystalline solid appears to be inherently a kind of atomically complex system.

1.7.1 Elemental For the elements, the sequence of S, Se, and Te shows that bonding changes from molecular, covalent, to metallic. Among these three elements, only Se is available as amorphous films and glassy ingots at room temperature. In contrast, amorphous S and Te are unstable at room temperature, immediately crystallizing, so that studies on these materials are relatively limited. Several molecular allotropes are known for S. Among those, the most stable appears to be S8 ring molecules. However, as illustrated in Fig. 1.15, the small diskshaped molecules can be regularly packed, which are easily crystallized. Glassy S, which is composed of S chains, is obtained when the melt stored above ∼160◦ C, the so-called polymerization temperature, is quenched to temperatures below the glass transition temperature of –30◦ C (Stolz et al. 1994). a-S films can be prepared through vacuum evaporation onto cooled substrates (Tanaka 1986). Se is the only elemental glass available at room temperature (Zingaro and Cooper 1974). The glassy structure is the simplest, consisting mainly of entangled −Se−Se− chains (Fig. 1.11). In addition, depending upon preparation procedures, small amounts of ring molecules such as Se8 may be included. Note that the stable structure of c-Se is composed of aligned helical chains, as shown in Fig. 1.15. An important property of a-Se is that the material exhibits peculiar photoconducting properties, which have been and are widely applied to photoconductor devices (see Section 7.6). Telluride is much more metallic, having less directional chemical bonds. As a result, the material is likely to crystallize, and the bulk glass cannot be prepared (Bureau et al. 2009). Studies on pure a-Te films are few (Takahashi and Harada 1982). It is mentioned here that pure pnictides (P, As, and Sb) can be prepared as

Fig. 1.15 Atomic structures of c-S consisting of S8 rings (left) and c-Se(Te) of helical chains (right)

16

1

Introduction

amorphous films, and bulk samples in some cases, while studies are very limited (Greaves et al. 1979).

1.7.2 Binary The binary alloys, which have been extensively studied, are As2 S(Se)3 (Fig. 1.16). These stoichiometric glasses are fairly covalent and stable, having optical gaps of ∼2.4 (∼1.8) eV and the glass transition temperatures of ∼200◦ C (Borisova 1981), both properties being convenient for experiments. As will be described in Section 3.5, the average atomic coordination number is 2.4, which is assumed to be a signature of stable glasses. Electrically, As2 S3 is a good insulator, and As2 Se3 is semi-conducting. On the other hand, As2 Te3 is substantially conductive and likely to crystallize, probably due to less-directional metallic bonds of Te, so that studies on the amorphous forms are few. To understand the property of a glass, we may need the corresponding crystal. However, it is difficult to prepare single-crystalline As2 S3 (Yang et al. 1986), and instead, we employ the corresponding mineral orpiment (Fig. 1.16) for experiments. On the other hand, single-crystalline As2 Se3 can be prepared through vapor growth (Kitao et al. 1969, Smith et al. 1979). As shown in Fig. 1.16, As2 S(Se)3 crystals have layer-type structures, exhibiting cleavage in the a–c plane. Experimental studies on GeS(Se)2 seem to be fewer than those on As2 S(Se)3 . The reason may be, at least, the following: One is that the preparation of GeS(Se)2

Fig. 1.16 An As2 S3 glass rod (Eg ≈ 2.4 eV and Tg ≈ 200◦ C) (upper left), an orpiment specimen (Eg ≈ 2.6 eV and Tm ≈ 300◦ C) (lower left), and its atomic structure orthogonal to the b axis (upper right) and to the c axis (lower right)

1.7

Variety in Chalcogenides

17

glasses is more difficult than that of As2 S(Se) and, in addition, glass properties critically depend upon preparation conditions (see Fig. 1.18 for GeS2 ). This feature may be connected with a greater average coordination number of 2.67 and/or to the existence of two crystalline polymorphs having layer and three-dimensional forms (with the optical gaps of ∼3.2 and ∼3.5 eV in c-GeS2 (Weinstein et al. 1982)). The other is that thermal vacuum evaporation of GeS(Se)2 is more difficult (see Section 1.8). Some researchers employ radio-frequency sputtering in Ar atmosphere (Utsugi and Mizushima 1978). Ge–Te is fairly metallic so that the glass is difficult to prepare except around the eutectic composition Ge15 Te85 , and most studies have been done for amorphous films (Takahashi and Harada 1982, Piarristeguy et al. 2009). Studies on other binary alloys, including non-stoichiometric compositions, are still fewer. For As(Ge)–S(Se,Te) glasses, it is interesting to note that, as shown in Fig. 1.17, selenide has the widest glass-forming regions. This feature may be ascribed to the covalent heteropolar bonds and the similar cation–anion sizes in the selenide systems. Other glasses have been less studied. Binary sulfides and selenides alloyed with B, P, and Si are relatively unstable, some being hygroscopic, and accordingly, experimental studies are few (Greaves and Sen 2007). SiS(Se,Te)2 are difficult to prepare and unstable (Jackson and Grossman 2001), which may be due to much smaller Si atoms (ion) than S(Se,Te) (see Fig. 1.9).

1.7.3 Ternary and More Complicated For ternary alloys, we can envisage several kinds of systems: the chalcogen mixture S–Se–Te, the anion-mixed system such as As–S–Se, and the cation-mixed system such as Ge–Sb–Te. Studies on ternary chalcogenide are relatively limited, except

As-S As-Se As-Te Ge-S Ge-Se Ge-Te

Fig. 1.17 Glass-forming regions of typical binary chalcogenide glasses (data from Borrisova 1981)

0

50 Chalcogen concentration [at.%]

100

18

1

Introduction

Fig. 1.18 An oxy-chalcogenide system, xGeO2 –(100–x)GeS2 (Terakado and Tanaka 2008, © Elsevier, reprinted with permission). Three kinds of colors for the same compositions seem to arise from small compositional deviations and different preparation conditions

some selected compositions as follows: First, sputtered Ge–Sb–Te films, specifically Ge2 Sb2 Te5 , have been extensively studied in recent applications to DVDs (see Section 7.4). Second, ionic chalcogenides such as Ga–La–S have been studied as host glasses for doping rare-earth atoms such as Er and Pr. The glass is utilized for light amplifiers (Section 7.2). Third, Ag and Li chalcogenides such as Ag–As–S and LiS–SiS2 attract considerable interest as (super-)ion-conducting glasses (Sections 3.6 and 7.7). Ionic bonds such as –S– Ag+ seem to provide semifree sites for Ag+ . We also note here that all the ionic and ion-conducting glasses cannot be binary. For instance, an ion-conducting Ag2 S becomes necessarily crystalline, but Ag–As(Ge)–S is a glassy ionic conductor. The reason may be speculated straightforwardly. In addition to multi-component chalcogenide glasses, we can prepare oxychalcogenide (Terakado and Tanaka 2008) and chalco-halide glasses (Lucas 1999, Balda et al. 2009). An example, GeO2 –GeS2 glass, is shown in Fig. 1.18. Such glasses may be useful for understanding an intrinsic property of the chalcogenide, since the property changes with the replacement of S by O atoms.

1.8 Preparation Non-crystalline solids with different macroscopic forms can be prepared through a variety of methods (Elliott 1990). Specifically, three forms are utilized, which are bulk, fiber, and film. In addition, we can prepare powdered and nano-scale samples.

1.8.1 Glass (Bulk, Fiber) What kinds of materials can vitrify? The thermodynamics predicts that if a melt is cooled down very slowly, all the melts will crystallize just below the melting temperature. On the other hand, molecular dynamics simulations demonstrate that if a melt is quenched very rapidly (∼1012 K/s) to 0 K, all the melts, even liquid Ar, will solidify into non-crystalline solids (Sano et al. 2004). Practical situations lie in between these extrema.

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Preparation

19

Hence, a more valuable question is the following: What kinds of materials can vitrify under practically available quenching rates slower than ∼107 K/s, which is obtainable in splat cooling (Elliott 1990)? Such a problem was considered as early as 1932 by Zachariasen from a microscopic point of view (Mackenzie 1987). Known criteria for the glass formation arise from kinetic, structural, and chemical factors (Liu and Taylor 1989, Chechetkina 1991, Doremus 1994). Though such analyses are important, persevering work is required for obtaining practical results. And, comprehensive data of the glass-forming region have been collected, e.g., by researchers in eastern Europe (Borisova 1981, Popescu 2000). In practical experiments, even for a fixed system, the glass-forming region depends upon many factors such as the reacting temperature Tq , from which a melt is quenched, quenching rate dT/dt (10−2 –102 K/s), and thermal capacity of quenched samples including an ampoule, which is employed for vacuum sealing of the melt. Figure 1.19 shows an example of reported glass-forming regions for the Ag–As–S system (Yoshida and Tanaka 1995). In addition, it should be underlined that also the property of melt-quenched glasses depends upon preparation procedures, as being exemplified for As2 S(Se)3 (Cimpl et al. 1981, Yang et al. 1986, Tanaka 1987) and GeS(Se)2 (Zhilinskaya et al. 1992, Holomb et al. 2005). Figure 1.20 shows that, in melt-quenched As2 S3 glass, the optical bandgap considerably depends upon the reacting temperature Tq and the quenching rate (Tanaka 1987). After preparation, the ingot may be shaped by polishing and/or annealed for stabilization. In some cases, annealing effects on electronic and thermal properties are substantial (Wang et al. 2007, Allen et al. 2008). For optical experiments, we may need thin samples, which can be prepared by polishing, the thinnest being ∼10 μm (Hamanaka et al. 1977). In addition, squeezing of viscous glasses under heating is a convenient way for obtaining thin bulk samples (Frerichs 1953, Brandes et al. 1970). On the other hand, we may also need thick (long) samples for investigation of low optical attenuations, for which fiber samples can be employed. Such optical fibers

Fig. 1.19 Glass-forming regions of Ag–As–S glass under three (solid, dashed, and dotted lines) different melt-quenching conditions (modified from Yoshida and Tanaka 1995)

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Fig. 1.20 Optical gap energies of g-As2 S3 as a function of the temperature Tq , from which the melt is slowly cooled ∼10 K/s (◦), rapidly quenched 10−2 K/s (•), and rapidly quenched and annealed at the glass transition temperature Tg () (Tanaka 1987, © American Physical Society, reprinted with permission). Tm and Tb depict the melting and the boiling temperature

are produced from glass rods, which are prepared in several ways, and by drawing the rod in inert atmosphere at around the glass transition temperature (Nishii and Yamashita 1998).

1.8.2 Film and Others Thin-film samples are produced in several ways such as evaporation and sputtering (Elliott 1990). The thickness can be varied from ∼10 nm to ∼50 μm. Needless to say, substrate cleaning by chemical and physical methods is very important, specifically for thin (≤500 nm) films. Here, the most serious problem may be the composition deviation along the deposition process. In addition, it is plausible that the composition varies along the film thickness. We should also note that, in general, atomic structures of as-deposited films are substantially different from those in bulk glasses. Deposited films are fairly unstable, which undergo structural relaxation upon storage. Otherwise, a film is annealed at some temperature for stabilization and homogenization, the annealing condition being intensively studied (Choi et al. 2010, Rowlands et al. 2010). For thick films, rapid thermal annealing (Ramachandran and Bishop 2005) seems to be effective for suppressing cracking arising from relatively large thermal expansions (Table 3.1). In addition, the substrate sometimes plays an important role, not only in the thermal expansion but in other properties. The most common substrates may be some oxide glass such as silica and borosilicate. However, a photoinduced phenomenon of As2 S3 on viscous grease (Section 6.3.12) manifests that the substrate exerts great mechanical constraints upon the film. The electrical conductivity may also be important, as seen in a photo-enhanced vaporization (Section 6.3.15). We also employ sapphire and Si wafer substrates, having high thermal conductivity, for suppressing temperature rises under light illumination.

1.8

Preparation

21

Thermal evaporation is the most common preparation method of chalcogenide films having simple compositions such as pure Se. The film property, however, is known to markedly depend upon the temperature of substrates, and when it is ∼50◦ C, a-Se films having high photoconductivity are obtained. It is plausible that the substrate temperature governs the atomic structure, including the ratio of ring and chain molecules and also their size and length. In addition, surprisingly, Suzuki et al. (1987) have demonstrated that mean Se chain lengths and xerographic properties of evaporated Se films depend upon chemical reaction temperature of employed bulk pellets. However, the details remain unknown. Evaporation of compounds is more difficult. For instance, contrary to common features, flash evaporation (through pouring a powdered sample onto a hightemperature boat) of As2 S3 causes substantial compositional deviation (Tanaka 1974). Slow evaporation with a deposition rate of ∼1 nm/s is preferred. Similar results are reported for As2 Se3 (Bando et al. 1991). Another feature, which is worth mentioning, is that GeS2 sublimates, not evaporates. Accordingly, Knudsen-type boats (covered crucibles) give smaller compositional deviations, while the deviation is still substantial as shown in Fig. 1.21 (Tanaka et al. 1984). In addition, as illustrated in Fig. 1.22, the film and bulk with nearly the same composition of GeS2 manifest largely different optical gaps of ∼2.5 and ∼3.2 eV (Tanaka et al. 1984). It should be also mentioned that Chopra’s group (Kumar et al. 1989) has discovered that obliquely deposited As and Ge chalcogenide films have substantially different film structures. Sputtering in Ar gas is also a common technique. Ge2 Sb2 Te5 films for DVD applications can be prepared through dc sputtering (Kato and Tanaka 2005). Ge–As–S(Se) films, which are electrically insulating, can be prepared using radiofrequency sputtering (Utsugi and Mizushima 1980, Tan et al. 2010). Oxide films such as SiO2 can also be radio-frequency sputtered, while the oxygen content tends

Fig. 1.21 Composition deviations in As100–x Sx and Ge100–x Sx films in vacuum evaporation. The compositions of evaporated films tend to approach the stoichiometric compositions As2 S3 and GeS2

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Fig. 1.22 Optical absorption edges of GeS2 and As2 S3 in bulk samples (solid lines), as-evaporated films (dotted lines), and annealed films (dashed lines)

to decrease. Accordingly, reactive sputtering using mixed Ar and oxygen gas is preferred. In general, the sputtering seems to produce more dense films that those prepared by the evaporation. Other thin-film preparation methods have also been employed. Spin coatings using appropriate solutions, originally developed for organic resists, provide a nonexpensive procedure for preparing thin chalcogenide films (Chern and Lauks 1982, Kohouteka et al. 2007, Song et al. 2010); the methods do not need vacuum. Glow discharge deposition, a technique widely employed for preparing a-Si:H films, has also been applied to deposition of hydrogenated chalcogenide films such as As(Ge,Si)–S(Se):H (Šmíd and Fritzshe 1980, Nagels et al. 2003). Chemical vapor deposition is also employed for obtaining hydrogenated samples (Katsuyama et al. 1986, Curry et al. 2005). Laser ablations, shown in Fig. 1.23, using pulsed (Hansen and Robitaille 1987, Wang et al. 2007) and continuous-wave (González-Leal et al. 2009) sources have been applied to As2 S3 and other materials. A pulsed method can produce not only films, but fibrous and spherical samples (Juodkazis et al. 2006).

Fig. 1.23 Two arrangements of laser ablation: (a) conventional type and (b) irradiation through transparent substrates

1.9

Dependence upon Experimental Variables

23

In addition, less common methods have been employed. Examples are sol–gel production of Ge–S films (Martins et al. 1999) and other chemical reactions, which have produced As2 S3 powders (Onodera et al. 1969), GeSx aerogels (Kalebaila et al. 2006), Se films (Peled 1986), Sb2 S3 films (Grozdanov et al. 1994), and nano-samples of As–S (Lee et al. 2007) and Se–Te (Kaur and Bakshi 2010). Amorphization by mechanical milling, which was developed for producing amorphous metals, has also been applied to Ge-chalcogenides (Tani et al. 2001), Se (Tani et al. 2001, Zhao et al. 2004), and Li-chalcogenide glasses (Minami et al. 2010).

1.9 Dependence upon Experimental Variables Measurements of some physical property as a function of thermodynamic variables are common tactics for understanding the property in solid-state science. Here, the thermodynamic variables are, in general, temperature and pressure. Temperature variations modify atomic vibrations, which may provide similar effects, irrespective of atomic periodicity, upon thermal expansions, heat capacities, etc. (see Section 3.4). On the other hand, the compression may cause different behaviors in crystals and non-crystals, as exemplified by Si and Se in the following. Envisage an ideal Si single crystal, a cubic crystal with the diamond structure consisting of only one type of bond. If it is subjected to hydrostatic compression, the atomic distance and cell dimension will be elastically reduced, which may be recovered to the initial state by depressurizing. However, if the material is a-Si(:H), which contains some atomic voids, the compression may preferentially collapse the voids. Actually, as shown in Fig. 1.24 (left), linear compression behaviors in c-Si and a-Si:H are substantially different. In a-Si:H, plastic shrinkage appears, and depressurizing to 1 atm produces densified samples (Minomura 1984), which will relax gradually. Similar compression behaviors can be pointed out for g-SiO2 (Pathasarathy and Gopal 1985). The situations are different in Se and chalcogenide glasses (Durandurdu 2009, Vaccari et al. 2009), which contain covalent and van der Waals bonds. Irrespective of c- and a-Se, hydrostatic pressure compresses preferentially the van der Waals bond first, and after that, the bond angle may be modified, the bond length being intact until ultimate compression or structural transitions occur. These features are not very different in c- and a-Se, as is suggested from the compression behaviors in Fig. 1.24 (left). In the Se solids, pressure effects are prominent due to the soft van der Waals bond, but the effect of disorder is comparatively small. For non-crystalline solids, the pressure study has provided fruitful insights. The compression can produce novel non-crystalline materials (Sen et al. 2006, Brazhkin et al. 2010) including pure Ge (Bhat et al. 2007). Valuable insights have also been obtained from uniaxial compression, which is assumed to change an isotropic amorphous structure to anisotropic (Tallant et al. 1988) or can produce anisotropic glasses (Tanaka 1989b). It should also be mentioned that the advent of diamond

24

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Introduction

Fig. 1.24 A diamond anvil cell for pressure optical experiments

anvil cells (Fig. 1.25) and related techniques since ∼1970 (Jayaraman 1986) has stimulated pressure experiments, specifically those using laser and x-ray beams. In addition to the thermodynamic studies, two experiments, which are more or less unique to amorphous materials, are on composition variations and preparation procedures. Importance of compositional studies, though the experiments are more or less monotonous, in amorphous materials should be emphasized. Specifically, since the covalent chalcogenide glass can be compositionally varied in atomic ratios, studies on continuous composition variations provide important insight, an example

Fig. 1.25 Linear compressions −L(P)/L (left) and optical bandgaps Eg (P) in several crystalline (c-) and amorphous materials as a function of hydrostatic pressure (Tanaka 1989a). Polyethylene and polyacetylene are abbreviated as PE and PA. In amorphous Ge and As, phase transitions to metallic crystalline phases occur at 60 and 40 kbar. For GeS2 , the film (f) and the melt-quenched glass (g) show different behaviors, while for As2 S3 no big differences appear

References

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being the concept of magic numbers, as will be described in Section 3.5. In addition, studies on preparation procedures are also invaluable due to quasi-stability (Section 1.3). It should be noted that such studies on composition and preparation are, in principle, needless or non-existing for (ideal) single crystals such as Si and GaAs.

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Introduction

Suzuki, K., Matsumoto, K., Hayata, H., Nakamura, N., Minari, N.: Mass spectroscopic study of evaporated Se films and melt-quenched Se glasses. J. Non-Cryst. Solids 95–96, 555–562 (1987) Takahashi, T., Harada, Y.: Photoemission study of the crystallization of amorphous Te film. J. NonCryst. Solids 47, 417–420 (1982) Tallant, D.R., Michalske, T.A., Smith, W.L.: The effects of tensile stress on the Raman spectrum of silica glass. J. Non-Cryst. Solids 106, 380–383 (1988) Tan, W.C., Solmaz, M.E., Gardner, J., Atkins, R., Madsen, C.: Optical characterization of a-As2 S3 thin films prepared by magnetron sputtering. J. Appl. Phys. 107, 033524 (2010) Tanaka, K.: Evidence for reversible photostructural change in local order of amorphous As2 S3 film. Solid State Commun. 15, 1521–1524 (1974) Tanaka, K.: Configurational and structural models for photodarkening in glassy chalcogenides. Jpn. J. Appl. Phys. 25, 779–786 (1986) Tanaka, K.: Chemical and medium-range orders in As2 S3 glass. Phys. Rev. B 36, 9746–9752 (1987) Tanaka, K.: Pressure studies of amorphous semiconductors. In: Borossov, M., Kirov, N., Vavrek, A. (eds.) Disordered Systems and New Materials, pp. 290–309. World Scientific, Singapore (1989a) Tanaka, K.: Pressure-induced squeezing phenomenon in uniaxially compressed glass. Jpn. J. Appl. Phys. 28, L679–L681 (1989b) Tanaka, K., Kasanuki, Y., Odajima, A.: Physical properties and photoinduced changes of amorphous Ge-S films. Thin Solid Films 117, 251–260 (1984) Tani Y, Shirakawa Y., Shimosaka A., Hidaka J.: Crystalline-amorphous transitions of Ge-Se alloys by mechanical grinding. J. Non-Cryst. Solids 293, 779–784 (2001) Terakado, N., Tanaka, K.: The structure and optical properties of GeO2 –GeS2 glasses. J. NonCryst. Solids 354, 1992–1999 (2008) Utsugi, Y., Mizushima, Y.: Photostructural change of lattice-vibrational spectra in Se-chalcogenide glass. J. Appl. Phys. 49, 13470–3475 (1978) Utsugi, Y., Mizushima, Y.: Photostructural change in the Urbach tail in chalcogenide glasses. J. Appl. Phys. 51, 1773–1779 (1980) Vaccari, M., Garbarino, G., Yannopoulos, S.N., Andrikopoulos, K.S., Pascarelli, S.: High pressure transition in amorphous As2S3 studied by EXAFS. J. Chem. Phys. 131, 224502 (2009) Wang, R.P., Rode, A., Madden, S., Luther-Davies, B.: Physical aging of arsenic trisulfide thick films and bulk materials. J. Am. Ceram. Soc. 90, 1269–1271 (2007) Weinstein, B.A., Zallen, R., Slade, M.L.: Pressure-optical studies of GeS2 glasses and crystals: Implications for network topology. Phys. Rev. B 25, 781–792 (1982) Yang, C.Y., Paesler, M.A., Sayers, D.E.: First crystallization of arsenic trisulfide from bulk glass: The synthesis of orpiment. Mater. Lett. 4, 233–235 (1986) Yoshida, N., Tanaka, K.: Photoinduced Ag migration in Ag-As-S glasses. J. Appl. Phys. 78, 1745–1750 (1995) Zallen, R.: The Physics of Amorphous Solids. Wiley, New York, NY (1983) Zanotto, E.D., Coutinho, F.A.B.: How many non-crystalline solids can be made from all the elements of the periodic table? J. Non-Cryst. Solids 347, 285–288 (2004) Zhao, Y.H., Lu, K., Liu, T.: EXAFS study of mechanical-milling-induced solid-state amorphization of Se. J. Non-Cryst. Solids 333, 246–251 (2004) Zhilinskaya, E.A., Valeev, N.Kh., Oblasov, A.K.: Gex S1−x glasses. II. Synthesis conditions and defect formation. J. Non-Cryst. Solids 146, 285–293 (1992) Zingaro, R.A., Cooper, W.C. (eds.): Selenium. Van Nostrand Reinhold Company, New York, NY (1974)

Chapter 2

Structure

Abstract Atomic and microscopic structures of chalcogenide glasses are discussed from theoretical and experimental points of view. Starting with discussion on an ideal glass structure, we will see continuous studies performed for grasping atomic structures in disordered materials. Experimental methods and deduced results for the short-range and medium-range structures (orders) in glasses are introduced. Structural defects, which are likely to produce localized states in the bandgap, are discussed. In addition to these atomic structures, we shed light upon inhomogeneity and nano-structures in chalcogenide glasses. Keywords Density · FSDP · Boson peak · Distorted layer · Wrong bond · Dangling bond · Homogeneity · Multi-layer

2.1 Ideal Structure What is an ideal glass structure? For a crystal, we can envisage its ideal structure as one in which the structure is perfectly periodic with no defects at all (Fig. 2.1). The atomic position can be uniquely determined. Such a structure could conceptually be obtained through infinitely slow cooling of the corresponding melt to 0 K. In a simplified theory, crystal surfaces are tentatively neglected under the so-called periodic boundary condition, and the structure becomes a starting framework for analyses of macroscopic properties (Kittel 2005). Or, in the exact opposite, we can envisage a completely random atomic structure in an ideal gas. In this case, the atomic position can neither be predicted nor fixed. But, its property such as pressure at a given temperature can theoretically be evaluated through statistical mechanics for an assembly

Fig. 2.1 Two-dimensional views of (a) crystal (close packed), (b) liquid and glass (dense random packing), and (c) gas 29 K. Tanaka, K. Shimakawa, Amorphous Chalcogenide Semiconductors and Related C Springer Science+Business Media, LLC 2011 Materials, DOI 10.1007/978-1-4419-9510-0_2,

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of point-like substances (atom or molecule) having no interactions. The physical properties are uniquely fixed under a fixed temperature and volume. Having seen these ultimate examples, we are tempted to assume that the ideal should imply a uniquely defined structure, at least, in a statistical sense. Ideal must be unique. Can we imagine such an ideal structure for a glass? It seems impossible to envisage the unique structure for a disordered lattice. For instance, in the two local structures illustrated in Fig. 2.2, both including fourfold coordinated one-kind atoms in (a) a 6-atom ring with a dangling bond and (b) a strained but completely bonded 5-atom ring, which has a smaller total (electron plus lattice) energy? The structure in (b) can be regarded as a part of the famous Polk model proposed for a-Si (Turnbull and Polk 1972), which contains no dangling bonds. Several authors may assume that such continuous random networks are ideal. But, the structure must be highly strained. And, even for such fully connected structures, a variety of atomic ring structures with different formation energies possibly exist. It seems that we cannot envisage an ideal glass structure. Disorder implies a lot of varieties between the two ideal (ultimate) structures of crystal and gas. The amorphous structure is neither periodic, as that in a crystal, nor completely random, as that in an ideal gas. The non-crystalline structure spans a wide range between the completely perfect and the completely random structure: single crystal (periodic) ← non-crystal → ideal gas (completely random). We must consider a variety of intermediates. It should be noted, however, that liquid has also a disordered structure. Then, what is the difference between a liquid and an amorphous material? In contrast to the liquid, which is thermodynamically equilibrated, the non-crystalline solid is in quasi-equilibrium, or is meta-stable. Strictly speaking, an amorphous material does not take a thermodynamically defined phase, but it takes just a spontaneous state, which necessarily changes with time. After infinitely long storage, the glass is believed to relax to a crystal. Actually, we know that a-Se films crystallize from surfaces within a few weeks when stored in humid atmospheres. We also know that the surface of glassy flakes, which are dug at prehistoric ruins, often appears micaceous or crystalline. In addition, a glass property depends upon preparation methods. Actually, as shown in Fig. 2.3, as-evaporated and annealed As2 S3 films give markedly different x-ray diffraction patterns.

Fig. 2.2 Two bonding structures for fourfold coordinated atoms such as Si. (a) A 6-membered ring with a dangling bond, and (b) a strained 5-membered ring

2.2

Practical Structure

31

Fig. 2.3 X-ray diffraction patterns of As2 S3 films in an as-evaporated state (◦) and after annealing (•) at 180◦ C (DeNeufville et al. 1973, © Elsevier, reprinted with permission)

Nevertheless, meta-stability has provided an unresolved problem on the uniqueness of glassy states. We here recall the so-called Kauzmann’s paradox, detailed in Section 3.2. The most stable glass may be obtained at the Kauzmann temperature TK , since the free energy can be uniquely defined. Kauzmann’s glass may be ideal. However, the idea is macroscopic, and we have never obtained the glass nor seen the atomic structure at the conceptual temperature TK .

2.2 Practical Structure Determination of atomic bonding structures is a prerequisite in solid-state science. For crystals, the structure can be determined in principle through analyses of Bragg peaks in x-ray diffraction patterns. However, as exemplified in Figs. 2.3 and 2.4, the non-crystalline solid does not provide sharp Bragg peaks but gives

Fig. 2.4 X-ray diffraction patterns of glassy and crystalline (hexagonal) GeO2 , obtained using the Cu Kα line, showing halos and sharp peaks

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2 Structure

Fig. 2.5 Comparison of the densities for glassy and crystalline As2 (Se-Te)3 alloys (Thornburg 1973, © Springer, reprinted with permission)

only broad halos. Considering such observations, Zachariasen (1932) proposed the so-called continuous random network model for oxide glasses such as Si(Ge)O2 , while the real structure could not be determined. We here see fatal limitations of the traditional structural analysis. The limitation still remains, posing the biggest problem in science on non-crystalline materials. Then, how can we get insight into the atomic structure? We can see just the tip of an iceberg as described below. A rough idea can be grasped from the macroscopic density (Fig. 2.5). It is known for simple glasses that the glass is less dense than the corresponding crystal by 10–20% (Thornburg 1973, Hobbs and Yuan 2000), which varies with preparation procedures and storage after preparation. This observation suggests that atomic packing in the glass and the crystal is not very different. More generally, the densities of a glass, the corresponding crystal, and the melt can be regarded roughly as the same in comparison with that in the gas, which has nearly completely random and time-varying atomic (molecular) structures with an average separation of ∼5 nm at 1 atm (Fig. 2.1). Specifically, since the glass is produced from the melt, it is reasonable to envisage that the structures have some resemblances. We then assume that the atomic potential, which fixes the bond distance and atomic coordination, governs the density in all condensed matters. To analyze the amorphous structure in atomic scales, we can classify it into two elements, as shown in Fig. 2.6: normal bonding structures and defective structures (Ovshinsky and Adler 1978). A normal bond can be defined as topologically

Atomic structure

Normal bonding structure short-range ~ coordination number, bond length, bond angle medium-range ~ dihedral angle, ring, intermolecular and dimensional structure Defects ~ ill-coordination such as dangling bond and wrong bond

Fig. 2.6 A classification of amorphous atomic structures

2.2

Practical Structure

33

Fig. 2.7 Structure models of (a) g-SiO2 (three-dimensional continuous random network), (b) g-As2 S3 (two-dimensional distorted layers), (c) g-Se (one-dimensional entangled chains), and (d) c-SiO2 . In (a) and (d), Si and O are shown by circles with four and twofold coordination. In (b), As and S are shown by solid and open circles with three and twofold coordination. Note that (a) includes a small ring and an E center, (b) contains wrong bonds (As−As and S−S), and (c) contains a few ring molecules. The bond lengths are 0.16 nm in SiO2 , 0.23 nm in As2 S3 , and 0.24 nm in Se so that side lengths of these illustrations are 2–3 nm

the same atom connection with that existing in the corresponding crystal. In SiO2 glass, it is SiO4/2 (≡Si–O–) tetrahedral connections, as illustrated in Fig. 2.7a. The normal bonding structure can further be divided into the short (0.5 nm) and the medium-range (0.5−3 nm) structure, as will be described later. On the other hand, the defective structure resembles a defect in practical crystals. The examples are an E center in g-SiO2 , which is a Si dangling bond (≡Si•), and a wrong bond (Halpern 1976), i.e., a Si homopolar bond (≡Si−Si≡), both non-existing in the ideal SiO2 crystal. We here underline that these defective structures are point-like defect (<0.5 nm). Defects such as dislocations and stacking faults, which sometimes play important roles in crystals, do not exist in amorphous materials. We also note that the point-like defect is spatially isolated from each other in normal bonding matrices. The isolation may be a consequence arising from the non-existence of long-range atomic periodicity in the glass. If the Si wrong bonds would gather, the assembly might become a Si nano-crystal. A note on small rings should be added. As known, c-SiO2 takes a variety of atomic structures, in which the most common is the quartz, or β-quartz (the hightemperature form, Fig. 1.1). The crystal structure is hexagonal (Fig. 2.7d) consisting of SiO4/2 tetrahedra, which contain 3 (6 atom)- and 6-membered (12 atom) rings. On the other hand, in g-SiO2 , it is plausible that a variety of rings exist. And, some researchers assume small rings such as 3- and 4-membered rings as defects. However, since the structure has spatial extension of ∼1 nm and the concentration may be greater than ∼1 at.% in some cases (Kohara and Suzuya 2005), it seems to be better to regard such small rings as strained normal bonds. As will be described later, the present classification is more useful to consideration of electronic structures, since the relaxed and strained normal bonds govern, respectively, the band and band-edge electronic states. On the other hand, the defects tend to produce mid-gap states. In the following, we will see how the non-crystalline structure has been explored. In principle, the normal bonding structure has been investigated through structural

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2 Structure

measurements using, e.g., x-ray diffraction and EXAFS (extended x-ray absorption fine structures) (Elliott 1990). We note here that, in these x-ray experiments, recent progress of synchrotron radiation sources can dramatically shorten the exposure time (∼40 ps) and increase the spatial resolution (∼100 nm) of the inspected area (Tanaka et al. 2009). In addition to these and other direct structural studies, versatile and circumstantial observations are also valuable for sketching the structure. For instance, pressure dependence of optical gaps (Fig. 1.25) gives insight into the amorphous structure, through comparing the result with those obtained for the corresponding crystal. Also, computer simulations have become valuable tools as described in Section 2.6.

2.3 Short-Range Structure 2.3.1 Experiments Provided that a glass is homogeneous and has a simple composition, we can experimentally determine its short-range structure (Greaves and Sen 2007). Here, the short-range structure is determined by three parameters: the coordination number Z of atoms, the bond length r, and the bond angle θ . The short-range structure can be inferred from radial distribution function ρ(r), which can be calculated from x-ray (e-beam and neutron) diffraction patterns, an example being shown in Fig. 2.8. Let us assume an elementary system such as a-Se; the diffracted intensity I at an x-ray wavenumber Q can be written as (Elliott 1990) I(Q) ∝ f (Q)2

4π r2 [ρ(r)−ρ0 ] (sin Qr)/(Qr) dr

with Q = 4π sin θ s/λ, (2.1)

where f is the atomic scattering factor, ρ 0 an average atomic density, 2θ s the scattering angle, and λ the x-ray wavelength. Accordingly, from measured I(Q), we can calculate ρ(r), which provides Z, r, and θ , respectively, from the first-peak intensity,

Fig. 2.8 Diffracted x-ray intensity I(Q) and calculated radial distribution function ρ(r) of a-Se (modified from Andonov (1982))

2.3

Short-Range Structure

35

Fig. 2.9 An illustration of a c-Se chain. The bond length is ∼0.24 nm, bond angle ∼103◦ , and dihedral angle (the angle between the triangular planes defined by ABC and BCD atoms) ±102◦

the first-peak position r1 , and the second-peak position r2 with r1 value. Note that this equation is useful also for crystals. Debye equation gives a deduced form of the above equation for a pair of atoms which are randomly oriented, as those in gas, liquid, and glass (Elliott 1990): I(Q) ∝

fi fj sin(Qrij )/(Qrij ),

(2.2)

ij

where rij is the distance between an atomic pair. We see that I(Q) of disordered materials appears as a summation of sinc functions (sin x/x), which provide broad halo patterns. Here, a straightforward analysis shows the following: Reflecting the functional shape, the halo at the smallest wavenumber gives the strongest peak at Q1 , which satisfies Q1 rij ≈ 7.7. This relation is useful for estimating the responsible pair distance rij (Tanaka 1990). However, for multi-component glasses, direct applications of the above procedures are difficult. We cannot determine the structure from only one diffraction pattern, since f changes with atom species. We may then utilize anomalous x-ray diffraction methods (Elliott 1990), in which f becomes also a function of x-ray wavelengths. If a glass contains n kinds of atoms, diffraction patterns using n +1 x-ray wavelengths can give n +1 simultaneous (coupled) equations: I(Q, λ) ∝

fi (Q, λ)fj (Q, λ)

4π r2 [ρij (r) − ρ0 ] (sin Qr)/(Qr) dr,

(2.3)

ij

which can uniquely determine ρij (r) for ij pairs (i and j ≤ n). The isotope-substituted neutron diffraction follows a similar principle (Petri et al. 2000), in which f changes with isotopes. Provided that the atomic discrimination is successful, these methods may give longer-range atomic correlation (Hosokawa et al. 2009) than that given by EXAFS, the principle being described below. EXAFS may give more direct information for the structure in multi-component systems (Elliott 1990, Armand et al. 1992, Vaccari et al. 2009). In EXAFS experiments, x-ray transmittance (or absorbance) of a sample of interest is measured as a function of x-ray energy E (= 2π c/λ). As illustrated in Fig. 2.10, the absorbance abruptly changes at a core-electron excitation energy, e.g., at the K edge EK , and

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2 Structure

Fig. 2.10 A schematic of EXAFS (left) and its emerging mechanism (right)

small intensity modulation “EXAFS” χi (E) appears just above this threshold energy at around E − EK ≤ 500 eV. Why does such an oscillation appear? The oscillating EXAFS χi (k) can be regarded as an x-ray transmission spectrum which is modulated by the interference of x-ray excited electron waves with a wavenumber of k = 2π/λe = [2m(E − EK )]1/2 /, where λe is the electron wavelength (∼0.2 nm) and m is the electron mass. In Fig. 2.10 (right), the electron wave spreading from the central atom and those being reflected back by surrounding (lower right) atoms interfere, which modulates x-ray transmittance through electron excitation efficiency.1 By scanning the x-ray energy E, the interference varies, and accordingly, the x-ray transmission spectrum has information of the surrounding atoms (atomic species, distance, number). Mathematically, at a slightly higher x-ray energy E than a core-electron excitation energy EK of specified single atoms i, χi (k) contains a term as (Elliott 1990) χi (k) ∝

Zij exp(−2rij /L) sin{2 krij + ϕj (k)},

(2.4)

j

where Zij is the number of atoms (coordination number) at a distance of rij around a specified i atom, L is the electron mean free path, and ϕj (k) is the phase change occurring when an excited electron is reflected at a neighboring atom j. If the phase change can be known using a reference material as related crystals, we can determine rij from oscillating EXAFS spectra. (In other words, when analyzing EXAFS oscillations, we implicitly assume the species of neighboring atoms.) The amplitude of χi (k) is proportional to the coordination number Z of the specified atom, i.e., the number of atoms reflecting the electron waves, which can also be determined with lower accuracy depending upon the value of L and so on. 1 Note that, in the optical Fabry–Perot-type interference, the sinusoidal fringe in transmission spectra is produced by modulation of multiply-reflected light. For the EXAFS, we may use a metaphor: imagine that we (x-ray photons) are walking in a swimming pool, producing water waves (electron waves) and feeling reflected waves (electron waves) from pool sides (surrounding atoms). Our walk may be smooth or difficult, depending upon the interference by the waves.

2.3

Short-Range Structure

37

We underline three characteristics for the EXAFS. First, the EXAFS is useful specifically for multi-component systems. Since EK is fixed by an atom, we can determine peripheral structures around the specified atom i. Second, as imagined from the principle, Fig. 2.10 (right), it is more or less difficult to obtain a second nearest-neighbor peak in close-packed atomic structures from EXAFS spectra. Finally, as known from the principle, EXAFS experiments prefer x-ray beams having not characteristic peaks, but smooth and continuous spectra. Accordingly, the conventional x-ray tubes are less appropriate. Intense beams obtained as synchrotron orbital radiation are much effective to reduce exposure time and improve spatial resolution. As an example, an EXAFS result around Ge in crystalline and glassy GeS2 is shown in Fig. 2.11 (Armand et al. 1992). We see in the right figure the strong first peak at ∼0.2 nm (Ge−S distance) and two weaker peaks at ∼0.26 and ∼0.31 nm, the latter being identified to the two kinds of second-nearest Ge−S−Ge pairs (in edgeand corner-sharing tetrahedra) illustrated in the inset. The peak positions are very similar to those of the crystal, which evinces existence of the short-range structural order in this glass. Direct images of amorphous structures can be obtained using two methods. Transmission electron microscopy is able to provide direct images and also diffraction patterns. For instance, Young and Thege (1971) take electron diffraction patterns of a-As2 S3 . However, the image for insulating materials such as sulfides and oxides tends to become blurred due to charge-up. To the authors’ knowledge, no atomic images have been obtained for such insulating glasses. On the other hand, scanning tunneling and atomic force microscopy have been applied for obtaining surface images (Tominaga et al. 1992, Ichikawa 1995). However, we may have some doubts about reliability and/or reproducibility of the surfacesensitive images. Nevertheless, atomic images obtained for Se films (Peled et al. 1995) and cleaved surfaces of oxide glasses (Poggemann et al. 2003) seem genuine. Specifically, Poggemann et al. (2003) take a histogram of obtained atomic images for a few glasses, as exemplified for g-SiO2 in Fig. 2.12, which appears

Fig. 2.11 An EXAFS spectrum for Ge in c-GeS2 (left) and RDFs for Ge in c- and g-GeS2 (right). The inset in the right-hand side shows the distances corresponding to the three peaks (Armand et al. 1992, © Elsevier, reprinted with permission)

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2 Structure

Fig. 2.12 An atomic force microscopy image of a vacuum-fractured surface of g-SiO2 (left) and the distribution of atomic (white regions) distances (right) (Poggemann et al. 2003, © Elsevier, reprinted with permission), which is compared with an x-ray radial distribution function (RDF) reported by Kohara and Suzuki (2005)

to be consistent with the radial distribution function ρ(r) deduced from x-ray patterns (Kohara and Suzuya 2005). Further studies including comparisons of surface structures of a glass and the corresponding crystal will be very interesting. In addition to these direct structural experiments, there are less direct ones. Those are vibrational spectroscopy (infrared transmission, Raman scattering, and inelastic neutron scattering), several spin-related methods, and photoelectron spectroscopy. Infrared and Raman spectroscopy measure the intensity and frequency (wavenumber) of vibrational modes (Elliott 1990). As known, the frequency is written as ω ∼ (κ/M)1/2 , where κ is the force constant of a spring connecting a pair of atoms (or atomic units) and M is the atomic mass. Accordingly, the peak frequency gives insight into the vibrational mode, which is an optical phonon in crystals (Kittel 2005) or a molecular vibration in disordered materials, e.g., vibrations of AsS3/2 in g-As2 S3 , as shown in Fig. 2.13. On the other hand, the spectral intensity I(ω, T) is written for disordered materials as (Shuker and Gammon 1970, Martin and Brenig 1974) I(ω, T) = g(ω) C(ω)[n(ω, T) + 1]/ω,

(2.5)

where g(ω) is the density of vibrational modes, C(ω) the opto-vibrational coupling constant, and n(ω, T) the Bose–Einstein (Planck) distribution. Here, it is known that infrared transmission and Raman scattering spectroscopy follow different selection rules in the coupling constant. However, disordered structures tend to make the selection rules loose. In addition, Raman scattering spectroscopy becomes experimentally more useful, due to the recent progress of lasers and imaging detectors at visible to near-infrared wavelengths. We can obtain not only the conventional Raman scattering spectra (Yannopoulos and Andrikopoulos 2004) in short exposure times for small probe areas (1 μm), but also resonant (Tanaka and Yamaguchi 1998) and nonlinear (Klein et al. 1977) Raman scattering spectra. Therefore, Raman scattering spectroscopy becomes more commonly employed.

2.3

Short-Range Structure

39

Fig. 2.13 Raman scattering spectra of (a) glassy, (b) as-evaporated, and (c) crystalline As2 S3 . Responsible vibrational modes are shown for (a)

As an example, Fig. 2.13 shows Raman scattering spectra of glassy, asevaporated, and crystalline As2 S3 . The broad and relatively sharp spectra of the glass and the as-evaporated film suggest that these are cross-linked and molecular, respectively (Lucovsky et al. 1975, Malyj and Griffiths 1987). On the other hand, the sharp peaks in the crystal correspond to optical phonons near the G point in the Brillouin zone (Kittel 2005). Spin-related methods can probe peripheral structures around a spin through its resonance frequency, peak width, etc. (Elliott 1990). Related studies for chalcogenide glasses include electron spin resonance (ESR) of Mn2+ in Mn-doped As–Se(Te) (Watanabe et al. 1976), nuclear magnetic resonance (NMR) of 31 P in P–Se (Lathrop and Eckert 1993) and 77 Se in selenide compounds (Bureau et al. 2004, Gjersing et al. 2010, Kibalchenko et al. 2010), nuclear quadrupole resonance (NQR) of 75 As in As–S(Se,Te) (Taylor et al. 2003), and Mössbauer spectroscopy of 125 Te in As–Te (Tenhover et al. 1983). These studies owe more or less the specific samples and/or measuring instruments, and accordingly, fixed groups have published their results. Finally, x-ray photoelectron spectroscopy (XPS) of core-electron states can probe the valence of constituent atoms through comparing with some references. It can discriminate Ge4+ and Ge2+ in Ge–S glasses (Takebe et al. 2001) and peripheral circumstances around Ge in a-Ge1 Sb2 Te4 films (Klein et al. 2008) and Ge–Se glasses (Golovchak et al 2009).

2.3.2 Observations Direct and indirect experimental studies suggest that the short-range (≤0.5 nm) structure of a glass is similar to that in the corresponding crystal. An example for Se is summarized in Table 2.1. The coordination number Z seems to satisfy the

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2 Structure

Table 2.1 Comparison of atomic parameters in c-Se (hexagonal) and g-Se (Andonov 1982)

Hex Se g-Se

Z

r (nm)

θ

Φ

ρ (g/cm3 )

2.0 2.0 ± 0.04

0.23 0.23 ± 0.002

105◦ 105±0.5◦

102◦ 70–110◦

4.80 4.25

Z is the atomic coordination number, r the bond length, θ the bond angle, Φ the dihedral angle (see Fig. 2.9), ρ the density

Table 2.2 Bond lengths (in nm) and bond angles around the VIb atoms (in parentheses) in the VIb elemental materials (O, S, Se, and Te) and amorphous As2 O(S,Se,Te)3 and GeO(S,Se,Te)2 . The bond angle in a-GeTe2 is unclear

Elemental AsGe-

O

S

Se

Te

0.12 in O2 0.18 (∼130◦ ) 0.18 (∼105◦ )

0.21 (106◦ ) 0.23 (∼100◦ ) 0.22 (80–110◦ )

0.23 (105◦ ) 0.24 (∼105◦ ) 0.24 (80–100◦ )

0.29 (103◦ ) 0.27 (∼90◦ ) 0.26 (?)

so-called 8−N rule (Mott and Davis 1979), where N is the atomic group number in the previous IUPAC form, with an accuracy of ∼10%, which may reflect experimental uncertainty and effects of dangling bonds. The bond distance r is fixed with an accuracy of r/r ≈ 1%. The bond angle also shows a similar result in Se. However, for alloys (Table 2.2), it seems difficult to accurately determine the bond angle, which distributes roughly at θ/θ ≈ 5 − 10%, where θ is the angle for a group VIb atom such as the Si–O–Si angle. (Note that the angle is not uniquely fixed even in the crystal, which contains different kinds of atomic units.) On the other hand, experiments show that the cation angle, such as O–Si–O and S–As–S, is more tightly fixed due to steric restrictions. In short, we regard that there exists the shortrange structural order in glasses. Note that the fluctuation ratios of r (∼ 1%) and θ (5–10%) imply comparable strain energies in bond distance and angle, kr (r)2 ≈ kθ (rθ)2 , since kθ /kr ≈ 1/10 in the force constants (Lucovsky et al. 1975). This result suggests that an energetic equilibrium is satisfied in the short-range scale. In more detail, there exist some variations in the short-range structures. First, the coordination number, which is a direct consequence of the electron configuration s2 p4 of the group VIb atoms, is modified when ionic and metallic characters are added. As described in Section 1.5, the metallic effect is appreciable in tellurides. Second, the bond length r increases in proportion to the period (2–5) in the periodic table, e.g., from 0.12 to 0.29 nm in the elements (Table 2.2), in accordance with the atomic size (Fig. 1.9). Third, and which should be underlined, we see that the bond angles are appreciably different between the oxide and the chalcogenide. As listed in Table 2.2, it is ∼130◦ in As2 O3 and ∼100◦ in As2 S(Se,Te)3 , which may be approximated very roughly to 180◦ (ionic) and 90◦ (covalent). These characteristic angles

2.4

Medium-Range Structure

41

are favorable to produce the so-called corner-shared and edge-shared configurations (see Fig. 2.15), which will be connected to the medium-range structure. Having seen the chemical bonding in elemental and stoichiometric binary glasses, we turn to more complicated glasses, including non-stoichiometric binary and ternary glasses. It was mentioned in Section 1.6 that the oxide can produce the mixtures, such as SiO2 –Na2 O, which consist of stoichiometric units, SiO2 and Na2 O. Naturally, as shown in Fig. 1.13, the glass contains only Si–O bonds, which are relatively covalent, and Na–O ionic bonds. The homopolar bond such as O−O may be included in a defective level. In contrast, it is straightforward to prepare non-stoichiometric chalcogenide glasses, e.g., As(Ge)–S(Se,Te) in the limited glassforming regions (see Fig. 1.17). As(Ge)-rich and As(Ge)-deficient glasses, which deviate from the stoichiometric compositions As2 S(Se,Te)3 and GeS(Se)2 , necessarily contain homopolar bonds, As(Ge)–As(Ge) and S(Se,Te)–S(Se,Te), respectively, in addition to the heteropolar bond As(Ge)–S(Se,Te). And, As15 S85 glass is demonstrated to be a mixture of As–S networks and S molecules (Tsuchihashi and Kawamoto 1971). Here, a principle on the atomic bonding seems to be the preference of heteropolar bonds (As–S, As–Te, Ge–S, etc.), since these have stronger bond energies than those of the homopolar bonds (As–As, S–S, etc.) (see Table 2.4). In non-stoichiometric ternary alloys such as As–S–Se, Ge–Sb–Te, and Ag(Cu)– As–S, we will face more critical problems. For instance, in Ge–As–S, which bond is preferred between Ge–S and As–S? Difference of the bond energies is subtle as listed in Table 2.4. We may also wonder if a Ge–As–S glass possesses an intermediate property between those in Ge–S and As–S glasses. Universal understandings, which should take also the quasi-equilibriumness into account, have not been obtained. As we have seen in this section, the short-range structure is determined by the chemical bonding, and accordingly, the existence of structural orders is plausible. Nevertheless, no further structural order could be envisaged, e.g., in the continuous random network model originally proposed by Zachariasen (1932). But, this view has been completely reformed as described below.

2.4 Medium-Range Structure Historically, the first implication of a medium-range order in glasses is believed to have been presented by Vaipolin and Porai-Koshits (1963) for g-As2 S(Se,Te)3 . Successive studies have demonstrated the existence of some medium-range structural orders with scales of 0.5–3 nm, at least, in simple glasses. However, the “some” order remains controversial, because there are no experimental tools explicitly determining the atomic structure having such scales in disordered materials. This has become one of the biggest subjects covering structures and properties in glasses. In the following, we will see the present status of our understanding on the medium-range order from short to longer scales (Elliott 1991), not along a historical sequence.

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2 Structure

2.4.1 Small Medium-Range Structure The short side length of ∼0.5 nm of the medium-range structure must be connected to the short-range structure covering atomic structures up to the second nearest neighbors. We then envisage a position of the third nearest-neighbor atom, which is determined by the dihedral angle (see Fig. 2.9) in twofold coordinated structures, the simplest example being Se. In the hexagonal-type c-Se, the atomic connection is all trans, being explicitly determined. On the other hand, the radial distribution function of a-Se gives no clear peaks corresponding to the third nearest neighbor (Fig. 2.8). This fact suggests that the dihedral angle is randomly distributed between trans and cis configurations (Andonov 1982), resulting in the so-called entangled chain structure (Fig. 2.7c). However, it is more or less difficult to experimentally distinguish between a long curled chain and a ring molecule. In the tetrahedral connection as in Si, we can envisage staggered and eclipsed conformations, illustrated in Fig. 2.14. As known, c-Si consists of only the staggered connection, while radial distribution functions of a-Si(:H) do not show a clear third-nearest peak, which suggests mixed structures with staggered, eclipsed, and intermediate configurations (Bodapati et al. 2006). In short, in a-Se and a-Si(:H), no third nearest-neighbor correlations seem to exist. However, such results are not universal as we see below. We next see the fourth nearest neighbor, which is involved in the corner- and edge-shared connections of atomic units, as illustrated in Fig. 2.15. Here, it is interesting to compare the chalcogenide glasses, As2 S(Se)3 and GeS(Se)2 , with the corresponding oxide glasses, As2 O3 and Si(Ge)O2 . It has been demonstrated that, in the chalcogenide glass, the corner- and edge-shared units of AsS(Se)3/2 and GeS(Se)4/2 exist, while the oxide glass contains only corner-shared connections (Kohara and

Fig. 2.14 Staggered and eclipsed conformations for tetrahedrally connected Si atoms

Fig. 2.15 Edge- (left) and corner-shared (right) tetrahedra (GeS4/2 ) in GeS2 . For As2 S(Se,Te)3 , envisage triangular pyramid structures without one S atom outside

2.4

Medium-Range Structure

43

Suzuya 2005). Pauling (1960) suggests that the corner- and edge-sharing can be related with the ionic and covalent bonds with the ideal bonding angles of 180◦ and 90◦ . Note that these connections of the atomic units automatically fix the third-neighbor distances. Next to these scales, we may consider the ring statistics (Greaves and Sen 2007). Here, the edge-shared connection contains a 2-membered (4-atom) ring, which tends to define rigid and flat segmental planes. On the other hand, disordered corner-shared structures are likely to produce three-dimensional continuous random networks, which cannot fix the ring size. In a-S(Se), entangled long chains and ring molecules consisting of several atoms (Fig. 2.7) may co-exist. However, we do not have any convincing experimental methods which can explicitly determine the ring statics and the chain length. We can just envisage the structure with a combination of experimental results and computer simulations such as reverse Monte Carlo method, which is introduced in Section 2.6. An exception, which has been partially resolved, is the ring statics in g-SiO2 . Through comparisons between theoretical calculations and Raman scattering spectra in g-SiO2 , Galeener’s group has identified the so-called D1 (495 cm−1 ) and D2 (606 cm−1 ) peaks, indicated in Fig. 2.16, to vibrational modes of 4- and 3-membered rings, respectively (Barrio et al. 1993). These small rings are assumed to be fairly stable, and its density is estimated at ∼1 at.%. (To the authors’ knowledge, the small rings do not produce any peaks in optical absorption spectra.) Similar studies have been done for B2 O3 (Nicholas et al. 2004). Small rings are also pointed out for a-Si:H (Du and Zhang 2005). We then wish to apply similar spectral analyses to other materials such as GeO(S,Se)2 and As2 S(Se,Te)3 . Actually, Kotsalas and Raptis (2001) have offered a plausible interpretation for the so-called A1 companion line, a small peak at ∼374 cm−1 above the main peak of 342 cm–1 , in g-GeS2 . However, Raman scattering spectra in heavier atomic systems shift to lower wavenumbers, consequently resulting in substantial overlaps of characteristic peaks, and the spectra make the peak identification difficult. More detailed analyses seem to be needed for obtaining convincing insights.

Fig. 2.16 Raman scattering spectra (HH and HV) of g-SiO2 (Barrio et al. 1993, © American Physical Society, reprinted with permission)

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2 Structure

2.4.2 First Sharp Diffraction Peak We then come to the big problem concerning the first (lowest wavenumber) sharp diffraction peak (FSDP). Vaipolin and Porai-Koshits (1963) discovered, as shown in Fig. 2.17, using the Cu Kα x-ray line that g-As2 S(Se)3 present relatively sharp halo peaks, referred to as the FSDPs, at θ ≈ 14◦ (QFSDP = 4π sin θ/λ ≈ 10 nm−1 = 1 A−1 ) with a peak width θ of ∼5◦ . In As2 Te3 , the peak merges into a shoulder. Provided that the Bragg equation is applicable to the peak position, we obtain a structural period of ∼0.6 nm. They also noticed that the FSDP position is similar to that of a Bragg peak appearing in As2 S(Se)3 layer crystals (Fig. 1.16). In addition, the Scherrer equation D λ/(θ cos θ ), being derived for polycrystalline materials, suggests a correlated domain size D of 2−3 nm. Taking these results into account, they have proposed the so-called distorted layer model for the glasses, i.e., deformed covalent layers with somewhat correlated interlayer distances of ∼0.6 nm (see Fig. 2.7b). The layer may be a “raft,” in which the edge is terminated by chalcogen dimers, in a structural model proposed by Phillips (1979). Note that these models are different from polycrystalline structures, in which the domains are crystallites. At first glance, the existence of such large correlated regions of 2−3 nm in the glass appeared anomalous. We may assume that the application of the Scherrer equation is problematic. On the other hand, a variety of experiments have been done for the FSDP. The experiments cover many kinds of chalcogenide glasses with different preparations and under varied temperatures and pressures (Busse 1984, Cervinka 1988, Elliott 1991). Through these studies, we tried to grasp atomic structures

Fig. 2.17 Comparisons of halo patterns and crystalline peaks in (a) As2 S3 , (b) As2 Se3 , and (c) As2 Te3 , shown from the top to the bottom (modified from Vaipolin and Porai-Koshits (1963))

2.4

Medium-Range Structure

45

giving rise to the FSDP. However, in short, the results have given an impetus of continuing controversy. We also underline that, before ∼1985, the FSDP had been assumed to be located at QFSDP ≈ 10 nm−1 , and that the peak was inherent to the chalcogenide glasses such as As2 S3 and GeSe2 . No one might assume that the oxide glass possesses a FSDP, since its first peak is located at Q ≈ 16 nm−1 . However, Wright et al. (1985) have presented a different definition. They noticed, as shown in Fig. 2.18, that the FSDP in the chalcogenide glasses satisfies a condition of QFSDP r ≈ 2 − 3, where r is the nearest-neighbor distance, and this criterion meets also the first, but not so sharp, diffraction peak in g-SiO2 . The FSDP was redefined as “QFSDP r ≈ 2 − 3,” and this definition has been applied to many oxide, halide, chalcogenide, and elemental glasses (Moss and Price 1985). Then, several researchers have tried to obtain unified understandings of this seemingly more universal criterion, QFSDP r ≈ 2−3. We should, however, note that the half-width of the peak in Si(Ge)O2 suggests a correlation distance of 1−2 nm (Greaves and Sen 2007, Lucovsky and Phillips 2009), substantially shorter than that in the chalcogenides. Since then, considerable studies have been performed for the FSDP in oxide glasses, specifically Si(Ge)O2 (Kohara and Suzuya 2005, Greaves and Sen 2007). It has been amply demonstrated that g-Si(Ge)O2 has continuous random network structures, and some researchers make efforts in answering the question “Why does the continuous random network exhibit such a peak?” Studies on complicated oxide glasses have also been performed. Gaskell et al. (1991) demonstrate a cation distribution order persisting over ∼1 nm in CaO–SiO2 glass. Other materials such as

Fig. 2.18 Comparison of x-ray structure curves S of (a) SiO2 and (b) GeSe2 in horizontal scales of Q (lower) and Qr (upper) (modified from Wright et al. 1985)

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2 Structure

glassy ZnCl2 (Salmon et al. 2005), a-As (Tanaka 1988), and a-P (Zaug et al. 2008) also present the FSDPs. In short, there seems to be a consensus that some kinds of medium-range orders with scales of 1–3 nm exist in simple glasses, while the real atomic structure is controversial. For the group VIb stoichiometric glasses such as Si(Ge)O2 and As2 S(Se)3 , there are roughly two ideas. One insists, taking QFSDP r ≈ 2 − 3 seriously, that the oxide and the chalcogenide possess qualitatively the same medium-range order, in which three-dimensional network structures have been presumed as a starting concept (Zaug et al. 2008, Massobrio and Pasquarello 2008, Lucovsky and Phillips 2009), the model hereafter referred to as a three-dimensional view. The others, including Zallen (1983), Cervinka (1988), and Bradaczek and Popescu (2000), assume that the oxide has three-dimensional and the chalcogenide has two-dimensional structures, the idea being consistent with the original view by Vaipolin and Porai-Koshit (1963). The present authors believe that this dimensional view is more intuitive and instructive, at least with the following three reasons. First, the dimensional view is consistent with interpretations made for zerodimensional (point-like) and one-dimensional molecular materials. Examples of the zero-dimensional materials are molecular CCl4 liquids (Salmon et al. 2005) and as-evaporated As2 S3 films (consisting of molecules such as As4 S4 ) (DeNeufville et al. 1973, Wright et al. 1985), and those of one-dimensional molecules are organic polymers such as polyethylene (Fischer and Dettenmaier 1978) and polysilane (Tanaka and Nitta 1989). These zero- and one-dimensional molecules exhibit clear FSDPs, as exemplified in Fig. 2.19, which are ascribed without any ambiguity to intermolecular correlation of van der Waals-type bonding. The fact that a-Se consisting of Se chains does not show a clear FSDP, but a shoulder, is ascribed to the short inter-chain distance (∼0.4 nm), which is similar to the second-nearest intrachain distance of ∼0.37 nm (Andonov 1982). Extrapolating these insights, we can assume that the two-dimensional (layer) structure gives the FSDP, which reflects the van der Waals-type correlation, in the chalcogenide glass. The peak in threedimensional glasses should be ascribed to different origins. Also consistent with

Fig. 2.19 Scattering curves of two one-dimensional organic materials, C12 H26 at 25◦ C (dashed line) and polyethylene at 160◦ C (solid line) consisting of chain molecules (Fischer and Dettenmaier 1978, © Elsevier, reprinted with permission)

2.4

Medium-Range Structure

47

the different origins of the first peaks are the appreciably different correlation distances, ∼2 and ∼1 nm, estimated from the FSDP widths in chalcogenide and oxide (Greaves and Sen 2007, Lucovsky and Phillips 2009). Second, the dimensional view is consistent with the material variation in the VIb glasses. We saw in Fig. 1.12b that the density in As2 O(S,Se,Te)3 and GeO(S,Se)2 does not monotonically change, showing clear minima at the sulfides. The density minimum at the sulfides can be understood by taking the dimensional view into account, including longer van der Waals distances (∼0.5 nm) than the covalent bond (0.2–0.3 nm), as described in Section 4.10. The third reason is posed from pressure dependence. Upon hydrostatic compression, the position of FSDPs in polyethylene (Yamamoto et al. 1977) and chalcogenide glasses (Tanaka 1998) dramatically shifts to lower diffraction angles, while that in Si(Ge)O2 is more or less intact (Guthrie et al. 2004). In addition, as illustrated in Fig. 2.20, it should be noted that pressure behaviors of the FSDP in g-GeS2 and the interlayer distance in layer-type c-GeS2 are similar (Tanaka 1986). We may imagine compression of crumpled (glass) and stacked (crystal) papers (covalent layers) here, in which the paper separations give the diffraction peaks. It should also be mentioned that pressure dependence of optical absorption edges (Fig. 1.25) is consistent with the dimensional view (Zallen 1983). In short, the authors’ standpoint can be summarized as follows: What is important in disordered materials science is an intuitive description of seemingly vague observations in terms of “simple pictures.” The picture should be useful also for understanding macroscopic properties of many kinds as possible. In this context, the dimensional view seems to be more instructive. Controversy between the dimensional and the three-dimensional view may arise from the terminology or the definition of FSDP: Q ≈ 10 nm−1 and QFSDP r ≈ 2 − 3. The universality QFSDP r ≈ 2 − 3 may be coincidental, which arises from the fact that the van der Waals distance is approximately equal to twice the covalent bond

Fig. 2.20 Comparison of atomic distances d in g-GeS2 glass (•) and the layer-type c-GeS2 (◦) under hydrostatic compression. The distance d is calculated for the glass from the FSDP position and for the crystal from the interlayer x-ray peak. Fractional change l/l in macroscopic linear compressibility for the glass is also shown by a dotted line with an error bar (Tanaka 1986, © Elsevier, reprinted with permission)

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2 Structure

distance. Note that the two models are in agreement for g-SiO2 and also a-Si:H, the structure being grasped unambiguously as three-dimensional continuous random networks.

2.4.3 Boson Peak Probably related with the FSDP is the so-called Boson peak in Raman scattering spectra, a broad peak appearing at 20–50 cm−1 (0.6–1.5 THz, ∼5 meV), which is lower than the conventional vibrational modes by an order. Krishnan (1953) may have been the first who noticed this anomalous low-frequency peak in a glass, SiO2 . (Note that such a low-frequency broad peak has never appeared in c-SiO2 and similar crystals, since the optical phonon is located at higher frequencies.) For the peak in chalcogenide glasses, Nemanich (1977) performed a comprehensive study, who gave the name of “Boson peak,” the reason being that the spectral shape at lowfrequency limits appears to be governed by the Bose factor, {n(ω, T) + 1}/ω ω−2 . Since then, many studies have been published for the peak in oxide and chalcogenide glasses (Greaves and Sen 2007) and even in proteins (Ciliberti et al. 2006). Because of this universal feature being inherent to disordered materials, a variety of characteristics have been investigated. For instance, in g-As2 S3 , the peak becomes smaller under hydrostatic compression (Fig. 2.21; Andrikopoulos et al. 2006) and is intensified by temperature rise (Yasuoka et al. 1986). The peak position depends upon preparation conditions of the glass ingot, such as quenching rate of the melt (Tanaka 1987). We also add that far-infrared absorption spectroscopy detects a similar peak (Ohsaka and Ihara 1994). Several models have been proposed for the origin of the Boson peak. The vibrational wavenumber k is given as k = (1/s)(κ/M)1/2 , where s is the sound velocity,

Fig. 2.21 Raman scattering spectra of As2 S3 as a function of hydrostatic compression (Andrikopoulos et al. 2006, © Elsevier, reprinted with permission)

2.4

Medium-Range Structure

49

κ a force constant, and M a reduced mass. Accordingly, we can ascribe the low wavenumber of Boson peaks to some vibrations of nearly-free atomic units having small κ, which may be related with van der Waals forces. Phillips (1981) followed this view, proposing that the Boson peak is a kind of rigid-layer modes, which are vibrations of crystalline layers held together by van der Waals forces. Or, the low wavenumber may be due to atomic clusters having large masses, which may be related with medium-range structures. Martin and Brenig (1974), assuming inhomogeneous cluster structures with the Gaussian-type correlation function characterized by a spatial scale σ , derived a peak shape for an acoustic Raman scattering mode in disordered materials as I(k) ∼ (σ 3 k3 /s5 ){n(k) + 1} exp (−k2 σ 2 /s2 ),

(2.6)

where n(k) is the Bose factor. This equation gives the position of Boson peaks at max ∼ s/σ . Nemanich (1977) followed this idea, obtaining σ ≈ 0.7 nm in As2 S(Se)3 , which is substantially smaller than the correlated scale of 2−3 nm inferred from the FSDP. Researches on the Boson peak appear to follow labyrinths as those of the FSDP. Malinovsky and Sokolov (1986) demonstrated, as shown in Fig. 2.22, that the shapes of Boson peaks of many glasses are the same if the spectrum is normalized with the peak frequency max , or the corresponding energy Emax . Novikov and Sokolov (1991) found a proportionality between the normalized FSDP position and the Boson peak wavenumber, QFSDP r ∝ max c/s, where c is the velocity of light. Afterward, the problem was extended to universal understandings of the FSDP and the Boson peak. Later, such studies have been further extended to understanding

Fig. 2.22 Boson peaks in several glasses, normalized by the peak energy Emax . (1) As2 S3 with Emax = 26 cm−1 , (2) Bi4 Si3 O12 with 34 cm–1 , (3) SiO2 with 52 cm–1 , (4) B2 O3 with 28 cm–1 , (5) B2 O3 –Li2 O with 88 cm–1 , and (6) GeS2 with 22 cm–1 (Malinovsky and Sokolov 1986, © Elsevier, reprinted with permission)

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2 Structure

correlations between the Boson peak, the FSDP, and thermal properties including the known low-temperature anomalies (Section 3.4) and glass transition parameters (Sokolov et al. 1993). The final elucidation remains (Grigera et al. 2003, Taraskin et al. 2006, Ruocco 2008, Baldi et al. 2010).

2.5 Defect Defect structures are also controversial. At the outset, we may recall what the defect is in disordered structures (see Section 2.2). In crystals, it is traditional to assume an ideal structure, and some deviations from that can be regarded as the defects, which are classified into point defects (color center in NaCl, etc.), line defects (dislocation, etc.), stacking faults, grain boundaries, etc. (Kittel 2005). However, since we cannot envisage the ideal amorphous structure, the definition of defects becomes necessarily vague. On the other hand, it is reasonable to assume that only point-like defects can exist in glasses, since the other defects require some long-range atomic correlations, which must be lacking in non-crystals. We define the defect in a non-crystalline solid as a connected or disconnected atomic bond, or a point defect-like structure, which cannot exist in the corresponding ideal crystal. This definition implicitly assumes that the defect arises in the short-range scale. Naturally, if the corresponding crystal does not exist, e.g., nonstoichiometric glasses such as Ge-doped g-SiO2 , this definition is meaningless. Otherwise, since the defect is a deviated structure from the normal bonding network, the defective site should be rare, e.g., being smaller than ∼1% of the total bonds. A dangling bond and an ill-coordinated bond are typical defects. Note that the density of ∼1% can be neglected in structural properties such as the elastic constant and heat capacity at room temperature, while the defect may provide substantial effects upon electronic properties if it produces a mid-gap state, which is more or less common. Is it possible to detect such a few point-like defects in disordered structures? X-ray measurements, including diffraction and EXAFS, seem to be insufficient in sensitivity (5 at.%), so that we usually employ two methods. One is the Raman scattering spectroscopy, while its sensitivity seems to be, at the best, ∼1 at.%. The other is the electron spin resonance (ESR), which seems to have a sensitivity of ppm (Griscom 2000). However, the method can detect only unpaired electrons, such as E centers in silica glasses and D0 defects in chalcogenide glasses. In addition to these methods, there are some non-direct methods. An example is the comparison of experimental optical spectra with some calculations, which may predict that a defect produces mid-gap absorption and/or photoluminescence peaks. Such optical investigations are more useful in the oxide than in the chalcogenide, since the former has a wider optical gap and the defect peak is likely to appear in the visible wavelength region, which can easily be detected. In the following, we will examine Si(Ge)O2 and As2 S3 (and Se) as examples of the oxide and the chalcogenide glass (Table 2.3). Ge-chalcogenides such as g-GeS(Se)2 are likely to possess intermediate properties between these materials.

2.5

Defect

51 Table 2.3 Defects in SiO2 and As2 S3 glasses

Related atoms

Normal bonding

D0

Wrong bond

Coordinational

Si

≡Si–

≡Si• (E )

−Si− (ODC)

O

–O–

As S

=As– –S– (C2 )

–O• (NBOHC), –O–O• (POR) =As• under exc.∗ -S• under exc.∗

≡Si–Si≡ (ODC) –O–O– (POL) =As–As= –S–S–

=As (P2 ) =S– (C3 )

Molecular

O2 , O3

A covalent and a dangling bond are represented by – and •, respectively. NBOHC stands for nonbridging oxygen hole center, ODC for oxygen-deficient center, POR for per-oxy radical, and POL for per-oxy linkage. P and C stand for pnictogen and chalcogen, respectively. In As2 S3 , ESR signal in the dark is below a detection limit (∼1015 cm–3 ), appearing only under light excitation (∗) at low temperatures

Defects in g-Si(Ge)O2 can be divided into Si(Ge) related and O related (Pacchioni et al. 2000). The most famous Si(Ge)-related defect is a kind of dangling bond, E center (≡Si•), which is ESR active, and accordingly, it can be easily detected. On the other hand, ESR-inactive defects are twofold coordinated Si (–Si–) and Si homopolar bond (≡Si–Si≡); the latter can be regarded as a kind of oxygendeficient center (ODC). Existence of these defects is suggested from optical studies. The O-related defect includes non-bridging oxygen hole center (NBOHC; oxygen dangling bond, –O•) and per-oxy radical (POR; –O–O•), which are ESR active, and per-oxy linkage (POL; oxygen wrong bond, –O–O–), which is ESR inactive. In addition, oxygen molecules, O2 and O3 , seem to be produced by radiation. It is plausible that the density of these defects, typically ∼ 1018 cm−3 , depends upon samples. For the chalcogenide glass, many kinds of defects have been proposed (Ovshinsky and Adler 1978), while experimentally confirmed ones are a few. Since the chalcogenide glass is covalent, it is straightforward to envisage the wrong bonds (Halpern 1976) or like-atom (homopolar) bonds in stoichiometric compositions. The wrong bond is neutral in charge in covalent materials, and because of this character the defect becomes appreciable in density. Actually, the wrong bonds, As−As and S−S (Fig. 2.23), in g-As2 S3 with concentrations of ∼1% are inferred from chemical analyses (Kosek et al. 1983) and Raman scattering studies (Tanaka 1987). In addition, Vanderbilt and Joannopoulos (1981) suggest the wrong-bond density of ∼0.5% in g-As2 Se3 using a canonical factor, exp(−E/kTg ), where E is the energy difference between hetero and homopolar bonds. In such calculations, however, we should be careful about the selection of bond energies, which depend upon the sources, as listed in Table 2.4. For g-GeSe2 , Zhou et al. (1991) did not detect any wrong bonds using EXAFS, while Petri et al. (2000) have found substantial numbers (∼4%) of wrong bonds using isotope-substituted neutron diffraction. The

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Fig. 2.23 Wrong bonds, As−As and S−S, in g-As2 S3 . The gray lobes attached to S depict lone-pair electrons

S S

As

As

As S As As S

S

Table 2.4 Bond energies of interest in units of kcal/mol, selected for As–S (Pauling 1960, Tsuchihashi and Kawamoto 1971, Popescu 2001) and Ge–S (Kawamoto and Tsuchihashi 1971, Popescu 2001) glasses

Pauling Tsuchihashi–Kawamoto Popescu

As–S

As–As

S–S

Ge–Ge

Ge–S

47 61 62

32 32 48

51 33 67

38 44

56 68 63

The values selected by Pauling may be obtained from related gases with different atomic coordination from that in the glasses, and accordingly, the value seems to provide unreasonable estimates in the present purpose

difference may be attributed to different sample preparations and/or experimental methods. The dangling bond is a known defect. However, in the chalcogenide glass, the common dangling bond having an unpaired electron, D0 in Mott’s notation, appears only in Ge–S(Se) (Arai and Namikawa 1973, Elliott 1990). Pure Se and As-chalcogenides present no ESR signals (<1016 cm−3 ) in the dark, which means that there are no neutral dangling bonds having unpaired electrons. In these materials, the ESR signal appears only under illumination at low temperatures (see Section 6.3.10). Mott and many researchers have related the appearance of D0 under illumination to the presence of charged dangling bonds (D+ and D− ) in the dark, the idea being discussed in Section 4.4. Note that here we neglect impurities, such as O in a-Se and Fe in g-As2 S3 (Churbanov and Plotrichenko 2004), and intentionally doped atoms such as H, F, and Cl in g-SiO2 (Pacchioni et al. 2000). Due to the disordered structure, however, it is common that a glass contains comparatively larger amounts of impurities than those in the corresponding crystal. Actually, a difficulty of studying g-SiO2 is that, in addition to small deviations from the 1:2 stoichiometric ratio, the glass is likely

2.6

Computer Simulations

53

to contain impurities such as Al and OH (Doremus 1994). Accordingly, the characterization of impurities is a prerequisite for studies of defect-related properties, e.g., mid-gap optical absorption and photoluminescence. For such impurity evaluations, we may utilize spectroscopic methods such as x-ray fluorescence, plasma emission, and infrared absorption, which possess detection sensitivities of ppm–ppb.

2.6 Computer Simulations Since the non-crystalline structure cannot be determined explicitly, structural modeling has played an important role. In early studies, the modeling employed physical “balls-and-sticks,” a known example being the so-called Polk model for a-Si (Turnbull and Polk 1972). Such approaches may still be valuable for obtaining intuitive ideas, since the model can be deformed by hand (Tanaka 1998). Gradually, computer simulations have become indispensable. A lot of studies have employed classical molecular dynamics (MD) calculations and other methods, which rely upon Newton’s equation and empirical potentials. For instance, Brabec (1991) and Antonio et al. (1992) have simulated, respectively, bonding structures of As2 S3 and SiSe2 glasses having 1790 and 5184 atoms. At present, most studies perform the so-called ab initio MD calculation. It is based upon Schrödinger’s equation taking all relevant wavefunctions into account. However, the calculation is limited to a system having 200−300 atoms contained in nanometer-sized cubes, which may be imposed on the periodic boundary condition (Greaves and Sen 2007, Drabold and Estreichen 2007). The simulation follows the “cook-and-quench” type, in which a liquid having a fixed atomic composition is first equilibrated, e.g., at 1000 K, followed by a thermal quench to 300 K. We expect that these ab initio calculations can reproduce not only the atomic structure but also a variety of macroscopic properties (Fig. 2.24). However, at present, the ab initio calculation seems to be valuable but with limited scope. It can reproduce experimental radial distribution functions and vibrational spectra, which characterize the short-range structure. However, the number of atoms 200–300, which corresponds to a cubic side number of ∼5 atoms, is still insufficient for obtaining insights into the medium-range structure. In addition, the

SIMULATION

Fig. 2.24 A goal of computer simulations, from which we may extract unified concepts

Atomic

Macroscopic

structures

properties

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biggest problem may be liquid quenching. In all MD simulations for glasses, the quenching rate from a melt is enormously fast, e.g., 1011 −1014 K/s, which is governed by needed computational times, and as a result, a simulated glass is likely to contain too many defects. Therefore, MD calculations may predict what kinds of defects can exist in the amorphous material, but it is nearly impossible to estimate the defect density in real samples. There are other computational methods. Specifically, the reverse Monte Carlo method is frequently utilized in analyses of experimentally obtained structural data (Kohara and Suzuya 2005, Greaves and Sen 2007, Itoh and Fukunaga 2009, Cliffe et al. 2010). In this method, we first distribute finite numbers (≤5000) of atoms in a cube having a volume, which gives an appropriate atomic density, and then move the atoms randomly until the resultant structure agrees satisfactorily with experimental data in wavenumber and/or real spaces. Otherwise, novel calculation methods as a statistical computation method, which is not limited by the time scale, may be more promising, while the system is limited to, e.g., 64 Se atoms (Mauro and Loucks 2007).

2.7 Homogeneity Up to now, we have implicitly assumed that the amorphous structure is continuous and homogeneous. Is this assumption justified? It should be kept in mind that almost all of the structural measurements described above, except real space measurements such as transmission electron microscopy and atomic force microscopy, presume structural homogeneity. Unfortunately, the present x-ray methods, Raman scattering spectroscopy, etc., cannot have spatial resolution better than ∼100 nm. These methods present structural information averaged over the probed area. However, the structural inhomogeneity is likely to arise, at least, from two origins: density fluctuations and chemical factors. Glass necessarily contains density fluctuations. This is because the glass is quenched from the corresponding melt, which undergoes time-varying density fluctuations. The fluctuating amplitude ρ/ρ of a few percent is theoretically derived (see Section 7.2). Experimentally, the amplitude and spatial scale (∼2 nm in silica) can be probed using small-angle x-ray and light scatterings (Greaves and Sen 2007). The density fluctuation is a critical problem in preparations of optical fibers and so forth. In addition, recent studies suggest that, during aging processes at temperatures below the glass transition temperature, so-called dynamic heterogeneity appears, which may lead to crystalline nucleation (Yunker et al. 2009). Apart from the density fluctuation, the reported microscopic views are not conclusive. Structural homogeneity in atomic bonding can be conjectured in the elemental a-Se (Andonov 1982), having entangled chain and ring structures. Simple stoichiometric glasses such as As2 S3 provide no small-angle x-ray scattering signals (Bishop and Shevchik 1974), suggesting certain homogeneity. Hosokawa et al. (2008) draw a similar conclusion for As2 S3 from inelastic x-ray scattering.

2.7

Homogeneity

55

However, a more sensitive method, positron lifetime spectroscopy, detects microvoids of ∼0.5 nm in diameter with a volume fraction of 10−5 –10−2 % in g-As2 Se3 (Jensen et al. 1994). As references, we note that a-Si:H and similar films present marked signals indicating the existence of small voids (Muramatsu et al. 1989). However, the glass structure critically depends upon preparation procedures and storage conditions, which are likely to govern homo and heterogeneity. Actually, Ležal et al. (1993) demonstrate that light scattering characteristics in g-As2 S3 depend upon the quenching rate of melts. Boolchand et al. (2001) assert that GeS(Se)2 is phase-separated in nano-scales through self-organization (Chen et al. 2008). Non-stoichiometric glasses such as As(Ge)-S(Se) tend to phase-separate (Tichý et al. 1984, Bychkov et al. 2006). More complicated glasses may be inhomogeneous, the examples being Ag-chalcogenide glasses (Mitkova et al. 1999) and modifier-mixed oxide glasses such as Na2 O(PbO)–SiO2 illustrated in Fig. 2.25, which is in contrast to a homogeneous structure, Fig. 1.13. Spinodal decomposition in multi-component oxide glasses has been well known (Doremus 1994). An oxychalcogenide glass GeO2 –GeS2 appears to be heterogeneous in electron microscopy images (Terakado and Tanaka 2008). Finally, it should be mentioned that partially

Fig. 2.25 A schematic illustration of an oxide glass consisting of phase-separated network former (gray) and modifier (white) regions (Greaves 1985, © Elsevier, reprinted with permission)

Fig. 2.26 A scanning-electron microscopy image of an obliquely deposited 1 μm-thick As2 S3 film (Starbov et al. 1992, © Elsevier, reprinted with permission)

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controlled inhomogeneity, a kind of nano-structures, can be produced by oblique evaporation, the examples being given for Se (Krišˇci¯unas et al. 1983) and As2 S3 in Fig. 2.26 (Starbov et al. 1992).

2.8 Surface and Nano-structures The surface gives a special problem in solid-state science. Particularly, in crystals, atomic periodicity is broken at the surface, and accordingly, surface atoms necessarily produce unique surface structures. In c-Si, the ideal surface must have many dangling bonds, while practical surfaces have undergone surface reconstruction or oxidation. In contrast, it is likely that, in amorphous materials, the surface has smaller roles than those in single crystals, since the interior atomic structure is already disordered. Despite such speculations, some surface effects have been reported for amorphous materials. Isobe et al. (1986) and Mamontova et al. (1988) demonstrate that surface structures affect photoconductive and electrical properties in (As-)Se. Inam and Drabold (2008) theoretically predict that oxidation changes surface conductance of Ge2 Sb2 Te5 films. In silica glass, it is well known that the surface is terminated by Si–OH groups (Doremus 1994). Recently, nano-structured materials have attracted substantial interest, as reviewed for chalcogenide by Tanaka (2004). Among the many topics, focus has been placed on surface manipulation. Here, we should note a characteristic difference of the surface manipulation in crystalline and non-crystalline solids. As known, using scanning tunneling microscopes, Eigler and Schweizer (1990) have manipulated single atoms on atomically flat surfaces of single crystals. However, such atomic manipulation seems to be difficult in amorphous materials, due to the existence of medium-range (2−3 nm) orders. In non-crystalline solids, the smallest structural unit which can be artificially manipulated may be attained not at the atomic scale, but at the nano-scale. The multi-layer system has been the most extensively studied nano-structure from a fundamental and technological point of view. And, notable studies have been reported for amorphous chalcogenide semiconductors. Nesheva et al. (2005) have comprehensively studied variations of the glass transition temperature, the optical gap, etc., as functions of layer thicknesses for GeS2 /CdSe multi-layers. However, as summarized in Fig. 2.27 (Tanaka 2004), thickness dependences of reported studies are not reproducible. In addition, we should be careful in interpretations. With a decrease in layer thickness, a blue shift of optical absorption edges (or optical gap Eg ) tends to appear, which is often interpreted as a quantum-well effect. However, the effect can appear only when the mean free path of electrons and/or holes is longer than the layer thickness (Kittel 2005). Nevertheless, the mean free path of electrons, e.g., in aSi:H films is reported to be ∼1 nm (Okamoto et al. 1991), and accordingly, the quantum-well interpretation may be misleading. The blue shift possibly appears as a

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Fig. 2.27 Dependence of thermal and optical properties on the thicknesses of films (solid symbols) and multi-layer periods (open symbols) (modified from Tanaka 2004). (a) The crystallization temperature Tc (dashed lines) of Se and GeTe and the glass transition temperature Tg (solid lines) of Se and As2 S3 are shown. (b) The optical gap Eg of Se, As2 S3 , and As2 Se3 is shown

result of vague layer boundaries, which are likely to govern macroscopic properties in thinner layer structures, since material diffusion becomes more evident in such systems (Adarsh et al. 2005). Finally, it may be valuable to refer to some related studies. Regarding technological developments, we note a pioneering study by Maruyama (1982) on multilayered chalcogenide films for vidicon targets. Chong et al. (2008) have studied crystalline–amorphous multi-layers using GeTe/Sb2 Te3 stacks. We also mention that substantial studies have been done for ultrathin films (Tanaka 2004, Raoux et al. 2008) and chalcogen-impregnated zeolites (Poborchii et al. 2002, Tanaka and Saitoh 2009), which provide nano-dot and/or single-chain structures.

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R., Yamada, N., Toriumi, K., Ohshima, T., Tanaka, H., Takata, M.: Development of picosecond time-resolved microbeam X-ray diffraction technique for investigation of optical recording process. Jpn. J. Appl. Phys. 48, 03A001 (2009) Tanaka, K., Nitta, S.: Pressure dependence of structural and electronics properties of polysilane alloys. Phys. Rev. B 39, 3258–3264 (1989) Tanaka, K., Saitoh, A.: Optical nonlinearities of Se-loaded zeolite (ZSM-5): A molded nanowire system. Appl. Phys. Lett. 94, 241905 (2009) Tanaka K., Yamaguchi, M.: Resonant Raman scattering in GeS2 . J. Non-Cryst. Solids 227–230, 757–760 (1998) Taraskin, S.N., Simdyankin, S.I., Elliott, S.R., Neilson, J.R., Lo, T.: Universal features of terahertz absorption in disordered materials. Phys. Rev. Lett. 97, 055504 (2006) Taylor, P.C., Su, T., Hari, P., Ahn, E., Kleinhammes, A., Kuhns, P.L., Moulton, W.G., Sullivan, N.S.: Structural and photostructural properties of chalcogenide glasses: Recent results from magnetic resonance measurements. J. Non-Cryst. Solids 326, 193–198 (2003) Tenhover, M., Boolchand, P., Bresser, W.J.: Atomic-structure and crystallization of Asx Te1-x glasses. Phys. Rev. B 27, 7533–7538 (1983) Terakado, N., Tanaka, K.: Nanoscale heterogeneous structures in GeO2 –GeS2 glasses. Jpn. J. Appl. Phys. 47, 7972 (2008) Thornburg, D.D., Physical properties of the As2 (Se,Te)3 glasses. J. Electron. Mater. 2, 495–532 (1973) Tichý, L., Ryšavá, N., Tˇríska, A., Tichá, H., Klikorka, J.: Qualitative calorimetry of some sulphur rich glasses. Solid State Commun. 49, 903–906 (1984) Tominaga, J., Haratani, S., Handa, T., Yanagiuchi, K.: Scanning tunneling microscopy image of GeSb2 Te4 thin films. Jpn. J. Appl. Phys. 31, L799–L802 (1992) Tsuchihashi, S., Kawamoto, Y.: Properties and structure of glasses in the system As-S. J. NonCryst. Solids 5, 286–305 (1971) Turnbull, D., Polk, E.: Structure of amorphous semiconductors. J. Non-Cryst. Solids 8–10, 19–35 (1972) Vaccari, M., Garbarino, G., Yannopoulos, S.N., Andrikopoulos, K.S., Pascarelli, S.: High pressure transition in amorphous As2 S3 studied by EXAFS. J. Chem. Phys. 131, 224502 (2009) Vaipolin, A.A., Porai-Koshits, E.A.: Structural models of glasses and the structures of crystalline chalcogenides. Sov. Phys.- Solid State 5, 497–500 (1963) Vanderbilt, D., Joannopoulos, J.D.: Theory of defect states in glassy As2 Se3 . Phys. Rev. B 23, 2596–2606 (1981) Watanabe, I., Inagaki, Y., Shimizu, T.: Electron spin resonance of Mn2+ in As-Se and As-Te glasses. J. Non-Cryst. Solids 22, 109–123 (1976) Wright, A.C., Sinclair, R.N., Leadbetter, A.J.: Effect of preparation method on the structure of amorphous solids in the system As-S. J. Non-Cryst. Solids 71, 295–302 (1985) Yamamoto, T., Miyaji, H., Asai, K.: Structure and properties of high pressure phase of polyethylene. Jpn. J. Appl. Phys. 16, 1891–1898 (1977) Yannopoulos, S.N., Andrikopoulos, K.S.: Raman scattering study on structural and dynamical features of noncrystalline selenium. J. Chem. Phys. 121, 4747–4758 (2004) Yasuoka, H., Onari, S., Arai, T.: Low frequency light scattering in amorphous As2 S3 . J. Non-Cryst. Solids 88, 35–42 (1986) Young, P.A., Thege, W.G.: Structure of evaporated films of arsenic trisulphide. Thin Solid Films 7, 41–49 (1971) Yunker, P., Zhang, Z., Aptowicz, K.B., Yodh, A.G.: Irreversible rearrangements, correlated domains, and local structure in aging glasses. Phys. Rev. Lett. 103, 115701 (2009) Zachariasen, W.H.: The atomic arrangement in glass. J. Am. Chem. Soc. 54, 3841–3851 (1932) Zallen, R.: The Physics of Amorphous Solids. Wiley, New York, NY (1983) Zaug, J.M., Soper, A.K., Clark, S.M.: Pressure-dependent structures of amorphous red phosphorus and the origin of the first sharp diffraction peaks. Nat. Mater. 7, 890–899 (2008) Zhou, W., Paesler, M., Sayers, D.E.: Structure of germanium-selenium glasses: An X-rayabsorption fine-structure study. Phys. Rev. B. 43, 2315–2321 (1991)

Chapter 3

Structural Properties

Abstract This chapter describes physical properties governed by normal atomic bonds. One of the biggest and long-standing problems is glass transition, at which specific heat, thermal expansion, and viscosity exhibit marked changes. Thermal crystallization is also studied extensively, specifically in relation to phase-change memories. We also take brief views of structural properties at low and room temperatures. Importance of the atomic coordination number, which affects structural properties, is also discussed. There exist magic coordination numbers at 2.4 (Phillips) and 2.67 (Tanaka); the origin of these numbers is discussed. We also refer to ion transport. Keywords Glass transition · Kauzmann temperature · Free volume · Fragility · Crystallization · Magic number · Ionic conduction

3.1 Structure and Properties What is the relationship between the three kinds (short range, medium range, and defect) of structural elements and structure-related (non-electronic) properties? We here can neglect the defect, since its density is smaller than ∼1 at.% and most of the structural properties, except those at low temperatures, are determined by normal bonding structures. (The defect may play important roles in electronic properties.) Accordingly, it is natural to assume that the short-range structure governs structural properties, which are possibly modified by medium-range structures. Examples of the structure-related properties are shown in Table 3.1. Among those, the most important may be the thermal and mechanical property, including glass transition and crystallization. In glass transition, specific heat and viscosity gradually change from liquidus to solidus values. On the other hand, thermal crystallization becomes an important problem, in relation to the phase change, the topic being described in Section 7.4. A related property is the thermal conductivity, which is smaller in a glass than that in the corresponding crystal, due to phonon localization. Another important property is elastic, including concepts of magic numbers. It is also known that chalcogenide glass has marked acoustic nonlinearity, while the origin has not been considered deeply. The last subject described in this chapter is ionic conduction, which is in general more prominent than that in the crystal. The feature will be utilized in solid-state batteries (Section 7.7.3). 63 K. Tanaka, K. Shimakawa, Amorphous Chalcogenide Semiconductors and Related C Springer Science+Business Media, LLC 2011 Materials, DOI 10.1007/978-1-4419-9510-0_3,

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Table 3.1 Comparison of density ρ, bulk modulus B, specific heat c, thermal conductivity κ, linear thermal expansion coefficient β, glass transition temperature Tg , and Debye temperature TD of the three materials (room temperature) polyethylene, g-As2 S3 , and g-SiO2 . Note that the Dulong–Petit specific value is 25 J/mol K for an elemental system. The thermal conductivity of As2 S3 scatters among reports Material

ρ (g/cm3 ) B(×1010 N/m2 ) c(J/mol·K) κ(W/m·K) β (×10−5 K−1 ) Tg (K) TD (K)

Polyethylene 0.95 As2 S3 3.2 SiO2 2.2

∼0.2 1.25 3.65

∼30 120 45

0.4 0.2–0.5 1.4

15 2.5 0.06

150 460 1450

∼50 450 500

We first note a remarkable difference between a glass and an amorphous material in the thermal transitions. Glass naturally shows glass transition because it is prepared from the corresponding melt. When heated, silica glass undergoes a glass transition and gradually becomes a liquid, without showing crystallization or melting transitions. An a-Se film, g-Se as well, undergoes a glass transition at ∼50◦ C, crystallizes to a hexagonal crystal at ∼120◦ C, and melts at 217◦ C (Fig. 3.2). But, an amorphous film does not necessarily show glass transition. a-Si:H films, when heated, exhaust H at ∼300◦ C and directly crystallize to c-Si above ∼500◦ C. Glass transition has never been experimentally detected (Hedler et al. 2004). We should also note that these thermal behaviors depend upon heating rates. If a-Se films are heated very slowly at the rate of 1◦ C/day, only crystallization may take place at a lower temperature. How can we understand these features?

3.2 Glass Transition Glass transition appears more or less commonly. It appears not only in inorganic glasses but also in organic materials including bio-polymers as proteins (Lee and Wand 2001). Because of such commonality, the phenomenon has been one of the biggest problems in solid-state science (Elliott 1990, Angell et al. 2000, Debenedetti and Stillinger 2001) since the pioneering work by Kauzmann (1948), but it remains vague. We here outline the fundamentals. It is known that when a glass rod is heated it gradually becomes viscous. Thanks to this gradual softening, we can deform the glass to an arbitrary shape through blowing, moulding, stretching, and so forth. The glass transition temperature Tg is defined as the transforming temperature between a glass and the viscous supercooled liquidus state. The left illustration in Fig. 3.1 shows enthalpy H curves as a function of a configuration coordinate1 at three temperatures. At a higher temperature (liquid) than the 1 The configuration coordinate is often used in these kinds of representations, while the meaning may not be correctly understood. Suppose we have a solid (molecule) consisting of N atoms. For uniquely identifying the atomic structure (position) in the three-dimensional space, we need 3 N −6 coordinates for an N ≥ 3 system. In other words, if we fix a single point in a (3 N − 6)-dimensional Hilbert space, the structure is uniquely determined. (The simplest example for a system of N = 2

3.2

Glass Transition

65

Fig. 3.1 Enthalpy H (or volume V) of a material as functions of atomic configuration (left) and temperature (right). TR is room temperature, and the suffixes of temperature T in the right-hand side illustration denote hypothetical (0), glass transition (g), crystallization (c), melting (m), and boiling (b)

(a) endothermic

(b)

Fig. 3.2 Relative specific heats of (a) a-Se and (b) hexagonal Se (modified from Andonov 1982)

melting temperature Tm , the liquid has a configuration with the smallest enthalpy. At room temperature TR , in general, the crystal has the smallest enthalpy. In contrast, a glass has a minimal energy, which corresponds to the quasi-equilibriumness. Next, let us trace the enthalpy H(T) of a material as a function of temperature, illustrated in the right-hand side in Fig. 3.1. Such curves can be obtained from the specific heat C(T) (Fig. 3.2), which can be taken using scanning thermal calorimeters (Kasap and Tonchev 2006) and successive integration, since H(T) = C(T)d T.2 is the atomic distance in H2 molecules, in which case the configuration coordinate becomes onedimensional.) We here symbolize the 3 N − 6 axes with a single (or may be double) axis, which is the configuration coordinate. In some special problems concerning a point defect, we may be interested only in an atomic distance around the defect. In such cases, the 3 N − 6 axes may be reduced to a single distance axis, which can be regarded also as the configuration coordinate. 2 Recall that the enthalpy is given as H = U + PV, Helmholtz free energy F = U − TS, Gibbs free energy G = H − TS (U is the internal mechanical energy, P the pressure, V the volume, T the

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3 Structural Properties

Fig. 3.3 Free energy F(= U − TS) as a function of temperature T

We here envisage an ideal crystal at 0 K (see Fig. 3.3). The entropy must be zero, and U governs the free energy, since F = U − TS. Heating increases TS, but when U TS, F ≈ U, and the crystal has the lowest free-energy structure. At the melting temperature Tm , however, we have a condition of Uc = Tm Sl and Fc = Fl , and accordingly, the first-order phase transition from a crystal (c) to a liquid (l) takes place. After the transition, F is governed by −TS term, and a higher entropy structure is preferred, which corresponds to the disordered liquid phase. Now, if the liquid is cooled down slowly, it undergoes crystallization at Tm . These crystal–liquid transformations occur under thermal equilibrium, the condition being satisfied under infinitesimally small temperature variations. Nevertheless, if the melt is rapidly cooled, it may deviate from the thermal equilibrium, being super-cooled without showing any signatures at Tm . Here, “rapid” means a time interval between 10−5 s−1 and 1 day, depending upon the material, in which the disordered atomic structure in a liquid cannot afford enough time to be relaxed into an ordered structure, due to viscosity. With decreasing temperature, as illustrated in Fig. 3.1, the viscosity η rapidly increases reflecting clustering of molecular units (Berthier et al. 2005). This viscosity increase is approximated for many materials by the Vogel–Tamman–Fulcher equation (Elliott 1990, Doremus 1994): η(T) ∝ exp[B/(T − T0 )],

(3.1)

where B and T0 (T0 ), the super-cooled liquid becomes a solid. Here, the solid is empirically defined as a condensed matter in which the temperature, and S the entropy), the specific heat at a constant volume cV = (∂U/∂T)V , and the specific heat at a constant pressure cP = (∂H/∂T)P . If the PV term can be neglected, H = U, and accordingly, F = G. The free energy is freely usable as work and TS is a thermodynamic energy which cannot be utilized as work.

3.2

Glass Transition

67

viscosity is greater than ∼1013 poise (= 1012 Pa · s), because above this value a matter retains its external shape in experimental timescales. At the glass transition temperature, the specific heat (cV or cP ) also changes from a liquidus to a solidus value, which is nearly the same in glass and crystal (as is seen from the parallel enthalpy curves in Fig. 3.1). Configurational freedom is frozen at this temperature, and only vibrational energy gives the specific heat. In short, glass transition can be grasped both in mechanical viscosity and in thermodynamic quantities. In addition, other properties may also change at the glass transition temperature, an example being photoconductivity in As2 Se3 (Thio et al. 1984). A big problem is at what temperature glass transition occurs. For the problem, the best known empirical relation may be Tg (2/3)Tm

(3.2)

(Kauzmann 1948, Wang et al. 2010). Or, as shown in Fig. 3.4, many simple glasses consisting of covalent (ionic) and van der Waals bonds follow a relationship ln Tg = 1.6Z + 2.3,

(3.3)

where Z(= 1 − 2.7) is the average coordination number of atoms (Tanaka 1985). Many other ideas have been proposed for the value of Tg (Elliott 1990, Tichy and Ticha 1995, Kerner and Micoulaut 1997, Naumis 2006). However, interpretations of these relations remain to be studied. More precisely, glass transition does not occur at a fixed temperature. We know that the melting temperature is uniquely determined at 1 atm. However, the glass transition temperature increases if the heating rate d T/d t in thermal analyses is

Fig. 3.4 Dependence of the glass transition temperature Tg of various materials on the average coordination number Z of constituent atoms (Tanaka 1985) (© Elsevier, reprinted with permission). The results for the molecules, which are held by hydrogen bonding, are denoted by open symbols

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3 Structural Properties

increased. It may vary over ∼50 K (Jund et al. 1997, Saiter et al. 2005). Accordingly, reported glass transition temperatures should be regarded as representative values. Otherwise, the temperature may be defined as a limiting value at d T/d t → 0. At this point, we may ask if glass transition is a kind of phase transition. On the basis of this problem, it can be answered unambiguously that practically observed glass transitions arise from relaxational phenomena, since the temperature is determined as a function of heating or cooling rates. However, Kauzmann (1948) pointed out a paradox, more than a half-century ago, with the concept of the so-called entropy crisis (Greaves and Sen 2007). If the temperature is lowered very slowly, and if crystallization can be suppressed, does Tg decrease infinitely? If it decreased, the enthalpy of a super-cooled liquid could make a cross-point X in Fig. 3.1, and it would become smaller than that of the corresponding crystal. But, this seems very unrealistic, or paradoxical. And, we may envisage a critical temperature TK (< Tg ), the so-called Kauzmann temperature, at which the enthalpy lines of super-cooled liquid and crystal make a cross-point. Empirically, this temperature TK , corresponding to X in Fig. 3.1, seems to appear at ∼T0 in the Vogel–Tamman–Fulcher equation (3.1). Following such a notion, we could envisage that a super-cooled state is retained down to TK , where the most stable (and probably uniquely determined) glass appears. In this view, the ideal glass transition can be regarded as a second-order phase transition. Nevertheless, such an ultimately stable glass has never been obtained experimentally or theoretically by computer simulations. Saiter et al. (2005) have examined using thermal analyses a relaxation process in Ge-Se glasses aged over 13 years, while the relaxation seems to be still incomplete. The idea of an ideal glass remains conceptual. Microscopic mechanisms of glass transition are extensively studied, and many ideas have been proposed (Elliott 1990, Das 2004, Greaves and Sen 2007). The simplest and the most intuitive may be the free volume concept proposed by Cohen and Turnbull (1959). Here, the “free volume” means a void in which an atom can move free from constraints (Zallen 1983). In this model, T0 in the Vogel–Tamman–Fulcher equation is regarded as the temperature at which the free volume VF disappears, i.e., VF ∝ T −T0 . However, the free volume may be too conceptual and the model cannot explain relaxational phenomena. At present, it is believed that microscopic dynamics of glass transition can be grasped by the mode-coupling theory (Das 2004), which takes a self-consistent nonlinear feedback interaction between density fluctuations. Otherwise, further developments of an energy landscape scenario (Stillinger 1995) will be valuable. The reader may refer to newer works including computer simulations (Langer 2006, Wilson and Salmon 2009). Relaxation behaviors in super-cooled liquids have also been studied extensively. We first note that, as shown in Fig. 3.1, the super-cooled liquid (a known example being honey) is also in quasi-equilibrium, while its thermodynamical state is uniquely determined as it is located on a straight line which is extrapolated from the melt. Angell (1988) has emphasized for the super-cooled liquid that there are two ultimate types of temperature dependence in the viscosity η(T). As shown in Fig. 3.5, strong glasses such as SiO2 follow an Arrhenius type η ∝ exp[E/(kB T)], where E is

3.3

Crystallization

69

Fig. 3.5 Viscosities η(T) of oxide, chalcogenide, and ZnCl2 glasses as a function of Tg /T (modified from Elliott (1990) and Tverjanovich (2002))

a temperature-independent activation energy, and fragile glasses such as Se follow the Vogel–Tamman–Fulcher behavior, η ∝ exp[B/(T − T0 )]. We may assume that, in the strong glass, T0 = 0 in this equation. Angell has also proposed a measure of glass fragility as (Angell 1995) m = d(log η)/d(Tg /T) T=Tg ,

(3.4)

which can encompass all the widespread behaviors between the two ultimates. In this definition, m ≈ 17 in SiO2 , ∼35 in As2 S3 , and ∼50 in Se. The fragility seems to be a useful macroscopic measure. However, the viscosity is a collective phenomenon encompassing atomic and macroscopic motions, and structural interpretations of m remain to be studied (Wilson and Salmon 2009, Angell and Ueno 2009). Finally, we note that glass transition occurs also as functions of pressure (Eisenberg 1963), chemical bonding (Corezzi et al. 2002), and electronic excitation (Hisakuni and Tanaka 1995). For instance, Yu et al. (2009) demonstrate that glass transitions appear in liquid S and Se upon rapid compression. It has also been demonstrated that ∂Tg /∂P > 0 in oxide and chalcogenide glasses including Se and As2 S3 (Tanaka 1984).

3.3 Crystallization Thermal crystallization occurs in many disordered solids when heated. Elemental amorphous solids such as S and Se are likely to crystallize, since the material has only topological structural disorders. a-Si films also crystallize above ∼500◦ C.

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3 Structural Properties

enthalpy

In contrast, crystallization can be appreciably suppressed in multi-component glasses, because of the compositional disorder. Actually, stable glasses such as SiO2 and As2 S3 do not crystallize, they just continuously transform to a liquid through the super-cooled states. Otherwise, As2 S3 can be partially crystallized by annealing at 300◦ C for 12 days (Yang et al. 1986). Selenides such as As2 Se3 are more likely to crystallize. Te-alloys easily crystallize or decompose, reflecting metallic and fairly isotropic atomic bonds. Crystallization brings some changes in macroscopic properties. When a transparent oxide glass is crystallized, it tends to become frosty, which may be problematic. On the other hand, crystallization (and amorphization) in Te-alloy films, accompanying optical and electrical changes, is a central subject in the recent phase-change memory (Section 7.4). Crystallization occurs also when an amorphous material is subjected to pressure (see Fig. 1.25). Similar to glass transition, crystallization is not a phase transition, but a relaxational phase change. The crystallization temperature Tc also becomes higher with the heating rate ∂ T/∂ t, which is set at 1–20 K/min in conventional calorimetry measurements. Then, what is the difference between glass transition and crystallization? A clear difference is, as suggested from Figs. 3.1 and 3.2, that glass transition appears endothermic but crystallization is exothermic. In addition, the change between a glass and the super-cooled liquid may be reversible, while a crystal cannot directly transform to the glass. Crystallization is a kind of disorder-to-order structural relaxation. Figure 3.6 implies that crystallization occurs with a rate of exp(−EB /kB T), where is a typical vibrational frequency (∼1013 Hz) and EB is the barrier height between a disordered state and the corresponding crystalline phase. In Ge2 Sb2 Te3 films, Tc ≈ 150◦ C and EB ≈ 2 − 4 eV, the latter being dependent upon sample preparations and measuring methods (Section 7.4). It seems that roughly at kTc ≈ EB /100 crystallization occurs, which proceeds through nucleation and growth (Doremus 1994). What determines the value of EB ? When a glass is transformed into a crystal, disordered bonds must be cut and re-connected to the ordered structure. Accordingly,

Fig. 3.6 Enthalpy of a glass and the crystal in a configurational space

configuration

3.4

Thermal and Other Properties

71

Fig. 3.7 Crystallization pressure Pc and temperature Tc as a function of (a) the bond energy (from Pauling) and (b) atomic coordination number for some elemental materials. Lines connect the atoms at the same periodicity in the periodic table

it may be plausible that EB , and accordingly Tc , correlates with the bond strength. However, as shown in Fig. 3.7a, Tc in elemental amorphous materials does not correlate with the bond energy (of Pauling). Nevertheless, we can see in Fig. 3.7b that Tc increases with the coordination number Z. Actually, Tc (K) 190Z seems to be a good approximation for the materials listed. This observation suggests that thermal bond rearrangement becomes more difficult in higher Z materials, having higher dimensional structures. Probably, the bond energy ranging between 1.4 and 2.2 eV plays a secondary role. In contrast, as shown in Fig. 3.7a, crystallization pressure Pc (evaluated at room temperature (Fig. 1.25)) for As, Ge, and Se seems to increase with the bond energy. (No data are available for Pc in Si, P, and S.) These contrasting observations imply that compression directly cuts the covalent bond, while heating induces thermal segmental motions, both leading to crystallization. Similar studies for alloys will be interesting.

3.4 Thermal and Other Properties Comparison of thermal properties in crystalline and non-crystalline materials at room temperature shows interesting features. We here discuss heat capacity and thermal conductivity, the behaviors resembling electronic heat capacity and electrical conductivity, described in Chapter 4. The lattice specific heat c at room temperature is mostly irrespective of (dis-) orderness of atomic structures. It may follow the Dulong–Petit law (Kittel 2005), c = 3 NkB , where N is the Avogadro’s number and kB the Boltzmann constant. In non-metals, the specific heat is given as c = ∂U/∂T, where U is the vibrational energy, which is given as U=

ω D(ω) n(ω) dω,

(3.5)

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3 Structural Properties

where D(ω) is the vibrational density of state and n(ω) is the Planck distribution function. Therefore, the similarity of crystalline and non-crystalline values is ascribed to similar vibrational spectra, which can be measured, e.g., using inelastic neutron scattering or estimated from Raman scattering spectroscopy (see Equation (2.5)). On the other hand, the thermal conductivity of a glass is substantially smaller than that of the corresponding crystal. For instance, it is smaller by an order in g-SiO2 than that in c-SiO2 . The thermal conductivity κ is given as κ = cvs L, where c is the specific heat, vs the sound velocity, and L the mean free path of phonons (Kittel 2005). Since c and vs are comparable in the two forms, the smaller thermal conductivity in g-SiO2 is attributable to a shorter mean free path of phonons in disordered networks. Actually, the values (at 80 K) in c- and g-SiO2 are reported to be 40 (Kittel 2005) and ∼1 nm (Graebner et al. 1986), the latter being a manifestation of phonon localization. The low-temperature anomaly of thermal and elastic properties in glasses has been a big topic, which still remains controversial (Pohl et al. 2002). After the discovery of universal temperature variations by Zeller and Pohl (1971), a lot of studies have been reported for g-SiO2 , while those for chalcogenides such as g-As2 S3 are fewer (Berret and Meissner 1988, Honolka et al. 2002). Table 3.2 summarizes the low-temperature thermal characteristics. As known (Kittel 2005), the specific heat and thermal conductivity in insulating single crystals are understandable using the Debye T3 law at low temperatures. On the other hand, insulating glasses manifest the heat capacity having linear temperature dependence below ∼1 K, the absolute value being greater than that in the corresponding crystal. We thus envisage additional vibrational modes in the glass, which give rise to this linear dependence. In addition, there exists some evidence which suggests that the responsible atomic structure has not a multi- (as the conventional harmonic oscillator), but two-level excitation states, the density being estimated at ∼1020 cm−3 . Studies have then been focused on the atomic structure, which is still vague. Or, the responsible structure may vary among materials and samples. As mentioned in Section 2.4, this topic seems to be related with FSDPs and Boson peaks, giving rise to challenging subjects. It should also be mentioned that, exceptionally, a-Si films, which consist of rigid tetrahedral networks, do not exhibit the anomaly (Pohl et al. 2002). Elasticity is an important macroscopic property of solids, including amorphous materials (Rouxel 2007). Experimental methods employed are common to all the solids. Elastic constants E under static states can be determined from stress– strain curves. The bulk modulus can directly be measured through compression experiments. Or, a dynamical elastic constant is calculated as E = ρvs 2 from

Table 3.2 Comparison of temperature dependences of specific heat c and thermal conductivity κ in crystal and glass such as SiO2 below ∼1 K

Crystal Glass

c

κ

T3 T1

T3 T1

3.4

Thermal and Other Properties

73

the material density ρ and the sound velocity vs . The latter can be measured using acoustic methods (Kittel 2005) and Brillouin scattering spectroscopy as ν = 2(vS /λ) sin(θ/2), where ν is the Brillouin shift, λ the laser wavelength in the material, and θ the scattering angle of the light. We here mention that, in many amorphous materials including a-Si:H films (Grimsditch et al. 1978), the light scattering experiment detects only longitudinal waves, transversal waves being undetectable (Nemanich 1977, Evich et al. 2004). The amorphous material behaves as a liquid at optical frequencies. Comparing static elastic properties of a chalcogenide glass and crystal, an example for Se being listed in Table 3.3, contrastive features are manifested. In general, the glass appears to be softer, which is attributable to less dense and disordered structures (Novikov and Sokolov 2004). In addition, it should be noted that the deformations in insulating glass and crystal are also contrastive. The crystal exhibits elastic and plastic deformations, the latter accompanying motions of defects such as dislocations and stacking faults (Kittel 2005). On the other hand, the glass, which does not contain those defects, is likely to deform viscously after elastic shape changes (Doremus 1994). It is known that solubility of the oxide and the chalcogenide glass is contrastive. As-S(Se) glasses are known to have durability in acid solutions, while these are easily soluble in alkaline solutions, as shown in Fig. 3.8 (Glase et al. 1957). Mamedov (1993) suggests that the solubility of As2 S3 in alkaline solutions initiates with As Table 3.3 Comparison of some elastic constants of glassy (Rouxel 2007) and crystalline (hexagonal) Se (Zingaro and Cooper 1974)

Fig. 3.8 Surface deformations (swelling and attack) of As2 S3 and Pyrex in solutions as a function of pH (modified from Glase et al. 1957)

Bulk modulus Young’s modulus (GPa) (GPa) Poisson’s ratio Glass 9.6 Crystal 17.4

10.3 23.4

0.32 0.27

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3 Structural Properties

oxidation: As2 S3 + 6OH− (alkali) → 2AsO3 3− + 3H2 S. On the other hand, it is known that common soda-silicate glasses, SiO2 –Na2 O, dissolve into acids such as SiO− Na+ + H+ (acid) → SiOH + Na+ (Doremus 1994), while the glass is relatively stable in alkaline. Exceptionally, however, some oxide glasses such as Pyrex (81SiO2 ·13B2 O3 ·4Na2 O·2Al2 O3 ) are stable in acids (Fig. 3.8).

3.5 Magic Numbers: 2.4 and 2.67 Continuous composition changes are inherent to the glass, for which many studies have been reported. Here, it should be recalled, as mentioned in Section 1.6, that there is the notable difference between the oxide and the chalcogenide. In the oxide glass the change occurs in molecular units as xNa2 O–(100−x)SiO2 , where x = 0 − 60 mol%, but the atomic ratio in Si–O can hardly be modified, being possible only at defective levels (less than percent). In the chalcogenide, by contrast, a wide change can occur in the atomic ratio as Asx Se100−x , where x can be varied at 0−60 at.% (Borisova 1981). Such a difference is ascribable to the ionicity and covalency in atomic bonds. In short, chalcogenide glass is intrinsically covalent, and the atomic composition can be continuously varied. In such systems, the average coordination number Z per atom becomes an important parameter, which can be defined as Z = {4x + 3y + 2(100 − x − y)}/100,

(3.6)

for Ge(Si)x As(P, Sb)y S(Se)100−x−y , where 4, 3, and 2 represent the coordination numbers of covalent bonds. Note that the coordination number of Te is likely to vary between 2 and 6, due to metallic character, and the atom may be excluded from the following argument. How does a property change with Z? Several types of composition dependence in Ge–As–S(Se) are summarized in Fig. 3.9 (Tanaka 1989, Wang et al. 2009, Yang et al. 2010): (a) glass transition temperature (Fig. 3.4) and FSDP position, (b) atomic volume and optical bandgap energy (Fig. 4.26), (c) elastic constant and Boson peak position, and (d) FSDP intensity and photodarkening. We see here marked signatures at Z = 2.4 (b) and 2.67 (b, c, and d). Phillips (1979) and other researchers (Döhler et al. 1980, Thorpe 1983) have emphasized the importance of Zc = 2.4 with the following idea: Suppose that the covalent bond (the bond length and the bond angle) is sufficiently rigid, and that this rigidity topologically fixes steric freedom of atom positions. Then, the number of spatial constraints NCO (Z) for a Z-coordinated atom can be written as Nco (Z) = Z/2 + (2Z − 3),

(3.7)

where Z/2 and 2Z − 3 arise from the distance and the angular constraints (see Fig. 3.10a). They further assume that when Nco (Z) = 3 (three-dimensional space) the network is the most stable, or just rigid. This equality with Equation (3.7) gives

3.5

Magic Numbers: 2.4 and 2.67

75

Fig. 3.9 Dependence of several physical properties on the average atomic coordination number Z

Fig. 3.10 Geometrical constraints of a covalent bond OA in (a) three- and (b) two-dimensional spaces

Zc = 2.4. If Z > 2.4 and Z < 2.4, the atomic bond is necessarily strained (rigid) and too flexible (floppy), and such glasses are assumed to become unstable due to strain and entropy. As2 S(Se)3 satisfies the critical condition Zc = 2.4, which can explain the stability of these glasses. Note that neither the chemical nature of bonds nor the medium-range order is taken into account in this idea. It is admirable that this very simple and revolutionary idea, just topological without using quantum mechanics and complicated calculations, has given a firm base for understanding the compositional variation in covalent glasses. The topological idea has then been developed, at least, to three directions. First, Tanaka (1989) has extended this idea to layered structures. In this case, we can write the constraint-dimension balance as Z/2 + (Z − 1) = 3 (see Fig. 3.10b), which gives Zc = 2.67. It seems that a two-dimensional amorphous structure is the most stable at the critical average coordination number of Zc = 2.67. These two magic numbers, 2.4 and 2.67, can explain the composition dependence of physical properties shown in Fig. 3.9 (Tanaka 1989). For instance, the

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3 Structural Properties

minimum atomic volume at 2.4 can be related to the most stable and compact amorphous structure. On the other hand, the maximal volume at 2.67 may be related to a two-dimensional structure, in which the van der Waals bond with wide interlayer separations provides the coarsest volume (Vateva et al. 1993). The physical properties ((b), (c), and (d)) exhibiting signatures at 2.67 are assumed to reflect the two-dimensional structure. For the details in optical gap and atomic volume, see Section 4.10. Second, Boolchand et al. (2001) have emphasized that the transition from floppy to rigid structures does not occur at the critical composition 2.4. Instead, they argue that there exists an intermediate region, called “Boolchand phase,” between the two. The phase is assumed to be self-organized. Since the self-organized structure can absorb some constraint, the threshold becomes a compositional region, not a fixed point. The glass has no more homogeneous continuous random network structures (Micoulaut and Phillips 2007). However, experimental evidence suggesting the intermediate phase is subtle, and the phase possibly depends upon sample preparation and storage conditions. In addition, how we can compromise the self-organized structure and the medium-range structure has not been known. Finally, Phillips’ idea has been extended to oxide glasses (Phillips and Kerner 2008). In their treatment, SiO2 forms a stable glass, because the number of constraint is 2.4, not 2.67 as in GeS(Se)2 , provided that the angular constraint of O atoms can be neglected due to ionicity. In a recent paper, they demonstrate the stability of window glass in a similar way with a composition of 74SiO2 ·16Na2 O·10CaO. It is surprising that just a combination of topological argument with short-range structures can explain the stability of such complicated glasses. However, we should note that the topological idea is not universal. For instance, as shown in Fig. 3.11, composition dependences of the glass transition temperatures in the P–S(Se) systems are markedly different, though the coordination numbers are common. We should consider some difference in constituent molecular units, i.e., a kind of medium-range structures. In addition, it is known that the Urbach

Fig. 3.11 Glass transition temperatures Tg in the Px S(Se)100−x systems (modified from Greaves and Sen 2007)

3.6

Ionic Conduction

77

energy EU shows minima at stoichiometric compositions (Fig. 4.15), not necessarily at Z = 2.4, which manifests the importance of chemical orders.

3.6 Ionic Conduction We know a marked ionic conduction in liquids such as NaCl-solved water, which is in contrast to a negligible conduction in NaCl crystals. However, in some solids, Group I cation such as Li and Ag is mobile, giving rise to prominent ionic conductions. Specifically, in some crystals such as AgI, at temperatures above 150◦ C, the ionic electrical conductivity σ ion is higher than ∼1 S/cm, being comparable to that of the ionic liquid, which deserves the name of a “super-ionic conductor” or “fast ion conductor.” For such materials, extensive researches have been performed, stemming from battery applications (see Section 7.7) and from understanding the conduction mechanism. Note that the anion conduction is not common, the reason being speculated straightforwardly. Figure 3.12 presents several marked features of the electrical conduction in crystals and glasses. First, we see three kinds of materials: the ion conductor being plotted on the left vertical line, the electronic conductor on the lower horizontal line, and the others being ion–electron (hole) mixed conductors. Second, a notable difference between crystal and glass is that there are binary ion-conducting crystals such as Ag2 S, but no binary ion-conducting glasses. The ion-conducting glass is ternary such as Ag–As–S or more complicated alloys. Third, for the same composition of AgAsS2 , the glass possesses a higher ionic conduction than that

Fig. 3.12 Electronic (σe ) and ionic (σi ) conductivities of some solids and NaCl solution (×). All the solids without g- and a- are crystalline. Filled and open circles at σi = 10−15 S/cm denote the electron and the hole conduction, respectively. Since conductivities less than 10−15 S/cm cannot be reliably measured, these are plotted at 10−15 S/cm

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of the crystal. This tendency is in marked contrast to that of the electronic conduction, as exemplified for c- and a-Se in the figure. The reason for a higher ionic conductivity in the glass may be related with less dense and more flexible glass structures containing free volumes, through which an ion can move freely (Tuller 2006). In more detail, we are interested in a universal microscopic model for understanding σ ion in a variety of glasses. Putting it concretely, we want to interpret dependence of the ionic conductivity σ ion on T, P, f, N, etc., where T is temperature, P pressure, f frequency of applied electric fields, and N cation concentration. Here, following the conventional way, we write for a group I cation as σion = e Nion μion

(3.8)

μion = e Dσ /(kB T),

(3.9)

and

where Nion is the mobile ion density, μion the mobility, and Dσ the corresponding diffusion coefficient. Accordingly, the problem is reduced to know the behaviors of Nion and μion , the typical values evaluated from an electrical time-of-flight measurement being 1019 cm−3 and 10−4 cm2 /V·s in g-Ag50 As17 S33 at room temperature (Tanaka et al. 1999). Note that the ion density is much smaller than the Ag concentration of ∼1023 cm−3 . Microscopically, we can write for a cation jumping process as μion = (e/kB T) γ a2 ν exp(Ea /EMN ) exp (−Ea /kB T),

(3.10)

where γ is a geometric factor which comes from a random-walk theory (= 1/6 for jumps in three dimensions), a the jump distance, ν an effective attempt frequency (∼1013 Hz), Ea the activation energy of jumps, and EMN the so-called Meyer–Neldel energy (Ngai 1998, Section 4.9.3), which is introduced for quantitative explanation of the prefactor. For instance, Belin et al. (2000) report Ea ≈ 0.3 eV in an Ag2 S–GeS2 glass. This equation gives ∂μion /∂T > 0, which is consistent with observed temperature dependence of ∂σion /∂ T > 0, the feature being similar to that in the electronic conduction in semiconductors. On the other hand, as exemplified for g-Ag1 As40 Se60 in Fig. 3.13, pressure dependence σion (P) tends to show ∂σion /∂ P < 0, which is opposite to that in the electronic conductivity in similar materials (g-As40 Se60 ). The negative dependence is ascribable to the importance of free volumes in the ionic conduction. The conventional interpretation of the activation energy Ea is to follow the Anderson–Stuart model (Elliott 1990, Doremus 1994). Following Fig. 3.14, we estimate Ea for a jump of a cation X from the left-hand side, where it is bonded to a non-bonding anion A, to the right-hand side, where it will be bonded to a non-bonding anion B as Ea = +ECoulomb (AX) − ECoulomb (XB) + Eelastic ,

(3.11)

3.6

Ionic Conduction

79

Fig. 3.13 Pressure dependence of the electrical conductivity, normalized at the 1 atm value, in g-As40 Se60 (hole conduction) and g-Ag1 As40 Se60 (Ag+ conduction) (Arai et al. 1973, © Elsevier, reprinted with permission)

Fig. 3.14 A schematic illustration of a cation in a binary glass, following the Anderson–Stuart model

A

X

B

r r

where the first and the second terms depict the Coulombic energies and the last term is the elastic energy needed for passing through the central channel produced by bonded atoms. Following the Anderson–Stuart model, we may assume that, with a decrease in r(AX), ECoulomb (AX) increases, giving rise to an increase in Ea . However, this picture seems to be too simplified. Plotting Ea in many ionconducting glasses as a function of the nearest-neighbor distance r around the ion, Fig. 3.15, we notice interesting features in the oxide and the chalcogenide (Tanaka et al. 1999), with an exceptional result of AgI–AgPO3 . One is that Ea of the chalcogenide is smaller than that of the oxide, which implies that σ ion is likely to become higher. The other is the opposite trend: With an increase in r, Ea tends to increase and decrease in the oxide and the chalcogenide, respectively. That is, the oxide glass appears not to follow the Anderson–Stuart model. For total understanding, we may need quantum-mechanical considerations. The oxide and the chalcogenide show another contrastive feature for the mobile atom. It seems that Cu is more mobile in the oxide while Ag is more mobile in the chalcogenide (Minami 1987, Bychkov 2009). Or, in the chalcogenide, Ag appears to be more mobile than Cu (Vlasov and Bychkov 1984, Abe and Nakamura 1988).

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Fig. 3.15 The activation energy Ea of ionic conductions in oxide and chalcogenide glasses as a function of the nearest cation–anion distance r and the corresponding Coulombic energy Ec (Tanaka et al. 1999, © Wiley-VCH Verlag GmbH & Co. KGaA., reprinted with permission)

In the atomic series of Cu, Ag, and Au, why does the larger Ag than Cu show a higher ionic conduction? An explanation is to ascribe the feature to the energy levels of Cu and Ag. Comparative structural (Salmon and Liu 1996) and photoemission (Itoh 1997) studies for selenide glasses suggest that Cu and Ag are more covalently and ionically bonded to Se, the characteristics being governed by the energies of valence electrons in Cu and Ag. Accordingly, Ag+ ions are mobile, and Cu atoms tend to strengthen the network connectivity (Liu and Taylor 1989), giving rise to an increase in the glass transition temperature (Borisova 1981). On the other hand, Au seems to exist as an isolated neutral atom (Kawaguchi et al. 1996). We also mention here that Ag and Cu in chalcogenide glasses possess a kind of mixed-cation effect (Rau et al. 2001): the existence of conductivity extrema at an intermediate composition between Ag and Cu, which is commonly observed in oxide glasses (Doremus 1994). For the dependence of Ea on the cation concentration N, as shown in Fig. 3.16, Bychkov (2009) has discovered for Ag+ in Ag2 S–As2 S3 glasses three regions separated by the boundaries at N ≈ 30 ppm and ∼5 at.%. He assumes that below 30 ppm, Ag+ ions are isolated (dilute limit); above 30 ppm percolative conduction channels appear; and above a few atomic percent, preferential conduction pathways are formed by highly connected ion units. However, the 30 ppm appears to be much lower than the percolative threshold, which commonly occurs at 10–20% (Zallen 1983). To compromise this quantitative discrepancy, he further proposed the “allowed volume” with a spherical radius of ∼2 nm for ion conduction, to which

References

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Fig. 3.16 Ag-diffusion activation energy in Ag2 S–As2 S3 glasses as a function of Ag concentration (Bychkov 2009, © Elsevier, reprinted with permission)

the percolative idea may be applied. However, physical meaning of the allowed volume seems to be vague. Phase-separated structures may be responsible (Mitkova et al. 1999). In addition, there are many unresolved characteristics, an example being σion (f ) ∝ f 1 (Dyre et al. 2009), which resembles that of electronic responses (Section 4.9.4). Finally, we refer to the ion–electron (hole) mixed conduction (Fig. 3.12). Since the oxide glass has bandgap energies wider than ∼5 eV, electronic conduction can be neglected in many cases. On the other hand, the chalcogenide has a gap of 1−3 eV, and accordingly, both the ionic and the electronic conduction are likely to co-exist (Shimakawa and Nitta 1978). Specifically, the selenide glass with Eg ≈ 2 eV behaves as an ion–hole mixed conductor (Vlasov et al. 1987). The mixed conduction plays important roles in the photodoping process (see Section 6.3.13).

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Belin, R., Taillades, G., Pradel, A., Ribes, M.: Ion dynamics in superionic chalcogenide glasses: Complete conductivity spectra. Solid State Ionics 136–137, 1025–1029 (2000) Berret, J.F., Meissner, M.: How universal are the low temperature acoustic properties of glasses? Z. Phys. B 70, 65–72 (1988) Berthier, L., Biroli, C., Bouchaud, J.P., Cipelletti, L., Masri, D.El., L Hôte, D., Ladieu, F., Pierno, M.: Direct experimental evidence of a growing length scale accompanying the glass transition. Science 310, 1797–1800 (2005) Boolchand, P., Georgiev, D.G., Goodman, B.: Discovery of the intermediate phase in chalcogenide glasses. J. Optoelectron. Adv. Mater. 3, 703–720 (2001) Borisova, Z.U.: Glassy Semiconductors. Plenum, New York, NY (1981) Bychkov, E.: Superionic and ion-conducting chalcogenide glasses: Transport regimes and structural features. Solid State Ionics 180, 510–516 (2009) Cohen, M.H., Turnbull, D.: Molecular transport in liquids and glasses. J. Chem. Phys. 31, 1164 (1959) Corezzi, S., Fioretto, D., Rolla, P.: Bond-controlled configurational entropy reduction in chemical vitrification. Nature 420, 653–656 (2002) Das, S.P.: Mode-coupling theory and the glass transition in supercooled liquids. Rev. Mod. Phys. 76, 785–851 (2004) Debenedetti, P.G., Stillnger, F.H.: Supercooled liquids and the glass transition. Nature 410, 259–267 (2001) Döhler, G.H., Dandoloff, R., Bilz, H.: A topological-dynamical model of amorphycity. J. NonCryst. Solids 42, 87–95 (1980) Doremus, R.H.: Glass Science 2nd ed. Wiley, New York, NY (1994) Dyre, J.C., Maass, P., Roling, B., Sidebottom, D.L.: Fundamental questions relating to ion conduction in disordered solids. Rep. Prog. Phys. 72, 046501 (2009) Eisenberg, A.: The multi-dimensional glass transition. J. Phys. Chem. 67, 1333–1336 (1963) Elliott, S.R.: Physics of Amorphous Materials 2nd ed. Longman Scientific & Technical, Essex (1990) Evich, R.M., Perechinskii, S.I., Gad’mashi, Z.P., Shpak, I.I., Vysochanskii, Yu.M., Slivka, V.Yu.: Mandelshtam-Brillouin scattering in As2 S3 and GeS2 chalcogenide glasses. Glass Phys. Chem. 30, 14–16 (2004) Glase, F.W., Blackburn, D.H., Osmalov, J.S., Hubbard, D., Black, M.H.: Properties of arsenic sulfide glass. J. Res. Natl. Bur. Stand. 59, 83–92 (1957) Graebner, J.E., Golding, B., Allen, L.C.: Phonon localization in glasses. Phys. Rev. B 34, 5696–5701 (1986) Greaves, G.N., Sen, S.: Inorganic glasses, glass-forming liquids and amorphizing solids. Adv. Phys. 56, 1–166 (2007) Grimsditch, M., Senn, W., Winterling, G., Brodsky, M.H.: Brillouin scattering from hydrogenated amorphous silicon. Solid State Commun. 26, 229–233 (1978) Hedler, A., Klaumünzer, S.L., Wesch, W.: Amorphous silicon exhibits a glass transition. Nat. Mater. 3, 804–809 (2004) Hisakuni, H., Tanaka, K.: Optical microfabrication of chalcogenide glasses. Science 270, 974–975 (1995) Honolka, J., Kasper, G., Hunklinger, S.: Correlation of low-energy excitations with photodarkening in a-As2 S3 . Europhys. Lett. 57, 382–388 (2002) Itoh, M.: Electronic structures of Ag(Cu)-As-Se glasses. J. Non-Cryst. Solids 210, 178–186 (1997) Jund, P., Caprion, D., Jullien, R.: Is there an ideal quenching rate for an ideal glass? Phys. Rev. Lett. 79, 91–94 (1997) Kasap, S., Tonchev, D.: Thermal properties and thermal analysis: Fundamentals, experimental technique and applications. In: Kasap, S., Capper, P. (eds.) Springer Handbook of Electronic and Photonic Materials, pp. 385–408. Springer, New York, NY (2006) Kauzmann, W.: The nature of the glassy state and the behavior of liquids at low temperatures. Chem. Rev. 43, 219–256 (1948)

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Chapter 4

Electronic Properties

Abstract Electronic density of states in the extended and localized states govern optical and electrical properties. We see, in this chapter, that studies on electronic properties have yielded a lot of valuable ideas, such as Tauc gap, mobility edge, and charged defects. In addition, concepts originally proposed for crystals such as polaron and Urbach edge bear special importance in chalcogenide glasses. We also consider optical nonlinearity, which is prominent in the chalcogenide glass. Electrical conduction mechanisms, under dc and ac electric fields, are also discussed. It is suggested that the Meyer–Neldel law is important to obtain full understanding of the transport mechanisms. The final section refers to composition dependence of the bandgap energy. Keywords Ioffe-Regel rule · Lone-pair electron · Polaron · Charged defect · Urbach edge · Nonlinear optics · Meyer-Neldel rule · Hopping

4.1 Electronic Structure As illustrated in Fig. 4.1, the electronic structures in crystals and non-crystals show characteristic features. For the crystal, we can calculate under a one-electron approximation, using Bloch functions in known periodic structures, the electron dispersion curve (electron energy E – wavenumber k), from which the electron density of state (DOS) D(E) is straightforwardly calculated (Kittel 2005). In contrast, Bloch functions cannot be assumed for disordered materials. The wavenumber k is no more a good quantum number, due to the localization of electron wavefunctions to spatial extent of r, which must satisfy the uncertainty

Bloch function

Atomic structure

E~k

atomic energy level and bonding

D(E)

D(E)

Crystal

Non-crystal

Fig. 4.1 Relationships between atomic and electronic structures in crystals and non-crystals

85 K. Tanaka, K. Shimakawa, Amorphous Chalcogenide Semiconductors and Related C Springer Science+Business Media, LLC 2011 Materials, DOI 10.1007/978-1-4419-9510-0_4,

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principle k·r ∼ 1. Or, the electron mean free path is assumed to be of the order of ∼ 1/k, which is the so-called Ioffe–Regel rule (Mott and Davis 1979, Elliott 1990). Accordingly, the dispersion curve cannot be delineated. However, the DOS is still a useful quantity, which may be estimated as follows: First, molecular energy levels are assumed from a bonding structure and the energy level (Fig. 1.10) of constituent atoms. The molecular level broadens into a band, reflecting partial extensions and overlaps of related wavefunctions, and the resulting energylevel density determines the DOS. Computer simulations will provide its detailed shape. It may be instructive to sketch out a rough view of relationships between atomic and band structures using the tetrahedrally coordinated two-dimensional lattices shown in Fig. 4.2. Note that the short-range structures of these three clusters are similar. (The bond angle may be strained in these two-dimensional lattices, but it can be reduced in the three-dimensional space.) We here consider the roles offered by the short-range, medium-range, and defective structures (Table 4.1). First, the DOS in a glass is similar to that in the corresponding crystal, since both are governed by the short-range atomic structure. Accordingly, the bandgap energies and also optical absorptions at ω > Eg are roughly the same.

Fig. 4.2 Three tetrahedrally coordinated clusters and the corresponding band structures: (a) crystal, (b) strained lattice with a dangling bond, and (c) strained fully connected network

Table 4.1 Effects of structural elements (left) upon some electronic properties Optical absorption Structure Short range Medium range Defect Impurity Inhomogeneity

(ω > Eg )

(ω ∼ Eg )

◦

◦

(ω < Eg )

Transport

Photoluminescence

? ?

? ?

? ?

◦ ◦

◦

◦ ◦

Polaronic effects are neglected. Double and single circles denote strong and medium effects, respectively. “?” remains to be studied.

4.1

Electronic Structure

87

Second, however, the band edge seems to critically depend upon the structural periodicity. In a hypothetical ideal single crystal (a), the edges of the conduction and the valence band are flat in space, and all the electron wavefunctions extend over the crystal. However, in disordered structures, the band edge may be modified by medium-range structures, e.g., (b) a 5-membered ring and (c) a strained 3-membered ring. And, the modifications may be different in the conduction and the valence band. Provided that the bond is of sp3 type as in Si, an angular strain gives greater effects upon the valence band edge, because it is governed by the directional p orbital, in contrast to the conduction band edge being governed by the spherical s orbital (Phillips 1973). Or, in the chalcogenide, the conduction and the valence band are composed of anti-bonding and lone-pair electron states (Fig. 1.11), which will reflect structural disorders differently. Third, a defect provides some effects. A dangling bond, if it is in solid Si, produces a mid-gap state. For this reason, pure a-Si has a lot of mid-gap states. The state will govern mid-gap optical absorption and photoluminescence. Instead, in a-Si:H, the dangling bond can be terminated by a H atom, and the mid-gap state is reduced. It is plausible that the preparation and prehistory affect more strongly the band edges and gap states than the gross electronic structure. It may be valuable to add a remark about atomic (impurity) doping and the Fermi energy. In single-crystalline semiconductors such as Si and GaAs, minute atomic doping (less than ∼0.01 at.%) can shift the energy position of the Fermi level from the mid-gap to a band edge, exhibiting a change in the electrical activation energy from Eg /2 (intrinsic) to ∼0 (extrinsic). However, such a doping effect hardly appears in oxide and chalcogenide glasses, with some exceptions (Ovshinsky and Adler 1978, Tohge et al. 1980, Narushima et al. 2004). In most of the chalcogenides, the activation energy is ∼Eg /2, which suggests that the Fermi level is pinned near the middle of the bandgap. Even in a-Si:H, percent-order (∼5%) dopants are needed for producing n- and p-type a-Si:H, which means that the doping efficiency is much lower in amorphous semiconductors. The fluctuating band structure may modify the states produced by dopants and/or the flexible amorphous structure may compensate the inherent (spatially constraint in the crystal) coordination of dopants. As illustrated in Fig. 4.3, in the band structure, an electron undergoes three kinds of movements: (i) energetic transition, (ii) transport including (de-)trapping, and

Fig. 4.3 Three kinds of electron movements, transition (solid arrows), transport (dashed arrow), and hopping (dotted double arrow), in a semiconductor having gap states

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(iii) local motions between gap states. The energetic transition occurs as a result of optical processes (absorption/emission) or thermal relaxation (vibrational). The transport can occur as drift and diffusion under dc electric fields and gradients of carrier densities. Finally, a carrier may move between gap states through tunneling. Here, it should be mentioned that “hopping” has been used in two ways: quantal and classical, which should be distinguished. Zallen (1983) states that “The term hopping is an abbreviation for the phonon-assisted quantum-mechanical tunneling of an electron from one localized to another.” We will follow this terminology. It should also be noted that, in the conventional band model, the atomic structure is assumed to be rigid. However, the polaron, originally proposed for ionic crystals (Kittel 2005), adds variety and complexity to electronic (electrical and optical) properties in flexible disordered lattices (Emin 1975, Abe and Toyozawa 1981, Emin 2008). The band model cannot enclose the polaron, and instead, we may employ the energy configuration diagram as in Fig. 4.4 for representing the dynamics. Here, the energy in the vertical scale is the total energy of an electron (or hole) and N deforming atoms (strained bonds). The horizontal configuration axis symbolizes a 3N Euclidean space of constituent atoms (see Fig. 3.1). In the simplest case, such as a point defect, the axis may represent the interatomic spacing near the electron. And, the energy curves of the ground and the excited states of this electron-atom system become parabolic under a harmonic approximation for strain energies. In this representation, the polaron can be expressed as the laterally shifted energy minimum of an excited state. (In a rigid lattice, the energy minimum is located above the point O.) As a consequence, in photoluminescence, the emission energy (EPL ) becomes smaller than the absorption energy (Eexc ), the energy difference Eexc − EPL appearing as a Stokes shift (Street 1976). We can also envisage more complicated systems such as bi-polaron, excitonic polaron, and self-trapped polaron.

Fig. 4.4 A polaron in an energy configuration diagram with schematic square-lattice structures, in which open and solid circles represent atoms and electrons, respectively

4.2

Band Structure

89

4.2 Band Structure How can we experimentally determine the DOS structure? Naturally, we probe the DOS with photons. The valence band DOS can be straightforwardly determined by photoelectron spectroscopy using ultraviolet and x-ray photons (Elliott 1990). On the other hand, the conduction band DOS can be investigated using inverse photoelectron spectroscopy, a kind of electron-excited luminescence spectroscopy (Matsuda et al. 1996, Ono et al. 1996). An example of structures obtained for Se is shown in Fig. 4.5. The energy resolution of these measurements is typically ∼0.5 eV, which is not sufficient for probing the band-edge and bandgap states. Another drawback of photoelectron spectroscopy is the limited escape depth of electrons (∼10 nm), i.e., it is surface sensitive. In addition, the charge-up of investigated insulating materials resulting from electron emission is likely to deform obtained spectra, which may be suppressed by carbon coating or compensated by intentional electron flooding. On the other hand, wide-range optical spectra contain information of the DOS (see Equation (4.1)). For instance, it is conventional to obtain spectral dielectric functions, which correspond to the joint DOSs of valence and conduction bands, from ultraviolet reflection spectra (Sobolev and Sobolev 2004). Otherwise, since the inverse photoemission is less sensitive, a combination of the photoelectron and the optical spectroscopy may be more useful for determination of the conduction and valence band structures (Lippens et al. 2000). The DOS has been theoretically analyzed. Originally, the analyses followed tightbinding calculations and, recently, ab initio computer simulations (Drabold and Estreichen 2007), in which gloss features are consistent. However, for band-edge

Fig. 4.5 DOSs of an amorphous (upper) and a crystalline (lower) Se determined by photoelectron and inverse photoelectron spectroscopy (Ono et al. 1996, © IOP Publishing Ltd., reprinted with permission)

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and gap states, the results depend upon calculations. In addition, it seems more difficult to take polaronic effects into account. The most important and unique feature in the electronic structures of simple oxides and chalcogenides, irrespective of glass and crystal, is the character of the valence band. As shown in Fig. 1.11, the upper edge (HOMO) of the valence band is produced by lone-pair electron states of chalcogen atoms (electron-filled pz states in Fig. 1.11) (Kastner 1972). The bandwidth is governed by the interaction among lone-pair electrons, as suggested by pressure studies (Zallen 1983, Tanaka 1989a). Below the lone-pair electron band, there exists another occupied band, which originates from bonding states, e.g., σ (As–S) in As2 S3 . On the other hand, the conduction band (LUMO) is produced from the anti-bonding state σ ∗ . Or, in oxides such as SiO2 , which is partially ionic, it is governed by vacant d states of cation Si4+ . Figure 4.6 compares (a) a chemical bond diagram for SiO2 and calculated dispersion curves for (b) c-SiO2 (Chelikowsky and Schl˝uter 1977) and (c) c-As2 Se3 (Tarnow et al. 1986). The common feature for the lone-pair electron bands can be pointed out in the dispersion diagrams at 0 to −4 eV in c-SiO2 and 0 to −5 eV in c-As2 Se3 . Below the lone-pair electron bands, there exists another band at around −10 eV, which arises from the bonding states. Note that the width of the lone-pair electron band in SiO2 is smaller than the σ -band width, while the opposite holds in As2 Se3 . This feature may reflect different strengths of interaction between lone-pair electrons. We also see in c-SiO2 that the electron effective mass (1/m∗ ∝ ∂E2 /∂ k2 ) is substantially smaller than the hole mass. A chemical interpretation of this result may be obtained by recalling the relatively spherical, and extended, d-state of Si. In contrast, such a clear mass difference is not seen in c-As2 Se3 . It is difficult to identify effects of medium-range structures on the electronic structure. For crystals, we can point out substantially different bandgap energies (3.5 and ∼3.6 eV) in three-dimensional GeS2 and two-dimensional GeS2 , both having

Fig. 4.6 (a) A chemical bond diagram for SiO2 and electronic dispersion curves in (b) c-SiO2 and (c) c-As2 Se3 (modified from Griscom 1977 and Tanaka 2004). Note that, for the vertical axes in the three figures, the tops of the valence band (HOMO level) and the scales are common

4.3

Bandgap and Mobility Edge

91

Fig. 4.7 Occupied (gray) and unoccupied (white) energy levels of Cu, Pb, and Na in SiO2 glass

similar short-range structures consisting of ≡Ge−S− connections (Weinstein et al. 1982). For non-crystals, known examples are limited. As2 S3 glass and its asevaporated film have nearly the same short-range structures including =As–S– linkages and similar optical gaps of ∼2.4 eV. In detail, however, the film exhibits a slightly wider optical gap by ∼50 meV, which may be ascribed to smaller widths of the valence band reflecting molecular structures in as-evaporated films (Fig. 2.3). Electronic structures in multi-component systems have been studied less deeply. Figure 4.7 summarizes energy levels of Na, Cu, and Pb in silica glass. Na and Cu atoms produce one band, while heavier Pb gives both HOMO and LUMO states. For the chalcogenide, limited materials such as Ag(Cu)–As–S(Se) (Simdyankin et al. 2005a) and Ge–Sb–Te (Xu et al. 2009) have been studied with specific reference to ionic conduction and phase change. However, if the concentrations of every component are comparable, for which we cannot apply a dilute limit approximation, it is difficult to obtain certain universal insights into the electronic structure. The electronic structure governs electronic properties: optical, electrical, and photo-electrical. The optical property is understandable in principle through the conventional transition-probability formulation, provided that the structure is rigid so that polaron effects can be neglected. The electrical property is more difficult to interpret, because the carrier transport is markedly influenced by band-edge and mid-gap states. Photo-electrical property is the most difficult to understand, because it appears through optical excitation and carrier transport.

4.3 Bandgap and Mobility Edge In a rigorous sense, the concept of the bandgap energy Eg in amorphous semiconductors still remains vague. In a crystalline semiconductor, if it is intrinsic, Eg o = Eg e , where Eg o and Eg e are optically and electrically determined (from the optical absorption edge and from temperature dependence of the electrical conductivity) bandgap energies. However, pioneering studies on amorphous semiconductors have demonstrated that Eg o < Eg e . This observation has delivered the so-called Mott-CFO model (Cohen et al. 1969, Mott and Davis 1979). In this model, as shown in Fig. 4.8, the DOS smoothly reduces around the band edges. In contrast, reflecting spatially fluctuating potentials, the mobility is assumed to abruptly (or

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Fig. 4.8 Spatial fluctuations of the band edges (center), the DOS (left), and the mobility (right) as a function of electron energy (Fritzsche 1971, © Elsevier, reprinted with permission)

discontinuously at 0 K) drop to zero at the band edges. This mobility edge distinguishes extended and localized wavefunctions (Baranovskii and Rubel 2006). Under this model, we assume that the optical gap Eg o is governed by the DOS, and the electrical Eg e is equal to the gap between the mobility edges. However, the Mott-CFO model should be regarded as a guiding idea. The model is a kind of modified band model, following a “frozen-lattice” approximation, and accordingly, it cannot account for polaron effects. The model may be applied to amorphous tetrahedral semiconductors, in which the conduction and the valence bands arise from anti-bonding and bonding states of fourfold coordinated (rigid) sp3 electrons. However, it seems difficult to apply the model to the chalcogenide, which contains the valence and the conduction band having different origins. The model also faces an experimental problem. To determine a value of the mobility gap, we may examine spectral dependence of photoconductivity, expecting an abrupt photocurrent increase at ω≥Eg e (>Eg o ). However, in some materials such as a-Se, there exists a so-called non-photoconducting gap, i.e., the photoconducting edge is blue-shifted from the optical gap, which is ascribed to geminate (exciton-like electron–hole pairs) recombination processes (see Section 5.4). In short, it is not straightforward to determine the mobility gap.

4.4 Gap States The defect is likely to produce a gap state. However, for obtaining experimentally reproducible results on the gap state, we need to adopt several precautions. First, when investigating the gap state, which may have a density less than ∼1018 cm−3 , we should have a sample with purity higher than ∼five 9’s. Raw materials for producing a sample may have a purity of six 9’s, while the value is just nominal, materials being often oxidized (Churbanov and Plotnichenko 2004). It is also known that electronic properties in a-Se are likely to be affected by minute impurities (Kasap et al. 2009, Benkhedir et al. 2009). Second, the gap state must be sensitive to preparation conditions and prehistory of the samples. Third, the measurement

4.4

Gap States

93

itself may have some problems. Gap states can be probed optically, electrically, and photo-electrically. Among these, the optical method seems to be the most reliable, since it does not need the electrode, which is likely to add interfacial effects on obtained results (Tsiulyanu 2004). On the other hand, theoretical results largely depend upon their formulations (Drabold and Estreichen 2007), because localized defect states are likely to have strong interaction with disordered lattices, the situation which is more or less difficult to analyze. The wrong bond, the existence in g-As2 S(Se,Te)3 being structurally confirmed (with densities of 1–10% as described in Section 2.5), possibly causes major gap states. However, its energy location is speculative. It seems that cation and anion wrong bonds, respectively, do and do not produce gap states. Halpern (1976) proposes that As–As σ bonds in As2 S3 produce states above the valence band. On the other hand, Vanderbilt and Joannopoulos (1981) and Tanaka (2002) propose that As–As σ ∗ states are located below the conduction band, which seem to provide gap states with a characteristic energy EW , giving rise to a weak absorption tail (Section 4.6). For GeS2 , it is known that the bulk and the evaporated film have substantially different optical bandgaps: 3.2 eV in bulk and ∼2.5 eV in film, for which the smaller film gap is ascribed to a lot of Ge–Ge wrong bonds (Tanaka et al. 1984). Actually, Hachiya (2003) demonstrated through first-principles calculations that the Ge–Ge wrong bond in GeS2 produces a σ ∗ state near the bottom of the conduction band. For SiO2 , Mukhopadhyay et al. (2005) theoretically predict that σ (Si–Si) bonds give rise to occupied states at ∼2 eV above the valence band edge. Other defects, which may produce gap states, have been proposed (Ovshinsky and Adler 1978, Tarnow et al. 1989, Simdyankin et al. 2005), while almost all have not been experimentally confirmed. A repeated subject on defects in chalcogenides is the charged dangling bond, D+ and D− in the notation by Street and Mott (1975). Here, D stands for an atom having a dangling bond. The atom is in general neutral, which is expressed as D0 . However, it was known that the chalcogenide glass, except Ge-chalcogenides, does not provide ESR signals. Or, more precisely, the spin density of unpaired electrons in a-Se and As-chalcogenide glasses is smaller than an instrumental detection limit of ∼1015 spin/cm3 (Agarwal 1973), which manifests the non-existence of D0 . Despite such observations, experiments demonstrate, e.g., pinned (doping-insensitive) Fermi level and trap-limited hole transport, which may suggest the existence of substantial numbers of gap states. To settle down these puzzling features, Street and Mott (1975) have proposed, taking the concept of negative electron correlation energy (attracting two electrons) proposed by Anderson (1975) into account, that positively and negatively charged dangling bonds, D+ and D− , exist in more stable ways than the neutral D0 . Note that these charged defects are ESR-inactive, consistent with the observation, since there are no unpaired electrons in D+ and D− . They also have estimated the density of the charged defect at 1017 − 1018 cm−3 . Later, Kastner et al. (1976) developed the concept, proposing a valencealternation pair model, which relates the charged defects to the ill-coordinated atoms (Fig. 4.9). They use notations such as C1 − , which denotes a onefold coordinated negatively charged chalcogen. In this model, formation energies of 2C1 0 (2D0 ) and

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−2Eσ −2Eσ+Δ −3Eσ − Eσ −Eσ+ULP Fig. 4.9 Structure of a chalcogen in normal (C2 0 ) and defective (other) states (Kastner et al. 1976, © American Physical Society, reprinted with permission) and the electronic energies. The energy level consists of the three: from the top σ ∗ , lone-pair electron, and σ states. Adjusting an energy scale for the lone-pair electron state as a reference, we define −Eσ to be the bonding energy, Eσ + the anti-bonding (∼bandgap) energy, and ULP the correlation energy between pairs of lone-pair electrons

C3 + + C1 − are estimated to be −2Eσ and −4Eσ + ULP , which suggests higher chemical stability of the charged pair and, accordingly, supports their existence. Rigorously speaking, the concepts by Street and Mott (charged dangling bond) and Kastner et al. (valence-alternation pairs) are somewhat different, while we will hereafter regard these models to be conceptually the same. The charged pair model has been widely employed and extended (Mott and Davis 1979). It is theoretically predicted that D− and D+ produce gap states, respectively, above the valence band and below the conduction band. Many observations such as the Urbach energy, ESR, and photoluminescence have been interpreted on the basis of this model (Kolobov et al. 1998, Taylor 2006). Some researchers extend this idea also to the oxide, SiO2 (Martin-Samos et al. 2007). On the other hand, Baranovskii and Karpov (1987) propose a model, which applies Anderson’s concept (1975) to polarons. In contrast to such wide applications, the charged pair model remains a subject of controversy. Structural experiments are unable to give convincing results. Indeed, we have no tools which can detect point-like defects with a density of ∼1018 cm−3 in disordered lattices. Raman scattering spectroscopy may be the most suitable for detecting ESR-insensitive defects, while its sensitivity seems to be ∼1%, ∼1020 cm−3 , at the best. In addition, some experiments provide negative results for the existence, an example being the viscosity in Se. Liquid Se is assumed to be a mixture of chain molecules, and as shown in Fig. 4.10 the lengths at the melting point Tm are estimated to be 105 −106 from viscosity and magnetic measurements (Warren and Dupree 1980). When quenched into a glassy state, chain ends will be connected, so that the chain will become longer. Thus, the dangling bond becomes fewer than 1016 cm−3 , which is substantially smaller than the predicted charged defect density of 1018 cm−3 .

4.5

Optical Property

95

Fig. 4.10 Average chain length of Se as a function of temperature (modified from Warren and Dupree 1980). Full curves are obtained from 77 Se NMR, MWP from magnetic susceptibility, and KB from viscosity. Tm is the melting temperature and Tc is the super-critical temperature

The model is questionable also from a theoretical point of view. In noncrystalline solids, any kind of (point) defects might exist, and accordingly, what is important is the number density N, which can be estimated from the formation energy G as N = N0 exp(−G/kB Tg ) under an assumption of local thermal equilibrium at the glass transition temperature Tg . If N < 1015 cm−3 , the defect will be neglected in practice. However, theoretical estimation of G is very difficult, since we should consider related charge distributions and lattice distortions. Actually, calculations for the simplest materials, a-Se (Vanderbilt and Joannopoulos 1983) and a-S (Itoh and Nakao 1986), cannot provide conclusive evidence of the (non-)existence. In short, although the charged pair model remains a good working hypothesis, its existence has not been confirmed.

4.5 Optical Property Having seen the relationship between the atomic and the electronic structure, the next subject is to relate the electronic structure with optical properties. Here, the fundamental optical properties are absorption and refraction with the coefficients α and n (or, equivalently, ε 1 and ε 2 ), which are connected through Kramers–Krönig relations (Kittel 2005). Which is a more intuitive quantity, α or n? Comparing absorption and refraction, we know that absorption is related more directly to the DOS with a simpler expression such as Equation (4.1). Accordingly, it is instructive to consider the absorption (or ε 2 ) first, the examples being given in Fig. 4.11, which will be transformed to

4 Absorption coefficient (cm–1)

96 106

Electronic Properties

10 K 10 K

104

180 K

102

SiO2

As2S3

100 10–2 10–4 10–6

0

1

2

3

4

5 6 7 8 9 Photon energy (eV)

10

11

12

13

Fig. 4.11 Optical absorption (solid lines) and photoconductive (dashed lines) spectra in As2 S3 and SiO2 glasses. Without the results indicated as 10 and 180 K, the spectra are obtained at room temperature (Tanaka 2002, © INOE, reprinted with permission)

the refractive index (or ε1 ) through the Kramers–Krönig relation. Note that the optical absorption at infrared regions arises from atomic vibrations, while this section focuses on the electronic transition.

4.6 Optical Absorption The optical absorption coefficient, α(ω), for electronic transitions in disordered semiconductors can be written as (Mott and Davis 1979) α(ω) ∝ |< ϕf | H|ϕi >|2

Df (E + ω) Di (E) dE,

(4.1)

where ϕ is an electron wavefunction (not Bloch functions, but atomic), H the electron–light interaction Hamiltonian, D the density of state, E the electron energy, and the subscripts i and f initial and final states, respectively. In this equation, the wave-vector conservation rule is neglected due to localized wavefunctions in disordered materials (Section 4.1). Absorption occurs through the so-called non-direct transition. In addition, the transition probability |< ϕf | H|ϕi >|2 is assumed to be independent of E, which seems to be a critical assumption. Polaron effects are also neglected implicitly. Under these frameworks, as given by Equation (4.1), the absorption coefficient can be expressed simply by a product of the transition prob ability |< ϕf | H|ϕi >|2 and the convolution integral Df (E + ω)Di (E)d E of the DOSs. On the other hand, experimentally obtained absorption spectra α(ω) in amorphous semiconductors such as As2 S(Se)3 have been approximated by the three functions. From high to low absorption regions, α(ω) ∝ (ω − Eg T )n , exp(ω/EU ), and exp(ω/EW ), as described below.

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Optical Absorption

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4.6.1 Tauc Gap At α 103 cm−1 , we approximate the absorption spectrum as (Mott and Davis 1979) α(ω) ∝ (ω − Eg T )n .

(4.2)

Here, Eg T is the so-called Tauc optical gap and n = 2 in simple materials such as As2 S(Se)3 and n = 1 in a-Se.1 At ω = Eg T , α ≈ 103 − 104 cm−1 in many materials. It should be noted that, for evaluating absorption spectra at these high absorption regions from optical transmittances, we need thin samples with thicknesses of ∼α −1 , which is 1–10 μm. Such thin samples may be prepared through vacuum deposition, while the property is likely to be different from that of the corresponding bulk glass. Taking such features into account, reproducibility of absorption spectra among many reports is acceptable, as exemplified for As2 S3 in Fig. 4.12. In oxide glasses, the absorption edge is located at ultraviolet regions, reflecting bandgap energies greater than ∼5 eV, so that the absorption spectra have been evaluated in a few materials such as Si(Ge)O2 (Saito and Ikushima 2000, Terakado and Tanaka 2008). Temperature dependence of Eg T (or Eg ) has been studied for several materials. As exemplified in Fig. 4.13 for As2 Se3 , ∂ Eg /∂ T < 0 in amorphous semiconductors

Fig. 4.12 Optical absorption edges of a-As2 S3 at room temperature, reported from several groups. Note that lower and higher absorptions than ∼103 cm−1 are measured using bulk samples and deposited films. Tauc gaps are located at 2.35–2.40 eV

1 Theoretically, we may multiply the right-hand side by 1/ω, while the factor gives least effects. Absorption with n = 2 appears also in indirect transitions in crystals, which suggests that static and vibrational disorders play similar (neglecting and suppressing wavenumber conservation) roles in the electronic excitation.

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Fig. 4.13 Temperature dependences of the optical gap Eg and the Urbach energy EU of As2 Se3 (modified from Andreev et al. 1976)

(Andreev et al. 1976, Tichý et al. 1996, Inagawa et al. 1997). The negative dependence can be interpreted following the conventional electron–phonon coupling model for semiconductors. On the other hand, pressure dependence is interesting. To the authors’ knowledge, all the amorphous semiconductors exhibit negative pressure dependence ∂ Eg /∂ P 0, as in Fig. 4.14 for g-As2 S3 (Weinstein et al. 1980). In detail, however, ∂ Eg /∂ P ≈ 0 in a-Si(Ge):H, while negative pressure dependence is prominent (∼10 meV/kbar) in the chalcogenide (Fig. 1.25), which is interpreted as a manifestation of widening of the lone-pair electron band resulting from enhanced intermolecular interaction by compression (Zallen 1983, Tanaka 1989). Note that ∂ Eg /∂ P > 0 in many (direct-gap) crystalline semiconductors such as ZnTe

Fig. 4.14 Optical transmittance of a-As2 S3 , in comparison with that in c-ZnTe, as a function of hydrostatic compression (Weinstein et al. 1980, © Elsevier, reprinted with permission). The upper and lower scales apply to ZnTe and As2 S3

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Optical Absorption

99

(Figs. 1.25 and 4.14), which can be ascribed to reductions in covalent bond lengths (Ghahramani and Sipe 1989). As shown in Fig. 4.12, the high absorption spectra experimentally obtained are fairly reproducible, while the interpretation remains vague. It has not been elucidated whether the Tauc curve arises from band-to-band (extended-extended states) or band-to-edge (extended-localized states) transitions. If the Tauc gap is governed by the transitions between the extended states, it should be equal to the mobility gap, which is not consistent with observations. (For a-C:H films, Cherkashinin et al. (2006) report a big difference: the mobility gap of ∼5.3 eV and the Tauc gap of ∼1 eV.) Such results probably evince that the Tauc gap arises from optical transitions between localized and extended states. Then, does the localized state belong to the valence band or the conduction band? In addition, why can the curve be fitted to such high photon energy regions up to (1.5 − 2) × Eg in a-As2 S3 ? We have not yet obtained clear answers.

4.6.2 Urbach Edge At 103 cm−1 α 100 cm−1 , α follows the so-called weakly temperaturedependent Urbach edge (Mott and Davis 1979). The curve has an exponential form as α(ω) ∝ exp (ω/EU ),

(4.3)

where EU is referred to as the Urbach energy. It possesses positive temperature dependence, ∂ EU /∂ T > 0 (Fig. 4.13), in many chalcogenide glasses (Andreev et al. 1976, Tichý et al. 1996), which is common to that in crystals such as AgBr and GaAs (Johnson and Tiedje 1995). On the other hand, as exemplified in Fig. 4.14, ∂ EU /∂ P > 0 for all the chalcogenide glasses examined (Tanaka 1989). We should mention, however, that not all the glasses exhibit the Urbach edge, as demonstrated for a ternary system As–S–Te (Farag and Edmond 1986). Origins of the Urbach edge are also unclear. The temperature-dependent Urbach edge, α ∝ exp(ω/kB T), appearing in polar crystals has been interpreted by assuming optical absorption by excitons in electric fields. In contrast, in many amorphous semiconductors, the Urbach edge is nearly temperature independent around room temperature (Fig. 4.13), which is interpreted in two ways. The first one ascribes it to a polaron effect (Fig. 4.4). If the lattice is flexible as in Se, electron–lattice interaction possibly governs the absorption spectrum (Abe and Toyozawa 1981). On the other hand, several studies using structural and optical experiments for aSi:H, As2 S3 , and SiO2 (Kranjˇcec et al. 2009) suggest close connections between EU and static structural disorder, which support an idea based on disorder-induced band tailings (Ihm 1985, Pan et al. 2008, Sadigh et al. 2011). It is also mentioned that Okamoto et al. (1996) have theoretically considered a correlation between Eg T and EU , the result requiring a total understanding of the Tauc and the Urbach curve.

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Electronic Properties

Fig. 4.15 The Urbach energy EU as a function of the average coordination number Z (Oheda 1979, Andreev et al. 1976) for the glassy systems listed

Coordination number Z

In addition to these ambiguous origins, the Urbach curve manifests, at least, two puzzling features as the following. One is the existence of a minimal Urbach energy of EU ≥ 50 − 60 meV in amorphous materials (Tanaka 2002). The value is surprisingly universal (Dunstan 1982) including SiO2 (Saito and Ikushima 2000), As2 S3 , Se, Ge2 Sb2 Te5 (Kato and Tanaka 2005), other chalcogenide alloys (Inagawa et al. 1997), and even a-Si:H and polyacetylene (Weinberger et al. 1984), despite big differences of Eg ≈ 1 − 10 eV. However, no ideas have been put forward on this universality. If the Urbach energy is determined by structural order, the minimal energy may imply a “minimal structural disorder.” In contrast, we should also note that some materials such as GeO(S)2 show less steep Urbach edges (Terakado and Tanaka 2008), which may be governed by defects. In addition, as shown in Fig. 4.15, in non-stoichiometric binary alloys, the Urbach energy tends to become greater than the minimal values at stoichiometric compositions. The other is the existence of an Urbach-edge focus. The feature has been discovered for a-Si:H films by Cody et al. (1981), which was pointed out later also for temperature variations in As2 S3 and SiO2 (Kranjˇcec et al. 2009). In α = α0 exp (ω/EU ), α 0 and EU have a relation as α0 = α00 exp(EU /E0 ), where α 00 and E0 are constants characterizing the focusing point. This relationship appears functionally similar to that of the Meyer–Neldel rule (Section 4.9.3), while its implication remains to be considered.

4.6.3 Weak Absorption Tail Below ∼100 cm−1 , α shows another more gradual exponential spectrum: α(ω) ∝ exp(ω/EW ),

(4.4)

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Optical Absorption

101

which is referred to as a “weak absorption tail” or “residual absorption” (Mott and Davis 1979). For instance, EW ≈ 200 meV in g-As2 S3 (Tanaka et al. 2002). Precise measurements of this absorption tail, however, are relatively difficult due to the small absorption (≤ 100 cm−1 ), which should be distinguished from light scattering. Accordingly, reported results are few. In some measurements, photo-thermal spectroscopy, which is less influenced by light scattering, has been employed (Tanaka et al. 2002). Note that it is not clear if a-Se exhibits the absorption tail (Tanaka et al. 2002). The situation in g-SiO2 is also unclear, which gives several absorption peaks (not the exponential tail) below the Urbach edge, which are attributed to defects and impurities (Kajihara et al. 2008). For the absorption tail in g-As2 S(Se)3 , impurities are undoubtedly an origin. An example is shown by the solid lines in Fig. 4.16a, in which the Fe content in As2 S3 is systematically changed (Tauc 1975). We see that Tauc’s purest As2 S3 sample, denoted as “pure,” has maximal absorption of 10−1 cm−1 at ∼1.5 eV, while the level is further decreased by one order in a more recent sample (Tanaka et al. 2002). In addition, Kitao et al. (1977) have demonstrated systematic increases in the tail absorption, without a notable change in the Urbach edge, by addition of Ag (<2.5 at.%) to As2 Se3 . Therefore, it is tempting to assume that the absorption tail will disappear in ultimately pure samples. Nevertheless, the composition dependence shown in Fig. 4.16b reveals another feature. In the As–S system, the weak absorption tail appears to be most prominent around the stoichiometric composition As2 S3 (Tanaka et al. 2002). We then envisage

103

103 200 ppm

101

120

100

26

10–1 pure

10–2 10

–3

101 100

1.5 2 2.5 Photon energy (eV)

(a)

3

100

–1

102

10–1 10–2 0

20 40 As at .%

60

x = 35

10–1

41 40 25 43

10–2 –3

1

101

α (cm )

102

Absorption coefficient (cm–1)

Absorption coefficient (cm–1)

104

10 0.5

17

1

1.5

2

2.5

3

Photon energy (eV)

(b)

Fig. 4.16 Dependences of the weak absorption tail on (a) purity in As2 S3 and (b) composition in Asx S100–x (modified from Tanaka et al. 2002). In (a), the solid lines are given by Tauc and circled spectra are by Tanaka for two kinds of samples. Note that the vertical scales of the two graphs are common. The inset in (b) shows the composition dependence of the absorption coefficient at ω = 1.5 eV

102

4

Electronic Properties

that the wrong bond such as As–As is responsible for the tail. Actually, as mentioned in Section 4.4, Vanderbilt and Joannopoulos (1981) theoretically suggest that an As–As σ ∗ bond produces a gap state below the conduction band in As2 Se3 . On the other hand, Andreev et al. (1976) assume that the tail in As2 Se3 reflects free-carrier absorption, since the absorption becomes higher at higher temperatures in proportion to the dc electrical conductivity. It seems that the weak absorption tail arises from several origins including impurities. However, why the tail is exponential has not been considered so far.

4.7 Refractive Index Once the absorption spectrum has being determined, now turn to the refractive index. Figure 4.17 presents n0 (ω) for g-As2 S(Se)3 (Young 1971, Butterfield 1974). We can calculate the refractive index spectrum n0 (ω) using Kramers–Krönig relation: n0 (ω) = 1 + (c/π ) P {α( )/( 2 − ω2 )}d , (4.5) which is derived from a causality principle (Kittel 2005). Here, c is the light velocity and P denotes the principal value. This equation shows that, for calculating n0 , we need the data of α( ) at = 0 − ∞, which is practically impossible. Accordingly,

Fig. 4.17 Refractive index spectra of g-As2 S3 (solid line) and g-As2 Se3 (dashed line). The wavelengths corresponding to the Tauc optical gaps are indicated

4.8

Optical Nonlinearity

103

W-D

Fig. 4.18 Relationship between an atomic bonding structure and optical properties (α, Eg , β, n0 , n2 ) with some equations connecting the properties (modified from Tanaka (2006)). The double arrows represent linear and nonlinear Kramers–Krönig relations and W-D stands for the Wemple–DiDomenico relation

some approximations are taken into account. For instance, assuming that absorption in semiconductors arises from a classical single oscillator, Moss (1985) has derived a simple equation, the so-called Moss rule: n0 4 Eg [eV] = 77 [eV].

(4.6)

Alternatively, Wemple and DiDomenico (1969) approximate the dispersion of refractive index as n0 (ω) = [1 + E0 Ed /{E0 2 − (ω)2 }],

(4.7)

where E0 is the oscillator energy, which is nearly equal to an average separation between the conduction (σ ∗ ) and the valence (lone-pair electron) band, and Ed is the oscillator strength. In As2 S3 , E0 ≈ 4.8 eV and Ed ≈ 22 eV. On the other hand, the refractive index in wide-gap materials may be expressed by the polarizability. An example often employed for the oxide glass is the Lorentz– Lorenz formula (Equation (6.2)).

4.8 Optical Nonlinearity The recent progress of nonlinear optics is remarkable, which corresponds to the advancement of laser technology. At present, a commercially available laser can emit light pulses with a peak power of 1 MW, and if the power is focused to a spot with a diameter of 1 μm, the irradiance reaches 1014 W/cm2 . (Note that the ionization energy of electrons in H atoms of 13.6 eV corresponds to the field irradiance of 5 × 1016 W/cm2 (Boyd 2003)). If such intense light is absorbed in a solid, its temperature rises, and ultimately the solid will vaporize. Or, if the irradiance is

104

4

Electronic Properties

short enough (∼fs), being shorter than thermal relaxation time (∼ps), the field may induce athermal nonlinear (multi-photon) phenomena, including nonlinear absorption, ionization, and sputtering. These phenomena are utilized for laser machining, harmonic generation, etc. Extensive studies have been performed on optical nonlinearity of the second and the third order (Boyd 2003). For simplicity, we take the polarization P and the electric field E to be scalar quantities. P can then be written down in CGS units as P = χ (1) E + χ (2) EE + χ (3) EEE + · · · ,

(4.8)

where the first term χ (1) E depicts the conventional linear response, which is related to the linear refractive index n0 via n0 = {1 + 4π χ (1) }1/2 . The second-order nonlinear susceptibility χ (2) can be utilized for generation of second-overtone (2ω) signals, but it is zero in materials having centro-symmetric structures such as conventional glass. It exists only in some crystals and poled glasses (Tanaka 2006). Hence, in common isotropic glasses, the last term becomes the lowest-order nonlinearity. This can be rewritten as χ (3) IE, where I is the light intensity. Accordingly, we may approximate the refractive index n in the glass as n = n0 + n2 I.

(4.9)

We here note that n2 in glasses may be smaller than that in crystals (Boyd 2003), because specific atomic structures cannot be produced. However, the glass can be lengthened as optical fibers, and thus, apparent nonlinearity can become greater. In addition, the nonlinearity can be added only to selected regions in a glass by lightinduced crystallization (Takahashi et al. 2009). For chalcogenide glasses, studied nonlinearities cover self-wave modulations such as self-(de)focusing (Hughes et al. 2009), optical bistability (Ogusu et al. 2008), white continuum generation (Psaila et al. 2007), stimulated scattering (Xiong et al. 2009), and third-harmonic generation (Douady et al. 2005) (see also Section 7.2). Under similar assumptions to those employed in the one-photon absorption (Equation (4.1)), the two-photon absorption (Fig. 4.19b) coefficient β(ω) can be written as (Tanaka 2006)

Fig. 4.19 Schematic illustrations of (a) one-photon, (b) two-photon, and (c) two-step absorption

4.8

Optical Nonlinearity

105

2 β(ω) ∝ < ϕf |H |ϕs >< ϕs | H|ϕi > /(Esi − ω)

Df (E + 2ω)Di (E) d E,

s

(4.10) where s is a (virtual) intermediate state and Esi = Es − Ei . In this equation, the convolution integral is essentially the same as that in Equation (4.1), except for replacement of ω by 2ω. However, the transition probability is markedly different with the addition of a denominator Esi − ω. Similar to the linear optical properties, the intensity-dependent refractive index n2 can practically be related with β as n2 (ω) ≈ (c/π ) P

{β()/(2 − ω2 )} d.

(4.11)

Reflecting these relations, as shown in Fig. 4.20, β and n2 spectra shift to ω ≈ Eg /2. In amorphous semiconductors having mid-gap states, the two-photon process tends to show different behaviors from those in the crystal in two respects. One is the occurrence of a two-step absorption, Fig. 4.19c, which referes to successive one-photon absorptions through a mid-gap state. The other is a resonant two-photon absorption, in which Esi − ω becomes zero for a mid-gap state. Which process is more dominant depends upon the cross sections of each process, which may vary with ω. Enck (1973) reports a pioneering experiment of two-photon absorptions for a-Se. The two-photon process is interesting from the point of view of application, and a lot of studies have been published for materials having high n2 . Boling et al. (1978) have demonstrated that, in transparent materials, n2 increases with n0 . On the other hand, Tanaka (2006) has adopted a universal relationship to glasses. The relationship, which was developed for crystalline semiconductors and insulators by Sheik-Bahae et al. (1990), takes the form of

(a)

(b)

Fig. 4.20 Spectral dependence of (a) linear absorption α, linear refractive index n0 , two-photon absorption β, and intensity-dependent refractive index n2 in direct-gap semiconductors and (b) α (dashed lines) and β (solid lines) in some glasses (Tanaka 2006, © Springer, reprinted with permission)

106

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Electronic Properties

Fig. 4.21 Dependences of n0 and n2 on Eg with experimental results of glasses, crystals, and zeolite-Se (Saitoh and Tanaka, 2011). Sheik-Bahae’s relation n2 ∼1/Eg 4 and Moss rule n0 ∼Eg 1/4 are shown by upper and lower lines

n2 (esu) = K G(ω/Eg )/(n0 Eg 4 ),2

(4.12)

where Eg is the bandgap energy (1–10 eV), K a fixed constant (= 3.4 × 10−8 for Eg in eV unit), and G(ω/Eg ) a spectral function. For a glass, we may take the Tauc gap as Eg , if it is known, or otherwise the photon energy ω at α ≈ 104 cm−1 . Note that this equation contains no fitting parameters. We see in Fig. 4.21 that the universal line gives reasonable, but not satisfactory, agreements with published data for glasses. The worse agreement in the glass compared to that in crystals (Sheik-Bahae et al. (1990)) may be partly due to experimental difficulties including quasi-stabilities in glasses. In addition, the band-tail states, which are not taken into account in the equation, possibly cause larger deviations in smaller bandgap glasses such as Ag20 As32 Se48 . From the fitting, we can predict that a maximal n2 obtainable in homogeneous materials at the optical communication wavelength of ∼1.5 μm is 10−3 cm2 /GW.

4.9 Electrical Conduction 4.9.1 Background Before describing the electronic transport in glasses, it may be valuable to recall the fundamentals in crystalline semiconductors (Kittel 2005). The electrical conductivity σ can be written in the Drude model for a unipolar (electron or hole) system as σ = eμN, where N is the carrier density and μ is the mobility, which is written as ∗ μ = eτ/m∗ using a collision time τ and an effective mass m . If the carrier is an electron, N is given as N = DC (E) F(E) d E, where DC (E) is the density of state of the conduction band and F(E) the Fermi distribution function. Under the condition 2A

slightly different expression was given later. See Saitoh and Tanaka (2011).

4.9

Electrical Conduction

107

of EC − EF kB T, where Ec is the energy of the conduction band bottom and EF the Fermi energy, σ can be approximated as σ ≈ eμNC exp[−(Ec − EF )/kB T] = σ0 exp(−E/kB T),

(4.13)

where NC is the effective density of state of the conduction band and E (= Ec −EF ) is the activation energy. In crystalline semiconductors, the conduction type as n and p is defined with respect to the species of majority carriers, which is connected with the position of the Fermi level EF . Experimentally, the carrier density N is determined from Hall effect measurements (∼1/eN). And, the (band) mobility μ is calculated from σ and N. However, in amorphous semiconductors, the Hall effect is useless for determination of the carrier type. The Hall voltage exhibits an opposite sign (holes and electrons give negative and positive voltages) to that determined by thermopower (Kittel 2005). This phenomenon is called the pn anomaly (Mott and Davis 1979, Elliott 1990), which is assumed to occur when the carrier mean free path approaches the interatomic distance. As a consequence, we cannot apply a standard transport theory based on Boltzmann equation to the amorphous semiconductor. A quantum interference effect of electron transport near the mobility edge may be needed for understanding the pn anomaly (Mott 1993). We then determine the conduction type using other methods. In relatively conducting materials such as As2 Te3 , thermopower is useful. Alternatively, the conduction type in insulating glasses such as As2 S(Se)3 has been probed using photo-electrical methods such as xerographic discharge, optical time of flight, or Dember effect, which are assumed to contain information of μτ (see Section 5.4). For instance, g-As2 S3 gives a time-of-flight signal only of holes. Accordingly, we can state that “the hole is mobile in g-As2 S3 ,” but it may cause misunderstanding if we write that “g-As2 S3 is of p-type.” We also note that the mobility determined from the time-of-flight method is not the so-called band mobility, but an effective one including (de-)trapping processes.

4.9.2 Carrier Transport It is known that carrier transports in the oxide and the chalcogenide glass are contrastive. A general tendency is, as listed in Tables 4.2 and 4.3, that electrons are mobile in the oxide but holes are mobile in the chalcogenide. Interestingly, in almost all of the corresponding crystals, electrons appear to be more mobile. Table 4.2 List of mobile carriers in the crystalline and glassy materials

SiO2 As2 S(Se)3 Se

Crystal

Glass

e e h (e)

e h h

∼4 2.0 1.9 2.2 2.4 ∼2.8 2.4 1.8 ∼2.1 0.8 3.2 2.2 ∼9 ∼10 5.8 ∼1.8

c-S g-Se c-Se(hex) c-Se(ring) g-As2 S3 c-As2 S3 c-As4 S4 g-As2 Se3 c-As2 Se3 g-As2 Te3 g-GeS2 g-GeSe2 g-SiO2 c-SiO2 g-GeO2 a-Si:H 46 33 100

50

53 130 73 ∼60 42

55

54

∼60 48

26

E0 V [meV]

58

EU [meV]

27

63

E0 C [meV]

0.2

0.2 20−40

5×10–4 5×10–3 , 7×10–3 X 2 X 1 0.02 X 1−10, 20−80

μe [cm2 /Vs]

0.01

0.04 < 10–5

1−10 0.10−0.2 6−28 0.2 10–5 , 10–10 0.1−1 12 10–5 X 10–3

μh [cm2 /Vs]

0.3

0.3 10–3

me ∗ /m0

5−10

9.3 0.3

1.1, 7.5

0.5, 4.5

mh ∗ /m0

4

Optical gaps of crystals are evaluated as photon energies at the absorption coefficient of ∼104 cm–1 . X means that no signals are obtained

Eg T [eV]

Material

Table 4.3 Tauc optical gap Eg T , Urbach energy EU , steepness parameters of the valence band edge E0 V and the conduction band edge E0 C , electron and hole mobilities μe and μh at room temperature, and theoretical effective masses me ∗ /m0 and mh ∗ /m0 (m0 is the free electron mass) (modified from Tanaka 2002)

108 Electronic Properties

4.9

Electrical Conduction

109

Why is a hole more mobile in the chalcogenide glass? Some proposals have been offered, but the origin is not elucidated. Kolobov (1996) ascribes the feature to relaxation of the valence-alternation defects, C3 + and C1 − , in which the former is assumed to be more effective in trapping electrons. Tanaka (2002) proposes that the immobility of electrons is governed by the tail state below the conduction band. The tail state in As2 S(Se)3 seems to arise from σ ∗ (As–As) states as mentioned previously, which reduce electron transport through trapping. We here note, however, that at least three kinds of electron-mobile noncrystalline chalcogenides are known to exist. First, Ovshinsky (1977) demonstrated the so-called chemical modification, which denotes an extrinsic conduction in sputtered chalcogenide films doped by transition metals (Ni, etc.). Such modification might be plausible, since a sputtered film could be far from equilibrium. Second, Tohge et al. (1980) discovered electron conductions in Bi- and Pb-containing chalcogenide glasses. Matsuda et al. (1996) have demonstrated using (inverse) x-ray photoelectron spectroscopy that, in Bi–Ge–Se films, the Fermi level approaches the conduction band with an increase in Bi. However, it has not been known if the same situation occurs in the bulk glass. Third, Narushima et al. (2004) demonstrated that a-In49 S51 films show prominent electron conduction with mobility of 26 cm2 /V s, which may be related to fourfold coordinated S atoms, in a similar way to that in c-CdS, etc. Figure 4.22, which compares reported mobilities μ in amorphous and crystalline semiconductors as a function of the bandgap Eg , presents interesting features. First, in the crystal, a general tendency is a decrease in the band mobility with an increase in Eg , which is understood through the kp perturbation theory predicting μ ∝ Eg −1 (Kittel 2005). We see similar tendencies in chalcogen (Te, Se, and S) and chalcogenide crystals (As2 Se3 , As4 Se4 , and As2 S3 ). Second, among the glasses, SiO2 shows an exceptionally high electron mobility of ∼30 cm2 /V s, which may be a macroscopic value, being limited by (de-)trapping processes. This electron mobility in g-SiO2 appears to be related with that in the corresponding crystal. We see in the dispersion curve (Fig. 4.6b) of c-SiO2 that the effective electron

Fig. 4.22 Relations between the energy gap Eg and the band and macroscopic mobilities μ for crystalline (square) and amorphous (circles) materials. Solid and open symbols depict electron and hole, respectively

110

4

Electronic Properties

Fig. 4.23 Tauc gap (solid line) and electron (•) and hole (◦) mobilities in As-Se system (data from Fisher et al. 1976 and Pétursson et al. 1991)

mass is appreciably (by an order) smaller than the hole mass. The result can be interpreted chemically, i.e., Si4+ d-electron wavefunctions extend more widely than O2− lone-pair electron wavefunctions. And, as known, the smaller mass gives a higher band mobility. In addition, the d-electron wavefunction is more spherical than the p-electron wavefunction, and accordingly, the former is possibly less sensitive to structural disordering, giving rise to ∼30 cm2 /V s. This high mobility is consistent with a long mean free path of electrons in g-SiO2 of ∼3 nm (Chua and Osterberg 2004). Third, except for SiO2 , (semi-)elemental materials including a-Se (hole) and a-Si:H (electron) have macroscopic mobilities of ∼1 cm2 /V s, which are substantially higher than those (10−2 −10−8 cm2 /V s) in binary chalcogenide alloys. Adriaenssens and Eliat (1996) have pointed out a similar tendency for a-Si(C,S):H films, which they ascribe to the difference in potential fluctuations in elemental and multi-component non-crystalline materials. Finally, we see that the hole mobility in amorphous As2 S(Se,Te)3 decreases with an increase in Eg . This trend may imply that trapping states with a depth of Et , which may scale with Eg , govern the hole transport. However, there remain many results which wait for further consideration. For instance, how can we interpret the composition dependence of electron and hole mobilities in As-Se glasses, shown in Fig. 4.23? Effects of impurities, such as oxygen, on the electrical conduction in a-Se have been repeatedly studied for two reasons (Belev et al. 2007). One is that the material is the simplest amorphous semiconductor, and the other is that a-Se films have been employed in photoconductive devices. However, impurity effects have not been elucidated. We also mention here that the mean Se chain length appears to be an important factor affecting photo-electric properties (Suzuki et al. 1987).

4.9.3 Meyer–Neldel Rule Amorphous semiconductors present a puzzling feature in the prefactor of electrical conduction (Elliott 1990, Mott 1993). As known, in a standard transport theory

4.9

Electrical Conduction

111

for disordered semiconductors, σ 0 in Equation (4.13) takes a constant value of eμN (∼150 S/cm). In contrast, Meyer and Neldel discovered in a variety of TiO2 samples that the prefactor σ 0 can be written as (Mehta 2010) σ0 = σ00 exp (E/EMN ),

(4.14)

where σ 00 is a constant (10−17 −1 S/cm−1 ), E the activation energy (Ec − EF for electron), and EMN (25−60 meV) a characteristic energy. This relation, which is now called as the “Meyer–Neldel rule,” universally holds for many groups of materials such as a-Si:H films (Stuke 1987) and As–S–Se glasses (Fig. 4.24) (Shimakawa and Abdel-Wahab 1997, Mehta 2010). The Meyer–Neldel rule is also found in organic semiconductors (Kemeny and Rosenberg 1970), liquid semiconductors (Fortner et al. 1995), and ionic conductors (Ngai 1998). The prefactor σ 0 can no more be regarded as a microscopic conductivity, since the largely varying value of σ 0 is not easy to be understood by the standard theory. Instead, σ 00 may have a physical meaning of a microscopic conductivity, i.e., σ00 = eμN. Although the universal interpretation of the Meyer–Neldel rule is still a matter of debate, the most accepted one for a-Si:H is to assume a statistical shift of Fermi levels, or a temperature-dependent Fermi level, EF (T) = EF (0) − γ T, where EF (0) is a constant and γ takes a positive value (Elliott 1990, Overhof and Thomas 1989). Then, the activation energy E for electrons becomes Ec −EF (T) = Ec −EF (0)+γ T. By inserting this E into Equation (4.13), we have σ = σ0 exp(−E/kB T) = σ0 exp(−γ /kB ) exp(−E(0)/kB T), where E(0) = Ec − EF (0). In such cases, the actual pre-exponential term appears to be not σ 0 in Equation (4.13), but σ0 exp(−γ /kB ), with E(0) corresponding to the observed activation energy E. We can also show that γ /kB becomes a function of E(0), in agreement with Equation (4.14). However, the model cannot quantitatively explain small σ 00 in other materials. For this problem, Emin (1975, 2008) interprets the value of 10−15 −10−5 S/cm in

Fig. 4.24 The pre-exponential factor σ 0 plotted as a function of the electrical activation energy E, the slopes corresponding to 1/EMN , for the three chalcogenide systems indicated (modified from Shimakawa and Abdel-Wahab 1997)

112

4

Electronic Properties

chalcogenide glasses using a polaron concept. Shimakawa and Abdel-Wahab (1997) interpret 10−17 −10−3 S/cm in organic semiconductors using an electron tunneling model. The latter model is applicable also to the transport in chalcogenide glasses, since the chalcogenide is assumed to have low-dimensional (chain, layer) structures and hence the carrier must tunnel through intermolecular potential barriers. Yelon et al. (2006) propose a model by introducing the concept of multi-excitation entropy. We here add two interesting features. One is a correlation, which is similar in form to Equation (4.14), which exists between σ 00 and EMN : σ00 = σ 00 exp (EMN /ES ),

(4.15)

for many chalcogenide glasses such as P(As)–S(Se,Te) (Shimakawa and AbdelWahab 1997), where ES is a constant (∼1.7 meV). No interpretation has been given for this correlation. The other is that the functional formula of the Meyer–Neldel rule and the Urbach-edge focus (see Section 4.6.2) are the same, which may be just a coincidence or, otherwise, may arise from a common origin.

4.9.4 AC Conductivity In ac electrical conductivity, disordered semiconductors exhibit a peculiar dependence on frequency. The complex electrical conductivity is defined as σ (ω) = iωε0 ε(ω), where ω is the angular frequency of applied electric fields and ε(ω) the complex dielectric constant, which is written as ε = ε1 − iε2 . Here, ωε0 ε2 (ω) is called the ac conductivity or ac loss, which is written also as σ (ω) for simplicity. The ac conductivity may arise from hopping of electrons, which can be treated as alternating atomic (or molecular) dipoles, and hence the response in general is given by a Debye-type equation, 1/(1 + iωτ ), where τ is a relaxation time (Kittel 2005). In contrast, it is known that many disordered semiconductors and insulators, including chalcogenides (Fig. 4.25) and a-Si:H films, exhibit σ (ω) with a power-law dependence at ω = 102 −1010 Hz: σ (ω) = Aωs ,

(4.16)

where A and s(< 1.0) are temperature-dependent parameters (Mott and Davis 1979, Elliott 1990). This dependence is often called “dispersive ac loss.” Interpretations of the dispersive loss may be performed in two ways (Elliott 1987). One is to postulate a distribution P(τ ) of τ in the Debye-type equation. Hopping conduction between impurities in compensated c-Si is analyzed using this idea, in which the electronic hopping distance is assumed to be equivalent to the dipole length. In this model, the parameter A corresponds to the number of dipoles, and hence, the number of hopping sites can be estimated from Equation (4.16). This model may be applied also to evaluations of defects in disordered semiconductors (Elliott 1987, Ganjoo and Shimakawa 1994). The other model assumes kinds

4.10

Compositional Variation

113

Fig. 4.25 AC conductivity in g-As2 Se3 at 300 K

vibrational

interband transition

electronic

of Maxwell–Wagner effects: the dispersive ac loss arising from macro- or mesoscopic scale inhomogeneities in disordered insulators. A classical effective medium approximation is useful for analyses of such inhomogeneous media (Kirkpatrik 1973, Shimakawa and Ganjoo 2002).

4.10 Compositional Variation We can analyze dependence of physical properties on constituent atoms in two ways. One is to characterize the atoms along horizontal directions in the periodic table, an example being the Z dependence described in the elastic property (Section 3.5). The other is along vertical directions in the table, or the periodicity. For the Z dependence in covalent chalcogenide glasses, we can point out similar dependences for the atomic volume Va and the optical gap Eg (Tanaka 1989). Figure 4.26 shows that both tend to decrease with increases in Z, accompanying (traces of) minima at 2.4 and maxima at 2.67. How can we grasp such resembling Z dependences? A plausible interpretation is as follows. The atomic volume (per mole) Va for a D-dimensional solid can be estimated as Va (D) Na rD R3−D ,

(4.17)

where Na is the Avogadro number and r and R denote the lengths of covalent (∼0.2 nm) and van der Waals (∼0.5 nm) bonds, respectively. We here assume that for a change in Z from 2 to 2.4, D changes from 1 to 2, which causes the decrease in Va . From 2.4 to 2.67, structural analyses (Section 2.4) imply that R increases from ∼0.5 to ∼0.6 nm and, accordingly, Va increases. From 2.67 to 4, it is reasonable to assume a gradual change in D from 2 to 3, giving rise to the Va decrease.

114

4

(a)

Electronic Properties

(b)

Fig. 4.26 Dependences of (a) atomic volume and (b) optical gap on the average coordination number Z in some sulfide and selenide glasses (Tanaka 1989, © American Physical Society, reprinted with permission)

On the other hand, the optical gap Eg can be written as Eg E0 − Ev /2 − Ec /2,

(4.18)

where E0 (5−10 eV) is the energy separation between the centers of the conduction and valence bands, and Ev and Ec are their band widths (∼4 eV). Here, provided that the atom periodicity is held constant, E0 remains constant, which reflects the bond strength in simple tight-binding models, or it is at least modified monotonically. Next, in lone-pair electron semiconductors such as the chalcogenide glasses, Ev ∝ exp(−R/ξ ), where ξ is assumed to be a constant representing a spatial extension of lone-pair electrons, and Ec ∝ Z, where represents a transfer integral, which increases with an increase in spatial extension of bonding electrons. We then can relate the decrease in Eg from 2 to 2.4 with the increase in Z. The increase in Eg from 2.4 to 2.67 is ascribed to the increase in R. Lastly, the Eg decrease from 2.67 to 4 again reflects the Z increase. Note that this kind of Z dependence cannot exist in the oxide glass and is less clear in the telluride material, due to their ionic and metallic characters. The Eg decrease with the periodicity can also be understood. For instance, Fig. 1.12c shows that Eg in As2 O(S,Se,Te)3 is ∼4, 2.4, 1.8, and 0.8 eV, which is understood to be a manifestation of a decrease in E0 , arising from reduction of the covalent bond strength, in Equation (4.18) (see Fig. 1.10). In addition, we can point out an interesting feature of Eg in the periodicity. As shown in Fig. 1.12c, Eg of the oxides, Si(Ge)O2 and As2 O3 , appreciably changes with the cation atoms (Si, Ge, As), while Eg in Si(Ge,As)–Te appears to be uniquely

References

115

determined by Te, mostly irrespective of the cation species. It seems that all the amorphous telluride materials have Eg of ∼1.0 eV. Why? A notion is to take the metallicity of Te into account. Jovari et al. (2008) demonstrate that, in As–Te, the metallicity causes a lot (∼50%) of Te–Te homopolar bonds, i.e., the atomic bond is chemically disordered. This observation may suggest that Te clusters govern the optical gaps in tellurides, which become nearly equal to that in pure a-Te.

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Chapter 5

Photo-Electronic Properties

Abstract Photo-excited electrons relax to ground states through several ways. One of the processes can be probed through photoluminescence, in which the most puzzling feature in amorphous chalcogenides may be the so-called half-gap rule of the peak energy. The origin will be discussed. Another photo-electronic property is the photoconduction. Most amorphous chalcogenides are good photoconductors, for which steady-state and transient characteristics are briefly discussed. Finally, we refer to a carrier avalanche effect in a-Se films, which has been applied to highly sensitive vidicons. Keywords Photoluminescense · Half-gap rule · Photoconduction · Nonphotoconducting gap · Avalanche breakdown · Time-of-flight · Dispersive transport · Dember effect

5.1 Photo-Excitation and Relaxation The photon provides two kinds of excitations in condensed matters: photo-electronic and photo-vibrational. These excitations relax through successive processes, and in many cases, the energy ω of photons is converted ultimately to a temperature rise of the matter. What happens in a semiconductor (or insulator) crystal when it is excited by a photon? In general, the photo-electronic excitation occurs with a photon having an arbitrary energy. An x-ray photon (ω Eg ) can excite a core electron, which may successively produce many electrons and holes in conduction and valence bands. If ω > Eg (super-gap excitation), an excited electron will relax to the bottom of the conduction band, emitting the excess energy of ω − Eg as several phonons (Evib ≈ 10 meV) within picosecond relaxation times. A bandgap photon with ω ≈ Eg of visible light or so is likely to generate a pair of electron and hole. A sub-gap photon with ω ≤ Eg may produce an exciton, a coupled electron-hole pair. Lastly, if the light is intense and pulsed, nonlinear excitation by photons with energy of nω ≥ Eg , where n is the number of photons simultaneously absorbed, may take place. And these electronic excitations will provide three kinds of responses: (i) temperature rise T; (ii) luminescence, which tends to become stronger when illuminated at lower temperatures; and (iii) photo-electric effects such as photoconduction (in a sample subjected to an electric field) and 121 K. Tanaka, K. Shimakawa, Amorphous Chalcogenide Semiconductors and Related C Springer Science+Business Media, LLC 2011 Materials, DOI 10.1007/978-1-4419-9510-0_5,

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Fig. 5.1 Relaxational processes of photo-excited electrons (•) and holes (◦) in an amorphous semiconductor: a geminate recombination, b sub-gap excitation and thermal hole-release, c bandgap excitation and (de-)trapping of a hole, d non-geminate recombination, and e polaron (electron) formation

photo-voltaic effects, an example being the Dember voltage (Section 5.3). On the other hand, an infrared photon with ω ≈ Evib Eg excites atomic vibrations called optical phonons, which thermalize through nonlinear phonon–phonon interaction, resulting in a temperature rise. The photo-excitation in amorphous semiconductors is somewhat different (Fig. 5.1), since the concepts of bandgap energies and phonons are vague. With an increase in the photon energy, several unique processes occur. Infrared photons with ω Eg excite spatially localized (molecular) vibrations, instead of the optical phonon, in disordered materials. If ω < Eg , the photon may be absorbed by midgap states and (b) an excited electron (hole) in the state may be thermally re-excited to a band. If ω ≤ Eg , the energy corresponding to the exciton excitation in crystals, (a) an excited electron–hole pair1 may geminately recombine2 non-radiatively, giving rise to a thermal spike, which will be localized in nanometer scales. Or, at low temperatures, it may radiatively recombine, giving rise to luminescence. On the other hand, a photon with ω ≥ Eg gives several relaxation paths, which are classified into vertical or horizontal transfers in a band picture, as illustrated in Fig. 5.1. Among these, the most common process may be (d) a non-geminate and nonradiative recombination, giving rise to a temperature rise. If the photon is absorbed

1 The authors are reluctant to use the word “exciton” in disordered systems (Kasap et al. 2006), since the exciton radius may be larger than the structural disorder in amorphous materials. The word “electron–hole pair” may cause less misunderstanding. 2 “Geminate recombination” means a recombination of a photoexcited electron–hole pair. It occurs when the thermalization process (with a distance of ∼ [D(ω − Eg )/Evib ]1/2 , where D is the diffusion coefficient of a mobile carrier), which dissipates the excess energy of ω − Eg , cannot overcome a Coulombic electron–hole attractive force.

Fig. 5.2 Temperature dependence of photoluminescence intensity (PL), photo-expansion (PE) (see Section 6.3.9), and photoconduction (PC) in g-As2 S3 (Tanaka 2000, © Elsevier, reprinted with permission)

123

100

PL

10 PE

10–1 5 PC 0

0

10–2 100 200 Temperature (K)

300

Photoconduction PC and Photoluminescence PL (arb. unit)

Photoluminescence

Photoexpansion PE (μm)

5.2

in an insulator, Dember voltages may appear. If the insulator is subjected to an electric field, excited carriers may transit the sample, giving rise to (c) photocurrents. Otherwise, in flexible atomic networks, (e) the electron may be self-trapped, forming a kind of polaron states, a coupled and relaxed electron–lattice system (Fig. 4.4). The polaron state may be quenched into quasi-stable structural changes, which can be regarded as a kind of photo-structural changes (see Chapter 6). We here note that, in many cases, the photoluminescence and the photoconduction are complementary, as exemplified in temperature dependence in Fig. 5.2. Photoluminescence intensity is proportional to gηβ, where g is the carrier generation rate, η the creation efficiency of geminate pairs, and β the fraction of geminate pairs which recombine radiatively. On the other hand, a photocurrent increases as g(1 − η)μτ , where μ is the carrier mobility and τ is the lifetime.

5.2 Photoluminescence The photoluminescence in chalcogenide and oxide glasses has been extensively studied. Historically, photoluminescence experiments had started using cw lasers, the results for the chalcogenide being comprehensively reviewed by Street (1976). The glass has a bandgap of ∼2 eV so that we can employ several kinds of lasers for excitation. However, photoluminescence detection at (near) infrared regions is more or less limited in sensitivity. Actually, photoluminescence studies for tellurides with Eg 1 eV are few. With developments of lasers, photoluminescence experiments shifted to those employing pulsed and/or polarized light excitations. In addition, more sophisticated measurements such as optically detected magnetic resonance (ODMR), which detects spin resonance of excited electrons by monitoring photoluminescence intensity (Elliott 1990), have been employed. On the other hand, the energy gap of the oxide is greater (5–10 eV), which limits available lasers for excitation. Upon ultraviolet excitations, however, the luminescence is likely to appear in visible regions, which can be detected with high sensitivity using the conventional photomultipliers and semiconductor devices.

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Since the photoluminescence is governed by mid-gap states, we may envisage strong impurity effects upon photoluminescence. However, the effect is not universal in chalcogenide glasses. Street (1976) asserts that special care about sample purity is not required for the experiments. Actually, Pfister et al. (1978) have demonstrated that Tl in As2 Se3 , which reduces hole mobility, has no effect upon photoluminescence (and photoinduced ESR). Bishop et al. (1979) also have demonstrated that a photoluminescence efficiency in As2 Se3 is insensitive to intentionally doped atoms such as Cu and I up to ∼1 at.%. Koós et al. (1981) arrive at a similar conclusion for GeSe2 . However, it has been repeatedly demonstrated that electrical properties of Se are very sensitive to (ppm orders of) O and Cl impurities (LaCourse et al. 1970, Benkhedir et al. 2009), which is consistent with a photoluminescence result (Bishop et al. 1979). In addition, variations of photoluminescence spectra in different-grade SiO2 samples are well known (Sakurai and Nagasawa 2000). These seemingly controversial behaviors may be ascribed to respective impurity– host combinations, in which the impurity does or does not produce an active mid-gap state. We should also take dependence upon preparation methods into account (Street 1976).

5.2.1 CW Photoluminescence Among several marked features in steady-state photoluminescence, the most puzzling may be the so-called half-gap photoluminescence (Figs. 5.3 and 5.4). In simple chalcogenide glasses such as As2 S(Se)3 and GeS(Se)2 , when excited by light with a photon energy of ω ≈ 0.9Eg (Urbach-edge regions), broad (∼0.3 eV) photoluminescence peaks appear, with strong Stokes shifts, at “EPL ≈ Eg /2.” We also see in Fig. 5.3 similar features for simple oxide glasses, SiO2 (Gee and Kastner 1980) and GeO2 (Terakado and Tanaka 2006). For understanding the origin of an empirical rule, EPL ≈ Eg /2, varieties of photoluminescence characteristics have been studied. Temperature dependence has manifested that the position and width of photoluminescence peaks change little (Street 1976). Nevertheless, as shown in Fig. 5.5, the photoluminescence intensity tends to exponentially decrease with an increase in temperature, ∼exp (−T/T0 ), where T0 ≈ 0.1Tg (Gee and Kastner 1980). The dependence can be accounted for by assuming phonon-assisted tunneling of carriers to non-radiative recombination paths. On the other hand, pressure studies are limited due to experimental difficulties of compressions at low temperatures. Weinstein (1984) has examined the feature in c-As2 S3 and a-As2 SeS2 at 13 K and demonstrated that both samples show the same pressure dependence: ∂EPL /∂P 0 with ∂Eg /∂P < 0, the latter being well demonstrated (see Fig. 4.14). As the consequence, the Stokes shift becomes smaller with compression, so that the half-gap rule tends to violate. Pulsed excitation gives more complicated results, such as a shift of the peak energy with delay time (Murayama 1983).

5.2

Photoluminescence

125

Fig. 5.3 Photoluminescence (PL), photoluminescence excitation (PLE), and absorption spectra (solid lines) of the three glasses as a function of a photon energy reduced by the optical gap (modified from Gee and Kastner 1980 and Terakado and Tanaka 2006)

Fig. 5.4 Photoluminescence (PL) peak energy as a function of photoluminescence excitation (PLE) peak energies for oxide and chalcogenide glasses and chalcogen crystals (c-). The line shows EPL = EPLE /2

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Fig. 5.5 Temperature variations of photoluminescence intensities in Suprasil (circles), As2 S3 (), and Se (). The temperature T is normalized by the glass transition temperature Tg (Gee and Kastner 1980, © Elsevier, reprinted with permission)

Material variations have also been studied. Roughly, photoluminescence behaviors in glass and the corresponding crystal appear to be similar, as demonstrated for As2 S(Se)3 (Street 1976). Crystalline samples such as c-As2 S(Se)3 also appear to follow the half-gap rule, though impurity effects may exist (Street 1976, Weinstein 1984). In contrast, we see in Fig. 5.4 that elemental chalcogens, S and Se, manifest considerable deviations from the half-gap rule. Photoluminescence in orthorhombic c-S, consisting of S8 molecules, gives a peak at 2.6 eV under excitation at 3.4 eV (Street 1976), i.e., EPL > Eg /2. A similar result is demonstrated also for polymeric g-S (Oda et al. 1984). On the other hand, both a- and c-Se show the opposite deviation, EPL < Eg /2 (Bishop et al. 1979, Lundt and Weiser 1983). It is reported that the half-gap rule is violated also in Ge-rich Ge-S(Se) glasses (Seki et al. 2003). It is also mentioned here that, for the intensity, luminescence in a-Se is known to be much weaker (10–1 –10–2 ) than that in As-S(Se) (Bishop et al. 1979). The origin of the half-gap photoluminescence remains to be studied. A straightforward interpretation is to postulate recombination centers at positions of ∼Eg /2 in the bandgap. However, the center is likely to produce ESR signals and also optical absorptions at ω Eg /2, which have been assumed not to exist. (The weak absorption tail described in Section 4.6 was neglected.) Then, Street and Mott (1975) proposed the charged defects concept (Section 4.4), in which the halfgap photoluminescence is assumed to arise from D0 states. Light excitation converts D+ and D– to D0 , which is assumed to become a radiative recombination center. Here, strong electron–phonon coupling with large Stokes shift is implicitly assumed.

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Photoluminescence

127

However, why the D0 state is located at ∼Eg /2 in lone pair electron systems remains unclear. (In contrast, in a-Si, it is reasonable to assume that D0 states are located at the mid-gap.) Instead, Baranovskii and Karpov (1987) have interpreted the rule using a polaron model. Later, Ristein and others have ascribed the halfgap photoluminescence to self-trapped triplet excitons (Ristein et al. 1990, Mao et al. 1993). However, similar to the defect model, these models cannot explain why the Stokes shift is ∼Eg /2. On the other hand, for the oxide glass such as SiO2 , photoluminescence has been ascribed to a kind of oxygen-deficient centers, e.g., twofold-coordinated Si atoms, Si2 0 (Trukhin 2000). In this model, the photoluminescence peak at around the half-gap is assumed to be accidental.

5.2.2 Time-Resolved Photoluminescence Although the photoluminescence in chalcogenide glasses under cw excitation appears to present a single peak (Fig. 5.3), time- or frequency-resolved experiments have manifested several peaks having different time constants. For g-As2 S3 , in Fig. 5.6, Murayama (1983) demonstrate, through a time-resolved measurement at a cryogenic temperature using bandgap excitation with a pulse of 10 ns, three decay components with time constants of 20 ns, 2 μs, and 200 μs. On the other hand, a frequency-resolved experiment by Aoki et al. (2005) detects two components having lifetimes peaking at ∼10 ns and ∼100 μs. This work does not detect the 2 μs component, which may be due to different excitation levels, the pulse being much more intense. These authors ascribe the fast components at 10−20 ns to latticedeforming electron–hole pairs (Murayama 1983) and singlet excitons (Aoki et al. 2005). The slowest components, 100–200 μs, are ascribed to localized electrons

Fig. 5.6 Transient (left) (Murayama 1983, © Elsevier, reprinted with permission) and frequencyresolved (right) (Aoki et al. 2005, © INOE, reprinted with permission) photoluminescence in g-As2 S3

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and holes (Murayama 1983) and triplet excitons (Aoki et al. 2005). Despite the different terminologies being employed, the real entities may be similar. It is plausible that the slowest component corresponds to the cw photoluminescence. Spectral investigations of transient photoluminescence have provided valuable, but controversial, insights into the mobility gap. Higashi and Kastner (1981) conclude, on the basis of measurements of luminescence characteristics as a function of excitation energy, that the mobility gap in As2 S3 is located at 2.3 eV, the position being similar to that of the Tauc optical gap. However, through similar experiments, Murayama concludes the mobility gap to be 2.6 eV (Murayama 1983), suggesting that the energy is similar to the bandgap in the corresponding crystal. Reasons for this quantitative discrepancy have not been examined.

5.3 Photo-Voltage The Dember voltage, i.e., photo-voltages arising from concentration gradients of photo-generated carriers, can determine the species (electron or hole) of mobile carriers (Goldman et al. 1978). Suppose an insulating material, which has a grounded back electrode, is illuminated by highly absorbed light and the surface voltage VD is measured through a floating electrode. The voltage is given as VD = (kB T/e) ln(ni /nb ),

(5.1)

where ni and nb are carrier densities at the illuminated and the back surface. And the polarity reflects the species of mobile carriers. Despite this simple principle, studies on Dember photo-voltages in amorphous semiconductors are a few (Fotland 1960, Kolomiets 1964, Wey and Fritzsche 1972, Tanaka et al. 1995).

5.4 Photoconduction 5.4.1 CW Photoconduction The photoconductivity, a current flow in an insulator or wide-gap semiconductor3 under electric fields and light excitation, was discovered for c-Se more than a century ago. For amorphous semiconductors, extensive studies were initiated by Weimer and Cope (1951) and by Kolomiets’ group (Kolomiets and Lyubin 1973). Many studies have been reported for Se and As2 Se3 , which demonstrate unique photoconductive characteristics in amorphous semiconductors, while a few for As2 S3 and other materials due to small photocurrents. These photoconductivity results

3 Experimentally, it is more or less difficult to distinguish photo-currents and photo-thermal currents in small-gap semiconductors such as a-As2 Te3 (Tanaka 2007). The ideal photocurrent flows under fixed temperatures, while light illumination necessarily rises sample temperature, which increases the electrical conductivity in proportion to exp(−Eg /2kB T).

5.4

Photoconduction

129

pose fundamental problems in electronic excitation and transport in disordered systems. Understanding the photoconductivity is required also for applications to devices such as Se-target vidicons (Section 7.6). For x-ray photoconductivity, see Section 7.6. The photocurrent ipc appears when photo-generated carriers in a sample drift between a pair of electrodes which are subjected to a bias voltage (Bube 1960). Under the simplest situation, where (de-)trapping processes could be neglected, the carrier density n is given as dn/dt = ηαI − n/τ ,

(5.2)

where η is a carrier generation efficiency, α an absorption coefficient, I incident light intensity taking light reflection into account, and τ a carrier lifetime governed by recombination. The equation gives the steady-state carrier density as n = ηαIτ , and accordingly, the steady photocurrent (current density) becomes ipc = enμE = eηαIτ μE, where τ μE = τ Vd is called “Schubweg” (flying distance). Important steady-state photocurrent characteristics are the variations with light intensity, spectrum, and temperature. The light intensity dependence follows the one formulated for crystalline materials (Bube 1960, Adriaenssens 2006). Here, we slightly modify the generation rate in Equation (5.2) as dn/dt = ηαI − n(n/τ1 + N/τ2 ),

(5.3)

where N is the density of recombination centers and τ 1,2 are recombination times for two processes. We then see that, with an increase in the light intensity and the corresponding n from n/τ1 N/τ2 to n/τ1 N/τ2 , the recombination changes from a monomolecular to a bimolecular type, giving rise to the variations of ipc ∝ I 1 and I 1/2 . This characteristic change in the intensity dependence can be employed for estimating the effective density n/τ 1 and N/τ 2 . More informative is the spectral dependence. In crystalline photoconductors, e.g., in c-Se shown in Fig. 5.7b, it is common that a photoconduction spectrum gives a

Fig. 5.7 Photocurrent and optical density spectra of (a) a-Se and (b) c-Se (modified from Gilleo 1951)

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peak near the optical absorption edge. At the sub-gap region (longer wavelengths), the efficiency decreases reflecting a lack of excitation energy. At the super-gap region, where photo-electronic excitation occurs very near to the surface due to high absorption, surface recombination of photo-generated carriers is likely to suppress the photocurrent. In amorphous materials, as shown in Fig. 5.7a, the high-energy reduction tends to become less noticeable, which suggests a smaller role of the surface recombination (Gilleo 1951, Shimakawa et al. 1974). We here mention that, for spectral measurements, the constant photocurrent method (CPM), which takes photoconductive spectra under fixed photocurrents (by varying light intensities), has often been employed for disordered semiconductors (Tanaka and Nakayama 1999, Adriaenssens 2006). In many amorphous materials, as exemplified in Fig. 5.7a for a-Se, the photoconduction spectrum appears to be blue shifted from the optical absorption edge. At least, three interpretations, including exciton, geminate recombination, and mobility gap, have been proposed for the blue-shifted spectra, while the distinction between these ideas seems to be indefinite. Evrard and Trukhin (1982) point out that, in g-SiO2 with Eg ≈ 10 eV, the shift is ∼2 eV (Fig. 4.11) and interpret it as an exciton effect, the concept in disordered materials still remaining an important topic (Messina et al. 2010). On the other hand, in a-Se with Eg ≈ 2 eV, the deviation of photoconduction spectrum is 0.4 eV (Fig. 5.7a), which is termed a “nonphotoconducting gap,” which has been understood as a manifestation of geminate recombination (Mott and Davis 1979, Elliott 1990). It should be mentioned that c-S with Eg ≈ 4 eV also exhibits a non-photoconducting gap of ∼0.5 eV (Spear and Adams 1966). We may then assume that the non-photoconducting gap is characteristic of low-dimensional solids, irrespective of structural order. Next, as shown in Fig. 4.11, g-As2 S3 presents a photoconductive edge at ∼2.6 eV at low temperatures (Tanaka and Nakayama 1999), where the Tauc gap is ∼2.4 eV. Recalling that the bandgap in c-As2 S3 is ∼2.6 eV, we can assume that the photoconductive edge corresponds to the mobility edge. The same conclusion is drawn by Murayama (1983) from photoluminescence spectra. Incidentally, in a-Si:H films, the optical and photoconductive edges are located at nearly the same positions (Tanaka and Nakayama 1999). Comparison of photoconductive, photoluminescence excitation, and absorption spectra provides two valuable insights (Tanaka 2001). As shown in Fig. 5.8, interestingly, the photoconductive spectrum (CPM) in g-As2 S3 does not show the weak absorption tail, which appears also in the photoluminescence excitation (PLE) spectrum. As listed in Table 4.2, g-As2 S3 is hole conductive (electrons are immobile), and accordingly, this result implies that, as illustrated in Fig. 5.8, the weak absorption tail arises from localized states below the conduction band. On the other hand, for the Urbach edge, optical absorption, photoconductive, and photoluminescence excitation spectra in Fig. 5.8 show similar slopes, which suggests that the Urbach edge is governed by the DOS above the valence band. Since the valence band is made up from lone pair electron states, we can assume that the Urbach edge in g-As2 S3 reflects interatomic interaction between lone pair electrons. The same picture can be drawn for other chalcogenides which have similar values of Urbach energy EU and the valence band edge steepness Eo v in Table 4.3.

Photoconduction

131

105 103 Density-of-state

Absorption coefficient (cm–1)

5.4

101 PLE

10–1 α

10–3 10–5

CPM

1

1.5 2 2.5 Photon energy (eV)

3

Energy

Fig. 5.8 Comparison of three spectra for g-As2 S3 at room temperature (left) and deduced DOS (right) (Tanaka 2001, © INOE, reprinted with permission). α is the optical absorption, PLE the photoluminescence excitation, and CPM the constant photocurrent method. The dotted line in the DOS indicates the mobility edge and the circles show an electron–hole pair

In addition, as shown in Fig. 5.9, g-As2 S3 manifests anomalous dependence of the photoconduction spectrum upon excitation levels (Tanaka 1998). It shows a redshift from ∼2.4 to ∼2.0 eV under higher excitations, which is interpreted as a filling effect of trap levels. a-Si:H films and g-As2 Se3 do not show such intensity dependence. The peculiar feature is attributable to slow carrier transits in g-As2 S3 . Studies on impurity effects are not comprehensive. Hammam et al. (1990) have demonstrated that photoconduction characteristics in As2 Se3 are influenced by intentionally added As2 O3 of ∼1 at.%, which is no more a doping level. On the other hand, the same group reports that, in evaporated a-Se, only ∼10 ppm Cl modifies photoconduction characteristics (Benkhedir et al. 2009). Why is only a-Se very sensitive to impurities?

Fig. 5.9 Photocurrent spectra in a-As2 S3 as a function of the light intensity indicated (Tanaka 1998, © American Institute of Physics, reprinted with permission). The crosses (+) are obtained using cw light and others are by 5 ns pulses

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5.4.2 Time-Resolved Photoconduction Photocurrent transients, which appear after pulsed light excitations, are governed by carrier generation and recombination, and in addition, by transport. Hence, the mobility becomes an important parameter for interpretations. As known, in the Drude model for a crystalline semiconductor, the mobility μ is written as μ = eτ /m∗ , where τ represents the scattering time (normally governed by phonons and impurities). In amorphous semiconductors, it is plausible that there exist many gap states with distributed energy depths, which tend to suppress the carrier transport through hopping, (de-)trapping, and recombination. Here, the (quantum mechanical) hopping is usually neglected at room temperature. The (de-)trapping and recombination are, respectively, governed by shallow and deep gap states. Nevertheless, in some experiments, in which photo-excited electrons and holes are spatially separated by electric fields, the recombination can also be neglected. In such cases, only the (de-)trapping governs the transient characteristic, and a measured drift mobility μd is reduced as μd = μ(Nc /Nt ) exp(−Et /kT),

(5.4)

where Nc is the effective DOS at the band edge (Equation 4.13) and Nt and Et are the trap density and the depth, respectively (Mott and Davis 1979). Or, it is more natural to assume that the trap density is distributed in energy in disordered semiconductors. Accordingly, the main interest of transient photocurrent measurements is to know the trap distribution Nt (E) or to obtain DOSs of localized states. There are several time-resolved photoconductive methods (Adriaenssens 2006). Among those, optical time of flight (TOF), transient photoconductivity, and xerographic discharge have been frequently employed. Experimentally, these methods need, respectively, sandwich, planar, and back electrode samples. The former two methods measure photocurrents under constant applied voltages, and the last monitors a decay of surface voltages after initial charging processes. In addition to these transient methods, a frequency-resolved method, the so-called modulated photoconductivity, can also be employed for obtaining DOSs of gap states. The optical TOF works as illustrated in Fig. 5.10. A pulsed super-bandgap light impinges upon an insulating sample having sandwich electrodes, which exert an electric field to the sample. The polarity of the voltage applied to the front electrode determines the species (electron or hole) of moving carriers. The pulsed light is strongly absorbed near the (semi-)transparent front electrode, and a photogenerated thin carrier packet drifts accompanying diffusion broadening through the sample, giving rise to a corresponding external current, which traces the carrier transport. The optical TOF experiment gives two kinds of responses: Gaussian (nondispersive) and dispersive transport (Mott and Davis 1979, Elliott 1990). In the Gaussian transport, which is observed commonly in insulating crystals and also in some amorphous materials, as a-Se at room temperature, a step-like current (a in Fig. 5.10) with a decay edge at tT = L/vd , where L and vd are a sample thickness and a carrier velocity, appears. On the other hand, a long featureless signal appears

5.4

Photoconduction

133

display

current

a

b initial

(a)

(b)

time

Fig. 5.10 A schematic illustration of optical time-of-flight experiments and the responses: (a) Gaussian (non-dispersive) transport and (b) dispersive transport on a display (center) and in a sample (right)

in many amorphous semiconductors such as As2 Se(Te)3 and also in a-Se at low temperatures, which is ascribed to the so-called dispersive transport. The featureless diffusion-controlled signal, when plotted in double logarithmic scales, gives two straight lines as I(t) ∼ t−(1−α) when t < tT

and

t−(1+α) when t > tT ,

(5.5)

where α is called as a dispersion parameter and tT gives a nominal carrier-transit time. The dispersive transport has been analyzed by Scher and Montroll (1975). They apply a continuous-time random walk theory to charge carriers in a disordered insulator which is subjected to an electric field. The motion of charge carriers at the band edge is interrupted by trapping by localized states; the carrier waiting there for a time interval of τ , and then, being thermally activated to a mobility edge. For the waiting time, the two models, (classical) multiple trapping and (quantal) multiple hopping, have been proposed (Elliott 1990). The above idea suggests that the dispersive current reflects the distribution D(τ ) of the waiting time, which is governed by the DOS of gap states D(E). In view of the multiple-trapping model, the detrapping time τ of carriers is estimated as τ ≈ −1 exp(Et /kB T),

(5.6)

where is the attempt to escape frequency (usually approximated by a vibrational frequency ∼1013 Hz), Et the trap depth, and T the temperature. Putting kB T = 25 meV and τ ≈ 10−8 s (TOF experiments can cover time spans of nanoseconds to milliseconds), we obtain Et ≈ 0.3 eV. That is, we can estimate the DOS at a depth of ∼0.3 eV. Practically, more elegant analyses using inverse Laplace transformation are employed for estimating the gap-state DOSs. Many studies have been conducted, mainly for Se and As–Se (Adriaenssens 2006). The transient photoconductivity gives similar insights (Naito et al. 1994, Adriaenssens 2006). The decay after pulsed excitation follows I(t) ∼ t−(1−α) , which

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is the same with that in the TOF at t < tT in Equation (5.5), as expected. Preparation of planar electrode samples is usually easier than that of the sandwich electrode, and accordingly, the transient photoconductivity becomes a convenient way for getting information of the trap distribution. Nevertheless, since the sample has the symmetric electrode structure, the method cannot distinguish the species of transit carriers: electrons or holes. The xerographic discharge method can be employed for probing deeper traps than ∼0.5 eV (Abkowitz 1992, Weiss and Abkowitz 2006). The method was developed for analyses of a xerographic copying process (Section 7.6), and it has been applied to examinations of trap-limited transport processes and DOSs of deep states. Many experiments have been performed for a-Se films, having a typical thickness of ∼50 μm, which are deposited onto, e.g., an Al plate. As shown in Fig. 5.11, the sample is corona charged, dark decayed, and photo discharged through photoconduction, during which the surface potential is monitored using a capacitively coupled electrometer. And, the time variations give several material parameters. For instance, a residual surface potential VR at a delay time τ d ≈ 1–104 s gives the density N(Et ) for trapped carriers with a depth of Et as N(Et ) ≈ τ d dVR /dt. Quantitatively, it is not difficult to measure a surface voltage of 5 V, which may correspond to the charge density as small as 1012 cm−3 .4 Insights into DOSs can be obtained also by using frequency domain experiments such as the modulated photocurrent method (Oheda 1979, Adriaenssens 2006). In this method, we measure the phase delay ( ) between modulated excitation light (∼I sin( t)) with photon energy of ω > Eg and its generating ac photocurrent ∼ipc sin( t + ) as a function of the modulation frequency . The current, which is

Fig. 5.11 A response of xerographic discharges. A typical charging duration is ∼1 min

that in the simplest case, VR = eNL2 /(2εR ε0 ), where L is the sample thickness, εR the relative dielectric constant, and 0 the vacuum dielectric constant.

4 Note

5.5

Avalanche Breakdown

135

Fig. 5.12 Reported DOSs for a-Se above the valence band. The solid line is reported by Koughia and Kasap (2006), the dashed line by Abkowitz (1992), and the dotted line by Song et al. (1999)

characterized with ipc and ( ), gives information of the localized state DOS; the higher is, the shallower trap levels are probed. Extensive studies using these photoconductive methods have given the DOSs in a-Se and a-As2 Se3 , while the results are controversial. For a-Se, as compared in Fig. 5.12 for the states (governing hole transport) above the valence band, two kinds of results have been repeatedly reported (Abkowitz 1992, Song et al. 1999, Koughia and Kasap 2006). One is an exponentially decaying distribution D(E) ∝ exp(−E/E0 ), where E0 = kB T/α and α is the dispersive parameter in Equation (5.5), and the other provides a broad peak at 0.3–0.4 eV above the valence band. The absolute values also scatter among the reports, which may be due to differences in a-Se films with respect to purities (Belev et al. 2007), evaporating conditions, post-storage durations, etc. For instance, Pfister and Morgan (1980) have demonstrated that as-evaporated As2 Se3 films are much more defective than annealed films. It seems that the exponential DOS is more plausible. The photoconductive DOS should be consistent with the results obtained from optical absorption, which gives a joint DOS of the valence and the conduction bands (Equation (4.1)). And we see in Section 4.6 that any peaks have never been uncovered for the optical absorption edge in chalcogenide glasses; just the exponential Urbach edge (EU ≈ 50 meV) and weak absorption tail. Therefore, the exponential DOS edge appears to be more universal. Otherwise, we may assume that the small and broad peaks at 0.3–0.4 eV in Fig. 5.12 are masked by the Urbach edge.

5.5 Avalanche Breakdown The avalanche breakdown under high electric fields is a common phenomenon in crystalline semiconductors, while it is unlikely to occur in amorphous semiconductors due to small carrier mobilities. Surprisingly, however, Juška and Arlauskas

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Fig. 5.13 A multiplication efficiency β of photo-generated holes β p and electrons β n as a function of the electric field E in a 70 μm thick a-Se film. β p→p is a multiplication efficiency solely by holes. The inset shows a typical time-of-flight signal of holes under charge multiplications (Juška and Arlauskas 1980, © Wiley-VCH Verlag GmbH & Co. KGaA., reprinted with permission)

(1980) have discovered the avalanche breakdown in a-Se at a threshold field of ∼106 V/cm (Fig. 5.13), which is twice that in c-GaP having a comparable bandgap ˇ of ∼2.3 eV (Cesnys et al. 2004). On the other hand, Tanioka et al. (1987) have discovered that the charge multiplication occurs also in vidicon targets (Section 7.6). Charge multiplications have been found also for junction structures in a-Si:H films (Toyama et al. 1995, Akiyama et al. 2002) and organic polymers (Katsume et al. 1996, Conwell 1998) at ∼107 V/cm. However, it remains to be studied if the mechanisms of these carrier multiplications are common. The avalanche breakdown in amorphous semiconductors has attracted substantial interest. As known, the avalanche breakdown in crystalline semiconductors is described by a Baraff’s model (Kasap et al. 2004). A carrier, accelerated under a high field, gains enough kinetic energy, giving rise to impact carrier ionization, and generated carriers repeat the carrier multiplication process. However, since the carrier in amorphous semiconductors is assumed to have a short mean free path, sufficient acceleration for the impact ionization seems to be difficult. On this problem, Kasap et al. (2004) have applied a lucky drift model, in which the carrier is assumed to undergo elastic collisions with disordered structures (and inelastic with lattice vibrations). Lucky elastic collisions can increase the carrier energy, ultimately giving rise to a sufficient energy (>Eg ) for the impact ionization. The reason why the avalanche breakdown is remarkable only in a-Se is ascribed to its relatively high hole mobility and small vibrational energy of ∼30 meV, which suppresses a contribution of inelastic collisions. Jandieri et al. (2009) apply this idea also to the electrical switching in a-Ge2 Sb2 Te5 films (Section 7.4.3). However, further studies seem to be necessary. A puzzling result is that the mean free path between elastic collisions in a-Se, obtained after parameter fitting, is just ∼0.5 nm (Kasap et al. 2004), which is comparable to the atomic distance. For such a short scale, can we apply a picture assuming particle (hole) acceleration?

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137

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Kasap, S., Rowlands, J.A., Baranovskii, S.D., Tanioka, K.: Lucky drift impact ionization in amorphous semiconductors. J. Appl. Phys. 96, 2037–2048 (2004) Katsume, T., Hiramoto, M., Yokoyama, M.: Photocurrent multiplication in naphthalene tetracarboxylic anhydride film at room temperature. Appl. Phys. Lett. 69, 3722–3724 (1996) Kolomiets, B.T.: Vitreous semiconductors (II). Phys. Status Solidi 7, 713–731 (1964) Kolomiets, B.T., Lyubin, V.M.: Photoelectric phenomena in amorphous chalcogenide semiconductors. Phys. Status Solidi (a) 17, 11–46 (1973) Koós, M., Kósa Somogyi, I., Vassilyev, V.A.: Photoluminescence in doped and annealed GeSe2 glass. J. Non-Cryst. Solids 43, 245–253 (1981) Koughia, K., Kasap, S.O.: Density of states of a-Se near the valence band. J. Non-Cryst. Solids 352, 1539–1542 (2006) LaCourse, W.C., Twaddell, V.A., Mackenzie, J.D.: Effects of impurities on the electrical conductivity of glassy selenium. J. Non-Cryst. Solids 3, 234–236 (1970) Lundt, H., Weiser, G.: Mid-gap luminescence and its excitation spectrum in trigonal selenium single crystals. Solid State Commun. 48, 827–830 (1983) Mao, J., Rapelje, K.A., Blodgett-Ford, S.J., Delos, J.B., König, A., Rinneberg, H.: Photoabsorption spectra of atoms in parallel electric and magnetic fields. Phys. Rev. A 48, 2117–2126 (1993) Messina, F., Vella, E., Cannas, M., Boscaino, R.: Evidence of delocalized excitons in amorphous solid. Phys. Rev. Lett. 105, 116401 (2010) Mott, N.F., Davis, E.A.: Electronic Processes in Non-crystalline Materials. Clarendon Press, Oxford (1979) Murayama, K.: Time-resolved photoluminescence in chalcogenide glasses. J. Non-Cryst. Solids 59–60, 983–990 (1983) Naito, H., Ding, J., Okuda, M.: Determination of localized-state distributions in amorphous semiconductors from transient photoconductivity. Appl. Phys. Lett. 64, 1830–1832 (1994) Oda, S., Kastner, M.A., Wasserman, E.: Transient photoluminescence and photo-induced optical absorption in polymeric and crystalline sulphur. Philos. Mag. B 50, 373–377 (1984) Oheda, H.: The exponential absorption edge in amorphous Ge-Se compounds. Jpn. J. Appl. Phys. 18, 1973–1978 (1979) Pfister, G., Liang, K.S., Morgan, M.: Hole transport, photoluminescence, and photoinduced spin resonance in thallium-doped amorphous As2 Se3 . Phys. Rev. Lett. 41, 1318–1321 (1978) Pfister, G., Morgan, M.: Defects in chalcogenide glasses l. The influence of thermally induced defects on transport in a-As2 Se3 . Philos. Mag. B 41, 191–207 (1980) Ristein, J., Taylor, P.C., Ohlsen, W.D., Weiser, G.: Radiative recombination center in As2 Se3 as studied by optically detected magnetic resonance. Phys. Rev. B 42, 11845–11856 (1990) Sakurai, Y., Nagasawa, K.: Radial distribution of some defect-related optical absorption and PL bands in silica glasses. J. Non-Cryst. Solids 277, 82–90 (2000) Scher, H., Montroll, E.W.: Anomalous transit-time dispersion in amorphous solids. Phys. Rev. B 12, 2455–2477 (1975) Seki, M., Hachiya, K., Yoshida, K.: Photoluminescence excitation process and optical absorption in Ge-S chalcogenide glasses. J. Non-Cryst. Solids 324, 127–132 (2003) Shimakawa, K., Yoshida, A., Arizumi, T.: Photoconduction of glasses in the Te-Se-Sb system. J. Non-Cryst. Solids 16, 258–266 (1974) Song, H.-Z., Adriaenssens, G.J., Emelianova, E.V., Arkhipov, V.I.: Distribution of gap states in amorphous selenium thin films. Phys. Rev. B 59, 10607–10613 (1999) Spear, W.E., Adams, A.R.: Photogeneration of charge carriers and related optical properties in orthorhombic sulphur. J. Phys. Chem. Solids 27, 281–290 (1966) Street, R.A.: Luminescence in amorphous semiconductors. Adv. Phys. 25, 397–453 (1976) Street, R.A., Mott, N.F.: Status in the gap in glassy semiconductors. Phys. Rev. Lett. 35, 1293–1296 (1975) Tanaka, K.: Free-carrier generation in amorphous semiconductors by intense subgap excitation. Appl. Phys. Lett. 73, 3435–3437 (1998)

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Chapter 6

Light-Induced Phenomena

Abstract Light-induced structural changes are the most exciting phenomena in amorphous chalcogenides. We will overview thermal and photon effects and their mechanisms. These include bulk effects such as irreversible, reversible, and transitory changes. There exist also photo-chemical reactions, the most known being photodoping. In addition, these changes are either scalar (isotropic) or vector (anisotropic) upon excitation of linearly polarized light. It is also shown that computer simulations aid to understand the mechanisms. Light-induced phenomena in oxide, a-Si:H, and polymers are briefly discussed for comparison. Keywords Photodarkening · Photo-crystallization · Photo-polymerization · Photodoping · Photo-deformation · Vector effects · E center · Staebler-Wronski effect

6.1 Overall Features Radiation effects are widespread in this world. Most common may be the photosynthesis in plants and the vision in animals. Moreover, Toyozawa suggests that the light triggers syntheses of biological lives (Toyozawa 2003). In solid-state science, we know the photographic reaction in Ag-halide crystals such as AgBrx Cl1–x (Itoh and Stoneham 2001), color center formation in alkali halides (Itoh and Stoneham 2001), and photo-polymerization in organic photoresist films (Kozawa and Tagawa 2010). In all these phenomena, the photo-electronic excitation induces successive structural changes. We also note that, for the photo-structural change to occur, two conditions are required, which are electron–lattice coupling and electron localization. The electron–lattice coupling is important also in crystals. Surveying the photostructural change in crystals, we see that two kinds of materials are liable to be modified (Itoh and Stoneham 2001, Toyozawa 2003). One is the ionic crystal as alkali halides, which is more likely to undergo the change than the covalent as c-Si. The other is low-dimensional crystals. Specifically, in low-dimensional organic crystals, a photoinduced atomic change can induce cooperative phase transitions. These observations suggest that the strong electron–lattice coupling is a prerequisite to the photo-structural change. On the other hand, comparing crystal and non-crystal, we see that the radiation effect is more prominent in the non-crystal (Itoh and Stoneham 2001, Toyozawa 141 K. Tanaka, K. Shimakawa, Amorphous Chalcogenide Semiconductors and Related C Springer Science+Business Media, LLC 2011 Materials, DOI 10.1007/978-1-4419-9510-0_6,

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2003). In the ideal crystal, the wavefunction of an excited electron extends over the whole sample volume, and accordingly, a quantum efficiency of photo-structural changes becomes very small. Otherwise, at finite temperatures, thermal lattice vibrations may spontaneously localize the electron wavefunction to some atomic site, which may undergo a bonding change. On the other hand, in the non-crystal, an excited electron and hole are promptly localized, due to disordered atomic structures, and as a result, some atomic change is likely to occur. Actually, the radiation effect in non-crystalline solids has attracted considerable interest for a long time. The first discovery may be traced to a note on photoinduced fluidity in a-Se by Vonwiller (1919). For the oxide glass, a lot of studies had been done before the 1970s in nuclear sciences (Lell et al. 1966). Weeks (1956) and Primak and Kampwirth (1968) found in g-SiO2 , respectively, the so-called radiation-induced E -center formation and a radiation compaction. However, these works appeared not to arouse extensive studies. World-wide researches seem to start after ∼1970 with two discoveries: optical and electrical phase changes in chalcogenides by Ovshinsky and coworkers (Ovshinsky and Fritzsche 1973) and a photoinduced refractive index change in silica glass fibers by Hill et al. (1978). These two discoveries manifest marked differences between the chalcogenide and the oxide. The chalcogenide, having smaller bandgap energy (1−3 eV) and more flexible atomic structures, is sensitive to illumination of visible light, as exemplified in Table 6.1. We also know that a-Si:H films with bandgap energy of ∼1.7 eV undergo the so-called Staebler–Wronski effect upon illumination of visible light, a kind of photoinduced defect creation phenomena. Some photo-sensitive organic polymers possess similar features. On the other hand, since the oxide glass has comparatively rigid structures with bandgap energies greater than ∼5 eV, radiation effects are less prominent, which appear under exposures of energetic beams such as γ-rays and intense light pulses. Or, the effects are likely to appear in optical fibers, since the fiber can provide sufficient light–matter interaction lengths. It should be mentioned that many kinds of structural changes are triggered in the chalcogenide also by other stimuli (Popescu 2001). Among the stimuli, electron beam effects have been extensively studied, since we can inspect the change Table 6.1 Typical photoinduced phenomena appearing in amorphous (glassy) oxide, sulfide, selenide, and telluride VIb atom

Photon

O S Se Te

Refractive index increase Darkening, fluidity

Photo-thermal

Thermal

Anisotropy Crystallization Phase change

In the first line, photon means a pure photo-electro-structural change, photo-thermal a photostructural change which is thermally activated in some temperature ranges, and thermal represents an optically induced thermal effect. With a decrease in the optical gap, the thermal contribution increases

6.2

Thermal Effects in Chalcogenide

143

in situ in electron microscopes and also can produce fine patterns just by scanning a focused beam. Studies on other stimuli are fewer, which include x-rays (Hayashi and Shimakawa 1996), γ-rays (Shpotyuk 2004), neutrons (Lukášik and Macko 1981), ions (Guorong et al. 2001, Suzuki and Hosono 2002), and mechanical impacts (Suzuki et al. 1980). Induced changes by these stimuli may appear to be similar to those induced by light, or there may be some differences due to the charge, energy, and mass of the excitations. X- and γ-ray photons have longer penetration depths than ∼50 μm, and accordingly, thick samples can be irradiated. Ion implantations can provide unique effects which depend upon the ion species. For the chalcogenide, a variety of light-induced phenomena have been discovered. These can be divided into the two, whether the light-induced temperature rise is determinative or not, i.e., thermal or photon (athermal) effects, which are described in Sections 6.2 and 6.3.

6.2 Thermal Effects in Chalcogenide The energy of photons absorbed in a solid is converted ultimately to a temperature rise in many cases. Accordingly, opto-thermal changes commonly occur upon intense light illumination. Pulsed-laser ablation is a known example. However, it is not clear if there are any characteristic differences between photo-electro-thermal changes, which are induced by bandgap light, and pure opto-thermal changes, which are induced through direct vibrational excitations by infrared light. In other words, it is unclear if the electronic excitation plays some roles in the photo-electrothermal change, partly because comparative opto-(non-electronic)-thermal studies have been few. At present, the most well-known thermal process in chalcogenides is the optical phase change in telluride films, Ge–Sb–Te. The principle was opened from Ovshinsky’s group around 1970, which is described in Section 7.4. The transmittance oscillation, Fig. 6.1, discovered by Hajtó et al. (1977) is a fantastic phenomenon. Suppose that a free-standing GeSe2 film with a thickness of 5 μm is exposed to focused light (∼200 μm in diameter) emitted from a conventional He–Ne laser (633 nm) with a light intensity of 10 mW. Then, surprisingly, the intensity of transmitted light oscillates with a typical frequency of ∼10 Hz, which can be noticed even by naked eyes. The phenomenon may be regarded as a kind of optical bistability. Substantial work has been done, while the mechanism remains controversial. Hajtó and Jánossy (2003) propose that the oscillation process is partially thermal. First, light exposure gives rise to a photodarkening phenomenon (see Section 6.3.8), which in turn decreases transmitted light intensity. At the same time, the increasing light energy absorbed in the film gives a temperature rise, which anneals the sample, recovering the initial higher transmittance. And, this process is repeated, resulting

144 Fig. 6.1 Transmittance oscillation in free GeSe2 films exposed to He–Ne laser light of 1.7 kW/cm2 (upper) and 2.6 kW/cm2 (lower)

6 Light-Induced Phenomena transmittance

time

in the oscillation. In contrast, Phillips (1982) assumes that the oscillation occurs as a result of athermal photo-crystallization and amorphization. Recently, Tao et al. (2009) have proposed an interference model, in which constructive and destructive interference in the film is assumed to cause the oscillation. Though the mechanism being controversial, if the oscillating frequency could be higher, the phenomenon would attract more interest in applications. Oscillation phenomena appear also in AsSe, As2 Se3 , As2 S3 (Hajtó and Jánossy 2003), and even in a-Si:H (Abdulhalim et al. 1989). Nevertheless, if the mechanisms of these phenomena are common remains to be studied. Matsuda and Yoshimoto (1975) have demonstrated light-induced transitory motion using bimetallic structures consisting of mica and Sb(As)-S films (Fig. 6.2). From temperature dependence and time constant of the effect, they conclude that the motion is caused by light-induced thermal expansion.

Fig. 6.2 A sketch of light-induced bending experiments and a typical response (Matsuda and Yoshimoto 1975, © American Institute of Physics, reprinted with permission)

6.3

Photon Effects in Chalcogenide

145

6.3 Photon Effects in Chalcogenide 6.3.1 Classification and Overall Features A variety of photo-electro-structural changes have been reported (Tanaka 1990, Shimakawa et al. 1995, Fritzsche 2000, Popescu 2001, Kolobov 2003), and some classification may be valuable for grasping a perspective. Here, it should be noted that the classification is likely to cause confusions due to the terminology, a phenomenon being named by its appearance or by its (estimated) mechanism. For instance, photo-bleaching (appearance) may appear as results of photo-oxidation and/or photoinduced bond conversion (mechanisms). Readers should take care of this point. First, a photon effect is classified whether it occurs in bulk samples or as chemical reactions with other elements as Ag (photodoping) or O (photo-oxidation). We here note that these two processes manifest contrastive temperature dependences. Many bulk effects, except photo-enhanced crystallization, are more prominent at lower temperatures, which implies the importance of localized atomic motions induced by excited electronic carriers. Thermal relaxation tends to reduce or erase the bulk photo-effects. In contrast, the photo-chemical reaction becomes less efficient at lower temperatures, probably because thermally activated atomic migration is a rate-limiting process. The bulk effect can be classified into memorized and transitory changes. The memorized means that the effect exists in (quasi-)stable after cessation of illumination, and the transitory means that the effect appears only during illumination, as the photoconductivity. In addition, these two kinds of changes may be either scalar or vector, whether the change does not or does reflect the polarization direction of excitation light. The scalar change is isotropic, being governed by the energy of photons, while the vector is anisotropic, being influenced by the light polarization. The memorized change can further be divided into irreversible and reversible, depending on if the change can be erased by an annealing treatment at some temperatures. In other words, the irreversible is a change toward a stabler equilibrium state, as exemplified by photo-crystallization in a-Se and photo-polymerization in as-evaporated As2 S3 films. On the other hand, the reversible change occurs toward an unstabler state, as in photodarkening and photoinduced electron spin resonance, which can be erased by annealing at temperatures of ∼Tg and ∼Tg /2. Roughly, the stabilization (irreversible) phenomena are more prominent, which may be a reason why the mechanisms have relatively been understood. It is valuable to grasp the irreversible and the reversible change in the scales of quasi-stability and structural disorder. Figure 6.3 shows the relationship between as-prepared (disordered), illuminated, and annealed (ordered) states. The annealed state must have the lowest free energy and smallest disorder, and photo-excitation always produces unstabler and more disordered states. Such a photoinduced change may resemble a defect creation in alkali halide crystals (Itoh and Stoneham 2001), and it is reversible. On the other hand, as-prepared states are likely to be energetically higher or lower than the illuminated state, depending upon preparation

146

6 Light-Induced Phenomena

(a)

(b)

Adiabatic potential

excited

k BT

disordered

illuminated

ordered

configuration

Fig. 6.3 Relationships among disordered (as-prepared), illuminated, and ordered (annealed) states in (a) stability disorder scales and (b) an energy configuration diagram. Solid and dashed arrows show photo- and thermally induced changes

methods. Probably, the vacuum evaporation produces substantially unstable and disordered structures, because the evaporation causes very rapid quenching of gaseous molecules to solids on substrates. Then, illumination effects become irreversible. The photoinduced change provides modifications in macroscopic properties, as exemplified in Table 6.2. The most common change, or the one being detectable with high sensitivities, appears in optical properties: absorption and refractive index. Changes in sample volume (density) and shape may also appear. Mechanical properties such as elastic constant, hardness, and viscosity are also likely to be modified. In addition, light illumination tends to change chemical etching characteristics. From a quantitative point of view, it had been believed (till ∼2000) that photo-chemical reaction such as photodoping gives the most prominent changes, irreversible the next, reversible following it, and vector the smallest. Recently, however, prominent vector deformations have been discovered, as described in Section 6.3.12. It is believed that the photoinduced phenomena are inherent to, or substantially prominent in, amorphous chalcogenides. For instance, it has been amply demonstrated that the photodarkening does not appear in c-As2 S3 (orpiment) (Hamanaka et al. 1977). The photodoping in c-As2 S3 is demonstrated to be very inefficient (∼1/100) (Imura et al. 1983). However, it should be mentioned that some relatively Table 6.2 Changes in some macroscopic properties with typical photoinduced phenomena Phenomena

Optical

Deformation

Elastic

Etching

Irreversible Reversible Vector Transitory Photodoping

? ?

◦

?

◦

◦

Question marks indicate no related studies to the authors’ knowledge

◦ ◦

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Photon Effects in Chalcogenide

147

unstable chalcogenide crystals as c-As2 S2 undergo photo-structural changes including photo-amorphization (Matsuda and Kikuchi 1973, Frumar et al. 1995, Shimakawa et al. 1995, Naumov et al. 2007).

6.3.2 Experimental Some remarks on experiments of photoinduced phenomena may be valuable. We here emphasize that, in analyses of observations, it is important to consider geometrical factors such as sample thickness, size of light spot, and substrate. The thickness should be compared with the penetration depth of excitation light. The light, which may be monochromatic and propagating along the x-axis, is absorbed as exp(–αx), where α is the absorption coefficient. Accordingly, we assume that the light is absorbed within a penetration depth of ∼α −1 , which is typically 0.1−1 μm for super-gap light, 1−10 μm for bandgap light, and ∼1 mm for sub-gap light. We hence can envisage that photo-excitation occurs in a layer from a sample surface to the penetration depth. If the sample is sufficiently thinner than the depth, a photoinduced effect occurs uniformly throughout the film thickness. In such cases, analyses of time variations are straightforward, e.g., the transmitting light intensity I(t) may exponentially decrease in a photodarkening process. However, if the sample is thicker than the depth, we should be careful of a selffeedback effect in optical changes. Actually, in the photodarkening, a photoinduced increase in absorption, which reduces α−1 , tends to limit a darkened layer to the penetration depth, despite prolonged exposures. The situation can be analyzed in a phenomenological way (Tanaka and Ohtsuka 1977). Provided that the reaction follows a first-order process, following Lambert’s law, we write down the spatiotemporal changes in α and I induced by monochromatic light as ∂α(x, t)/∂t = K I(x, t) {αs − α(x, t)} and ∂ I(x, t)/∂x = −α(x, t)I(x, t),

(6.1)

where K and α s are a reaction constant and a saturated absorption coefficient. The analysis demonstrates that for a photodarkening process, in which αs > αi (initial absorption coefficient), the reacted region is practically restricted to a surface layer of ∼αi −1 . Here, the transmitted light intensity may appear as a Kohlrausch–Williams–Watts-type stretched exponential, exp[−(t/τ )β ], where β < 1.0 (Shimakawa et al. 2009). It should be noted, however, that if carrier diffusion is prominent, as in photodoping (Tanaka 1991), the thickness restriction is relaxed. Excitation light is sometimes focused to a spot with a diameter of ∼10 μm in order to increase the irradiance. When the size of light spots is much smaller than the penetration depth and the sample thickness, volume effects can appear, as will be described for a giant photo-expansion (Section 6.3.9). In addition, Nakamura et al. (1996) demonstrate the importance of boundary effects on photocrystallization of a-GeSe2 films, the material having two crystalline forms of twoand three-dimensional.

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Finally, we note that a variety of sample forms have been employed for studying the photoinduced phenomenon. Commonly employed are polished bulk samples, fibers, films on rigid substrates as oxide glasses, and Si wafers. Less studied are bimetallic structures (Figs. 6.2 and 6.26). In addition, Tanaka and coworkers have recently demonstrated that As2 S3 films deposited upon viscous substrates manifest anomalous shape changes under illumination (Fig. 6.27). The substrate appears to exert big constraints on macroscopic deformations of deposited films.

6.3.3 Computer Simulation Notable computer-aided studies have been performed on bulk photon effects, as reviewed by Drabold et al. (2003) and Simdyankin and Elliott (2007). Historically, in the beginning, calculations followed the conventional tight binding analyses for some modeled structures. Then, the calculation shifted to structures produced by classical molecular dynamics. Recently, most studies follow the so-called ab initio simulations (see Section 2.6), which may be divided into two: quantal molecular dynamics calculations using density functional theories for disordered structures and quantum chemical calculations for clusters (Shimojo et al. 1998). In addition, Kugler’s group has developed tight binding molecular dynamics simulations (Hegedus et al. 2005, Lukács et al. 2008). These recent studies treat photoinduced effects as follows: First, plausible atomic structures have been constructed through, e.g., relaxing presumed clusters or the ab initio molecular dynamics following “melt and quench” procedures (see Section 2.6). Then, an electron is taken from HOMO (valence band) and added to LUMO (conduction band), and resulting structural changes are traced as a function of time, which may be bond distortions, defect creation, and/or structural relaxation. Analyzed materials are mostly simple ones such as pure S(Se) and As2 S(Se)3 . Reported time variations are instructive, while some cautions are needed for interpreting the results. First, there exist some crucial problems for the initial atomic structures, as described in Section 2.6. Second, in most studies, the excited carrier still exists in HOMO and LUMO in the final state. The simulated structure is during illumination (transitory change), not after illumination as the photodarkening. Third, the calculations have not been able to treat rigorously the photo-electronic excitation process. We cannot predict the position where a photo-electronic excitation is induced by a photon having a fixed energy. In addition, illumination effects of polarized light have not been analyzed.

6.3.4 Photo-Enhanced Crystallization Photo-enhanced crystallization in a-Se is a well-known irreversible change, which was comprehensively studied by Dresner and Stringfellow (1968). When evaporated a-Se films were exposed to light (∼1 W/cm2 ) emitted from a mercury lamp

6.3

Photon Effects in Chalcogenide

149

Fig. 6.4 Spherulites (with a diameter of ∼0.1 mm) produced by photo-irradiation on the surface of an a-Se film. The color is artificial

at ∼50◦ C, crystal growths became dramatically faster, i.e., giving a rate increase by two orders than that in the dark. Opto-thermal temperature rise could be neglected under their experimental conditions. They also demonstrated that illumination at lower temperatures cannot crystallize a-Se, which suggests that the illumination just enhances the thermal crystallization. Accordingly, the word “photo-enhanced” may be preferred to “photoinduced.” It was also demonstrated that the crystal growth can be controlled by a flux of holes, not electrons, toward crystalline–amorphous boundaries. We thus speculate that the hole cuts entangled chain molecules, which assist thermal alignment of Se molecules and successive crystal growth. The photo-enhanced crystallization of a-Se films is a big problem in photoconductive applications (see Section 7.6), which attract renewed interest. In many cases, small amounts of As are added to a-Se for suppressing the crystallization, but the addition concomitantly reduces the mobility of holes (see Fig. 4.23). a-Se films show related phenomena to the photo-crystallization. Larmagnac et al. (1982) demonstrate that photo-relaxation occurs as a prelude to the crystallization. It is also known that, upon illumination of linearly polarized light, oriented crystallization, or vector crystallization appears (Innami and Adachi 1999). In addition, Roy et al. (1998) have demonstrated, by tuning the photon energy of excitation light, a light-selective suppression of photo-crystallization. Since a-Se is the simplest amorphous semiconductor, we expect that studies on the material will reveal fundamental insights into the photoinduced phenomenon. Other materials show similar or related phenomena. Raman scattering spectroscopy, which is more sensitive than direct microscope observations, has been applied to investigate photo-crystallization behaviors in GeSe2 (Sakai et al. 2003) and As-Se (Mikla and Mikhalko 1995). Brazhkin et al. (2007) have recently reported photo-crystallization of pressure-synthesized AsS bulk glass, which is composed with As4 S4 molecules. Pattern formation discovered in liquid S by Sakaguchi and Tamura (2007) may be a kind of photo-crystallization. It should also be mentioned that a photo-crystallization occurs also in protein (Murai et al. 2010), the fact suggesting that the phenomenon is common to one-dimensional molecular systems. In c-As2 S3 (Frumar et al. 1995) and c-As1 Se1 (Shimakawa et al. 1995), an apparently opposite phenomenon to the photo-crystallization, i.e., photo-amorphization occurs. Finally, it should be mentioned that if the photo-crystallization bears

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some relation to the photo-thermal phase change in telluride films, described in Section 7.4, awaits further studies.

6.3.5 Photo-Polymerization DeNeufville et al. (1974) have reported a comprehensive study of irreversible photoinduced changes in as-evaporated As2 S(Se)3 films. When an as-evaporated As2 S3 film with Eg ≈ 2.4 eV and n ≈ 2.5 is exposed to bandgap illumination at room temperature, the film shows a redshift of the optical absorption edge “irreversible photodarkening” by ∼0.1 eV (Fig. 6.5a), a refractive index increase of ∼0.1, a thickness compaction of ∼1% (Kasai et al. 1974), and elastic hardening of ∼20% (Tanaka et al. 1981). In addition, there appear dramatic changes in etching rates of the film by alkali solutions and plasmas (Lyubin 2009). Thermal annealing at glass transition temperatures of ∼200◦ C, which yields stabler As2 S3 networks, gives similar, but not the same, macroscopic changes. The principal mechanism has been understood to be photo-polymerization (DeNeufville et al. 1974). Vacuum-evaporated As2 S3 films seem to consist of molecular species such as As4 S4 , As4 S6 , and S clusters, as illustrated in Fig. 6.5b, and these species undergo mutual polymerization upon bandgap illumination, resulting in As2 S3 networks. This microscopic structural change has been confirmed using several methods such as x-ray diffraction (Fig. 2.3). A markedly sharp x-ray

Fig. 6.5 Irreversible changes in (a) the optical absorption edge (DeNeufville et al. 1974, © Elsevier, reprinted with permission) and (b) an atomic model for as-evaporated As2 S3 films (modified from Nemanich et al. 1978)

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FSDP, which probably reflects the size of the molecules in as-evaporated films, becomes weaker and broader with the polymerization. Since the As2 S3 network is constructed with As–S bonds, this polymerization accompanies conversions from homo- (As–As and S–S in As4 S4 and S clusters) to heteropolar As–S bonds, which are stabler (see Table 2.4). The appreciable redshift (∼0.1 eV) of the optical absorption edge in Fig. 6.5a, i.e., a reduction of the bandgap, may be ascribed to a change in electron wavefunctions from molecular to more extended ones. Reduction of an etching rate may be ascribed to the formation of stronger heteropolar bonds. In a pioneering work, Keneman (1971) applied this phenomenon to holographic storages of refractive index and relief types. It is plausible that some irreversible photo-polymerization appears in any as-deposited films, since the irreversible change is a kind of stabilization processes. Koseki et al. (1978) demonstrate that Se films evaporated onto cooled substrates form the so-called red Se structure, being composed of Se ring molecules, which are polymerized to chain molecules upon light illumination. Yellow As also seems to show photo-polymerization (Rodionov et al. 1995). On the other hand, As2 Se3 films undergo less prominent changes than those in As2 S3 (DeNeufville et al. 1974, Trunov et al. 2009), probably because as-evaporated species are not molecular as those in As2 S3 . Ge–S(Se) films, which are obtained by vacuum sublimation, do not show clear photo-polymerization. Irreversible changes have also been reported, e.g., for Cu–As–Se (Asahara et al. 1975), Ga–La–S (Youden et al. 1993), and S-rich As–S bulk glasses (Kyriazis and Yannopoulos 2009).

6.3.6 Giant Photo-Contraction Singh et al. (1979) have discovered giant photo-contraction in obliquely evaporated Ge–Se films. As shown in Fig. 6.6, obliquely evaporated GeSe3 films (incident angle of 80◦ ) with a thickness of ∼1 μm undergo a volume contraction of 10–20% upon bandgap illumination. Irradiation of He+ ions gives a contraction of, surprisingly, ∼40% (Chopra et al. 1982). Naturally, it is plausible that properties such as optical absorption and etching rates substantially change. Structural studies have

Fig. 6.6 Giant photo-contraction in obliquely deposited GeSe3 films (∼1 μm thick) as a function of the oblique angle (modified from Singh et al. 1979)

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demonstrated that micro-voids existing in between columnar structures (Fig. 2.24) in obliquely evaporated films collapse with illumination (Kumar et al. 1989). Thus, for this phenomenon, we know the initial and final structures. However, further problems remain. Why does the void collapse upon irradiation? And, why is the phenomenon remarkable in Ge–Se films, especially GeSe3 ? Viscosity reduction and surface tension may be responsible. On this problem, Lukács et al. (2008) recently report tight-binding molecular dynamics simulations for pure Se.

6.3.7 Other Irreversible Changes Photo-bleaching, an increase in optical transmittance reflecting a blueshift of optical absorption edge, sometimes appears. Berkes et al. (1971) have reported a pioneering study on the photo-bleaching in As–S(Se) films. Tanaka and Kikuchi (1973) demonstrate a photo-bleaching phenomenon in flash-evaporated films of As2 S3 . It is reasonable to assume that photo-decomposition (phase-separation) causes the photo-bleaching. In the flash-evaporated films, the intense heating tends to reduce the S content, producing As-rich Asx S3 (x > 2) films, which seem to exhibit higher optical absorption than that in illuminated As2 S3 films (Tanaka and Ohtsuka 1978). Then, a photoinduced decomposition, Asx S3 (x > 2) → As + As2 S3 , may occur in the As-rich As–S films or in locally As-rich regions in As2 S3 films. Decomposed As atoms seem to migrate through unknown mechanisms over macroscopic distances, segregating and producing As clusters, which may be oxidized to c-As2 O3 , as actually detected (Section 6.3.15). Evaporated Ge–S(Se) films also undergo photo-decomposition. In addition, anomalous irreversible changes have been reported for As–S(Se) systems. Photo-hardening is reported for g-As3 Se2 (Asahara and Izumitani 1974) and annealed films (Kolomiets and Lyubin 1978). In ternary alloys such as Ge–As–S films, irreversible volume expansions appear upon illumination (Knotek et al. 2009). In multi-layer structures consisting of As2 S3 /Se, photo-diffusion of Se atoms over the layer structures appears (Tanaka et al. 1990, Adarsh et al. 2005).

6.3.8 Reversible Photodarkening and Refractive Index Increase 6.3.8.1 Overall Features Reversible photodarkening, often referred to as “photodarkening,” and corresponding refractive index increase are phenomena universally observed in covalent chalcogenide glasses. The phenomena are simple, bulky, and quantitatively reproducible in stoichiometric compositions, and accordingly, it has attracted great interest, as reviewed several times, e.g., by Tanaka (1990), Pfeiffer et al. (1991), Shimakawa et al. (1995), Fritzsche (2000), and Kolobov (2003).

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Fig. 6.7 Photodarkening in an As2 S3 film at 80 K

Many experiments have been performed for As2 S3 , due to its proper Eg (∼2.4 eV) and Tg (∼200◦ C∼470 K). Samples can be As2 S3 films or polished bulk flakes (being preferred for fundamental studies), which have been annealed at ∼180◦ C, just below the glass transition temperature. The thickness should be thinner than ∼10 μm, which corresponds to the penetration depth of bandgap light with ω ≈ Eg . When such a sample is exposed to bandgap illumination at room temperature, it undergoes a (nearly) parallel redshift E by ∼50 meV of the optical absorption edge (Fig. 6.7), or more precisely, a redshift of the Urbach edge and a reduction of the Tauc gap, which cause a color change of the sample from yellowish to orange, the naming origin of photodarkening.1 The shift can be recovered with a successive annealing treatment at ∼180◦ C, and the illumination–annealing cycle can be repeated many times. The redshift of ∼50 meV accompanies a refractive index increase of ∼0.03 at transparent wavelengths, which are quantitatively connected through the Kramars–Krönig relation or simply by the so-called Moss rule (Utsugi 1999). A variety of photodarkening characteristics have been investigated, which will be discussed in the following sections. For the time dependence of photodarkening processes, see Section 6.3.2. 6.3.8.2 Dependence upon Temperature and Pressure The photodarkening has been investigated as functions of temperature Ti and pressure Pi , respectively, at which a sample is illuminated (Tanaka 1990, Pfeiffer et al. 1 The word “photodarkening” may refer to, in general, a decrease in optical transmittances, and actually, it is employed in that sense by some researchers. However, it should be noted that, in the present context, the photodarkening represents a redshift of optical absorption edges.

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(b) (a)

Fig. 6.8 Magnitudes of the redshift E as functions of (a) temperature Ti normalized to Tg for several stoichiometric chalcogenides listed and (b) hydrostatic pressure P in Se

1991, Shimakawa et al. 1995, Fritzsche 2000). For the temperature dependence, it has been demonstrated, as shown in Fig. 6.8a (Tanaka 1983), that E in elemental and stoichiometric chalcogenides decreases with an increase in Ti /Tg and becomes zero at Ti /Tg ≈ 1. This dependence manifests that thermal relaxation suppresses the photodarkening. On the other hand, it is fairly difficult to examine pressure effects, since the glass transition temperature tends to become higher under compression as shown in Fig. 6.8b (Tanaka 1990, Ikemoto et al. 2002), and the illumination– annealing should be performed under fixed pressures. Following such procedures, Tanaka (1990) has demonstrated, as shown in Fig. 6.8b, that E in Se first increases with compression, which can be related to an increase in Tg , while E turns to decrease above ∼1.5 GPa (=15 kbar). As described in Section 2.4, x-ray studies have demonstrated that compression reduces the intermolecular van der Waals (interlayer) distance, ultimately producing isotropic bonds. Therefore, E decrease implies that photodarkening relies upon the dual bonding structure, consisting of covalent and van der Waals bonds. 6.3.8.3 Dependence upon Excitation Light It is natural to assume that the photodarkening is induced by absorbed light (Tanaka 1990, Pfeiffer et al. 1991, Shimakawa et al. 1995, Fritzsche 2000). Alternatively, non-absorbed light cannot put any energy to a material for inducing some photoelectro changes. Actually, as shown in Fig. 6.9a, efficiency of the photodarkening in As2 S3 normalized by an absorbed photon shows a dramatic decrease at ω ≤ Eg (∼2.4 eV). This observation suggests that excitation of lone pair electrons is a

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Photon Effects in Chalcogenide

(b)

quantum efficiency

(a)

155

Fig. 6.9 Dependence of (a) a quantum efficiency and (b) saturated redshift and refractive index increase on the photon energy of excitation in As2 S3 (Eg ≈ 2.4 eV) (modified from Shimakawa et al. 1995)

prerequisite to the photodarkening. However, we see in Fig. 6.9b that the saturated E and the corresponding refractive index increase n, after prolonged illumination, provide much milder dependence upon the photon energy. Urbachedge light with photon energy of 2.0–2.4 eV can also give marked (∼1/2) optical changes. It seems that the quantum efficiency is governed by photo-excitation process, while the saturated value reflects an equilibrated state determined by excitation and thermal relaxation (Tanaka 1990). Illumination with other photon energies appears to give a different excitation process from that of the photodarkening. Mid-gap light with ω ≈ Eg /2 may excite localized states, and if it is intense, nonlinear optical excitation occurs, inducing a refractive index increase without photodarkening (Tanaka 2004). On the other hand, effects of (ultra-)super-gap light, i.e., soft x-ray, which can excite core electrons and/or bonding electrons, remain to be studied (Hayashi and Shimakawa 1996). Dependence upon light intensity was investigated for bandgap illumination. It has been demonstrated that the reciprocity law between the intensity and the exposure time holds only in a rough sense. In detail, as shown in Fig. 6.10 (Tanaka 1990), E increases in proportion to ln I, where I is the light intensity (∼50 mW/cm2 ). However, the figure also shows that the intensity dependence becomes negligible at 80 K. These results can be quantitatively understood as E being determined from a balance between photo-excitations and thermal relaxations. It should be mentioned that dependence of E on I of sub-gap light shows a slightly different behavior (Fig. 6.16).

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Fig. 6.10 Dependence of photodarkening E upon the intensity I of bandgap light (∼2.54 eV) in As2 S3 at exposure temperatures of 80 and 290 K (Tanaka 1990, © Elsevier, reprinted with permission). The solid point at 290 K is obtained using a pulsed dye laser, for which the horizontal scale depicts the time-averaged power. The solid lines show theoretical results with the right-hand side scale

Effects of cw and pulsed bandgap illuminations seem to be controversial. Tanaka (1990) demonstrates for As2 S3 that if the total doses are fixed, cw and pulse excitations (3 ns, 488 nm, 0.5 MW/cm2 ) give the same E (Fig. 6.10). On the other hand, Rosenblum et al. (1999) have reported a “strong” photosensitivity increase in AsSe films upon pulse excitations of 5 ns, 532 nm, and 10 MW/cm2 . The difference may be due to different materials and/or peak intensities. 6.3.8.4 Dependence upon Materials Dependence upon materials and glass compositions may be more interesting (Tanaka 1990, Shimakawa et al. 1995, Reznik et al. 2006). The photodarkening appears universally in covalent chalcogenide glasses, including elemental S and Se, stoichiometric (as As2 S3 ), and non-stoichiometric multi-component alloys (as Ge–As–S). Naturally, the magnitude varies with materials. As shown in Fig. 6.8, for elemental and stoichiometric glasses, when scaled with Ti /Tg , E decreases in the order of sulfide, selenide, and telluride. Tellurides hardly show the photodarkening (Tanaka 1990, Hayashi et al. 1997). It is known that, in this order, the dual bonding structure, consisting of covalent and van der Waals bonds, changes to a metallic character. Therefore, the dependence on the chalcogen species reinforces the idea that the dual bonding structure is essential for photodarkening. Regarding compositional variations in binary As(Ge)–S(Se) systems, as shown in Fig. 3.9d, the material with Z = 2.67 tends to exhibit maximal photodarkening (Tanaka 1990). This result is probably governed by, at least, two factors. One is that, as shown in Fig. 3.9a, with increasing Z, the glass transition temperature Tg becomes higher, so that Ti /Tg at Ti ≈ 300 K decreases, which increases E, as suggested in the temperature dependence. On the other hand, in glass with Z ≥ 2.67, the amorphous structure becomes to be three-dimensionally cross-linked, i.e., the role of

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157

the van der Waals interaction is reduced, which seems to suppress photodarkening. It should be mentioned, however, that photodarkening characteristics in As–S(Se) and Se films are not modified by hydrogenation (Fritzsche et al. 1981, Nagels et al. 1995), which may decrease Z. In contrast, it is interesting to point out that some materials do (or may) not show the photodarkening. First, photodarkening does not appear in ultrathin (∼10 nm) As2 S3 films (Hayashi and Mitsuishi 2002). We may speculate that photo-excited carriers diffuse over ∼10 nm and recombine at the surface of films, thereby giving rise to no photo-structural changes. Second, photodarkening does not appear in the crystal as c-As2 S3 (orpiment) (Hamanaka et al. 1977). The disorder seems to be a prerequisite. Third, behaviors in ionic chalcogenide glasses are controversial. Liu and Taylor (1987) have demonstrated that Cu-alloyed As2 S(Se)3 do not exhibit photodarkening, which can be interpreted in two ways: fourfold coordination of S in the alloy makes the glass network too rigid or the Cu–S(Se) level existing at the valence band top masks the modification of lone pair states (Aniya and Shimojo 2006). The photodarkening neither appears in Na–Ge–S glasses (Tanaka et al. 2003), which is understandable following similar ideas. We also note that, in an ion-conducting glass as Ag–As–S, photo-ionic effects (described in Sections 6.3.13 and 6.3.14) tend to mask the photodarkening. In contrast, Loeffler et al. (1998) report reversible photoinduced structural changes in Ga–Ge–S glasses upon pulse exposures. Fourth, results for the oxide glass are also controversial. Taylor’s group demonstrated a parallel redshift (∼0.8 eV) of the optical absorption edge (at ∼3 eV) in g-As2 O3 under x-ray irradiation (Hari et al. 2003). But, Terakado and Tanaka (2007) have detected no redshifts in g-GeO2 upon exposures to bandgap light. In the glassy GeS2 –GeO2 system, photodarkening becomes smaller with an increase in the GeO2 content, disappearing at around 50GeS2 –50GeO2 . Finally, it is inconclusive if the photodarkening appears in the pnictide such as a-As (Mytilineou et al. 1980) and a-P (Hosono et al. 1985). We also mention here that, in As-rich As–Se and Ge– S(Se) films, quantitative reproducibility of the photodarkening is worse, probably due to strong dependence of amorphous structures upon preparation conditions. 6.3.8.5 Mechanisms Why does the photodarkening, i.e., the photoinduced redshift of absorption edges, occur in the chalcogenide? It is known that the redshifts are induced also by temperature rising and hydrostatic compression (Figs. 4.13 and 4.14), so that a comparison of these three changes may be interesting (Tanaka 1990). However, as described, photodarkening is erased by annealing and suppressed by compression. We thus assume that photodarkening appears through a unique structural change. Several circumstantial evidences support that the valence band broadening causes photodarkening (Tanaka 1990, Shimakawa et al. 1995, Fritzsche 2000). For instance, Eguchi and Hirai (1990) have demonstrated for thin a-As2 S3 (Eg ≈ 2.4 eV) films that the photodarkening is a manifestation of broadening of the main optical absorption band centered at ω ≈ 5 eV, which reflects optical transitions from lone pair electron (valence band) to covalent anti-bonding states (conduction

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band). Here, the conduction band is possibly intact due to a rigid anti-bonding character. Accordingly, it is reasonable to ascribe the photodarkening to a broadening of the valence band. (Unfortunately, the photoelectron spectroscopy has not sufficient spectral resolution for detecting this change.) The problem is, therefore, reduced to a broadening mechanism of the lone pair electron band with light illumination. For this problem, Malinovsky and Novikov (1986) have suggested that thermal spikes, which are produced by recombination of localized electronic carriers, cause local structural disordering, which may broaden the valence band. However, such conceptual models face a difficulty in explaining detailed features as the light intensity and the composition dependence. As reviewed by several researchers (Tanaka 1990, Pfeiffer et al. 1991, Shimakawa et al. 1995), the configuration coordinate model delineates more detailed features for atomic structural changes. For instance, Tanaka (1990) has proposed a model, illustrated in Fig. 6.11, which can quantitatively explain the photodarkening variations with temperature, light intensity, and exposure time. He assumes that an adiabatic potential of photodarkening sites is expressed with a single- and double-well model, an excited state having a single minimum of Z and ground states having a stable X and a quasi-stable Y configuration. The density of such sites is estimated to be ∼1% of total atoms. (Note that this density corresponds to an atomic site in a cube with a side length of five atoms, i.e., 1–2 nm, or, one site in a volume pertaining to the medium-range order.) The excitation energy of Y is smaller than that of X, and accordingly, we can assume that E ∝ NY , where NY is the number of atomic sites having Y configuration. Then, in the annealed state, it is reasonable to envisage that all the sites have X configuration. Bandgap excitation induces an energy configuration change as X → Z → Z → Y, which gives rise to photodarkening. On the other hand, annealing assists a thermal relaxation process Y→X, surmounting the barrier in between. Here, the barrier height EB seems to vary from site to site, and in g-As2 S3 , it is estimated at 0.5–1.5 eV. An important problem is the atomic structure, which can possess an energy configuration relation as that in Fig. 6.11. Despite many experiments and theoretical models, however, we cannot attain the final elucidation of structural mechanisms.

Fig. 6.11 An energy configuration model for photodarkening

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The main reason is subtle structural changes, which cannot be experimentally identified. Structural studies demonstrate that the nearest-neighbor configuration remains intact, at least, in a-Se and stoichiometric alloys (Pfeiffer et al. 1991, Kolobov et al. 1997). It is plausible that the structural disordering, which appears as broadening of FSDPs (Tanaka 1975), is an origin of the redshift (Kolobov et al. 1997, Honolka et al. 2002, Lucas et al. 2005). Nevertheless, the origin of FSDP remains controversial, as described in Section 2.4. Since the initial and the final structures cannot be identified, the transformation dynamics remain necessarily more speculative. The atomic structural modification may arise from medium-range structures, as intermolecular disordering, or from defective structures (Tanaka 1990, Pfeiffer et al. 1991, Shimakawa et al. 1995). A bond-twisting motion illustrated in Fig. 6.12a, which quantitatively satisfies the bistable configuration model (Fig. 6.11), causes such intermolecular disordering (Tanaka 1990). Shimakawas’ model, Fig. 6.12c, assuming Coulombic repulsion between segmental structures induced by photogenerated immobile electrons, also ascribes the photodarkening to the interlayer disordering (Shimakawa et al. 1998). On the other hand, defective models have been repeatedly presented (Fritzsche 2000, Simdyankin and Elliott 2007). For instance, it is assumed that the conversion of normal bonds to D+ and D− is the origin of photodarkening. Otherwise, the bond conversion from heteropolar to homopolar

(b)

(a) (c)

Fig. 6.12 Structural models for the photodarkening assuming (a) bond-twisting (Tanaka 1990), (b) structural changes through defects (Kolobov et al. 1997), and (c) Coulombic layer movements (Shimakawa et al. 1998)

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may be responsible, while the model cannot be applied to pure S and Se. Kolobov et al. (1997) propose, on the basis of EXAFS studies for a-Se, that both the intermolecular disordering and charged defects are produced by bandgap illumination, as illustrated in Fig. 6.12b.

6.3.9 Other Reversible Changes It has been demonstrated that bandgap illumination induces reversible changes in a variety of properties (Pfeiffer et al. 1991, Shimakawa et al. 1995). Experiments using x-ray diffraction (Tanaka 1975) and vibrational spectroscopy (Iijima and Mita 1977) have detected structural changes, which suggest enhancement of structural disorders. As for macroscopic properties, reversible changes in sample volumes (Hamanaka et al. 1976), thermal properties (Kolomiets et al. 1979), mechanical properties (Kolomiets and Lyubin 1978), chemical properties (Kolomiets and Lyubin 1978), and electrical properties (Hamada et al. 1972) have been discovered, as described later. However, at the present stage, it is not necessarily clear if these changes are directly connected with the photodarkening. There is a possibility that bandgap illumination causes several kinds of atomic changes, including structural disordering and creation of defects, which cause these changes individually (Lucas et al. 2005, Holomb et al. 2006, Yang et al. 2009). It is also plausible that super- and sub-bandgap illuminations induce different structural changes. In addition, we should be careful about temporal behaviors. Tanaka (1998) has demonstrated different growth rates of the photodarkening (redshift) and a photoinduced volume expansion. However, since the redshift is probed with transmitted light and the expansion is evaluated at the surface, which needs transfers of some atomic changes to the surface, the different temporal changes may necessarily appear, even if the both originate from a common atomic change. Nakagawa et al. (2010) have also demonstrated different time variations of the photodarkening, volume expansion, and photoconductive degradation, giving rise to a conclusion of no direct relationship between the three. However, their measurements are carried out in situ, and accordingly, the results may be influenced by transitory changes (Section 6.3.11). 6.3.9.1 Photoinduced Electrical Changes Since the photodarkening is a change in optical absorption, we straightforwardly envisage resulting photoconductive changes. Actually, Hamada et al. (1972) discovered in Ge1 As4 Se5 films a photoconductivity decrease by light illumination, which was removed by annealing near the glass transition temperature. The phenomenon appears to be similar to the so-called Staebler–Wronski effect, a photoinduced photoconductivity degradation in a-Si:H films (Section 6.5.2), and such similarity has motivated further studies for the chalcogenide (Shimakawa et al. 1995,

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Fig. 6.13 Temperature dependence of dark current (dashed line) and photocurrent under light illumination of 2.8 eV and 1 mW/cm2 in annealed (solid line) and light-soaked (dotted line) in g-As2 S3 . Solid arrows indicate the changes induced by light soaking (Hg lamp for 30 min) (Toyosawa and Tanaka 1997, © American Physical Society, reprinted with permission)

Toyosawa and Tanaka 1997, Kounavis and Mytilineou 1999). As illustrated in Fig. 6.13 for As2 S3 , the photo-degradation depends on temperature at which the illumination was performed. It shows a maximal decrease at ∼300 K, while at lower temperatures than ∼150 K the photocurrent increases upon light illumination. The decrease and increase may be caused by defect creation and enhanced absorption. Due to these degradation effects, it remains vague if the photoconduction spectrum redshifts with the photodarkening. It has also been demonstrated that the photoinduced photoconductivity degradation becomes less prominent with a decrease in the bandgap of materials: No and a little changes appear in As2 Te3 (Eg ≈ 0.84 eV) (Hayashi et al. 1997, Toyosawa and Tanaka 1997) and Sb2 Se3 (Eg ≈ 1.24 eV) (Aoki et al. 1999), which are consistent with small photodarkening in narrow-gap chalcogenide glasses. Light illumination also affects ac conductivities (Shimakawa et al. 1995). Bandgap illumination increases capacitance (imaginary part of the ac conductivity) by ∼15% in As-Se films, which is recovered by subsequent annealing at 170◦ C. It has also been demonstrated that the ac conductivity (real part) in a-As2 S3 increases after prolonged illumination However, the annealing characteristic is not simple. Although the conductivity increase induced by illumination at 90 K is annealed out at around 200 K, the increase induced at room temperature is removed by annealing near the glass transition temperature. This result suggests that two kinds of defective centers are photoinduced: One is quasi-stable at low temperatures and the other at high temperatures. The photoconductive degradation and ac conductivity increase can be ascribed to photo-creation of defective centers. To interpret the details, Shimakawa et al. (1995) have adopted the modified charged defect model, proposed by Kastner et al. (see Section 4.4). They assume that there are two kinds of spatial arrangements of the charged defect; randomly-isolated and paired (intimate) defects. The former may act as recombination centers for photo-excited carriers, reducing photocurrents, and the latter may be responsible for the ac conductivity change.

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Fig. 6.14 A setup for measuring thickness changes in g-As2 S3 and an obtained trace on the recorder (Hamanaka et al. 1976, © Elsevier, reprinted with permission), which shows a photoinduced expansion of ∼10 nm

6.3.9.2 Photoinduced Volume Changes Hamanaka et al. (1976) have discovered that bandgap illumination gives a volume change. They detect, after illumination at room temperature, a volume (film thickness) expansion of ∼0.4% in As2 S3 and contraction of ∼0.2% in Ge1 As4 Se5 , both of which can be recovered by annealing at the glass-transition temperatures. Similar volume changes have been uncovered in annealed films or bulk samples of chalcogenides (Mikhailov et al. 1990, Calvez et al. 2009), and even in a-Se films at room temperature (Asao and Tanaka 2007). Why do the expansion and contraction appear? On this problem, Tanaka (1998) has found an interesting tendency. The amorphous material having a compact structure exhibits an expansion and vise versa. Here, the degree of compactness can be evaluated using a density ratio R = ρ g /ρ c , where ρ g and ρ c are the densities of a glass and the corresponding crystal, respectively. In an ultimate case, in alkali-halide single crystals (R = 1), irradiation produces Schottky defects, which may appear as a volume expansion (Kittel 2005). This fact implies that, in relatively dense materials, the photoinduced disordering causes a volume expansion. In similar ways, as listed in Table 6.3, the amorphous material with R 0.85 appears to photoexpand. On the other hand, in a glass having relatively open structures as g-SiO2 , irradiation tends to compress the structure through some photo-electro-structural mechanisms. What is the motive force of the volume expansion? There are roughly two ideas. One is an atomic mechanism. Tanaka (1998) assumes that the disordering in intermolecular distances, which may be caused by the photoinduced bond twisting (Fig. 6.12a), is responsible for the expansion. If a glass structure is not dense, interchanges in atomic bonds may cause a volume contraction, as observed in SiO2 and Ge1 As4 Se5 . On the other hand, Shimakawa et al. (1998) propose an electrical model (Fig. 6.12c). Coulombic repulsion forces produced by photo-generated electrons, which are immobile in the chalcogenide glass of interest, trigger the expansion. However, this idea has difficulty in explaining the contraction. We also note that all

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Table 6.3 Radiation-induced volume changes and related data in some glassy (g-) and crystalline (c-) materials (Tanaka 1998, Asao and Tanaka 2007, Terakado and Tanaka 2007) Material

Excitation

V/V (%)

ρg

ρc

R

g-Se g-As2 S3 g-As2 Se3 g-GeS2 g-GeO2 g-Ge1 As4 Se5 g-SiO2 g-SiO2 Na2 O c-SiO2 c-KBr

Light Light Light Light Light Light e-Beam, neutron Light e-Beam, neutron X-ray

+0.3 +0.4, +0.7 +0.7 +0.5 +0.2 −0.2 −3 + +10, +15 +0.0001

4.25 3.2 4.58 2.7 3.7

4.80 3.43 4.75 2.94 4.2

0.89 0.93 0.96 0.92 0.88

2.2

2.65

0.83

the models cannot offer quantitative interpretations (Emelianova et al. 2004). For instance, why does g-As2 S3 expand by ∼0.4% at room temperature? Hisakuni and Tanaka (1994) have discovered that the volume expansion in As2 S3 becomes ∼5%, greater by an order, when exposed to intense sub-gap light of ∼2.0 eV. Upon exposures at 10 K, an actual expansion amounts to ∼20 μm (Tanaka et al. 2006). This giant expansion by sub-gap illumination was a big surprise, because as shown in the spectral dependence (Fig. 6.9), it had been believed that the photo-structural change became prominent under bandgap illumination (ω ≈ 2.4 eV in As2 S3 ). Why can the less energetic photons, i.e., Urbach-edge light, give such a giant volume expansion? The giant photo-expansion appears, as illustrated in Fig. 6.15, through a volumetric enhancement of the conventional expansion (Hisakuni and Tanaka 1994). Suppose that an illuminated cylinder, with a light spot of size 2r and a penetration depth L (≈ α −1 ), is expanding with a ratio of V0 /V. The expansions toward sideand rear-ward directions, however, cannot occur, due to the existence of peripheral un-illuminated regions. Here, we assume a kind of fluidity in the illuminated volume (see Fig. 6.22), which is able to transform the expansions toward the free surface. Then, an observed expansion L/L appearing at the surface can be written

Fig. 6.15 Giant photo-expansion in g-As2 S3 (left) (Hisakuni and Tanaka 1994, © American Institute of Physics, reprinted with permission) and its mechanism (right)

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as L/L = (V0 /V)(1+L/r). This r dependence with V0 /V ≈ 0.4%, which is an intrinsic volume expansion in g-As2 S3 at room temperature (Hamanaka et al. 1976), has given quantitative agreements with experimental results. We here underline that L > r is a necessary condition for the giant expansion, which can be satisfied for sub-bandgap light. In other words, the giant photo-expansion appears as a result of a geometrical amplification of the conventional photo-expansion. This quantitative agreement also suggests that the intrinsic fractional expansion is independent of the photon energy of illumination at 2.0–2.4 eV. Here, we should be careful about light intensity. Figure 6.16 shows the photodarkening E, the fractional expansion L/L, and the photoinduced fluidity η−1 (Section 6.3.11) as a function of the absorbed light intensity αI in g-As2 S3 . We see that, under bandgap illumination of 2.4 eV, E ∝ ln I (Fig. 6.10) and L/L ≈ 0.4%, as described. On the other hand, under sub-gap illumination of 2.0 eV (α ≈ 1 cm−1 ), E becomes comparable to that induced by bandgap illumination at αI ≥ 102 W/cm3 , where the giant photo-expansion becomes greater with the light intensity. We also note that the photoinduced fluidity (η−1 ) becomes prominent at the same region. This intensity dependence gives an interesting insight (Tanaka 2003). The absorbed light intensity of ∼102 W/cm3 corresponds to a photon number of ∼1020 s–1 cm–3 . Then, suppose a photo-electronic excitation with a quantum efficiency of unity, the same number of carriers is excited, which is trapped instantaneously (with timescales of picosecond). A typical trap depth can be assumed to be ∼0.5 eV, for which the thermal releasing time becomes ∼1 ms, and accordingly, the trapped carrier density is 1017 –1018 cm−3 in steady state. This is the density giving rise to a transitory photoconduction redshift, which has been interpreted to arise from the filling up of trapping states (Section 5.4.1). It seems that

Fig. 6.16 Dependence of the photodarkening E (solid line (–) and circles ( )), the fractional expansion L/L (squares ()), and the photoinduced fluidity η–1 (triangles ()) upon absorbed light intensity in g-As2 S3 (Tanaka et al. 2006, © INOE, reprinted with permission). The solid line and solid squares are obtained using bandgap light (2.4 eV) and others are by Urbach-edge light (2.0 eV)

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the intense Urbach-edge light, which has longer penetration lengths, behaves as if it were bandgap light. 6.3.9.3 Photoinduced Thermal, Mechanical, and Chemical Changes Bandgap illumination induces reversible changes also in structural properties. First, the glass-transition temperature becomes higher with illumination (Kolomiets et al. 1979, Lucas et al. 2005). Second, reversible changes in mechanical properties appear (Kolomiets and Lyubin 1978). Tanaka et al. (1981) have evaluated, using surface acoustic waves propagating in a-As2 S3 films, reductions of elastic constants to be ∼10%. Honolka et al. (2002) have discovered for As2 S3 at low temperatures a strong effect of the photodarkening upon tunneling states. Third, etching properties also change (Lyubin 2009), i.e., irradiated regions in annealed films tend to be etched more easily. All these changes imply some structural disordering with illumination, which is consistent with other observations.

6.3.10 Photoinduced Phenomena at Low Temperatures 6.3.10.1 Observations At low temperatures of Ti /Tg 0.5, bandgap illumination induces specific phenomena, in addition to the photodarkening (Shimakawa et al. 1995). The phenomena include the so-called photoluminescence fatigue (intensity decrease), mid-gap absorption formation, and ESR signal emergence. A common feature to these changes is, as shown in Fig. 6.17, the disappearance upon heating to ∼Tg /2, which is 200−300 K in g-As2 S(Se)3 (Hautala et al. 1988). Note that the photodarkening, which does not accompany induced ESR signals, disappears at ∼Tg . It should be mentioned that the corresponding crystal such as c-As2 S3 shows no similar photoinduced phenomena. It should also be mentioned that Ge-alloy glasses present different and complicated changes. In Ge–S glasses, not only the photoluminescence fatigue, but also a photoluminescence enhancement appears (Seki and Hachiya

Fig. 6.17 Annealing behaviors of photoinduced ESR (total, type I, and type II), mid-gap absorption, and photodarkening in g-As2 S3 (modified from Hautala et al. 1988)

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2003). In g-GeO2 , photoinduced ESR appears, while photoluminescence and mid-gap absorption scarcely change (Terakado and Tanaka 2006). The low-temperature photoinduced phenomenon was first noticed by Cernogora et al. (1973) as the fatigue of photoluminescence in g-As2 Se3 . Afterward, decreases in the photoluminescence intensity to 1/2–10−2 have been observed in many chalcogenide glasses (Street 1976). The fatigue remains stable at low temperatures, while it can be recovered by heating or infrared irradiation. Detailed studies have demonstrated complicated features in inducing and annealing kinetics and also in photoluminescence spectra (Tada and Ninomiya 1991). Putting such observations aside, we can assume that the photoluminescence fatigue represents a density increase in non-radiative recombination centers. However, since the origin of photoluminescence appearing at the half-gap in chalcogenide glasses is speculative (see Section 5.2), the fatigue remains unanswered. A few years later, Bishop et al. (1977) discovered a photoinduced mid-gap absorption, the spectrum distributing at Eg /2−Eg (Fig. 6.18). As shown in Fig. 6.17, a thermal annealing behavior of the mid-gap absorption is similar to that of the photoluminescence fatigue. Bishop et al. (1977) also discovered an emergence of ESR signals at around g ≈ 2.00, the so-called photoinduced ESR. The density of induced spins varies at 1017 –1020 cm−3 , depending upon the intensity of excitation light. For low intensity (∼1 mW/cm2 ) at 4.2 K, the density saturates at ∼1017 cm−3 in As2 S(Se)3 and ∼1016 cm−3 in Se. These centers, denoted type I in Fig. 6.17, are annealed out at around 200 K. The center is also bleached by infrared irradiation with the photon energy in the optically induced mid-gap absorption band. At high excitation

Fig. 6.18 Optical absorption spectra of g-As2 S3 reported from three groups (Biegelsen and Street 1980, © American Physical Society, reprinted with permission). The right-hand side “INITIAL” is the spectrum of annealed samples, which is redshifted by light excitation of 2.41 and 2.54 eV. Sub-gap light of 1.92 eV recovers partially the redshift (to the photo-darkened state). Quantitative differences may arise from different experimental conditions as sample thicknesses

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intensities (≥100 mW/cm2 ), the spin density exceeds 1020 cm−3 (Biegelsen and Street 1980, Hautala et al. 1988). This stabler center, denoted type II in Fig. 6.17, is annealed out at ∼300 K. 6.3.10.2 Mechanisms It is still vague if the three changes (photoinduced changes in photoluminescence, mid-gap absorption, and ESR) arise from a common structural change. Specifically, to the authors’ knowledge, no studies have been reported for dependence of the mid-gap absorption upon excitation light intensity. In addition, since we are dealing with the spin density as small as ∼1016 cm−3 , impurity effects should be carefully examined. Nevertheless, it seems highly plausible that newly created “some kinds of defects” dominate these photoinduced changes. The conventional interpretation is to use the charged defect model (Shimakawa et al. 1995). We can envisage a conversion of D+ and D− to D0 upon photoexcitation. The neutral dangling bond D0 , which inherently produces a spin signal, possibly acts as a non-radiative recombination center for excited carriers. However, if D0 can accompany the mid-gap, absorption is not clear (see Section 4.4). Using the concept, Shimakawa et al. (1995) have proposed a detailed conversion mechanism. As shown in Fig. 6.19 for a-As2 S3 , they ascribe the low-level (∼1017 cm−3 ) ESR centers to the conventional D0 defects, (a) −S−As• −S− and • S−As=, where – and • denote a covalent bond and an unpaired electron, respectively, and the high-level (∼1020 cm−3 ) centers to combinations of wrong and dangling bonds, (b) =As−As• −S− and =As−S−S• . This idea is consistent with the experimental results reported by Bishop et al. (1977) and Hautala et al. (1988). However, as repeatedly argued, there is no direct experimental evidence of the charged defects (Tanaka 2001a). Otherwise, we may speculate that the D0 defect is produced, not from the charged defects D+ and D− , but from normal bonds and other defects. The example is given by Hautala et al. (1988), who assume that photoinduced breaking of =As−As= wrong bonds in As2 S(Se)3 , which results in an unpaired electron of =As• , is a primary origin of the mid-gap absorption and

(a)

(b)

S−

As0

Fig. 6.19 Schematic illustrations of photo-generation processes of (a) an intimate pair (left) and a random pair (right) of neutral defects, As0 and S0 , and (b) combined defects of wrong and dangling bonds =As−As0 and −S−S0 , respectively (modified from Shimakawa et al. 1995)

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ESR signal. We should admit that there still remain unclear and unsolved problems in the defect structure in chalcogenide glasses (Zhugayevych and Lubchenko 2010).

6.3.11 Transitory Changes 6.3.11.1 Optical Changes Several kinds of transitory changes, which appear only during illumination or just after pulsed excitation, have been demonstrated. Matsuda et al. (1974) may be the first, who noticed such an optical change, the optical stopping effect. As shown in Fig. 6.20, they utilized an optical-guided wave structure consisting of a prism coupler and an AsS4 film, in which He–Ne laser light (633 nm) was propagated as guided light streak. When a blue light beam emitted from a He–Cd laser (442 nm) hitted the red-guided streak, the streak appeared to stop at the point. If the blue light was turned off, the streak propagated again. Later, Vasilyev et al. (1977) performed a spectral study, which demonstrate that As2 S3 films present transitory optical absorption at Eg /2 – Eg , if the spectrum is probed during bandgap illumination. Figure 6.21 shows a similar result reported by Iijima and Kurita (1980). These transient absorptions induced by cw illumination seem to correspond to a transitory (dynamical) refractive index increase (Tanaka 1980) and also to transient optical changes induced by pulsed light (Tanaka 1989, Sakaguchi and Tamura 2008). Here, a repeated question is if the transitory change is related to, or a part of, a memory effect. The spectral shape in Fig. 6.21 distributing at sub-gap regions suggests that the absorption is attributable to creation of transient mid-gap states, which may also give rise to the mid-gap absorption appearing at low temperatures (Fig. 6.18). However, the responsible atomic structure is speculative, as described previously. On the other hand, Kolobov et al. (1997) have demonstrated through in situ EXAFS experiments that the coordination number (Z ≈ 2) in a-Se increases by ∼5% during illumination, which implies an increase in the number of threefoldcoordinated Se atoms. It awaits further studies to connect these optical and structural changes.

Fig. 6.20 An experimental setup demonstrating the optical stopping effect and a response (Matsuda et al. 1974, © American Institute of Physics, reprinted with permission)

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Fig. 6.21 A measuring setup of transitory absorptions and the spectra obtained for g-As2 S3 films (Iijima and Kurita 1980, © American Institute of Physics, reprinted with permission)

6.3.11.2 Mechanical Changes Transitory mechanical changes appear under illumination. As reviewed by Yannopoulos and Trunov (2009), hardness reduction and photo-viscous effects continue to attract considerable interest. Specifically, since the first note by Vonwiller (1919), extensive studies have been done for Se under bandgap illumination (Koseki and Odajima 1982, Poborchii et al. 1999, Palyok et al. 2002). However, the glass transition temperature of a-Se is just above room temperature, and accordingly, distinction between photo-electronic and opto-thermal effects is not straightforward. Under these circumstances, Hisakuni and Tanaka (1995) have discovered that As2 S3 (Eg ≈ 2.4 eV) exposed to intense sub-gap illumination presents dramatic athermal photoinduced fluidity or photoinduced glass transition. The time variation in Fig. 6.22 manifests that the sample undergoes a dramatic elongation only

Fig. 6.22 Photoinduced fluidity in a g-As2 S3 flake under illumination of He–Ne laser light (Tanaka 2003, © Wiley-VCH, reprinted with permission)

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under illumination. The upper left inset is a photograph of an As2 S3 flake with millimeter size and micrometer thickness, which has been exposed three times to a focused He–Ne laser (633 nm, 2.0 eV) beam under a stretching force. The three deformed regions are produced by the elongations of three times. Quantitatively, a maximal photoinduced viscosity (the inverse of fluidity) is estimated at ∼1012 P (≈ 1011 Pa s), which is a typical value obtained at the glass transition temperature, ∼200◦ C. Since the opto-mechanical experiment is more or less difficult, known features of the photoinduced fluidity are mostly qualitative (Tanaka 2003). First, two necessary exposure conditions for this phenomenon in As2 S3 are the high intensity (>102 W/cm2 ) and the photon energy (∼2.0 eV) lying in the Urbach-edge region. Second, it has been demonstrated that the phenomenon becomes greater when the exposure is provided at lower temperatures in an investigated range of 284–312 K. This temperature dependence manifests that the phenomenon cannot be understood as a thermal fluidity but a photo-electronic fluidity. Third, material variation has not been investigated in detail. However, since the giant photo-expansion (Fig. 6.15) is understandable to appear through some motive forces and the fluidity, we can assume that the photoinduced fluidity is believed to be universal in, and limited to, the covalent chalcogenide glass (Gump et al. 2004, Calvez et al. 2008, Gueguen et al. 2010). Polyethylene sheets and Pyrex-glass fibers showed only thermal fluidity upon violet or ultraviolet illumination. Mechanisms of the photoinduced fluidity remain speculative. It is plausible that the electronic excitation gives rise to bond breaking and successive bond interchange, as previously suggested for a-Se by Koseki and Odajima (1982). It is also noted that the related trapped carrier density is 1017 –1018 cm−3 (see Fig. 6.16). We therefore assume that the trap behaves as a knot in As2 S3 networks, which is electronically released by photo-carriers. This phenomenon may be regarded as an amorphous version of the so-called electronic melting (the melting induced not by thermal but by electronic excitation), the concept being proposed for crystalline semiconductors by Van Vechten et al. (1979). Since the lifetime of trapped carriers in amorphous semiconductors is much longer than that of free carriers in crystalline semiconductors, the softening may occur under moderate light intensities. Ikeda and Shimakawa (2004) have demonstrated transient volume expansions. Under illumination of 100 mW/cm2 of 532 nm light, an As2 Se3 film with a thickness of ∼500 nm undergoes a thickness (volume) expansion of ∼10 nm, which corresponds to a fractional expansion of ∼2%. However, a problem for this observation may be the thermal expansion which inevitably appears. Probably consistent with their experimental observation is the one given by Hegedus et al. (2005), who demonstrate using computer simulation that electron addition to the conduction band in a-Se yields a volume expansion, which gives rise to a greater contribution than a contraction produced by holes. Further studies are valuable for the correspondence between the experiment and the simulation.

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6.3.12 Vector Effects 6.3.12.1 Optical Changes Zhdanov and Malinovsky (1977) have discovered a photoinduced anisotropic change in optical properties in g-As2 S(Se)3 , a phenomenon similar to the Weigert effect long been known for photographic plates. When an As2 S3 film is exposed to linearly polarized bandgap light, in addition to the conventional photodarkening (E ≈ 50 meV) and related refractive index increase (n ≈ 0.03), a dichroic absorption edge shift (dichroism) of ∼5 meV (Fig. 6.23) and a birefringence of ∼0.002 at transparent wavelengths appear (Kimura et al. 1985, Tanaka 2001b, Lyubin and Klebanov 2003). Interestingly, the induced anisotropy in covalent chalcogenide glasses is negative,2 i.e., E(//) < E(⊥) and n(//) < n(⊥), where // and ⊥ symbolize the states of linearly polarized excitation and probe light. In addition to these optical anisotropies, Lyubin and Klebanov (2003) have found an anisotropic photoconductivity for a-As50 Se50 films. Photocurrents are greater in the direction orthogonal to the electric field of light, which may be consistent with the negative optical anisotropy. It is mentioned that the glass exhibits photoinduced gyrotropy (circular birefringence) (Lyubin and Klebanov 2003), which remains to be studied. It is also mentioned that in AgAsS2 films the photoinduced anisotropy is positive (Tanaka 2001). Is the optical anisotropic change (vector effect) related to photodarkening and the corresponding photoinduced refractive index change (scalar effect)? Since the

Fig. 6.23 Photoinduced dichroism in an annealed As2 S3 film at 25◦ C (modified from Kimura et al. 1985). E(//) and E(⊥) show the positions of absorption edges probed by linearly polarized light with parallel and perpendicular polarizations to the exciting linearly polarized bandgap light. The difference between “annealed” and “illuminated” corresponds to the conventional photodarkening

2 We

follow this terminology, though the usage of “negative” and “positive” is confusing.

172 Fig. 6.24 Anisotropic elements in a macroscopically isotropic glass represented by the three thick bars directing to x-, y-, and z-axes

6 Light-Induced Phenomena y z x

anisotropic change is ∼1/10 of the isotropic in magnitude, some researchers have assumed that the anisotropic change is a part of the isotropic. However, variations of the anisotropy with light intensity, spectrum, and illuminating temperature have manifested some qualitative differences between the two (Tanaka 2001b). Therefore, at present, it is common to assume that different structural changes are responsible for the anisotropic optical changes (Fritzsche 2009). Fritzsche has presented a clear-cut phenomenological explanation for the negative optical anisotropy (Fritzsche 2000). We naturally assume for a glass that the initial state is isotropic, which is modeled in Fig. 6.24 with three orthogonal anisotropic elements parallel to the x-, y-, and z-axes. Suppose linearly polarized light with the electric field along the x-direction is incident upon the x–y plane of the sample. Under the condition, if a dipole orientation along the electric field were responsible, the situation commonly appearing in dielectrics under dc electric fields, the orientation would provide a positive change. Alternatively, he has assumed that electrons and holes in x-elements are selectively excited, and when these carriers will relax, the x-element may turn to the y- or z-direction through thermal vibrations. As a result, the number of x-elements becomes fewer than that of y, resulting in negative anisotropy. This model can explain several features including optical anisotropy induced by unpolarized light which is incident upon a sample sidewall, the y–z plane in Fig. 6.24 (Tanaka 2001). However, a problem is the entity of the anisotropic element (Tanaka 2001, Fritzsche 2009). Notable structural studies have been reported, while the results seem to be controversial. It seems that structural determinations of the element will be very challenging, since the vector change is just ∼1/10 of the scalar. On the other hand, several ideas have been proposed for the microscopic changes, as illustrated in Fig. 6.25, including orientations of defects and layer (chain) structures. The chain orientation model (e) is consistent with photoinduced oriented crystallization in a-Se (Innami and Adachi 1999). 6.3.12.2 Anisotropic Shape Changes Krecmer et al. (1997) have discovered a photoinduced transitory anisotropic (vector) deformation, called “opto-mechanical effect” (Stuchlik and Elliott 2007). As illustrated in Fig. 6.26, a bilayer cantilever consisting of an As–S(Se) film and a miniature Si3 N4 probe for atomic force microscopes bends upwardly and downwardly, in response to the polarization direction of incident linearly polarized

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Fig. 6.25 Proposed atomic structures of anisotropic elements (Tanaka 2001, © Academic Press, reprinted with permission). The illustrations show, from atomic (∼0.2 nm) to medium-range scales (∼2 nm), orientations of (a) lone pair electrons, (b) covalent bonds, (c) charged defects, (d) AsS(Se)3/2 triangular units, (e) chains, and (f) segmental layers Fig. 6.26 Schematic illustration of the opto-mechanical effect, in which a thermal bimetallic effect is neglected for clarity

bandgap light. When the illumination is switched off, the cantilever becomes flat. Light illumination also gives a bias bending which reflects thermal expansions (Fig. 6.2), while the polarization-dependent deflection cannot be ascribed to thermal effects (Asao and Tanaka 2007). On the other hand, memorized vector deformations offer a surprising variety. Tanaka et al. (1999) have discovered that a cat-whisker pattern (Fig. 6.27a) appears in a-AgAsS2 films when exposed to linearly polarized bandgap light. The pattern seems to reflect Ag concentration modifications produced by streaks of scattered light. Saliminia et al. (2000) have demonstrated for a-As2 S3 films that, under exposure to focused linearly polarized bandgap light, the giant scalar expansion (Fig. 6.15) gradually changes to an anisotropic M-shaped deformation along the electric field (Fig. 6.27b). The M-shaped deformation ultimately changes to chaotic patterns upon prolonged exposures, as shown in the right-hand side photograph of Fig. 6.27b (Tanaka and Asao 2006). In addition, as reviewed by Tanaka and Mikami (2009) and Yannopoulos and Trunov (2009), partially or semi-free As–S(Se) shows dramatic deformations. Among those, the vector deformation, Fig. 6.27c, appearing in semi-free As2 S3 flakes (Tanaka 2008) may be the most dramatic deformation in abiotic solids. Here,

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50 µm

(a)

(b)

(c)

Fig. 6.27 Vector deformations in (a) an AgAsS2 film (2.0 eV, 500 W/cm2 , 3 h) (Tanaka et al. 1999, © American Institute of Physics, reprinted with permission), (b) an As2 S3 film deposited onto slide glass (2.3 eV and 200 W/cm2 for 0.5, 30 min, and 25 h) (Tanaka and Asao 2006, © INOE, reprinted with permission), (c) and an As2 S3 flake (∼0.1 mm in diameter) laid on grease (Tanaka 2008, © Japan Society of Applied Physics, reprinted with permission). The electric field of linearly polarized light is vertical in all these photographs

semi-free means that the As2 S3 flake is laid (or deposited) on viscous grease, not deposited upon rigid substrates as commonly employed. Or, the flake, which is fixed to a rigid base as a cantilever, shows the same deformations. Illumination of linearly polarized light to such semi-free As2 S3 flakes gives two kinds of deformations: an anisotropic U-shaped deformation with the direction being parallel to the electric field and successive screwing elongation, which is orthogonal to the electric field. On the other hand, semi-free As2 S3 films, when exposed to linearly polarized light, undergo sinusoidal wrinkling, the direction being orthogonal to the electric field (Tanaka and Mikami 2009). It is also mentioned that under two-beam interference of polarized light, grating formations in chalcogenide films depend upon the polarization state (Trunov et al. 2010). Several ideas have been put forth for these transitory and memorized vector deformations (Tanaka and Mikami 2009, Yannopoulos and Trunov 2009). The most common is to assume some kinds of atomic motions, such as photoinduced alignment of microscopic structures (Fig. 6.25). Similar ideas have been assumed for photo-deformations in dye-doped organic polymers. On the other hand, Tanaka and Mikami (2009) propose an optical force model for deformations in semi-free samples, in which photon momentum (wavenumber) and spin (polarization) provide the motive forces. Further studies will be valuable.

6.3.13 Photo-Chemical Effects 6.3.13.1 Photodoping The photodoping is a surprising phenomenon, which was first reported by Kostyshin et al. (1966). Comprehensive reviews are given by Kolobov and Elliott (1991) and

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Frumar and Wagner (2003). Suppose we have a bilayer structure consisting of a semi-transparent Ag film (∼10 nm thick) and an a-AsS2 film (∼1 μm), which seems to be the best material combination for the phenomenon. This bilayer sample is fairly stable if it is stored in the dark. Nevertheless, when it is exposed to light, e.g., using a high-pressure mercury lamp, the Ag film is readily dissolved, or “doped,” into the chalcogenide film. The photodoping gives a remarkable optical change from metallic reflectivity of the Ag/As–S structure to semi-transparent orange color of an Ag–As–S/As–S film. In addition, the reaction causes marked changes in chemical properties as etching rates. A variety of photodoping characteristics have been investigated (Kolobov and Elliott 1991, Frumar and Wagner 2003). As shown in Fig. 6.28, the Ag profile is step like with a nearly fixed Ag concentration of ∼25 at.%, i.e., the doped layer being roughly a-AgAsS2 , which is very different from the conventional diffusion profile. We can assume, accordingly, that the bilayer structure consisting of Ag/AsS2 changes to Ag/AgAsS2 /AsS2 , and ultimately, to an AgAsS2 /AsS2 . Or, if the initial thicknesses of Ag and AsS2 films are optimal, the photodoping produces a single layer of a-AgAsS2 . For the material combination, it has been demonstrated that photodoping occurs widely in Ag/As(Ge)–S(Se) structures. For the metal, Cu is less efficiently photodoped, despite it being more efficiently thermally diffused. For the chalcogenide, all the binary compositions seem to exhibit the photodoping in some degrees. The photodoping appears to be inherent to the hole-mobile covalent chalcogenide glass. On the other hand, Ag/S(Se) thermally reacts to c-As2 S(Se). Behaviors in electron mobile chalcogenide glasses, containing Bi, are not conclusive (Tanaka 1991). The photodoping does not occur, or at least very inefficient, in Ga2 S3 -based glasses (Kitagawa et al. 2006) and in chalcogenide crystals, c-GeS2 and c-As2 S3 . The photodoping neither occurs in a-P (Kawashima et al. 1990) nor g-GeO2 (Terakado and Tanaka 2009). A repeated problem is the motive force of Ag dissolution into the chalcogenide. Experiments suggest that Ag migrates as a cation. Actually, Saji and Ohoka (1985) demonstrate for Ag/GeS2 films that an application of electric fields (∼104 V/cm) changes a photodoping rate by a factor of a half. In addition, Tanaka and Sanjoh (1993) assert through several experiments that the diffusion of photo-generated

Fig. 6.28 An intermediate state (Ag/AgAsS2 /AsS2 ) of the photodoping in Ag/AsS2 system. (a) Ag concentration profile, (b) band diagram, and (c) schematic atomic structure, in which the black circle is an Ag atom, the big open circle an As, and the small open circle an S

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Fig. 6.29 Glass-forming regions in the Ag–As–S system (left) and estimated free energy curve along As–S and Ag–S lines (right)

holes governs the motion of Ag+ ions. In short, we can conclude that the motive force of the Ag dissolution is the counterflow of holes: j(Ag+ ) = j(hole). Another important problem is why the composition of the doped region is fixed at, i.e., AgAsS2 in the Ag/As–S system. On this problem, Owen et al. (1985) have pointed out an interesting fact: the composition of the doped region corresponds to a glass formation region in the Ag–As–S system (Fig. 6.29). This finding implies that the photodoping occurs between the compositions of minimal free energies, from As–S to AgAsS2 . This idea is consistent with several observations on compositions. For instance, the photodoping rate in the Ag/Asx S100 –x system is maximal at x ≈ 33 at.%, which is AsS2 (Kolobov and Elliott 1991). The photodoping is efficient also for Ag2 S/As2 S3 , since the tie-line of the two compositions passes through AgAsS2 (Fig. 6.29). By contrast, the Ag/As2 S3 system produces inhomogeneous photodoped regions. The photodoping is less efficient in the Ag/As–Se system (Ogusu et al. 2004), which has no isolated glass-forming regions such as AgAsS2 . Despite the understandings of fundamental features of the photodoping, further studies remain. It will be fruitful to analyze the photo-electro-ionic process in more details. Specifically, the interaction between holes and Ag+ ions in a-AgAsS2 , which is an ion-hole mixed conductor (see Sections 3.6 and 7.7), is a valuable subject to be studied. In addition, it is interesting to consider why the photodoping is prominent for Ag. Are the group Ia atoms such as Li also photodoped? 6.3.13.2 Photo-Surface Deposition and Photo-Chemical Modification Maruno and Kawaguchi have discovered a “photoinduced surface deposition,” a seemingly opposite phenomenon to the photodoping (Kawaguchi et al. 2001). When

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Photon Effects in Chalcogenide

Fig. 6.30 Scanning electron microscopy images of photo-surface deposited Ag on bulk Ag45 As15 S40 glasses after illumination of an ultrahigh-pressure Hg lamp with intensities of (a) 200 and (b) 530 mW/cm2 (Kawaguchi et al. 2001, © Academic Press, reprinted with permission)

(a)

177

(b)

Ag-chalcogenide glasses such as Ag45 As15 S40 and Ag35 Ge20 Se45 are exposed to light, dendritic (or flower)-like Ag particles with diameters of micrometers segregate to the illuminated surface, the examples being shown in Fig. 6.30. Here, a marked point is that the sample glass contains a lot of Ag. The photo-surface deposition does not appear in Cu-chalcogenide systems. Later, Yoshida and Tanaka (1995) have found a phenomenon called “photochemical modification.” In a-AgAsS2 films, Ag always accumulates to illuminated regions, where the Ag content can increase by ∼5 at.%. Note that, in this phenomenon, Ag always gathers to an illuminated region upon repeated exposures, which is in contrast to the (nearly) irreversible Ag motions in the photodoping and photo-surface deposition (Kawaguchi et al. 2001). Ag–As–S films also show anisotropic deformations when exposed to linearly polarized light (Fig. 6.27a). Mechanisms of the photo-surface deposition and photo-chemical modification can be understood using the two ideas proposed for the photodoping (Kawaguchi et al. 2001). The motive force of Ag+ motion is the photo-electro-ionic, j(Ag+ ) = j(hole), both flowing in opposite directions, for satisfying the charge neutrality. On the other hand, Owens’ model assumes the minimal free energy at AgAsS2 , so that Agx AsS2 glasses with x > 1 (25 at.%), employed for the photo-surface deposition, tend to separate to Ag and AgAsS2 , in which the reaction is assumed to be assisted by the photo-electronic force. In the photo-chemical modification in AgAsS2 , the Ag content is forced to be modulated (∼5 at.%) by the flow of photo-generated holes. The fringes and streaks in Fig. 6.27a are understood as deformations reflecting the photo-chemical modification, which is induced by interference and scattered light. 6.3.13.3 Photo-Oxidation Photo-oxidation is a phenomenon commonly observed when a chalcogenide film is exposed to (super-)bandgap light in oxygen ambient, as in air (Berkes et al. 1971, DeNeufville et al. 1974, Apling et al. 1975). When as-evaporated As2 S(Se)3 (or As-rich As–S) films are exposed to (super-)bandgap light, the film surface is

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Fig. 6.31 An As2 O3 crystal (∼3 μm) on an as-evaporated As2 S3 film produced by x-ray irradiation (Apling et al. 1975, © Elsevier, reprinted with permission)

covered by fine As2 O3 crystals (Fig. 6.31), which make the film smoggy. The powdered c-As2 O3 can easily be detected using x-ray diffraction. Interestingly, the photo-oxidation becomes less marked if Ag or Cu is added to As2 Se3 films (Ogusu et al. 2005). The photo-oxidation can be understood as a kind of photo-chemical reactions. It must be triggered by bond breaking with a photon, followed by clustering of As atoms, i.e., the photo-decomposition (Section 6.3.7), which will be oxidized. The reaction process can qualitatively be written as (DeNeufville et al. 1974) As-rich As−S → As2 S3 + As and As + O2 → As2 O3 . Here, As-rich regions may exist even in As2 S3 films due to structural heterogeneity, or As–As bonds may work as embryos of the reaction. It probably depends upon film structures and ambient atmosphere if the photo-bleaching is due simply to the photo-decomposition (Section 6.3.7) or the photo-oxidation. Related features in Ge-chalcogenides are somewhat different. As-evaporated Ge–S(Se) films seem to contain a lot of Ge dangling bonds, which are easily photooxidized, as detected by, e.g., infrared spectroscopy (Márquez et al. 1997). Horton et al. (1996) demonstrate that the photo-oxidation of GeS2 films markedly changes sticking behaviors of Ag and Zn films. However, in these materials, c-GeO2 does not appear. There may exist some difference in atomic migrations between As and Ge. 6.3.13.4 Photo-Enhanced Vaporization Janai et al. (1978) have discovered a phenomenon named “photo-enhanced vaporization.” When an as-evaporated As2 S3 film is illuminated in air at ∼200◦ C using, e.g., an Hg lamp (∼10 mW/cm2 ), the film becomes thinner through vaporization with a rate of ∼1 nm/s. High humidity enhances the vaporization rate, which suggests the vaporization of photo-produced As2 O3 . Spectral studies demonstrate that the vaporization becomes efficient upon exposure of ∼2.5 eV photons, the energy substantially higher than the optical gap of ∼2.0 eV in As2 S3 at ∼200◦ C. This spectral result implies that the excitation of σ electrons, not lone pair electrons, of

6.4

Photon Effects in Oxide Glasses

179

As–S (and/or As–As) is responsible for the oxidation. Interestingly, the vaporization rate depends upon substrates, glass or metal, which implies the existence of some electronic effects.

6.4 Photon Effects in Oxide Glasses The oxide glass has a substantially wider bandgap (>5 eV) than that in the chalcogenide, and accordingly, studies on photoinduced phenomena have been comparatively limited. Before ∼1970, we had known only two kinds of radiation effects induced by high-energy beams such as γ-rays; formation of defects, including color and E centers (Lell et al. 1966), and the so-called radiation compaction (Primak and Kampwirth 1968). In addition, the radiation-induced amorphization of c-SiO2 was known for a longer time (Lell et al. 1966). A revolutionary change appeared with the advent of optical fibers. The optical fiber, giving rise to long light–matter interaction lengths, afforded to discover a photoinduced refractive index grating (Hill et al. 1978), which is now commercialized. Many studies stemming from fundamental and applied viewpoints have followed, as described below (Pacchioni et al. 2000). Hill et al. (1978) discovered a photoinduced refractive index increase (∼10−3 ) in Ge-SiO2 fibers (∼1 m long) using cw Ar lasers. This discovery attracts much interest, since it can produce in a simple way a fiber Bragg grating, which is utilized as wavelength selectors (Section 7.3). The induction mechanism has been studied extensively. It is demonstrated from spectral and compositional studies that defect (Ge E center) creation is responsible for the optical change. In addition, Poumellec et al. (1995) noticed a volume compaction upon illumination of ultraviolet light, which may be regarded as a kind of radiation compactions. In Ge–SiO2 fibers, it is

Fig. 6.32 Density (∼1/volume) changes in c- and g-SiO2 upon neutron irradiation (modified from Lell et al. 1966)

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highly plausible that photo-electronic excitation occurs around Ge atoms, which act as “atomic dyes,” and in response, the Ge E centers will be produced (Pacchioni et al. 2000). However, why does the volume compaction occur? And, why does the refractive index increase? Radiation effects have been studied also for nominally pure g-SiO2 using excimer and fs lasers (Pacchioni et al. 2000). Roughly, the photoinduced phenomena appear to be similar to those in Ge–SiO2 , with smaller efficiencies. However, for g-SiO2 , which is likely to contain various defects (E centers, etc.) and impurities such as Al, Cl, and OH, it is difficult to identify the location of photo-electronic excitation. It should also be mentioned that the radiation effect changes in different samples. For instance, Smith et al. (2001) demonstrate that H2 -loaded g-SiO2 expands upon ultraviolet (248 nm) pulse excitations. In addition, other photoinduced phenomena have been discovered for g-SiO2 . Super-bandgap illumination (10−100 eV) induces photo-decomposition, producing Si crystals (Boero et al. 2005). Photoinduced anisotropy is also discovered (Borrelli et al. 2002). What is the relationship among the refractive index increase, the defect creation, and the volume compaction in silica glasses? It seems that the defect formation cannot quantitatively account for the refractive index increase (Pacchioni et al. 2000). Instead, the volume compaction possibly governs the optical change as follows: The Lorentz–Lorenz formula for the refractive index n in an insulator having dipoles with a concentration Ni and a polarizability α i is written in cgs unit as (Kittel 2005). (n2 − 1)/(n2 + 2) = (4π/3) αi Ni

(6.2)

Here, suppose α i = 0, we obtain n/n = − (n2 − 1)(n2 + 2)/(6n2 ) V/V,

(6.3)

i.e., a volume compaction, V < 0, gives rise to a refractive index increase, n > 0. We can actually obtain a quantitative agreement. A problem is, therefore, why the radiation causes the volume compaction. A plausible scenario is as follows (Uchino et al. 2002): A photon creates a defect, probably an E center, which triggers the volume compaction through some mechanism presently unspecified. The defect may behave as a catalyst. Note that, in terms of the Lorentz–Lorenz formula, the photodarkening in the chalcogenide (Section 6.3.8), which accompanies a refractive index increase, should be related with an increase in α i Ni , since it occurs in general with the volume expansion, not the compaction as that in the oxide. It is interesting to compare the photoinduced changes in a typical oxide, SiO2 , and a chalcogenide, As2 S3 . Here, since the bandgap energy Eg (∼10 and 2.4 eV) and the glass transition temperature Tg (∼1500 and ∼450 K) in SiO2 and As2 S3 are substantially different, some normalization is needed for grasping material dependence. Figure 6.33 shows notable photoinduced phenomena in normalized representations on ω/Eg and Ti /Tg axes, where ω is the photon energy of excitation light and Ti is the temperature at which the sample is illuminated. For SiO2 , when illuminated

6.5

Light-Induced Phenomena in Amorphous Si:H Films

Fig. 6.33 Comparison of photoinduced phenomena in SiO2 and As2 S3 glasses as functions of the normalized photon energy ω/Eg and illumination temperature Ti /Tg . The arrows show the positions at Ti = 300 K. SiO2 shows a refractive index increase n and decomposition, while As2 S3 shows all the changes indicated

181

Δn SiO2

As2S3

at room temperature, Ti /Tg ≈ 0.2, bandgap and pulsed mid-gap exposures provide, respectively, photo-decomposition and a refractive index increase, the latter being related to the densification (radiation compaction), as described above. On the other hand, As2 S3 shows all the phenomena: the photo-decomposition upon super-gap illumination at room temperature (Ti /Tg ≈ 0.5), the photodarkening upon bandgap and intense sub-gap illuminations at room temperature, the mid-gap absorption at low temperatures of Ti /Tg ≈ 0.2, and the refractive index increase upon mid-gap excitation. In short, important remarks are as follows: A common feature to these glasses is that photoinduced phenomena do not appear when Ti /Tg ≈ 1. Or, many photoinduced phenomena can be recovered with annealing at Tg . In addition, in both glasses, super-bandgap light gives rise to the photo-decomposition, producing wrong bonds or micro-crystals. Existence of the defect creation processes at Ti /Tg ≈ 0.2 may also be common, which appear as the refractive index increase in SiO2 and mid-gap absorption in As2 S3 . However, a marked difference is that the photodarkening appears only in As2 S3 . The phenomenon appears to be inherent to the chalcogenide glass consisting of covalent and van der Waals bonds.

6.5 Light-Induced Phenomena in Amorphous Si:H Films 6.5.1 Thermal Effects in Amorphous Si:H Films Laser-induced crystallization of a-Si(:H) films has attracted great interest due to applications to thin-film transistors (Suzuki 2006). In technology, XeCl excimer lasers (λ = 308 nm with pulse duration of ∼30 ns) are employed for crystallization of a-Si(:H) films (∼50 nm in thickness) deposited upon a-SiO2 layers. The most important characteristic in this application is a high mobility as possible, for

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which the grain size of crystallized films should be large. At present, obtained lateral sizes (∼50 μm) of crystalline grains are much greater than the film thickness. The crystallization mechanism is believed to be purely thermal, i.e., through a rapid melt-mediated phase transformation with a super-lateral growth mode (Im et al. 1993). Despite the thermal growth, however, Horita et al. (2007) demonstrate that the crystallization can be controlled by the electric field of linearly polarized laser pulses. Accordingly, it may be interesting to compare this thermal crystallization with the photo-enhanced crystallization of a-Se (Section 6.3.4). It is also mentioned that amorphization of c-Si films can be induced using fs laser pulses (Jia et al. 2004).

6.5.2 Photon Effects in Amorphous Si:H Films 6.5.2.1 Observations The so-called Staebler–Wronski effect is the most known and problematic photoinduced phenomenon in a-Si:H films (Morigaki 1999, Shimizu 2004). As shown in Fig. 6.34, upon bandgap illumination, which is sometimes referred to as “light soaking” in this research area, with intensity of 200 mW/cm2 for 2 h at room temperature, the photo- and dark conductivities decrease by one and four orders of magnitude. The degraded state is meta-stable, which can be recovered by annealing at ∼450 K. It is mentioned that a smaller bandgap material such as a-Ge:H films (Eg ≈ 1.1 eV) exhibits smaller degradation. Since the effect is serious in device applications, specifically in solar cells, a huge number of studies have been

Fig. 6.34 Staebler–Wronski effect and Morigaki’s model (1988)

6.5

Light-Induced Phenomena in Amorphous Si:H Films

183

published, as reviewed by Morigaki (1999), Shimizu (2004), and others. However, the final elucidation and countermeasure remain. In addition to the photoconductive degradation, the light soaking changes a variety (at least, nine) of electronic and structural properties, as listed below (Morigaki 1999, Shimizu 2004). We see that some photoinduced changes, specifically electronic, strongly resemble those in the chalcogenide glass (Section 6.3.10). Electronic changes are as follows: First, under excitation of bandgap light of ω ≈1.8 eV at low temperatures, a broad photoluminescence at ∼1.3 eV fatigues, and at the same time a low-energy peak at ∼0.8 eV appears. There seem to be two photoluminescence centers having different kinetics in thermal recovery. Second, it is discovered that prolonged illumination at cryogenic temperatures increases ESR signals roughly by an order. The induced spins are thermally annealed partially at ∼100 K and completely at 430 K. Third, optical spectra are also modified in two spectral regions. One is an increase in mid-gap absorption after prolonged irradiation, which has been detected using photo-deflection spectroscopy and a constant photocurrent method. Annealing kinetics of the induced absorptions is not simple. The other is a slope decrease in the Urbach edge, which has been attributed to an increase in structural disorder. Fourth, the ac conductivity also changes. Light soaking of a-Si:H films at room temperature increases and decreases the ac conductivity (measured at ∼1 kHz) at 1–80 and 80–300 K (Shimakawa et al. 1995). These conductivity changes are removed by thermal annealing at 430 K. Fifth, polarized electro-absorption is modified by illumination, which is recovered by annealing at 470 K. The change may imply some gross structural changes, not creation of defects as dangling bonds. In addition, we also see intrinsic structural changes. First, it has been discovered that an intensity of small-angle neutron scattering, which is sensitive to H distributions, increases after prolonged illumination. The result suggests clustering of H atoms. Second, a photoinduced change in the infrared absorption spectra appears. The intensity of the Si–H stretching mode at ∼2000 cm−1 is increased by ∼1% by light soaking and recovered by annealing. Third, a reversible change in xray photoelectron spectroscopy appears. The Si 2p peak at around −100 eV shifts by ∼0.1 eV to a lower binding energy with light soaking. Such a change does not occur in (non-hydrogenated) a-Si films. Fourth, light soaking provides a volume expansion with a fraction of 4 × 10−6 in a-Si:H films, the value being much smaller than that (∼4 × 10−3 ) in g-As2 S3 . Time evolutions of the photoinduced expansion and ESR signals, probed at room temperature, are similar, which may suggest an intimate correlation between the structural and electronic changes. However, later studies have demonstrated that the volume change critically depends upon the method of film depositions. 6.5.2.2 Mechanisms As seen above, many photoinduced phenomena appear in a-Si:H films, while the interrelation remains unclear. Among those, the most problematic is the photoconduction degradation, Staebler–Wronski effect, and accordingly, its mechanism has been extensively studied.

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It is believed that the Staebler–Wronski effect is caused by the formation of defects (Morigaki 1999, Shimizu 2004). The defect is probably dangling bonds of Si atoms (∼1017 cm−3 ). Nevertheless, how the dangling bond is photo-created is speculative. Specifically, it is still ambiguous whether the defect creation is related with H atoms or not. A process proposed by Morigaki (1988) is shown in Fig. 6.34, in which a defect is created through photoinduced cessation of weak Si–Si bonds and successive H diffusion. The produced dangling bond may also trigger structural changes such as the increase in Si–H stretching mode and the volume expansions. Otherwise, the defect may have some correlation with micro-voids, the inner surface being covered by H atoms. In addition to understand the mechanism, the most important technological subject is a method which can suppress the Staebler–Wronski effect, but it remains midway to the achievement. Here, it is tempting to envisage some similarities between the three photoinduced processes: the Staebler–Wronski effect in a-Si:H films, the defect creation in chalcogenide glasses at low temperatures (Section 6.3.10), and Hills’ gratings in Ge-doped SiO2 (Section 6.4). However, since a-Si:H films do not show the glass transition, it is challenging to apply unified treatments to these photoinduced phenomena (Shimakawa et al. 1995).

6.6 Photon Effects in Organic Polymers We sometimes experience sunburn, a kind of photoinduced phenomena. Organic molecules seem to be susceptible to radiation effects. It may start with photo-electronic bond cessation and successive polymerization and/or oxidation. Otherwise, in small molecules as dyes, it may appear as photoinduced twisting motions of atomic bonds. The most known photoinduced phenomenon in organic polymers is probably the photo-polymerization process (Kozawa and Tagawa 2010). In the conventional photoresist process in semiconductor industries, it is combined with etching for producing fine patterns. At present, irradiation of laser light with a wavelength of ∼200 nm and successive dry etching make it possible to reproduce patterns with a resolution finer than ∼50 nm. The polymerization process accompanies an increase in refractive indices, which can be utilized for holographic storages. As described in Section 6.3.5, as-evaporated As2 S3 films also undergo the photo-polymerization and etching endurance, which is employed as an inorganic photoresist process. Photoinduced phenomena in azobenzene-doped polymers have attracted wide interest recently (Barrett et al. 2007). As illustrated in Fig. 6.35, the dye shows reversible isomerization between cis- and trans-conformation upon illumination of ultraviolet (∼365 nm) and visible (∼570 nm) light. When the dye is illuminated by polarized light, the transformation can produce anisotropic structures, which accompany not only optical changes as birefringence but also prominent changes in macroscopic shapes if the transformation occurs cooperatively. In some cases, the

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Fig. 6.35 Photoinduced change from trans- to cis-configurations of an azobenzene molecule and the thermal (or photo-) recovery

shape change resembles the vector change in chalcogenide glasses (Section 6.3.12). Due to versatile molecular engineering techniques, the dye-doped organic polymer is promising for advanced photoinduced materials. A notable difference between the photoinduced changes in the chalcogenide glass and the polymer is the following: In the dye–polymer system, it is conceivable that light excites the dye, and its isomerization process causes successive structural changes in surrounding molecules. Accordingly, a problem in a photoinduced process is focused upon the successive structural change. On the other hand, in the chalcogenide, the excited species cannot be identified, which may be some defective sites or disordered structures. It is plausible that the excited species change with the photon energy of excitation, light intensity, temperature, and so forth. As a result, following structural changes become largely speculative.

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Chapter 7

Applications

Abstract A variety of applications, present and potential, of non-crystalline insulators and semiconductors including amorphous chalcogenides are described in a “tree growth manner.” History and trend of optical devices, fibers, and waveguides are described. Great success has been attained in phase change memories (DVDs), x-ray medical image sensors, highly sensitive vidicons, and xerography. We refer also to other applications such as holographic memories, nonlinear devices, solar cells, and ionic devices. Keywords Optical fiber · Phase change · DVD · Image sensor · Vidicon · Xerography · Solar cell · Ionic device

7.1 Overall Features The tree in Fig. 7.1 shows relationships between fundamentals and applications of non-crystalline insulators and semiconductors. We see the two roots. One is a disordered structure, which also raises the liquid, except for liquid crystals. Nevertheless, photo-electronic applications of non-crystalline liquids are very limited, an example being Kerr cells using polar liquids as nitrobenzene (C6 H5 NO2 ). Accordingly, we may focus upon the disordered solid, i.e., amorphous material, which grows also from the other root of quasi-equilibriumness. On the other hand, macroscopic shapes of the opto-electric devices have three branches: fiber, film, and others.

195 K. Tanaka, K. Shimakawa, Amorphous Chalcogenide Semiconductors and Related C Springer Science+Business Media, LLC 2011 Materials, DOI 10.1007/978-1-4419-9510-0_7,

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Fig. 7.1 A tree of non-crystalline devices

In more detail, the fundamentals (bold), characteristic properties, and applications (italics) of amorphous chalcogenides and related materials can be connected as follows: Disordered structure → multi-component and varied compositions → EDFA → small impurity effect, inefficient dopant effect → higher ion mobility → solid-state battery, ionic memory → localized electron wavefunction → small electron mobility, electrically insulating, (avalanche multiplication?) → vidicon, X-ray imager → localized lattice vibration → small thermal conductivity Quasi-equilibriumness → fast sample preparation →low cost and big sample → fiber, thin-film solar cell, TFT → dependence upon preparation methods and prehistory → photo(electro)-induced phenomena → Bragg reflector fiber, DVD, PRAM

Table 7.1 lists some photo-electronic applications of non-crystalline oxide and chalcogenide (group VIb) solids. Here, we see an interesting trend. The application changes, in correspondence to a decrease in the optical gap energy from the oxide (5–10 eV) to the telluride (∼1 eV), from optical, photo-structural, photo-conductive,

7.2

Optical Device

197

Table 7.1 Representative optical and electrical properties and applications of group VIb amorphous materials (glasses)

Material

Transparent wavelength (µm) (photon Refractive energy [eV]) index

Resistivity ( cm) Optical

Oxide

0.2–2 (0.6–5)

1.6

1015

2.5

>1015

Bragg reflector IR optics Holometer

2.8

1012

IR optics

3.0

104

Sulfide

0.6–10 (0.1–2.5) Selenide 0.8–15 (0.08–2.0)

Telluride 1–20 (0.06–1.0)

PhotoStructural

PhotoOptoConductive thermal

Fiber

Copy Vidicon X-ray Imager DVD

and opto-thermal (Table 6.1). Such a trend is understandable through a comparison of the optical gap Eg with the visible light energy (ω ≈ 2 eV) That is, for optical applications, the glass must be transparent, which requires Eg > 3 eV, being satisfied with the oxide (Section 7.2). Photo-structural changes are prominent in sulfides, which are covalent and molecular (Section 7.3). For photoconductive applications, the condition of Eg > 2 eV must be satisfied, so that the chalcogenide, specifically pure a-Se, is the most suitable (Section 7.6). As known, a-Se has the highest carrier (hole) mobility in the chalcogenide glass, which is also important in applications such as x-ray detectors. Finally, the telluride has some metallic character with less directional atomic bonds and small Eg , which are required for optical (DVD) and electrical, thermally induced phase-change recordings (Section 7.4).

7.2 Optical Device Oxide and chalcogenide glasses are employed as light-transmitting media. As shown in Fig. 7.2, SiO2 is transparent from a deep ultraviolet to near-infrared region (λ ≈ 200 nm to 3 µm), in which the ultraviolet and infrared transmission edges are governed by electronic and lattice-vibrational absorptions, respectively. An important photonics application is the optical fiber for communications at λ 1.55 µm (Section 7.2.1). On the other hand, infrared transmission is a unique characteristic of the chalcogenide glass. As2 Te3 can transmit infrared light at a wavelength region of λ ≈ 2 − 20 µm. However, as shown in Fig. 7.2, the transmittance in chalcogenide glasses at transparent regions is lower (≤70%) due to higher light reflection arising from greater refractive indices (n ≥ 2.5). Accordingly, anti-reflection coating is preferred. Another characteristic of the chalcogenide glass is relatively low

198

7

Applications

Fig. 7.2 Comparison of ultraviolet–infrared transmission spectra of several glass plates with a thickness of ∼2 mm (modified from Kumta and Risbud 1990)

glass transition temperatures. Owing to that, glass can be shaped through squeezing or molding into, e.g., infrared-transmitting lenses for night viewers. In addition, the high refractive index affords new devices as multi-layered mirrors at infrared regions (Clement et al. 2006, Kondakci et al. 2009) and photonic crystals (Popescu et al. 2009, Kohoutek et al. 2011). In addition to the optical transparency, the glass has notable characteristics when compared with other materials (see Figs. 1.5 and 1.6). In comparison with crystals, the glass can be produced in large sizes, and it can be shaped into arbitrary forms by polishing, molding, and drawing. Note that the molding and drawing are entirely due to the existence of glass transitions. Also, wide-area non-crystalline films can be prepared through vacuum evaporation, sputtering, sol–gel technique, etc., as described in Section 1.8. In comparison with organic polymers, the glass is more thermally stable and radiation resistant. The polymer cannot be infrared transmitting, due to high-frequency atomic vibrations. However, the glass is heavier, more breakable, and generally, more expensive than the polymer.

7.2.1 Optical Fiber The optical communication has progressed concomitantly with attenuation reduction and functionalization of silica fibers. The concept of optical fiber communication was proposed by Kao and Hockham (1966), and Kao was awarded the 2009 Nobel Prize in physics. Indeed, we are surprised at dramatic developing history of the fiber communication. Around 1970, a minimal transmission loss of a glass fiber was 20 dB/km (1 cm−1 = 434 dB/m, 1 dB/m = 0.0023 cm−1 ), the value being governed by impurities. Although short (∼m) fibers had been utilized for medical inspections, few researchers expected that the fiber would afford distant signal transmission. Gradually, the loss was reduced with inventions of new preparation methods such as vapor axial deposition using purified gases. And, the product enabled us to communicate through the optical fiber, in which one digitalized optical signal with a modulation frequency of ∼50 Mb/s was transferred. The optical signal

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naturally weakened when transmitting over long (∼10 km) distances. Accordingly, the optical signal was detected by a photo-detector, electrically amplified, and then converted again to an optical signal using a modulated laser diode. At present, such an elementary system has completely been revolved. The transmission loss has been reduced to 0.2 dB/km (Thomas et al. 2000), as shown in Fig. 7.3, and it becomes practical to transmit a signal through a fiber with a length of ∼80 km. In 2005, as schematically illustrated in Fig. 7.4, a single fiber transmits digital signals of 32 different wavelengths in parallel, each being modulated at 10 Gbit/s, the system being referred to as “wavelength division multiplexing” (WDM). In this system, signals with different wavelengths are combined into and resolved from a fiber using dispersive elements as prisms or fiber Bragg gratings (FBGs) (see Section 7.3). And the 32 signals are optically amplified through stimulated emission by an Er3+ -doped fiber amplifier (EDFA) (Section 7.2.2). The WDM

Fig. 7.3 Optical absorption in g-SiO2 (solid lines) and c-SiO2 (dashed line) (modified from Griscom 1991). The inset shows a magnified view at around the optical communication region (modified from Thomas et al. 2000)

Fig. 7.4 A schematic illustration of a WDM system, equipped with an Er-doped optical amplifier, which transmits four signals with different wavelengths of ∼1.55 µm (modified from http://www. moritex.co.jp/products/opt/optical-fiber-filter.php)

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is now changing to dense WDM (DWDM) having transmission capacities of Tbit/s per fiber. For the optical fiber made from silica glass, we still seek superior performances. A fundamental one may be more reduced light attenuation (= loss). Here, the attenuation is determined by absorption and scattering, i.e., attenuation = absorption + scattering. The absorption can be electronic, vibrational, defective, and impurity originated (Thomas et al. 2000) as described in Section 4.6. The electronic and vibrational are inherent to a material, but the defective and impurity originated should be suppressed as possible by sophisticated purification and preparation procedures. On the other hand, the light scattering is caused by spatial fluctuations of fiber shapes and glass density, the latter being inevitable to the glass, since it is quenched from a density-fluctuating liquid. The scattering loss αs arising from such intrinsic density fluctuation, which has been formulated by Smoluchowski and Einstein, can be written as (Ikushima et al. 2000) αs (8π 3 /3λ4 )n8 p2 βT kB Tg ,

(7.1)

where λ is the wavelength, n the refractive index, p the photoelastic constant, β T the isothermal compressibility, and Tg the glass transition temperature. This equation suggests that a glass having a lower glass transition temperature is preferred for reducing the scattering loss. In this context, SiO2 having the highest Tg (∼1500◦ C) among the glass appears to be inappropriate. Nevertheless, simple (stoichiometric) glass is preferred for obtaining atomically homogeneous structures. If we might employ SiO2 –Na2 O glass having a lower Tg , the compositional disorder would increase the light scattering. It seems that further reduction of the fiber attenuation is challenging. Another development is in progress. As known, the present communication system utilizes the 1.5 µm wavelength (ω 0.8 eV) band. This band has been selected taking the two factors into account (Fig. 7.3): one being the λ−4 scattering loss (see Equation (7.1)), originating from the so-called Rayleigh scattering, and the other being vibrational absorption rising at λ ≈ 2 µm in silica. However, for wider wavelength communications, an absorption peak at 1.4 µm due to –OH vibrations was an obstacle, which has been recently suppressed through chemical reductions. The communication wavelength will be extended from 1.5–1.6 µm to a wider 1.3–1.6 µm band (DWDM). The chalcogenide glass can also be drawn as fibers, which transmit infrared light. The fiber is employed for spectroscopy and power transmission for, e.g., biological and medical (surgery) purposes (Nishii and Yamashita 1998, Snopatin et al. 2009, Bureau et al. 2009). For instance, the fiber can transmit 10–100 W infrared light (λ = 5 and 10.6 µm) emitted from CO and CO2 gas lasers. Here, a fundamental problem is again the transmission loss, which is substantially higher than that (∼0.2 dB/km) in silica, due to lower glass purity, higher refractive index (αs ∝ n8 ), and other problems (Snopatin et al. 2009). The loss has been decreased to 12 dB/km in an As2 S3 multi-mode fiber at a wavelength of 3 µm (Snopatin et al. 2009), which is comparable to 10 dB/km in halide (AlF3 ) glass fibers. It should be mentioned that

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relatively low glass transition temperature of the chalcogenide glass will be suitable for preparing micro-structured fibers including photonic structures (Coulombier et al. 2010). These fibers are also useful for nonlinear applications at near- (Liao et al. 2009, Xiong et al. 2009, Shinkawa et al. 2009, Florea et al. 2009) and midinfrared regions (Hu et al. 2010, Ung and Skorobogatiy 2010, Cherif et al. 2010).

7.2.2 Metal-Doped Fiber The atomic doping plays an important role in functional fibers. The disordered and flexible atomic structure of glasses is appropriate for incorporating metallic elements, such as transition metal atoms and rare earth ions (Tver’yanovichi and Tverjanovich 2004). Using this characteristic, we can prepare not only passive fiber devices as Co-doped attenuators (Morishita and Tanaka 2003) but also active devices as rare earth ion-doped amplifiers (Desurvire 1994). In the fiber amplifier, rare earth ions work as stimulated emission centers (Desurvire 1994). Rare earth atoms are likely to be charged in the valence of 3+, and accordingly, the ion has an unfilled 4f electron state which is shielded by outermost electrons in 5s and 5p orbital. In Er, for instance, the structure of outer electrons is 4f12 5s2 5p6 6s2 , so that Er3+ has 4f12 5s2 5p5 electrons. (Note that the f state is able to have 14 electrons.) Accordingly, in some conditions, radiative f–f transitions can occur with relatively high efficiencies. Actually, as shown in Fig. 7.5, Er3+ , when excited by 0.8 µm light (4 I15/2 → 4 I9/2 ), can amplify 1.5 µm light (4 I13/2 → 4 I15/2 ). Here, a quantum efficiency η of the amplification is approximately written as

Fig. 7.5 Energy levels of Er3+ (left) and Pr3+ (right) ions with transition energies presented in light wavelength (modified from Tver’yanovichi and Tverjanovich 2004)

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η ≈ WR /(WR + WNR ) ,

Applications

(7.2)

where WR and WNR are radiative and non-radiative transition rates. WR is estimated using the so-called Judd–Ofelt theory. On the other hand, WNR is governed by multiphonon emission to a host glass as follows: WNR ≈ {1 − exp (−Ev /kT)}− E/Ev ,

(7.3)

where E is the energy difference between an excited state and the next lower energy state (∼6500 cm−1 for 4 I13/2 in Er3+ ) and Ev (∼1200 cm−1 ) is a typical vibration wavenumber of the host (silica) glass. In consequence, the silica EDFA (Fig. 1.7) has given a satisfactory performance for the 1.5 µm amplification, while it is not satisfactory for the DWDM system operating at a wider band of 1.3−1.6 µm. The chalcogenide glass is promising for the DWDM amplifier. We first note that Er3+ has no appropriate energy levels for amplification of 1.3 µm light. Instead, we may employ Pr3+ (1 G4 → 3 H5 ), which has smaller E (∼3000 cm−1 ), so that the oxide glass having the high Ev is not suitable for a host due to increased WNR . The chalcogenide glass, reflecting heavier atomic mass, has lower Ev (∼300 cm−1 ), and accordingly, WNR becomes smaller, giving rise to higher η. Using this feature, Ohishi et al. (1994) have fabricated Pr3+ -doped As–S fiber amplifiers, PDFA. In such applications, however, the chalcogenide is competitive with the halide glass (Lucas 1999). Or, chalco-halide glasses may be more preferred. Here, we should select special chalcogenide glasses in the optical amplifier. For efficient PDFAs, Pr3+ ions must be doped with a concentration of ∼1000 ppm (Tver’yanovichi and Tverjanovich 2004). But, covalent chalcogenide glasses such as As2 S3 cannot afford such a high doping, resulting in precipitation of metallic particles. Instead, we may employ ionic chalcogenide glasses, which are compounds with Na, Al, Ga, La, etc. Such cation is likely to polarize S atoms, which become an anion, providing a stable location for Pr3+ . In Ga2 S3 –GeS2 glasses, for instance, a suggested local structure around a rare earth ion R3+ is ≡Ga∼S∼R3+ ∼S∼Ga≡, where ≡ of Ga represents threefold coordination, and ∼ stands for an ionic bond. The chalcogen can afford such structural flexibility. However, a problem is that these ionic chalcogenide glasses tend to react with water vapor (as NaCl does). One of the interesting features of the rare earth ion-doped chalcogenide glasses is the photoluminescence through host excitation (Bishop et al. 2000). In the oxide glass, optically excited rare earth ions emit photons after some non-radiative relaxation. The host glass acts just as a perturbing matrix. Such a process, ω0 →ω2 in Fig. 7.6, also exists in the chalcogenide. On the other hand, Bishop et al. (2000) have discovered, e.g., in Er-doped GaGeAsS glasses, that photons having an energy comparable to the Urbach edge of the host chalcogenide glass can provide luminescence of the rare earth ion (ω1 →ω2 ). This result suggests a process, which consists of host photo-excitation, energy transfer from the host to rare earth ions, and light emission from the ion. The energy transfer process, which may be a resonant transfer, has not been elucidated. Since the Urbach edge is spectrally more extended than

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Fig. 7.6 Direct (ω0 ) and host (ω1 ) excitations of rare earth ions (REI) in a chalcogenide glass emitting ω2 photons

the sharp absorption peaks of rare earth ions, the broadband excitation of rare earth ions can be attained. Excitation using sunlight may be possible. However, the host excitation is likely to induce the photodarkening as well, which gives a fatigue in luminescence efficiency (Harada and Tanaka 1999). It is mentioned that the host excitation is demonstrated also for Er-doped a-Si:H films (Fuhs et al. 1997). We here note that other types of optical fiber amplifiers have been proposed and demonstrated. The most promising may be the one which employs nonlinear effects such as stimulated Raman and Brillouin scattering (Abedin 2005, Jackson and Anzueto-Sánchez 2006, Stegeman et al. 2006). Due to higher optical nonlinearities (see Section 4.8), the chalcogenide glass is superior to the oxide also in these applications.

7.2.3 Waveguide Optical communication now needs waveguide devices, which can be more compact than the fiber. It will be very convenient if we can fabricate the rare earth ion amplifier in optical integrated circuits with a size of ∼1 cm. Or, such waveguides may be integrated with semiconductor and ferroelectric devices. Actually, pioneering studies on chalcogenide glass waveguide have been reported since the 1970s (Matsuda et al. 1974, Watts et al. 1974, Klein 1974). The waveguide with a high refractive index of ∼2.5 is suitable for confining propagating light. Recently, such studies are advanced with combinations of a variety of thin-film preparation techniques as pulsed laser deposition (Seddon et al. 2006). In addition, sophisticated structures such as three-dimensional Ge22 As20 Se58 waveguides buried in g-As2 S3 , having a propagation loss of 0.04 dB/cm at a wavelength of 9.3 µm (Coulombier et al. 2008), are fabricated. Extensive studies have also been directed toward the ultra-fast (picosecond range) all-optical waveguide switch using optical nonlinearity (Suzuki et al. 2009, Vo et al. 2010, Eggleton et al. 2011). As described in Section 4.8, the refractive index n of a glass can be written as n = n0 + n2 I, and by using the intensitydependent second term n2 I, we can modify the optical path length of an arm in a waveguide interferometer. For instance, in Fig. 7.7, the control beam with

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Fig. 7.7 An all-optical waveguide switch using a Mach–Zehnder interferometer

intensity of I switches on and off the output signal. The device will replace electrooptical switches presently utilized, which employ the Pockels effect and direct laser modulation. In such nonlinear applications, the chalcogenide glass seems to be very promising. In the optical integrated circuits with a waveguide length of ∼1 cm, sufficiently high nonlinearity is needed at the communication wavelength of ∼1.5 µm, or the photon energy of EOC ≈ 0.8 eV. As described in Section 4.8, the optical nonlinearity increases with a ratio of EOC /Eg (< 1), and accordingly, the chalcogenide glass having smaller Eg (≈ 1∼3 eV) than the oxide appears to have feasible potentials. Nevertheless, at least, two problems must be settled. One is the connection between a chalcogenide device and a silica fiber. A smaller Eg of the chalcogenide provides a higher refractive index (∼2.5), which is likely to cause high reflection loss at the connection. Anti-reflection devices (or coating) are required. The other is that, for compact all-optical switches, the nonlinearity appears to be still insufficient. The waveguide switch may require higher nonlinearities by two to three orders of magnitude than that available with a chalcogenide glass having an appropriate optical gap of ∼2.0 eV. For this purpose, nano-structured (Tanaka and Saitoh 2009) or photonic-structured (Suzuki et al. 2009) chalcogenide waveguides may be promising, provided that we can compromise a high nonlinearity and a fast response. In addition, optical absorption of the chalcogenide glass may also be problematic. With respect to the so-called figures of merit (Table 7.2), which take optical absorptions into account, the chalcogenide glass is not superior to the oxide. Needless to say, in nonlinear applications, the chalcogenide glass is competitive also with other materials such as crystalline semiconductors (Kamiya and Tsuchiya 2005) and organic materials (Haque and Nelson 2010). We here point out other nonlinearities. As listed in Table 7.3, it has been demonstrated that, not only the optical, but elastic nonlinearity (Rouvaen et al. 1975) and photo-elastic constants (Lainé and Seddon 1995) in the chalcogenide glass are substantially greater than that in the oxide glass such as silica. However, to the authors’ knowledge, no developments have been reported in practical applications.

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Table 7.2 Linear (Eg , n0 , α 0 ) and nonlinear (n2 , β max ) optical properties and figures of merit of nonlinearity (2βλ0 /n2 , n2 /a0 ) in some glasses Glass

Eg (eV)

n0

α 0 (cm–1 )

SiO2 BK-7 SF-59 As2 S3 BeF2

10 4 3.8 2.4 10

1.5 1.5 2.0 2.5 1.3

10–6 10–3

n2 (×10–20 m2 /W) 2 3 30 200 0.8

β max (cm/GW)

2βλ0 /n2

n2 /α 0 (cm3 /GW)

1

<10

0.2

10 50

0.1

0.02

Eg is an optical gap energy, n0 the refractive index, α 0 the attenuation coefficient, n2 the intensitydependent refractive index, and β max the maximal two-photon absorption coefficient. Except Eg and β max , the values are evaluated at wavelengths of 1−1.5 µm. BK-7 is a borosilicate glass and SF-59 represents data for lead-silicate glasses with ∼57 mol.% PbO Table 7.3 Comparison of nonlinear coefficients in As2 S3 and SiO2 glasses Material

M2 (×1015 /s3 kg)

Ma (×10−12 s2 /kg)

χ (3) (×10−14 esu)

As2 S3 SiO2

433 1.5

240 0.4

500 3

M2 is the photo-elastic figure of merit, Ma the nonlinear acoustic figure of merit, and χ (3) the third-order nonlinear optical susceptibility

7.3 Photo-Structural Device Photo-structural devices may be unique to the amorphous group VIb materials. At present, Bragg-reflector fibers (permanent) and optical phase-change disks (erasable) have been commercialized. In addition, a lot of applications have been proposed and demonstrated. In the following, we will see these applications in oxides and chalcogenides, except the phase change device, which is described in Section 7.4. Bragg-reflector fibers, the production principle being discovered by Hill et al. (Section 6.4), have been commercialized and widely utilized as wavelength filters in WDM systems (Askins 2000). As illustrated in Fig. 7.8, the refractive index in the core, consisting of Ge–SiO2 , of optical fibers can be spatially modulated by exposures to excimer laser light through photoinduced refractive index change of n ≈ 10−3 . The sinusoidally modulated structure, or the so-called Hills’ grating, reflects light with a wavelength of λ which satisfies the Bragg condition λ = 2d, where d is the modulated periodicity. For photoinduced phenomena in sulfides and selenides such as As2 S3 and GeSe2 , there are many proposals, but few have been commercialized. Those include holographic memories, photoresists, and other active and passive optical devices. For the fundamental of these phenomena, see Chapter 6. The optical memory can be non-erasable or erasable. Zembutsu et al. (1975) demonstrated using sputtered Ge–As–S–Se films and gas lasers that one page of

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Fig. 7.8 A fiber Bragg grating (FBG). The input consists of four signals with different wavelengths, in which only one selected signal is reflected and the remaining three are transmitted through the grating (modified from http://www.moritex.co.jp/products/opt/optical-fiber-filter.php)

newspapers can be holographically stored in a memory spot of 1.5 mm in diameter, which can be thermally erased using an infrared lamp (Fig. 7.9). The holographic memory has been developed, e.g., as “Holometer” (González-Leal et al. 2003) and other systems (Teteris 2003, Ozols et al. 2006), which employ semiconductor lasers, optical fibers, and computers. However, at the present stage in an optical memory market, DVD flourishes (see Section 7.4), and accordingly, it is questionable if there is an open space for analogue holographic memories. We also note that ultimate storage capacities in the holographic and binary memories, 1 Tbit/cm3 , are principally the same (Van Heerden 1963). To dramatically enhance the capacity in optical

Fig. 7.9 An erasable holographic memory system using Ge–As–Se films (left), a hologram (center), and a reconstructed image (right) (modified from Zembutsu et al. 1975). In the system illustration, O is a memorized object and sample is the chalcogenide film

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memories, we must utilize spectrum and polarization multiplexing (Zijlstra et al. 2009). Many researchers have demonstrated applications of the photo-polymerization (Section 6.3.5) to photoresist processes (Jain and Vlcek 2008). Keneman (1974) reported a pioneering work on relief holograms, which are produced in as-evaporated As2 S3 films through light illumination and chemical etching. A Bulgarian group produced, using chalcogenide films as inorganic photoresists, linear scales and gratings up to 1.6 m long, circular encoder gratings, and diffraction and kinoform optical elements (www.clf.bas.bg). Lyubin et al. (2008) and other researchers applied three-dimensional photoresist processes in sulfides and selenides to production of photonic crystal structures. As described in Section 7.7, relief structures have been produced also through the photodoping process. In such photoresist applications, however, the chalcogenide is competitive with organic resists in versatility and cost. Photoinduced phenomena have been applied to formation of optical waveguides and the devices. There are many proposals of such studies from the 1970s (Zakery and Elliott 2003, Petit et al. 2008). High-quality channeled waveguides are produced through wet and dry etchings of irradiated films (Choi et al. 2008). Chalcogenide waveguides, employing the optical stopping effect (Zou et al. 2006) and the photoinduced refractive index change (Tanaka et al. 1985), have been applied also to all-optical switches, though the response speed is not fast. In addition, photoinduced phenomena have been utilized for fabrication of passive optical devices. Tanaka et al. (1995) produced self-induced Bragg gratings in As2 S3 optical fibers and also microlenses (∼10 µm diameter), the examples being shown in Fig. 7.10. The production principle has been applied also to selfdeveloping microlenses for optical fibers and laser diodes (Saitoh and Tanaka 2003).

Fig. 7.10 Photoinduced lenses (spherical and cylindrical) (left) and the focusing images (right) (Hisakuni and Tanaka 1995). The minimal scale on the right-hand side photographs is 10 µm

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Shokooh-Saremi et al. (2006) produce, using an interferometer, Bragg gratings in As2 S3 rib waveguides. Sudoh et al. (1997) and Song et al. (2006) apply the photoinduced refractive index change to wavelength tuning of semiconductor lasers. The refractive index change can also be employed for preparing photonic structures (Lee et al. 2009). In addition, Gelbaor et al. (2011) utilize the vector effect (Section 6.3.12) in As2 S3 for alignment of liquid crystals. Here, it should be mentioned that not light beams but electron beams are also useful for preparing micro-scale patterns (Handa et al. 1980, Ruan et al. 2007, Liu et al. 2008). These applications wait for further advances (Calvez et al. 2010).

7.4 Phase Change 7.4.1 Background The most widely commercialized product using chalcogenide films at present is undoubtedly the optical phase-change disk, named DVD (digital versatile disk). The phase change is now being applied also to a rewritable electrical memory, the socalled PRAM (phase-change random access memory). As shown in Figs. 7.11 and 7.12, the phase changes have simple dynamics. Or, the operating principles of the electrical and the optical are believed to be essentially the same, i.e., electrical Joule heating (Ovshinsky 1968) and optical heating (Feinleib et al. 1971), which can change the structure of telluride films between amorphous and crystalline states (Fig. 7.12). For amorphization, the crystalline film is heated above the melting temperature (∼600◦ C), which is followed by rapid quenching. For crystallization, the amorphous film is heated to the crystallization temperature (∼150◦ C), stored there a little bit for crystal growth, and cooled down to room temperature. These amorphous–crystalline structural transformations in the telluride film modify its electrical resistance by four orders of magnitude (see Fig. 7.16) and optical reflectivity by ∼5%, which are read using low-voltage and weak-light pulses.

Fig. 7.11 Dynamics of temperature rising induced optically or electrically in amorphous telluride films

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Phase Change

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Fig. 7.12 Free energy as a function of atomic configuration (left) and temperature (right) for a phase-change material, Ge2 Sb2 Te5 . Note that there exist two crystalline phases of cubic (fcc) and hexagonal. See also Fig. 7.16

However, applications of the phase change required long developments. The phase changes, both electrical and optical, in amorphous telluride films such as Te81 Ge15 Sb2 S2 were discovered in Ovshinsky’s group in the 1960s (Ovshinsky 1968, Feinleib et al. 1971). And, in the 1970s, many researchers tried to produce random access memories using the electrical phase change. However, the crystallization process was too slow, requiring electrical pulses with durations of sub-milliseconds. This operation speed could not be competitive with that (sub-microseconds) in c-Si devices at that time. On the other hand, at the beginning of 1970s, we did not have compact lasers of ∼30 mW class, and accordingly, the optical phase change was studied using big gas (Ar and Kr) lasers. Of course, such lasers could not be employed for commercial products. With these reasons, despite the initial sensational announcement by Ovshinsky, the phase change seemed to be gradually forgotten. However, later, Yamada et al. (1991) discovered that the ternary alloys consisting of GeTe–Sb2 Te3 (see Fig. 7.13) often abbreviated as GST (Ge–Sb–Te) exhibit rapid crystallizations. Specifically, a stoichiometric composition Ge2 Sb2 Te5 (GST225) exhibits a crystallization time less than ∼50 ns upon excitation by laser pulses. Then, the optical phase change using GST films, with combination of semiconductor lasers, was developed to DVD systems. The best DVD system available in 2010 has a memory capacity of 50 GB/disk, which utilizes a blue semiconductor laser emitting light with a wavelength of 405 nm. The film shows fast phase changes also upon electrical pulses, and accordingly, electrical RAMs are being developed.

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Fig. 7.13 A ternary composition diagram depicting phase-change alloys, with their years of discovery as a phase-change material and their uses (in squares) in optical storage products. The crystallization time becomes faster from the left-hand side (∼10 µs) to the right-hand side (∼30 ns) (modified from Wuttig and Yamada 2007)

7.4.2 Optical Phase Change (DVD) The optical phase change has been believed to be induced by direct optical heating. Here, the two important performances are the operation speed and the memory capacity. The operation speed is governed by writing and erasing times of a memory spot, with the reading much faster. The writing (amorphization) is attained using a short (∼10 ns) and intense light pulse, which heats crystalline GST films above the melting temperature, followed with a rapid quenching, which is governed by heat conduction to peripheral layers (see Fig. 7.14). On the other hand, erasing includes the crystallization (crystallite nucleation and growth) of amorphous marks, which naturally needs longer duration. We are then interested in the reason why the GST film exhibits a fast crystallization time of ∼50 ns. It is also an important subject to be answered if the crystallization time can further be shortened. To understand the fast crystallization mechanism, atomic changes accompanying the phase change should be revealed. However, at present, the change remains controversial (Lucovsky and Phillips 2008, Sun et al. 2010), because of experimental difficulties in determination of atomic structures in thin (∼20 nm) GST films, which are sandwiched in between protective layers as ZnS–SiO2 (Fig. 7.14). There seems to be, at least, two ideas. One is the conventional, assuming phase changes between crystalline (ordered) and amorphous (disordered) structures (Wuttig and Yamada 2007). An ab initio molecular dynamics simulation of the crystallization process by Hegedüs and Elliott (2008) seems to support this

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Fig. 7.14 A cross-sectional view of tri-layer DVDs developed in Panasonic. Thin films are deposited onto polycarbonate substrates of 1.1 mm thickness (modified from Yamada et al. 2009)

model. The other, which has been proposed by Kolobov et al. (2004), emphasizes, not the amorphous–crystalline change, but an octahedral–tetrahedral configurational change of Ge atoms, which are bonded to Te. In the latter model, the short-range structure clearly changes. The understanding will be necessary for further development of phase change memories (Kolobov et al. 2004). On the other hand, new materials exhibiting much shorter crystallization times are intensively explored (Lencer et al. 2008). Interestingly, the optical phase-change behavior seems to be relatively insensitive to impurities in the materials (Jiang and Okuda 1991, Seo et al. 2000). We here mention that a possibility of athermal electronic phase changes has been repeatedly suggested or demonstrated (Feinleib et al. 1971, Solis et al. 1996, Zhang et al. 2007). The atomic bonding may change within picosecond scales just after photo-electronic excitation, before the rising of lattice temperature. If such a process, a kind of electronic melting (see Section 6.3.11), could be practically available, the operation speed would become faster by three to four orders than the present one. The other important issue is the memory capacity, which is determined in principle by the size of memory bits. In the optical system, the bit size is governed by the size d of a laser light spot, which is limited by diffraction as d ≈ λ/N, where λ is the wavelength of a laser and N is the numerical aperture of focusing lenses. Here, λ (∼405 nm) and N (∼0.85) with a Gaussian light intensity distribution give rise to a minimal memory diameter of ∼150 nm, which is nearly an optical limit. Then, for obtaining smaller spots, some groups have proposed ideas of new optical systems, which employ near-filed effects (Matsumoto et al. 2004) or nonlinear phenomena

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(Simpson et al. 2010). Another idea for increasing the memory capacity per disk is to increase the number of GST layers. In 2010, we can purchase DVDs having doubly stacked layers, which have a memory capacity of 50 GB. Further, Yamada et al. (2009) have developed a tri-layer disk, shown in Fig. 7.14, having 100 GB capacity.

7.4.3 Electrical Phase Change (PRAM) Recently, studies on the electrical phase change are dramatically increasing with developments of PRAMs (Fig. 7.15). The reader may refer to, e.g., a recent note by Atwood (2008) and a review by Terao et al. (2009). Though the basic mechanism of the thermal phase changes being common to that of the optical, the electrical process has some intrinsic features and also inherent problems. Figure 7.16 shows the resistivity of sputter-deposited amorphous Ge2 Sb2 Te5 films as a function of temperature (Kato and Tanaka 2005). We see the four states: amorphous, crystalline including cubic and hexagonal phases, and liquidus. And, at room temperature, between the amorphous state and the cubic phase there exists a difference in resistivity by four orders of magnitude. Accordingly, we can utilize electrically conducting marks, written in amorphous films, as bits in PRAMs. Since the resistivity difference is very big, PRAMs can operate, not only binary, but multi-valued memories (Wu et al. 2009). However, several problems remain. One concerns the atomic structure. As described in Section 7.4.2, the structural change between the two states has not been identified. Accordingly, why the electrical resistivity exhibits such a big change has not been understood (Jang et al. 2010, Cai et al. 2010). In addition, a role of the metallic hexagonal phase remains vague (Youm et al. 2007). When a bit mark is written in an amorphous state (set process), we just heat the film up to ∼200◦ C, obtaining the cubic phase. The glass transition at ∼100◦ C (Kalb et al. 2007) does not appear in the resistivity curve. On the other hand, when a crystalline bit with the cubic phase is erased (reset process), it is melted above 600◦ C, and the liquid is quenched into the amorphous state. But, we see in Fig. 7.16 that there exists the hexagonal phase at 300−600◦ C. Is the hexagonal phase by-passed in the amorphization process? Or, is it possible to induce

Fig. 7.15 A PRAM chip produced in Samsung Electronics (© Samsung Electronics Co., Ltd., reprinted from http://www.samsung.com/global/business/semiconductor/newsView.do?news_id= 322, with permission)

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phase changes between an amorphous state, the cubic phase, and the hexagonal phase? The other problem is the mechanism of electrical switching, which must occur before the thermal crystallization (Madam and Shaw 1988, Krebs et al. 2009, Pandian et al. 2009, Lee et al. 2010, Yeo et al. 2010, Choi and Lee 2010). As shown in Fig. 7.16, the amorphous state in GST films has a high resistivity, e.g., ∼104 cm, which must be switched to a conducting state, a prerequisite of generating sufficient Joule heats for thermal crystallization. Experiments have demonstrated that the conducting state appears as electric filaments. Nevertheless, it remains to be an unresolved problem for a long time why such conducting filaments are produced. Many models have been proposed on the formation mechanism, which are trap filling by injected carriers, avalanche multiplication, etc. Alternatively, Nardone et al. (2009) have proposed a non-thermal field-induced nucleation model. Compositional stability upon the electrical phase change is also a crucial issue. When a conducting crystalline state in c-GSTs is converted to the amorphous state through a liquidus state, electrical decomposition or phase separation seems to occur (Saitoh et al. 2008, Nam et al. 2008), which possibly limits the repeatability of the phase change process. We may need new materials suitable for the electrical phase change. As we see in Fig. 7.16, the cubic c-GST is fairly conductive, so that the structural change from that to the amorphous state needs a high current (Fujisaki 2010). For this

amorphous

Tg

cubic

Tc2 Tc1

hexagonal

Tm liquid

Fig. 7.16 Temperature dependence of resistivity in two Ge2 Sb2 Te5 films with thicknesses of 110 nm (open symbols) and 510 nm (solid symbols). The symbols are changed for amorphous (◦, •), cubic (, ), hexagonal (), and liquid (∇) forms (modified from Kato and Tanaka 2005). See also Fig. 7.12

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problem, Kim et al. (2007) have proposed to add nitrogen to GSTs, which can increase the electrical resistance. Alternatively, Devasia et al. (2010) have suggested replacement of Te to Se. Otherwise, new compositions may be preferred (Zhu et al. 2010). Finally, it should be mentioned that the electrical process can reveal an ultimate characteristic of the phase change phenomenon. As easily understood, in the electrical phase change, the mark size is governed by the size of electrodes. Using this feature, several groups have demonstrated that the minimal size of phase change marks obtainable at room temperature is 10–50 nm (Satoh et al. 2006, Hamann et al. 2006), which seems to be governed by amorphous–crystalline interfacial energy. This size is also favorable to reductions in the switching current (Xiong et al. 2011). This ultimate size could be the biggest advantage of this kind of atomic memories over electronic and/or dipolar memories (Scott 2004, Fujisaki 2010).

7.5 Electrical Device Are there any purely electrical applications of amorphous chalcogenides? Except for the PRAM, such products have been very limited (Glebov 2004). We know wide uses of thin-film field effect transistors (TFTs) using amorphous and lasercrystallized Si:H films in liquid-crystal panels. We also know that amorphous oxide semiconductors appear to be promising for TFTs (Chong et al. 2010). But, why is the chalcogenide limited? A plausible reason is the smaller carrier mobility and lower electrical conductivity (see Section 4.9). In addition, the gap state, which seems to exist in amorphous chalcogenide films, suppresses the conductance control by gate voltages in TFTs. Nevertheless, some studies of interest are referred to below. Hosono’s group has performed notable studies. Narushima et al. (2004) have demonstrated surprisingly high electrical conductivity and electron mobility of 0.1 S/cm and 26 cm2 /V s, respectively, in a-In49 S51 films. These values suggest that the Fermi level is located near the conduction band bottom, which provides the n+ conduction, a kind of metallic conductivity. This amorphous film is more or less flexible, which may be employed as transparent electrodes, instead of crystalline SnO2 or In–Sn–O (ITO) films. The group also demonstrates TFTs using amorphous oxide semiconductors, which are deposited upon plastic substrates (Nomura et al. 2004). However, a trial of preparing TFTs using a-CuGaS(Se)2 films has not been succeeded (Hiramatsu et al. 2008), probably due to mid-gap states. Use of electrical switching (or phase-change) films for three-terminal devices appears to be attracting. Such studies have been reported since the 1980s (Coldren et al. 1980). Recently, Song et al. (2008) employed GSTs for fabricating TFTs. The device may operate as a transistor memory. Rectifying properties have been investigated for hetero-, glass–metal, and glass–crystal junctions which include amorphous chalcogenide films (Tsiulyanu 2004).

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7.6 Photo-Electric Device Unique photoconductive properties of a-Se have been utilized for a long time. The most known is the xerography, patented by Carlson in 1937, which was commercialized by Xerox Corp in 1950. Otherwise, we may trace the use of Se to c-Se photocells, the function being discovered in the 19th century. Developments are still in progress (Wang et al. 2009, Goldan et al. 2010). Other chalcogenide films such as As2 Se3 have not been utilized, probably due to lower hole mobility. In comparison with photo-electric devices using crystalline semiconductors such as Si and GaAs, the amorphous device has, at least, three notable features. First, light emitting devices using amorphous semiconductors have not been reported. Second, as described below, the photoconducting films are available, but no photovoltaic devices have been produced using the chalcogenide. Third, the amorphous photoconductors, which may have large areas, exhibit slower response times than those of the crystalline. Reasons of these features are worth to be considered.

7.6.1 Copying Photoreceptor The xerographic photoreceptor for copying machines was the first practical application of a-Se films (Pai and Springett 1993). This usage owes a unique feature of a-Se films: electrically insulating in the dark and highly photoconductive (see Fig. 5.11). In addition, the film with a thickness of ∼50 µm and lateral sizes of ∼30 cm, the width corresponding to that of copied papers, can easily be deposited onto cylindrical metal drums (for continuous operation) using vacuum evaporation. The copying process runs through the eight steps (Fig. 7.17): (a) electrical charging (positive for a-Se) of the a-Se film by corona discharge of air and

(a)

(b)

(c)

(d)

(e)

(f)

Fig. 7.17 Schematic illustrations (cross-sectional) of the xerographic copying process (modified from Mott and Davis 1979): (a) corona charge, (b) image exposure, (c) hole drift, (d) latent image, (e) toner development, and (f) toner transfer

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water molecules, which deposits such ions as (H2 O)n H+ and H+ ; (b) image exposure, which generates electrons and holes; (c) hole drift; (d) recombination of photo-generated electrons with the surface ions, which produces a latent image; (e) development by (negatively charged) toner particles; (f) toner transfer from a-Se film to a paper (using positive corona discharge), which is followed by (g) toner fixing by heating and (h) photoreceptor cleaning (not shown). This imaging process has been applied also to laser printers, in which the image exposure is provided through scanning laser light which is modulated by digital signals. In these applications, however, a-Se photoreceptors have been replaced by organic polymer films (Weiss and Abkowitz 2006), probably due to cost and environmental problems. As known, the organic film can be prepared just by coating without using the vacuum process.

7.6.2 Vidicon and X-Ray Imager Photoconduction of chalcogenide films has been utilized in vidicons, vacuum tube television cameras. In the vidicon, illustrated in Fig. 7.18, an optical image is focused upon a chalcogenide film, converted to a photoconductive pattern, and finally transformed to a current signal through scanning an electron beam. Since the device is a kind of vacuum tubes with a typical glass tube size of 4 cm in diameter and 15 cm in length, being liable to be broken, it has been replaced by CCDs (charge-coupled devices). However, HARP (high-gain avalanche rushing amorphous photoconductor) vidicons, which utilize avalanche multiplication of photo-excited carriers in a-Se films (Fig. 7.18), are demonstrated to have higher sensitivity by ∼100 times than that of CCDs (Tanioka 2007). Using such advantage, the vidicon is employed as night scopes. However, the glass tube is still bulky and fragile. To overcome these drawbacks, researchers in NHK (Japan Broadcasting Corporation) have combined the a-Se avalanche multiplication film with an active matrix electron emitter array. The device is now becoming more compact and rigid with a diameter of ∼5 cm and a thickness of ∼1 cm (Negishi et al. 2007).

Fig. 7.18 A photograph (left) of a 2/3 in. HARP vidicon (© Nippon Hoso Kyokai, reprinted from http://www.nhk.or.jp/strl/publica/dayori-new/jp/qa-9904.html with permission) and schematic cross-sectional views (right) of a conventional (upper) and a HARP (lower) vidicon

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Fig. 7.19 An x-ray imager using an a-Se film with a thickness of 1 mm and a lateral size of 23×23 cm2 . The segment is square shaped with a side length of 150 µm

Thick a-Se films are employed also for x-ray detection, illustrated in Fig. 7.19 (Adachi et al. 2000, Kasap et al. 2009). The operation principle is essentially the same as that of the photoconductor, with a difference detecting not visible but x-ray photons. a-Se is suitable for photo-electronic x-ray detection, because it can efficiently absorb x-ray photons, due to the heavy atomic weight.1 In addition, we can prepare smooth and homogeneous (no grain boundaries) thick (∼1 mm) a-Se films. The films deposited upon TFTs have been demonstrated to be suitable for taking medical images with high resolution. Further, the x-ray sensitivity and the avalanche multiplication, developed for the vidicon, are now combined into x-ray HARP-FEA (field emitter array) detectors (Miyoshi et al. 2008).

7.6.3 Solar Cell The solar cell (Fig. 1.2) is believed to be vitally important for settling environmental problems. The operation principle of a solar cell, a photo-voltaic effect in a semiconductor p–n junction, was demonstrated using c-Si by Chapin et al. in 1954, which has been applied also to amorphous semiconductors, a-Si:H films, by Carlson and Wronski (1976).

1 Note μ(cm−1 ) ∝ ρλ3 N 3 , where μ is the x-ray absorption coefficient, ρ the density, λ the x-ray wavelength, and N (= 34 in Se) the atomic number. Te appears to be preferred in this context, but it is semi-metallic, and not photoconductive.

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Among several characteristics of the solar cell, the most important is undoubtedly the conversion efficiency from light to electrical power. A theoretical calculation predicts that, under solar radiation, the maximal efficiency of ∼30% is obtainable for a single p–n junction cell of a semiconductor having the energy gap of ∼1.5 eV. Actually, practical (single or poly-) crystalline cells provide an efficiency of ∼20%, but the a-Si:H cell is limited to ∼10%. What causes this difference of 20 and 10%? In comparison with c-Si cells, the a-Si:H cell has, at least, two disadvantages. One is a wider optical gap (∼1.7 eV) than 1.1 eV in c-Si. As the result, the amorphous film cannot absorb sun light of ω ≤ 1.7 eV (λ ≥ 0.7 µm), where the solar spectrum has considerable energy. (Nevertheless, the open-circuit voltage tends to increase with the energy gap. Actually, it is ∼0.9 and ∼0.5 V in a- and c-Si devices.) The other factor affecting the efficiency arises from a transport process of photoexcited carriers. For instance, the mobility-lifetime (μτ ) product (or, equivalently the carrier diffusion length) is, typically, ∼10−6 cm2 /V in a-Si:H films (Hoheisel and Fuhs 1988) and ∼10−2 cm2 /V in c-Si. The small value of μτ product in a-Si:H means that photo-excited carriers are likely to be trapped and/or recombined before reaching output electrodes. To overcome this inferior transport property in a-Si:H films, we now employ the drift of carriers using p–i–n cell structures, not diffusion in a p–n structure, the latter being employed in the conventional c-Si solar cells. However, a thickness of the i-layers, 300−400 nm, selected for obtaining substantial internal fields, makes light absorption smaller. Therefore, we face a trade-off between the light absorption and the carrier transport. Otherwise, we will prefer tandem junction cells consisting of varied bandgap layers. Despite these disadvantages, why is the amorphous solar cell widely utilized? The biggest advantage is a lower cell price, which may be governed by two factors. One is the amount of Si sources. The thicknesses of a-Si:H and c-Si cells are typically ∼1 and ∼100 µm, which are selected taking higher and lower optical absorption coefficients by two orders, resulting from non-direct (wavenumber negligible) and indirect (phonon-assisted) transitions (see Section 4.6). The other is that the amorphous film can be prepared through low-temperature processes in vacuum, such as glow discharge and photo-enhanced chemical vapor depositions, which are specifically suitable to fabricate wide area cells on flexible substrates as polymer films. These deposition processes are appropriate also for preparing highperformance cells having tandem (e.g., three) junctions with controlled bandgaps of 1.5–2.0 eV. Are there any ideas of solar cells using oxide and chalcogenide glasses? There are a few: the one being to use a p–n hetero-junction such as Au/As2 Se3 / Ge20 Bi11 Se69 /Au (Tohge et al. 1988). Nevertheless, if such chalcogenide devices can be competitive in many respects, including cost, with a-Si:H devices it seems to be pessimistic. Another idea is a photo-chemical cell, the principle being demonstrated using Ag–As–S ion-hole mixed conducting films (Yoshida et al. 1997). In the cell, photo-excited carriers force to move Ag+ ions (charge), which give an electric power in the dark as discharge currents. The idea, a device combining a solar cell and a battery, appears to be promising, while its efficiency must be improved.

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7.7 Ionic Device and Others Chalcogenide glasses, containing cation such as Ag+ and Li+ have been applied to ionic devices including memory, photoresist, sensor, and battery. To the authors’ knowledge, however, commercialization still remains. It should be also noted that insulating, relatively soft, and stable sulfide glasses can be employed as sealing materials. In a pioneering work, Flaschen et al. (1960) demonstrate that annealed As2 S3 films work as good sealing materials. It can also be utilized as an insulating layer for GaAs and InP semiconductor devices (Mada and Wada 1998).

7.7.1 Ionic Memories The ion moves under electric fields, and the position of ions can be employed for storing information. Using the principle, Utsugi (1990) demonstrated nano-scale write-once ionic memories (Fig. 7.20), in which Ag+ ions in Ag/Ge–Se bilayer structures are forced to move by electric fields in a scanning tunneling microscope. Detailed studies have been reported also by Ohto and Tanaka (1997). What is the potential of an erasable ionic memory? We may assume that a slower motion of ions than that of electrons is problematic. However, if the bit size can be reduced to nanometer scales, an ion is able to move with a response time of approximately nanoseconds. Based on such concepts, several ideas have been proposed for erasable ionic memories using amorphous chalcogenides (Kozicki et al. 2005, Chen et al. 2009). Photodoping, described in Section 6.3.13, has provided a lot of photoresist applications (Frumar and Wagner 2003). The process, in combination with chemical etching, also produces infrared optical devices as gratings. Not only wet etching but

Fig. 7.20 A nano-Einstein, with a scale of 100 nm (courtesy of Utsugi 1990)

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dry (plasma) etching has been employed for converting irradiated regions to reliefs (Jain and Vlcek 2008). A Japanese group has demonstrated ultrahigh resolution (∼1 nm) of the photodoping process, and applications to photoresist process using synchrotron orbital radiation (Saito et al. 1988) and to x-ray holograms (Somemura et al. 1992). Optical recording characteristics in GeS2 /Ag(Cu) films have also been studied (Kato et al. 2006).

7.7.2 Ion Sensor The first demonstration of chalcogenide ion sensors may be the one reported by Baker and Trachtenberg (1971) in Texas Inst. The principle is simple, but practical operations still remain vague, as reviewed by Vassilev and Boycheva (2005), Schoning et al. (2007), and Conde Garrido et al. (2009). In Fig. 7.21, the central membrane is made from a chalcogenide glass containing A+ ions, the left-hand side solution 1 is a reference, and the right is a liquid to be inspected for the concentration of A+ ions. Then, the voltage V appearing between the electrodes 1 and 2 is given as V = (RT/nF) ln(a1 /a2 ),

(7.4)

where R is the gas constant (=kB Na ), T the temperature, n the charge number of measured ions, F the Faraday constant (=eNa ), and a the activity, which is equal to the mole concentration x for an ideal mixture. Accordingly, by measuring V, we can estimate x2 . Following this principle, Vassilev and Boycheva (2005) demonstrate Cu2+ -ion sensing using Cu–As–Se glasses. However, the sensor must satisfy several conditions, such as the sensitivity only to an inspected ion, i.e., total insensitivity to other ions, and chemical durability to ion-containing liquids, which are more or less difficult. The sensor is being developed as miniature field effect transistor types, toward “electronic nose” or “electronic tongue.”

Fig. 7.21 A principal configuration of ion sensors (modified from Baker and Trachtenberg 1971)

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7.7.3 Battery Efficient and light-weight batteries have been required in many areas, including electronics and vehicles. The battery has a structure of anode/electrolyte/cathode, in which the glass is a promising candidate for the electrolyte in all solid-state batteries. (Note that common electrolytes at present are liquidus or paste like.) Hence, considerable studies have been performed for glassy electrolytes. Note that not films, but powder forms are preferred for the electrolyte, since the powder can increase the area of reacting interfaces. Here, a comparison of oxide and sulfide, e.g., Li2 O(S)–SiO(S)2 , shows an interesting trend. The sulfide provides a higher conductivity (∼10−4 S/cm) of Li+ ions, which is understood to be a manifestation of higher polarizability of S than O atoms, which gives greater freedom to the ion. Indeed, Kitaura et al. (2010) have produced a high-performance rechargeable batteries having a three-layer structure consisting of In (cathode), 80Li2 S20P2 S5 glass-ceramic powder (electrolyte), and a composite powder containing LiCoO2 (anode). Provided that reliability and safety are overcome, the compact and light-weight battery will be utilized for electric vehicles in a near future.

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Chapter 8

Future Prospects

Abstract In this chapter, we summarize notable problems that are unresolved and also try to predict future prospects of amorphous chalcogenides. Keywords Unresolved problems · Future applications · Photonics · Electronics · Ionics · Se · GST

8.1 Fundamentals The goal of solid-state science is to connect atomic structures and macroscopic properties using simple theories (Fig. 2 in Preface). However, we cannot yet identify the amorphous structure. In addition, macroscopic properties are likely to vary depending upon the quasi-stability of non-crystalline solids. Needless to say, in theoretical analyses, such an assumption as the periodic boundary condition cannot be applied to the disordered structure, and hence, the amorphous materials science remains far behind the crystalline materials science. We here summarize marked progresses and the remaining problems. For details, see the related chapters. With regard to atomic structures (Chapter 2), we have grasped the short-range (≤0.5 nm) structure in simple glasses. However, we are still at speculative levels on the medium-range (2–3 nm) structure and ESR-insensitive defects, the main reasons being insufficient experimental tools. In addition, heterogeneous structures with correlation lengths of ∼10 nm scales may exist, which are more difficult to determine. In structural properties (Chapter 3), the importance of the magic numbers, 2.4 and 2.67, for understanding compositional variations has been amply demonstrated. However, the glass transition and the crystallization remain to be big problems in amorphous materials. The glass transition appears to be influenced by the mediumrange structure, for which we are groping in the dark. In addition, to obtain an elucidation of the universal low-temperature properties, we wish to identify responsible atomic structures. Electronic properties (Chapters 4, 5, and 6) should be studied further. It can be said that we have been able to connect the short-range structure to gross electronic structures. However, many problems remain to be considered. For optical properties, why do most of amorphous materials exhibit the exponential Urbach edge? And, why does the Urbach-edge energy in simple glasses such as As2 S3 229 K. Tanaka, K. Shimakawa, Amorphous Chalcogenide Semiconductors and Related C Springer Science+Business Media, LLC 2011 Materials, DOI 10.1007/978-1-4419-9510-0_8,

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and SiO2 , and even in a-Si:H, show a common value of ∼50 meV? Note that, despite this fixed Urbach energy, the optical gaps widely vary at 1–10 eV. The meaning of the Tauc gap also remains to be vague. For the photoluminescence, the unique half-gap spectrum has been interpreted by using D0 , but why is the D0 level located at the mid-gap in lone pair electron semiconductors? Alternatively, the photoluminescence spectrum has been interpreted using the idea of self-trapped excitons, but why should the exciton emit universally the half-gap photons? For the electronic transport, why are holes more mobile in almost all the chalcogenide glasses? What is the reason for the Meyer–Neldel rule in electrical conductivity? How can we compromise the concepts of the mobility edge and the polaron in chalcogenide glasses? Why is the avalanche multiplication unique to a-Se? Photo-structural changes also present many challenging problems, but we need definite insights into the initial structure (before illumination) for obtaining firm understandings. In short, there remain several unanswered scientific problems in qualitative, and more in quantitative, senses. To advance the science, we need tempting motivations, which may arise from applicable potentials.

8.2 Applications What are the future applications of the group VIb glass (Chapter 7), specifically the chalcogenide glass? History shows that future prediction entails a lot of hard work. Actually, in the 1970s, few people could have imagined an earth surrounded by optical fiber networks. Yet in the 1990s, we could not have imagined the present prosperity of optical phase-change memories, which have been revived by the discovery of fast phase-change GeTe–Sb2 Te3 films. Despite the difficulty, it may be challenging to predict the future in some area. First, it is beyond doubt that the optical fiber communication system will develop still further, and related optical devices with ultimate performances are required. Fiber devices as optical amplifiers and Bragg reflectors will be improved for dense wavelength division multiplexing systems. Functional optical integrated circuits using optical nonlinearities are needed, in which the glass will compete with semiconductor and ferroelectric materials. Related micro-optical components will be developed. Second, what is the future of memories? Simple extrapolation of the present technology predicts that the capacity of DVD memories will reach ∼1 TB/disk with developments of, e.g., multi-layer and multi-level recording techniques. On the other hand, a dramatic increase in the operating speed in a near future will be difficult. We should recognize, however, that the optical memory must compete with magnetic memories as hard disks in many applications. The hard disk is approaching a capacity of ∼1 TB/pack with a faster operation speed, which may be superior to the phase-change memory. For the optical memory, holographic recording using sulfide films may be an alternative, while its capacity is still limited by light

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wavelength. Then, one promising direction of optical memories is to use spectral multiplexing. We can expect that the persistent spectral hole burning system combined with wavelength-tunable compact lasers will be able to memorize 1000 bits in a diffraction-limited light spot in a three-dimensional space, which will be capable of producing peta-byte memories. For that purpose, stable (organic or inorganic) sensitizer-doped amorphous films must be developed. Finally, at present, a future prediction of PRAM seems to be very critical. The potential is still being explored, while there are several competing devices as magnetic and ferroelectric memories. What is the future for the photoconductive devices? X-ray detection and avalanche-multiplied photoconduction are surely the greatest advantages of a-Se applications in recent years. The performance will be developed further, not only limited to medical and television purposes. We here recognize that Se remains to be a tempting material both from science and application over nearly a century. Despite that, we cannot yet understand attracting fundamental properties even in this simplest system, a-Se, as described in the present text! Ionic applications are more difficult to be predicted. Ionic memories, sensors, and batteries are surely important, while there exist competing materials such as organic polymers and ceramic crystals. We may recall here that the xerographic photoreceptor has been completely replaced from a-Se to organic photoconductors, due to the price and ecological issue. Therefore, some unique advantages, utilizing ionic and/or ion-hole conductions, should be emphasized in the forthcoming applications.

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Appendix: Publications on Related Crystals Comparisons of the glass and crystal provide valuable insight, as described in this text, since elemental and stoichiometric glasses have the corresponding crystals with the same composition and the crystalline physics is much more advanced than that of the non-crystalline. We here list related publications in a historical order on simple chalcogenide crystals of interest. In addition to these publications below, we may consult Landolt–Bornstein (Group III Condensed Matter, Numerical Data and Functional Relationships in Science and Technology, Volume 41C: Non-Tetrahedrally Bonded Elements and Binary Compounds I), which contains comprehensive data on some chalcogenide crystals.

S and Se Cook, B.E., Spear, W.E.: The optical properties of orthorhombic sulphur crystals in the vacuum ultraviolet. J. Phys. Chem. Solids 30, 1125–1134 (1969) Zingaro, R.A., Cooper, W.C.: Selenium, Van Nostrand Reinhold, New York, NY (1974) Nielsen, P.: Photoemission studies of sulfur. Phys. Rev. B 10, 1673–1682 (1974) Salaneck, W.R., Lipari, N.O., Paton, A., Zallen, R., Liang, K.S.: Electronic structure of S8 . Phys. Rev. B 12, 1493–1500 (1975) Robins, L.H., Kastner, M.A.: Recombination and excited-state absorption at photoluminescence centres in crystalline and amorphous arsenic triselenide. Philos. Mag. B 50, 29–51 (1984) Abass, A.K., Ahmad, N.H.: Absorption edge of pure and selenium-doped α-sulfur single crystals. Phys. Status Solidi (a) 91, 627–630 (1985) Oda, S., Kastner, M.A.: Transient photoluminescence and photo-induced optical absorption in polymeric and crystalline sulphur. Philos. Mag. B 50, 373–377 (1984) Nagata, K., Miyamoto, Y., Nishimura, H., Suzuki, H., Yamasaki, S.: Photoconductivity and photoacoustic spectra of trigonal, rhombohedral, orthorhombic, and α-, β-, and γ -monoclinic selenium. Jpn. J. Appl. Phys. 24, L858–L860 (1985) Lundt, H., Weiser, G.: Defect luminescence and its excitation spectra in As-doped Se single crystals. Philos. Mag. B 51, 367–380 (1985) Chen, C.Y., Kastner, M.A., Robins, L.H.: Transient photoluminescence and excited-state optical absorption in trigonal selenium. Phys. Rev. B 32, 914–917 (1985) Chen, C.Y., Kastner, M.A.: Transient photoinduced optical absorption spectroscopy in trigonal selenium. Phys. Rev. B 33, 1073–1075 (1986) Povoa, J.M., Leal Ferreira, G.F.: Anomalies in the electronic time-of-flight current trace in sulfur. Phys. Rev. B 47, 1610–1612 (1993)

As2 S(Se)3 Evans, B.L., Young, P.A.: Optical properties of arsenic trisulphide. Proc. R. Soc. A297, 230–243 (1967) Kolomiets, B.T., Mamontova, T.N., Babaev, A.A.: Radiative recombination in vitreous and single crystal As2 S3 and As2 Se3 . J. Non-Cryst. Solids 4, 289–294 (1970) Drews, R.E., Emerald, R.L., Slade, M.L., Zallen, R.: Interband spectra of As2 S3 and As2 Se3 crystals and glasses. Solid State Commun. 10, 293–296 (1972) Zallen, R., Slade, M.: Rigid-layer modes in chalcogenide crystals. Phys. Rev. B 9, 1627–1637 (1974)

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233

Zallen, R., Blossey, D.F.: The optical properties, electronic structure, and photoconductivity of arsenic chalcogenide layer crystals. Physics and Chemistry of Materials with Layered Structures, edited by E. Mooser (D. Reidel Publishing Company, Dordrecht, 1976) pp. 231–272. Smith, B.A., Cowlam, N., Shamah, A.M.: The crystal growth and atomic structure of As2 (Se,S)3 compounds. Philos. Mag. B 39, 111–132 (1979)

As2 S3 Morimoto, N.: The crystal structure of orpiment (As2 S3 ) refined. Mineralogical J. 1, 160–169 (1954) Mullen, D.J.E., Nowacki, W.: Refinement of the crystal structure of realgar, AsS and orpiment, As2 S3 . Z. Kristallogr. 136, 48–65 (1972) Lisitra, M.P., Berezhinsky, L.I., Valakh, M.Ya., Yaremko, A.M.: Exciton peculiarities in the As2 S3 layer crystal. Phys. Lett. 42A, 51–52 (1972) Perrin, J., Cazaux, J., Soukiassians, P.: Optical constants and electronic structure of crystalline and amorphous As2 S3 in the 3 to 35 eV range. Phys. Status Solidi (b) 62, 343–350 (1974) Blossey, D.F., Zallen, R.: Surface and bulk photoresponse of crystalline As2 S3 . Phys. Rev. B 9, 4306–4313 (1974) Schein, L.B.: Temperature independent drift mobility along the molecular direction of As2 S3 . Phys. Rev. B 15, 1024–1034 (1977) Murayama K., Bösch, M.A.: Radiative recombination in crystalline As2 S3 . Phys. Rev. B 23, 6810–6812 (1981) Rebenstorff, D., Weiser, G.: Electric-field-modulated spectra of orpiment (As2 S3 ) near the energy gap. Philos. Mag. B 46, 207220 (1982) Weistein, B.A.: Anomalous pressure studies of luminescence in c-As2 S3 and a-As2 SeS2 : Consequences for defect structure in chalcogenides. Philos. Mag. B 50, 709–729 (1984) Shimoi, Y., Fukutome, H.: Degeneracy in the crystal structure of As2 S3 . J. Phys. Soc. Jpn. 59, 1264–1276 (1990) McNeil, L.E., Grimsditch, M.: Elastic constants of As2 S3 . Phys. Rev. B 44, 4174–4177(1991) Zallen, R.: Effect of pressure on optical properties of crystalline As2 S3 . High Pressure Res. 24, 117–118 (2004) Espeau, P., Tamarit, J.Li., Barrio, M., Lopez, D.O., Perrin, M.A., Allouchi, H., Ceolin, R.: Solid state studies on synthetic and natural crystalline arsenic(III) sulfide, As2 S3 (orpiment): New data for an old compound. Chem. Mater. 18, 3821–3826 (2006) Bonazzi, P., Bindi, L.: A crystallographic review of arsenic sulfides: Effects of chemical variations and changes induce by exposure to light. Z. Kristallogr. 223, 132–147 (2008) Gibbs, G. V., Wallace, A. F., Zallen, R., Downs, R. T., Ross, N. L., Cox, D. F., Rosso, K. M.: Bond paths and van der Waals interactions in orpiment, As2 S3 . J. Phys. Chem. A 114, 6550–6557 (2010)

As4 S4 Street, G.B., Gill, W.D.: Photoconductivity and drift mobilities in single crystal realgar (As4 S4 ). Phys. Status Solidi 18, 601–607 (1966) Mullen, D.J.E., Nowacki, W.: Refinement of the crystal structures of realgar, AsS and orpiment As2 S3 . Z. Kristallogr. 136, 48–65 (1972)

234

8 Future Prospects

Street, R.A., Austin, I.G., Searle, T.M.: Photoluminescence in chalcogenide crystals showing small polaron conduction; Orthorhombic sulphur and As4 S4 . J. Phys. C: Solid State Phys. 8, 1293–1300 (1975)

As2 Se3 Kitao, M., Asakura, N., Yamada, S.: Preparation of As2 Se3 single crystals. Jpn. J. Appl. Phys. 8, 499–500 (1969) Shaw, R.F., Liang, W.Y., Yoffe, A.D.: Optical properties, photoconductivity, and energy levels in crystalline and amorphous arsenic triselenide. J. Non-Cryst. Solids 4, 29–42 (1970) Sussmann, R.S., Searle, T.M., Austin, I.G.: Absorption and electro-absorption in single-crystal As2 Se3 near the fundamental edge. J. Phys. C: Solid State Phys. 8, L564–L568 (1975) Marshall, J.M.: Electron transport in arsenic triselenide single crystals. J. Phys. C: Solid State Phys. 10, 1283–1290 (1977) Althaus, H.L., Weiser, G., Nagel, S.: Optical spectra and band structure of As2 Se3 . Phys. Status Solidi (b) 87, 117–128 (1978) Sussmann, B.S., Searle, T.M., Austin, I.G.: The excitonic gaps and Urbach tail in crystalline As2 Se3 : Absorption and electroabsorption studies. Philos. Mag. B 44, 665–683 (1981) Kanishcheva, A.S., Mikhailov, Yu.N., Zhukov, E.G., Grevtseva, T.G.: Redetermination of the crystal structure of As2 Se3 and a comparison of the coordination of As(III) in chalcogenides and their analogs. Inorg. Mater. 19, 1744–1748 (1984) Marshall, J.M., Barclay, R.P., Main, C., Dunn, C.: The transient photodecay process and its interpretation in the case of disordered single crystals of arsenic triselenide. Philos. Mag. B 52, 997–1004 (1985) Brunst, G., Weiser, G.: Defect-controlled conductivity in As2 Se3 single crystals. Philos. Mag. B 51, 67–77 (1985) Antonelli, A., Tarnow, E., Joannopoulos, J.D.: New insight into the electronic structure of As2 Se3 . Phys. Rev. B 33, 2968–2971 (1986) Tarnow, E., Antonelli, A., Joannopoulos, J.D.: Crystalline As2 Se3 : Electronic and geometric structure. Phys. Rev. B 34, 4059–4073 (1986) Tarnow, E., Antonelli, A., Joannopoulos, J.D.: Crystalline As2 Se3 : Optical properties. Phys. Rev. B 34, 8718–8727 (1986) Kitao, M., Nishimoto, T., Yamada, S.: Emission and excitation spectra of photoluminescence of As2 Se3 single crystals. Phys. Status Solidi(a) 103, K149–K152 (1987) Ristein, J., Weiser, G.: Thermalization of excited carriers through band states studied by photoluminescence in As2 Se3 and Se single crystals. Philos. Mag. B 56, 51–62 (1987) Ristein, J., Weiser, G.: Recombination of germinate pairs in As2 Se3 single crystals. Philos. Mag. B 54, 533–542 (1987) Robins, L.H., Kastner, M.A.: Anomalous magnetic properties of triplet excited states in crystalline and amorphous arsenic triselenide. Phys. Rev. B 35, 2867–2885 (1987) Ristein, J., Weiser, G.: Microscopic structure of the radiative centre in As2 Se3 crystals. Solid State Commun. 66, 361–365 (1988) Ristein, J., Taylor, P.C., Ohlsen, W.D., Weiser, G.: Radiative recombination center in As2 Se3 as studied by optically detected magnetic resonance. Phys. Rev. B 42, 11845–11856 (1990)

GeS(Se)2 Inoue, K., Matsuda, O., Murase, K.: Raman spectra of tetrahedral vibrations in crystalline germanium dichalcogenides, GeS2 and GeSe2 , in high and low temperature forms. Solid State Commun. 79, 905–910 (1991)

Appendix: Publications on Related Crystals

235

Ho, C.H., Lin, S.L., Wu, C.C.: Thermoreflectance study of the electronic structure of Ge(Se1−x Sx )2 . Phys. Rev. B 72, 125313 (2005)

GeS2 Zachariasen, W.H.: The crystal structure of germanium disulphide. J. Chem. Phys. 4, 618–619 (1936) Prewitt, C.T., Young, H.S.: Germanium and silicon disulfides: Structure and synthesis. Science 149, 535–537 (1965) Rubenstein, M., Roland, G.: A monoclinic modification of germanium disulfide, GeS2 . Acta Crystallogr. B27, 505–506 (1971) Dittmar, Von G., Schäfer, H.: Die Kristallstructur von H.T.-GeS2 . Acta Cryst. B31, 2060–2064 (1975) Saji, M., Kubo, H.: Electrical properties of GeS2 single crystals. Rept. Nagoya Inst. Technol. 32, 213–221 (1980) (in Japanese) Weinstein, B.A., Zallen, R., Slade, M.L.: Pressure-optical studies of GeS2 glasses and crystals: Implications for network topology. Phys. Rev. B 25, 781–792 (1982)

GeSe2 Aspens, D.E., Phillips, J.C., Tai, K.L.: Optical spectra and electronic structure of crystalline and glassy Ge(S,Se)2 . Phys. Rev. B 23, 816–822 (1981) Popovi´c, Z.V.: Optical absorption band edge of single crystal β-GeSe2 . Phys. Lett. A 110, 426–428 (1985) Popovi´c, Z.V., Gaji´c, R.: New vibrational modes in the far-infrared spectra of germanium diselenide. Phys. Rev. B 33, 5878–5879 (1986) Nikolic, P.M., Todorovic, D.M., Vujatovic, S.S., Djuric, S., Mihailovic, P., Blagojevic, V., Radulovic, K.T., Bojicic, A.I., Vasiljevic-Radovic, D., Elazar, J., Urosevic, D.: Anisotropy in thermal and electronic properties of single crystal GeSe2 obtained by the photoacoustic method. Jpn. J. Appl. Phys. 37, 4925–4930 (1998) Popovi´c, Z.V., Jakši´c, Z., Raptis, Y.S., Anastassakis, E.: High-pressure Raman-scattering study of germanium diselenide. Phys. Rev. B 57, 3418–3422 (1998)

Material Index

A Ag1 As40 Se60 , 78–79 Ag20 As32 Se48 , 106 Ag2 S, 18, 77 Ag2 S-As2 S3 , 80–81 Ag2 S-GeS2 , 78 Ag45 As15 S40 , 177 Ag-As-S, 18–19, 77, 157, 175–177, 218 AgAsS2 , 5, 77, 171–177 AgBrx Cl1-x , 141 a-Ge:H, 182 AlF3 , 200 As, 15, 21, 24, 33, 51, 71, 73–74, 114, 175, 178 As(Ge, Si)-S(Se):H, 22 As100-x Sx , 21 As2 O(S, Se, Te)3 , 13–14, 47, 114 As2 S3 , 3, 12, 14, 16, 19–24, 30–31, 33, 37–39, 44–46, 48–57, 64, 69–70, 72–74, 90–91, 93, 96–103, 107, 126–128, 144–145, 148, 150–157, 161–163, 165, 168–171, 174–176, 178, 180–181, 184, 200, 202, 204–207, 219, 229 As2 Se3 , 16, 21, 44, 57, 67, 70, 90, 97–98, 101–102, 109, 124, 128, 131, 135, 144, 151, 170, 178, 215 As2 Te3 , 16, 44, 107, 161, 197 As3 Se2 , 152 a-Si:H, 2–3, 5–7, 22–23, 43, 48, 55–56, 64, 73, 87, 99–100, 110–112, 130–131, 136, 142, 144, 160, 182–183, 203, 217–218, 230 As-S, 9, 23, 41, 52, 101, 151–152, 178–179, 202 As-Se(Te), 39 Asx S3 , 152 Azobenzene, 184–185

B B2 O3 , 43, 49 B2 O3 -Li2 O, 49 Bi-Ge-Se, 109 Bi4 Si3 O12 , 49 BK-7 (borosilicate glass), 204 C C12 H26 , 46 c-As2 S2 , 147 c-As2 S3 , 108, 124, 130, 146, 149, 157, 165, 175 c-As2 Se3 , 90, 108 CCl4 , 46 CdO, 12 CdS, 12 c-S, 15, 125, 130 c-GeS2 , 17, 37, 47, 175 c-SiO2 , 33, 48, 72, 90, 108, 163, 179, 199 c-Se, 15, 35, 40, 42, 108, 126, 128–129, 215 c-SnO2 , 214 Cu(Ag)-As(Sb)-S(Se), 12 Cu-As-Se, 151, 220 CuGaS(Se)2 , 214 E Er-doped a-Si:H, 203 Er-doped chalcogenides, 202 F Fe2 O3 , 9 G GaAs, 12, 25, 87, 99, 215, 219 Ga-Ge-S, 157 Ga-La-S, 18, 151 Ge100-x Sx , 21 Ge15 Te85 , 17

237 K. Tanaka, K. Shimakawa, Amorphous Chalcogenide Semiconductors and Related C Springer Science+Business Media, LLC 2011 Materials, DOI 10.1007/978-1-4419-9510-0,

238 Ge1 As4 Se5 , 160, 162 Ge2 Sb2 Te5 (GST), 18, 21, 56, 100, 136, 209–214 Ge-As-S, 41, 152, 156, 206 GeO(S, Se)2 , 43, 47 GeO(S, Se, Te)2 , 13, 40 GeO2 -GeS2 , 18, 55 GeS2 , 17, 21, 24, 37, 42, 49, 90, 93, 178 GeS2 -GeO2 , 157 50GeS2 -50GeO2 , 157 Ge-Sb-Te, 12, 17–18, 41, 91, 143, 209 Ge-Se, 17, 39, 68, 151–152 GeSe2 , 14, 45, 124, 143–144, 149, 205 GeSe3 , 151–152 Ge-SiO2 , 179–180, 205 GeTe-Sb2 Te3 , 209, 230 GST, 209–214 H Hydrogenated amorphous silicon, 2, 182–185 I In49 S51 , 109, 214 In-Sn-O (ITO), 214 N Na2 O, 13–14, 41 Na2 O(PbO)-SiO2 , 55 NaCl, 3, 9, 50, 77, 202 Na-Ge-S, 157 P P, 15, 17, 71 Polyethylene, 7, 24, 46–47, 64, 170 Pr-doped chalcogenides, 202

Material Index P-Se, 39 Pyrex, 73–74, 170 S S, 10, 12–15, 17–18, 40–42, 51–52, 69, 71, 109, 125, 142, 149–152, 156–157, 160, 175, 202 Sb, 12, 15 Se, 10–13, 15, 21, 23, 33, 37, 39–40, 42, 46, 50, 52, 54, 56, 65, 69, 71, 73, 80, 89, 94–95, 99, 106–107, 124–126, 128, 133, 142, 148–149, 151–152, 154, 156–157, 160, 166, 169, 214–217, 231 SF-59 (lead-silicate glass), 204 Si, 2, 11–12, 17, 23, 30, 33, 42, 51, 87, 90, 114, 127, 148, 180, 184, 214, 217 Si(C, S):H, 110 SiO(S, Se, Te)2 , 13 SiO2 , 2–3, 14, 33, 45, 90–91, 96, 109, 124, 204–205 SiO2 -Al2 O3 , 9 SiO2 -Na2 O, 9, 13, 41, 74, 200 74SiO2 -16Na2 O-10CaO, 13, 76 SiS(Se, Te)2 , 17 T Te, 10, 12–16, 40, 70, 74, 109, 114, 142, 211, 214, 217 Te81 Ge15 Sb2 S2 , 209 X xGeO2 -(100-x)GeS2 , 18 xNa2 O-(100-x)SiO2 , 74 Z ZnCl2 , 46, 69 ZnO, 12

Subject Index

A Ab-initio, 53, 89, 148, 210 Ac conductivity, 112–113, 161, 183 Anisotropic shape change, 172–174 Anomalous x-ray diffraction, 35 Atomic coordination number, 16, 40, 63, 71, 75 Atomic force microscopy (AFM), 37–38, 54 Atomic periodicity, 3, 23, 56 Atomic volume, 74, 76, 3 Avalanche breakdown, 135–136 Average atomic density, 34 B Birefringence, 3, 171, 184 Blue-shift, 92, 130 Bond ionicity, 12–13 twisting, 159 Boolchand phase, 76 Boson peak, 48–50, 72, 74 Brillouin scattering, 203 Bulk modulus, 64, 72–73 C Carrier lifetime, 129 Carrier multiplication, 136 Carrier-transit time, 133 Chain, 7, 11, 15, 21, 33, 35, 42–43, 54, 57, 94–95, 110, 149, 151, 172–173 Charge coupled device (CCD), 6, 216 Charged defect, 93–94, 126, 160–161, 167, 173 Chemical doping, 6, 18, 87, 131 Chemical vapor deposition (CVD), 22, 218 Cis-conformation, 184 Configuration coordinate, 64–65, 158

Conservation rule, 96 Constant photocurrent method (CPM), 130–131, 183 Continuous random network, 30, 32, 33, 41, 43, 45, 48, 76 Cook-and-quench method, 53 Corner-share, 41–43 Coulombic layer movement, 159 Covalency, 12–17, 23–24, 40–41, 43–44, 47, 51, 67, 71, 75, 80, 99, 113–114, 141, 152, 154, 156–157, 167, 170–171, 173, 175, 181, 197, 202 Crystallization, 14, 57, 63–66, 68–71, 104, 144–145, 147–150, 172, 181–182, 208–213, 229 D Dangling bond, 4, 10, 29–30, 32–33, 40, 50–52, 56, 86–87, 93–94, 167, 178, 183–184 D0 center, 10, 50–52, 93, 126–127, 167, 230 Debye relaxation, 112 temperature, 64 Defect creation, 142, 145, 148, 161, 180–181, 184 Dember, 107, 121–123, 128 Dense random packing, 29 Density-functional theory, 148 (De-)trapping, 87, 107, 109, 122, 129, 132 Diamond-anvil cell, 24 Dichroism, 171 Digital versatile disk (DVD), 5–6, 208 Dihedral angle, 32, 35, 40, 42 Dispersive transport, 132–133 Distorted layer, 7, 33, 44 Drift mobility, 132 Drude model, 106, 132

239

240 E E center, 10, 33, 50, 142, 179–180 Eclipsed conformation, 42 Edge-share, 41–43 Effective density-of-states, 107 Elastic constant, 50, 72–74, 146, 165, 200, 204 Electrical phase-change, 142, 208, 212–214 Electrical switching, 136, 213–214 Electrolyte, 221 Electron density-of-state (DOS), 85–86, 89, 91–92, 95–96, 130–135 Electro-negativity, 12 Electronic melting, 170, 211 Electron-lattice interaction, 5, 99 Electron spin resonance (ESR), 39, 50–52, 93–94, 124–125, 145, 165–168, 183, 229 Erbium doped fiber amplifier (EDFA), 8, 199, 202 Evaporation, 8, 15, 17, 20–22, 56, 146, 198, 215 EXAFS, 34, 35–37, 50–51, 160, 168 Exciton, 88, 92, 99, 121–122, 127–128, 130, 230 F Fabry–Perot type interference, 36 Fast ion-conductor, 77 Fiber amplifier, 8–9, 199, 201–203 Fiber Bragg grating (FBG), 179, 199, 206 Figure-of-merit, 205 First sharp diffraction peak (FSDP), 44–50, 72, 74, 151, 159 Flash evaporation, 21, 152 Floating method, 8–9 Formal valence-shell model, 12 Free-carrier absorption, 102 Free volume, 68, 78 Frequency-resolved photoluminescence, 127–128 G Geminate recombination, 122, 130 Giant photo contraction, 151–152 expansion, 147, 163–164, 170 Glass transition temperature, 2, 15–16, 20, 54, 56–57, 64, 66–68, 74, 76, 80, 95, 126, 150, 153–154, 156, 160–162, 165, 169–170, 180, 198, 200 Glow discharge, 8, 22, 218

Subject Index H Half-gap photoluminescence, 124–125 Holographic storage, 151, 184 HOMO, 90–91, 148 Hopping, 87–88, 112, 116, 132–133 Hund rule, 11 I Ideal glass, 29–30, 68 Impact ionization, 136 Impurity, 3, 53, 86–87, 124–125, 131, 167, 198 Infrared spectroscopy, 178 Intimate pair of defect, 161, 167 Ioffe–Regel rule, 86 Ionicity, 12–14, 74, 76 Ionic transport, 77–81 Ion mobility, 5 Irreversible photoinduced change, 145–146, 150 K Kauzmann’s paradox, 31 Kramers–Krönig relation, 95–96, 102–103, 153 L Laser ablation, 22, 143 Lattice vibration, 4, 136, 142, 196–197 Light induced bending, 144 soaking, 161, 182–183 Liquid crystals, 1, 195, 208 Lone-pair electron, 11–12, 52, 87, 90, 94, 98, 103, 110, 114, 127, 130, 154, 157–158, 173, 178, 230 Long-range structure, 12, 33, 50 Low-temperature anomaly, 50, 72 Lucky drift, 136 LUMO, 90–91, 148 M Magic number, 25, 63, 74–77, 229 Maxwell–Wagner effect, 113 Mean-free path, 36, 56, 72, 86, 107, 110, 136 Medium-range structure, 41–50, 53, 63, 76, 87, 90, 159 Melting temperature, 2, 18, 65–67, 95, 208, 210 Melt-quench, 2–3, 19, 24 5-Membered ring, 30, 87 6-Membered ring, 30 Metallicity, 12–14, 115 Meyer–Neldel rule, 78, 100, 110–112, 230

Subject Index Micro-lense, 207 Mid-gap optical absorption, 53, 87 Mobility edge, 91–92, 107, 130–131, 133, 230 Mobility gap, 92, 99, 128, 130 Molecular dynamics (MD), 18, 53–54, 148, 152, 210 Monte Carlo method, 43, 54 Mossbauer spectroscopy, 39 Moss rule, 103, 106, 153 Mott-CFO model, 91–92 Multi-layer structure, 152 N Nano-structure, 55–57, 204 Network former, 13, 55 modifier, 13 Neutron diffraction, 34–35, 51 Nonlinear vibrational spectra, 38 Non-photoconducting gap, 92, 130 Non-radiative recombination, 122, 124, 166–167 Normal bond, 32–33, 50, 63, 159, 167 8–N rule, 12, 40 Nuclear magnetic resonance (NMR), 39, 95 Nuclear quadrupole resonance (NQR), 39 O Obsidian, 1, 8–9 Optical absorption, 4, 22, 43, 47, 53, 56, 86–87, 91, 96–102, 125, 130–131, 135, 150–153, 157, 160, 166, 168, 199, 204, 218 bandgap, 19, 24, 74, 93 fiber, 4–5, 19, 54, 104, 142, 179, 197–200, 203, 205–207, 230 induced thermal change, 142 nonlinearlity, 103–106, 203–204 phase-change, 5, 143, 205, 208–211, 230 phonon, 38–39, 48, 122 stopping effect, 168, 207 waveguide, 203–204, 207 Opto-mechanical, 172–173 P Penetration depth, 143, 147, 153, 163 Phase-change random-access memory (PRAM), 208, 212–214, 231 Photo amorphization, 147, 148 bleaching, 145, 152, 178 chemical modification, 176–177

241 conduction, 121, 123, 128–135, 161, 164, 183, 216, 231 crystallization, 144–145, 147, 149 darkening, 74, 143, 145–147 diffusion, 152 doping, 81, 145–147, 174–177, 207, 219–220 electric devices, 215–219 electron spectroscopy, 38–39, 89, 109, 158, 183 enhanced crystallization, 145, 148–150, 182 vaporization, 20, 178–179 induced anisotropy, 171, 180 bond conversion, 145 defect creation, 142 degradation, 160–161, 183 ESR, 124, 165–166 fluidity, 142, 164, 169–170 mid-gap absorption, 166 luminescence, 50, 53, 86–88, 94, 123–128, 130–131, 165–167, 183, 202, 230 fatigue, 165–166 oxidation, 145, 177–178 polymerization, 141, 145, 150–151, 184, 207 surface deposition, 176–177 thermal change, 101, 142, 150, 165 voltage, 128 voltaic effect, 217 Photo-deflection spectroscopy (PDS), 183 Photonics glass, 9–10 Piezo-electricity, 3 Plasma emission spectroscopy, 53 Pn anomaly, 107 Poisson’s ratio, 73 Polaron, 85–86, 88, 90–92, 94, 96, 99, 112, 122–123, 127, 230 Polk model, 30, 53 Polymerization temperature, 15 Positron lifetime spectroscopy, 55 μτ-Product, 218 Q Quantum efficiency, 142, 155, 164, 201 Quasi-equilibrium, 4, 6–7, 30, 41, 65, 68, 195–196 R Radial distribution function (RDF), 34, 37–38, 42, 53 Radiation compaction, 142, 179, 181

242 Radiative recombination, 126 Raman scattering, 38–39, 43, 48–51, 54, 72, 94, 149 γ-Ray, 142–143, 179 Red-shift, 131, 150–151, 153–155, 157, 159–161, 164, 166 Refractive index, 96, 102–105, 142, 146, 150–160, 168, 171, 179–181, 197–198, 200, 203–205, 207 Reverse Monte Carlo method, 43, 54 Reversible photoinduced change, 145–146, 157, 160, 183 Ring, 15, 21, 30, 32, 42–43, 54, 87, 151 S Scalar effect, 171 Scanning tunneling microscopy (STM), 37, 56 Schubweg, 129 Se8 ring, 15 Second-harmonic generation, 3, 6 Self-focusing, 104 Short-range structure, 34–42, 53, 63, 76, 86, 91 Silica glass, 4–5, 50, 56, 64, 91, 142, 180, 198, 200, 202 Single crystal, 3–5, 16, 23, 25, 30, 56, 72, 87, 162 Small-angle x-ray scattering, 54 Solar cell, 2, 5–6, 182, 196, 217–218 Sol-gel, 23, 198 Solid-state battery, 195 Specific heat, 63–66, 71–72 Spin coating, 22 Spinodal decomposition, 55 Sputtering, 17, 20–22, 104, 198 S8 ring, 15 Staebler–Wronski effect, 142, 160, 182–184 Staggered conformation, 42 Stoichiometry, 13–14, 16–17, 21, 41, 46, 51–52, 54, 77, 100–101, 152, 154, 156, 159, 200, 209, 232 Stokes shift, 88, 124, 126–127 Stretched exponential function, 147 Sub-gap light, 147, 155, 163, 166 Supercooling liquid, 3 Super-gap light, 132, 147, 155, 177 T Tauc gap, 85, 97–99, 106, 110, 130, 153, 230 Thermal conductivity, 5, 20, 63–64, 71–72

Subject Index equilibrium state, 4 expansion, 20, 23, 63–64, 144, 170, 173 relaxation, 88, 104, 145, 154–155, 158 spike, 122, 158 Thermopower, 107 Thin-film transistor (TFT), 181, 214 Tight-binding, 114, 152 Time of flight, 78, 107, 132–133 Trans-conformation, 184 Transient photoconductivity, 132–134 Transitory change, 145, 148, 160, 168 Transmittance oscillation, 143–144 Two-photon absorption, 104–105, 205 Two-step absorption, 104–105 U Urbach edge, 99–101, 124, 130, 135, 153, 155, 163–164, 170, 183, 202, 229 energy, 94, 98–100, 108, 130, 230 V Valence alternation pair, 94 van der Waals force, 49 Vector effect, 171–174 VIb glass, 14, 47, 230 Vidicon, 6, 57, 129, 136, 195, 197, 216–217 Viscosity, 63, 66–69, 94–95, 146, 152, 170 Vogel–Tamman–Fulcher equation, 66, 68 W Wavelength division multiplexing (WDM), 198–199, 205, 230 Weak absorption tail, 93, 100–102, 125, 130, 135 Wrong bond, 14, 32–33, 51–52, 93, 102, 167, 181 X Xerographic, 9, 21, 107, 132, 134, 215, 231 X-ray diffraction method, 35 fluorescence spectroscopy, 53 imager, 195, 197, 216–217 photoconduction, 216, 231 X-ray photoelectron spectroscopy (XPS), 39 Y Young’s modulus, 73

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Metastable States in Amorphous Chalcogenide Semiconductors (Springer Series in Materials Science)

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Trap Level Spectroscopy in Amorphous Semiconductors

Semiconductors and Semimetals, Volume 21, Part A: Hydrogenated Amorphous Silicon : Preparation and Structure (Semiconductors and Semimetals)

Semiconducting Chalcogenide Glass III, Volume 80: Applications of Chalcogenide Glasses (Semiconductors and Semimetals)

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

The Materials Science of Semiconductors

The Materials Science of Semiconductors

Fundamentals of Semiconductors: Physics and Materials Properties

Nitride Semiconductors: Handbook on Materials and Devices

Plasma Deposition of Amorphous Silicon-Based Materials (Plasma-Materials Interactions)

Advances in Amorphous Semiconductors (Advances in Condensed Matter Science)

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Domain Structure in Ferroelectrics and Related Materials

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Chalcogenide Photovoltaics

Properties, Processing and Applications of Gallium Nitride and Related Semiconductors

Sharing Publication-Related Data and Materials

Conservation of Leather and Related Materials

Semiconducting Chalcogenide Glass I, Volume 78: Glass Formation, Structure, and Simulated Transformations in Chalcogenide Glasses (Semiconductors and Semimetals)

Semiconducting Chalcogenide Glass II: Properties of Chalcogenide Glasses

Conducting Organic Materials and Devices, Volume 81 (Semiconductors and Semimetals) (Semiconductors and Semimetals)

Semiconductors and Semimetals, Volume 71: Recent Trends in Thermoelectric Materials Research: Part Three (Semiconductors and Semimetals)

Porous Semiconductors: Optical Properties and Applications (Engineering Materials and Processes)

Semiconductors and Semimetals, Volume 70: Recent Trends in Thermoelectric Materials Research, Part Two (Semiconductors and Semimetals)

Semiconductors and Semimetals, Volume 69: Recent Trends in Thermoelectric Materials Research, Part One (Semiconductors and Semimetals)

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