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
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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
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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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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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Appendix: Publications on Related Crystals . . . . . . . . . . . . . . . .
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Material Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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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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This is Blank Page Integra
xiv
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.
1.8
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)
20
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Introduction
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
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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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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
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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 ( 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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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)
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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
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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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Kawaguchi, T., Maruno, S., Elliott, S.R.: Effect of addition of Au on the physical, electrical and optical properties of bulk glassy As2 S3 . J. Appl. Phys. 80, 5625 (1996) Kerner, R., Micoulaut, M.: On the glass transition temperature in covalent glasses. J. Non-Cryst. Solids 210, 298–305 (1997) Kittel, C.: Introduction to Solids State Physics 8th ed. Wiley, New York, NY (2005) Langer, J.S.: Excitation chains at the glass transition. Phys. Rev. Lett. 97, 115704 (2006) Lee, A.L., Wand, A.J.: Microscopic origins of entropy, heat capacity and the glass transition in proteins. Nature 411, 501–504 (2001) Liu, J.Z., Taylor, P.C.: A general structural model for semiconducting glasses. Solid State Commun. 70, 81–85 (1989) Mamedov, S.: On the macromolecular mechanism of dissolution of As2 S3 films in organic solutions. Thin Solid Films 226, 215–218 (1993) Micoulaut, M., Phillips, J.C.: Onset of rigidity in glasses: From random to self-organized networks. J. Non-Cryst. Solids 353, 1732–1740 (2007) Minami, T.: Recent progress in superionic conducting glasses. J. Non-Cryst. Solids 95–96, 107–118 (1987) Mitkova, M., Wang, Yu., Boolchand, P.: Dual chemical role of Ag as an additive in chalcogenide glasses. Phys. Rev. Lett. 83, 3848–3851 (1999) Naumis, G.G.: Variation of the glass transition temperature with rigidity and chemical composition. Phys. Rev. B 73, 172202 (2006) Nemanich, R.J.: Low-frequency inelastic light scattering from chalcogenide glasses and alloys. Phys. Rev. B 16, 1655–1674 (1977) Ngai, K.L.: Meyer-Neldel rule and anti Meyer-Neldel rule of ionic conductivity – Conclusions from the coupling model. Solid State Ionics 105, 231–235 (1998) Novikov, V.N., Sokolov, A.P.: Poisson s ratio and the fragility of glass-forming liquids. Nature 431, 961–963 (2004) Phillips, J.C.: Topology of covalent non-crystalline solids I: Short-range order in chalcogenide alloys. J. Non-Cryst. Solids 34, 153–181 (1979) Phillips, J.C., Kerner, R.: Structure and function of window glass and pyrex. J. Chem. Phys. 128, 174506 (2008) Pohl, R.O., Liu, X., Thompson, E.: Low-temperature thermal conductivity and acoustic attenuation in amorphous solids. Rev. Mod. Phys. 74, 991–1013 (2002) Rau, C., Armand, P., Pradel, A., Varsamis, C.P.E., Kamitsos, E.I., Granier, D., Ibanez, A., Philippot, E.: Mixed cation effect in chalcogenide glasses Rb2 S-Ag2 S-GeS2 . Phys. Rev. B 63, 184204 (2001) Rouxel, T.: Elastic properties and short- to medium-range order in glasses. J. Am. Ceram. Soc. 90, 3019–3039 (2007) Saiter, J.M., Arnoult, M., Grenet, J.: Very long physical ageing in inorganic polymers exemplified by the Gex Se1-x vitreous system. Physica B 355, 370–376 (2005) Salmon, P.S., Liu, J.: The coordination environment of Ag and Cu in ternary chalcogenide glasses. J. Non-Cryst. Solids 205–207, 172–175 (1996) Shimakawa, K., Nitta, S.: Influence of silver additive on electronic and ionic natures in amorphous As2 Se3 . Phys. Rev. B 18, 4348–4354 (1978). Stillinger, F.H.: A topographic view of supercooled liquids and glass formation. Science 267, 1935–1939 (1995) Tanaka, K.: Photodarkening in amorphous As2 S3 and Se under hydrostatic pressure. Phys. Rev. B 30, 4549–4554 (1984) Tanaka, K.: Glass transition of covalent glasses. Solid State Commun. 54, 867–869 (1985) Tanaka, K.: Structural phase transitions in chalcogenide glasses. Phys. Rev. B 39, 1270–1279 (1989) Tanaka, K., Miyamoto, Y., Itoh, M., Bychkov, E.: Ionic conduction in glasses. Phys. Status Solidi (a) 173, 317–322 (1999)
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Thio, T., Monroe, D., Kastner, M.A.: Evidence for thermally generated defects in liquid and glassy As2 Se3 . Phys. Rev. Lett. 52, 667–670 (1984) Thorpe, M.F.: Continuous deformations in random networks. J. Non-Cryst. Solids 57, 355–370 (1983) Tichy, L., Ticha, H.: Covalent bond approach to the glass-transition temperature of chalcogenide glasses. J. Non-Cryst. Solids 189, 141–146 (1995) Tuller, H.L.: Ionic conduction and applications. In: Kasap, S.O., Capper, P. (eds.) Springer Handbook of Electronic and Photonic Materials, Chap. 11, pp. 213–228. Springer, New York, NY (2006) Tverjanovich, A.: Calculation of viscosity of chalcogenide glasses near glass transition temperature from heat capacity or thermal expansion data. J. Non-Cryst. Solids 298, 226–231 (2002) Vateva, E., Skordeva, E., Arsova, D.: Average coordination number dependence of photostructural changes in amorphous Ge-As-S films. Philos. Mag. B 67, 225–235 (1993) Vlasov, Yu.G., Bychkov, E.A.: Ionic and electronic conductivity in the copper-silver-arsenicselenium glasses. Solid State Ionics 14, 329–335 (1984) Vlasov, Yu.G., Bychkov, E.A., Seleznev, B.L.: Compositional dependence of ionic conductivity and diffusion in mixed chalcogen Ag-containing glasses. Solid State Ionics 24, 179–187 (1987) Wang, L.M., Li, Z., Chen, Z., Zhao, Y., Liu, R., Tian, Y.: Glass transition in binary eutectic systems: Best glass-forming composition. J. Phys. Chem. B 114, 12080–12084 (2010) Wang, R.P., Smith, A., Luther-Davies, B., Kokkonen, H., Jackson I.: Observation of two elastic thresholds in Gex Asy Se1-x-y glasses. J. Appl. Phys. 105, 056109 (2009) Wilson, M., Salmon, P.S.: Network topology and the fragility of tetrahedral glass-forming liquids. Phys. Rev. Lett. 103, 157801 (2009) Yang, G., Bureau, B., Rouxel, T., Gueguen, Y., Gulbiten, O., Roiland, C., Soignard, E., Yarger, J.L., Troles, J., Sangleboeuf, J.-C., Lucas, P.: Correlation between structure and physical properties of chalcogenide glasses in the Asx Se1−x system. Phys. Rev. B 82, 195206 (2010) 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) Yu, P., Wang, W.H., Wang, R.J., Lin, S.X., Liu, X.R., Hong, S.M., Bai, H.Y.: Understanding exceptional thermodynamic and kinetic stability of amorphous sulfur obtained by rapid compression. Appl. Phys. Lett. 94, 11910 (2009) Zallen, R.: The Physics of Amorphous Solids. Wiley, New York, NY (1983) Zeller, R.C., Pohl, R.O.: Thermal conductivity and specific heat of noncrystalline solids. Phys. Rev. B 4, 2029–2041 (1971) Zingaro, R.A., Cooper, W.C.: Selenium. Van Nostrand Reinhold Company, New York, NY (1974)
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.
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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.
4.6
Optical Absorption
97
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
4.6
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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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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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 (< 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)
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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
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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)
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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.
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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
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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).
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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
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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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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
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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)
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Photon Effects in Chalcogenide
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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
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(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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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
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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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(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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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)
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(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
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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
