The World Scientific Reference of Amorphous Materials: Structure, Properties, Modeling and Main Applications (Volume 1) 9789811215551, 9789811215568, 9789811215582, 9789811215605

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Materials and Energy Print ISSN: 2335-6596 Online ISSN: 2335-660X Series Editors: Leonard C. Feldman (Rutgers University) Jean-Luc Brédas (King Abdullah University of Science & Technology, Saudi Arabia) Richard A. Haight (IBM Thomas J. Watson Research Ctr, USA) Angus Alexander Rockett (University of Illinois at Urbana-Champaign, USA) Eugene A. Fitzgerald (MIT, USA, Cornell, USA & The Innovation Interface, USA) Gary Brudvig (Yale University, USA) Michael R. Wasielewski (Northwestern University, USA)

Energy and sustainability are keywords driving current science and technology. Concerns about the environment and the supply of fossil fuel have driven researchers to explore technological solutions seeking alternative means of energy supply and storage. New materials and material structures are at the very core of this research endeavor. The search for cleaner, cheaper, smaller and more efficient energy technologies is intimately connected to the discovery and the development of new materials. This collection focuses onmaterials-based solutions to the energy problem through a series of case studies illustrating advances in energy-related materials research. The research studies employ creativity, discovery, rationale design and improvement of the physical and chemical properties of materials leading to new paradigms for competitive energy-production. The challenge tests both our fundamental understanding of material and our ability to manipulate and reconfigure materials into practical and useful configurations. Invariably these materials issues arise at the nano-scale! For electricity generation, dramatic breakthroughs are taking place in the fields of solar cells and fuel cells, the former giving rise to entirely new classes of semiconductors; the latter testing our knowledge of the behavior of ionic transport through a solid medium. Inenergy-storage exciting developments are emerging from the fields of rechargeable batteries and hydrogen storage. On the horizon are breakthroughs in thermoelectrics, high temperature superconductivity, and power generation. Still to emerge are the harnessing of systems that mimic nature, ranging from fusion, as in the sun, to photosynthesis, nature's photovoltaic. All of these approaches represent a body of materials–based research employing the most sophisticated experimental and theoretical techniques dedicated to a commongoal. The aim of this series is to capture these advances, through a collection of volumes authored by leading physicists, chemists, biologists and engineers that represent the forefront of energy-related materials research.

Published Vol. 15

The World Scientific Reference of Amorphous Materials Structure, Properties, Modeling and Main Applications (In 3 Volumes) edited by Alexander V. Kolobov (Herzen State Pedagogical University of Russia, Russia), Koichi Shimakawa (Gifu University, Japan), Ivar E. Reimanis (Colorado School of Mines, USA), Nikolas J. Podraza (University of Toledo, USA) and Robert W. Collins (University of Toledo, USA)

For further details, please visit: http://www.worldscientific.com/series/mae (Continued at the end of the book)

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Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library.

Materials and Energy — Vol. 15 THE WORLD SCIENTIFIC REFERENCE OF AMORPHOUS MATERIALS Structure, Properties, Modeling and Main Applications (In 3 Volumes) Volume 1: Structure, Properties, Modeling and Applications of Amorphous Chalcogenides Volume 2: Structure, Properties and Applications of Oxide Glasses Volume 3: Structure, Properties, and Applications of Tetrahedrally Bonded Thin-Film Amorphous Semiconductors Copyright © 2021 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the publisher.

For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher.

ISBN 978-981-121-555-1 (set_hardcover) ISBN 978-981-121-593-3 (set_ebook for institutions) ISBN 978-981-121-594-0 (set_ebook for individuals) ISBN 978-981-121-556-8 (vol. 1_hardcover) ISBN 978-981-121-557-5 (vol. 1_ebook for institutions) ISBN 978-981-121-558-2 (vol. 2_hardcover) ISBN 978-981-121-559-9 (vol. 2_ebook for institutions) ISBN 978-981-121-560-5 (vol. 3_hardcover) ISBN 978-981-121-561-2 (vol. 3_ebook for institutions) For any available supplementary material, please visit https://www.worldscientific.com/worldscibooks/10.1142/11697#t=suppl Desk Editor: Rhaimie Wahap Typeset by Stallion Press Email: [email protected] Printed in Singapore

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Preface by Editor-in-Chief

Amorphous solids (including glassy and non-crystalline solids) are ubiquitous since the vast majority of solids naturally occurring in our world are amorphous.∗,1 Although this field is diverse and complex, the attached three volume set covers the vast majority of the important concepts needed to understand these materials and their principal practical applications. One volume discusses the most important subset of amorphous insulators, namely oxide glasses; the next two volumes discuss the most important subsets of amorphous semiconductors, namely tetrahedrally coordinated amorphous semiconductors and amorphous and glassy chalcogenides. Together these three volumes provide advanced graduate students, postdoctoral research associates, and researchers wishing to change fields or sub-fields a comprehensive set of theoretical concepts and practical information needed to become conversant in the field of amorphous materials.

∗

The term amorphous does not have a universally accepted scientific definition. In the oxide glass community amorphous materials are defined as those disordered materials not undergoing a glass transition. In this case glasses are a class of materials distinct from amorphous materials. Other scientific communities, including the semiconducting glass community, define amorphous materials as those disordered materials that lack long range periodic order. In this case glasses are a subset of amorphous materials. These discrepancies notwithstanding, the distinction is purely semantic. v

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The topics covered in these three volumes include: • concepts for understanding the structures of amorphous materials, • techniques to characterize the structural, electronic, and optical properties of amorphous materials, • the roles of defects in affecting the electronic and optical properties of amorphous materials, and • the concepts for understanding practical devices and other applications of amorphous materials. Applications discussed in these volumes include transistors, solar cells, displays, bolometers, fibers, non-volatile memories, vidicons, photoresists, and optical disks. The editors of these volumes and the authors of each chapter are internationally-recognized experts in their respective fields. Taken together, these experts cover all the essential aspects needed for researchers entering the field of amorphous materials to succeed. As the editor of this three-volume set, I am indebted to them without whom this endeavor would not have been possible. References 1. Michael Pollak, European Phys. J. 227, 2221–2240 (2019).

P. Craig Taylor Colorado School of Mines 1 March 2020

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Preface by Volume Editors

This volume is dedicated to amorphous chalcogenides, namely, chalcogenide glasses and phase-change alloys. The observation by B. T. Kolomiets and N. A. Goryunova in the mid-1950s of semiconducting properties of chalcogenide glasses opened a new field in the physics of semiconductors: amorphous semiconductors. This discovery was highly unexpected since, until then, is was believed that the presence of the forbidden energy gap, characteristic of semiconductors, was a consequence of the presence of long-range crystalline order, which is, by definition, absent in glasses. Phasechange alloys comprise materials whose properties exhibit a pronounced property contrast between the amorphous and crystalline phases. These materials are widely used in optical memories (from CDs to BluRay discs) and now also in the latest generation of nonvolatile electronic memory recently commercialized by Micron and Intel under the trade name of Optane. The volume consists of three part, where we tried to keep balance between basic and applied aspects of amorphous chalcogenides. In Part I, the fundamental issues of of chalcogenide glasses are described such as glass formation, structure and defects, and also optical and electrical properties, as well as non-thermal lightinduced structural modification (photostructural changes). Theoretical approaches to the study of glasses from first principles are also illustrated.

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In Part II, fundamentals of phase-change alloys are discussed such as specific features of their structure and crystallization process and the resistance drift phenomenon. A dedicated chapter describes pressure-induced amorphization of phase-change materials. Part III is dedicated to applied aspects of amorphous chalcogenides and covers their applications ranging from memory devices to visible and X-ray detectors, from optical nonlinear materials and high-resolution photoresists to chalcogenide photonics. We hope that this book will be useful for graduate students in physics, chemistry, and material science as well as for researchers and engineers working in this field. During years of research in the field of amorphous semiconductors, we immensely benefited from collaboration with many colleagues. In particular, AK is deeply indebted to Profs B. T. Kolomiets and V. M. Lyubin, who introduced him into the field, as well as to S. R. Elliott, H. Fritzsche, Kazunobu Tanaka, P. Fons, J. Tominaga and S. R. Ovshinsky for numerous useful advice, discussions and encouragement. KS acknowledges Kazuo Morigaki and Ted Davis for guidance to the field of disordered materials.

Alexander V. Kolobov Herzen State Pedagogical University of Russia and National Institute of Advanced Industrial Science & Technology, Japan Koichi Shimakawa Gifu University, Japan

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Contents

Preface by Editor-in-Chief

v

Preface by Volume Editors

vii

Part I: Chalcogenide Glasses Chapter 1.

Glass Transition and Relaxation of Chalcogenides: Insight from Structure, Topology, and Rigidity

1

3

Matthieu Micoulaut Chapter 2.

Structure and Defects

51

Koichi Shimakawa and Sandor Kugler Chapter 3.

Modeling of Glasses: Electronic Conduction Mechanisms in GeSe3 :Ag and Al2 O3 :Cu

79

Kashi N. Subedi, Kiran Prasai, and David A. Drabold Chapter 4.

Chalcogenide Glassy Semiconductors: History of Discovery and Research Konstantin D. Tsendin and Nikita A. Bogoslovskiy ix

107

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Chapter 5.

Electronic Structures

125

Keiji Tanaka Chapter 6.

Optical Properties

145

Keiji Tanaka Chapter 7.

Electrical Transport Properties

177

Koichi Shimakawa Chapter 8.

Ionic Conductivity and Tracer Diffusion in Glassy Chalcogenides

203

Igor Alekseev, Daniele Fontanari, Anton Sokolov, Maria Bokova, Mohammad Kassem, and Eugene Bychkov Chapter 9.

Athermal Photoelectronic Effects in Non-Crystalline Chalcogenides: Current Status and Beyond

251

Spyros N. Yannopoulos

Part II: Phase-Change Alloys Chapter 10. Phase-Change Alloys: Structural Aspects

321 323

Paul Fons and Alexander V. Kolobov Chapter 11. Drift Phenomena in Phase Change Memories

341

Daniele Ielmini Chapter 12. Crystallization of Phase-Change Chalcogenides

367

Jiri Orava, Tae Hoon Lee, Stephen R. Elliott, and A. Lindsay Greer Chapter 13. Pressure-Induced Amorphization Milos Krbal

403

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Contents

Part III: Applications Chapter 14. Optical Non-linearities in Chalcogenide Glasses and Their Applications

xi

431 433

Abdolnasser Zakery and Stephen R. Elliott Chapter 15. Phase Change Material Photonics

487

Robert E. Simpson and Tun Cao Chapter 16. X-Ray Photoconductivity of Stabilized Amorphous Selenium

519

Safa Kasap Chapter 17. High-Gain Avalanche Rushing Pickup Tube

539

Kenkichi Tanioka Chapter 18. Metal-Doped Chalcogenides

593

Tomas Wagner, Bo Zhang, Max Fraenkl, Silvya Valkova, Radim Vala, and Tomas Hrbek Chapter 19. High-Resolution Photoresists

651

Karel Palka, Stanislav Slang, and Miroslav Vlcek Chapter 20. Phase Change Materials for Optical Disc and Display Applications

681

Yuta Saito, Kotaro Makino, and Paul Fons Chapter 21. Non-Volatile Memory

713

Paolo Fantini Index

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b2530   International Strategic Relations and China’s National Security: World at the Crossroads

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b2530   International Strategic Relations and China’s National Security: World at the Crossroads

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CHAPTER 1

Glass Transition and Relaxation of Chalcogenides: Insight from Structure, Topology, and Rigidity Matthieu Micoulaut Laboratoire de Physique Th´eorique de la Mati`ere Condens´ee, Sorbonne Universit´e, Paris

1.1. Introduction Appropriate mixtures of Group III, IV, and V elements (e.g., silicon, arsenic, germanium, . . .) with chalcogens (sulphur, selenium, tellurium) permit to form glasses over extended ranges in composition by cross-linking the chalcogen chain-like structure. This leads to a network that is imposed at the very local level by building blocks typical of a short range order [1], for example, the GeSe4/2 tetrahedron in GeSe2 . The disordered arrangement of such building blocks on longer scales is then representative of glasses, which form a cross-linked network of chemical bonds. An appropriate alloying of such components permits one to tune dynamic quantities of glass-forming liquids in a nearly systematic fashion, allowing for the detection of anomalies, which provide an increased insight into the glass transition phenomenon that proceeds 3

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as follows. When the crystallization point at the temperature Tm has been avoided, liquids become “supercooled,” which represents a thermodynamic metastable state with respect to the corresponding crystal. Upon further cooling, the relaxation time τ to equilibrium and the viscosity η continue to increase and reach η = 1012 Pa.s at a reference temperature that is defined in the literature as the glass transition temperature Tg . Below this temperature, the material displays all the typical macroscopic features of a solid. Timescales are dramatically increased and corresponding relaxation times are of the order of τ  100s–1000s, so that glasses are usually considered as being “out of equilibrium” given that the system timescale now exceed the experimental timescale. There is still, however, some thermal evolution toward equilibrium although it can be only partially accessed because properties of a glass evolve slowly with time, and measurements will depend on the waiting time at which they have begun, a phenomenon known as “ageing.” Although such dynamic quantities remain almost continuous across the glass transition, rapid changes in some physical, thermal, rheological, mechanical and so on properties are observed across Tg , and these induce important variations in heat capacity, thermal expansion coefficient, and/or viscoelastic properties. In this chapter, experimental and theoretical methods for the characterization of glassy relaxation in chalcogenides are reviewed. Here, the role of structure, as in many other network-forming glasses appears to be central as in many other glass-forming liquids. While structural properties control, indeed, a large part of the dynamics and the relaxation phenomena taking place in the vicinity of the glass transition, chalcogenides display the unique property to be formed over extended ranges in composition, and contain quasimolecular defects, which are believed to play a crucial role in their increased glass-forming tendency [2, 3]. These extended glassforming domains permit to obtain trends in relaxation properties and this provides clues for an increased understanding of the salient features of the glass transition. In addition, such systems undergo subtle changes in network properties that can be characterized using simple minded albeit powerful approaches, which build on the

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notion of network rigidity. This has stimulated a certain number of important contributions in the recent years. 1.2. Viscosity Change and Fragility 1.2.1. Viscosity Plots The evolution of viscosity (η) (or relaxation time (τα )) is certainly one of the most spectacular observed changes as the melt is cooled down to its glass transition. In Fig. 1.1(a) represented the evolution of the viscosity with temperature for select chalcogenide liquids (selenium, GeSe4 , and As2 Se3 ), which can be compared to other prototypal glass-forming liquids including organic materials (o-terphenyl [OTP]) or silica. When compared to such organic liquids, the behavior of chalcogenides appears to be more moderate, although similar viscosities (1012 Pa.s) are obtained at the reference temperature Tg that is

12 SiO2 As2Se3

log10η (Pa.s)

10

Gese4 Se OTP

8 6

12

Ge10Se90

10

Ge20Se80 Ge22Se78

10

8

Ge25Se75 Ge33Se67

8

6

MD (diffusion) MD (viscosity)

6

4

4

4

2

2

2

0

0

0

-2

-2

-2

-4 0

500 1000 1500 2000

0

0.2

0.4

0.6

0.8

-4 1 0.2

0.4

0.6

T (K)

Tg/T

Tg/T

(a)

(b)

(c)

0.8

log10 η (Pa.s)

12

-4 1

Fig. 1.1. (a) Behavior of the liquid viscosity η of different supercooled liquids as a function of temperature. (b) Uhlmann–Angell plot rescaling the same data with respect to Tg /T where Tg is defined by η(Tg ) = 1012 Pa.s. Data taken from [4–6]. (c) Viscosity behavior in a given family of chalcogenides showing the strong dependence on composition. Data from [5, 7, 8]. Experimental data can eventually be compared to a direct molecular dynamics calculation of e.g., GeSe2 using the Green–Kubo formalism of viscosity [9] or extracted from diffusivity calculations [10]. Such data can then be fitted using appropriate functionals.

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usually found to be somewhat higher than the one of organic glass-forming liquids. This temperature usually serves to rescale the viscosity data in an appropriate plot [11, 12]. In this plot, the inverse temperature is rescaled with respect to this reference Tg at which the liquid reaches 1012 Pa.s, and the same viscosity data of Fig. 1.1(a) are now shown in Fig. 1.1(b). The latter reveals that certain liquids such as silica follow an Arrhenius law of the form η = η∞ exp[EA /T ], whereas other liquids now exhibit a viscosity evolution that shows an important bending [5] at intermediate values of Tg /T , the most pronounced curvature being obtained for organic glass formers (e.g., OTP) that can be parametrized with a super-Arrhenius functional η = η∞ exp[EA (T )/T ] and a temperature dependent activation energy EA (T ) allowing for a nonlinear behavior of η in this representation. In chalcogenides, the viscosity dependence itself is strongly dependent on temperature and composition, as exemplified for the case of Ge–Se liquids, which have probably received most attention (Fig. 1.1(c)), and important variations can be found between GeSe2 and GeSe4 , or even pure selenium. A simple way to characterize the viscosity behavior is provided by the “strong” versus “fragile” classification which uses a “fragility index” M, which is defined by the slope of log η(T ) (or relaxation time given that one has η = G∞ τ with G∞ the infinite frequency bulk modulus) versus Tg /T at Tg :   d log10 η (1.1) M≡ dTg /T T =Tg From Fig. 1.1(b), one realizes that large slopes (i.e., large M) will, indeed, correspond to so-called “fragile” glass formers displaying an important curvature, a temperature dependent activation energy EA (T ) and a rapid evolution of η as one approaches Tg , while small M values will correspond to so-called “strong” glass formers having a nearly Arrhenius variation and a temperature independent activation energy EA for viscous flow. Once examined over a wide variety of glass chalcogenide liquids, M is found to vary between 90 and 129

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for Ge2 Sb2 Te5 [13, 14] to a low value of 14.8 for the network-forming liquid Ge22 Se78 [15], the largest fragility being measured for a polymer (M = 214), and M = 20 being reported for the canonical example of silica [16]. 1.2.2. Useful Mathematical Forms A useful mathematical form describing appropriately the temperature dependence of viscosity data is given by the Vogel–Tammann– Fulcher (VFT) equation [17]: log10 η = log10 η∞ +

A , T − T0

(1.2)

where A has the dimension of an activation energy, and T0 a reference temperature that leads to an Arrhenius behavior for T0 = 0. Another more recent mathematical form is due to Mauro and coworkers [18] and provides a viscosity model (MYEGA) that permits an accurate prediction of the viscosity, especially at high temperature:   C K exp . (1.3) log10 η = log10 η∞ + T T An alternative and maybe more insightful form of the VFT Eq. (1.2) using explicitely the fragility and the glass transition temperature Tg writes: log10 η(T ) = log10 η∞ +

(12 − log10 η∞ )2 . (1.4) M(T /Tg − 1) + (12 − log10 η∞ )

From Eq. (1.2), one realizes that for T = T0 < Tg , the viscosity can become infinite, and this might indicate a possible phase transition that cannot be attained. Note that the MYEGA Eq. (1.3) avoids this VFT divergence at low temperature. In a systematic study on Ge–Se liquids, it was shown that a VFT fit of viscosities leads to a temperature T0 that is minimum for 22% Ge [19], that is, at the same composition at which a fragility minimum has been measured [15]. The region of T < Tg might have another characteristic albeit unattainable temperature that is known in the literature as the Kauzmann temperature TK [20], a temperature at which the excess

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entropy of the liquid with respect to the corresponding crystal is supposed to vanish. While this “entropy crisis” is rather counterintuituive given that one does not expect to have the entropy of a glass becoming lower than the one of the corresponding crystal, there is no indication that the behavior of the entropy extrapolates to zero at some finite temperature given the slowing down of the dynamics and the divergence of the timescale for equilibrium measurements. Another interesting and insightful link between the configurational entropy of the liquid and the relaxation (or viscosity) has been suggested by Adam and Gibbs [21] and has turned out to be very useful for the description of topological constraints in chalcogenides, as discussed below:   A . (1.5) η = η∞ exp T Sc Equation (1.5) provides an important connection between a kinetic and a thermodynamic viewpoint of the glass transition. Here, the configurational entropy variation with decreasing temperature is believed to result from the reduction of the number of possible minima in the complex energy landscape [22] characterizing the material. The slowing down of the relaxation and the dramatic increase of τ with decreasing T then result from the reduced ability of the system to explore the landscape in order to locate the energy minimum, driven by the strong reduction of the number of accessible energy minima. Ultimately, structural arrest might occur, and since for an ideal glass at T = TK , one has a single energy minimum only, the configurational entropy vanishes and the relaxation time diverges. 1.3. Other Signatures of Glassy Relaxation 1.3.1. Calorimetric Signatures The changes occurring at the glass transition and subsequent signatures for relaxation can be detected and measured from thermal changes. Given that equilibration cannot proceed further on experimental timescales due to the rapid increase of the relaxation

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time, volume, or enthalpy curves deviate from their high temperature equilibrium line as T  Tg , with Tg depending on the cooling rate of the liquid. A faster cooling rate will lead to a higher glass transition temperature, whereas a lower cooling rate will allow for equilibration to lower temperatures so that Tg decreases with the cooling rate. As both enthalpy and volume display a different slope below or above Tg , their derivative with respect to temperature (heat capacity, thermal expansion) will lead to an abrupt change with a nearly step-like change across Tg that can be measured as a function of the cooling rate. When reheated from low temperature, the glass will relax to a lower energy state leading to lower volumes or lower enthalpies. This leads to enthalpy/volume curves upon reheating, which are markedly different from the cooling curve. Differential scanning calorimetry (DSC) permits to track such relaxation effects, and when the heat flow is measured during an upscan a hysteresis loop appears, causing a heat capacity overshoot at the glass transition (H˙ T in Fig. 1.2(a)). This endothermic peak simply reveals that previously frozen degrees of freedom during the quench are now excited, so that the overshoot is a direct manifestation of the relaxation taking place between the laboratory temperature and Tg . Such measurements also depend substantially on the heating rate q of the upscan, and the measured glass transition temperature can be embedded in simple dependence known as the phenomenological Kissinger equation [32]: d ln(q/Tg2 ) EA =− , d(1/Tg ) R

(1.6)

or, alternatively, the Moynihan equation [33]: EA d ln q =− . d(1/Tg ) R

(1.7)

Note that under the assumption that the activation energy involved in Eqs. (1.6) and (1.7) is the same as the one involved in the Arrhenius relaxation of the viscous flow, a measurement of Tg at different scan rates q leads to a determination of the fragility for strong

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2

-1 -1

Heat Flow Rate [mcal.g s ]

Mauro et al.

8

.

HT 6

4

2

0

Naumis

Ge-Se Si-Se Si-Te Ge-Te Ge-S

. H

1.6

Tg

rev

.

1.8

1.4

Micoulaut

Hnr

1.2

Glass transition temperature Tg/T0

10

1

340

360

380

400

0

10

20

30

T (K)

Composition (%)

(a)

(b)

40

Fig. 1.2. (a) Calorimetric scan of a As45 Se55 glass showing the deconvolution of the total heat flow H˙ tot accessed from differential scanning calorimetry (DSC) (adapted from [23]). This component can be decomposed into a reversing (H˙ rev ) and non-reversing part (H˙ nr ) when the modulated DSC (mDSC) technique is employed. The area between the setup baseline and H˙ nr permits one to define a non-reversing enthalpy ΔHnr (shaded area). (b) The inflection point of the DSC signal usually serves to determine Tg , which can be examined as a function of chalcogen composition. Tg follows either a moderate linear increase with composition (Ge–Te [24] or Si–Te [25]) or non-linear variations (Ge–Se [26], Ge–S [27], Si–Se [28] that can be accurately modelled (curves, [29–31]). The anomalous behavior of Ge–S (red circles) is linked with sulfur segregation at low modified content [27].

glass formers via M = EA ln10 2/RTg using Eq. (1.1), such as for Ge–As–Se [51]. Note that an improved technique, modulated DSC (mDSC), superposes a sinusoidal variation on the usual linear DSC ramp. In direct space, this technique permits to deconvolute [35, 36] the total heat flow (H˙ tot ) into a reversing and a non-reversing component. The reversing component (H˙ rev ) tracks the temperature modulation at the same frequency ω while the difference term (denamed as nonreversing), H˙ nr = H˙ tot − H˙ rev does not, and captures most of the kinetic events associated with the slowing down of the relaxation close to the glass transition (Fig. 1.2). These are embedded in a

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non-reversing enthalpy ΔHnr (Fig. 1.2) that can be analyzed as function of composition or thermal conditions. 1.3.2. Stress and Calorimetric Relaxation Due to the high quenching rates and the inability to relax to some equilibrium positions once T < Tg , glasses exhibit residual frozen stresses. The associated stress relaxation therefore represents an interesting phenomenon that can be used to probe the dynamics in the glass transition region [37, 38]. In practice, stress (σ(t)) is analyzed as function of time, and a relaxation function Φ(t) can be related to the relaxation modulus G(t) = σ(t)/0 and its initial value G(0) when the strain 0 is imposed at t = 0 (Fig. 1.3). In chalcogenides, experiments have shown that such measured relaxation functions Φ(t) can be conveniently fitted with a stretched Kohlrausch–Williams–Watts (KWW) exponential exp[−(t/τ )β ] that seem to decay to zero at t → ∞. Measurements using different methods have been made on for example, Ge–Se [39–41], Te–As– Ge [42], As–Ge–Se [43], and can be related to structural aspects.

0,8

Relaxation function φ(t)

Te-As-Ge 0,6

GeSe4

Ge3Se17

0,4

0,2 GeSe9 0

1

10

100

1000

Time (days)

Fig. 1.3. Relaxation function Φ(t) in Ge–Se and Te–As–Ge glasses from stress relaxation measurements [39]. Lines represent fits using a stretched exponential exp[−(t/τ )β ] function.

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They also reveal that a significant part of the stress does not release on experimental timescales (months) in certain compositions for given systems (e.g., GeSe4 in Ge–Se [39]). For chalcogen-rich glasses, an interesting perspective is provided by the comparison with the generic behavior of organic polymers [44] since amorphous (Se, S) can be considered as glassy polymers made of long chains that are progressively cross-linked by the addition of alloying elements. Stress relaxation is also thought to have some impact on the resistance drift phenomena [45] that is crucial for the functionalities of heavier chalcogenides such as amorphous phase change tellurides (Ge2 Sb2 Te5 ). Calorimetric relaxation can be also accessed from mDSC experiments analyzed in Fourier space, and in this case the imaginary part of the heat capacity, Cp∗ (iω), is seen as a complex response function, similarly to the dielectric permittivity ∗ (iω) in dielectric relaxation measurements [46]. The decomposition of the complex Cp∗ (ω) into real (in-phase) and imaginary (out-of-phase) parts leads to curves, which have the characteristic forms of the complex susceptibility of a relaxation process (Fig. 1.4(a)). In particular, for a given temperature the imaginary part Cp peaks at a frequency ωmax τ = 1, which permits to access to the relaxation time with thermodynamic conditions (T , composition). This calorimetric method was shown to lead to similar results regarding τ (T ) and fragility when compared to dielectric measurements [47]. When such determined relaxation times τ = 1/ωmax are represented in an Arrhenius plot close to the glass transition, the T dependence of τ (T ) permits determining the fragility (Fig. 1.4(b)) using Eq. (1.1). 1.3.3. Link with Structure and Composition The fragility index M is obviously also linked to structural properties, which are modified by composition. Figure 1.5(a) shows the behavior of M of different binary chalcogenides, which indicate that relaxation depends strongly on the modifier content. Here, the anomalous trend (i.e., the fragility minimum) is linked with aspects of rigidity, as discussed below. An alternative viewpoint brings up the role of chemical order [51], and especially the deviation from

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(a)

(b)

Fig. 1.4. (a) An example of in-phase and out-of-phase components of complex Cp from modulated-DSC scans as a function of modulation frequency (1/tm ) for Ge10 Se90 [15]. (b) Log of relaxation time (τ ) as a function of Tg /T yielding fragility for enthalpic relaxation, m, and activation energy Ea from the slope of the Arrhenius plots at indicated compositions (10%, 22%, and 26%).

stoichiometry, and it is suggested that fragility does not follow predictions from rigidity percolation, but instead correlates with structural dimensionality. Specifically for the ternary As–Ge–Se liquids, a minimum in M is claimed to be associated with a maximum in structural heterogeneity consisting of appropriate ratios of Se-chains and GeSe4/2 tetrahedra. Such correlations are, however, contradicted

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Fragility M

30

Ge-S Ge-Se As-Se

mDSC viscosity mDSC (homogeneity controlled)

50

AsxSe100-x

25 40

30

20

20 15 10 20 30 Composition (%) (a)

40

0

10

20 30 40 Composition (%) (b)

50

Fig. 1.5. (a) Fragility dependence in select binary chalcogenides showing the evolution with composition in Ge–Se [15], Ge–S [27], and As–Se glasses [48]. (b) Fragility depending on measurement method [49] and sample preparation method [48, 50].

by an early work of Angell and collaborators emphasizing the connection between topology/rigidity and the fragility index in the same chalcogenide liquid [6]). The correlation with chemical order is also debated by different authors who have evidenced the link between fragility and relaxation minima and isostatic compositions [10, 15, 27, 48, 52], that is, compositions that are close to the rigidity percolation threshold. The link between topology and fragility is also detected from the investigation of ionic diffusion on a series of ironbearing alkali-alkaline earth silicate glasses [53]. For the specific case of As–Se melts, Fig. 1.5(b) now exemplifies that aspects of sample preparation modify the value of the measured fragility index. While the global trend with As content remains the same for all studies, a careful investigation [54] of the effect of melt homogeneity on the measurement of M shows, furthermore, that inhomogeneous melts can lead to a spread in measurements and fragility indexes that are somewhat larger than those determined from carefully homogeneity controlled melts. The situation appears

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to be especially met for strong liquids having the highest viscosities (e.g., GeSe4 ), and the smallest fragilities. A universal fragility scaling with network connectivity has been proposed by Sidebottom [55]. A two-state model for the glass transition separating the intact bond state from a thermally excited broken bond state leads to a fragility index M behavior that is determined solely by the entropy increase. From bonds between atomic species [56], the construction can be generalized via a coarse-graining approach to bonds between local structures or even bonds between intermediate range order (IRO) structures. A generic behavior of the index M is then obtained (Fig. 1.6(a)), which demonstrates a universal dependence of the glass-forming fragility on the topological connectivity of the network. In a more quantitative fashion, the investigation of Nuclear Magnetic Resonance (NMR) spectra as a function of temperature

Fragility M

80

60

Ultraphosphates Aluminophosphates Lithium borates Sodium borates Chalcogenides

40

20 2 2.2 2.4 2.6 2.8 3 Atomic or IRO connectivity

(a)

Se-Se-Se peak width (ppm)

300

r < 2.34

250 200 150

r > 2.40 100 50 0

0.7 0.8 0.9

1

1.1 1.2 1.3

T/Tg (b)

Fig. 1.6. (a) Fragility scaling [55] of various network-forming liquids as a function of connectivity (mean coordination number r¯ or mean local connectivity or mean intermediate range order connectivity. (b) Full width at half maximum of a 77 Se Nuclear Magnetic Resonance (NMR) resonance associated with Se–Se–Se chains as a function of temperature in Gex Se1−x glass-forming liquids [57]. Systems have been separated into subclasses satisfying r¯ = 2 + 2x ≥ 2.4 or r¯ ≤ 2.34. Here, r¯ = 2.4 represents the rigidity pecolation threshold [58] (see below).

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and/or composition also permits accessing properties of relaxation with network connectedness [59]. The typical time T1 of spin– lattice relaxation (SLR) can be used to link the dynamics of certain chalcogenide structural fragments resolved by NMR with timescales that can be related with T1 . This time is, indeed, associated with the mechanism that couples the equilibration of magnetization for a given linewidth (i.e., a local structure) with the effect of the (lattice) neighborhood. In the liquid state, the evolution with temperature of the NMR linewidth characteristics (e.g., full width at half maximum) provides direct indication of how structural fragments relate to the thermal evolution with time and temperature. Linewidths are, indeed, expected to narrow upon temperature increase and since such linewidths can be associated with specific structural features or species, one can have access to aspects of relaxation. In the glassy state, applications to binary Ge–Se have shown that such SLR time are significantly smaller for Se–Se–Se chain environments (10−9 s) as compared to Ge–Se–Ge fragments (10−6 s, [60, 61]). This seems to be consistent with the fact that these chains are mechanically flexible, and lead to an enhanced ease to relaxation [57] that is also driven by composition (Fig. 1.6(b)).

1.3.4. Network Connectivity and Glass Transition Temperature The glass transition temperature is also strongly dependent on the composition and structure (Fig. 1.2(b)) and a certain number of relationships with network connectivity have been proposed in the literature. There is, indeed, much to learn from the evolution of Tg with connectivity. Besides thermodynamic or vibrational factors such as the wellknown “two-third rule” stating that Tg scales as 2/3Tm [20], there are, in fact, structural factors, and, in particular aspects of network connectivity or network mean coordination number r¯, which influence the value of Tg . One of the first quantitative relationships has been derived by Varshneya and coworkers [62, 63] using a modified Gibbs– Di Marzio equation [64] initially proposed for cross-linked polymers.

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Here cross-links are supposed to be associated with for example, Ge atoms whereas the polymer is supposed to be represented by the chalcogen chains: r) = Tg (¯

Tg (¯ r = 2) , 1 − β(¯ r − 2)

(1.8)

with the parameter β depending on the coordination number rB of the cross-links (Ge, Si) [30, 65]: r  1 B = (rB − 2) ln . (1.9) β 2 The prediction of Tg in multicomponent chalcogenide glass systems can be obtained in most of binary chalcogenides. Using stochastic agglomeration of basic local structures representative of the glass [30, 66], a parameter-free analytical Tg prediction for binary Ax B1−x and ternary glasses has been established that seems to be satisfied in the low modified regime (x ≤ 10%) for a variety of chalcogenide glasses (broken line, Fig. 1.2(b)). In the binary A1−x Bx , the slope at zero modification has a particular simple form:   Tg (x = 0) dTg T   = 0 , = (1.10) dx x=0 ln rrBA ln rrBA where rB and rA = 2 (chalcogen) are the coordination numbers of the atoms or species B and A, respectively, acting as local building blocks of the glass structure. For a ternary system, a parameter-free relationship between Tg and the network mean coordination number r¯ can be also derived on the same basis [67]. Using the general relationship:  kB T ∞ g(ω) dω, (1.11) r 2 (t) = m 0 ω2 with g(ω) the vibrational density of states and the mean-square displacement r 2 (t), Naumis has derived from the Lindemann criterion of solidification a relationship between the network mean coordination number and the glass transition temperature [31]. The glass transition temperature can then be predicted as a function of

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composition (solid line in Fig. 1.2(b)). While such analytical models emphasize the central role played by network connectivity on Tg variation, the results actually help in decoding further anomalies such as Tg extrema measured in for example, Ge–Se [26] or As–Se glasses [68]. Given that the glass transition temperature is, indeed, an intrinsic measure of network connectivity, these Tg maxima have been interpreted as the manifestation of nanoscale phase separation that is driven by broken chemical order [68, 69] in stoichiometric GeSe2 and As2 Se3 . Such effects are believed to lead to a reduction of the network connectivity at compositions where a Tg maximum is measured. 1.4. Rigidity Theory of Network Glasses There is an attractive way to analyze and predict relaxation and glass transition of network glasses using rigidity theory (or topological constraint theory). Historically, glassy chalcogenides have served as test materials for the verification of the theoretical predictions. The concept of rigidity in glasses [70], pressurized amorphous networks [71] or sphere packing [72] traces back to the early work of Maxwell on the stability of trusses and macroscopic structures such as bridges, and to the introduction of mechanical constraints by Lagrange. These ideas and results were then extended to atomic networks by Phillips who highlighted the notion of mechanical isostaticity as promoting glass-forming tendency of covalent alloys [73]. Specifically, it was recognized that so-called “good” glass formers usually form at an optimal network connectivity or mean coordination number r¯ = r¯c satisfying the Maxwell stability criterion of isostatic structures, that is, nc = nd , where nc is the atomic constraint density arising from interactions, and nd is the dimensionality in which the network is embedded, usually nd = 3 in 3D. 1.4.1. Zero Temperature Mean-Field Approach Assuming that in covalent disorderd networks, the dominant interactions are near-neighbor bond-stretching (BS) and next-near-neighbor bond-bending (BB) forces, the number of constraints per atom can

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be exactly computed in a mean-field way, and is given by:  r r≥2 nr [ 2 + 2r − 3]  , nc = r≥2 nr

19

(1.12)

where nr is the concentration of species being r-fold coordinated. The contribution of the two terms in the numerator is obvious because each bond is shared by two neighbors, and one has r/2 BS constraints for an r-fold atom. For BB (angular) constraints, one notices that a two-fold atom involves only one angle, and each additional bond needs the definition of two more angles, leading to the estimate of (2r − 3). For one-fold terminal atoms (chalcohalides), a special count is achieved as no BB constraints are involved for the halogens [74], and in certain situations, some constraints may be ineffective [75]. By defining the network mean coordination number r¯ of the network by:  r≥2 rnr , (1.13) r¯ =  r≥2 nr one can reduce (1.12) to the simple equation: nc =

r¯ + 2¯ r − 3. 2

(1.14)

Applying the Maxwell stability criterion, isostatic glasses (nc = 3) are expected to be found at the magic average coordination number [73] of r¯ = 12/5 = 2.40 in 3D, corresponding usually to a nonstoichiometric composition where glass-forming tendency has been found to be optimized experimentally [76, 77]. Note that for Ge–Se binary, the isostatic condition applies for GeSe4 because one has r¯ = 2(1 − x) + 4rGe = 2 + 5x = 2.4 for x = 20%. The locus of isostatic stability actually coincides with the presence of an elastic phase transition at zero temperature. This has been revealed from the vibrational analysis of bond-depleted random networks constrained by harmonic BB and BS interactions [58]. At the transition (¯ r = 2.38 [78]), the density of zero frequency (floppy) modes f (i.e., the eigenmodes of a dynamical matrix) vanishes and rigidity percolates for an increased network connectivity. The Maxwell condition nc = nd therefore also defines a mechanical

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stiffness transition, an elastic phase transition, above which redundant constraints produce internally stressed networks, identified with a stressed-rigid phase [78, 79]. Here, r¯ acts as the control parameter for the transition as does the temperature in a ferromagnetic phase transition, and the floppy mode density f is the control parameter. For nc < nd however, floppy modes can proliferate, and these lead to a flexible phase where local deformations with a low cost in energy (typically 5 meV [80]) are possible, their density being exactly given by: f = 3 − nc [78]. There have been numerous experimental validations of this peculiar transition from for example, Raman scattering [81], stress relaxation [82], viscosity measurements [6], vibrational density of states [80], Brillouin scattering [83], Lamb–Mossbauer factors [76], resistivity [84], and Kohlrausch exponents [6, 82, 85]. For a full account of experimental probes and early verification of rigidity theory, readers should refer to books devoted to the subject [19, 86, 87]. 1.4.2. Rigidity Hamiltonians Although constraint or rigidity theory provides an interesting framework to understand many physical features induced by changes in composition, the lack of thermodynamics in early applications has been a serious drawback. The enumeration of bonding constraints in Eq. (1.12) is, indeed, performed on a fully connected network at zero temperature with infinite energy barriers for bonds or constraints breaking (see however [88]), and absence of the effect of structural relaxation. The use of the initial theory [58, 73, 78] may be valid as long as one is considering strong covalent bonds or when the viscosity η is very large at T < Tg , given that η is proportional to the bonding fraction, but Eq. (1.12) is obviously not valid in a high temperature liquid. However, NMR studies have partially addressed this issue and have shown that glassy relaxation at T  Tg and related relaxational phenomena in Ge–Se supercooled liquids can be understood from a low temperature rigidity concept, thus extendeding the glass approach to the liquid state with confidence [57]. The same argument has been used for the analysis of Ge–As–Se liquids [6].

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Naumis and coworkers [89, 90] have pointed out that the fraction of cyclic variables in phase space are identified with the fraction of floppy modes f = 3 − nc because when one of these variables is changed, the system will display a change in energy that is negligible. This means that in the simplest model for network atomic vibrations in the harmonic approximation [90], the Hamiltonian can be given by: 3N (1−f ) 3N   1 Pj2 + mωj2 Q2j , H= 2m 2 j=1

(1.15)

j=1

where Qj (position) and Pj (momentum) are the j-th normal mode coordinates in phase space, and ωj is the corresponding eigenfrequency of each normal mode. Since it is assumed that floppy modes have a zero frequency, they will not contribute to the energy so that the sum over coordinates runs only up to 3N (1 − f ), the floppy modes providing a channel in the energy landscape between two local minima of the Hamiltonian. Equation (1.15) then serves as a starting point for the statistical mechanics derivation of various thermodynamic quantities [89] influenced by the degree of rigidity. The partition function derived from Eq. (1.15) leads to a free energy F and the specific heat can be calculated [90], both depending on the density of floppy modes: 

3N (1−f ) 2πmkB T 2πkB T kT  3N kB T ln ln − , (1.16) F =− 2 2 h2 2 mω j j=1 Cv = 3N kB −

3N kB f, 2

(1.17)

the latter expression indicating, furthermore, that the specific heat in such model systems corresponds to the Dulong–Petit value that is decreased by a floppy mode contribution. As the variables associated with f are cyclic variables of the Hamiltonian, the energy of the system does not depend upon a change in a floppy mode coordinate and for a given local minimum characterized by ωj , the number of channels is proportional to f , which increases the available phase

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space allowed to be visited. Consequently, the number of accessible states Ω(E, V, N ) can be calculated in the microcanonical ensemble, and using the Boltzmann relation Sc = kB ln Ω(E, V, N ), one finds that the configurational entropy provided by the channels in the landscape is simply given by: Sc = f N kB ln V.

(1.18)

The link between floppy modes and configurational entropy has been also investigated from simulations. From a short range square potential, the basin free energy of a potential energy landscape has been determined [91], and it can be separated into a vibrational and a floppy mode component, allowing for an estimate of the contribution of flexibility to the dynamics, and for this particular class of potentials it has been found that Sc scales as f 3 . 1.4.3. Temperature Dependent Constraints Building on this connection between floppy modes and the configurational entropy Sc (Eq. (1.18)), Gupta and Mauro have extended topological constraint counting to account explicitely for temperature effects [29]. Here, a two-state thermodynamic function q(T ) quantifies the number of rigid constraints as a function of temperature. One has two obvious limits because all relevant constraints can be either intact at low temperature (q(T ) = 1) as in the initial T = 0 theory [58, 73] or entirely broken (q(∞) = 0) at high temperature. At a finite temperature however, only a fraction of these constraints can become rigid once their associated energy is less than kB T . This modifies Eq. (1.12) which becomes:  r r r r≥2 nr [qα (T ) 2 + qβ (T )(2r − 3)]  , (1.19) nc (T ) = r≥2 nr where qrα (T ) and qrβ (T ) are step functions associated with BS and BB interactions of an r-coordinated atom, respectively, so that nc now explicitely depends on temperature. Different forms can be proposed for q(T ) among which a function based an energy landscape

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approach [92]: q(T ) = (1 − exp(−Δ/T ))νtobs ,

(1.20)

ν being the attempt frequency and tobs the observation time, the behavior of q(T ) being also directly computed from molecular dynamics (MD) simulations [94, 129]. A certain number of thermal and relaxation properties of network glass-forming liquids can now be determined, and a simple step-like function (i.e., for νtobs → ∞) with an onset temperature Tα for various constraints leads to analytical expressions for fragility and glass transition temperature that are essentially derived for multicomponent oxide glasses [95–98]. In order to get such analytical expressions, two central assumptions are necessary. First, it is considered that the Adam–Gibbs model for viscosity (Eq. (1.5)), η = η∞ exp(A/T Sc ), holds in the temperature range under consideration, and that the corresponding barrier height A is a slowly varying function with composition. This means that only the configurational entropy Sc will contain the temperature and composition dependence. Secondly, it is assumed that the Naumis Eq. (1.18) relating the configurational entropy to topological degrees of freedom (floppy mode density) is valid. A strong support to the latter is given by a test of the MYEGA viscosity modelling curve (Eq. (1.3)), which uses these two basic assumptions and has been verified with success over more than a hundred of different glassforming liquids [18]. By furthermore stating that Tg is a reference temperature at which η(Tg (x), x) = 1012 Pa.s for any composition, Eqs. (1.5) and (1.18) can be used to write: Sc (Tg (xR ), xR ) f (Tg (xR ), xR ) 3 − nc (Tg (xR ), xR ) Tg (x) = = = , Tg (xR ) Sc (Tg (x), x) f (Tg (x), x) 3 − nc (Tg (x), x) (1.21) and Tg (x) can be determined with composition x from a reference compound having a composition xR and a glass transition Tg (xR ), knowing the number of topological degrees of freedom (i.e., 3 − nc ) for compositions x and xR , and the behavior of the step functions q(T ).

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Using the expression for Sc (Tg (x), x) in Eq. (1.21), and the definition of fragility (Eq. (1.1)), one can furthermore extract an expression for the fragility index M as a function of composition: 

∂ ln Sc (T, x)

M(x) = M0 1 +

∂ ln T T =Tg (x) 

∂ ln f (T, x)

, (1.22) = M0 1 + ∂ ln T T =Tg with M0 a reference fragility. Typical applications for the prediction of the glass transition temperature concern Gex Se1−x glasses [29], and the glass transition is given by: ⎧ 1 3 ⎪ ⎪ ⎨ T0 3 − 5x , 0 ≤ x ≤ 3 (1.23) Tg (x) = ⎪ 1 2 3 ⎪ ⎩ T0 , ≤x≤ , 7x − 1 3 5 which reproduces quite accurately experimental data (dot-dashed curve in Fig. 1.2(b)). In oxides, Eq. (1.22) usually leads to a good reproduction of fragility data with composition, but fails to predict the fragility evolution for Ge–Se and the observed anomaly (Fig. 1.5(a)). The approach also requires a certain number of onset temperatures Tα that can be only estimated from basic (sometimes crude) assumptions, or might act as fitting parameters for the theory. 1.5. MD-Based Topological Constraints An interesting connection between constraint theory and molecular simulations is provided by MD-based topological constraint counting that permits to establish the number of constraints nc (x, T, P ) for any thermodynamic condition from atomic-scale trajectories, including under pressure [70]. This is achieved by performing classical or first principles MD (FPMD) using for example, a Car–Parrinello scheme [99] built from density functional theory, and Newton’s equation of motion is solved for a system of N atoms or ions, representing a given material (see elsewhere in this book). For glassy

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chalcogenides, attempts to use classical MD with a parametrized force field [100–102] have failed to reproduce the details of the chemical bondings in simulated chalcogenides and especially homopolar defects. These are present in a variety of materials, including in stoichiometric compounds (GeSe2 [103], As2 Se3 [104]). More recent contributions using either three-body force fields [105, 106] or polarizable ion models [107, 108] still do not reproduce accurately the structure of chalcogenides in detail. One has therefore to rely on FPMD which can account for all the electronic features of the chemical bonding and its change with temperature or composition while also allowing for the computation of properties inaccessible from classical MD. Recent investigations have led to a very precise reproduction of structural properties of most archetypal chalcogenides (Ge–Se [99, 109, 110], As–Se [111–113], Ge–S [114], As–Ge–Se [115], Si–Se [116, 117], Te [118], GeTe [119], and ternary tellurides [120, 121] in the glassy or liquid state, and at ambient or densified conditions [122, 123]. Once such structural models are validated from a realistic reproduction of structure functions (structure factor ST (k), Fig. 1.7, or pair correlation function g(r)), a topological constraint analysis is performed on the generated atomic scale trajectories. Radial and angular motion of atoms can then be connected directly to the enumeration of BS and BB constraining interactions, which are the relevant ones in the constraint count. Instead of treating mathematically the forces and querying about motion, which is the standard procedure of MD simulations for obtaining trajectories, as in classical mechanics, an alternative scheme is followed. Here, the atomic motion associated with angles or bonds can be related to the absence of a restoring force, this strategy being somewhat different from the “Culture of force” analyzed by F. Wilcek [127] given that one does not necessarily need to formulate the physical origin of the forces to extract constraints. In the case of atomic systems, since one attempts to enumerate BS and BB constraints, one is actually not seeking for motion arising from large radial and angular excursions, but for the opposite

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ST(k)

3 GeSe3 2 As2Se3 1

0

0

2

4

6

8

10

12

14

-1

k (Å ) Fig. 1.7. Validation of structural models from first principles molecular dynamics (FPMD) simulations. Calculated structure factor ST (k) (black lines) [99, 112, 114] compared to experimental data for amorphous GeS4 [124], GeSe3 [125], and As2 Se3 [126] (green curves). The red curve is a result from a classical molecular dynamics (MD) simulation using a force field [106].

behavior and also for atoms displaying a small motion (vibration) that maintains corresponding bonds and angles fixed around their mean value. These can ultimately be identified with a BS or BB interaction constraining the network structure at the molecular level. Having generated the atomic scale configurations at different thermodynamic conditions from MD, a structural analysis is applied in relation with the constraint counting of Rigidity Theory such as sketched in Eq. (1.12). 1.5.1. Constraint Counting Algorithms To obtain the number of BS interactions, one focuses on neighbor distribution functions (NDF) around a given atom i [128]. A set of NDFs can be defined by fixing the neighbor number N (first, second, etc.) during bond lifetime, the sum of all NDFs (Fig. 1.8(a)) yielding the usual i-centred pair correlation function gi (r) whose integration up to the first minimum gives the coordination numbers ri , and hence the corresponding number of BS constraints ri /2 [99, 113, 129].

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Neutron diffraction MD simulation BAD (arb. units)

g(r)

3

27

2

1

0

3

4 r (Å) (a)

5

6

30

60

90 120 Angle (deg)

150

180

(b)

Fig. 1.8. (a) Decomposition of the calculated pair correlation functions g(r) (black solid line) of amorphous As2 Se3 into neighbor distribution functions (colored curves). Comparison with experiments (circles) from neutron diffraction [126]). (b) 15 Selenium partial bond angle distributions (PBAD) in amorphous GeSe2 for an arbitrary N = 6 [128]. The red curve correspond to the PBAD having the lowest standard deviation (15◦ ). The sharp peaks at θ  40◦ correspond to the hard-core repulsion.

The BB constraint counting from MD simulations is based on partial bond angle distributions (PBADs) P (θij ) and defined as follows [129, 130]: for each type of a central atom 0, the N first neighbors i are selected, leading to N (N − 1)/2 possible angles i0j (i = 1, . . . , N − 1, j = 2, . . . , N ), that is, 102, 103, 203, and so on. The standard deviation (second moment) of each distribution P(θij ) represents a quantitative estimate of the angular excursion around a mean angular value and provides a measure of the BB strength. When such standard deviations are small, an intact BB constraint is identified and contributes to the rigidity of the network. Figure 1.8(b) shows the Selenium based PBADs for glassy GeSe2 [128]. Broad angular distributions are found for all angles except the one involving the first two neighbors of the central Se atom. The corresponding PBADs for Group IV atoms display six angles with nearly identical and sharp distributions (not shown, see [128]), and these are the six angles defining the tetrahedra with a mean value that is centred

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close to 109◦ [99]. For the pnictide Group V atoms, the corresponding number of PBADs leading to rigid angles is three [94], consistently with the mean-field angular constraint count of Eq. (1.12). 1.6. Rigidity and Dynamics with Composition Applications of such MD-based counting have been performed on a variety of chalcogenides [94, 113, 114, 132, 158] but we focus in the forthcoming on Ge–Se glasses and liquids, which are probably the most well documented alloys in the field of rigidity transitions. 1.6.1. Topological Constraints The enumeration of constraints on realistic models of Ge–Se glasses [99] and liquids [110] shows that six Ge standard deviations have a low value for the standard deviation (10◦ ), that is, four times smaller than all the other angles. One thus recovers the result found for the stoichiometric oxides (SiO2 , GeO2 [128]). A more detailed inspection has revealed that there is a clear difference between compositions (10%, 20%, and 25% Ge) having the six standard deviations σGe nearly equal, and compositions that are stressed-rigid (33%, 40%). As the Ge content is increased, the intra-tetrahedral angular motion becomes distorted for selected angles, as detected for example, GeSe2 by the important growth of standard deviations involving the fourth neighbor of the Ge atom. When the six standard deviations σGe defining the tetrahedra are represented as a function of the Ge content (Fig. 1.9(a)), it is found, indeed, that the angular motion involving the fourth neighbor (PBADs 104, 204, 304) exhibits a substantial increase once the system is in the stressedrigid phase (x > 25%), while the others (102, 103, 203) are left with a similar angular excursion close to the one found for oxides (SiO2 , GeO2 ), which have perfectly rigid tetrahedra [128]. The result is also compatible with a more detailed analysis focusing on individual constraints (Fig. 1.9(b)). An enumeration shows that the fraction ξ of broken constraints is about 17.2% and 21.4% for GeSe2 and Ge2 Se3 , respectively [99]. This implies a reduction of the number of

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25 stressed rigid

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102/103/203 104/204/304

0.25

Ge2Se3

104 204 304

15

102 103 104

10

10

15 20 25 30 35 Ge composition (%)

(a)

40

Distribution f(σ)

20 σGe (deg)

29

0.2 GeSe2

0.15

GeSe3

0.1

GeSe4

0.05

GeSe9 0

0 10 20 30 40 Individual standard deviations σ (deg)

(b)

Fig. 1.9. (a) Standard deviations σGe as a function of Ge composition in amorphous Ge–Se [128], split into a contribution involving the fourth neighbor (red line, average of 104, 204, and 304) and the other contributions (black line). The shaded area corresponds to the Boolchand (isostatic) intermediate phase [133] (see below). A simple bar structure represents the nature of the different elastic phases (see text for details). (b) Distribution of Ge angular standard deviations using individual constraints [99]. The total distributions have been split, depending on the neighbor rank: angles involving the first three neighbors (102, 103, 203, red symbols), and the fourth neighbor (104, 204, 304, black symbols). The solid curves are Gaussian fits, which serve to estimate the population of broken constraints at high x content.

Ge BB constraints by a quantity Δnc = 3xξ, that is, 0.17 and 0.26 for the aforementioned compositions so that nc reduces from 3.67 (the mean-field estimate [58]) to 3.5, and from 4.00 to 3.74 for GeSe2 and Ge2 Se3 , respectively. Similar results have been obtained for the Ge–S glasses [114]. The present evolution with composition indicates that the standard deviation of PBAD is an indicator of stressed rigidity [99] which sets on for x ≥ 25% Ge in Gex S100−x [27], Gex Se100−x [15], and Six Se100−x [28], the limit of the glass-forming region being somewhat larger than 33% for nearly all such binary Group IV chalcogenides. In addition, the presence of stress will lead to asymetric intra-tetrahedral bending, which involves an increased motion

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for selected triplets of atoms, and this indicates that some BB constraints have softened to accommodate stress. A similar situation is encountered in densified silicates [134] or in hydrated calcium silicate networks [113] for which angular motion associated with the tetrahedra SiO4/2 undergoes a substantial change with pressure or composition. The origin of this softening can be sketched from a simple bar network when stretching motion is considered instead (Fig. 1.9(a)), and this connects to the well-known relationship between stressed rigidity and bond mismatch in highly connected covalent networks [135]. In such highly cross-linked systems, atoms having a given coordination number can indeed not fulfill all their bonds at the same length and a full relaxation toward identical bond lengths is more difficult. In the simplified bar structures sketched in Fig. 1.9(a), all bars can have the same length in flexible (0%–20% at. Ge) and isostatic networks (20%–25% at. Ge) but once the structure becomes stressed-rigid, at least one bar (e.g., the colored bar in Fig. 1.9) must have a different length. A similar argument holds for angles. In the stressed-rigid Ge–Se and Ge–S, because of the high network connectivity, Ge tetrahedra must accomodate for the redundant cross-links which force softer interactions [80] (i.e., angles) to adapt and to break a corresponding constraint. This leads to increased angular excursions for atomic Se–Ge–Se triplets (Fig. 1.9) involving the farthest (fourth) neighbor of a central Ge atom. 1.6.2. Rigidity and Dynamic Anomalies The constraint enumeration can also be linked with liquid properties obtained from ensemble averages of atomic scale trajectories. Recent studies have focused on the effect of dynamics in chalcogenide melts such as Ge–Te [136, 137], Ge–Sb–Te [14] or Ge–Se [10, 52], the latter study being explicitely connected to rigidity properties. In the statistical physics of liquids, diffusivities can be calculated from the calculated mean-square displacement: N  α  1 2 |riα (t) − riα (0)| , (1.24) rα2 (t) = Nα i=1

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where riα (t) is the coordinate of the ith particle of the chemical species α at time t and Nα is the total number of particles of type α. The onset of the diffusive regime is acknowledged at long times, and in an equilibrated liquid the diffusion coefficient can be calculated using Einstein’s relation Di = rα2 (t)/6t. In Gex Se100−x liquids, it has been found that Se atoms are more mobile compared to Ge atoms, due to their lighter atomic weight [10]. A global decrease in the diffusivity has been detected with increasing Ge content, along with the stiffening of the network as the liquid becomes more and more cross-linked by the addition of Ge atoms. However, at some moderate temperature (1050 K) the values of DGe and DSe decrease even more within a small compositional range (18%–22%), the effect being enhanced for Ge atoms (Fig. 1.10). The obtained trend in diffusivity is compatible with the evolution of the relaxation time τα to equilibrium that is calculated from the intermediate scattering function Fs (k, t), which encodes the relaxation behavior of density-density correlations. The long-time evolution of Fs (k, t) can, indeed, be fitted by a stretched KWW 5

1.2

3 0.8

2

4 3.5

300 K

3 1050 K

2.5

3 c

4.5

2.5 2

4

1.5 1

3.5

0.4 1

10 15 20 25 30 35 Ge content (%)

(a)

Variance σn

4

3.5

BB

-5

1.6

Constraints (nc)

Relaxation time τα (ps)

5

Bond bending (nc )

2 -1

Diffusion coefficient (10 cm s )

2

0.5 2

10 15 20 25 30 35 Ge content (%)

10 15 20 25 30 35 Ge content (%)

(b)

(c)

Fig. 1.10. (a) Calculated Ge diffusion coefficient in liquid (1050 K) Gex Se100−x . Right axis (red symbols) represent the relaxation time τα . (b) Global constraint count nc in the glass (black symbols) and in the liquid (red). The broken line is the mean-field estimate nc = 2 + 5x [58]. (c) Calculated Ge bond-bending (BB) constraint density (black) and corresponding variance σnc [10, 52]. The gray zones indicate the Boolchand intermediate phase (see below) [133].

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exponential decay exp[−(t/τα )β ] with τα the structural relaxation time and β the Kohlrausch exponent [138]. Results (Fig. 1.10(a), right axis) indicate that there is an enhanced slowing down of the relaxation, which relates to the anomalous diffusion interval. In particular, it has been found [52] that for Ge22 Se78 Fs (k, t) exhibits a much slower dynamics and Fs (k, t) is shifted to longer times, leading even to the presence of a cage-like dynamic behavior that manifests in a typical β-relaxation plateau. These anomalous features are absent at higher temperatures in Ge–Se (1373 K), and it reveals that the network rigidity has softened with thermal excitation, as also emphasized independently from a phenomenological model [29] which suggests a complete breakdown of thermally activated constraints at high temperature. The evolution of the calculated constraint density (Fig. 1.10(b)) indicates that the anomalous relaxation is linked to the flexible to rigid transition. It is seen that the locus for extrema in dynamic properties coincides with the presence of isostatic liquids, which have been found to be critical [139], and at room temperature nc (x, T ) follows exactly the mean-field estimate nc = 2 + 5x [58, 99] leading to an isostatic condition (nc = 3) for x  20% Ge that agrees with the experimentally measured threshold value [133]. More importantly, the calculated nc (x, T ) displays a minimum change with temperature for 20%–22% Ge, a feature that is compatible with the presence of a minimum in liquid fragility (Fig. 1.5) because of the weaker variation of the term dnc /dlnT in Eq. (1.22) at x  22%. In addition, for such anomalous compositions, the spatial distribution of certain constraints is found to be homogeneous [10] and the Ge BB constraint density maximizes to its nearly low temperature value = 5, Fig. 1.10), which reduce the possible spatial fluctuations. (nBB c (Fig. 1.10(c), right axis) is a measure of The variance of nBB c the degree of heterogeneity of such atomic interactions leading to rigid constraints. Liquids in the region 20%–23% have, thus, the remarkable property to display homogeneous stress. As a result, a more stable state of matter is achieved and this induces a cascade of dynamic anomalies and minimal thermal or viscosity changes, typical of strong glass formers.

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Such numerical results are actually compatible with signatures of rigidity transitions in melts close to the glass transition as detected from fragility data which exhibit a minimum in liquids fulfilling nc = 3 (Fig. 1.5(a)). This suggests that isostatic networks will lead to a singular relaxation behavior with weaker energy barriers, as also detected from MD simulations in certain oxides [94, 134], and both activation energies and diffusivities are found to display a minimum. These conclusions actually parallel those made from a simplified Kirkwood–Keating model describing BB and BS interaction [140] with activation energies for relaxation being minimum in isostatic glass-forming liquids. 1.7. Reversibility Windows 1.7.1. MD Signature Chalcogenide glasses furthermore display reversibility windows (RW), that is, a tendency to display small or minimal thermal changes across the glass transition. Such features can be simulated from MD cycles performed at fixed quenching rates, and a hysteresis is obtained between the cooling and heating curve, similarly to current experimental observation. This behavior simply reflects the off-equilibrium nature of glasses that are able to slowly relax at T < Tg , and increase volume V or enthalpy H as the glass is heated back to the liquid phase. In densified liquids, it has been found [134] that liquids in a certain pressure interval exhibit a minuscule hysteresis curve and cooling/heating curves nearly overlap. When the area AH (AV ) of the enthalpy (volume) hysteresis is investigated as a function of pressure, a deep minimum is found which reveals a RW (Fig. 1.11) [134, 141]. The observation of Fig. 1.11 forces to revise the traditional picture of rigidity transition that lead to a solitary transition when nc = 3. Equation (1.12) implictely assumes a mean-field treatment because an average constraint count is performed over all the atoms of the network. This assumes that the system is homogeneous at the microscopic scale, and neglects the possibility of atomic-scale phase separation or large fluctuations in constraints or coordination

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1 NS2 0.8

ΔHnr (cal/mg)

Aρ (kJ/mol.K)

500

400

300

intermediate

Ge-S

0.6 Ge-Se 0.4 0.2

200

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0 1.5

2

2.5

3 3

ρ (g/cm ) (a)

3.5

10

15

20

25

30

35

Ge content (%) (b)

Fig. 1.11. (a) Area of the energy hysteresis curve as a function of density in densified silicates (NS2) for two different quenching rates [141], defining a reversibility windows (RW) (gray zone). (b) Measured non-reversing enthalpy ΔHnr in Ge–Se [133] and Ge–S glasses [27]. Alternative results for ΔHnr in Ge–Se: black open boxes, [142] and green circles [26]. In the Ge–Se system, all measurements differ by sample preparation method. In the mean-field picture of rigidity, chalcogen-rich compositions are flexible and Ge-rich glasses are stressedrigid. The abrupt boundaries define a so-called “intermediate phase” (gray zones) that is still actively debated.

numbers as the phase transition is approached. FPMD simulations of liquid Ge–Se indicate that this obviously not the case (Fig. 1.10(c)). For oxide liquids, the RW has been linked with the isostatic nature the network using the MD-based constraint count [134]. A calculation of the total number of constraints shows, indeed that nc saturates to its isostatic value and one obtains a plateau-like behavior over the entire RW interval. The detail shows that angular (BB) adaptation drives the mechanical evolution of the liquid under pressure because of both BS constraint and coordination increase [134]. At some threshold pressure, further compression leads, indeed, to a decrease of the number of BB constraints, indicative of a softening of the more weaker angular interactions. Upon further compression, this evolution holds as long as the system is in the RW but for elevated pressures an important growth in nc takes place. Such results indicate an obvious correlation between the RW

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threshold pressures/densities (Fig. 1.11) and those obtained from the constraint count, while also relating for such selected systems the isostatic nature of networks to the RW.

1.7.2. Experimental Signature from Calorimetry A vast literature has been accumulated on this topic during the last 15 years. One of the most direct signatures of RW having a nearly one to one correspondence with the result from MD (Fig. 1.11(a)) arises from mDSC measurements (such as sketched in Fig. 1.2), the relevant quantity, a non-reversing heat flow ΔHnr , exhibiting a square well minimum or even a vanishing in selected cases (Fig. 1.11(b)). In many situations, the sharp boundaries permit the definition of a compositional window displaying these enthalpic anomalies (e.g., 20% < x < 25% for Gex Se100−x [133]) where the kinetic events leading to the corresponding heat flow are small because of the strong character of the glass-forming liquid. The use of such calorimetric methods to detect the nearly reversible character of the glass transition has not been without controversy [143, 144] because the intrinsic measurement of ΔHnr depends on the imposed frequency, and relates to the imaginary part of the heat capacity Cp (ω) [47]. Frequency corrections [145] have to be taken into account in order to avoid the spurious effects arising from the frequency-dependence of the specific heat [36]. Systematic studies on Ge–Se [26, 54, 133] have shown that ΔHnr is not only sensitive to impurities and inhomogeneities but also to the relaxation state of the glass [15, 48], the melt dynamics being seriously reduced for RW compositions (e.g., Ge22 Se78 , Fig. 1.10), as also exemplified from the dependence of the spread in fragility data with sample batch and reaction time [54]. Note that this situation is also encountered in supercooled As–Se as evidenced from Fig. 1.5(b). The existence of such special relaxation phenomena with minimal fragilities for selected compositions leads to various other anomalous behaviors in the RW, and these provide other possible evidences of the RW signature. When the atomic sizes are comparable (e.g., A, and rSe = 1.17 ˚ A for the covalent radius in Ge–Se), it rGe = 1.22 ˚

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has been suggested that glasses will display an increased tendency to space-filling because of the isostatic nature of the networks (i.e., absence of stress [145]), which manifests by a minimum in the molar volume, a feature that has been reported for certain systems [15, 48, 132]. The stress-free nature of such RWs has been detected from pressure experiments [145] showing the vanishing of a threshold pressure prior to a pressure-induced Raman peak shift. This peak shift serves usually to quantify and to measure residual stresses in crystals. In a careful review on structural properties related to RWs in Ge–Se, Zeidler et al. do not point to an obvious structural origin from diffraction [142], and correlate rather the vanishing of the non-reversing heat flow with dynamic properties such as fragility or viscosity evolution in the liquid. While structural signatures might, indeed, be absent in total scattering functions [142, 143], they are detected from partial correlation functions in simulations [113, 146] and from X-ray absorption studies [147]. Issues related to the structural origin of the RW continue, therefore, to be debated in the literature, if not disputed. A large number of chalcogenide glasses display RWs, and these are summarized in Fig. 1.12. In certain of these systems, for example, for the simple binary network glasses such as Gex S1−x or Six Se1−x , the experimental boundaries of the RW are found to be similar [27, 28, 133], that is, located between 20% < x < 25%, and aspects of topology fully control the evolution of rigidity with composition, given that there is a weak effect in case of isovalent Ge/Si or S/Se substitution. This compositional interval defining the RW connects to the mean-field estimate of the isostatic criterion (Eq. (1.14)) satisfying nc = 3 because coordination numbers of Ge/Si and S/Se can be determined without any ambiguity from the 8-N (octet) rule to yield an estimate of the constraints nc = 2 + 5x using Eq. (1.12). In fact, for these Group IV chalcogenides, the lower boundary of the RW (x = 20%) coincides with the Phillips–Thorpe [58, 73] mean-field rigidity transition nc = 3 and r¯ = 2.4. However, this simple picture appears sometimes deceitful. For certain systems indeed, the constraint count (Eq. (1.12)) and the

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SixGe15Te85-x Ge15Te80-xIn5Agx SixGexTe1-2x GexSbxSe1-2x GexPxS1-2x GexPxSe1-2x GexAsxS1-2x GexAsxSe1-2x Ge25S75-xIx Ge25Se75-xIx PxS1-x PxSe1-x AsxS1-x AsxSe1-x 10

20

30

40

50

Modifier concentration x (%)

GexSe1-x SixSe1-x GexS1-x 2.9

3

3.1

3.2

3.3

3.4

Number of constraints nc

Fig. 1.12. Location of experimental reversibility windows driven by composition for different chalcogenides [134]: Si–Se [28], Ge–Se [133], Ge–S [27], As–Se [48], As–S [148], P–Se [149], P–S [150], Ge–Se–I [151], Ge–S–I [152], Ge–As–Se [153], Ge–As–S [154], Ge–P–Se [155], Ge–P–S [156], Ge–Sb–Se [157], Si–Ge–Te [158, 159], Ge–Te–In–Ag [160]. Using the 8-N (octet) rule, the location of reversibility windows (RWs) can be represented in select systems (bottom panel) as a function of the number of constraints nc using the mean-field estimate of nc (Eq. (1.12)).

isostatic composition does not correspond to the location of the corresponding RW, this situation being for example, met in another archetypal chalcogenide (Asx Se100−x ) for which nc = 3 is satisfied for x = 40% As whereas a RW is found between 20% and 37% [48]. For other systems, specific structural models need to be established to determine the isostatic criterion and eventually locate a corresponding RW. This becomes already obvious when Group V selenides/sulphides are considered (Fig. 1.12) because different RW locations are found for isovalent compounds, for example, differences

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emerge between As- and P-bearing chalcogenides, and between sulphides and selenides. Local structural features have been put forward to explain the trends due to chemistry [48, 148–150], as well as the special effect of sulfur segregation in sulphide-rich glasses (see Fig. 1.2(b)), and these have also served for the characterization of related ternaries [153–156]. The validity of these structural models is still debated in the literature, although rather well established in some cases from spectroscopic studies [149, 150]. Such general statements regarding structural uncertainties remain valid when tellurides are considered, and the complexity of the treatment increases because of a more important electronic delocalization leading to a breakdown of the 8-N rule with mixed local geometries that are now composition dependent [132, 158]. These are either sp3 tetrahedral or defect octahedral for Ge atoms, and a proper constraint count must now rely on accurate simulations, in conjunction with MD-based constraint counting algorithms such as those derived above [130, 132, 158]. 1.7.3. Insight from Models: Evidence for an Elastic Intermediate Phase A certain number of scenarios have been proposed to describe the observed behaviors depicted in Figs. 1.11 and 1.12. Theoretical approaches emphasize either the role of fluctuations [162–164, 166] in the emergence of a double threshold/transition or suggest that coordination fluctuations might be limited, but with a possibility for atoms to be coupled spatially via elasticity. In the latter case, which is inspired by mean-field aspects of jamming, atoms can organize locally into distinct configurations and may promote an intermediate phase (IP) between the flexible and the stressed-rigid phase. With the established relationship between reversibility at the glass transition and isostatic character of corresponding liquids [134], several authors have attempted to modify the modelling of the initial mean-field theory [58, 73] that leads to a solitary phase transition when nc = 3 (or r¯ = 2.4 if all BS and BB constraints are considered as intact). These contributions usually assume that amorphous networks will adapt during the cooling through the glass transition,

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similarly to the angular adaptation revealed from MD [99, 134], in order to avoid stress from additional cross-linking elements. Using a graph-theoretical approach, Thorpe and coworkers [165, 166] have developed an algorithm (a Pebble Game, [167]) that takes into account the non-local characteristics of rigidity, and allows to calculate the number of floppy modes, to locate over-constrained zones of an amorphous network, and ultimately identify stressed-rigid clusters for simple bar-joint networks. In the case of simulated selforganized or adaptive networks, the addition of bonds in a network with increasing average connectivity will be accepted only if this leads to isostatically rigid clusters, so that the emergence of stressed-rigid clusters is delayed. However, with a steady increase of the connectivity, the network will undergo percolation of rigidity (a rigidity transition at r¯c1 ), which leads to an unstressed (isostatic) structure. The addition of new bonds will contribute to the occurrence of stressed-rigid clusters that finally percolate at a second transition (¯ rc2 ), identified with a stress transition, and both transitions define, indeed, a window in connectivity Δ¯ r = r¯c2 − r¯c1 , and an IP. Other approaches have built on the same idea, using either a spin cavity method [162] or cluster expansions [163, 167]. These theories lead to a solitary floppy to rigid transition in absence of self-organization, and to an IP corresponding to a window in composition/connectivity in which the network is able to adapt in order to lower the stress due to constraints. However, some of these models do not take into account the fact that rigid regions cost energy, exemplified by the Pebble Game [166] and the cavity method [162] which apply on T = 0 networks with infinite energy barriers for bond change/removal. Thermal effects have been included [88, 164] and an equilibrated self-organized IP has been recovered for twodimensional lattice-based models. An important outcome from these models is that an increased sensitivity upon single bond addition or removal exists close to the IP, and this suggests that the system is maintained in a critical state on the rigid-flexible boundary throughout the IP. Using the phenomenology of the elasticity of soft spheres and jamming transitions, Wyart and coworkers follow an alternative path

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and have shown that the RW could occur in a certain number of physical situations [168]. By considering a lattice spring model for rigidity transitions with weak non-covalent (Van der Waals) interactions [72, 169, 170], it is found that temperature considerably affects the way an amorphous network becomes rigid under a coordination number increase, and the existence of an isostatic reversibility window not only depends on T but also on the relative strength of the weak forces. In a strong force r´egime, an RW can be found, which is revealed by a finite width in the probability to have a rigid cluster spanning the system, driven by fluctuations in coordination, similarly to the results of the Pebble Game ([167]. However, when weak interactions are present, the RW disappears below a certain temperature suggesting that the transitions become mean-field at low temperature and coalesce. Furthermore, weak interactions lead to an energy cost for coordination number fluctuations, which decay at finite temperature. These results are partially supported by MD simulations [134] taking into account long-range interactions (Coulomb, Van der Waals) allowing to probe the weak-force r´egime. Here coordination fluctuations are found to be small given the weak abundance of for example, five-fold Si atoms (10%–20%), and fluctuations are essentially found in angular constraints, which show a non-random distribution [171]). However, the vibrational analysis [168] suggests that in the IP vibrational modes are similar to the anomalous modes observed in packings of particles near jamming, thus providing also an interesting connection with the jamming transition [72] that might also be embedded in the anomalous variation of the molar volume of for example, Ge–Se glasses [133]. A more recent contribution suggests that entropy might favor heterogeneous structures in the vicinity of the rigidity transitions, and a homogeneous IP then emerges from an appropriate constraint count. The phase is found inside two heterogeneous (flexible and stressed-rigid) phases when a stress energy becomes dominant at low temperature [172], consistently with the spread determined in certain interactions [10]. Such mean-field scenarios of the IP are also those followed in a rigidity percolation model on a Bethe lattice [173, 174] that is

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based on a binary random bond network with a possibility of having two types of degrees of freedom. Under certain conditions, two discontinuous transitions are found, and the associated IP displays an enhanced isostaticity at the flexible boundary. As a result, the entire IP has a low density of redundant bonds and has, therefore, a low self-stress. The double transition solution is found to depend on the coordination and the degrees-of-freedom contrast. This might be directly comparable to experiments although important coordination contrasts do not necessarily correspond to situations encountered in chalcogenides.

1.8. Conclusion It is clear that recent theoretical and experimental efforts attempting to reconsider the usefulness of rigidity theory represent attractive venues for an improved quantitative description of chalcogenides and, more generally, non-crystalline solids [70]. A promising way to extend such approaches to the liquid state is provided by MD-based constraint counting which permits to calculate various properties from ensemble averages, and to connect to the constraint density. Given the general use of such simulations in the description of glasses and liquids, this recent extension now offers the possibility to rationalize the design of new families of chalcogenides and to understand their property evolution with composition or thermodynamic conditions. An alternative and powerful means is also offered by temperature dependent constraints [29] although applications to chalcogenides have been restricted to Ge–Se glasses and liquids only. Regarding the IP, there is probably no need of advocates [142]. Results on a variety of glass systems continue to be accumulated in a rigourous fashion, albeit often challenged, but stimulate both theory and additional experimental investigations. A special emphasis is spend on the characterization of the dynamic and structural properties of IP compositions, and it is recognized that certain features can be reproduced from theory work and simulations. The difficulty of the reproduction of the calorimetric results has raised the question of glass data reproductibility in relationship with sample preparation,

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an important topic that has been widely overlooked in the literature. Independently of the scientific debate on its physical origin, the exploration and a full understanding of the nature of the IP would be of great interest for applications given the remarkable stability of corresponding glasses and their associated anomalous behavior. References 1. Zachariasen, W. H. (1932). Journal of the American Chemical Society, 54, p. 3841 2. Chechetkina, E. A., and Optoelectr, J. (2011). Advanced Materials, 13, p. 1385. 3. Dembovsky, S. A., and Russian, J. (1977). Inorganic Chemistry, 22, p. 3187. 4. Angell, C. A., Poole, P. H., and Shao, J. (1994). Nuovo Cimento D, 16, p. 993. 5. Stølen et al. (2006). 6. Tatsumisago, M., et al. (1990). Physical Review Letters, 64, p. 1549. 7. Gueguen, Y., et al. (2011). Physical Review B, 84, p. 064201. 8. Senapati, U., and Varshneya, A. K. (1996). Journal of NonCrystalline Solids, 197, p. 210. 9. Micoulaut, M., Flores-Ruiz, H., and Bauchy, M. (2015). Molecular Dynamics Simulations of Disordered Materials (Springer Series in Materials Science), pp. 215, 275. 10. Yildirim, C., Raty, J-Y., and Micoulaut, M. (2016). Nature Communications, 7, p. 11086. 11. Laughlin, W. T., and Uhlmann, D. R. (1972). The Journal of Physical Chemistry, 76, p. 2317. 12. Angell, C. A. (1995). Science, 67, p. 1924. 13. Orava, J., et al. (2012). Nature Materials, 11, p. 279. 14. Flores-Ruiz, H., and Micoulaut, M. (2018). The Journal of Chemical Physics, 148, p. 034502. 15. Gunasekera, K., Bhosle, S., Boolchand, P., and Micoulaut, M. (2013). The Journal of Chemical Physics, 139, p. 164511. 16. Huang, D., and McKenna, G. B. (2001). The Journal of Chemical Physics, 114, p. 5621. 17. Vogel, H. (1921). Phys. Z, 22, p. 645; Tamman, G., and Hesse, W. (1926). Anorg, Z. All. Chem., 156, p. 245; Fulcher, G. S. (1925). Journal of the American Ceramic Society, 8, p. 339. 18. Mauro, J. C., et al. (2009). Proceedings of the National Academy of Sciences of the United States of America, 106, p. 19780.

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89. Huerta, A., and Naumis, G. G. (2002). Physics Letters, 299, p. 660; Huerta, A., and Naumis, G. G. (2002). Physical Review B, 66, p. 184204. 90. Naumis, G. G. (2005). Physical Review B, 71, p. 026114. 91. Foffi, G., and Sciortino, F. (2006). Physical Review E, 74, p. 050401. 92. Gupta, P. K., and Mauro, J. C. (2007). The Journal of Chemical Physics, 126, p. 224504. 93. Bauchy, M., and Micoulaut, M. (2011). Journal of Non-Crystalline Solids, 357, p. 2530. 94. Bauchy, M., and Micoulaut, M. (2013). Physical Review Letters, 110, p. 095501. 95. Smedskjaer, M. M., Mauro, J. C., and Yue, Y. (2010). Physical Review Letters, 105, p. 115503. 96. Hermansen, C., Youngman, R. E., Wang, J., Yue, Y. (2015). The Journal of Chemical Physics, 142, p. 184503. 97. Rodrigues, B. P., Mauro, J. C., Yue, Y., and Wondraczek, L. (2014). Journal of Non-Crystalline Solids, 405, p. 12. 98. Hermansen, C., Mauro, J. C., and Yue, Y. (2014). The Journal of Chemical Physics, 140, p. 154501. 99. Micoulaut, M., et al. (2013). Physical Review B, 88, p. 054203. 100. Iyetomi, H., Vashishta, P., and Kalia, R. K. (1989). Solid St. Ionics, 32–33, p. 954. 101. Vashishta, P., Kalia, R. K., Antonio, G. K., and Ebbsj¨ o, I. (1989). Physical Review Letters 62, p. 1651. 102. Iyetomi, H., and Vashishta, P. (1993). Physical Review B, 47, p. 3063. 103. Petri, I., Salmon, P. S., and Fischer, H. E. (2000). Physical Review Letters, 84, p. 2413. 104. Hosokawa, S., et al. (2006). Journal of Non-Crystalline Solids, 352, p. 1517. 105. Mauro, J. C., and Varshneya, A. K. (2005). Journal of the American Ceramic Society, 89, p. 1091. 106. Mauro, J. C., and Varshneya, A. K. (2007). Journal of the American Ceramic Society, 90, p. 192. 107. Sharma, B. K., and Wilson, M. (2006). Physical Review B, 73, p. 060201. 108. Wilson, M., Sharma, B. K., and Massobrio, C. (2008). The Journal of Chemical Physics, 128, p. 244505. 109. Massobrio, C., Micoulaut, M., and Salmon, P. S. (2010). Solid State Sciences, 12, p. 199. 110. Micoulaut, M., Vuilleumier, R., and Massobrio, M. (2009). Physical Review B, 79, p. 214204.

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111. Drabold, D. A., Li, J., and Tafen, D. N. (2003). Journal of Physics: Condensed Matter, 15, p. S1529. 112. Bauchy, M., Micoulaut, M., Boero, M., and Massobrio, C. (2013). Physical Review Letters, 110, p. 165501. 113. Bauchy, M., Kachmar, A., and Micoulaut, M. (2014). The Journal of Chemical Physics, 141, p. 194506. 114. Chakraborty, D., Boolchand, P., and Micoulaut, M. (2017). Physical Review B, 96, p. 094205. 115. Opletal, G., Drumm, D. W., Wang, R. P., and Russo, S. P. (2014). The Journal of Physical Chemistry B, 118, p. 4790. 116. Celino, M., and Massobrio, C. (2003). Physical Review Letters, 90, p. 125502. 117. Massobrio, C., et al. (2009). Physical Review B, 79, p. 174201. 118. Akola, J., et al. (2010). Physical Review B, 81, p. 094202. 119. Micoulaut, M., Piarristeguy, A., Flores-Ruiz, H., and Pradel, A. (2017). Physical Review B, 96, p. 184204. 120. Bouzid, A., et al. (2017). Physical Review B, 96, p. 224204. 121. Flores-Ruiz, H., et al. (2016). Physical Review B, 92, p. 134205. 122. Bouzid, A., et al. (2016). Physical Review B, 93, p. 014202. 123. Le Roux, S., et al. (2016). The Journal of Chemical Physics, 145, p. 084502. 124. Bytchkov, A., et al. (2013). Physical Chemistry Chemical Physics, 15, p. 8487. 125. Salmon, P. S. (2007). Journal of Non-Crystalline Solids, 353, p. 2959. 126. Xin, S., and Salmon, P. S. (2008). Physical Review B, 78, p. 064207. 127. Wilcek, F. (2004). Physics Today, 57, p. 10. 128. Bauchy, M., et al. (2011). Physical Review B, 83, p. 054201. 129. Bauchy, M., and Micoulaut, M. (2011). Journal of Non-Crystalline Solids, 357, p. 2530. 130. Micoulaut, M., Otjacques, C., Raty, J. Y., and Bichara, C. (2010). Physical Review B, 81, p. 174206. 131. Micoulaut, M., Gunasekera, K., Ravindren, S., and Boolchand, P. (2014). Physical Review B, 90, p. 094207. 132. Gunasekera, K., Boolchand, P., and Micoulaut, M. (2014). Journal of Applied Physics, 115, p. 164905. 133. Bhosle, S., Boolchand, P., Micoulaut, M., and Massobrio, C. (2011). Solid State Communications, 151, p. 1851. 134. Bauchy, M., and Micoulaut, M. (2015). Nature Communications, 6, p. 6398. 135. Mousseau, N., and Thorpe, M. F. (1995). Physical Review B, 52, p. 2660.

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136. Sosso, G. C., Behler, J., and Bernasconi, M. (2012). Physica Status Solidi, 249, p. 1880. 137. Sosso, G. C., et al. (2014). The Journal of Chemical Physics, 118, p. 13621. 138. Ngai, K. L., and Yeung Tsang, K. (1999). Physical Review E, 60, p. 4511. 139. Bauchy, M., and Micoulaut, M. (2017). Physical Review Letters, 118, p. 145502. 140. Micoulaut, M. (2010). Journal of Physics: Condensed Matter, 22, p. 285101. 141. Mantisi, B., Bauchy, M., and Micoulaut, M. (2015). Physical Review B, 92, p. 134201. 142. Zeidler, A., et al. (2017). Frontiers in Materials, 4, p. 32. 143. Golovchak, R., et al. (2008). Physical Review B, 78, p. 014202. 144. Shpotyuk, O., and Golovchak, R. (2011). Physica Stat. Solidi C, 8, p. 2572. 145. Wang, F., et al. (2005). Physical Review B, 71, p. 174201. 146. Micoulaut, M., and Bauchy, M. (2013). Physica Status Solidi, 250, p. 976. 147. Inam, F., Chen, G., Tafen, D. N., and Drabold, D. A. (2009). Physica Status Solidi, 246, p. 1849. 148. Chen, P., et al. (2008). Physical Review B, 78, p. 224208. 149. Georgiev, D. G., et al. Europhys. Lett., 62, p. 49. 150. Boolchand, P., Chen, P., and Vempati, U. (2009). Journal of NonCrystalline Solids, 355, p. 1773. 151. Wang, F., Boolchand, P., Jackson, K. A., and Micoulaut, M. (2007). Journal of Physics: Condensed Matter, 19, p. 226201. 152. Wang, Y., et al. (2001). Physical Review Letters, 87, p. 5503. 153. Wang, Y., Boolchand, P., and Micoulaut, M. (2000). Europhysics Letters, 52, p. 633. 154. Qu, T., and Boolchand, P. (2005). Phil. Mag., 85, p. 875. 155. Chakravarty, S., Georgiev, D. G., Boolchand, P., and Micoulaut, M. (2005). Journal of Physics: Condensed Matter, 17, p. L1. 156. Vempati, U., and Boolchand, P. (2004). Journal of Physics: Condensed Matter, 16, p. S5121. 157. Gunasekera, K., Boolchand, P., and Micoulaut, M. (2013). The Journal of Physical Chemistry B, 117, p. 10027. 158. Micoulaut, M., Gunasekera, K., Ravindren, S., and Boolchand, P. (2014). Physical Review B, 90, p. 094207. 159. Das, C., Kiran, M. R. S. N., Ramamurty, U., and Asokan, S. (2012). Solid State Communications, 152, p. 2181.

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160. Varma, G. S., Das, C., and Asokan, S. (2014). Solid State Communications, 177, p. 108. 161. Thorpe, M. F., Jacobs, D. J., Chubynsky, M. V., Phillips, J. C. (2000). Journal of Non-Crystalline Solids, 266–269, p. 859. 162. Barr´e, J., Bishop, A. R., Lookman, T., and Saxena, A. (2005). Physical Review Letters, 94, p. 208701. 163. Micoulaut, M., and Phillips, J. C. (2003). Physical Review B, 67, p. 104204. 164. Bri`ere, M. A., Chubynsky, M. V., and Mousseau, N. (2007). Physical Review E, 75, p. 056108. 165. Thorpe, M. F., and Chubynsky, M. V. (2001). Phase Transitions and Self-organization in Electronic and Molecular Networks (New York, NY, Kluwer Academic, Plenum Publishers), p. 43. 166. Thorpe, M. F., Jacobs, D. J., Chubynsky, M. V., and Phillips, J. C. (2000). Journal of Non-Crystalline Solids, 266–269, p. 859. 167. Micoulaut, M., and Phillips, J. C. (2007). Journal of Non-Crystalline Solids, 353, p. 1732. 168. Yan, L., and Wyart, M. (2014). Physical Review Letters, 113, p. 215504. 169. Wyart, M., Liang, H., Kabla, A., and Mahadevan, L. (2008). Physical Review Letters, 101, p. 215501. 170. Ellenbroek, W, G., Zeravcic, Z., van Saarloos, W., and van Hecke, M. (2009). Europhysics Letters, 87, p. 34004. 171. Bauchy, M., and Micoulaut, M. (2013). Europhysics Letters, 104, p. 56002. 172. Yan, L. (2018). Nature Communications, 9, p. 1359. 173. Moukarzel, C. (2013). Physical Review E, 88, p. 062121 5800. 174. Moukarzel, C. F. (2003). Physical Review E, 68, p. 056104.

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CHAPTER 2

Structure and Defects Koichi Shimakawa∗ and Sandor Kugler† ∗

Center of Innovative Photovoltaic Systems Gifu University, Gifu, Japan † Department of Theoretical Physics Budapest University of Technology and Economics Budapest, Hungary

While the experimental and analyzing techniques are advanced in a few decades, understanding of atomic-scale structure of chalcogenide glasses is still missing. This chapter is to review what is the most important issue on the structural study in chalcogenide glasses. Any diffraction measurement is a projection from a three-dimensional (3D) real structure to a one-dimensional (1D) function. It is not easy to get back 3D real structure from a 1D function. Computer simulations help the derivation of the real structures from a 1D function. The term of defects here is defined as lack of structural continuity in atomic scale. It is shown that the charged defects with negative-correlation energy introduced into chalcogenide glasses is a useful concept, while there is no direct experimental evidence.

2.1. Introduction Understanding of the atomic-scale structure of materials should be the most essential for deriving various physical aspects of those materials. The main result of any diffraction measurement is a projection from a three-dimensional (3D) real atomic structure to a one-dimensional (1D) function. We therefore deduce the 3D real structure from a virtual 1D function. This is a so-called inverse problem and is a not easy task, since the projection (1D function) 51

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causes an information loss due to different possible disordered atomic positions (pair correlation function or radial distribution function [RDF]) [1–4]. Let us first briefly introduce three major experimental techniques of diffraction studies: (i) Standard and conventional technique should be X-ray diffraction involving extended X-ray absorption fine structure (EXAFS) that may give direct information of short-range order (SRO), for example, in multi-component systems [1]. (ii) In the electron diffraction technique, using scanning electron microscope, the scattering is stronger than for X-ray because of the Coulombic repulsive interaction. This technique, however, requires very thin films. (iii) Neutrons, having no charge, interact with the nuclei of atoms and hence there is no relationship between atomic number and cross section. X-ray and electron beam are sensitive to the electron distribution Thermal neutrons with a de Broglie wavelength of 0.1–0.2 nm are very useful for atomic-scale structural studies. It is therefore possible to derive partial correlation functions of different components in multi-component systems. Computer simulations are required for approaching real 3D structures. We give a brief summary of simulation works. Through abovementioned techniques, we discuss short- and medium-range orders (MROs) in chalcogenide glasses. Interesting feature in the diffraction peak, called the first sharp diffraction peak (FSDP), will be also discussed in Section 2.2. 2.2. Short- and Medium-Range Structures 2.2.1. Short-Range Order Under an assumption that a glass is homogeneous, we can get an information of short-range structure [1, 2, 5]. Note that the shortrange structure is determined by the following three parameters: the coordination number Z, the bond length r, and the bond angle θ. As shown in Fig. 2.1, the RDF J(r) is defined as the number of atoms lying at distances between r and r+dr from the center of an arbitrary origin atom, and is written as J(r) = 4πr 2 ρ(r),

(2.1)

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Fig. 2.1. Schematic for the radial distribution function (RDF).

Fig. 2.2. Atomic pair correlation function ρ(r).

where ρ(r) the atomic pair correlation (distribution) function and ρ(r)dV is proportional to the probability of finding a particle inside a volume dV (Fig. 2.2). The correlation with the atom at the origin is lost at large r, implying that ρ(r) tends to unity (or the density ρ0 ), depending on the normalization. The positions of the peaks in J(r) provide the radii of the different coordination shells of atoms surrounding an average atom. The area under the peaks derives the coordination numbers of the shells of atoms. In a standard diffraction measurement, for example, X-ray, electron beam, and neutron, the diffraction intensity I(Q) at an wavenumber Q is linked to J(r) by the following equation [1–3]:  sin Qr 2 dr, (2.2) 4πr 2 [ρ(r) − ρ0 ] I(Q) ∝ f (Q) Qr

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where Q is given by 4π sin θs /λ, f the atomic scattering factor, 2θs the scattering angle, and λ the wavelength. A familiar example for I(Q) and J(r) obtained from the X-ray diffraction in glassy Se is shown in Fig. 2.3 [6]. Calculated ρ(r) provides Z, r, and θ, respectively, from the first-peak intensity, the first-peak position r1 , and the second-peak position r2 . It is understood that the shortrange structure (r < 0.5 nm) of glassy Se is almost the same as that of corresponding crystalline state [6], as listed in Table 2.1. Neutron-diffraction measurements have been performed on the SLAD instrument at Studsvik NFL, Nyk¨oping, Sweden [7]. Crystalline Se powder (3 g) was ball milled under an argon atmosphere for 6 hr in a Spex mixer/mill. The milling procedure consisted of milling for 15 min followed by 45 min of rest to avoid heating and then repeating the cycle. Total milling time of 6 hr was reached. The amorphous Se powder was contained in a thin-walled vanadium

Fig. 2.3. Diffracted X-ray intensity I(Q) [left] and calculated radial distribution function (RDF) J(r) [right] in Se glass [6]. After [2]. Table 2.1. Comparison of atomic parameters between hexagonal Se and glassy Se [6]. Z, r, θ, Φ, and ρ are the coordination number, the bond length, the bond angle, the dihedral angle, and the density, respectively.

Hexagonal Se Glassy Se

Z

r (nm)

θ

Φ

ρ (g/cm3 )

2.0 2.0 ± 0.04

0.23 0.23 ± 0.002

105◦ 105◦ ± 05

102◦ 70◦ –110◦

4.80 4.25

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container. The experimental structure factor S(Q) obtained was compared to three other earlier measured data within the interval of 8–120 nm−1 and pair correlation functions were presented derived unconstrained Reverse Monte Carlo (RMC) computer simulations. For multi-component glasses, for example, As2 S3 , GeS2 , Ge2 Sb2 Te5 , on the other hand, direct applications of the procedures mentioned earlier are not possible. It is not able to determine the structure from only one diffraction pattern, since f changes with atom species, while the neutron-diffraction technique is useful for multi-component systems as stated in Section 2.1. The EXAFS may produce direct information for the structure in multi-component systems [1, 2]. In EXAFS experiments, X-ray absorbance is measured as a function of X-ray energy E. As illustrated in Fig. 2.4, the absorbance abruptly changes at a core-electron excitation energy, for example, at the K edge energy EK , and small intensity modulation (oscillation) “EXAFS” χi (E) appears just above this threshold energy at around E − EK ≤ 500 eV. The oscillation of X-ray transmission spectrum is attributed to the interference of X-ray excited electron-waves with a wavenumber of k = 2π/λe = [2m(E − EK )]1/2 /, where λe is the electron wavelength (∼0.2 nm) and m the electron mass. As shown in Fig. 2.4 (right), the electron wave spreading from the central atom and those being reflected back by surrounding atoms interfere, which modulates

Fig. 2.4. A schematic extended X-ray absorption fine structure (EXAFS) (left) and its emerging mechanism (right). After [2].

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X-ray transmittance through electron-excitation efficiency. By scanning the X-ray energy E, the interference pattern is modified and the X-ray transmission spectrum, therefore, has information of the surrounding atoms (atomic species, distance, number). At a slightly higher E than a core-electron excitation energy EK of specified single atoms i, χi (k) contains a term as [1] χi (k) ∝ Σj Zij exp(−2rij /L) sin{2kr i + ϕj (k)},

(2.3)

where Zij is the number of atoms (coordination number) at a distance of rij around a specified i atom, L the electron mean-free-path, and ϕj (k) the induced phase change when an excited electron is reflected at a neighboring atom j. If the phase change is known using a reference material, ri can be deduced from oscillating spectra. The amplitude of χi (k) is proportional to the coordination number Z of the specified atom. As already stated, the EXAFS is useful specifically for multicomponent systems, since EK is fixed by an atom, we can determine peripheral structures around the specified atom i. The intense beams obtained from synchrotron orbital radiation are much effective to reduction in exposure time and improvement of spatial resolution. As a case example, the EXAFS result around Ge in crystalline and glassy GeS2 is shown in Fig. 2.5 [8]. As shown in R-space (bottom), the strong first peak at ∼0.2 nm (Ge–S distance) and two weaker peaks at ∼0.26 and ∼0.31 nm, the latter being identified to the two kinds of second-nearest Ge–S–Ge pairs (in edge- and cornersharing tetrahedra) illustrated in the inset. The peak positions are very similar to those of the crystal, which evinces existence of the short-range structural order in this glass. 2.2.2. Medium-Range Order We must discuss now Medium-Range Structure (0.5–3 nm) in Chalcogenide glasses. Existing of a MRO was first suggested in glassy As2 S(Se,Te)3 [9]. There is no experimental technique to determine such a scale of atomic structures, the term “MRO” is still a controversial issue. The current understanding of the MRO in chalcogenide glasses is now briefly reviewed [2]. The length scale ∼0.5 nm of the

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Fig. 2.5. Extended X-ray absorption fine structure (EXAFS) spectrum for Ge in c-GeS2 (above) and radial distribution function (RDFs) for Ge in c- and g-GeS2 (bottom). The inset in the above shows the distances corresponding to the three peaks. After [2].

MRO can be connected to the short-range structure up to the secondnearest neighbors. For the simplest glassy Se (g-Se), for example, a position of the third-nearest neighbor atom can be determined by the dihedral angle. In the hexagonal-type crystalline Se, the atomic connection is all trans, being explicitly determined. On the

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other hand, as shown in Fig. 2.3, the RDF of g-Se gives no clear peaks corresponding to the third-nearest neighbor, suggesting that the dihedral angle is randomly distributed between trans and cis configurations [6]. The so-called entangled-chain structure (like a random coil molecular structure) should be kept in g-Se. Next to these scales, we should consider the ring structures [5]. Entangled long chains and ring molecules consisting of several atoms may co-exist in amorphous S(Se). However, there is no convincing experimental technique that can explicitly determine the ring statics and the chain length. We can just envisage the structure with a combination of experimental results and hence computer simulations can be useful technique, which will be introduced in Section 2.3. 2.2.3. First Sharp Diffraction Peak A relatively sharp halo peaks in X-ray diffraction appears at around QFSDP = 10 nm−1 in chalcogenide glasses (As2 S(Se)3 , etc.), which is called the FSDP [9]. This FSDP position corresponds to that of a Bragg peak appearing in As2 S(Se)3 layered crystals. So-called distorted layer model for the glasses, that is, deformed covalent layers with somewhat correlated interlayer distances of ∼0.6 nm was proposed. After then, a variety of experiments have been performed for the FSDP. The experiments cover many kinds of chalcogenide glasses with different preparations and under different temperatures and pressures [1, 10, 11]. It was tried to grasp atomic structures giving rise to the FSDP. All discussions are not easy to review and hence several reviews [1, 2] are only recommended here. There seems to be a consensus that some kinds of MROs with scales of 1–3 nm exist in simple glasses, while controversial is the real atomic structure. For the group VIb stoichiometric glasses, for example, Si(Ge)O2 and As2 S(Se)3 , there are roughly two ideas. One insists, taking QFSDP r ≈ 2 ∼ 3 seriously, that the oxide and the chalcogenide possess qualitatively the same MRO, in which 3D network structures have been presumed as a starting concept [12–14]; the model hereafter referred to as a 3D view. The others [11, 15] assume that the oxide has 3D and the chalcogenide

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has two-dimensional structures, the idea being consistent with the original view by Vaipolin and Porai-Koshit [9]. Finally, we must discuss what happen in glassy Se. The fact that amorphous selenium (a-Se) consisting of Se chains does not show a clear FSDP, but a shoulder, is ascribed to the short inter-chain distance (∼0.4 nm), which may be related to the second-nearest intrachain distance of ∼0.37 nm [6]. We assume that the two-dimensional (layer) structure gives the FSDP, which reflects the van-der-Waals type correlation, in the chalcogenide glass. The peak in 3D glasses should be ascribed to different origins. It is thus suggested that the origin of the FSDP should not be the same among different systems (no universal origin). 2.2.4. Boson Peak The Boson peak observed in Raman scattering spectra is expected to relate with the FSDP. A broad peak at 20–50 cm−1 (∼5 meV), which is lower than the conventional vibrational modes by an order. This anomalous low-frequency peak was found firstly in SiO2 glass [16]. This type low-frequency broad peak has never observed in crystalline SiO2. Nemanich [17] performed a comprehensive study of broad peak in chalcogenide glasses and called the term Boson peak. A reason why termed Boson peak is that the spectral shape at low-frequency limits can be dominated by the Bose factor, {n(ω, T ) + 1}/ω  ω −2 . Since then, many studies have been performed in oxide and chalcogenide glasses [5]. This can be a universal feature in disordered materials. Figure 2.6 shows an example of glassy As2 S3 . The shapes of Boson peaks of many glasses are the same if the spectrum is normalized with the peak frequency Ωmax [19]. The peak becomes smaller under hydrostatic compression [18] and is intensified with temperature [20]. The peak position depends upon preparation conditions such as quenching rate of the melt [21]. Several models have been proposed for the origin of the Boson peak. The vibrational wavenumber k is given as k = (1/s)(κ/M )1/2 , where s is the sound velocity, κ the force constant, and M the reduced mass. The small wavenumber of Boson peak can be attributed to

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Fig. 2.6. Raman scattering spectra of As2 S3 as a function of hydrostatic compression. After [18].

some vibrations of nearly free atomic units with a small κ, which may be related with van-der-Waals forces. Phillips [22] proposed that the Boson peak is a kind of rigid-layer modes, which are vibrations of crystalline layers held together by van-der-Waals forces. The low wavenumber may also be due to atomic clusters having large masses, which may be dominated by its medium-range structures. It is of interest to show a communality between the FSDP and the Boson peak: Novikov and Sokolov [23] found a proportionality between the normalized FSDP position and the Boson peak wavenumber. This issue therefore was extended to universal understandings of the correlation among FSDP, Boson peak, and thermal properties known as low-temperature anomaly [24]. The final elucidation is still under debate [25–28].

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2.3. Computer Simulations Results obtained from the diffraction study are only a 1D representation of the atomic distribution in 3D. The knowledge of the 3D atomic arrangement is an essential prerequisite to understand the physical and chemical properties. The main purpose is the 3D structure derivation from 1D function. As stated already, the projection causes an information loss and several different possible atomic structures can display the same 1D pair correlation function. No experimental technique has been discovered so far for the determination of microscopic 3D atomic distributions. In the last decades the research focused on construction of realistic atomic configurations for amorphous materials using computer simulations. Computations should not substitute for lack of knowledge of atomicscale configuration. It is only a useful tool for constructing 3D atomic structure models. There are two main families for structural modeling methods of disordered configurations: a stochastic method, namely Monte Carlo (MC)-type, and a deterministic way, namely Molecular Dynamics (MD) simulations. 2.3.1. Monte Carlo-Type Methods for Structure Derivation The MC method involves the use of random numbers to govern atomic displacements during computer simulation processes. Several different algorithms on the MC method have been developed: traditional MC, reverse MC, Quantum MC, kinetic MC, path integral MC methods, and so on. In this section, only the first two techniques are discussed. The traditional MC method generating a 3D atomic configuration of amorphous materials searches for a minimum of total energy. Two different interactions are usually applied for energy calculation: Classical empirical potentials and the other are based on different quantum-mechanical approaches such as tight-binding (TB) model or density functional theory or Hartree–Fock approximations. The initial configuration can be any non-crystalline atomic arrangements. A randomly chosen atom is displaced to a new position which is determined randomly. If a MC step provides us a downhill

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motion on the energy hypersurface, then the new configuration is introduced and this reordered structure becomes the initial atomic arrangement for the next MC step. In the uphill case, the new position is rejecting only conditionally, which is a very important step. This decision is the essential part of MC simulations. A simple explanation of this selection rule is the following: if uphill motion is always rejected, then the procedure reaches the first shallow energy minimum and there is no chance to find a deeper minimum, which probably belongs to a more realistic atomic configuration. 2.3.2. Atomic Interactions The simplest versions of atomic interactions are the classical empirical potentials, which are computationally the cheapest method for structural modeling. The parameters describing the atomic interaction can be derived either from experimental observations or from advanced quantum-mechanical calculations. For sigma-bonded semi-conductor structures, simple pair potential such as Morse or Lennard-Jones potentials or other potentials are not suitable because the directional nature of sigma bonds must be taken into account. Therefore, the potential must have at least two- and threebody terms. A short range means the total potential energy of a given particle is dominated by interaction with neighboring atoms that are closer than a cut-off distance. An important class of amorphous semiconductors is chalcogenides. Model element for them is selenium. An empirical three-body potential has been developed by Oligschleger et al. [29]. Its analytical form is given by   V2 (rij ) + h(rij , rkj , θijk ) + cyclic permutations. (2.4) U= i 2, substantial experimental and theoretical studies have been performed for binary systems; As– S [80], As–Se [43, 46, 49], Ge–Se [29, 35, 81–83], and Ge–Te [4, 19, 39]. By contrast, studies for ternary compounds are a few, including As–S–Se [15] and Ge–As–S(Se, Te) [22, 67, 84]. Here, a guiding concept for analyses is the topological thresholds at Z = 2.4 and 2.67 [22, 49, 63, 67, 81, 82]. Besides, the most important chemical variation is the ratio between the hetero- and homo-polar bonds, for which many studies assert the preference of heteropolar bonds, favoring chemically ordered networks in stable amorphous

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Fig. 5.6. Comparisons of photoemission spectra (circles) and theoretical (lines) density of states (DOS) in amorphous Ge–Se. (Reprinted from [35] with permission from American Physical Society.)

structures [39, 42, 46, 85]. We actually see in Fig. 5.6 that the lone-pair and conduction bands (at around −1 and +3 eV) become appreciably smoother with a change from GeSe2 to Ge2 Se3 , which may be ascribed to the coordination increase to Z > 2.67 and/or emergence of Ge–Ge homopolar bonds. 5.3.3. Metal-Chalcogenides A variety of metals have been added to amorphous chalcogenides [1, 2, 6, 62, 86, 87]. However, most of the metals are dissoluble only below a few at.%, which scarcely affects gross electronic structures. Exceptions include n-type compounds such as Bi–Ge–Se [12] and In–S [88], covalent Cu–As–S(Se) [89–91], ionic Na–Ge–S [16] and Ga–Ge–Se(Te) [40, 92], and ion-conducting Ag–As(Ge)–S(Se) [41, 52, 68, 90, 93]. In these alloys, Z is likely to vary with compositional changes or it cannot be defined, and the electronic structures exhibit unique

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Fig. 5.7. Comparison of photoemission spectra in Ag(Cu)–As2 Se3 glasses with the Ag(Cu) content in atomic % [90] and theoretical density-of-states (DOSs) in Ag25 As25 S50 [68] and Cu11 As36 S53 [91].

characters. Most of these materials are no longer lone-pair semiconductors. For instance, as shown in Fig. 5.7, the valence bands in Ag(Cu)–As–S(Se) glasses are governed by Ag(Cu)-S(Se) bonds, which cause sharp peaks at around −5 and −3 eV [68, 90, 91], the positions reflecting 4d and 3d levels (−6.41 and −6.92 eV below the vacuum level [54]) of Ag and Cu atoms, respectively. Agchalcogenides are known to behave electrically as ion- and ion–hole mixed conductors, the detail being described elsewhere. We also note Z ≈ 4 in Cu(Ag)–As–S(Se), the fact being interpreted using a formal valence-shell model [89, 91], which assumes a formal transfer of lonepair electrons from S(Se) to Cu(Ag).

5.4. Conclusions Studies so far have revealed principal features of the electronic structure in amorphous chalcogenides, including the following concepts and/or ideas:

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(i) The gross DOS structure is governed by short-range atomic configurations; the so-called Ioffe–Regel rule [4]. However, whether the amorphous structure were homogeneous in longer scales remains to be a pending problem. (ii) Chalcogens and covalent chalcogenides (with Z = 2) are regarded as the lone-pair electron semiconductors. However, in Te-compounds, the metallic character tends to mask the directional covalent bonds, which makes experimental and theoretical analyses more subtle. (iii) Since the amorphous material is not in thermal equilibrium, even stoichiometric compositions may contain a lot of homopolar bonds, that is, wrong bonds, which are likely to modify the DOS structure. (iv) In non-stoichiometric systems, the topological structural transitions at Z = 2.4 and 2.67 leave traces in the electronic structure. (v) In metal-chalcogenides (with Z > 2), the electronic states arising from the metal tend to substantially affect the band structures. Those materials can no longer be regarded as the lone-pair semiconductors, some of which possess unique electrical properties such as n-type, ion, and ion-hole-mixed conductions. References 1. Borisova, Z. U. (1981). Glassy Semiconductors (New York, NY, Plenum Press). 2. Popescu, M. A. (2000). Non-Crystalline Chalcogenides (Dordrecht, the Netherlands, Kluwer Academic Publishers). 3. Kastner, M. (1972). Bonding bands, lone-pair bands, and impurity states in chalcogenide semiconductors, Physical Review Letters, 28, pp. 355–357. 4. Mott N. F., and Davis E. A. (1979). Electronic Processes in NonCrystalline Materials, 2nd Ed. (Oxford, England, Clarendon Press). 5. Elliott S. R. (1990). Physics of Amorphous Materials, 2nd Ed. (Essex, England, Longman Scientific & Technical). 6. Tanaka, K., and Shimakawa, K. (2011). Amorphous Chalcogenide Semiconductors and Related Materials (New York, NY, Springer).

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7. Terakado, N., and Tanaka, K. (2008). The structure and optical properties of GeO2 -GeS2 glasses, Journal of Non-Crystalline Solids, 354, pp. 1992–1999. 8. Lucas, J., and Zhang, X. H. (1990). The tellurium halide glasses, Journal of Non-Crystalline Solids, 125, pp. 1–16. 9. Shevchik, N. J., Cardona, M., and Tejeda, J. (1973). X-ray and faruv photoemission from amorphous and crystalline films of Se and Te, Physical Review B, 8, pp. 2833–2841. 10. Hosokawa, S., et al. (1993). Inverse-photoemission study of the conduction bands in amorphous GeSe2 , Physical Review B, 47, pp. 15509– 15514. 11. Hosokawa, S., et al. (1993). Inverse-photoemission spectra of amorphous chalcogenides, Journal of Non-Crystalline Solids, 164–166, pp. 1199–1202. 12. Matsuda, O., et al. (1996). Photoemission and inverse-photoemission study of the electronic structure of p- and n-type amorphous Ge–Se–Bi films, Journal of Non-Crystalline Solids, 198–200, pp. 688–691. 13. Ono, I., et al. (1996). A study of electronic states of trigonal and amorphous Se using ultraviolet photoemission and inverse-photoemission spectroscopies, Journal of Physics: Condensed Matter, 8, pp. 7249– 7261. 14. Richter, J. H., et al. (2014). Hard x-ray photoelectron spectroscopy study of Ge2 Sb2 Te5 ; as-deposited amorphous, crystalline, and laserreamorphized, Applied Physics Letters, 104, p. 061909. 15. Li, W., Seal, S., Lopez, C., and Richardson, K. A. (2002). X-ray photoelectron spectroscopic investigation of surface chemistry of ternary As–S–Se chalcogenide glasses, Journal of Applied Physics, 92, pp. 7102–7107. 16. Tanaka, K., Nemoto, N., and Nasu, H. (2003). Photoinduced phenomena in Na2 S–GeS2 glasses, Japanese Journal of Applied Physics, 42, pp. 6748–6752. 17. Zallen, R., and Blossey, D. F. (1976). The optical properties, electronic structure, and photoconductivity of arsenic chalcogenide layer crystals. In: Physics and Chemistry of Materials with Layered Structures, edited by Mooser, E. (Dordrecht, the Netherlands, D. Reidel Publishing Company), pp. 231–272. 18. Sobolev, V. V. (2002). Optical spectra of arsenic chalcogenide glasses over a wide energy range of fundamental absorption, Glass Physics and Chemistry, 28, pp. 399–416. 19. Park, J. W., et al. (2009). Optical properties of pseudobinary GeTe, Ge2 Sb2 Te5 , GeSb2 Te4 , GeSb4 Te7 , and Sb2 Te3 from ellipsometry and density functional theory, Physical Review B, 80, p. 115209.

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61. Halpern, V. (1976). Localized electron-states in arsenic chalcogenides, Philosophical Magazine, 34, pp. 331–335. 62. Ovshinsky, S. R., and Adler, D. (1978). Local structure, bonding, and electronic properties of covalent amorphous-semiconductors, Contemporary Physics, 19, pp. 109–126. 63. Greaves, G. N., and Sen, S. (2007). Inorganic glasses, glass-forming liquids and amorphizing solids, Advances in Physics, 56, pp. 1–166. 64. Tanaka, K. (1987). Chemical and mediun-range orders in As2 S3 glass, Physical Review B, 36, pp. 9746–9752. 65. Hosokawa, S., et al. (2013). Does the 8-N bonding rule break down in As2 Se3 glass?, Europhysics Letters, 102, p. 66008. 66. Bauchy, M., and Micoulaut, M. (2013). Structure of As2 Se3 and As–Se network glasses: Evidence for coordination defects and homopolar bonding, Journal of Non-Crystalline Solids, 377, pp. 34–38. 67. Wang, R. P., Rode, A. V., Choi, D. Y., and Luther-Davies, B. (2008). Investigation of the structure of glasses by x-ray photoelectron spectroscopy, Journal of Applied Physics, 103, p. 083537. 68. Akola, J., et al. (2014). Structure, electronic, and vibrational properties of amorphous AsS2 and AgAsS2 : Experimentally constrained density functional study, Physical Review B, 89, p. 064202. 69. Kim, J. et al. (2007). Electronic structure of amorphous and crystalline (GeTe)1−x (Sb2 Te3 )x investigated using hard x-ray photoemission spectroscopy, Physical Review B 76, p. 115124. 70. Sarkar, I., Perumal, K., Kulkarni, S., and Drube W. (2018). Origin of electronic localization in metal-insulator transition of phase change materials, Applied Physics Letters, 113, p. 263502. 71. Welnic, W. et al. (2006). Unravelling the interplay of local structure and physical properties in phase-change materials, Nature Materials, 5, pp. 56–62. 72. Caravati S., et al. (2009). First-principles study of crystalline and amorphous Ge2 Sb2 Te5 and the effects of stoichiometric defects, Journal of Physics: Condensed Matter, 21, 255501 (14pp). 73. Kato, T., and Tanaka, K. (2005). Electronic properties of amorphous and crystalline Ge2 Sb2 Te5 films, Japanese Journal of Applied Physics, 44, pp. 7340–7344. 74. Boolchand, P., et al. (2002). Nanoscale phase separation effects near r = 2.4 and 2.67, and rigidity transitions in chalcogenide glasses, Comptes Rendus Chimie, 5, pp. 713–724. 75. Liu, A. C. Y., Chen, X., Choi, D.-Y., and Luther-Davies, B. (2008). Annealing-induced reduction in nanoscale heterogeneity of thermally evaporated amorphous As2 S3 films, Journal of Applied Physics, 104, p. 093524.

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76. Terakado, N., and Tanaka, K. (2008). Nanoscale Heterogeneous Structures in GeO2 –GeS2 Glasses, Jpn. Journal of Applied Physics, 47, pp. 7972–7974. 77. Soyer-Uzun, S., Benmore, J. C., Siewenie, J. E., and Sen, S. (2010). The nature of intermediate-range order in Ge–As–S glasses: Results from reverse Monte Carlo modeling, Journal of Physics: Condensed Matter, 22, p. 115404. 78. Darmawikarta, K., Li, T., Bishop, S. G., and Abelson J. R. (2013). Two forms of nanoscale order in amorphous GexSe1−x alloys, Applied Physics Letters, 103, p. 131908. 79. Solieman, A., and Abu-sehly, A. A. (2011). Determination of the optical constants of amorphous Asx S100−x films using effective-medium approximation and OJL model, Materials Chemistry and Physics, 129, pp. 1000–1005. 80. Kondrat O. et al. (2017). Coherent light photo-modification, mass transport effect, and surface relief formation in Asx S100−x nanolayers: Absorption edge, XPS, and Raman spectroscopy combined with profilometry study, Nanoscale Research Letters, 12, p. 149. 81. Taniguchi, M., et al. (1996). Photoemission and inverse-photoemission studies of glassy Gex Se1−x , Journal of Electron Spectroscopy and Related Phenomena, 78, pp. 507–510. 82. Hosokawa, S. (2001). Atomic and electronic structures of glassy GeX Se1−X around the stiffness threshold composition, Journal of Optoelectronics and Advanced Materials, 3, pp. 199–214. 83. Tafen, D. N., and Drabold, D. A. (2005). Models and modelings schemes for binary IV–VI glasses, Physical Review B, 71, p. 054206. 84. Lippens, P. E., et al. (2000). Electronic structure of Ge–As–Te glasses, Journal of Physics and Chemistry of Solids, 61, pp. 1761–1767. 85. Pethes, I., et al. (2016). Short-range order in selenide and telluride glasses, The Journal of Physical Chemistry B, 120, pp. 9204–9214. 86. Pfister, G., and Taylor, P. C. (1980). Experimental investigation of defect states in amorphous chalcogenide glasses, Journal of NonCrystalline Solids, 35–36, pp. 793–805. 87. Kawaguchi, T., Maruno, S., and Elliott, S. R. (1996). Effect of addition of Au on the physical, electrical and optical properties of bulk glassy As2 S3 , Journal of Applied Physics, 80, pp. 5625–5632. 88. Narushima, S., et al. (2004). Electrical properties and local structure of n-type conducting amorphous indium sulphide, Philosophical Magazine Letters, 84, pp. 665–671. 89. Liu, J. Z., and Taylor, P. C. (1989). The formal valence shell model for structure of amorphous semiconductors, Journal of Non-Crystalline Solids, 114, pp. 25–30.

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90. Itoh, M. (1997). Electronic structures of Ag(Cu)–As–Se glasses, Journal of Non-Crystalline Solids, 210, pp. 178–186. 91. Aniya, M., and Shimojo, F. (2006). Atomic structure and bonding properties in amorphous Cux (As2 S3 )1−x by ab initio molecular-dynamics simulations, Journal of Non-Crystalline Solids, 352, pp. 1510–1513. 92. Petracovschi, E., et al. (2018). Short and medium range structures of 80GeSe2 -20Ga2 Se3 chalcogenide glasses, Journal of Physics: Condensed Matter, 30, p. 185403. 93. Hosokawa, S., et al. (1996). A soft-x-ray core absorption study on the electronic states in Ag- and Cu-photodissolved amorphous GeSe2 using synchrotron radiation, Journal of Physics: Condensed Matter, 8, pp. 1607–1614.

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CHAPTER 6

Optical Properties Keiji Tanaka∗ Department of Applied Physics, Graduate School of Engineering Hokkaido University, Kita 13, Nishi 8, Kita-ku Sapporo, Hokkaido 060-8628, Japan

6.1. Introduction This chapter provides a concise review of optical spectra and related properties, including linear absorption and photoconduction in simple amorphous chalcogenides. Photoluminescence is touched slightly, since the subject has been reviewed repeatedly [1, 2]. Regarding nonlinear responses, readers may refer to Chapter 14 and recent reviews [3, 4]. For non-stoichiometric ternary component and more complicated glasses, reported results are diverse, which are not dealt in this chapter. So far we have obtained detailed optical spectra stemming from electronic and vibrational excitations in simple and/or topical, amorphous chalcogenide materials [5–8]. Nevertheless, how to understand fundamental and/or universal features in electronic responses remains vague or controversial. In this chapter, starting from reproducible observations, we will consider how those can be interpreted, with indications of related problems. ∗

Emeritus Professor 145

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6.1.1. Fundamental Among several kinds of optical spectra, the absorption coefficient α(ω) is of fundamental importance, an example being shown for As2 S3 in Fig. 6.1. It consists of electronic (ω ≥ 0.5 eV) and vibrational (≤0.5 eV) contributions. The electronic absorption edge at ω ≈ 2.5 eV is assumed to arise from non-direct (the wavenumber being neglected) transitions from occupied i to unoccupied f states with the densities of states Ds [5–8];  2 (6.1) Df (E + ω)Di (E)dE, α(ω) ∼ |M | where M (∼φf |H  |φi  with electron wavefunctions φ and lightelectron interaction Hamiltonian H  ) is the transition matrix, which is assumed in general to be independent of ω [16], while it is a pending problem [6, 17–19]. Df and Di are, in covalent chalcogenide glasses, dominated by anti-bonding states and lone-pair electron states of chalcogen atoms, respectively (see Chapter 5). Note that polaron and thermal effects are neglected in the equation.

Fig. 6.1. Typical two spectra (solid and dashed lines) of absorption/attenuation [5, 9–12] and refractive-index [9, 13, 14] in As2 S3 . The dotted line is an extrapolated Tauc curve. The star at ∼0.4 eV indicates the attenuation in a bestquality optical fiber [15]. The horizontal scale is expanded at 0–0.5 eV.

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On the other hand, it is common to relate lattice absorption spectra in chalcogenide glasses to molecular vibrations [5, 20]. Such treatments can provide good approximations, since vibrations of atomic units, such as AsS(Se)3/2 and GeS(Se)4/2 , in chalcogenide glasses are mostly decoupled through the bond angles of ∼90◦ , which reflects the p-type wavefunction in s2 p4 electron orbitals of chalcogen atoms. The refractive index n(ω) is a useful quantity characterizing transparent materials. The dispersion can quantum mechanically be formulated using oscillator parameters, while a simpler scheme is to relate it with α(ω) through a Kramers–Kronig relationship [8] as;  n(ω) − 1 = (c/π)℘ {α(Ω)/(Ω2 − ω 2 )}dΩ (6.2) where c is the light velocity and ℘ denotes the principal value of the integral. Since α(ω) possesses a prominent electronic peak at an ultraviolet wavelength, it governs n(ω) at transparent regions. Accordingly, the spectrum can be approximated using one-oscillator models, formulated by, for example, Wemple and DiDomenico [8, 21, 22]; n(ω)2 − 1 = Ed E0 /{E02 − (ω)2 },

(6.3)

where E0 (≈ 2 − 5 eV ≈ 2EgT ) and Ed (≈ 20 − 30 eV) are the resonant and the dispersion energy of an effective oscillator. Herein, the Moss rule n40 Eg [eV] = 95 [eV], where n0 is a refractive index at transparent wavelengths and Eg is the optical gap, is often employed as a useful approximation [8]. As shown in Fig. 6.1, reported refractive indices are fairly reproduced; for bulk As2 S3 glasses n = 2.43 ± 0.03 at λ = 1.2 μm [9, 13, 14, 23]. It is known that the overall optical property can also be grasped using the complex dielectric constant; ε∗ = ε1 +iε2 = (n+ik)2 , where k(=(λ/4π)α in the MKS unit) is the extinction coefficient. In other words, ε1 = n2 − k2 ≈ n2 and ε2 = 2nk ∝ α. 6.1.2. Experimental 6.1.2.1. Optical Measurements The absorption spectrum α(ω) can straightforwardly be determined from the optical transmittance T (ω). Neglecting interference effects,

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we write T as; T ≈ (1 − R2 ) exp(−αd),

(6.4)

where R represents the intensity reflectivity and d is a sample thickness. The equation is simple, while some cautions are needed for measurements in limiting cases. When αd 1, we may employ very thin films of d ≈ 10 nm, which are likely to be oxidized and/or pin holed, causing appreciable errors. Otherwise, we may employ reflection spectroscopy, which is able to display ε∗ (ω), while the result is also sensitive to surface conditions. When αd 1, T approaches (1 − R)2 , and light-scattering effects tend to affect T , which makes evaluations of α difficult. Or, in some compositions, only thin films are available, for which evaluations of small absorption may be needed. For such cases, we prefer some indirect measuring methods, in which the signal increases with α; the example being photothermal and photoconductive techniques. For the former, among several kinds of methods [24], the photo-deflection spectroscopy (PDS) [25], in which the output signal is proportional to absorption-induced temperature rises, seems to possess the highest sensitivity at room temperature for thin-film samples deposited on transparent substrates [26–28]. For the latter, the constant photocurrent method (CPM) has repeatedly been employed, the principle being described in 6.1.2.2. Note that both methods cannot provide absolute absorption coefficients, so that obtained spectra are matched at some points to transmission results. The refractive index can directly be determined using several methods [9, 13, 14, 23, 29]. The most conventional for bulk glasses is to measure refractive angles in prism-shaped samples [13, 14]. For thin films, we can evaluate it from reflectance spectra, spectral interference fringes, and ellipsometric measurements [9, 23, 29]. 6.1.2.2. Photoconductive Methods As known, the photo-current ipc is governed by photo-carrier generation and transport processes, and it can be written down as [6]; ipc ≈ enμF ≈ e(I/ω)αητ μF,

(6.5)

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where e is the electron charge, n the steady-state photo-carrier density, μ the carrier mobility, F the applied electric field, I the light intensity, α the absorption coefficient, η the photo-carrier generation efficiency, and τ the carrier lifetime. Accordingly, holding I(ω)/ω constant, we can evaluate α(ω) from ipc (ω), which can be measured with high sensitivity. However, the change in n is likely to modify μτ in semiconductors having many traps, which is likely to cause deviations from the proportionality, ipc ∼ α. The CPM is more appropriate in that respect [30]. Here, we measure I(ω) under a fixed ipc , and evaluate α(ω) from I(ω)−1 . Since n is plausibly held constant, the obtained spectra are not distorted by the μτ variation. Measurements are performed in many cases using samples with planar (inter-digital), not sandwiched, electrodes [31]. However, the photoconductive methods have several drawbacks. Evaluations of small absorption are restricted by maximal I(ω) at fairly transparent, long-wavelength regions. Specifically, at low temperatures, ipc becomes smaller, and we need powerful light sources such as a 500 W Xe lamp with an efficient monochromator. Nevertheless, under intense illumination, sample temperature is likely to rise, and photothermal (bolometric) currents flow, which become appreciable in narrow-gap semiconductors such as Te alloys [32]. Moreover, photoconductive spectra are liable to be influenced by electrode materials, excitation levels, applied voltages, chopping frequencies in lock-in measurements, and so on. In short, the most reliable α(ω) may be obtained using pure optical methods, including PDS. 6.2. Electronic Absorption 6.2.1. Overall Features 6.2.1.1. Spectral Variations Electronic absorption edges in simple chalcogenide glasses have been studied for more than a half century, the pioneering work being reviewed by Tauc [5]. We now have grasped fundamental features, which are summarized as follows [5–8, 19]. The edge in many materials consists of three regions: With increasing ω, there appears weak absorption tail (WAT) at

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α ≤ 1 cm−1 , Urbach edge at α ≈ 102 cm−1 , and Tauc curve at α ≥ 103 cm−1 , with the typical functional forms, respectively, of; α ∝ exp(ω/EW ), 0 )/EU } α = α0 exp{(ω − EU

αω ∝ (ω − EgT )n ,

(6.6a) and

(6.6b) (6.6c)

0 fix where EW (≥200 meV) is a characteristic WAT energy, α0 and EU an extrapolated Urbach edge with the Urbach energy EU (≥50 meV), EgT (≈1–4 eV) is the Tauc optical gap, and n = 1 in Se, 2 in simple materials such as As2 S(Se)3 , and 3 in complicated compositions such as Si5 Ge5 As25 Te55 [5, 6, 33]. For the Tauc curve and Urbach edge, considerable studies have been performed, including variations with temperature, pressure, electric filed, composition, and preparation procedure, as summarized below. By contrast, such analyses for the WAT are few, probably due to experimental difficulties. Upon rising temperature, both the Tauc curve and the Urbach edge tend to red-shift [5, 6, 8, 34–39]. The temperature variation at low temperatures is relatively small, probably being masked by disordered potentials. However, at around room temperature (>Tg /2, where Tg is the glass-transition temperature) it is comparable to that in the conventional crystalline semiconductors; ∂EgT /∂T ≈ −1 meV/K, which is ascribed to electron–phonon coupling effects [37]. The red-shift of the Urbach edge is likely to occur with increasing EU ; the edge becoming more gradual, and the variation may provide 0 ) [6, 38] (see, Fig. 6.3). Besides, the red-shift the focus point at α(EU tends to overlap with the WAT at high temperatures [5, 34, 36]. Hydrostatic compression produces marked red-shifts of the absorption edge [8, 40]. For instance, ∂EgT /∂P ≈ −10 meV/Kbar in amorphous and also in crystalline chalcogenides, which are contrastive to ∂EgT /∂P ≈ 0 in tetrahedral semiconductors. The marked red-shift correlates with dramatic densification, with small bulk moduli of ∼102 Kbar (∼1/5 of g-SiO2 ), and accordingly, it is reasonable to ascribe the red-shift to enhanced overlapping of lone-pair electron states, which dominate the top of the valence

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band (see Chapter 5). The dramatic pressure effects are consistent with high photoelastic constants [41]. For the Urbach edge, we note ∂EU /∂P > 0 for all the chalcogenide glasses examined [40], the compression effect being similar to that induced by temperature rising. Incidentally, to the author’s knowledge, no pressure variations have been reported for the WAT, which may be due to experimental difficulties in setting thick samples in high-pressure cells. Electric field effects upon the absorption edge have been studied in considerable details [5, 6, 18, 42]. The purpose may be to examine Franz–Keldysh and excitonic Stark effects on the Urbach edge. However, the conclusion appears to be left vague. More fundamentally, if the “exciton” can be defined in chalcogenide glasses is still controversial [19]. Instead, we may prefer expressions as “excitonic” or “geminate” pair, the latter being a classical concept. Electro-optic effects were also explored [43]. 6.2.1.2. Compositional and Quasi-Equilibrium Effects A lot of studies have been performed for compositional variations; specifically for the Ge(As)–Se systems, which have wide glassforming regions. Here, the first problem to be concerned is if the non-crystalline structure is homogeneous over atomic to nanoscales [3, 33, 35, 44–46]. The homogeneity has been presumed in many cases, while it remains to be a pending subject [8, 47]. Provided that the structure is uniform, the most important index characterizing covalent chalcogenide glasses is the average coordination number Z [6]. Taking the atomic coordination number predicted by the 8 − N rule (N ; valence number) into account, we define Z = 4x + 3y + 2(1 − x − y) for Gex Asy S(Se)1−x−y systems. And, topological notions assert the existence of thresholds at Z = 2.4 and 2.67 [8, 48]. Actually, we see in Fig. 6.2 that the As–Se system exhibits minimal EgT and EU at Z ≈ 2.4. More accurately, P´etursson et al. [35] observe the minimal EgT at As43 Se57 , while the deviation may be influenced by preparation procedures of bulk ingots [50]. On the other hand, EgT in the Ge–Se system appears to exhibit a slope change at Z ≈ 2.4 and a maximum at Z = 2.67 [49, 51], which can be related with variations in the glass density,

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Fig. 6.2. The Urbach energy EU (dashed lines with open circles) and the optical gap EgT (solid lines with filled circles) in As-Se [35] and Ge–Se [49] glasses at room temperature as a function of the average coordination number Z. EgT in Ge–Se is approximated with the photon energy at α = 103 cm−1 .

the atomic volume, or structural dimensions [8, 52]. Since As2 Se3 and GeSe2 are the stoichiometric compositions, for understanding these characteristics, we need to take also chemical bond effects into account, which are completely neglected in the topological models. However, it should be noted that similar thresholds also appear in ternary glasses such as As–Ge–S(Se) [8, 53]. The amorphous material exists in quasi-equilibrium states, and consequently, its properties necessarily vary with preparation procedures and prehistory. For instance, EgT (≈2.4 eV at room temperature) in As2 S3 films in as-evaporated, annealed, and illuminated states become smaller in this order by ∼50 meV each [8, 10, 54]. The as-evaporated film is demonstrated to be molecular with substantial numbers of wrong bonds. Annealed films are polymerized, possessing similar structures to those in melt-quenched glasses. And, illumination makes the annealed film more disordered, the difference between the annealed and the illuminated state being known as (reversible) photodarkening, as described in Chapter 9. Moreover, even for a fixed glass composition, optical properties are known to depend upon melt-quenching conditions [8, 14]; for example, the optical gap in melt-quenched As2 S3 varies by ∼80 meV, depending upon quenching procedures such as the melting temperature and quenching rate. On the other hand, for GeS(Se)2 , preparations of

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good-quality glassy samples and thin films are more-or-less stringent [55], which may be due to the high average coordination number of 2.67, the existence of the two crystalline polymorphs with layer and three-dimensional types, and/or the existence of edge- and cornershared GeS(Se)4 units. Specifically, evaporated GeS2 films, which are deposited through sublimation (not vaporization), are known to exhibit markedly red-shifted absorption edges, reflecting many Ge–Ge wrong bonds (with slight composition deviations) [8]. Radiofrequency sputtering may produce films with properties similar to those in the bulk glass. 6.2.2. Optical Spectra in Topical Materials In the following, we compare absorption, photoconduction and photoluminescence spectra for three materials. Optical properties in chalcogenide glasses may have most extensively been investigated for As2 S3 , Se has been examined in relation to photoconductivity, and Ge2 Sb2 Te5 is known to be an innovative phase change material. 6.2.2.1. As2 S3 The optical absorption edge in As2 S3 has continuously been studied. This is probably because stable samples in the forms of thin films, big ingots, and long fibers are available, and also its absorption edge is located at visible and near-infrared regions, where sensitive measuring methods including PDS and CPM are feasible [8]. We have reproducible spectra also for As2 Se3 , while GeS(Se)2 spectra are highly dependent upon preparations [56, 57]. Figure 6.3 shows optical absorption edges in As2 S3 [5, 23, 31]. Here, it should be noted that the spectra at α ≥ 102 cm−1 and ≤103 cm−1 are obtained using film and bulk samples, and the two curves are connected smoothly. (The same situation applies to other sulfides and selenides including a-Se in Fig. 6.4.) Accordingly, the fact that the results form a single line is coincidental1 in a rigorous sense and/or artificial. 1

It is plausible that the absorption edge in as-evaporated As2 S3 films is blueshifted by molecular structures and is red-shifted by wrong bonds, the two effects being canceled out.

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Fig. 6.3. Comparisons of several spectra in a-As2 S3 ; absorption α (orange) at 450 (dashed), 300 (solid) and 10 K (dotted), CPM (violet) at 300 (solid) and 175 K (dotted), and photoluminescence PL and photoluminescence excitation PLE at 5 K [1, 2]. Note that only PL is plotted with linear vertical scale. Also shown is an absorption spectrum (blue) of crystalline As2 S3 at 300 (solid) and 10 K (dotted) [39]. The two arrows indicate the positions of the band-gap related parameters at (extrapolated to) 0 K.

We see that the optical absorption edge α in the amorphous state markedly red-shifts from the crystalline edge, and it consists of the Tauc curve, Urbach edge, and exponential WAT. At room temperature the Tauc curve gives EgT ≈ 2.35 eV, and Urbach edges at 300–450 K are extrapolated to a cross-point at α0 ≈ 107 cm−1 0 ≈ 2.8 eV. On the other hand, it has been demonstrated and EU that crystalline As2 S3 (orpiment), which is a layer-type crystal, has a direct bandgap of ∼2.8 eV at room temperature [9, 39]. It is interesting to compare the optical and photoconductive edges. We see in Fig. 6.3 that the photoconductive (CPM) edge mostly duplicates the optical Urbach edge at room temperature, while at 175 K the curve at α ≥ 100 cm−1 appears to markedly blue-shift, producing a spectral difference of ∼0.5 eV from the optical edge, which can be regarded as a non-photoconducting gap, long been known in a-Se (see Sections 6.2.2.2 and 6.2.3.3). It should be mentioned that As2 Se3 and GeS(Se)2 exhibit similar non-photoconducting gaps [31, 56].

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Figure 6.3 also includes photoluminescence spectra at 5 K. The excitation spectrum of photoluminescence (PLE) has a peak at EPLE (≈ 2.3 eV), which is located in the Urbach and nonphotoconducting gap region. And, luminescence appears with a peak at ∼EPLE /2(≈ 1.1 eV), satisfying the so-called half-gap rule [1, 2, 6]. Below the Urbach edge we see the WAT, for which we can mark two points. One is that little photoconductive response appears in PC ) the spectral region. Or, fitting an exponential curve ∼ exp(ω/EW PC ≈ 100 meV, much smaller (sharper) to the CPM tail, we obtain EW than that (EW ≈ 300 meV) in the optical tail. On the contrary, the PLE exhibits a WAT-like spectral response at ω ≤ 2 eV with a similar slope. These contrastive features of the photoconductivity and PLE spectra suggest that the WAT arises from radiative localized centers. 6.2.2.2. Elemental Se Photoconduction in a-Se (and stabilized a-Se films containing 0.2 at.% As and 20-ppm Cl [59, 60]) has been studied nearly a century with two motivations [58, 59]. One is that a-Se films, which are evaporated onto substrates held at 50◦ C–60◦ C, are highly photoconductive, which has promoted extensive application-oriented researches [59]. The other is fundamental; the material can form only one elemental glass (with no wrong bonds) having fair stability at room temperature. Besides, the optical spectra are simple, which may be suitable to examine band-edge concepts such as the mobility edge and non-photoconducting gap. Figure 6.4 shows the absorption-edge spectrum α(ω), consisting of the Tauc curve with n = 1 (in Eq. (6.6c)), Urbach edge, and residual tail. From the Tauc curve we estimate EgT ≈ 2.0 eV at room temperature [6, 37], which is higher and lower than the optical gaps of 1.85 eV [58] and ∼2.4 eV [58] in the trigonal (t–) and monoclinic (m–) crystals [6]. The Urbach edge is substantially temperaturedependent, giving rise to the Urbach focus point at α0 ≈ 107 cm−1 0 ≈ 2.4 eV [6]. For the residual tail, if it forms an exponential and EU shape remains vague, due to different results. For instance, in a pure bulk sample the response reduces to α ≤ 10−2 cm−1 , while in a film

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Fig. 6.4. Several optical spectra in a-Se; absorption α (300 and 10 K), photoconduction quantum efficiency η (300 K), and CPM (300 and 150 K) at 300 K (solid lines) and low temperatures (dashed lines) [31], and PL and PLE at 10 K in linear vertical scales [1]. Also plotted are α’s at room temperature in trigonal (the electric filed orthogonal to the chain axis) and monoclinic crystals [58]. The solid and arrows indicate the positions of the band-gap related parameters at room temperature.

the level increases to ∼101 cm−1 [12]. Besides, transient photocurrent analyses assert the existence of gap-state peaks in (stabilized) a-Se films [60, 61], while no related optical absorptions have been detected. It seems difficult to conclude at present that these observations are not influenced by O impurities, Se crystallites, dopants, electrodes, and so on [62]. Figure 6.4 also shows two kinds of photoconductive spectra, a quantum efficiency η at room temperature and those obtained by a CPM. Note that η = 1 at ω ≈ 3 eV is experimentally determined [63], while the vertical position of the CPM spectrum is arbitral. Nevertheless, we see that the two spectra have similar shapes, which are clearly different from the absorption spectrum in two points. One is that the photoconducting Urbach edge (at α ≈ 103 cm−1 ) blue-shifts from the absorption edge, which produces

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the so-called non-photoconducting gap (see Section 6.2.3.3). The other is that the photoconduction spectra demonstrate marked drops at ω ≈ 1 eV, or possess incomplete WAT-like responses, which may be common to the feature in As2 S3 (Fig. 6.3). Finally, it has been known that photoluminescence of a-Se is exceptional from those in As2 S(Se)3 at least in two points [1, 2, 59, 64]. One is the weakness, being weaker than that in As2 S(Se)3 by 1–2 orders, and the other is the spectral position of EPL ≈ 0.4 EPLE , clearly deviating from the half-gap rule. The reason may be ascribed to substantially mobile holes and/or formation of self-trapped polarons arising from strong electron-lattice interaction, which has been delineated using energy-configuration diagrams [1, 6, 8, 65]. However, we also envisage possible effects of impurities such as O on the photoluminescence behaviors, and accordingly, further studies using ultrahigh-purity samples will be needed before re-considering these exceptional behaviors. 6.2.2.3. Ge2 Sb2 Te5 At the outset, we should mark three unique characters. First, as in many telluride materials, melt-quenched Ge2 Sb2 Te5 glass can hardly be prepared [66], and hence, all experiments for amorphous states have been performed using deposited films (with thicknesses less than ∼3 μm [67]). Second, since EgT ≈ 0.7 eV, the Urbach edge and subgap absorption are located at infrared regions, where spectral measurements are more-or-less restricted. Actually, to the author’s knowledge, no results of photoluminescence and its excitation spectrum have been reported. Third, steady-state photoconductive spectra cannot be evaluated in such a narrowgap, low-mobility semiconductor, since the response is masked by photothermal currents [32]. We see in Fig. 6.5 that a-Ge2 Sb2 Te5 has the Tauc curve with n = 2 and EgT ≈ 0.7 eV, and a clear Urbach edge with EU ≈ 50 meV, in consistent with other results EgT ≈ 0.7–0.8 eV and EU ≈ 50–100 meV [27, 66–70]. It has also been demonstrated that ∂EgT /∂T = −0.6 meV/K [68], which is in harmony with other data. Nevertheless, below the steep edge, no WAT seems to exist. Instead, using PDS

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Fig. 6.5. Optical absorption edges in amorphous (◦ and a solid line), cubic () and hexagonal () Ge2 Sb2 Te5 films prepared through dc-sputtering [26, 27, 68]. The peak at 0.45 eV is ascribed to -OH vibrations in silica-glass substrates, while the arrowed peak at 0.41 eV arises from Ge2 Sb2 Te5 .

measurements, Olson et al. [67] and Gotoh [26] detect absorption peaks at 0.56 and 0.41 eV (Fig. 6.5), respectively, the latter height increasing with annealing temperatures (≤260◦ C). A similar peak at ∼0.45 eV is detected also in amorphous GeTe films [28]. Further studies, including reproducibility of peaks at ∼0.5 eV and identification of the atomic structure that is responsible for the peak [26–28, 68], will give valuable insights into the phase change mechanism. 6.2.3. Origin and Interpretation Despite of the detailed and reproducible features, as described earlier, interpretations of absorption characteristics and related energy parameters remain to be studied. We henceforth consider some topics for obtaining universal insights. 6.2.3.1. Mobility and Tauc Gaps Relationship between the Tauc optical gap and the mobility gap is a long-standing subject in amorphous semiconductor physics [5, 6, 8]. One assumes that the Tauc gap represents the mobility gap, while another argues that the Tauc gap is smaller than the mobility gap.

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Fig. 6.6. Several bandgap-related energy parameters for topical materials: Tauc optical gap (• with a solid line), Urbach-edge focus point (), Faraday-rotation gap (), photoconducting gap (◦ with a dotted line) and bandgap of the corresponding crystals ( with a dashed line). ‘c’ and ‘h’ for GST, ‘t’ and ‘m’ for Se, and ‘2’ and ‘3’ for GeS(Se)2 stand for, respectively, cubic, hexagonal, trigonal, monoclinic, and two- and three-dimensional. Modified from [71].

Figure 6.6 compares some bandgap-related parameters of several chalcogenides, SiO2 , and a-Si:H as a function of the Tauc gap energy EgT . We see, except tellurides that distribute at EgT ≤ 1 eV, that EgT is smaller by 0.2–0.5 eV than the energies of Urbach-edge focus point 0 , photoconducting gap E , Faraday rotation gap E FR [72], and EU pc g bandgap Ex in the corresponding crystals,2 the all being roughly the same. This fact suggests that these four energy parameters can be measures of the mobility gap Egµ , that is, the minimal energy gap between extended states. We then assume that the Tauc curve arises from photo-electronic transitions between localized and extended states. Note that it is difficult to assign the Tauc curve to 2

For Se and GeS(Se)2 , two crystalline results are plotted, and this Ex should be referred to those of the ring- and layer-type crystals, not of the chain and three-dimensional.

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Fig. 6.7. An electronic density-of-state DOS (left) and the band diagram (right), in which localized potentials are illustrated as square-wells. The solid curves with an extrapolated dashed line trace the DOS of three-dimensional crystals. In the band diagram, the solid, dashed and dotted arrows represent band-to-band, Urbach and WAT absorption, respectively. (Modified from [71]).

photoelectronic transitions between localized states due to its wide spectral coverage (∼1 eV). Hence, taking the plausible origins of the Urbach edge and WAT into account (see the next sections), we relate EgT and Egµ as illustrated in Fig. 6.7 [71]. This is a kind of the Cohen– Fritzsche–Ovshinsky model [5, 6, 8] with the Fermi level Ef being located at around mid-gap, below the WAT-related levels. The Tauc gap represents the energy separation between the conduction- and valence-band edges, with the latter being extrapolated from the conventional density of states (DOS). And, the mobility gap is wider reflecting potential fluctuations producing the Urbach edge, which is located at the valence-band top, as described in Section 6.2.3.2. On the basis of this model, we can interpret gross features of the optical absorption spectra in chalcogenide glasses such as As2 S(Se)3 . Besides, the WAT states act as strong electron traps, which is consistent with more mobile holes in the glasses. Note that the model presumes no charged gap states [6, 8]. However, some problems still remain unresolved. Provided Egµ being located higher by 0.2–0.5 eV than EgT , we may expect some

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change in the transition probability M in Eq. (6.1) at ω ≈ Egµ [6], which is likely to cause a deviation from the Tauc curve. Nevertheless, no such traces can be pointed out for a-Se and As2 S(Se)3 [35], as exemplified in Figs. 6.1, 6.3, and 6.4. More basically, how can we understand the n(=1, 2, and 3) value in Eq. (6.6c)? In a simple band theory, the value can be related to the DOS curves, Di (−E) ∼ E p and Df (E) ∼ E q , as n = p + q + 1. And, following the conventional crystalline theory, Davis and Mott ascribed n = 1 in a-Se to one-dimensional (chain-like) atomic structures with p + q = 0 [6]. However, a recent numerical calculation manifests no such simple D(E) curves [73], which poses re-considerations of the transition matrix M [6, 18, 33, 72, 74]. Returning to Fig. 6.6, we see that all the amorphous tellurides have nearly the same Tauc gap of ∼0.8 eV, which is greater than those of the corresponding crystals. This nearly constant Tauc gap implies that the value is governed, not by As or Ge, but by Te atoms, which have large radii in anionic or metallic states. And, the fact that Ex < EgT may be ascribed to higher densities of the crystals, for example 6.2 and ∼5.7 g/cm3 in c– and g–As2 Te3 [75], which causes stronger interactions between lone-pair electrons and/or a resonantbond effect [76]. 6.2.3.2. Urbach Edge Another long-standing problem is the origin of the exponential absorption edge. For this fairly universal spectrum, which does not markedly change with temperature in amorphous semiconductors, many models have been proposed over a half century [5, 6, 8, 16, 77–79]. The ideas may be referred to four kinds of situations; those being produced by combinations of one-particle transitions or excitonformation processes in disordered structures, which may be rigid (as in a-Si:H) or flexible (as in a-Se). For the rigid-lattice model, a common assumption is that the exponential spectrum reflects the shape of the DOS D(E) of localized states, not a transition-matrix effect. If so, does it arise from the conduction-band bottom or from the valenceband top? The latter seems to be more plausible, since the valenceband width is more likely to be affected by structural disorder, due

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to the band origin of lone-pair electron states. Besides, in As2 S(Se)3 , and so on, similar energies appear in EU and in a photocurrent-decay parameter obtained through analyses which assume multiple-trapping transport of holes [31, 80]. Then, why is the edge exponential over such wide absorption coefficients as more than three orders? Here, it may be valuable to refer to Economous’ idea for rigid disorder systems [81]. They take the central limit theorem that predicts a Gaussian probability distribution p(ε) ∼ exp(−ε2 /constant) for a random variable ε, which is the depth of localized potentials in the present case. They also demonstrate that the binding energy E (bars in Fig. 6.7) of the localized state exhibits an approximate proportionality, |E| ∼ ε2 . Combining these two proportionalities, we straightforwardly obtain the exponential variation, D(E) ∼ exp{−|E|/constant}. Note that the same explanation can be applied to the exponential WAT in As2 S3 and so on. We also see the existence of minimal EU of ∼50 meV in noncrystalline materials, as shown in Fig. 6.8. All the disordered insulators, including water, appear to possess the Urbach edges with EU ≥ 50 meV. This value becomes smaller a bit at low temperatures, while the gross feature is contrastive to, for example, EU ≈ 25 meV in crystalline AgBr at room temperature, which markedly decreases at cryogenic temperatures [82]. It may also be interesting to note that the EU of many chalcogenide glasses distribute at around the minimal value. Tanaka has tried to relate the minimal energy to intrinsic density fluctuation in glasses [79], which is responsible for light scattering (Eq. (6.10)). However, since the observations are more universal covering vapor-deposited films such as a-Te and aSi:H, further considerations are needed. 6.2.3.3. Photoconductive Spectra Relationships between the optical and photoconductive spectra have attracted considerable interests, the examples having been shown in Figs. 6.3 and 6.4. Specifically, (stabilized) a-Se films are highly photoconductive, which arouses a lot of fundamental and application-oriented studies [59]. And, among several related topics,

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Fig. 6.8. The Urbach energy EU as a function of the optical gap Eg or EgT at room temperature for chalcogenides, oxides, tetrahedrals, organics, and liquids. (Modified from [79].)

the most important may be the “non-photoconducting gap” which is conspicuous in a-Se (and also in ring-type crystalline Se) but does not exist in trigonal Se (see [15] in [31]). At present, it is accepted in general that the non-photoconducting gap is governed by carrier-generation process, which can be delineated using the so-called geminate-recombination model [6, 8, 83]. It treats photo-excited electrons and holes as classical charged particles, which undergo Brownian motions under applied electric fields, and eventually geminate pairs having small kinetic energies recombine, giving rise to no photocurrents. Under the model, the photo-generation efficiency η(ω) can be approximated as [84]; η(ω) ∼ exp{−(ω − Egpc )−1/2 } for ω ≥ Egpc

(6.7a)

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Fig. 6.9. Comparison of optical and photoconductive spectra; absorption α, photo-generation quantum efficiencies η(KD) [63] and η(PE) [83], CPM [31], and theoretical η (Eq. (6.7) with Egpc = 2.35 eV) for a-Se at room temperature (modified from [84]).

and ∼ exp{(ω − Egpc )/kB T } for ω ≤ Egpc .

(6.7b)

We see in Fig. 6.9 that Eq. (6.7a) with the photoconducting gap Egpc (= 2.35 eV), which is determined as a fitting parameter, gives satisfactory agreements between the theoretical and the experimental spectra (two ηs and a CPM spectrum) at ω ≥ Egpc .3 On the other hand, regarding Eq. (6.7b), we see that there exists an exponential spectrum with a slope of kB T , which may be referred to as “photoconducting Urbach edge” However, the edge tends to be masked by residual responses extending at 1.1–2.2 eV, which have been demonstrated to be governed by hole currents [63], with its origin being unknown. 3

Egpc has been assumed to approximate the mobility gap Egµ (arising from oneparticle transport in disordered potentials) in Section 6.2.3.1, which is different from the present interpretation of the geminate-carrier recombination. The relationship is pending.

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6.2.3.4. Weak Absorption Tail (WAT) Characterization and interpretation of the WAT seem to be vitally important due to its low-energy, spectral position. It suggests that the WAT arises from gap states, which may govern electrical and photoelectric properties. So far, we have revealed exponential WATs for several glasses such as As2 S3 , As2 Se3 , Ge20 Se80 and Ge–As(Sb)– Se [5, 8, 11]. On the other hand, features in Se have not been reproduced [12, 59], and Ge2 Sb2 Te5 exhibits small peaks at midgap regions [26, 27, 67] (Fig. 6.5). It should also be emphasized that the understanding of origins giving rise to the residual absorption is necessitated for devising more transparent (near-) infrared optical fibers. However, we may not yet have attained intrinsic WAT spectra. Experimentally, we should evaluate the absorption with levels of α ≤ 10 cm−1 , under distinguishing it from light scattering. Specifically, the intensity of Rayleigh scattering follows ∼1/λ4 dependence, monotonically decreasing with increasing ω in a similar way to a typical WAT does, and accordingly the distinction needs sophisticated measurements [5, 12, 24]. Besides, the absorption tail is known to be raised by impurities, such as Fe in As2 S3 (Fig. 6.10) [5, 85], O in Cu6 As4 S9 [86], and Ag in As2 Se3 [87]. (Note that metallic impurities such as Cu, Ag, and Au also affect upon the Tauc gap and Urbach edge.) Nevertheless, as shown in Fig. 6.10, even in high-purity As2 S3 ingots, the WAT still exists [11, 12]. In addition, in the As–S system, the tail varies with the composition, being most prominent at around As2 S3 [12]. These observations strongly suggest that the exponential WAT is intrinsic to some glasses. Here, we should also recall that the residual response in As2 S3 is much suppressed in the photoconductive spectrum (Fig. 6.3), while in the excitation spectrum of photoluminescence (PLE) a WAT-like exponential curve appears. This fact evinces that the WAT arises from the localized gap states that contribute to radiative recombination but do not to electrical transport.

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Fig. 6.10. Absorption spectra of a high-purity bulk As2 S3 ingot (open circles) and its as-evaporated film (solid circles), evaluated using PDS. Also shown by solid lines are those in Fe-doped As2 S3 glasses with the Fe concentration indicated. (Reproduced from [26] with permission of AIP Publishing.)

Since electrons are practically immobile in most chalcogenide glasses, we envisage as shown in Fig. 6.7 that the WAT reflects photo-electronic transitions to tail states below the conduction band. Photo-excited carriers may form trapped electrons and paired holes, which undergo instantaneous recombination, giving rise to no photocurrents. This idea also implies that the photoluminescence with a peak at ∼Eg /2 arises through recombination of the pairs. What is an atomic origin of the WAT? It seems that wrong bonds [88], the existence being inherent in covalent chalcogenide glasses, are responsible for the WAT. This assertion is consistent with several observations [8, 89]; the compositional WAT variation in the As–S system, the different WAT levels in bulk and As-evaporated As2 S3 (Fig. 6.10), and non-existence of exponential residual tails in a-Si:H and SiO2 glass. Theoretical calculations for As2 S3 and GeS2

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also suggest that the anti-bonding states of As–As and Ge–Ge bonds produce tail states below the conduction band [2, 90]. Incidentally, As–O bonds produce no gap-states [62]. Finally, the present idea predicts that S(Se)-rich As–S(Se) glasses are more suitable for producing low-loss optical fibers than the stoichiometric As2 S(Se)3 . Nevertheless, it remains to be a crucial subject that if ultrapure a-Se is completely transparent. 6.3. Infrared Transparency It has long been known that one of unique characters of chalcogenide glasses, in comparison with those in oxides, is the infrared transparency [5, 91], as exemplified in Fig. 6.1. It is known that the infrared absorption in semiconductors is governed by vibrational modes, the typical frequency distributing at around (k/Ma )1/2 , where k is the force constant (∼104 dyn/cm) and Ma is an effective atomic mass, which varies with vibrational modes. And, the marked infrared transparency is due primarily to the heavier atomic mass of the chalcogen (∼10−22 g) than that of oxygen (∼10−23 g). Nevertheless, as shown in Fig. 6.1, the transparency is suppressed by spectral losses arising from several factors; impurity absorption, multi-phonon absorption, free-carrier absorption, WAT, and light scattering [11, 15, 91, 92]. The impurity absorption in infrared regions is dominated by resonant vibrations of light atoms, for example, C, -SH, and -OH, and so on, producing sharp peaks in Fig. 6.1, which will be ultimately reduced by sophisticated purification procedures [15]. The multi-phonon absorption is approximated as; α ∼ C1 exp(−C2 /λ),

(6.8)

where Cs are constants. The free-carrier absorption in an intrinsic semiconductor with the energy gap of Eg is formulated as; α ∼ λ2 exp{−Eg /(2kB T )},

(6.9)

and accordingly, it becomes appreciable in tellurides with Eg ≈ 1 eV at high temperatures [93]. On the other hand, the minimal scattering

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loss αs is governed by the Rayleigh scattering; αs ∼ n8 p2 (δρ)2 /λ4 ,

(6.10)

where n is the refractive index, p the photoelastic constant, and (δρ)2  represents the Einstein–Smolukovskii density fluctuation which is inherent to the glass prepared through quenching from the melt; (δρ)2  ≈ kB Tg ρ2 /(BV ), where Tg is the glass-transition temperature, ρ the density, B the bulk modulus, and V (≥(10 nm)3 ) a typical scale of fluctuation. In multi-component glasses, compositional fluctuation further increases light scattering. Obviously, voids should be reduced as much as possible [92]. Applications to infrared optical devices such as lenses and fibers have substantially been developed. For instance, Shiryaev and Churbanov [15] document that the best quality multimode fiber with an As2 S3 /As–S structure attains a propagation loss L (absorption plus scattering) of 12 dB/km at λ = 3 μm. This corresponds to an attenuation coefficient4 of 10−5 cm−1 at ω = 0.4 eV, the point being indicated by a star symbol in Fig. 6.1. However, this loss is still much higher than that (∼0.1 dB/km) arising from the intrinsic scattering, Eq. (6.10) [11, 15]. The discrepancy may be due to the WAT, impurities, and/or non-ideal fiber structures. 6.4. Conclusions with Future Perspectives We now have obtained detailed optical data of simple and/or topical chalcogenide glasses. Many studies have unveiled characteristics concerning the Tauc curve, Urbach edge, photoconductive, and vibrational spectra. And, the present chapter suggests that the electronic spectra could be interpreted using the refined CohenFritzsche–Ovshinsky model. However, further studies are needed for spectra below the optical gap, including WAT and photoluminescence, which are likely to be affected by some impurities. Ultra-pure samples are needed to reveal intrinsic, gap-state-related properties. For instance, we cannot yet 4

L(dB/m) ≈ 434 α(cm−1 ).

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convincingly answer such a simple question “Is a-Se as transparent as the ideal crystalline semiconductor?”. The transparency has been presumed in the charged-defect model [6], while it is questionable if the concept could be primarily in the covalent stoichiometric glass, which inherently contains many wrong bonds. It should also be mentioned that the limited transparency in the WAT region poses an unavoidable problem for further improvements of (near-) infrared optical fibers. In more details, many fundamental features remain unresolved. For instance, how can we understand the functional form of the Tauc curve, which provides satisfactory fits to experimental data over wide spectral regions covering estimated positions of the mobility gaps? Why do the Urbach edge and WAT appear to be exponential? The Economous’ idea is tempting for rigid-lattice systems, while we wonder if it could be applied to a-Se having flexible atomic structures. We also need to refine a proposed interpretation on the minimal Urbach energy of ∼50 meV, which stands not only for chalcogenides but also for SiO2 and a-Si:H. More basically, new insights into defective, medium-range, and inhomogeneous atomic structures are invaluable to innovate in the chalcogenide-glass optical science. Acknowledgment The author would like to thank Professor V. Shiryaev for private information on transparency in Se fibers and Dr. T. Gotoh for supplementary PDS results. References 1. Street, R. A. (1976). Photoluminescence in amorphous semiconductors, Advances in Physics, 25, pp. 397–453. 2. Tanaka, K. (2013). Photoluminescence in chalcogenide glasses: Revisited. The Journal of Optoelectronics and Advanced Materials, 15, pp. 1165–1178. 3. Sanghera, J., and Gibson, D. (2014). Optical properties of chalcogenide glasses and fibers. In: Chalcogenide Glasses, edited by. Adam, J. L., and Zhang, X. (Oxford, England, Woodhead Publishing Limited), Chapter 5, pp. 113–138.

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4. Tanaka, K. (2017). Optical nonlinearity in photonic glasses. In: Handbook of Electronic and Photonic Materials, edited by Kasap, S., and Capper, P. (New York, NY, Springer), pp. 1081–1094. 5. Tauc, J. (1974). Amorphous and Liquid Semiconductors (London, England, Plenum Press). 6. Mott, N. F., and Davis, E. A. (1979). Electronic Processes in NonCrystalline Materials (Oxford, England, Clarendon Press). 7. Popescu, M. A. (2000). Non-Crystalline Chalcogenides (Dortrecht the Netherlands, Kluwer Academic Publishers). 8. Tanaka, K., and Shimakawa, K. (2011). Amorphous Chalcogenide Semiconductors and Related Materials (New York, NY, Springer). 9. Young, P. A. (1971). Optical properties of vitreous arsenic trisulphide. Journal of Physics C: Solid State Physics, 4, pp. 93–106. 10. Eguchi, H., and Hirai, M. (1990). Spectral variation of amorphous As2 S3 after the initial annealing and photodarkening, Journal of the Physical Society of Japan, 59, pp. 4542–4546. 11. Nishii, J., and Yamashita, T. (1998). Infrared fiber optics. In: Chalcogenide Glass-Based Fibers, edited by Sanghera, J. S., and Aggarwal, I. D. (Boca Raton, FL: CRC Press), Chapter 4, pp. 143–184. 12. Tanaka, K., Gotoh, T., Yoshida, N., and Nonomura, S. (2002). Photothermal deflection spectroscopy of chalcogenide glasses, Journal of Applied Physics, 91, pp. 125–128. 13. Rodney, W. S., Malitson, I. H., and King, T. A. (1958). Refractive index of arsenic trisulfide, Journal of the Optical Society of America, 48, pp. 633–636. 14. Cimpl, Z., Kosek, F., Husa, V., and Svoboda, J. (1981). Refractive index of arsenic trisulfide, Czechoslovak Journal of Physics B, 31, pp. 1191–1194. 15. Shiryaev, V. S., and Churbanov, M. F. (2017). Recent advances in preparation of high-purity chalcogenide glasses for mid-IR photonics, Journal of Non-Crystalline Solids, 475, pp. 1–9. 16. Sadigh, B., et al. (2011). First-principles calculations of the Urbach tail in the optical absorption spectra of silica glass, Physical Review Letters, 106, p. 027401. 17. Dersch, U., Gr¨ unewald, M., Overhof, H., and Thomas, P. (1987). Theoretical studies of optical absorption in amorphous semiconductors, Journal of Physics C: Solid State Physics, 20, pp. 121–143. 18. Weiser, G. (1989). Evidence for energy dependent optical matrix elements in the electroabsorption spectra of amorphous semiconductors, Journal of Non-Crystalline Solids, 114, pp. 250–252. 19. Singh, J., and Shimakawa, K. (2003). Advances in Amorphous Semiconductors (London, England, Taylor & Francis).

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20. Lucovsky, G., Sremaniak, L. S., Mowrer, T., and Whitten, J. L. (2003). A new approach for calculating the electronic structure and vibrational properties of non-crystalline solids: Effective charges for infrared-active normal mode vibrations in oxide and chalcogenide materials, Journal of Non-Crystalline Solids, 326–327, pp. 1–14. 21. Wemple, S. H. (1973). Refractive-index behavior of amorphous semiconductors and glasses, Physical Review B, 7, pp. 3767–3777. 22. Tich´ a, H., and Tich´ y, L. (2002). Semiempirical relation between non-linear susceptibility (refractive-index), linear refractive index and optical gap and its application to amorphous chalcogenides, The Journal of Optoelectronics and Advanced Materials, 4, pp. 381–386. 23. Tan, W. C., et al. (2010). Optical characterization of a-As2 S3 thin films prepared by magnetron sputtering, Journal of Applied Physics, 107, p. 033524. 24. Mandelis, A. editor (1987). Photoacoustic and Thermal Wave Phenomena in Semiconductors (New York, NY, North-Holland). 25. Jackson, W. B., and Amer, N. M. (1982). Direct measurement of gapstate absorption in hydrogenated amorphous-silicon by photothermal deflection spectroscopy, Physical Review B, 25 pp. 5559–5562. 26. Gotoh, T. (2012). Sub-gap states in Ge2 Sb2 Te5 phase change films, Journal of Non-Crystalline Solids, 358, pp. 2366–2368. 27. Gotoh, T. (2019). Defect absorption in Ge2 Sb2 Te5 phase-change films, Physica Status Solidi B, 1900278. 28. Raty, J. Y., et al. (2015). Aging mechanisms in amorphous phasechange materials. Nature Communications, 6, p. 7467. 29. Todorov, R. et al. (2013). Ellipsometric characterization of thin films from multicomponent chalcogenide glasses for application in modern optical devices, Advances in Condensed Matter Physics, 2013, p. 308258. 30. Vanecek, M., et al. (1983). Density of the of the gap states in undoped and doped glow-discharge a-Si:H, Solar Energy Materials and Solar Cells, 8, pp. 411–423. 31. Tanaka, K., and Nakayama, S. (1999). Band-tail characteristics in amorphous semiconductors studied by the constant-photocurrent method, Japanese Journal of Applied Physics, 38, pp. 3986–3992. 32. Lee, B. S., et al. (2007). Response to “Comment on ‘Investigation of the optical and electronic properties of phase change material in its amorphous, cubic, and hexagonal phases’ ” [Journal of Applied Physics, 97, 093509 (2005)], Journal of Applied Physics, 101, p. 026112. 33. Meherun-Nessa, Shimakawa, K., Ganjoo, A., and Singh, J. (2000). Fundamental optical absorption on fractals: A case example for amorphous

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chalcogenides, The Journal of Optoelectronics and Advanced Materials, 2, pp. 133–138. Andreev, A. A., et al. (1976). Temperature dependence of the absorption edge of As2 Se3 and AsSe in the solid and liquid states, Soviet Physics Solid State, 18, pp. 29–31. P´etursson, J., Marshall, J. M., and Owen, A. E. (1991). Optical absorption in As-Se glasses, Philosophical Magazine B, 63, pp. 15–31. Hosokawa, S., Sakaguchi, Y., Hiasa, H., and Tamura, K., (1991). Optical absorption spectra of liquid As2 S3 and As2 Se3 over a wide temperature range, Journal of Physics: Condensed Matter, 3, pp. 6673– 6677. Tich´ a, H., et al. (2000). Temperature dependence of the optical gap in thin amorphous films of As2 S3 , As2 Se3 and other basic non-crystalline chalcogenides, Journal of Physics and Chemistry of Solids, 61, pp. 545– 550. Tich´ y, L., and Tich´ a, H. (1992). The temperature dependence of the optical gap of glassy GeSe2 , Materials Letters, 15, pp. 198–201. Zallen, R., Drews, R. E., Emerald, R. L., and Slade, M. L (1971). Electronic structure of crystalline and amorphous As2 S3 and As2 Se3 , Physical Review Letters, 26, pp. 1564–1567. Tanaka, K. (1989). Pressure studies of amorphous semiconductors. In: Disordered Systems and New Materials, edited by Borossov, M., Kirov, N., and Vavrek, A. (Singapore, World Scientific), pp. 290–309. Galkiewics, R. K., and Tauc, J. (1972). Photoelastic properties of amorphous As2 S3 , Solid State Communications, 10, pp. 1261–1264. Weiser, G., Dersch, U., and Thomas, P. (1988). Polarized electroabsorption spectra of amorphous semiconductors, Philosophical Magazine B, 57, pp. 721–735. Mazets, T. F., et al. (1986). The electrooptic effect — a comparative study of a-Si:H and chalcogenide glasses, Journal of Non-Crystalline Solids, 83, pp. 237–240. Liu, A. C. Y., Chen, X., Choi, D. Y., and Luther Davies, B. (2008). Annealing-induced reduction in nanoscale heterogeneity of thermally evaporated amorphous As2 S3 films, Journal of Applied Physics, 104, p. 093524. Soyer-Uzun, S., Benmore, C. J., Siewenie, J. E., and Sen, S. (2010). The nature of intermediate-range order in Ge–As–S glasses: Results from reverse Monte Carlo modeling, Journal of Physics: Condensed Matter, 22, p. 115404. Darmawikarta, K., Li, T., Bishop, S. G., and Abelson, J. R. (2013). Two forms of nanoscale order in amorphous Gex Se1−x alloys, Applied Physics Letters, 103, p. 131908.

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47. Boolchand, P., et al. (2002). Nanoscale phase separation effects near r = 2.4 and 2.67, and rigidity transitions in chalcogenide glasses, Comptes Rendus Chimie, 5, pp. 713–724. 48. Phillips, J. C. (1979). Topology of non-crystalline solids. 1. Short-range order in chalcogenide alloys, Journal of Non-Crystalline Solids, 34, pp. 153–181. 49. Oheda, H. (1979). The exponential absorption edge in amorphous Ge–Se compounds, Japanese Journal of Applied Physics, 18, pp. 1973– 1978. 50. Yang, G., et al. (2010). Correlation between structure and physical properties of chalcogenide glasses in the Asx Se1−x system, Physical Review B, 82, p. 195206. 51. Gurman, S. J., Choi, J., and Davis, E. A. (1998). Prediction and measurement of the optical properties of amorphous Gex Se1−x , Journal of Non-Crystalline Solids, 227–230, pp. 833–836. 52. Yang, G., et al. (2013). Physical properties of the Gex Se1−x glasses in the 0 < x < 0.42 range in correlation with their structure, Journal of Non-Crystalline Solids, 377, pp. 54–59. 53. Yang, Y., et al. (2016). Composition dependence of physical and optical properties in Ge–As–S chalcogenide glasses, Journal of Non-Crystalline Solids, 440, pp. 38–42. 54. deNeufville, J. P., Moss, S. C., and Ovshinsky, S. R. (1973/74). Photostructural transformations in amorphous As2 Se3 and As2 S3 films, Journal of Non-Crystalline Solids, 13, pp. 191–223. 55. Terakado, N., and Tanaka, K. (2008). The structure and optical properties of GeO2 –GeS2 glasses, Journal of Non-Crystalline Solids, 354, pp. 1992–1999. 56. Tanaka, K., and Nakayama, S. (2000). Where is the mobility edge in amorphous semiconductors? The Journal of Optoelectronics and Advanced Materials, 2, pp. 5–11. 57. Kumar, R. T. A., Lekhab, P. C., Sundarakannana, B., and Padiyan, D. P. (2012). Influence of thickness on the optical properties of amorphous GeSe2 thin films: Analysis using Raman spectra, Urbach energy and Tauc parameter, Philosophical Magazine, 92, pp. 1422–1434. 58. Stuke, J. (1974). Optical and electrical properties of selenium. In: Selenium, edited by Zingaro, R. A., and Cooper, W. C. (New York, NY, Van Nostrand Reinhold Company), pp. 174–297. 59. Tanaka, K. (2019). Amorphous selenium and nanostructures. In: Springer Handbook of Glass, edited by Musgrave, J.D., Hu, J., and Calvez, L. (Springer International Publishing) pp. 473–513. 60. Kasap, S., et al. (2015). Charge transport in pure and stabilized amorphous selenium: Re-examination of the density of states distribution in

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the mobility gap and the role of defects, Journal of Materials Science: Materials in Electronics, 26, pp. 4644–4658. Adriaenssens, G. J., and Benkhedir, M. L. (2008). Energy levels and charge state of intrinsic defects in amorphous selenium, Journal of Non-Crystalline Solids, 354, pp. 2687–2690. Tanaka, K. (2015). Gap states in non-crystalline selenium: Roles of defective structures and impurities, The Journal of Optoelectronics and Advanced Materials, 17, pp. 1716–1727. Knights, J. C., and Davis, E. A. (1974). Photogeneration of charge carriers in amorphous selenium, Journal of Physics and Chemistry of Solids, 35, pp. 543–554. Derbidge, C., and Taylor, P. C. (2005). Photoluminescence and optical absorption in glassy Asx Se1−x , Journal of Non-Crystalline Solids, 351, pp. 233–238. Tanaka, K. (2017). Excitation-induced effects in selenium clusters: Molecular-orbital analyses, The Journal of Optoelectronics and Advanced Materials, 19, pp. 586–594. Vinod, E. M., et al. (2010). Temperature dependent optical constants of amorphous Ge2 Sb2 Te5 thin films, Journal of Non-Crystalline Solids, 356, pp. 2172–2174. Olson, J. K., et al. (2006). Optical properties of amorphous GeTe, Sb2 Te3 , and Ge2 Sb2 Te5 : The role of oxygen, Journal of Applied Physics, 99, p. 103508. Kato, T., and Tanaka, K. (2005). Electronic properties of amorphous and crystalline Ge2 Sb2 Te5 films, Japanese Journal of Applied Physics, 44, pp. 7340–7344. Lee, B. S., et al. (2005). Investigation of the optical and electronic properties of Ge2 Sb2 Te5 phase change material in its amorphous, cubic, and hexagonal phases, Journal of Applied Physics, 97, p. 093509. Gotoh, T., and Kawarai, K. (2010). The study of structural changes of amorphous Ge2 Sb2 Te5 films after annealing by optical absorption spectroscopy, Physica Status Solidi A, 207, pp. 639–641. Tanaka, K. (2016). Have we understood the optical absorption edge in chalcogenide glasses? Journal of Non-Crystalline Solids, 431, pp. 21–24. Vanhuyse, B., Grevendonk, W., Adriaenssens, G. J., and Dauwen, J. (1987). Constant-dipole-matrix-element model for Faraday-rotation in amorphous semiconductors, Physical Review B, 35, pp. 9298–9300. ´ Di Matteo, O., and Rubel, O. (2012). Darbandi, A., Devoie, E., Modeling the radiation ionization energy and energy resolution of trigonal and amorphous selenium from first principles, Journal of Physics: Condensed Matter, 24 p. 455502.

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74. Hosokawa, S., et al. (1993). Inverse-photoemission spectra of amorphous chalcogenides, Journal of Non-Crystalline Solids, 164–166, pp. 1199–1202. 75. Thornburg, D. D. (1973). Physical properties of the As2 (Se, Te)3 glasses, Journal of Electronic Materials, 2, pp. 495–532. 76. Shportko, K., et al. (2008). Resonant bonding in crystalline phasechange materials, Nature Materials, 7, pp. 653–658. 77. Chopra, K. L., and Bahl, S. K. (1972). Exponential tail of the optical absorption edge of amorphous semiconductors, Thin Solid Films, 11, pp. 377–388. 78. Studenyak, I. P., Kranjˇcec, M., and Kurik, M. (2014). Urbach rule in solid state physics, International Journal of Optics and Applications, 4, pp. 76–83. 79. Tanaka, K. (2014). Minimal Urbach energy in non-crystalline materials, Journal of Non-Crystalline Solids, 389, pp. 35–37. 80. Monroe, D., and Kastner, M. A. (1986). Exactly exponential band tail in a glassy semiconductor, Physical Review B, 33, pp. 8881–8884. 81. Bacalis, N., Economou, E. N., and Cohen, M. H. (1988). Simple derivation of exponential tails in the density of states, Physical Review B, 37, pp. 2714–2717. 82. Moser, F., and Urbach, F. (1956). Optical absorption of pure silver halides, Physical Review, 102, pp. 1519–1524. 83. Pai, D. M., and Enck, R. C. (1975). Onsager mechanism of photogeneration in amorphous selenium, Physical Review B, 11, pp. 5163–5174. 84. Tanaka, K. (2015). Photoconducting Urbach edge in amorphous Se, Journal of Non-Crystalline Solids, 426, pp. 32–34. 85. Fowler, T. G., and Elliott, S. R. (1983). Optical and electronicproperties of Fe doped bulk a-As2 S3 . Journal of Non-Crystalline Solids, 59, pp. 957–960. 86. Girlani, S. A., Yan, B., and Taylor, P. C. (1998). Doping in metal chalcogenide glasses, Semiconductors, 32, pp. 879–883. 87. Kitao, M., Mochizuki, T., and Yamada, S. (1973), Variation of photoconductivity spectra of amorphous As2 Se3 with light chopping frequency, Japanese Journal of Applied Physics, 12, pp. 1077–1078. 88. Halpern, V. (1976). Localized electron states in the arsenic chalcogenides, Philosophical Magazine A, 34, pp. 331–335. 89. Tanaka, K. (2002). Wrong bond in glasses: A comparative study on oxides and chalcogenides, The Journal of Optoelectronics and Advanced Materials, 4, pp. 505–512. 90. Hachiya, K. (2003). Electronic structure of the wrong-bond states in amorphous germanium sulphides, Journal of Non-Crystalline Solids, 321, pp. 217–224.

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91. Kokorina, V. V. (1996). Glasses for Infrared Optics (Boca Raton, FL, CRC Press). 92. Sanghera, J. S., Busse, L. E., and Aggarwal I. D. (1994). Effect of scattering centers on the optical loss of As2 S3 glass fibers in the infrared, Journal of Applied Physics, 75, pp. 4885–4891. 93. Inagawa, I., Morimoto, S., Yamashita, T., and Shirotani, I. (1997). Temperature dependence of transmission loss of chalcogenide glass fibers, Japanese Journal of Applied Physics, 36, pp. 2229–2235. 94. Tanaka, K. (2013). Excitation-energy-dependent photoluminescence in glassy As–S and crystalline As2 S3 , Physica Status Solidi B, 250, pp. 988–993.

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CHAPTER 7

Electrical Transport Properties Koichi Shimakawa Center of Innovative Photovoltaic Systems Gifu University, Gifu, Japan

The aim of this chapter is to review the current understanding of electronic and ionic transports in chalcogenide glasses. When the conduction, either electronic or ionic, is thermally activated, it is shown that the prefactor of conductivity itself depends on the activation energy. It is called the Meyer–Neldel rule, which is a long-standing puzzling issue. The pn anomaly is also an unsolved problem in chalcogenide glasses. Another unsolved issue for ionic transport is the mixed cation effect, which was originally found in oxide glasses. Origin of all these long-standing puzzles will be discussed in this chapter.

7.1. Introduction The electronic transport in solids, in general, is controlled by phonons. We should therefore discuss the two extreme cases; either the transport in a rigid lattice at which the electron–phonon coupling is ignored or in a deformable lattice at which a carrier accompanies lattice distortion. We briefly review the theoretical background on these issues in chalcogenide glasses. In a rigid network of atoms in a disordered semi-conductor, electrons (holes) are assumed to move through the band (extended) states and/or through the localized states, without being subjected to the lattice deformations. The electron–phonon coupling is therefore ignored in this case [1]. The electronic configuration of individual 177

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Fig. 7.1. Electronic density of states D(E). The mobility edge divides the delocalized (above Ec and below Ev ) and localized states (shaded area).

atoms in a solid remains the same in both crystalline and disordered solids. Therefore, the electronic density of states (DOS) for disordered solids in the extended states is similar to that in crystalline solids: It can be approximated by the square root of the energy in three-dimensional (3D) configuration. In this regime, the electrical properties should be dominated by the electronic DOS as shown in Fig. 7.1. The nature of carriers gets altered when a charge carrier crosses the energies Ec and Ev , which separate the extended and localized states and are called the mobility edge. The transport above Ec is the band conduction type for electrons and transport below Ev is band conduction type for holes. However, due to the lack of long-range orders, the carrier mean free path approaches the length scale of atomic separation, which may produce various anomalies in the electronic transport in disordered solids [2]. The lack of long-range order and presence of dangling bond (defects), producing localized tail states (shaded region between Ev and Ec ) and localized gap states, respectively. Note that deep localized states (gap states) are not shown in this figure. As these states dominate the AC transport, details of the gap states will be discussed in Section 7.2. An extra electron or hole in crystalline or non-crystalline system can distort its deformable surroundings. A carrier accompanied by such distortion lowers its overall energy and it is called a polaron [1, 3–5]. When the spatial extent of the wavefunction of such a carrier

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is less than or comparable with the inter-atomic or inter-molecular separation, it is called a small polaron (strong electron–phonon interaction), otherwise it is a large polaron (weak electron–phonon interaction) [4]. It is known that small polarons exist, for example, in alkali halides, molecular crystals, rare-gas solids, and some glasses [4, 5]. It is not clear whether the small polaron dominates the electronic transport in chalcogenide glasses [1, 6]. We therefore discuss here only the electronic transport in rigid lattice. 7.2. Electronic Transport in Extended States We know that the majority carrier is hole in chalcogenide glasses [1, 2]. We therefore discuss the non-degenerate hole transport (p-type) through in the extended state. The temperature-dependent density of free holes p in the valence band (VB), beyond the energy Ev , near room temperature, is given as   EF − EV (7.1) p = Nv exp − kT where Nv is the effective DOS for the VB and EF the Fermi level. The conductivity is therefore given by   EF − Ev , (7.2) σ = epμ0 = eNv μ0 exp − kT where μ0 is the microscopic mobility. As EF − Ev can be approximated to vary linearly with the temperature as EF − Ev = EF (0) − γT − Ev , where EF (0) is the Fermi level at T = 0 and γ the temperature coefficient, the conductivity is then given as   γ  EF (0) − Ev exp − σ = epμ0 = eNv μ0 k kT   EF (0) − Ev . (7.3) ≡ σ0 exp − kT The conductivity is thermally activated with the activation energy ΔE = EF (0) – Ev . EF (0) lies between Ec and Ev . Note that the abovementioned equations stand on the Boltzmann transport theory and hence depend on the assumption that the mean free

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path, for example, is large enough as compared with the lattice constant. Equation (7.3) is therefore valid for ordered (crystalline) semi-conductors. When the mean free path is of the order of a lattice constant, the Boltzmann formula breaks down [2], in which σ0 cannot be given by eNv μ0 exp(γ/k). Strictly speaking in glasses, a proper theoretical understanding of the pre-factor σ0 is still lacking. For a degenerate electron (hole) in glasses (metallic glasses), that is, Fermi energy EF lies above Ec (below Ev ), metallic behavior for electronic transport is expected. When it lies below Ec (above Ev ), the transport occurs through localized states at low temperatures and the conductivity at zero temperature vanishes. Thus, when the Fermi level crosses the mobility edges, a discontinuous conductivity, that is, from a finite value to zero, was expected to occur. This finite value of conductivity was called the minimum metallic conductivity σmin : The pre-factor σ0 was given by σmin , which is taken roughly y to be 200 Scm−1 [1, 2]. This famous concept of the minimum metallic conductivity proposed by Mott was survived by the beginning of 1980 in the field of localization theory [2]. However, this concept is no longer supported by the scaling theory [7] and some experimental results in which conductivity is tending continuously to zero at zero temperature [8, 9]. In chalcogenide glasses, EF lies in the bandgap (between Ec and Ev ) and hence the electronic conductivity can be always given by a standard theory (Eqs. (7.1)–(7.3)) [10]. First, we will show the experimental results of the DC conductivity of the most chalcogenide glasses (ChGs) (amorphous chalcogenide thin films as well) near room temperature, which is thermally activated with the activation energy ΔE [1, 11] and is given by   ΔE , (7.4) σ = σ0 exp − kT where σ0 is a constant and the relation of ΔE ∼ (Ec – Ev )/2 suggests that the band transport dominates the DC electrical conduction. As will be discussed later, the p-type (hole) signature is reported in the thermoelectric power measurements and hence ΔE is given as

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Ev −EF (0) (see Eq. (7.3)). Most ChGs are known to be weakly p-type materials. It is believed that the significant density of charged defects (D+ , D− ) (see Chapter 21) may pin the Fermi level closer to the VB edge. It should be noted that the Hall measurement in ChGs does not give correct signature of carrier type in ChGs, while in crystalline semi-conductors the Hall measurement is a principal technique for determining the carrier type (p or n), which will be discussed later. It should be noted that there is still an important issue that is not properly understood. This is called the Meyer–Neldel rule (MNR) or the compensation law [12]. The pre-factor in Eq. (7.3) σ0 is not a constant and it correlates with the activation energy ΔE as σ0 = σ00 exp(ΔE/EMN ),

(7.5)

where EMN is called the Meyer–Neldel characteristic energy and σ00 is a constant. Example of the NMR is shown in Fig. 7.2 for some ChGs [13]. The relation between ln σ0 and ΔE for As–Se–S system produces EMN = 43 meV and σ0 = 1 × 10−15 S cm−1 . Note for ChGs

Fig. 7.2. The pre-exponential factor σ0 plotted as a function of ΔE in several chalcogenide glassy systems. After [11]

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In(σ00/S.cm–1)

–10 a-Si:H P-Se (2) As-S Se-S-Te As-S-Se As-S-I P-Ge-Se As-Ge-Se (2) As-Se-K

–20 –30 –40

–50 0.00

0.02

0.04

0.06

P-Se (1) P-Se (3) As-P-Se Se-S-Te-Ge-As As-Se-I As-Se-Bi As-Ge-Se (1) Ge-Te-Cu

0.08

0.10

EMN (eV)

Fig. 7.3. Correlation between σ00 and the Meyer–Neldel energy EMN for some chalcogenide glasses and a-Si:H. After [13]

that EMN lies in the range 25–60 meV and σ00 in the range 10−5 – 10−15 S cm−1 . A similar effect is also found in hydrogenated amorphous silicon (a-Si:H), which is well explained by the statistical shift of the Fermi level (i.e., the temperature variation of the Fermi level) [14]. Although EMN lies in almost the same range for both a-Si:H and ChGs, σ00 for ChGs is very much smaller than that (∼1 Scm−1 ) for a-Si:H. The σ00 in a-Si:H is close in value to the microscopic conductivity, eμ0 Nc (see Eq. (7.2)), for the standard band transport model. Note that similar values of σ00 (10−3 –10−15 S cm−1 ) have been found in organic semiconductors [13]. The common features for small σ00 between ChGs and organic semi-conductors can be attributed to quantum tunneling through barriers, which may exist in relatively low-dimensional soft materials. Figure 7.3 shows a surprising correlation between σ00 and EMN reported in ChGs:  exp(EMN /ε), σ00 = σ00

(7.6)

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where ε is a constant (1.7 meV), meaning that a large EMN produce larger pre-exponential term [13]. This correlation is not found in aSi:H ( ), which suggests the difference of the origin of the MN rule. It should be noted that the MNR is also found in some kinetics such as the reaction rate that is thermally activated. The kinetic rate, for example, the hopping rate ν is followed by ν = ν0 exp(−U /kT ) = ν00 exp(U/EMN ) exp(−U /kT ),

(7.7)

where U is the energy barrier. This kind of compensation law is found in ionic transport even for crystalline solids, and this can be explained in terms of phonon absorption and emission processes with lattice distortion [15]. As the MNR is universally observed in a wide class of materials, the multi-excitation entropy is suggested to be important in some kinetics and thermodynamics. As a general explanation, multi-phonon excitations for example, hopping of small polarons should be a candidate for explaining the MNR, in which the pre-factor σ0 is proportional to the number of ways of assembling these excitations (entropy effect) [12] and hence EMN corresponds to the optical phonon energy. However, there is no clear evidence that the small polarons exist and dominate the electronic transport in ChGs and/or a-Si:H [12, 13]. Next important issue is what happen if the carrier scattering time is very short ( EF and is positive for E < EF . S for holes associated with the VB is given as [17]     k Es k EF − Ev +1 = +1 , (7.14) S= e kT e kT where Es = EF − Ev . The value of Es that appeared in S should be the same as Eσ (= ΔE). However, Es is always smaller than Eσ , that is, Eσ = Es + ΔW , in ChGs, similarly to a-Si:H. The value of ΔW is reported to be around 0.2 eV in ChGs. Why such a difference of ΔW is appeared in ChGs and a-Si:H [16]? If the conduction or VB edge

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fluctuates energetically ΔW for some reasons, for example, the VB edge Ev takes various energies. Es is given by EF −Ev , resulting Eσ = Es +ΔW : Note here that the energy ΔW can be canceled out through carriers up and down, when “thermal” energy (thermoelectric power) is measured, while for “charge” transport (conductivity) ΔW should be involved [17]. This explanation looks similar to the two-channel model of conduction, that is, the carrier transport occurs via tail and band states, since hopping energy ΔW (up and down) is not involved in the thermoelectric power as stated earlier [16]. The model of the small polarons also involves the energy ΔW , that is, Eσ = Es + ΔW , since the hopping energy is canceled out in thermoelectric power [6]. The ΔW therefore corresponds to the hopping activation energy, and hence the small polaron binding energy is 2ΔW [4, 6]. There is no direct argument to prove which mechanism, two-channel or small polaron, is valid. In the case of a-Si:H, as stated, a macroscopic potential fluctuation in the band state has been considered as an acceptable mechanism [14]. 7.3. Electronic Transport in Localized States Carrier transport occurs also between localized states. Carrier transport via localized states is therefore completely different from that of the band conduction. The rate-determining process is the hopping of an electron from an occupied localized state (O) below the Fermi level to an empty state above (E). The probability ν per unit time for this event to occur is given by [1, 2]   W 2R − , (7.15) ν = ν0 exp − a kT where R and W , respectively, are the spatial distance and the energy difference between the states O and E, a is the Bohr radius of localized state, and the pre-factor ν0 is of the order of phonon frequency (∼1012 s−1 ). Note that the factor exp(−2R/a) represents the extent of overlapping of the wavefunction and exp(−W/kT ) the Boltzmann factor.

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A hopping of carrier resembles to the dipolar relaxation, that is, eR appeared in the hopping process can be equivalent to the electric dipole [19]. The complex dielectric constant ε∗ (ω), for example, for the Debye response in the field direction exp(iωt), is given as ε∗ (ω) = ε,∞ +

εs − ε∞ ≡ ε1 − iε2 , 1 + iωτ

(7.16)

where εs and ε∞ are the static (at low frequency) and background (high frequency) dielectric constants, respectively, and τ the dielectric relaxation time. The complex conductivity is defined as σ ∗ (ω) = iωε0 ε∗ (ω), where ε0 is dielectric constant in vacuum. So-called AC conductivity or AC loss is the real part of the conductivity given by ωε0 ε2 (ω). When the localized carrier is assumed to be confined within a pair of localized states (pair approximation: PA) and AC hopping, conductivity is given in the general form as [19]  ω2τ P (τ )dτ , (7.17) σ(ω) = Np α(τ ) 1 + ω2 τ 2 where Np is the number of pairs (dipoles), α(τ ) the polarizability, and P (τ ) the probability distribution function of τ . It is known for the most disordered solids that σ(ω) is nearly proportional to ω when P (τ ) is proportional to 1/τ [20, 21]. Note, however, that σ(ω) in this PA approximation does not give DC conductivity since σ(ω) becomes zero at ω = 0. In the context of the PA approximation, σ(ω) cannot account for the experimental data if both DC and AC transports occur by the same mechanism. A proper approach to hopping AC (and DC) conductivity can be a continuous-time random-walk (CTRW) approximation [22]. A simple form of the complex AC conductivity based on the CTRW is given as [23] σ ∗ ω = σ(0)

iωτm , ln (1 + iωτm )

(7.18)

where τm is the maximum hopping time (inverse minimum hopping rate) in the hopping process and σ(0) is the DC conductivity

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given as [24] nh (eR)2 . σ(0) = 6kT τm

(7.19)

Note here that the values of R and/or W in Eq. (7.15) are assumed to be distributed randomly. In earlier stage of the AC conductivity study in ChGs [20, 21], the AC and DC losses were thought to have different origins; that is, free holes in VB contribute to the DC transport and two electrons, as a bipolaron, can hop between oppositely charged coordination defect sites (e.g., using − notations C+ 3 − C1 in the top right sketch (ii)) as shown in Fig. 7.4, which induces AC loss; two electrons (or holes) hopping between − + − − + C+ 3 − C1 pair means that C3 + 2e → C1 and C1 + 2h → C3 , which accompany lattice relaxation [21]. The interconversion of their places induces the AC loss. Note that the neutral dangling bond C01 is not stable, which is shown in a configurational coordinate diagram (bottom of Fig. 7.4). To understand the bipolaron hopping mechanisms in details, readers need knowledges of the nature of defects, which are given in Chapter 3 and elsewhere [1, 25]. In the following, the brief summary on the bipolaron hopping proposed for ChGs is presented: The hopping time of bipolaron that surmount of barrier W is given as   W , (7.20) τ = τ0 exp − kT where τ0 is a characteristic time (∼10−12 s) and W the Coulombic potential energy between charged centers, which is correlated with site separation R. Therefore, this process is called the correlated barrier hopping (CBH) model [21]. Starting from Eq. (7.17), the real part of AC conductivity of bipolaron hopping is given as [21] σ(ω) =

π3 2 N ε0 ε∞ ωRω6 , 6 T

(7.21)

where NT is the density of charged defects, ε0 ε∞ the background dielectric constant, Rω the hopping distance (site separation R) at ωτ = 1. As Rω is known to be changed approximately with ω s−1

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(ii)

Fig. 7.4. Formation of charged defects in amorphous selenium (a-Se) and its configuration coordinate diagram. The overall energy is lowered by the effective + correlation energy Ueff . Interconversion of the states between C− 1 and C3 induces the AC loss.

(s < 1.0) [20, 21], σ(ω) is proportional to ω s , which is experimentally observed in the radio frequency range. As stated already, the CBH model is based on the PA, predicting σ(0) → 0, which is far from the experimental results. When the DC conductivity, σDC , is dominated by the band transport, then the overall conductivity can be obtained from the sum of σ(ω) + σDC . If two contributions, DC and AC, are the same, that is, the DC conductivity is dominated by the bipolaron hopping, the present CBH model cannot be a proper approach. A proper approach for

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As2 Se3

10–8

σac (S.cm–1)

10–9

10–10 104 Hz 10–11 dc 10–12

10–13

1.2 × 102 Hz

3

4

5 1000/T

6

7

8

(K–1)

Fig. 7.5. Temperature dependence of the AC conductivity at various frequencies in As2 Se3 glass. The solid and dashed curves represent the continuous-time random-walk (CTRW) and the PA, respectively. After [26]

overcoming the above drawback on the PA should be the CTRW approximation. A simple form of the AC conductivity based on CTRW is given by Eq. (7.18) [23]. At high frequency, Eq. (7.18) also predicts σ(ω) ∝ ω s (s < 1.0). Figure 7.5 shows the same experimental data for amorphous As2 Se3 , which were analyzed by the CTRW equation, that is, a random walk (RW) of bipolarons was taken into consideration, and by the PA (CBH). The solid lines are the prediction by the CTRW model with NT = 2.0 × 1017 cm−3 , and the dashed lines are those from the PA with NT = 2.4 × 1019 cm−3 which is two orders of magnitude larger than that (1016 –5 × 1017 cm−3 ) from the other measurements, (e.g., drift mobility and light-induced electron spin resonance) It is therefore suggested that the CTRW approach is more realistic than the PA [17, 26]. 7.4. Impurity Doping into Chalcogenide Glasses As we already stated, ChGs are weakly p-type semi-conductors and electronic applications are limited by the extraordinary difficulty in

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obtaining n-type ChGs. In some ChGs, for example, Ge(S, Se, Te) with very highly Bi or Pb doping (∼10 atomic % [at.%]), n-type ChGs have been realized [27]. Amorphous Se with alkaline elements shows also n-type behavior [28]. All these materials did not show device quality pn-junction. Very recently, it was reported that ion implantation of Bi into GeTe and GaLaSO, producing n-type conduction [29]. Note that both GeTe and GaLaSO are classified into the phase-change material family, as well as GeSbTe (GST) which is known to be the most useful material for the digital versatile disk (DVD) and also for phase-change random access memory (PCRAM) [30]. The electrical doping effect of Bi occurs at 100 times lower concentration than Bi melt-doped Ge-ChGs. X-ray photoelectron spectroscopy (XPS) measurements indicate that the Bi species responsible for n-type in GeTe and GaLaSO are Bi+ or Bi2+ , which provide free electrons. The fact that the Bi concentration at which the n-type transition occurs (thermopower measurement) is too low for it to be caused by a percolation threshold, that is, the transition is not interpreted in terms of a percolation theory, which requires 10% ∼ 30% of some inclusions (species). When Ag or Cu is introduced into chalcogenide glasses, Ag or Cu easy to become movable cation, Ag+ or Cu+ and hence ionic transport occurs in these chalcogenide systems. These are categorized into the superionic conductors. In Section 7.5, we will discuss the ionic transport in chalcogenide glasses, while the ionic transport will be discussed from the different point of view in Chapter X.

7.5. Ionic Transport While ionic transport in glassy materials has been studied for long time, the transport mechanism is still not fully understood. Below typical vibrational frequencies (1012 s−1 ), ion motion can be described by thermally activated hopping between sites separated by a potential barrier. As shown in Fig. 7.6, ions must hop by surmounting potential barriers (dashed line): The potential-energy landscape for mobile ions in a glass is expected to be irregular and

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Fig. 7.6. One-dimensional description of the potential-energy landscape. At high frequencies, a local motion (dashed line) contributes to the AC conductivity (loss). To occur DC transport, ions must hop over the maximum potential barrier Um in the transport path.

contains a distribution of depth and barrier heights in 3D space, while Fig. 7.6 is simple one-dimensional (1D) description. In the following sections, DC and AC transports will be discussed in ChGs. 7.5.1. DC and AC Transports The CTRW approach already discussed for the electronic transport in the previous section should give a formula for ionic transport processes as well. The random barrier model (RBM), in which mobile ions hop the potential barriers being distributed randomly, is mathematically the same as the CTRW of localized electrons under a certain condition. The complex ionic conductivity σi∗ (ω) based on the CTRW is given as [23] σi∗ (ω) = σi (0)

iωτm , ln (1 + iωτm )

(7.22)

where σi (0) is the DC conductivity and τm the maximum hopping time among many jumping times. The jumping time τ is given as   U , (7.23) τ = τ0 exp kT where τ0 is a characteristic time. As will be discussed later, it is known that τ0 itself depends on U and is given by   −U , (7.24) τ0 = τ00 exp EMN

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where τ00 is a constant and EMN is a characteristic energy (called Meyer–Neldel energy). This type relation in thermally activated processes is called the MNR or the compensation law [12] (see Section 7.2). The τm in Eq. (7.22) is taken to be the maximum τ (written as τm ) in Eq. (7.23) when we take U = Um (maximum potential barrier). Similar to the CTRW in the electronic processes discussed in Section 7.2, the DC ionic conductivity is given by (see Eq. (7.18)) σi (0) =

Ni (eR)2 , 6kT τm Hv

(7.25)

where Ni is the density of mobile ions, Hv the Haven ratio [31], and R the hopping length. Note here in ionic transport that Hv is related to the geometry of transport path. It should be noted that the present CTRW approach leading to Eq. (7.22) is zeroth order approximation. More accurate analytical presentation of the RBM is given by [32]   8 i˜ ω −1/3 i˜ ω 1+ , (7.26) ln σ ˜= σ ˜ 3σ ˜ ˜ = ω/ω ∗ is a scaled frequency (ω ∗ = where σ ˜ = σi∗ (ω)/σ(0) and ω 1/τm ). Let us show the typical example. As Ag-doped ChGs possess high ionic conductivity such as 2–3 orders of magnitude higher than that of oxide glasses with the same mobile ion concentration [33, 34]. Impedance spectroscopy (IS) can be a powerful method of characterizing many electrical properties of materials [35–38]. Figure 7.7 is an example of ρ1 –ρ2 plane for Ag25 As25 S50 glass, where ρ1 and ρ2 are the real and imaginary parts of resistivity, respectively [35, 36]. The open circles and square represent the experimental data at the applied voltage Va = 0.1 and 0.3 V, respectively, and the solid and dashed lines are the model calculations that will be stated later. The observed curve shows a typical ionic conductivity behavior containing a high-frequency semi-circle (smaller ρ1 and ρ2 ) that represents the bulk properties of the materials and the low-frequency tail (higher resistivity side) that is the response of

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Fig. 7.7. Complex ρ1 –ρ2 plane in Ag25 As25 S50 glass. The solid and dashed lines are the model calculations, the open circles and squares are the experimental data at the applied voltage Va = 0.1 and 0.3 V, respectively. After [35]

interfacial (electrode) polarization, which depends on the applied voltage. In principle, there are two ways of analyzing IS. The most popular one is the conventional equivalent electrical circuit (EEC) analysis [37]. The other one is the solution of the Poisson–Nernst–Planck (PNP) equation [38]. The EEC method has many merits leading to a fast data analysis from a complex impedance Z1 –Z2 plane, where Z1 is the real part of impedance and Z2 the imaginary part. The physical parameters such as bulk resistance and capacitance can be extracted using EEC. The EEC approach has some drawbacks: (i) the arrangement of equivalent circuit elements in different ways can provide the same Z1 –Z2 plane, (ii) the EEC method does not provide physical parameters, such as the relaxation time and the diffusion coefficient, and the number of mobile ions [35, 36]. The EEC analysis itself can be a macroscopic approach. The PNP model should also be a macroscopic approach, since the relations between the electronic potential and the diffusing (drifting) ionic particles are derived macroscopically by using the Maxwell equation. The PNP approach is not so popular, even though the solution of PNP provides the important parameters such as diffusion

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coefficient and the number of mobile ions [37]. This may be due to the complexity involved in solving the PNP equation. A new approach based on a RW of mobile ions overcomes some drawbacks encountered in the traditional IS, which analyze the impedance data without using EEC. It extracts more physical parameters than the conventional methods mentioned above [35, 36]. The dynamics of mobile ions and the physical parameters are deduced from the RW approach. Note that the interfacial region is connected in series with the bulk and electrode and hence the overall complex conductivity σ ∗ (ω) can be given as 1 σ ∗ (ω)

=

f σi∗ (ω)

+

1−f , σb∗ (ω)

(7.27)

where f is the spectral weight of the interfacial conductivity, and the subscript i and b indicate interface and bulk, respectively. Note here that ρ∗ (ω) = 1/σ ∗ (ω) is obtained from Eq. (7.22). Fitting of Eqs. (7.22), (7.25), and (7.27) produces the physical parameters shown in Table 7.1. The interfacial effect highly depends on the applied voltage and a large deviation between the fitting and the experimental data at 0.1 V may be due to involving nonlinear effect at interface. It should be noted that the diffusion coefficient D is calculated from D=

R2 , 6τm

(7.28)

where R is the hopping site separation and the Haven ratio Hv was assumed to be 1.0. Both the bulk and interfacial contributions can be separately discussed in the context of RW approach. Table 7.1. Physical parameters extracted from the impedance spectroscopy (IS) data taken at 300 K in Ag25 As25 S50 glass at the applied voltage of 0.1 V.

Bulk Interface

σ(0)(S cm−1 )

Nion (cm−3 )

τm (s)

D(cm2 s−1 )

2.8 × 10−6 6.7 × 10−12

3.4 × 1021 3.4 × 1021

3.2 × 10−6 1.3

1.3 × 10−10 3.2 × 10−16

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7.5.2. Power Law Compositional Dependence It is of interest to discuss the so-called power-law dependence of ionic conductivity and diffusion coefficient on metallic compositions into oxide [39–41] and chalcogenide glasses [33, 34]. For example, in Ag–Ge–S glasses [33, 34, 42], the relations σdc ∝ (xAg )α and DAg ∝ (xAg )β are found experimentally, where xAg is the at.% of Ag content (between 0.003 and 5 at.%) in the system, σdc the DC conductivity that is usually measured by the IS method, DAg the tracer diffusion coefficient, and the parameters, α and β, are the temperature-dependent constants. Note that no significant structural change has been reported in this composition range. Thus, the powerlaw dependence itself cannot be a structure-related issue in moderate doping range and has been widely discussed so far [33, 34]. It should be noted, however, that both the conductivity and the diffusion coefficient deviate from the power-law composition dependence in highly doped range. The reason why is the same as stated earlier (change in the activation energy): A structural change in highly doped range disturbs a homogeneous mixture of dopants. There are several models [39–42] to interpret the power law. To explain the steep rise of conductivity (or diffusion coefficient) with cation or metallic elements, a percolation model has been proposed [33, 39]. Observations of conduction thresholds in mixtures of conducting and nonconducting materials are called the percolation threshold. Roughly speaking in 3D materials, when 30% by volume of the compact is metallic (random mixture), the material system gets metallic nature from insulator. Note that a percolation-like behavior occurs at very low concentration of silver atom as stated earlier. Under an exponential distribution of hopping site energy where ions accommodate, the occupation probability of mobile ions in sites is calculated. As the highest energy of occupied sites corresponds to the highest chemical potential, an increase of cation density reduces the energy required for surmounting potential barriers (lower activation energy U in Eq. (7.23)). Another percolation approach [33] requires much larger volume of ions, which is called the allowed volume, to explain a percolation

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threshold behavior, since in a classical percolation theory the powerlaw exponent appears near a certain threshold in network conductivity. Another different view can be the dynamic structure model [39]: The principal assumption is that mobile ions themselves dominate a glass structure, which is not frozen-in until far below the glass transition temperature. Note that the power exponent is related to the energy difference between sites. The simplest model to account the experimental data may be the configuration entropy change (CEC) model recently proposed [42]: The Gibbs free energy G (= H0 − T0 S), where H is the enthalpy, S the entropy, T0 the fictive temperature, is given as G = G0 − kT0 ln(|x|),

(7.29)

where G0 is a constant and x = xAg , for example, Ag-doped materials. Note that the free enthalpy G corresponding to U here is given for one ion and hence the unit is given in eV. When the potential barrier follows (7.29), the power law should be observed in the diffusion coefficient and hence conductivity (details are presented in [42]). As shown in Fig. 7.8, there are also important contributions to the field of ionic transport in ChGs and some ChGs, for example, 0.5[(1 − x)Rb2 S − xAg2 S] − 0.5GeS2 glasses [43], which is similar to the mixed alkali effect on oxide glasses. This effect first found in glassy alkali conductors of the general formula xX2 O(1 − x)Y2 O − (SiO2 , B2 O3 , GeO2 , etc.) where X2 O and Y2 O are different alkali oxides [31, 41, 44]. An increase in the activation energy of the conductivity of one type ion (Ag; x) is observed, when it is replaced by a second type ion (Rb), keeping total metallic additive (cation) constant. The ionic conductivity therefore goes through a deep minimum as x is varied. While considerable theoretical effort has been made to interpret the origin of the MCE as an important glass science, no universally accepted model has been proposed so far. This is still a long-term mystery of glass sciences. However, we should introduce the probable models based on experimental results on oxide glasses [45]. These

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Fig. 7.8. Conductivity at 293 K and activation energy as a function of composition for 0.5[(1 − x)Rb2 S − xAg2 S] − 0.5GeS2 glasses. After [43]

models suggest that each cation maintains its own environment even in the presence of a dissimilar cation: The migration of metal ions of one type to sites previously occupied by another type ions is inhibited [45]. This idea for oxide glasses can be applied to the MCE observed in the chalcogenide glasses. 7.6. Summary Current understandings of the electrical conduction processes, through the both theories and experimental data, were discussed in chalcogenide glasses. Chalcogenide glasses doped with metallic elements exhibit ionic transport behavior. Free carriers are transported via extended states (band conduction) and localized carriers hop between localized states. The following unsolved issues on the glass science, in particular the electronic and ionic transports on chalcogenide glasses, are summarized: (1) When the conduction, either electronic or ionic, is thermally activated (Arrhenius-type conduction), the factor of activation energy is always involved in the pre-exponential factor, which

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is called the MNR. While the reason for this is still under a matter of debate for more than ∼80 years, a proper discussion, for example, extracting valid physical parameters from the experimental data, cannot be possible without taking this rule into the discussion. We should not ignore the Meyer–Neldel law on the electronic and ionic transport in glasses. (2) The pn anomaly is a long-term puzzling issue (∼50 years) found in ChGs as well as hydrogenated amorphous silicon. There is no pn anomaly in the transparent oxide IGZO films. The short mean free path in glassy materials can be the origin of the anomaly. In fact, the mean free path for IGZO is enough compared with that for ChGs. Quantitative argument taking into consideration of the mean free path is therefore necessary. (3) The power-law correlation between ion diffusion coefficient and cation content in chalcogenide glasses is found when the metallic elements are introduced. Probably, the present power-law correlation can be related to the mixed alkali effect in OGs and the mixed cation effect in ChGs. Recall the mixed alkali effect from this point may be of interest to renew this issue: One type of mobile alkali ions interferes the movement of another type of alkali ions is also a long-term issue (∼120 years after the first discovery). This is regarded as the most interesting subjects on the glass science. Acknowledgments The author would like to thank Professors K. Tanaka and T. Wagner, V. Zima, and M. Frumar for fruitful discussion on glass sciences. References 1. Mott, N. F., and Davis, E. A. (1979). Electronic Processes in NonCrystalline Materials, 2nd Ed. (Oxford, England, Clarendon). 2. Mott, N. F. (1993). Conduction in Non-Crystalline Materials, 2nd Ed. (Oxford, England, Clarendon). 3. Holstein, T. (1959). Studies of polaron motion: Part II, Annals of Physics, 8, pp. 343–389; Holstein, T. (1973). Sign of the Hall

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coefficient in hopping-type charge transport, Philosophical Magazine, 27, pp. 225–233. Emin, D. (1975). Phonon-assisted transition rate I. Optical-phononassisted hopping in solids, Advances in Physics, 24, pp. 305–348. Emin, D. (2008). Generalized adiabatic polaron hopping: Meyer-Neldel compensation and Poole-Frenkel behaviors, Physical Review Letters, 100, p. 166602. Seager, C. H., Emin, D., and Quinn, R. K. (1973). Electrical transport and structural properties of bulk As–Te–I, As–Te–Ge, and As–Te chalcogenide glasses, Physical Review B, 8, pp. 4746–4760. Abraham, E., Anderson, P. W., Liciardello, D. C., and Ramakrishnan, T. V. (1979). Scaling theory of localization: Absence of quantum diffusion in two dimensions, Physical Review Letters, 42, pp. 673–676. Hertel, G., et al. (1983). Tunneling and transport measurements at the metal-insulator transition of amorphous Nb:Si, Physical Review Letters, 50, pp. 743–746. Rosenbaum, T. F., Andres, K., Thomas, G. A., and Bhatt, R. N. (1980). Sharp metal-insulator transition in a random solid, Physical Review Letters, 43, pp. 1723–1725. Elliott, S. R. (1990). Physics of Amorphous Materials, 2nd Ed. (Harlow, England, Longman Scientific & Technical). Tanaka, K., and Shimakawa, K. (2011). Amorphous Chalcogenide Semiconductors and Related Materials (New York, NY, Springer). Yelon, A., Movaghar, B., and Crandal, R. S. (2006). Multi-excitation entropy: Its role in thermodynamics and kinetics, Reports on Progress in Physics, 69, pp. 1145–1194. Shimakawa, K., and Abdel-Wahab, F. (1997). The Meyer-Neldel rule in chalcogenide glasses, Applied Physics Letters, 70, pp. 652–654. Overhof, H., and Thomas, P. (1989). Electronic Transport in Hydrogenated Amorphous Semiconductors (Berlin, Germany, Springer). Shimakawa, K., and Aniya, M. (2013). Dynamics of atomic diffusion in condensed matter: Origin of the Meyer-Neldel compensation law, Monatshefte fur Chemie, 144, pp. 67–71. Nagel, P. (1979). Electronic transport in amorphous semiconductors. In Amorphous Semiconductors, edited by Brodsky, M. H. (New York, NY, Springer), pp. 113–158. Jai Singh, and Shimakawa, K. (2003). Advances in Amorphous Semiconductors (New York, NY, Taylor & Francis). Okamoto, H., Hattori, K., and Hamakawa, H. (1993). Hall effect near the mobility edge, Journal of Non-Crystalline Solids, 164–166, pp. 445–448.

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19. Pollak, M., and Geballe, T. H. (1961). Low-frequency conductivity due to hopping processes in silicon, Physical Review, 122, pp. 1742–1753. 20. Long, A. R. (1982). Frequency-dependent loss in amorphous semiconductors, Advances in Physics, 31, pp. 553–637. 21. Elliott, S. R. (1987). A.C. conduction in amorphous chalcogenide and pnictide semiconductors, Advances in Physics, 36, pp. 135–217. 22. Scher, H., Shlesinger, M. F., and Bendler, J. T. (1991). Time-scale invariance in transport and relaxation, Physics Today, 44, pp. 26. 23. Dyre, J. C. (1988). The random free-energy barrier model for ac conduction in disordered solids, Journal of Applied Physics, 64, pp. 2456–2468; Dyre, J. C. (1993). Universal low-temperature AC conductivity of macroscopically disordered nonmetals, Physical Review B, 48, pp. 12511–12516. 24. Shimakawa, K., and Miyake, K. (1988). Multiphonon tunneling conduction of localized π electron in amorphous carbon films, Physical Review Letters, 61, pp. 994–996. 25. Davis, E. A. (1979). States in the gap and defects in amorphous semiconductors. In Amorphous Semiconductors, edited by Brodsky, M. H. (New York, NY, Springer), pp. 41–72. 26. Ganjoo, A., and Shimakawa, K. (1994). Estimation of density of charged defects in amorphous chalcogenides from a.c. conductivity: Random-walk approach for bipolarons based on correlated barrier hopping, Philosophical Magazine Letters, 70, pp. 287–291. 27. Tohge, N., Minami, T., Yamamoto, Y., and Tanaka, M. (1980). Electrical and optical properties of n-type semiconducting chalcogenide glasses in the system Ge–Bi–Se, Journal of Applied Physics, 51, pp. 108–1053. 28. Belev, G., and Kasap, S. O. (2006). Reduction of the dark current in stabilized a-Se based X-ray detectors, Journal of Non-Crystalline Solids, 352, pp. 1616–1620. 29. Hughes, M. A., et al. (2014). Curry: n-type chalcogenides by ion implantation, Nature Communications, doi:10.1038/ncomms. 30. Wuttig, M., and Yamada, N. (2007). Phase-change materials for rewriteable data storage, Nature Materials, 6, pp. 824–832. 31. Dyre, J. C., Maass, P., Roling, B., and Sidebottom, D. L. (2009). Fundamental questions relating to ion conduction in disordered solids, Reports on Progress in Physics, 72, p. 046501-15. 32. Schroder, T. B., and Dyre, J. C. (2008). ac Hopping conduction at extreme disorder takes place on the percolating cluster, Physical Review Letters, 101, p. 025901-4.

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33. Bychkov, E. (1996). Percolation transition in Ag-doped germanium chalcogenide-based glasses: conductivity and silver diffusion results, Journal of Non-Crystalline Solids, 208, pp. 1–20. 34. Bychkov, E. (2000). Tracer diffusion studies of ion-conducting chalcogenide glasses, Solid State Ionics, 136–137, pp. 1111–1118; Bychkov, E. (2009). Superionic and ion-conducting chalcogenide glasses: Transport regimes and structural features, Solid State Ionics, 180, pp. 510–516. 35. Patil, D. S., et al. (2013). Evaluation of impedance spectra of ionictransport materials by a random-walk approach considering electrode and bulk response, Journal of Applied Physics, 113, p. 143705-5. 36. Patil, D. S., Shimakawa, K. Zima, V., and Wagner, T. (2014). Quantitative impedance analysis of solid ionic conductors: Effects of electrode polarization, Journal of Applied Physics, 115, p. 143707-6. 37. Macdonald, J. R. (1953). Theory of ac space charge polarization effects in photoconductors, semiconductors, and electrolytes, Physical Review, 92, pp. 4–17; Macdonald, J. R. (2013). Utility and importance of Poisson-Nernst-Planck immitance-spectroscopy fitting model, The Journal of Physical Chemistry C, 117, pp. 23433–23450. 38. Macdonald, J. R. (2010). Addendum to Fundamental questions relating to ion conduction in disordered solids, Journal of Applied Physics, 107, p. 101101-9. 39. Hunt, A. (1994). Statistical and percolation effects on ionic conduction in amorphous systems, Journal of Non-Crystalline Solids, 175, pp. 59–70. 40. Bunde, A., Ingram, M. D., and Maass, P. (1994). The dynamic structure model for ion transport in glasses, Journal of Non-Crystalline Solids, 172–174, pp. 1222–1236. 41. Bunde, A., Funke, K., and Ingram, M. D. (1998). Ionic glasses: History and challenges, Solid State Ionics, 105, pp. 1–13. 42. Shimakawa, K., and Wagner, T. (2013). Origin of power-law composition dependence in ionic transport glasses, Journal of Applied Physics, 113, p. 143701. 43. Rau, C., et al. (2001). Mixed cation effect in chalcogenide glasses Rb2 S– Ag2 S–GeS2 , Physical Review B, 63, p. 184204. 44. Day, D. E. (1976). Mixed alkali glasses, Journal of Non-Crystalline Solids, 21, pp. 343–372. 45. Maass, P., Bunde, A., and Ingram, M. D. (1992). Ion transport anomalies in glasses, Physical Review Letters, 68, pp. 3064–3067.

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CHAPTER 8

Ionic Conductivity and Tracer Diffusion in Glassy Chalcogenides Igor Alekseev∗ , Daniele Fontanari† , Anton Sokolov† , Maria Bokova† , Mohammad Kassem† , and Eugene Bychkov†,‡ ∗

V. G. Khlopin Radium Institute, St. Petersburg, Russia Universit´e du Littoral Cˆ ote d’Opale, LPCA, Dunkerque, France ‡ [email protected] †

8.1. Introduction Chalcogenide glasses were first known as optical materials for active and passive applications in mid-infrared (IR) because of extended IR transmission, low phonon density of states, and significant nonlinear optical properties [1–3]. The golden era of amorphous semiconductors has started in the sixties, and glassy chalcogenides have attracted a great deal of interest because of photoinduced and switching phenomena [4, 5] later resulted in phase change materials for memory applications [6, 7]. Ionic conductivity in chalcogenide glasses was discovered in the late 1960s [8, 9], and fast ion-conducting lithium and sodium glassy chalcogenides appear to be promising systems for stationary and mobile energy storage using all-solid-state batteries [10, 11].

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Ion-conducting chalcogenide glasses are also suitable model materials to study the relationships between the glass composition, atomic structure at the short- and intermediate-range scale, and ion transport features. Numerous experimental results and underlying theories were reported starting from the late seventies with a fascinating renaissance at the present time related to alternative energy sources and zero carbon emissions. The main goal of this work is to follow dramatic changes in the ion transport properties of glassy chalcogenides over a wide composition range, rarely reported in a large majority of the published papers. 8.2. Ion Transport Regimes Over a Wide Composition Range Ionic transport in glasses has been discovered in the 19th century following the classical work of Warburg [12]. Since then, a considerable progress has been achieved in both theoretical understanding and practical applications of ion conducting vitreous systems (see, e.g., [10, 13, 14] and references therein). Nevertheless, the ion migration mechanisms and ion transport regimes in disordered solids still need additional studies using both traditional macroscopic methods (AC and DC electrical conductivity, tracer diffusion, and ion transport number measurements), and advanced structural techniques on third-generation synchrotrons and spallation neutron sources over a large range of the scattering vector Q supported by comprehensive atomistic modelling. A limited number of the reported results deal with ion transport studies over a wide composition range covering several orders of magnitude in the mobile ion content. Consequently, a significant piece of information is missing related to the ion transport regimes in diluted or extremely diluted glasses. One of the first papers devoted to the AC conductivity measurements of (Na2 S)y (B2 S3 )1−y glasses, where 10−3 < y < 0.8, that is, over ≈3 orders of magnitude in the sodium content x, was published by Martin and co-workers [15, 16]. They found a significant change in the frequency dispersion of the

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ionic conductivity as a function of x and have observed a power-law composition dependence of the DC conductivity, σdc ∝ xt , where t is the power-law exponent. The conductivity measurements alone do not guarantee that the measured conductivity of a chalcogenide glass has ionic character, especially, at the ppm level of mobile ions. First combined studies using both conductivity and tracer diffusion experiments were published in 1996 by Bychkov et al. [17] dealing with silver thiogermanate and silver selenide four-component glasses over 3.5 orders of magnitude in the silver content x, from xmin = 83 ppm Ag to xmax = 25 atomic % (at.%) Ag. Later, the composition range was extended to nearly five orders of magnitude in x and also to various mobile cation systems (Cu+ , Ag+ , Na+ , K+ , Rb+ , Tl+ ) studied using 64 Cu,108m,110m Ag, 22 Na, 86 Rb, and 204 Tl tracers [18–28]. 8.2.1. Electronic Insulators Versus Ionic Conductors Silver diffusion measurements have shown that below xc  30 ppm Ag, the silver sulfide glasses (Ag2 S–GeS–GeS2 , Ag2 S–As2 S3 , etc.) are essentially electronic insulators with the silver ion transport number tAg+  0.2 [19, 20]. The silver tracer diffusion coefficient DAg is hardly dependent on composition at x ≤ xc , and the diffusion activation energy Ed is comparable with that in pure glassy host. The tAg+ rapidly increases with x > xc , and more concentrated silver sulfide glasses appear to be pure ionic conductors, tAg+ ≈ 1, at x  300 ppm Ag (Fig. 8.1). The ionic conductivity is hidden in diluted silver selenide vitreous alloys caused by the enhanced p-type electronic transport, σe ≈ σp = 10−8 − 10−6 S cm−1 [29, 30], and especially in silver telluride alloys, σe ≈ 10−4 − 10−3 S cm−1 [30, 31]. Consequently, the selenide and telluride glasses become nearly pure Ag+ conductors at higher x (Fig. 8.1) Nevertheless, the DAg (x) composition dependences are very similar in all three types of silver chalcogenide systems, and the percolation threshold for bulk ionic transport, xc ≈ 30 ppm Ag, seems to be universal whatever the nature of chalcogen.

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Fig. 8.1. Effect of electronic conductivity in glassy host: the silver ion transport number tAg+ in silver sulfide [17–20], silver selenide [17, 29, 30], and silver telluride [30, 31] glasses.

Fig. 8.2. Effect of mobile cation radius: the ion transport number tM+ in sodium sulfide [32, 33], rubidium sulfide [28, 33], and thallium sulfide [24, 25] glasses.

Sodium sulfide glasses [26, 28, 32, 33] also become nearly pure ion conductors at x > xc ≈ 30 ppm Na (Fig. 8.2). However, the ionic conductivity in slow cation vitreous alloys (rubidium and thallium thiogermanates) exceeds the electronic transport at significantly higher mobile cation content x > 10 at.% [24, 25, 27, 32].

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The combined conductivity and tracer diffusion results for diluted M+ conducting chalcogenide systems are consistent with similar behavior in alkali oxide counterparts intensively studied in the 1980s [34–42]; however, much lower electronic conductivity in glassy oxides compared to chalcogenides appears to be a key factor in the data analysis exempt from electronic transport contribution. 8.2.2. Critical Percolation 8.2.2.1. Fast Ion Glasses Diluted silver and sodium sulfide glasses show a very similar behavior. Just above the percolation threshold at xc , the tracer diffusion coefficient exhibits a step-like increase (about two orders of magnitude at room temperature) with a simultaneous decrease of Ed by 0.1 to 0.2 eV [19]. Further composition changes of the ionic conductivity σi (x) and tracer diffusion DM (x) follow a power-law dependence over three orders of magnitude in the mobile ion content x (xc < x < ≈ 1000xc ) (Fig. 8.3) [17, 23]: σi (x, T ) = σi (1, T )xt(T ) , DM (x, T ) = DM (1, T )xt(T )−1 ,

(8.1) (8.2)

with temperature-dependent power-law exponent: t(T ) = t0 +

T0 ∼ T0 , = T T

(8.3)

where σi (1, T ) and DM (1, T ) are the ionic conductivity and diffusion coefficient of a hypothetical phase at the mole fraction x = 1, t0 is small and could be neglected in Eq. (8.3), T0 is the critical fictive temperature, which will be discussed later. The difference between the conductivity, t(T ), and tracer diffusion, t(T ) − 1, critical exponents is simply related to the Nernst–Einstein equation, connecting the ionic conductivity and the diffusion (conductivity) coefficient Dσ : Dσ =

kT −1 x σi , (Ze)2

(8.4)

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(a)

(b) 108m,110m

Fig. 8.3. (a) Conductivity and (b) Ag tracer diffusion coefficient in silver thiogermanate glasses [17, 20] plotted on a log–log scale; the tracer diffusion critical exponent tD (T ) ∼ = t(T ) − 1.

where Ze is the electric charge of the carrier ion, k and T have their usual meaning. Extremely diluted silver and sodium sulfide glasses exhibit the strongest increase in ionic conductivity with increasing mobile cation content x; nearly one-half of the total conductivity changes reaching from 9 to 12 orders of magnitude at room temperature [17–20, 26, 28]. The rapid increase of conductivity in a limited concentration range and the power-law dependences of the ionic conductivity and tracer diffusion isotherms are reminiscent of a percolation-controlled mechanism. Kirkpatrick [43–45] has shown that the power-law form: G(p) ∝ (p − pc )t ,

(8.5)

is a general behavior of the conductance, G(p), in the critical region just above the percolation threshold, which occurs at the critical bond or site fraction, pc , for three different percolation models (bond percolation, site percolation, and correlated bond

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Table 8.1. The critical exponent t and the percolation threshold pc for site, bond, and correlated bond geometrical percolation models of different dimensionality [43–45].

Dimensionality t pc

Three dimensional (3D)

Two dimensional (2D)

One dimensional (1D)

1.6−1.7 0.12−0.43

1.0−1.2 0.35−0.70

0 1

percolation). The critical exponent t and the percolation threshold pc in classical percolation models depend on the network dimensionality (Table 8.1). The experimental results for glasses and predictions from the classical percolation are different in two aspects: (i) the values of the experimental and theoretical percolation threshold are very dissimilar, xc /pc ≈ 10−4 and (ii) the experimental critical exponent t(T ) is temperature dependent. The allowed volume approach [17] was used to explain the difference of four orders of magnitude between xc and pc . This approach is based on the Eggarter and Cohen’s construction to determine a mobility edge by using percolation arguments (an electron localized in a “pseudobubble”) [46]. Likewise, Bychkov et al. [17] suggested that the effective volume of glass vM , accessible to a mobile cation 0 = M+ , exceeds greatly the atomic size of mobile cation, vM x→1 x→1 is the glass molar volume extrapolated to Vm /NA , where Vm 3 0 ≈ 19 ± 1 ˚ A ). Consex = 1, and NA the Avogadro constant (vAg quently, the critical volume fraction at the percolation threshold vc determined as follows: vc =

vM 0 xc , vM

(8.6)

is expected to be in the range 0.12 ≤ vc ≤ 0.43 for three-dimensional (3D) glasses. In a spherical approximation, the radius rAV of the allowed A ≤ rAV ≤ 25 ˚ A (Fig. 8.4). The derived volume vM appears to be 16 ˚ characteristic limit for mobile ion migration at the percolation threshold is consistent with a transport distance deduced from the

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Fig. 8.4. The allowed volume approach [17] in a spherical approximation 0 , with the accessible volume comparing the atomic volume of the mobile ion, vM of a glass limited by mean-square displacements of the mobile ion.

local mean-square displacements of Na+ ions measured using the AC conductivity over a wide frequency range for Na2 O–GeO2 glasses approaching the values of 20–22 ˚ A in the limit of low sodium concentrations (60–70 ppm Na) [47]. In addition, this rather rough approxthreshold = imation yields the average M–M separation distance, rM−M ˚ 2rAV = 32–50 A, comparable with that  calculated at xc using −1

Vm (xc )x−1 a Wigner–Seitz type relation, rWS ∝ c (NA ) , where xc A ≤ rM−M ≤ 80 ˚ A. Vm (xc ) is the glass molar volume, and giving 60 ˚ Schematically, the formation of an infinite percolation cluster at x > xc is shown in Fig. 8.5. The allowed volumes are bound together implying a long-range ionic diffusion within the diluted glass network. However, no direct contacts of mobile cation-related structural units are expected and the average M–M separation is much longer than typical second neighbor distances in M–X–M linkages of 3–4.5 ˚ A, where X = S, Se, Te. The temperature dependence of the critical exponent t(T ), Eq. (8.3), can easily be understood taking into account thermally activated σi (T ) and DM (T ). In this case, Eqs. (8.1)–(8.3) can be 3

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Fig. 8.5. Schematic representation of the diluted glass network containing an infinite percolation cluster formed by connected allowed volumes for mobile ions. No direct contacts of cation-related structural units are expected.

rewritten giving for the ionic conductivity the following relations:   E(x) , (8.7) σi (x, T ) = σ0 T −1 exp − kT   x , (8.8) E(x) = E0 − kT0 ln xc where E0 is the activation energy at the percolation threshold xc , and the term kT0 ln(x/xc ) seems to be a configuration entropy term related to infinite percolation cluster(s). The critical temperature T0 is thus a unique parameter, which governs the ion transport properties over the entire critical percolation region. Two equivalent methods can be used to extract T0 from the experimental data: (i) the conductivity or diffusion isotherms plotted on a log–log scale (Fig. 8.3) or (ii) the Ea (x) and/or Ed (x) composition dependences plotted versus ln x/ log x (Fig. 8.6). The two methods yield very similar results. A single percolation parameter T0 implies the transport characteristics of the whole system in the critical percolation domain

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Fig. 8.6. Composition dependences of the conductivity activation energy Ea (x) for Ag2 S–GeS–GeS2 [17] and Ag2 S–As2 S3 [18] glasses in the critical percolation and modifier-controlled domains.

can be represented as a master plot [23]. Figure 8.7 shows this approach for a number of Ag+ and Cu+ conducting chalcogenide and chalcohalide glasses, when the 110m Ag and 64 Cu tracer diffusion data [17–22] are plotted as log [DM (x, T )x1−T0 /T ] versus reciprocal temperature T −1 . This figure allows two important points to be mentioned. (i) The combination of Eqs. (8.1), (8.2), and (8.8) really gives an appropriate scaling, that is, the experimental data points for different glass compositions in the critical percolation region are well approximated by a single line. (ii) The master plots for the MI–As2 Se3 and M2 X–As2 X3 glass families, where M = Ag, Cu and X = S, Se, appear to be very close to each other, within approximately half an order of magnitude, having also very similar values of T0 , 273 K ≤ T0 ≤ 311 K. However, they differ significantly from the master plots for the Ge-based systems. Basic conclusions from these observations can be formulated as follows [23]. Neither the

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Fig. 8.7. Master plots of the 110m Ag and 64 Cu tracer diffusion coefficients for a number of Ag+ and Cu+ conducting chalcogenide and chalcohalide glasses in the critical percolation regime [17–22].

nature of the mobile cation (Ag+ or Cu+ ), nor the chemical form of the dopant (metal halide or chalcogenide) play any important role in the critical percolation domain. The chemical form of the host matrix (sulfide or selenide) is not important either. Recent conductivity measurements of AgY–As2 S3 glasses, where Y = Br or I [48], shown in Fig. 8.8 together with similar AgY–A2 X3 systems (A = As or Sb; X = S, Se, Te) [18, 19, 31, 49–51], confirm these conclusions. The configuration entropy term in Eq. (8.8) suggests the critical temperature T0 is related to intra- and/or interconnectivity of the percolation cluster(s) [23]. Plotting the critical temperature versus connectivity of the vitreous matrix, reflected by the average coordination number n0 : n0  =

 i

ci N ij ,

(8.9)

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(a)

(b)

Fig. 8.8. Room temperature ionic conductivity isotherms of AgY–As2 S3 (Y = Br, I) [48], AgY–As2 X3 (Y = Cl, Br, I; X = Se, Te) [31, 49, 50], AgY–Sb2 S3 (Y = Cl, Br, I) [51], and Ag2 S–As2 S3 [18, 19] glasses; (a) linear concentration scale, (b) a log–log plot. The bold green solid line shows chemically invariant power-law composition dependence of σ298 (x), Eq. (8.1), for three families of silver thioarsenate glasses in the critical percolation domain. The modifier-controlled region is highlighted in light blue.

where ci and Nij are the atomic fraction and the local coordination number of species i in the glassy host, one obtains a simple linear dependence (Fig. 8.9): T0 ∝ n0 −2,

(8.10)

indicating the percolative transport is absent for chain structures, T0 = 0 at n0  = 2, which is identical to the classical percolation models [43–45] stating the absence of percolation for one-dimensional (1D) networks (Table 8.1). The Haven ratio HR is a simple experimental parameter easily accessible either from a combined (tracer diffusion DM and ionic conductivity σi ) experiment or from a single electrodiffusion or

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Fig. 8.9. Critical fictive temperature T0 plotted as a function of the average local coordination number n0  of the host matrix for a number of silver chalcogenide and chalcohalide glasses. All data points, except for AgY–As2 S3 [48], were taken from [23].

Chemla [52] measurement: HR =

DM , Dσ

(8.11)

where Dσ is the diffusion coefficient calculated from σi using the Nernst–Einstein relation (Eq. 8.4)). In a very simple case (noninteracting charge carriers in ionic crystals), the Haven ratio can be associated with a Bardeen–Herring tracer correlation factor f [53] reflecting geometrical aspects of successive atomic jumps in the lattice: ∞  ∼f =1+2 cos θ1,1+j , (8.12) HR = j=1

where cos θ1,1+j is the cosine of the angle between the first and (j + 1)th jumps. The tabulated values of f are given in diffusion textbooks, see for example [54, 55]. Usually, they cover the range between 1 and 1/3, depending only on the lattice and diffusion mechanisms. In systems with interionic interactions, the Haven ratio

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can be represented by [53]. HR =

f , fi

(8.13)

where fi is the physical or conductivity correlation factor reflecting ion–ion and defect-ion interactions. Both oxide and chalcogenide glasses exhibit a characteristic composition dependence of the Haven ratio. The diluted glasses are characterized by HR ≈ 1 indicating mostly uncorrelated ionic diffusion. With increasing x, the Haven ratio decreases monotonically and remains nearly constant, HR ≈ 0.2, at x  10 at.%. This universal trend has been observed for many different oxide systems, see for example [34–42, 56–59] and references therein. Two approaches were proposed to explain the HR (x) systematics. (i) A multi-diffusion model [60], popular in the sixties and seventies, was based on a unique value of HR for a given diffusion mechanism and therefore suggests changes in the diffusion mechanism with increasing x. (ii) A single diffusion approach [61] introduces ion–ion and/or defection interactions in the ion and tracer dynamics, while the diffusion mechanism itself is considered to be unique. Neither approach has been verified experimentally. Basically, the same universal trend of HR (x) was found for chalcogenide systems but with two new features (Fig. 8.10). The Haven ratio decreases almost linearly in the critical percolation domain from HR ≈ 1 to HR ≈ 0.55 as a function of the reciprocal random )−1 calculated on the basis of a M–M separation distance (rM−M random mobile cation distribution in the glass network: HR = 1 −

const . random rM−M

(8.14)

In the cation-rich glasses, the Haven ratio shows a distinct step-like random = 6–7 ˚ A and remains rather constant and small, decrease at rM−M 0.2 ≤ HR ≤ 0.4, indicating a strongly correlated ion motion.

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Fig. 8.10. The Haven ratio HR in silver sulfide and silver selenide glasses [18– 20, 62] plotted as a function of the reciprocal Ag–Ag distance calculated using a Wigner–Seitz type relation. The solid line in the critical percolation domain represents a least-square fit of the experimental data points to Eq. (8.14).

The observed features of HR (x) in the critical percolation domain imply a random distribution of the mobile cations and increasing interionic correlations with increasing x, consistent with the single diffusion approach [61]. 8.2.2.2. Slow Cation Glasses The conductivity studies of diluted potassium, rubidium, and thallium sulfide glasses provide very limited information on slow cation transport since the ionic conductivity appears to be negligible compared to predominant electronic or hole transport, tM+  te (Fig. 8.2). Typical examples are shown in Figs. 8.11 and 8.12 for Tl2 S–GeS–GeS2 and MCl–Ga2 S3 –GeS2 glasses (M = K, Rb) [24, 27] in comparison with fast ion counterparts, Ag2 S–GeS–GeS2 and NaCl–Ga2 S3 –GeS2 [17, 26]. As expected, the slow cation glasses show a much smaller conductivity, from three to five orders of magnitude at room temperature, but also different slopes t(T ) = ∂(ln σ)/∂(ln x) for the same glassy matrix, confirming the measured conductivity is essentially electronic.

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Fig. 8.11. The room temperature conductivity isotherms for M2 S–GeS–GeS2 glasses (M = Ag, Tl) [17, 24].

Fig. 8.12. Room temperature conductivity of MCl–Ga2 S3 –GeS2 glasses (M = Na, K, Rb) on (a) semi-logarithmic and (b) log–log scales [26–28].

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˚ ≤ The question arises whether big and slow cations, 1.4 A + + + + ˚ rslow ≤ 1.8 A (K , Rb , Cs , Tl ) behaves identically or differently compared to fast and small ions, 0.6 ˚ A ≤ rfast ≤ 1.0 ˚ A (Li+ , Na+ , Cu+ , Ag+ ), that is, whether they exhibit the critical percolation and modifier-controlled ion transport regimes in different composition domains. The tracer diffusion measurements appear to be the only way to address this question in a reliable manner. The 204 Tl diffusion coefficients in thallium thiogermanate glasses reach the lower limit of the tracer sectioning technique; DTl ≈ 10−15 cm2 s−1 for the diffusion anneal time up to 17 months. Consequently, the most diluted Tl2 S–GeS–GeS2 glass, for which the diffusion experiments were carried out, contains already 0.83 at.% Tl, roughly the upper concentration limit of the critical percolation domain. As a result, it was impossible to follow the composition dependence of DTl (x) at x < 0.83 at.% Tl, but the tracer diffusion results do not contradict the hypothesis of the two ion transport regimes (Fig. 8.13). The silver thiogermanate glasses exhibit much higher diffusion coefficients compared to the thallium vitreous alloys, DAg /DTl ≈ 105 at x < 5 at.%. The silver diffusion coefficient follows Eq. (8.2) at low x, a power-law dependence of DAg (x) over 2.5 orders of magnitude in x, shown by the solid line on a log–log scale. Similar composition dependence seems to be possible for the Tl2 S– GeS–GeS2 glasses, but the available 204 Tl tracer diffusion data are insufficient. Nevertheless, the analysis of the total conductivity σ(x) and 204 Tl tracer diffusion D (x) results allows the thallium ion transTl port number tTl+ and Tl+ ionic conductivity σi to be calculated. The ionic conductivity and tracer diffusion coefficient are related through the Nernst–Einstein Equation (8.4) and the Haven ratio, Eq. (8.11). On the other side, the ionic conductivity is related to the total conductivity using the definition of the ion transport number: σi = tM+ σ.

(8.15)

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Fig. 8.13. 204 Tl and 110m Ag tracer diffusion coefficients at 493 K for (•) Tl2 S– GeS–GeS2 [24] and (•) (Ag2 S–GeS–GeS2 [17] glasses. The solid line at x ≤ 5 at.% Ag in the silver thiogermanate glasses and the dotted lines correspond to the critical percolation model (Eq. (8.2)). The other solid lines at x > 5 are drawn as a guide for the eye.

Combining Eqs. (8.4), (8.11), and (8.15), the apparent Haven ratio tM+ HR can calculated as follows: tM + H R =

DM , Dσ(total)

(8.16)

where the conductivity coefficient Dσ(total) was calculated replacing the ionic conductivity in Eq. (8.4) by σ = σi /tM+ . For mixed conducting chalcogenide glasses, the apparent Haven ratio reveals a maximum tM+ HR = 1 at x = x0 , where x0 is the mobile cation concentration separating semiconducting (x < x0 , tM+ < 1, HR = 1) and ion conducting (x > x0 , tM+ = 1, HR < 1) glasses. For silver and sodium sulfide glasses, this limiting concentration, x0 ≈ 200 ppm M+ , is comparable with the percolation threshold, 3 ≤ x0 /xc ≤ 10

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Fig. 8.14. Thallium ion transport numbers tTl+ for several composition lines in the Tl2 S–GeS–GeS2 ternaries calculated using the 204 Tl tracer experimental results [24, 25, 28]. Below 16.6 at.% Tl, the thallium thiogermanate glasses are predominantly electronic conductors, 10−3 ≤ tTl+ < 1. Only Tl-rich vitreous alloys are nearly pure ionic conductors.

(Figs. 8.1 and 8.2). However, silver and copper selenide vitreous alloys, silver telluride, and slow cation glasses exhibit the x0 values above 1 at.% M+ . For thallium thiogermanate glasses, the limiting concentration appears to be x0 ≈ 16.7 at.% Tl (Fig. 8.14). Using the calculated thallium ion transport numbers (Fig. 8.14), the Tl+ ion conductivity was derived and plotted in Fig. 8.15 in comparison with the Ag+ ion transport for the silver sulfide counterparts. The Tl+ ion conductivity clearly shows a low-x power-law tail indicating the onset of the critical percolation regime. Higher rubidium diffusion coefficients in the sulfide vitreous host make possible to study the critical percolation regime in RbCl–Ga2 S3 –GeS2 glasses. Figure 8.16 shows the 22 Na and 86 Rb tracer diffusion in fast and slow alkali halide families at 573 K [27, 32].

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Fig. 8.15. Room temperature ionic conductivity σi = t+ M σ for (•) Tl2 S–GeS– GeS2 [24] and (•) Ag2 S–GeS–GeS2 [17] glasses. The solid lines at x ≤ 5 at.% and the dotted lines for the silver and thallium thiogermanate glasses correspond to the critical percolation, Eq. (8.2). The other solid lines at x > 5 are drawn as a guide for the eye.

In spite of the five orders of magnitude difference between DNa and DRb , the composition dependences of the tracer diffusion coefficient follow the power-law DM (x) ∝ xT0 /T −1 with similar critical temperatures T0 = 690 ± 30 K corresponding to the connectivity of the Ga–Ge–S host. Plotting the critical temperature T0 for alkali and silver chalcogenide and chalcohalide glasses as a function of the average local coordination number n0  of the glassy host (Fig. 8.17), one observes the expected percolation behavior (Eq. (8.10)); however, the ∂T0 /∂n0  derivative appears to be slightly higher for alkali sulfide glasses, ≈20%. The observed trend, however, should be verified for complementary alkali chalcogenide systems.

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Fig. 8.16. 22 Na and 86 Rb tracer diffusion coefficients at 573 K for MCl–Ga2 S3 – GeS2 glasses (M = Na, Rb) [27, 32]. The solid lines correspond to the critical percolation regime, Eq. (8.2), at low alkali content, x < 1 at.%, and exhibit a similar slope, tD (T ) = ∂(ln DM )/∂(ln x) for the two glass families.

Fig. 8.17. The critical temperature T0 for alkali [15, 26, 28] and silver [23, 48] chalcogenide and chalcohalide glasses plotted as a function of the average local coordination number n0  of the glassy host.

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8.2.3. Modifier-controlled Regime Dramatic changes in the ion transport properties were observed for mobile cation-rich glasses, x  10 at.% [15, 17, 23, 24, 28]. First, the transport parameters depend essentially on the modifier (Ag, Cu, Na, K, Rb, Tl) content and not any longer on the local structural organization of the host matrix. Figure 8.6 shows a typical example when two drastically different composition dependences of the percolation-controlled activation energy ∂E(x)/∂x ∝ T0 , Eq. (8.8), for silver thioarsenate and thiogermanate glasses converge into one unified plot above 10 at.% Ag depending exclusively on the silver content. Second, a significant differentiation in the tracer diffusion coefficients between Ag+ and Cu+ conducting glasses, Ag2 S- and Ag2 Se-containing systems, silver or copper selenide, and iodide glass families becomes evident (Figs. 8.18 and 8.19) in contrast to chemically invariant ion transport in the critical percolation domain (Figs. 8.7 and 8.8). The two ion transport regimes are also distinguished by the composition dependence of the Haven ratio (Fig. 8.10). The observed dramatic changes in the ion transport with increasing mobile ion content should be reflected in the structural organization of glasses. Nevertheless, an obvious structural correlation with the short- or intermediate-range order is lacking for silver and copper chalcogenide systems. Neither mobile (Cu+ , Ag+ ) nor network-forming (As, Ge) cation local coordination is crucial for the ion transport. An enormous difference of 4–5 orders of magnitude between DAg and DCu for these d10 mobile cation chalcogenide and chalcohalide glasses in the modifier-controlled domain (Figs. 8.18 and 8.19) coexists with the same trigonal, NM−S(Se) = 3, or tetrahedral M+ local coordination in the two glass families [63–68]. On the contrary, very similar 110m Ag tracer diffusion coefficients were observed for the Ag2 S–As2 S3 (NAs−S = 3 [66]) and Ag2 S–GeS– GeS2 (NGe−(S,Ge) = 4 [20]) glassy systems in the modifier-controlled region, in marked contrast to DAg (x, T ) in the critical percolation domain [23].

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Fig. 8.18. Room temperature 110m Ag and 64 Cu tracer diffusion coefficients for the MI–As2 Se3 glasses (M = Ag, Cu) [21, 23]. The DAg and DCu values are very similar in the critical percolation domain (x  3 at.% M) but differ by a factor of 104 in the modifier-controlled region, x > 10 at.% M.

The intermediate-range order in chalcogenide glasses reflected by the first sharp diffraction peak (FSDP) at the scattering vector A−1 in the structure factor S(Q) is not 1.0 ˚ A−1 ≤ Q1 ≤ 1.4 ˚ related to the ion transport characteristics either. The FSDP reflects intermediate-range ordering of the network-forming cations, that is, As–As or Ge–Ge correlations at a characteristic periodicity L1 ≈ A, confirmed by anomalous X-ray scattering [69–71] 2π/Q1 = 5–8 ˚ and neutron diffraction with isotopic substitution [20, 63, 64, 72]. The lack of correlation between the FSDP amplitude and/or position and the ion transport parameters means that the intermediate-range order in the host glassy matrix and its change with the mobile cation alloying has no obvious influence on the M+ ion transport.

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Fig. 8.19. Room temperature 110m Ag and 64 Cu tracer diffusion coefficients in the modifier-controlled domain for a number of silver and copper chalcogenide glasses [21, 23]. The largest DM ≥ 10−10 cm2 s−1 were observed for the Ag–As–Se glasses with the highest connectivity of the Ag-related subnetwork.

This exciting puzzle was solved by analyzing the high-resolution real-space correlation functions obtained through the usual Fourier transform of the S(Q)s over a large range of the scattering vector Q up to 40 ˚ A−1 . Pulsed neutrons on a spallation source or hard X-rays on a third-generation synchrotron allow these new possibilities to be explored. Typical total correlation functions for silver chalcogenide glasses obtained using time-of-flight neutron diffraction, TN (r), and high-energy X-ray diffraction, TX (r), are shown in Fig. 8.20, taking as an example the Ag2 S–As2 S3 glasses [66, 68]. As expected, the TN (r) and TX (r) real-space functions are similar, but one should note that the neutron and X-ray coherent scattering cross sections are different for the elements involved. In particular, Ag-related correlations (Ag–S, Ag–Ag, etc.) are more pronounced in the TX (r). This difference and combined analysis of the two sets of

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Fig. 8.20. (a) Neutron TN (r) and (b) X-ray TX (r) total correlation functions for As2 S3 and silver-rich Ag2 S–As2 S3 glasses [66, 68]. The Ag–Ag correlations at ≈3.0 ˚ A highlighted in red are clearly visible. The Ag–Ag coordination number NAg−Ag = 2.0–2.5 indicates that the edge-sharing AgS3 pyramids form chains and/or cross-linking chains in the glass structure.

the data allows more reliable results to be extracted. The first peak in the T (r) at ≈2.3 ˚ A and the second one at ≈2.6 ˚ A correspond to As–S and Ag–S first-neighbor correlations, respectively. The ≈2.3 ˚ A peak decreases and the ≈2.6 ˚ A peak increases with increasing x, but the local arsenic and silver trigonal coordination remains intact. A special attention should be paid to the third peak at ≈3.0 ˚ A, which also increases with x and corresponds to Ag–Ag second neighbor contacts. Similar peaks were observed in many other Ag-rich chalcogenide and oxide glasses and identified as Ag–Ag correlations using neutron diffraction with isotopic substitution [20, 73–75]. In the copper A selenide systems, Cu2 Se–AsSe and Cu2 Se–As2 Se3 , a peak at ≈2.7 ˚ was found and identified as Cu–Cu contacts [64]. Similarly, the copper chalcohalide glasses CuI–Sb2 Se3 exhibit short Cu–Cu correlations at ≈4 ˚ A [76]. These relatively short M–M correlations indicate

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Fig. 8.21. Schematic representation of an Ag2 S4 dimer formed by two edgesharing AgS3 pyramids [66, 67]. This structural unit seems to be a primary building block to construct preferential conduction pathways in the modifiercontrolled domain of silver chalcogenide glasses, which depending on the system, assumed to be chains, cross-linking chains, two-dimensional (2D) sheets, threedimensional (3D) tunnels, and so on.

direct contacts of MX3 pyramids, which become primordial in the modifier-controlled domain and explain dramatic differences in the ion transport between the critical percolation and modifier-controlled regimes. A schematic representation of this hypothesis is shown in Fig. 8.21, taking silver sulfide glasses as an example [66, 67]. Simple geometrical considerations confirm that two edge-sharing ES–AgS3 pyramids with a Ag–S first-neighbor distance of 2.5–2.6 ˚ A would ˚ have an Ag–Ag second neighbor distance of 2.9–3.1 A. The proposed Ag2 S4 dimer (NAg−Ag = 1) was assumed to be a primary building block to construct oligomeric structural units (1 ≤ NAg−Ag ≤ 2), chains or cross-linking chains (2 ≤ NAg−Ag ≤ 3), sheets, tunnels, and other two-dimensional (2D) and three-dimensional (3D) objects (NAg−Ag ≥ 3). The Ag–Ag coordination number appears to be an essential structural parameter for distinguishing between different types of the silver-related network structure. At least two direct implications of the proposed structural model are as follows: (i) The mobile cation distribution in the glass network

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exp random = 5–7 ˚ ˚ < rM−M is no longer random since rM−M = 2.7–4.0 A A; the last distance was calculated assuming a random mobile cation distribution in the modifier-controlled domain. (ii) If the mobile cation-related subnetwork forms preferential conduction pathways, as it was proposed in the modified random network model for alkali oxide glasses [77], one can expect certain relationships between the ion transport characteristics and specific structural parameters NM−M and rM−M . The conductivity and tracer diffusion results for silver and copper chalcogenide and chalcohalide glasses as well as the diffraction and small-angle scattering studies are consistent with these two assumptions.

(i) The universal trend of the Haven ratio in glasses and particularly in silver chalcogenide systems can be explained using a single diffusion approach [61] and different Ag distributions in the two domains. In the critical percolation region, the random silver distribution means that the average Ag–Ag separation distance decreases with increasing x. Consequently, the interionic interactions become increasingly strong, leading to a monotonic decrease of HR . In the modified-controlled domain, the interionic interactions are mostly controlled by an invariant Ag–Ag second neighbor distance at ≈3 ˚ A, and HR appears to be constant. Additionally, the low HR values, ≈0.32 for the silver sulfide glasses and ≈0.2 for their selenide counterparts, are in excellent agreement with the short Ag–Ag correlations and hence strong interionic interactions. A strongly correlated cooperative ion motion has therefore a clear structural explanation. Compelling evidence in favor of the proposed scenario was given by the Haven ratio itself. The intersection of the two HR branches (for critical percolation and modifier-controlled regimes) in Fig. 8.10 gives the Ag–Ag separation distance of 3.5 ± 0.5 ˚ A! In other words, the interionic interactions corresponding to the modifier-controlled domain are induced by ion–ion separations very similar to those found in a direct diffraction experiment. This result suggests that the Ag-related subnetwork is indeed responsible for the change in an ultimate diffusion parameter, HR , and thus yields

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a strong evidence in favor of preferential conduction pathways to be formed by Ag-related structural units. (ii) This assumption was also validated by several examples. An important difference between silver-rich Ag–As–S and Ag–As–Se glasses is the value of NAg−Ag . Edge-sharing ES–AgS3 pyramids form chains or cross-linking chains in the silver sulfide glasses (NAg−Ag = 2.0–2.5). In contrast, their silver selenide counterparts are characterized by NAg−Ag = 2.7–3.1. The higher connectivity of the Ag-related subnetwork in the latter case is giving rise to quasi-2D conduction pathways suggesting the enhanced mobility and diffusivity of the Ag+ ions for the silver selenide glassy system. The 110m Ag tracer diffusion data are remarkably consistent with this suggestion (Figs. 8.19 and 8.22).

Fig. 8.22. 64 Cu and 108m,110m Ag tracer diffusion coefficients [17–22] for a number silver and copper chalcogenide and chalcohalide glasses interpolated to the mobile cation content x = 15 at.% and plotted as a function of the Ag–Ag or Cu–Cu coordination number, NM−M , corresponding to the short M–M second neighbor A [64–68, 76]. distances, 2.7 ˚ A  rM−M  4.1 ˚

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At x = 15 at.% Ag, the difference in DAg is about two orders of magnitude. The same scenario is valid for copper selenide glasses, which are characterized by the DCu values from four to five orders of magnitude lower than DAg in the respective silver chalcogenide families. A much lower connectivity of the Cu-related subnetwork is the most probable reason. In both the Cu2 Se–AsSe [64] and Cu2 Se–As2 Se3 [67] systems, the ES– CuSe3 pyramids and/or CuSe4 tetrahedra with a short Cu–Cu second neighbor distance of ≈2.7 ˚ A form predominantly dimers (NCu−Cu = 0.8–1.0). As a result, the mobility and diffusivity of the Cu+ ions appears to be small (Figs. 8.19 and 8.22). Small-angle neutron scattering (SANS) of homogeneous Ag2 S– As2 S3 glasses belonging to the critical percolation (x = 1.2 at.%) and modifier-controlled (x = 25 and 31.6 at.% Ag) domains gave evidence about random versus non-random silver distribution in the glass network [22, 67]. A common mesoscopic feature of the two glass series was density fluctuations with a characteristic Debye– Bueche [78] correlation distance of 160 ± 15 ˚ A. However, the Agrelated difference scattering functions, ΔI Ag (Q)/σcoh , appear to be different for Ag-poor and Ag-rich glasses. Figure 8.23 shows the ΔI Ag (Q)/σcoh functions for the Ag2 S–As2 S3 glasses derived by subtraction of the weighted I(Q)/σcoh for glassy As2 S3 from the normalized SANS scattering I(Q)/σcoh of silver thioarsenate glasses, where σcoh is the coherent neutron cross section of a given glassy sample. The ΔI Ag (Q)/σcoh for diluted glass sample from the critical percolation region (x = 1.2 at.%) oscillates in the vicinity of zero, indicating the absence of the excessive scattering intensity even at the lowest scattering vectors Q < 0.03 ˚ A−1 . In contrast, the ΔI Ag (Q)/σcoh functions for the Ag-rich homogeneous samples show a systematic increase with decreasing Q ≤ 0.03 ˚ A−1 , related to a nonrandom silver distribution in the modifier-controlled domain. These qualitative SANS data are in agreement with the neutron diffraction results with isotopic substitution showing the absence of short Ag– Ag correlations at ≈3 ˚ A for Ag-diluted glasses [73, 79] in opposite to silver-rich vitreous alloys [66, 73].

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Fig. 8.23. Silver-related difference scattering function ΔI(Q)/σcoh for the Ag2 S– As2 S3 glasses from the critical percolation (x = 1.2 at.%) and modifier-controlled (x = 25 and 31.6 at.% Ag) domains [22, 67].

8.3. Origin of Preferential Conduction Pathways in Chalcogenide Glasses Comprehensive atomistic simulations using ab initio molecular dynamics (AIMD) allow a deeper insight into the nature of preferential conduction pathways and mobile cation features compared to direct structural or spectroscopic analysis [23]. In the following sections, the main attention will be focused on AIMD simulations of diluted and concentrated silver thioarsenate glasses to reveal the difference in the mobile cation distribution, and on the nature of preferential conduction pathways in fast (silver) and slow (thallium) thiogermanate glasses. The Born–Oppenheimer molecular dynamics calculations were performed with the CP2K package [80] using the generalized gradient approximation and the PBEsol exchangecorrelation functional [81]. Basically, the employed AIMD technique was similar to that used in previously published reports on analogous chalcogenide glass systems [82–84].

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8.3.1. Silver Distribution in Diluted and Concentrated Glasses The first question to be addressed was whether the AIMD modelling reproduces a random mobile cation distribution in the critical percolation domain. The answer is shown in Fig. 8.24. The final optimized AIMD simulation box for a (Ag2 S)0.03 (As2 S3 )0.97 glass (x = 1.2 at.% Ag) from the critical percolation domain reveals a rather random distribution of silver species, clearly seen in Fig. 8.24(b). The connectivity analysis of the silver distribution PAgAg (r) in (Ag2 S)0.03 (As2 S3 )0.97 is shown in Fig. 8.25(a). The ∂P AgAg (r)/∂r derivative appears to be asymmetric. Only few Ag–Ag AIM D ≤ contacts occur at low Ag–Ag separation distances, 6 ˚ A ≤ rAg−Ag 9˚ A. The majority of silver species are located between 9.5 and 12.5 ˚ A

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Fig. 8.24. Final ab initio molecular dynamics (AIMD) simulation box for a (Ag2 S)0.03 (As2 S3 )0.97 glass (x = 1.2 at.% Ag) from the critical percolation domain: (a) the entire box containing 12 Ag, 388 As, and 588 S atoms, (b) the same box with only 12 silver species shown and rather randomly distributed over the box volume. The box size corresponds to the experimental number density of the (Ag2 S)0.03 (As2 S3 )0.97 glass.

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Fig. 8.25. (a) Connectivity analysis of Ag–Ag distributions in the x = 1.2 at.% Ag (critical percolation region) and x = 31.6 at.% Ag (modifier-controlled domain) glasses. The analyzed ab initio molecular dynamics (AIMD) data correspond to the simulation boxes containing either 988 (x = 1.2 at.% Ag) or 1007 (x = 31.6 at.% Ag) silver, arsenic, and sulfur atoms. (b) The Haven ratio HR in Ag2 S–As2 S3 , Ag2 S–GeS–GeS2 , and AgI–As2 Se3 glasses [17–20, 62] plotted as a function of reciprocal Ag–Ag distance, calculated assuming a random distribution of silver. The solid magenta squares additionally show the HR for the x = 1.2 and 31.6 at.% Ag glasses plotted using the derived Ag–Ag distances from AIMD modelling. The solid line in Fig. 8.25(b) represents the result of a least-square fit of the experimental data points to Eq. (8.14). All other lines are drawn as a guide to the eye.

˚. The most probable from each other with a maximum at ≈12 A Ag–Ag separation distance appears to be nearly identical to that calculated for a random silver distribution (12.8 ˚ A). In contrast, the ∂PAgAg (r)/∂r maximum for the (Ag2 S)0.6 (As2 S3 )0.4 glass, x = 31.6 at.% Ag, arises at shorter distances than expected for a random distribution, in accordance with the reported diffraction data for silver-rich chalcogenide glasses [66–68, 73–76] and recent AIMD modelling of a (Ag2 S)0.5 (As2 S3 )0.5 glass [83]. Figure 8.25(b) reproduces Fig. 8.10 but with two additional data points corresponding to x = 1.2 and 31.6 at.% Ag. The respective HR AIM D values are plotted as a function the derived AIMD distances rAg−Ag (solid magenta squares) illustrating a similarity of the random Ag–Ag random and r AIM D in the critical percolation domain separation rAg−Ag Ag−Ag and their difference in the modifier-controlled region. The shorter AIMD distance for the Ag-rich glass (x = 31.6 at.% Ag) compared

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random also suggests that a step-like H decrease between the two to rAg−Ag R −1

random ) ≈ composition ranges at the reciprocal Ag–Ag separation (rAg−Ag −1 0.16 ˚ A (Figs. 8.10 and 8.25(b)) will disappear if the Haven ratio in the modifier-controlled domain will be plotted as a function of the real shorter M–M interatomic distances. The empirical Eq. (8.14) describing thus the entire composition range will need further theoretical development.

8.3.2. Isolated Sulfur Species and Conduction Pathways in Sulfide Glasses 8.3.2.1. Silver Sulfide Glasses The AIMD modelling of a silver-rich thiogermanate (Ag2 S)0.45 (GeS2 )0.55 glass, x = 30 at.% Ag, has also showed a non-random silver distribution easily seen even on simple facial snapshots of the simulation box (Fig. 8.26). The connectivity analysis of the AIMD simulation boxes for the silver-rich thioarsenate (Ag2 S)0.6 (As2 S3 )0.4 and thiogermanate (Ag2 S)0.45 (GeS2 )0.55 glasses has revealed a common feature of the modifier-controlled domain: one quarter of sulfur species (let us call them isolated sulfur, Siso ), 0.20 ≤ [Siso ]/[Stot ] ≤ 0.28, are connected only to silver. The Siso species have no direct bonding to germanium or arsenic, but the stoichiometric ratio to the connected Ag+ cations was found to be [Ag]/[Siso ] ≈ 2. In other words, 70%–80% of silver in both (Ag2 S)0.6 (As2 S3 )0.4 and (Ag2 S)0.45 (GeS2 )0.55 are bound to isolated sulfur Siso . Figure 8.27 shows the entire AIMD simulation box for glassy (Ag2 S)0.45 (GeS2 )0.55 and the box containing only the Siso species with the connected silver cations. The connected Ag–Siso fragments are going through the entire box forming the preferential conduction pathways and ensuring high ionic conductivity in silver sulfide glasses. Isolated sulfur also appears in Ag2 S–GeS2 crystals when [Ag2 S]/[GeS2 ] > 2 (Fig. 8.28). In crystalline argyrodite, Ag8 GeS6 = 4Ag2 S–1GeS2 , one-third of sulfur species are isolated from germanium and bound only to silver [85]. In the Ag2 S–GeS2 glasses, however, the Siso species appear far below the stoichiometric limit for crystals. The (Ag2 S)0.45 (GeS2 )0.55 glass contains already

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Fig. 8.26. Typical facial snapshots of the ab initio molecular dynamics (AIMD) simulation box displaying a certain heterogeneity in the atomic distributions for glassy Ag2 S–GeS2 (x = 30 at.% Ag).

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Fig. 8.27. Ab initio molecular dynamics (AIMD) simulation box for glassy (Ag2 S)0.45 (GeS2 )0.55 : (a) the entire box containing 1020 atoms (306 Ag, 187 Ge, and 527 S); (b) the isolated sulfur species Siso with connected Ag cations forming preferential conduction pathways and going through the entire simulation box.

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Fig. 8.28. Ternary crystalline compounds in the Ag2 S–GeS2 system: (a) Ag8 GeS6 [85], (b) Ag10 Ge3 S11 [87], (c) Ag2 GeS3 [86], and binary (d) HT–GeS2 [88]. The Siso species appear at [Ag2 S]/[GeS2 ] > 2.

≈21% of Siso , in contrast to crystalline Ag2 GeS3 = 1Ag2 S–1GeS2 without Siso [86] (Fig. 8.28). We should also note that isolated sulfur is missing in the critical percolation domain. The AIMD modelling confirms the previous suggestion related to the role of Ag–Ag connectivity for the fast ion transport. The Ag–Ag partial pair-distribution functions, gAgAg (r), for the two silver-rich glasses are shown in Fig. 8.29. They exhibit a strong peak at 3 ˚ A, consistent with the experimental results [20, 66, 68] and Fig. 8.20. The experimental and derived Ag–Ag connectivity, reflected by the Ag–Ag coordination number NAgAg , are also very similar. However, the direct analysis yields the average parameters for the entire glass, while the atomistic simulation allows further details to be accessed. In particular, the Ag–Ag connectivity is higher within the preferential conduction pathways formed by connected Ag–Siso fragments (Fig. 8.29(b)) emphasizing again the key role of isolated sulfur for ion transport properties. The gAgAg (r) partial for monoclinic β-Ag2 S, space group P 21 /n [89], also shown in Fig. 8.29(a), reveals

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Fig. 8.29. The derived Ag–Ag partial pair-distribution functions gAgAg (r) for (a) (Ag2 S)0.6 (As2 S3 )0.4 and (b) (Ag2 S)0.45 (GeS2 )0.55 glasses. In the last case, the gAgAg (r)s are shown for the entire box (dark green) and for Ag–Siso connected fragments (light green). The gAgAg (r) for monoclinic β-Ag2 S [89], is also shown (the dotted magenta line).

a striking similarity to that in g-(Ag2 S)0.6 (As2 S3 )0.4 , indicating an approximate resemblance between monoclinic silver sulfide and an Ag-related subnetwork glass structure, mostly Ag–Siso -based preferential conduction pathways. The observed similarity is also reflected by the 110m Ag tracer diffusion coefficients (Fig. 8.30). The silver diffusion is nearly identical in β-Ag2 S [90] and glassy (Ag2 S)0.625 (As2 S3 )0.375 (x = 33.3 at.% Ag) [19, 20]. The superionic silver thiogermanate glass, (Ag2 S)0.45 (GeS2 )0.55 (x = 30 at.% Ag) exhibits a different Ag–Ag connectivity, characterized by a significant contribution of corner-sharing CS–AgS3 units with longer Ag–Ag second neighbor distances at ≈4 ˚ A, Fig. 8.29(b). This mixed ES/CS connectivity appears to be more effective for the fast ion transport within the Ag–Siso preferential conduction pathways. The 110m Ag

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Fig. 8.30. 110m Ag tracer diffusion coefficients in monoclinic β-Ag2 S and superionic cubic α-Ag2 S crystals [90] below and above the α–β phase transition at 450 K (the solid magenta lines), and in superionic silver sulfide glasses (Ag2 S)0.5 (GeS2 )0.5 (dark green) [91] and (Ag2 S)0.625 (As2 S3 )0.375 (dark blue) [19, 20].

tracer diffusion in glassy (Ag2 S)0.5 (GeS2 )0.5 (x = 33.3 at.% Ag) [91] is by a factor of ≈10 higher at room temperature compared to the superionic thioarsenate glass (Ag2 S)0.625 (As2 S3 )0.375 with the same mobile cation concentration (Fig. 8.30). The room temperature DAg in glassy (Ag2 S)0.5 (GeS2 )0.5 is roughly three orders of magnitude lower than the tracer diffusion coefficient in superionic α-Ag2 S [90], extrapolated to 298 K (Fig. 8.30). We should however note that the silver content in the thiogermanate glass is also lower by a factor of 2. 8.3.2.2. Thallium Sulfide Glasses In addition to the critical percolation regime, the slow cation glasses show similar structural features in the modifier-controlled domain matching the fast ion glasses as revealed by the AIMD modelling.

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Fig. 8.31. Ab initio molecular dynamics (AIMD) atomistic simulations of glassy (Tl2 S)0.5 (GeS2 )0.5 : (a) the entire simulation box containing 1020 atoms (340 Tl, 170 Ge, and 510 S), (b) the Siso species with connected thallium cations, (c) the remaining Ge, S, and Tl atoms after removing the Tl–Siso connected fragments.

The final optimized simulation box for a nearly pure ionconducting Tl-rich thiogermanate glass (Tl2 S)0.5 (GeS2 )0.5 (x = 33.3 at.% Tl, tTl+ ∼ = 1), containing 340 Tl, 170 Ge, and 510 S species, is shown in Fig. 8.31(a). Likewise, the connectivity analysis unveils about 28% of isolated sulfur connected only to thallium, [Siso ]/[Stot ] = 0.28 ± 0.02 and [Tl]/[Siso ] = 2.0 ± 0.1 (Fig. 8.31(b)). As a result, the large majority of thallium cations (84 ± 3%) has isolated sulfur as the nearest neighbor. The remaining atoms in the simulation box (Fig. 8.31(c)) roughly represent the original glassy host GeS2 with occasionally embedded Tl species. We also note the absence of random distribution for Tl and Siso species. They are forming the connected pathways going through the entire simulation box. There is no Tl-rich crystalline compound in the Tl2 S–GeS2 system, similar to argyrodite Ag8 GeS6 (Fig. 8.32). However, trigonal Tl2 S has a distorted anti-CdI2 type layer structure [95], where 2D-layers also have stoichiometry Tl/S = 2. The derived Tl–S partial correlation function TTlS (r) for glassy (Tl2 S)0.5 (GeS2 )0.5 appears to be slightly different for the entire simulation box and Tl–Siso connected fragments (Fig. 8.33(a)).

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Fig. 8.32. Ternary crystalline compounds in the Tl2 S–GeS2 system: (a) Tl4 Ge4 S10 , x = 22.2 at.% Tl [92], (b) Tl4 Ge2 S6 , x = 33.3 at.% Tl [93], and (c) Tl4 GeS4 , x = 44.4 at.% Tl [94]. There are no Tl2 S–GeS2 crystals with isolated sulfur species. short ≈ 2.6 ˚ A small fraction of short Tl–S interatomic distances at rTl−S A increases within the Tl–Siso pathways compared to the entire box while the total Tl–S first-neighbor coordination number decreases from NTl−S = 4.8 (entire box) to NTl−S = 4.0 (Tl–Siso ). This local Tl–S coordination is still higher than that in trigonal Tl2 S, NTl−S = 3 A [95] (Fig. 8.33(a)). Nevertheless, the thallium at rTl−S = 2.90 ˚ coordination is markedly higher in the ternary Tl–Ge–S crystalline compounds [92–94], 6 (Tl4 GeS4 ) ≤ NTl−S ≤ 9 (Tl4 Ge4 S10 ) and decreases with x simultaneously with the average Tl–S distances: 3.44 ± 0.27 ˚ A (22.2 at.% Tl) → 3.11 ± 0.07 ˚ A (33.3 at.% Tl) → 3.02 ± 0.10 ˚ A (44.4 at.% Tl). In contrast, the Tl–Tl partial correlation function TTlTl (r) for glassy (Tl2 S)0.5 (GeS2 )0.5 remains essentially intact between the entire box and Tl–Siso pathways (Fig. 8.33(b)). Likewise, the TTlTl (r) for the simulated glass is reminiscent of the Tl–Tl partial in trigonal Tl2 S and dissimilar to those in crystalline Tl2 S–GeS2 compounds. In

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(a)

(b)

Fig. 8.33. The ab initio molecular dynamics (AIMD) partial correlation functions TTlX (r) in glassy (Tl2 S)0.5 (GeS2 )0.5 : (a) X = S; (b) X = Tl. The orange lines correspond to the entire simulation box, the dark green lines to the Tl-Siso subnetwork (see text for further details). The TTlX (r) partials for trigonal Tl2 S, space group R3 [95], are highlighted in light green.

other words, the preferential conduction pathways based on isolated sulfur in slow thallium and fast silver thiogermanate glasses both chemically and structurally are related to the binary sulfides M2 S. The last conclusion for the thallium-rich glasses is consistent with the 204 Tl tracer diffusion results. Crystalline thallium (I) sulfide Tl2 S is a semiconductor [96–98]. Nevertheless, our tracer diffusion measurements have demonstrated the presence of a non-negligible Tl+ ion transport in this compound hidden by a relatively high electronic conductivity. The thallium ion transport number was found to be tTl+ = 0.07 ± 0.02, and the 204 Tl diffusion coefficient in Tl2 S appears to be comparable with DTl in thallium-rich ionconducting thiogermanate glasses (Fig. 8.34).

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Fig. 8.34. Temperature dependences of the 204 Tl tracer diffusion coefficient in trigonal Tl2 S and (Tl2 S)x (GeS)0.5−x (GeS2 )0.5−x/2 glasses (x = 0.4 and 0.5). The diffusion coefficients for stoichiometric (Tl2 S)0.5 (GeS2 )0.5 were calculated from the ionic conductivity values using the Nernst–Einstein relation and the Haven ratio HR = 0.4.

8.4. Conclusions Ionic conductivity σi and tracer diffusion DM studies of fast (Ag, Na, Cu) and slow (K, Rb, Tl) ion conducting chalcogenide and chalcohalide glasses over a wide composition range covering up to 5 orders of magnitude in the mobile cation content and 12 (7) orders of magnitude in σi (DM ) have shown two drastically different ion transport regimes: critical percolation and modifier-controlled ion transport. Macroscopic transport properties combined with advanced structural studies using pulsed neutrons and hard X-rays and comprehensive atomistic modelling have revealed a random mobile cation distribution in the critical percolation domain (x  1–3 at.% M)

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and formation of preferential conduction pathways in the modifiercontrolled region (x  10 at.% M). The origin of preferential conduction pathways in mobile cation thioarsenate and thiogermanate glasses appears to be isolated sulfur, that is, the sulfur species connected only to mobile cations without direct chemical bonding to the network-forming species (As or Ge). Chemically and structurally, the preferential conduction pathways are reminiscent of but not identical to binary M2 S sulfides. Except a drastic difference in the ionic conductivity and tracer diffusion coefficients, reaching several orders of magnitude, chalcogenide and chalcohalide glasses containing both fast and slow cations exhibit similar structural trends and compositional tendencies, emphasizing the two ion transport regimes are invariant of ionic size. Acknowledgments Many colleagues and friends have participated either in experiments or in stimulating and valuable discussions. We would like to thank Jaakko Akola, Chris Benmore, R´emy Boidin, Alexander Bolotov†, Aleksei Bytchkov, Arnaud Cuisset, Yuly Grushko, Alex Hannon, Robert Jones, Shinji Kohara, David Le Coq, Steve Martin, Pascal Masselin, Mariana Milochova, Yohei Onodera, Alla Paraskiva, Annie Pradel, David Price, Michel Ribes†, Phil Salmon, Keiji Tanaka, Vadim Tsegelnik, Takeshi Usuki, and Rayan Zaiter. The authors thank the R´egion Hauts de France and the Minist`ere de l’Enseignement Sup´erieur et de la Recherche (CPER Climibio) as well as the European Fund for Regional Economic Development for their financial support. The AIMD simulations have been carried out using the CALCULCO computing platform, supported by SCoSI/ULCO (Service COmmun du Syst`eme d’Information de l’Universit´e du Littoral Cˆ ote d’Opale). This work was also granted access to the HPC resources of IDRIS, CINES, and TGCC under the allocation 2018-A0050910639 made by GENCI (Grand Equipement National de Calcul Intensif).

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References 1. Hilton, A. R. (2010). Chalcogenide Glasses for Infrared Optics (New York, NY, McGraw-Hill). 2. Sanghera, J., and Aggarwal, I. D. (1998). Infrared Fiber Optics (Boca Raton, FL, CRC Press). 3. Zakery, A., and Elliott, S. R. (2007). Optical Nonlinearities in Chalcogenide Glasses and Their Applications (Berlin, Germany, Springer). 4. Mott, N. F., and Davis, E. A. (1979). Electronic Properties in NonCrystalline Materials, 2nd Ed. (Oxford, England, Clarendon Press). 5. Tanaka, K., and Shimakawa, K. (2011). Amorphous Chalcogenide Semiconductors and Related Materials (Berlin, Germany, Springer). 6. Raoux, S., and Wuttig, M. Editors. (2008). Phase Change Materials: Science and Applications (Berlin, Germany, Springer). 7. Kolobov, A. V., and Tominaga, J. (2012). Chalcogenides: Metastability and Phase Change Phenomena (Berlin, Germany, Springer). 8. Kawamoto, Y., Nagura, N., and Tsuchihashi, S. (1973). Journal of the American Ceramic Society, 56, p. 289. 9. Kawamoto, Y., Nagura, N., and Tsuchihashi, S. (1974). Journal of the American Ceramic Society, 57, p. 489. 10. Hayashi, A., Noi, K., Sakuda, A., and Tatsumisago, M. (2012). Nature Communications, 3, p. 856. 11. Bachman, J. C., et al. (2016). Chemical Reviews, 116, p. 140. 12. Warburg, E. (1884). Annals of Physics, 21, p. 622. 13. Habasaki, J., Leon, C., and Ngai, K. L. (2017). Dynamics of Glassy, Crystalline and Liquid Ionic Conductors (Heidelberg, Germany, Springer). 14. Pradel A., and Ribes, M. (2014). In: Chalcogenide Glasses: Preparation, Properties and Applications, edited by Adam, J.-L., and Zhang, X. (Woodhead, Cambridge), p. 169. 15. Patel, H. K., and Martin, S. W. (1992). Physical Review B, 45, p. 10292. 16. Patel, H. K. (1993). Ph. D. Thesis, (Ames, IA, Iowa State University). 17. Bychkov, E., et al. (1996). Journal of Non-Crystalline Solids, 208, 1. 18. Bychkov, E., Bychkov, A., Pradel, A., and Ribes, M. (1998). Solid State Ionics, 113–115, p. 691. 19. Drugov, Yu., et al. (2000). Solid State Ionics, 136–137, p. 1091. 20. Bychkov, E., Siewenie, J., Benmore, C. J., and Alekseev, I. (2005). 15th International Conference on Solid-State Ionics, 17–23 June 2005, Baden-Baden, Germany. 21. Bychkov, E., et al. (2001). Defect and Diffusion Forum, 194–199, p. 919.

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22. Bychkov, E. (2007). International Symposium on Physics of Ion Transport in Disordered Systems, 13 December 2007, (Kumamoto, Japan, Kumamoto University). 23. Bychkov, E. (2009). Solid State Ionics, 180, p. 510. 24. Bokova, M., et al. (2013). Solid State Ionics, 253, p. 101. 25. Bokova, M., Alekseev, I., and Bychkov, E. (2015). Journal of Electroceramics, 34, p. 63. 26. Paraskiva, A., Bokova, M., and Bychkov, E. (2017). Solid State Ionics, 299, p. 2. 27. Bokova, M., et al. (2015). GOMD-DGG 2015 Meeting, 17–21 May 2015 (Miami, FL). 28. Paraskiva, A. (2017). Ph. D. Thesis, Universit´e du Littoral Cˆote d’Opale. 29. Vlasov, Yu., and Bychkov, E. (1984). Solid State Ionics, 14, p. 329. 30. Vlasov, Yu., Bychkov, E., and Seleznev, B. (1987). Solid State Ionics, 24, p. 179. 31. Alekseev, I., et al. (2013). Solid State Ionics, 253, p. 181. 32. Alekseev, I., et al. unpublished results on 22 Na tracer diffusion in NaCl– Ga2 S3 –GeS2 glasses. 33. Bychkov, E. (2018). Solid State Chemistry, 2018, 16–21 September, 2018 (Pardubice, Czech Republic). 34. Lim, C., and Day, D. E. (1978). Journal of the American Ceramic Society, 61, p. 329. 35. Kelly III, J. E., and M. Tomozawa, (1980). Journal of the American Ceramic Society, 63, p. 478. 36. Kelly III, J. E., Cordaro, J. F., and Tomozawa, M. (1980). Journal of Non-Crystalline Solids, 41, p. 47. 37. Keldly III, J. E., and Tomozawa, M. (1982). Journal of Non-Crystalline Solids, 51, p. 345. 38. Rothman, S. J., et al. (1982). Journal of the American Ceramic Society, 65, p. 578. 39. Thomas, M. P., and Peterson, N. L. (1984). Solid State Ionics, 14, p. 297. 40. Mundy, J. N., Jin, G. L., and Peterson, N. L. (1986). Journal of NonCrystalline Solids, 84, p. 320. 41. Mundy, J. N., and Jin, G. L. (1986). Solid State Ionics, 21, p. 305. 42. Mundy, J. N., and Jin, G. L. (1987). Solid State Ionics, 24, p. 263. 43. Kirkpatrick, S. (1973). Reviews of Modern Physics, 45, p. 574. 44. Kirkpatrick, S. (1978). AIP Conference Proceedings, 40, p. 99. 45. Kirkpatrick, S. (1979). In: Ill-Condensed Matter, edited by R. Balian, R. Maynard, G. Toulouse (Amsterdam, North-Holland), p. 321.

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46. Eggarter, T. P., and Cohen, M. H. (1970). Physical Review Letters, 25, p. 807; Eggarter, T. P., and Cohen, M. H. (1971). Physical Review Letters, 27, p. 129; Eggarter, T. P. (1972). Physical Review A, 5, p. 2496. 47. Roling, B., Martiny, C., and Funke, K. (1999). Journal of NonCrystalline Solids, 249, p. 201. 48. Zaiter, R. (2018). Ph. D. Thesis (Dunkirk, France, Universit´e du Littoral Cˆote d’Opale). 49. Usuki, T., et al. (2002). Journal of Non-Crystalline Solids, 312, p. 570. 50. Onodera, Y., et al. (2006). Solid State Ionics, 177, p. 2597. 51. Ben-Shaban, Y. M. (1997). Ph. D. Thesis (Petersburg, Russia, St. Petersburg University). 52. Chemla, M. (1956). Annals of Physics, 1, p. 959. 53. Murch, G. E. (1982). Solid State Ionics, 7, p. 177. 54. Manning, J. R. (1968). Diffusion Kinetics for Atoms in Crystals (Princeton, NJ, Van Nostrand). 55. Le Claire, A. D. (1970). In: Physical Chemistry — An Advanced Treatise, Vol. 10, edited by Eyring, H., Henderson, D., and Jost, W. (New York, NY, Academic Press), p. 261. 56. Evstrop’ev, K. K. (1970). Diffusion Processes in Glass (Leningrad, Russia, Stroiizdat). 57. Terai, R., and Hayami, R. (1975). Journal of Non-Crystalline Solids, 18, p. 217. 58. Beier, W., and Frischat, G. H. (1985). Journal of Non-Crystalline Solids, 73, p. 113. 59. Mehrer, H. (2011). Defect and Diffusion Forum, 312–315, p. 184. 60. Haven, Y., and Verkerk, B. (1965). Physics and Chemistry of Glasses, 6, p. 38. 61. Jain, H., Peterson, N. L., and Downing, H. L. (1983). Journal of NonCrystalline Solids, 55, p. 283. 62. Zhabrev, V. A., and Kazakova, E. A. (1982). Fizika i chimija stekla, 8, p. 51. 63. Benmore, C. J., and Salmon, P. S. (1993). Journal of Non-Crystalline Solids, 156–158, p. 720. 64. Benmore, C. J., and Salmon, P. S. (1994). Physical Review Letters, 73, p. 264. 65. Bychkov, E., Bolotov, A., Armand, P., and Ibanez, A. (1998). Journal of Non-Crystalline Solids, 232–234, p. 314. 66. Bychkov, E., and Price, D. L. (2000). Solid-State Ionics, 136–137, p. 1041.

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67. Bychkov, E., Price, D. L., and Lapp, A. (2001). Journal of NonCrystalline Solids, 293–295, p. 211. 68. Bychkov, E., Price, D. L., Hannon, A. C., and Benmore, C. J. (2002). Solid State Ionics, 154–155, p. 349. 69. Fuoss, P. H., Eisenberger, P., Warburton, W. K., and Bienenstock, A. (1981). Physical Review Letters, 46, p. 1537. 70. Armand, P., et al. (1992). Journal of Non-Crystalline Solids, 150, p. 371. 71. Zhou, W., et al. (1993). Physical Review B, 47, p. 686. 72. Petri, I., Salmon, P. S., and Fischer, H. E. (2000). Physical Review Letters, 84, p. 2413. 73. Penfold, I. T., and Salmon, P. S. (1990). Physical Review Letters, 64, p. 2164. 74. Dejus, R. J., et al. (1992). Journal of Non-Crystalline Solids, 143, p. 162. 75. Lee, J. H., et al. (1996). Physical Review B, 54, p. 3895. 76. Salmon, P. S., and Xin, S. (2002). Physical Review B, 65, p. 064202. 77. Greaves, G. N. (1985). Journal of Non-Crystalline Solids, 71, p. 203. 78. Debye, P., and Bueche, A. M. (1949). Journal of Applied Physics, 20, p. 518. 79. Salmon, P. S., and Liu, J. (1996). Journal of Non-Crystalline Solids, 205–207, p. 172. 80. https://www.cp2k.org/ 81. Perdew, J. P., et al. (2008). Physical Review Letters, 100, p. 136406. 82. Matsunaga, T., et al. (2011). Nature Communication, 10, p. 129. 83. Akola, J., et al. (2014). Physical Review B, 89, p. 064202. 84. Akola, J., et al. (2015). Journal of Physics: Condensed Matter, 27, p. 485304. 85. Gorochov, O. (1968). Bulletin de la Soci´et´e Chimique de France, p. 2263. 86. Nagel, A., and Range, K.-J. (1978). Zeitschrift f¨ ur Naturforschung B, 83, p. 1461. 87. Fedorchuk, A. O., et al. (2013). Journal of Alloys and Compounds, 576, p. 134. 88. Dittmar, G., and Sch¨ afer, H. (1975). Acta Crystallographica B, 31, p. 2060. 89. Frueh, Jr., A. J. (1958). Zeitschrift f¨ ur Kristallographie — Crystalline Materials, 110, p. 136. 90. Allen, R. L., and Moore, W. J. (1959). The Journal of Physical Chemistry, 63, p. 223. 91. Bychkov, E. (2000). Solid State Ionics, 136–137, p. 1111.

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92. Eulenberger, G. (1976). Acta Crystallographica B, 32, p. 3059. 93. Eulenberger, G. (1978). Acta Crystallographica B, 34, p. 2614. 94. Eulenberger, G. (1977). Zeitschrift f¨ ur Kristallographie — Crystalline Materials, 145, p. 427. 95. Giester, G., Lengauer, C. L., Tillmanns, E., and Zemann, J. (2002). Journal of Solid State Chemistry, 168, p. 322. 96. Ewald, A. W. (1951). Physical Review, 81, p. 607. 97. Estrella, V., Nair, M. T. S., and Nair, P. K. (2002). Thin Solid Films 414, p. 289. 98. Belyukh, V. M., Danylyuk, A. D., Glukhov, K. E., and Stakhira, I. M. (2013). Physics of the Solid State, 55, p. 2317.

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CHAPTER 9

Athermal Photoelectronic Effects in Non-Crystalline Chalcogenides: Current Status and Beyond∗ Spyros N. Yannopoulos Foundation for Research and Technology Hellas — Institute of Chemical Engineering Sciences (FORTH/ICE-HT), P.O. Box 1414, GR-26504, Rio-Patras, Greece

9.1. Premise and Scope of the Review The current critical review aims to be more than a simple summary and reproduction of previously published work. Many comprehensive reviews and collections can be found in the literature [1–4]. The main intention is to provide an account of the progress made in selected aspects of photoinduced phenomena in non-crystalline chalcogenides, presenting the current understanding of the mechanisms underlying such effects. An essential motive for the present review article has been to assess critically published experimental work in the field. There are examples where terminology has been misleading; this has led to classify underrepresented phenomena as new effects.

∗ Dedicated to Professor George N. Papatheodorou on the occasion of his 80th birthday.

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To make this review self-contained, basic concepts are briefly introduced to render the topic more accessible for non-specialists to assess the current level of understanding of photoinduced phenomena. Then, an epigrammatic overview of the current state of photoinduced phenomena is presented, followed by identification and discussion of the key light-driven athermal phase changes placing the emphasis on “solid”-to-“fluid” (photoplastic) transitions, amorphous-to-amorphous changes, and reversible amorphousto-crystalline transitions. The last two kinds of transitions are much less explored in comparison to the photoplastic effects. However, the underlying mechanism for all types of transitions mentioned above, which is key to applications, is yet far from being understood either due to misconceptions or because the relevant phenomenology is still not rich enough. No matter how real or exalted the applications of chalcogenides are, the interest in deciphering unique photoinduced phenomena will continue to fascinate scientists. As a mature now, and possibly declining field of research in the near future, photoinduced phenomena observed in non-crystalline chalcogenides have on the one hand offered a number of fascinating concepts and ideas, but has on the other side being pervaded with weaknesses and frailties. It is acceptable that some degree of speculation would be unavoidable in devising structural models of involved atomic reconfigurations. However, in several cases the proposed structural changes are system-specific, and hence their generalization to any material goes far beyond realism. In addition, the accidental or occasional “deliberate” ignorance of previously published work has led to “rediscovery” of known effects, added in the quiver of the photoinduced effects with different terminology. In some cases, this has triggered a blurred scenery, which can rather easily again lead to misconceptions and fallacies. Finally, despite some other categories of materials (liquid crystalline polymers, etc.) exhibit a dazzling similarity in photoinduced effects, the field of amorphous chalcogenides has demonstrated remarkable introversion with negligible cross talk between the two disciplines. Only very recently some parallelisms have been envisaged.

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9.2. Introductory Remarks The term chalcogen was historically coined unofficially by W. Fischer, back in 1932, to describe the atoms of group 16 in the periodic table, i.e., O, S, Se, Te, and Po [5]. This composite term derives from the Greek words chalkos (χαλκ´ oς) and genos (γ ε´νoς) meaning copper and gender, respectively, which at a first glance seems irrelevant for the above purpose. It was only after 1941, when IUPAC officially adopted this term in the nomenclature of Inorganic Chemistry, when the term chalcogen became widely popular as it seemed analogous to the term halogen. Despite that oxygen compounds are traditionally called oxides, literally, all compounds containing at least one of the chalcogen atoms are termed as chalcogenides. Alloying chalcogens with elements such as pnictogens (group 15; P, As, Sb), tetrels or tathogens (group 14; Si, Ge), and triels (group 13; Ga, In, Tl) non-crystalline chalcogenides — either as bulk glasses or in the form of amorphous thin films — can be prepared in a number of preparation techniques [6]. Strong interest for another family of chalcogen-based layered compounds, the so-called transition metal dichalcogenides of the form MX2 (M: Mo, W, Ta, etc.; X: S, Se, Te) has recently resurfaced to the frontline of materials science owing to new methods for their growth in mono- and few-layer twodimensional (2D) crystals exhibiting novel physics compared to their bulk counterparts [7]. Non-crystalline chalcogenides continue to attract the attention of research community, throughout more than 60 years after their discovery [8], for both scientific and technological reasons. One of the first striking findings was that chalcogenide glasses exhibited electric conductivity as high as 10−3 Ω−1 cm−1 , i.e., almost five orders of magnitude higher than that of oxide glasses, which is of a purely electronic origin. Their semiconducting nature was initially challenged by theoretical solid state physicists [9] who supported that without the lack of long range order (crystal lattice) a three-dimensional system could not preserve a bandgap. A rigorous theoretical proof for the existence of a bandgap in amorphous semiconductors was undertaken by Weaire and Thorpe [10]. Exploiting their semiconducting properties

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and the moderate bandgap exhibited by these materials, illumination by visible light with energy comparable to the bandgap energy can create electron-hole pairs. The fate of the photoexcited carriers determines the response of the material to light: (i) electrical response (separation), (ii) photoluminescence (radiative recombination), and (iii) atomic arrangement change (non-radiative recombination). The last case, being the origin of photoinduced structural (PiS) changes, is perhaps the most intriguing one. Impurity content, temperature, and the concentration and charge state of native defects are factors that control the recombination of the photoexcited carriers. PiS changes are the hallmark of non-crystalline chalcogenides underlying a vast number of changes in physical/chemical properties, known as photoinduced phenomena. The term photoinduced throughout this chapter adopts the purely athermal nature of the effects where no energy is transferred as heat from the irradiation source to the material. Although the studies of photoinduced effects abound in the current archival literature, a significant fraction of putative photostructural changes is essentially — either partly or solely — thermally induced. The PiS changes give rise to hierarchical changes in the shortand intermediate-range structural order, proliferating from the local “molecular” level to macroscopic scales, hence affecting macroscopically observed physical/chemical properties such as density, mechanical properties (hardness, elastic constants), rheological properties (viscosity, the glass transition temperature), optical and electronic transport properties, as well as the capacity of chemical solubility. Applications of amorphous chalcogenides exploit either their transparency to infrared light (passive) or their responsiveness to nearbandgap illumination (active). The latter, i.e., the external-stimuli control of the structure and properties of chalcogenides is perhaps scientifically the most interesting case in view of the challenges it poses for a microscopic understanding of photoinduced phenomena. 9.3. Basic Concepts and Definitions Lacking all the beneficial consequences derived from the concept of lattice in crystals, such as Brillouin zones, Bloch states, and so on,

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amorphous materials are devoid of a corresponding rigorous mathematical description. Although the lack of these mathematical tools debilitated our efforts and stymied for long our understanding of relevant phenomena, other properties accompany non-crystalline media endowing them unique properties. These new features, arising from the loss of long range periodicity, promote structural changes induced by light, rendering amorphous solids, arguably, more interesting than their crystalline counterparts. Band tailing and localization of photoexcited carriers are two such attributes arising from disorder, affecting the fate of the carriers. This will further affect the probability for changes in atom arrangements and the valency of the atoms. The electronic structure of the outer shell of chalcogens contains six electrons; two of them are paired in an s state and four electrons are in the p state. Two out of the p electrons are paired. The electron configuration reads as ns2 p1x p1y p2z . Therefore, chalcogens form two bonds via the unpaired electrons of the px and py orbitals, while the lone pair (LP) of electrons in the pz orbital plays a vital role in PiS changes. The electronic structure of chalcogen atoms and chalcogen solids is illustrated in Fig. 9.1. The s, σ, and LP states form the valence band (VB), with the LP being at the top of the VB, while the p orbitals form the conduction band (CB). The theory of electronic structure in non-crystalline chalcogenides was primarily formulated by Mott [11] and Cohen et al. [12]. Mott introduced the concept of mobility edge, which defines a critical density of states in the amorphous solid below which all states are localized, but above which free carriers exhibit a finite mobility for all states. In contrast to Bloch states in crystalline solids, which describe the extended nature of the electron wavefunction, the electronic states in amorphous solids may be characterized by localized states. Quantum mechanical tunneling between localized states could possibly lead to apparently extended states, as far as transport is concerned. The energy separation between the mobility edges of the valence and CBs defines the mobility gap. By conception, the model on electronic structure developed by Mott [11] and Cohen et al. [12] tacitly assumed that all atoms are normally coordinated obeying the 8-N rule (N ≥ 4), where N is the number of valence electrons. Hence, localized states in the gap are caused by disorder whose origin

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σ*

CB

EF

p

Eg LP

σ

VB

s Fig. 9.1. Electronic structure of an isolated chalcogen atom (left) and its evolution when two such atoms bond together. A new configuration appears (middle) where two extra electrons come from the neighboring atom. The σ, σ ∗ , and the lone pair (LP) energy states split as designated. These states transform to bands in the solid (right).

arises predominantly from bond length and angle deviations from the norm and possibly also comes from wrong bonds between atoms. However, structural studies have shown that atoms with coordination deviating from the 8-N rule constitute an appreciable fraction in amorphous solids. These atoms and their immediate environment are called defects. It should be noted that defects in crystals are primarily imperfections of the lattice, appearing as dislocations, vacancies, interstitials, and so on, which obviously have no meaning in amorphous solids. The coordination number, the charge of each atom, and the type of neighbors are parameters used to account for defects in disordered solids. A schematic representation of the above description is shown in Fig. 9.2. Cohen et al. [12] proposed that for solids with high degree of disorder, the valence and CB tails, which describe the localized states, could be extended to such range that overlap in the center of the gap, providing a finite density of states at the Fermi energy (EF ) and hence causing pinning of the EF . In this context, the material could be considered as a semiconductor if the density of states at EF is less

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Fig. 9.2. Schematic diagram of the density of states in crystalline (up) and amorphous solids (down).

than the critical value, which defines the mobility edge. Otherwise, the solid would be an amorphous metal. To account for the apparent contradiction between the pinning of the EF and the lack of unpaired electrons in amorphous chalcogenides, as no electron spin resonance signal is observed, Anderson [13] suggested a mechanism through which almost all spins can become paired and hence negatively charged (defects) upon the adoption of an extra electron. This process increases the energy due to Coulombic interactions among electrons by an amount known as the Hubbard energy, U. The low coordination number of chalcogen atoms brings in structural flexibility that enhances the possibility of a strong electron–lattice interaction. The energy gain resulting from this interaction, as a consequence of disorder (i.e., the distortion of the chemical bond), overcompensates the repulsion developed within each electron pair. Thus, the effective Hubbard energy becomes negative, at sufficiently strong electron–lattice interaction, and the charged defect center atomic configuration is more stable than the neutral one.

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The following notation will be used Xnq , where X denotes the type of atom, n is the coordination number, and q symbolizes the charge of the atom under consideration. Representing C, P, and T atoms from groups 16, 15, and 14, respectively, then the normal bonding state is provided by the configurations C20 , P30 , and T40 . Deviations from these configurations imply the formation of defects. Typical defect pairs with low formation energy are C3+ − C1− , C3+ − P2− , C3+ − T3− , etc. A schematic of their structure is shown in Fig. 9.3. The overcoordinated and undercoordinated atoms are positively and negatively charged, respectively. Their creation is the result of the existence of the electron LP of the chalcogen atoms. Removing one

(a)

(b)

(c)

Fig. 9.3. Schematic illustration of various VAPs configurations. (a) The formation of a VAP in elemental Se where a positively charged dangling bond C1+ bonds to a two-fold (normal) coordinated C20 atoms to form an overcoordinated C3+ defect (adapted from [14]). (b) A normal coordination (left) of pnictogen– chalcogen system transforms to an intimate VAP (left) as a self-trapped exciton. (c) Photoinduced structural (PiS) changes involving bond reorientation mediated via a self-trapped exciton.

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electron from a chalcogen atom creates a positively charged ion C + , which can form an additional bond. The electron that has been removed undermines an existing bond to an atom it is attached. The average coordination number is preserved in each such pair. Atoms involved in the abovementioned mechanism are called valence alternation pairs (VAPs). The rather low creation energy of VAPs, which refers to the Coulomb energy (resulting from the presence of the extra electron on the negatively charged center), implies a density of 1018 –1020 VAPs cm−3 frozen-in at the glass transition temperature. The VAP defects shown in Fig. 9.3 have transient character and the dissipation of the energy during the non-radiative recombination takes place via structural deformation mediated by phonon emission. It is highly probable that the original configuration will be restored, but other atomic arrangements may arise as well with high likelihood. In this last case, the structure is severely modified as bond interchange involves atomic motions reminiscent to diffusion. The idea of a strong electron–phonon coupling at defects, mentioned above, is central to understanding localized states in noncrystalline chalcogenides [15, 16]. The strong phonon coupling is the result of the energy released when an atom (defect) adopts a bonding rearrangement to a local coordination different from the bulk and provides a plausible mechanism to explain the faster rate of non-radiative release of excitation energy in comparison to the radiative process [17]. Based on these arguments, Street envisaged a mechanism for the fast non-radiative recombination, according to which the photoexcited electron-hole pair forms local transient bonding arrangement [18]. The latter consists of a self-trapped exciton (Fig. 9.4) or else a coordination defect pair, i.e., the VAP. In general, the creation of a defect pair reaction can be written as − A0m + Bn0 ↔ A+ m+1 + Bn−1

(9.1)

Charge transfer from an atom to another lowers the activation energy for the defect creation. When the two VAPs are close enough forming an intimate VAP, they could self-annihilate, as is described by the back arrow in Eq. (9.1). For example, in the case of a

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Exciton

Shelftrapped exciton

Energy

II Ground state

I

Configuration

Fig. 9.4. Configuration coordinate diagram showing two possible recombination paths after photoexcitation in amorphous chalcogenides. (I) Direct recombination to the ground state. (II) Creation of a metastable state (VAP) in a potential well that requires energy (heat) to restore the equilibrium state. Based on [18], c 1977 Published by Elsevier Ltd. Copyright 

pnictogen–chalcogen system, the above concept for the formation and annihilation of the transient defect state can be expressed as P30 + C20 → P4+ + C1− → P30 + C20 . A schematic configuration-coordinate diagram, proposed by Street, showing how a transient bonding arrangement can dissipate the recombination energy is illustrated in Fig. 9.4. The rich variety of local bonding environments in amorphous solids and the structural flexibility, which configurations with low steric hindrance offer, renders the interconversion of such defects possible via the reaction (9.2), − − + A+ m+1 + Bn−1 ↔ Am−1 + Bn+1

(9.2)

VAP pairs can capture two carriers of the appropriate charge thus reverting its charge. This valence change will alter the coordination number, rendering, e.g., the initially positive overcoordinated defect A to a negative undercoordinated state.

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9.4. A General Perspective on PiS Changes: Unique to Non-Crystalline Chalcogenides or Universal Property? Because the very first photoinduced effects explored in non-crystalline chalcogenides such as photodarkening and photodissolution of metals (photodoping) were shown to be extremely suppressed in their crystalline counterparts, the general perception that prevailed was that this is an intrinsic merit of non-crystalline semiconductors. Although not widely known, PiS changes are not unique to non-crystalline chalcogenides. In certain cases, where light illumination causes electronic excitations with sufficiently long lifetimes, observable effects on various types of phase transitions follow. Typical examples of such transitions include structural transformations, nonmetal-tometal transitions, changes related to supercooling, supersaturation, and so on [19]. A general conception that is frequently adopted in such non-equilibrium process is depicted in Fig. 9.5. The potential energy surface (PES), representing the Gibbs potential, separates two states or two phases A and B by a high barrier that can be overcome by thermally activated processes, when the system is in the ground state. Electron excitation brings about changes in bonding and the new atomic configuration may be described by a lower barrier height in the non-equilibrium state. This scenario presupposes that the excited electrons have a long enough lifetime allowing the system to respond via structural changes. Typical phase transitions in the above context include athermal melting observed experimentally by ultrafast time-resolved X-ray diffraction techniques, in an amorphous semiconductor InSb [20] and single-crystal Ge films [21], showing that non-thermal or electronic melting of materials might be a universal property. Photoinduced bond weakening is the origin of athermal photomelting, while optically induced bond strengthening can cause effects such as non-thermal vapor condensation or transitions of liquids into solids [22]. A more elaborate discussion on photoinduced phase transition can be found elsewhere [23]. Another well-explored case of materials undergoing interesting PiS changes are polymers containing azo groups (-N=N-). These materials have been intensively studied as they exhibit remarkably

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Potential Energy Landscape

“Non-thermal” transition

Excited State Light Thermal transition

Ground state

Configuration coordinate

Fig. 9.5. Configuration coordinate diagram showing a path of photoinduced changes of the potential energy surface from state A to state B. The much smaller energy barrier in the excited non-equilibrium state in comparison to the ground state, implies practically an athermal transition as the ambient temperature could provide the necessary energy for the transition with no additional external temperature rise. Adapted from [19].

similar effects under light illumination with chalcogenides [24]. The trans–cis photoisomerization is the photochemical reaction standing as the basis of the effects in azo-polymers. Notably, the same terminology is being used for azo-based polymers, while the two research sectors, i.e., chalcogenides and azo-polymers have progressed in parallel over the years with almost no interaction. 9.5. Types of Photoinduced Phenomena in Non-Crystalline Chalcogenides and Their Classification A large number of photoinduced phenomena, straddling a wide gamut of related physicochemical properties, has been reported up until now for non-crystalline chalcogenides. These phenomena involve elemental chalcogens, binary, ternary and more complex systems. However, as will be discussed in detail in the next

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sections, photoinduced changes appear more prominent at certain compositions, since local structural motifs can facilitate atomic rearrangement. The underlying light-induced changes range from relatively subtle ones concerning minimal atomic displacements to more extensive atomic and molecular rearrangements including the formation of new species (i.e., molecular units formed in networklike structures). The proliferation of these structural reconfigurations causes a variety of physical and chemical changes. We should stress that although in several descriptions, PiS changes are treated separately from photoinduced physicochemical changes (observed as a change in some observable property), this distinction is pointless as changes in the structure (i.e., atomic configuration) are ultimately the origin of physicochemical modifications. Alternatively, when structure changes, properties also vary. Photoinduced phenomena can be categorized into various classes based primarily on their magnitude and the reversibility pathways they exhibit following cessation of the irradiation. In this sense, modifications can be as follows: (i) Transient; persisting only as long as illumination lasts (light on conditions) (ii) Partially reversible; the illuminated volume attains partly its original properties after applying an external stimulus, most frequently heat but also light in rare cases (iii) Fully reversible; the application of the external stimulus reverts the illuminated volume back to its initial state (iv) Irreversible or permanent; the modifications in structure cannot be eliminated by any means of post-treatment (v) A mixture of transient and reversible/irreversible; essentially, it is plausible to consider that all photoinduced effects bear a transient character, which depends upon the type of photostructural changes involved. The extent of the transient change in relation to the residual one after light cessation can be realized only if measurements are conducted in situ. On another front, the changes can be scalar or isotropic and vectoral or anisotropic denoting the influence or not of the orientation

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of the light polarization, respectively. Several review articles and chapters have compiled the various photoinduced phenomena proving details about their origin and the existing controversies for the nature of such effects, which will not be discussed here in depth [2, 3, 25–28]. Besides the presence of LP electrons and their role in promoting photoinduced phenomena in non-crystalline chalcogenides, another crucial reason for facilitating PiS changes is the possibility to form homonuclear or so called “wrong” bonds between cation atoms in stoichiometric compounds. Indeed, such bonds can readily be created (by light) and annihilated (by heat) as the bond formation of such atoms (M: metals and metalloids of groups 14 and 15) have formation energies in the range 150–220 kJ mol−1 , which is comparable to heteronuclear bonds between these and chalcogen atoms (C). In general, the following reaction describes usual PiS changes: hv, T

−−−−−→ |M − M | + |C − C| 2|M − C| ←

(9.3)

Typically, illumination shifts the equilibrium to the right creating chemical disorder, whereas annealing restores chemical order by shifting the equilibrium to the left. Well-annealed films and bulk glasses prepared by melt-quenching (which are fairly well-annealed due to their slow cooling) exhibit predominantly reversible effects. On the contrary, as-prepared and poorly-annealed films prepared mainly by thermal evaporation and ultrafast quenched glasses exhibit certain irreversible changes that are primarily morphological, structural, or compositional. The differential evaporation rate of various elements and/or species is the main cause leading to films with different structure in comparison to the bulk glass. An early Raman study (Fig. 9.6, left) on the irreversible thermo- and photo-structural transformations in As2 S3 films has been reported by Solin and Papatheodorou [29], assigning the observed changes to photoinduced polymerization of metastable molecular units formed during the deposition process. Further Raman studies on the thermo- and photo-structural transformations in As2 S3 films were reported by Frumar et al. [30] (Fig. 9.6, right). The Raman spectra show that partial photopolymerization takes place in the course of irradiation, as sharp

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(a)

(b)

(c)

Fig. 9.6. (Left) Raman spectra of As2 S3 (a) an evaporated as-deposited film, (b) annealed at 180◦ C for 1 h, (c) bulk glass. Reprinted (Fig. 9.1) with permission from [29]. (Right) Reduced Raman spectra of As2 S3 thin films and bulk glass. 1: as-evaporated, 2: exposed, 3: annealed, 4: bulk glass. Reprinted with permission from [30].

Raman bands indicative of the molecular species are detected. Annealing causes more extensive polymerization, re-attaining the chemical order that is observed in the bulk glass. Sharp bands of As–As bonds at energy lower than 250 cm−1 and S–S bonds at ∼490 cm−1 are evident supporting the equilibrium reaction (9.3), which assumes the form 2|As2 S3 | ↔ |As4 S4 | + S2

(9.4)

A more detailed combined resonance and off-resonance Raman study of the photo- and thermo-structural changes in bulk glassy As2 S3 (studied under vacuum) was reported by Yannopoulos et al. [31]. Bandgap illumination was found to induce much stronger structural changes than ever reported for this bulk glass, which was attributed

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Fig. 9.7. (Left) Raman spectra of glassy As2 S3 , excited by bandgap light, at various illumination times as shown in the legend. Solid-dots lines represent the Raman spectrum of the glass at 25◦ C recorded at conditions very far from resonance (1064 nm, 1.17 eV). The spectra have been normalized at the intensity maximum near 340 cm−1 . (Right) Time dependence of the peak area ratio λ(t) = A234 /A340 of glassy As2 S3 under bandgap irradiation. The peak at 234 cm−1 arises from photo-induced As–As wrong bond, while the peak at 340 cm−1 denotes the As–S vibrational mode of the AsS3 pyramidal unit. The horizontal solid line at λ = 0.008 corresponds to the value obtained under nonc 2012, resonant Raman scattering (1064 nm). Reprinted from [31], Copyright  John Wiley and Sons.

to the absence of oxygen in the course of illumination. The formation of As–As bonds (band at ∼234 cm−1 ) is the main light-induced structural change (Fig. 9.7, left). This observation, together with the absence of S–S bond formation, points to the failure of models adopting the formation of realgar-type structures via the frequently adopted reaction (9.4) and calls for new structural defects based on centers with an increased coordination number. The kinetics of photostructural changes exhibits moderate departure from the single exponential behavior and the characteristic timescale is of the order

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Potential Energy Landscape

Strong chemical disorder

267

Lightinduced defects

Light Heat

• As-deposited films • Ultrafast quenched glasses

• Irradiated state • Bulk glasses and • Well-annealed films

Configuration coordinate

Fig. 9.8. (Left) Schematic representation of the free energy vs. configuration; the depth of each minimum denotes the stability of the state. Single and double arrows symbolize irreversible and reversible processes, respectively. Solid- and dashedline arrows denote light and heat processes, respectively. (Right) Changes in the coordination number (up) and the means square relative displacement (down) of amorphous Se at various treatment steps. Reprinted (Fig. 9) with permission from [33] by the American Physical Society.

of several minutes. This timescale was found to be comparable to the characteristic scale of the time dependence of photodarkening for the same glass [32]. Summarizing the various states that non-crystalline chalcogenides can adopt under the action of the two main external stimuli, i.e., heat and light, Fig. 9.8 illustrates the interrelationships among them. The structure of as-deposited films and ultrafast quenched glasses contains an appreciable fraction of structural defects, trapped-in during the preparation procedure. These defects tend to increase the degree of disorder. Reversible transformations can take place between the annealed and irradiated states. The right panels in Fig. 9.8 show modifications in the coordination number and the mean square relative displacement when amorphous Se is subjected to various treatments [33]. Under irradiation, the mean square relative displacement is higher than the post-irradiated state, denoting the partially transient character of the effect. Appreciable

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Fig. 9.9. Synopsis of the classification of photoinduced effects.

transient photostructural changes measured upon illumination take place for As50 Se50 films prepared by pulsed laser deposition; this observation will be discussed in detail in Section 9.8.1. A general classification of the various photoinduced effects that have been explored and reported in the literature is compiled in the diagram shown in Fig. 9.9. In certain cases, the effects have been exhaustively studied for decades, while in other instances there are only a few reports. However, in both cases, the structural models that have been developed to account for the origin of these effects appear in certain cases to be inconclusive or self-contradictory, as they fail to clarify all aspects of the phenomenon under question. Despite that certain photoinduced effects may have common origin, different terminology has been coined to express the same effect, adding confusion. This is common for the photoplastic effects that are described in detailed in Section 9.6. Finally, it should be stressed that most of these effects have some transient character, while some other may exhibit a reversible and an irreversible part as well.

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9.6. Unified Perspective on Several Photoinduced Phenomena Underpinned by the Photoviscous Effect Several of the photoinduced phenomena described in the previous section, especially those related to optical properties, have been thoroughly studied and are now considered as sufficiently understood. In contrast, the situation concerning photoinduced changes in mechanical and rheological properties is not yet clear. The main reason is that no systematic attempt has been made to unify the effects, which appear as ramifications of the underlying cause of such effects, i.e., the athermal photoinduced lowering of viscosity under illumination, the so-called photoviscous effect. This effect pertains to the photoinduced transformation of the illuminated volume from a solid glassy state to a highly viscous “fluid” or alternatively to a transition from a brittle state to a plastic one. A detailed account of the confluence of such effects has been provided by Yannopoulos and Trunov [34], who suggested that several phenomena following the photo-viscous effect may bear a common origin. In particular, there has been confusion on the terminology and misconception in the nature of various photoinduced effects in the literature concerning mechanical and rheological properties, such as elastic constants, microhardness, stress relaxation, viscosity, glass transition temperature (Tg ), mass transport, surface morphology, and so on. Therefore, miscellaneous changes observed under illumination of the abovementioned properties have been called in a number of ways including terms such as photodeformation, photohardening, photosoftening, photofluidity, photoinduced structure (stress) relaxation, photoinduced mass transport, photoinduced relief grating, photomelting, and optomechanical effect. It should be noted that slight variations of the experimental parameters, e.g., size of the sample, adherence to the substrate (i.e., free-standing or mounted), duration of illumination, etc., can result into qualitatively different observations, albeit the underlying phenomenon might the same. This has led to exaggeration in claiming the invention of new putative photoinduced effects.

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In their pioneering works, Nemilov and Tangatsev [35–38] coined the term photoviscous effect and explored in detail the athermal decrease of viscosity upon irradiation. It is essential to stress that increasing the material’s fluidity under irradiation, as a result of bond rearrangement, renders the material amenable to mechanical modifications and morphological transformations. These changes can be observed either as shape changes under the application of external forces or as relief gratings formed as the result of mass transport. For clarification, if only illumination by light is involved the term “photoviscous” seems more appropriate, while in the combined action of light and an external mechanical stimulus the term “photoplastic” appears more suitable to account for the emerging morphic effects. Notably, even the above distinction might not be entirely clear since morphic effects, such as surface relief deformations, can appear in the absence of an external mechanical stimulus. 9.6.1. A Brief Timeline of Photoviscous and Photoplastic Effects 9.6.1.1. Early Studies: Photoplastic Effects in Crystalline Semiconductors Perhaps, the first report on photoplastic effects appeared almost a century ago by Vonwiller on the photoinduced changes of the elastic properties of glassy Se [39]. Upon illumination, the material exhibited enhanced yielding compared to the “dark” behavior under the application of distorting forces. Similar effect was observed for crystalline Se albeit of much lower magnitude in relation to the glass. A question that resurfaces over the years is whether photoinduced effects are unique to non-crystalline or aperiodic solids or if they are also observed for crystals. The general perception is that crystals exhibit much less ability to be molded by light owing to the restrictions imposed by lattice periodicity, as the atoms must lie on certain positions. This constraint limits the various scenarios offered for the recombination details of electron-hole pairs. The effect of disorder-induced localization of electron and hole states at band edges avails amorphous materials offering more possibilities for

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the photogenerated electron-hole pairs. However, although structural inflexibility renders crystalline solids less amenable to photoinduced effects in comparison to amorphous solids, photoplastic effects in crystals were reported several decades ago. These effects concern the athermal light-induced plasticity in crystalline semiconductors and have been explored since 1957 for crystalline Ge, Si and InSb [40]. Even at such early times, the term photomechanical effect was coined for the observed effect, since it refereed to the considerable hardness (flow stress) increase of the illuminated crystal surface, triggered by infrared and ultraviolet light. This is usually mentioned as the positive photoplastic effect (photohardening), while for some crystals the opposite behavior was observed (negative photoplastic effect, photosoftening) [41]. Illumination power, temperature, and light wavelength are parameters that affect the photomechanical effect. In particular, the effect saturates at high photon fluxes, while it exhibits unexpected (anomalous) behavior, i.e. photoinduced hardening decreases at elevated temperature. Finally, the effect demonstrates strong spectral dependence, being maximized for light energy comparable to the bandgap of the crystal. The explanation of the photomechanical effect was based on the idea that the electron distribution within a dislocation affects strongly the energy of dislocation. Thus, the redistribution of electrons upon illuminating a semiconductor exerts a significant effect on the mechanical properties, through the increased mobility of dislocations due to photoinduced increase of carrier concentration. First attempts to account for the photohardening effect were based on the modification of the motion of dislocations during illumination due to the change of free electrons interacting with the moving dislocations [42–44]. It was also postulated that the photoexcited holes are trapped, which can generate doubly charged ions. These ions can interact strongly with dislocations, thus enhancing flow stress by dislocation locking [45, 46]. Such effects have been documented for several single crystals [47], and were assigned to the decrease of microhardness due to chemical bond weakening and isotropization of the crystal caused by the “photogenerated antibonding quasiparticles.”

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9.6.1.2. Photoinduced Deformation in Amorphous Chalcogenides: Conversion of Light Energy to Mechanical Energy Matsuda et al. reported perhaps the first reversible deformations observed in amorphous chalcogenide films, i.e. As20 S80 and Sb2 S3 deposited on mica substrates under bandgap light illumination, which were attributed to photoinduced structure relaxation [48, 49]. Thermal expansion processes, due to absorption of the incident light, were suggested to play a dominant role in this effect, as the temperature rise due to illumination affects structural relaxation. In parallel, a larger number of chalcogenides, members of the As–Ge family were explored by Igo et al. [50], while details on photoinduced stress relaxation of a-Se/mica film bilayer was reported by Koseki et al. [51] The configurational coordinate diagram was invoked to account for the photoinduced stress relaxation which was considered as the result of non-radiative recombination processes. Rykov and coworkers [52, 53] devised a more elaborate method to study in detail the photoinduced deformation in amorphous films (Se) and bulk glasses (As2 S3 ). Polarization dependent reversible contractions and dilations of a-As50 Se50 deposited on a cantilever’s surface have also been reported [54]. Some other aspects of scalar and vector photodeformations in amorphous chalcogenides are described elsewhere [55]. It would be instructive to mention that photoinduced deformations are very common in azobenzene containing materials. Light enables the interconversion between the two geometrical isomers and the cumulative effect becomes evident as macroscopic mass transport. Typically, illumination triggers trans→cis isomerization, while the opposite transformation takes place either by light of heat [56, 57]. Impressive reversible light-induced deformations observed on millimeter-scale films of a liquid crystal is shown in Fig. 9.10. Analogous studies have failed to demonstrate so nicely and in a controlled way photoinduced deformation (light-induced actuation) in amorphous chalcogenides [55].

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Photomechanical effect of a polymer film

Fig. 9.10. Controlling the bending direction of a film by linearly polarized light. UV light (white arrows) at 366 nm induce bending, while visible light (>540 nm) flattens the film. Film dimensions: 4.5 × 3 mm2 , thickness 7 μm. The deformation and flattening time scales are both of ca. 10 s. Reprinted from [57], Copyright c 2003, Springer Nature. 

9.6.2. The Photoviscous Effect in Bulk Chalcogenide Glasses Nemilov and Tagantsev undertook the most systematic exploration to account for the origin of light-induced morphic effects [35–38], which will be surveyed in the current section. They followed an approach enabling them to conduct in situ measurements of viscosity changes under illumination for a number of bulk chalcogenide glasses. The light-induced, athermal decrease of the material’s viscosity under equilibrium conditions was described as the photoviscous effect. In their series of experiments, Nemilov and Tagantsev were able to

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discriminate between genuine light-induced viscosity changes from those arising due to temperature non-uniformity as a cause of illumination-induced heating. A great deal of information was provided by Nemilov and Tagantsev concerning the dependence of the photoviscous effect on various parameters such as (i) the intensity of the incident light, (ii) the wavelength of the radiation that spanned a wide wavelength range (300–1200 nm), including sub- and above-bandgap conditions, and (iii) the glass transition temperature, which was reported to decrease considerably upon illumination. The viscosity of the illuminated volume was found to depend exponentially on light intensity, following the form, η(I ill ) = η(0) exp(−aI ill ), where a is a material-dependent constant. A verification of the athermal nature of the effect was the finding that the influence that the light exerts on viscosity decreases at elevated temperature, signifying a counterintuitive or anomalous temperature dependence. The maximum of the photoviscous effect was found to lie in the energy range of localized states. In summary, in the theory of the photoviscous effect, the photo-assisted decrease of viscosity was associated with a decrease in the potential, which should be overcome to permit configurational reorganizations. Investigating the photoviscous effect in situ in glassy Se by the penetration method, Repka et al. [58] reached similar conclusions, as those presented by Nemilov and Tagantsev. 9.6.3. Light Effects on the Glass Transition Temperature (Tg ) and the Structural Relaxation Given the context of Section 5.3 and the fact that Tg is typically defined as the temperature where the viscosity attains a value of 1013 –1014 Poise, it is conceivable that the illuminated volume — becoming more fluid than the equilibrium glass — can be assigned to a decreased “glass transition temperature,” Tgill . Stephens was among the first who reported a change (increase) of Tg after illumination of

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evaporated a-Se films [59]. However, this work cannot be considered relevant to photoviscous effect as the light was used to anneal the film structure prior to the thermal studies. Similar light-enhanced annealing effects of a-Se films were studied by Koseki et al. [60, 61] whose results showed that the thermal history of a-Se determines the positive or negative change of Tg measured after illumination. Nemilov and Tagantsev found that the difference in glass transition temperature in dark and upon illumination, Tg − Tgill can reach 25◦ C for the AsSe glass [48]. Kolomiets et al. [62] examined the photoinduced changes in glass transition in evaporated As2 S3 and As–Se films using an indirect method, i.e., determining the Tg as the temperature at which an initially inscribed scratch on the film surface disappears. It was found that the Tg of the illuminated films increases by 12–15◦ C only for the As3 Se2 film, while no photoinduced change on Tg was observed for other compositions. The effect was fully reversible for several cycles of illumination and annealing. The sensitivity of the As–As bonds to light was considered as the main structural origin of the effect. In parallel, Larmagnac et al. [63, 64] reported comprehensive investigations of the photosensitivity of structural relaxations of amorphous Se films at T < Tg . Data on enthalpy relaxation were fitted by adopting a thermal and a photostructural relaxation time, with activation energies of 372 and 278 kJ mol−1 , respectively. This result demonstrated a drastic facilitation of the structural relaxation upon irradiation. They also found that the most prominent increase of the relaxation rate takes place for strongly absorbing light (404 nm); an energy that is considerably above the optical bandgap of Se. In contrast, Nemilov and Tagantsev, found the largest photoviscous effect at bandgap light, denoting the absence of the effect for light energy in the deep band transitions. However, in both cases — bandgap and above-bandgap photoelectronic effects on Tg — the penetration depth is quite low to justify volume effects. Notably, both groups offered similar explanation, invoking that PiS changes diffuse from the processed surface to the bulk volume.

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9.6.4. Photoinduced Effects on Elastic Constants Only a few, yet inconclusive, studies have dealt with the athermal role of light on the elastic constants of non-crystalline chalcogenides, studied mainly by monitoring the changes on the sound velocities. Photoinduced changes, manifested as increase in elastic constants, were observed for evaporated As2 S3 films upon bandgap illumination, as demonstrated by the systematic increase in ultrasound velocities of acoustic surface waves [65]. The changes saturate after ∼10 minutes of illumination, i.e., a timescale comparable to that of photodarkening in the same sample. However, in contrast to photodarkening, the hardening of the elastic constants was found to be irreversible. The changes are minor (∼6% in sound velocity) and primarily relate to irreversible structural changes of the evaporated film, such as photopolymerization of molecular species. Koman and Klish measured the changes of the (acoustic) speed of hypersonic waves for deposited As2 Se3 thin films near bandgap illumination (He-Ne laser, 1.25 × 102 W cm−2 ) [66]. Laser irradiation caused increase in the sound velocity as a result of the elastic constant hardening; the effect was seen to saturate in ∼30 minutes. The C11 and C44 elastic constants exhibited increase upon illumination by 26% and 14%, respectively. Trapping of photoexcited carriers at local defect centers was invoked to account for this observation. More systematic studies were conducted by Boolchand and coworkers who measured the elastic constants in a number of binary Gex Se1−x (15 < x < 33) glasses via near-bandgap Brillouin scattering [67]. A significant athermal light-induced softening of the longitudinal elastic constant over a narrow compositional range close to the mean-field rigidity transition composition. The effect is maximized, reaching almost to 50% reduction of the magnitude of elastic constants, at the composition x = 0.19, which is the limit between the floppy and intermediate phase, as shown in Fig. 9.11. In contrast to the previous-mentioned irreversible photohardening of As2 S3 films detected by an ultrasonic study, the experiment at hypersoninc frequencies for Ge–Se binary glasses revealed a reversible photosoftening phenomenon.

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35 Intermediate Phase

Floppy

30

C11 (GPa)

2 25 3 Stressed Rigid 20 4 5

15

6 Xc=20

Xc=19 10 15

20

25

30

Ge concentration [%] Fig. 9.11. Dependence of the longitudinal elastic constant C11 (x) in binary Gex Se1−x bulk glasses at various illumination power levels (indicated in mW for each curve). xc and xt denote the observed thresholds for photosoftening of C11 and the mean-field rigidity transition, respectively. Reprinted from [67] (Fig. 4) with permission from by the American Physical Society.

9.7. Photoplasticity: Combining the Photoviscous Effect with Mechanical Stimuli 9.7.1. Mechanical and Rheological Studies The photoviscous effect forms the ground for understanding a number of morphic-type photoinduced effects, and in particular, effects that become evident under the simultaneous action of light and an external mechanical stimulus, which facilitate the change of the shape of the illuminated object. A number of in situ and ex situ studies will be surveyed in this section. Monitoring microhardness changes upon and/or after illumination has been employed as a means to study photoinduced effects into mechanical properties. Asahara and Izumitani found that the illuminated regions of As3 Se2 films become less pliable to scratching than unilluminated areas, providing evidence for hardening of the post-illuminated material [68].

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The effect was found to be reversible upon annealing at Tg . The photodecomposition mechanism proposed by Berkes et al. [69] was put forward by the authors to account for the effect. Deryagin et al. [70] were the first who conducted in situ studies to measure microhardness changes upon illumination on thick films of a-Se and bulk glassy As2 Se3 , reporting a significant photoinduced decrease of microhardness of about ∼20%–25% for a-Se and ∼50% for glassy As2 Se3 . These authors coined the term photomechanical effect being influenced by similar studies in crystals [40]. No evidence for a spectral dependence of the magnitude of the photoinduced changes in microhardness was found, while intramolecular bond changes were considered to be at the structural origin of the effect. Kolomiets et al. [71] provided quantitative studies, using the Vickers method, on the photohardening effect for As60 Se40 films. They showed that microhardness oscillates reversibly between two well-defined values upon repeated cycles of illumination and annealing. The role of composition, and hence structure, on the photoinduced hardness changes in Asx S100−x (15 ≤ x ≤ 50) and Asy Se100−y (40 ≤ y ≤ 80) evaporated films was explored by Manika and Teteris [72]. They showed that the modifications in microhardness of films exhibits maxima near x = 45 and y = 55. The origin of this observation was attributed to photoinduced polymerization of As–Se molecular units (at y = 55). Anomalous temperature dependence of the microhardness of irradiated films was observed over a temperature range from ambient up to Tg . The “modern” era of investigations of photoplastic changes using in situ microindentation techniques began by Trunov and coworkers in early 1990s. A brief review on the subject was published a few years later that described the relevant effects as following a light-driven brittle-to-ductile transition [73]. An important piece of information can be gained by in situ studies of photoplastic effects employing micro- and nano-indentation experiments. PiS relaxation in evaporated As–S and As–Se films using microindentation kinetic experiments reveal a purely optical photoinduced decrease of the viscosity down to 1012 –1013 Poise, which corresponds to the viscosity of the material near the Tg [74–76]. Microindentation techniques

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exhibit certain drawbacks that do not allow for a complete study of photoinduced elastic-to-plastic transformations, such as the relatively large indented area and the lack of the possibility to determine other important parameters. Depth-sensing instrumental indentation (nanoindentation) was used by Trunov and coworkers to study the photoplastic response in As50 Se50 -evaporated films [77]. In situ nanoindentation experiments upon illumination, conducted for asdeposited and annealed As2 S3 films, showed that the penetration depth of the indenter in the former is much deeper (by a factor of 2) than the corresponding one in the latter [78]. Tanaka and coworkers demonstrated quantitative aspects of photoinduced ductility (elongation) in As2 S3 fibers and photoinduced deformation (bending) in As2 S3 flakes by sub-bandgap light under mechanical forces [79, 80]. The term photofluidity was coined to describe the observed morphic effect, which seems improper for this case, given the context of the discussion on photoviscous effect presented in Sections 5.3 and 5.4. Indeed, in conformity to the photoviscous effect and some photohardening experiments, these photoplastic effects exhibited by flakes follow anomalous temperature dependence, lending support to a common microscopic origin of these effects. Notably, qualitative and quantitative different behavior of the temperature dependence between flakes and fibers was reported [80], as the temperature dependence of the photoplastic effect in fibers is not anomalous, contrary to the results concerning the flakes. The structural differences of As2 S3 owing to the different preparation conditions between flakes (evaporation) and fibers (melt quenching) play presumably a dominant important role concerning the contrasting behavior of the temperature dependence of the photoplastic effect. More recent studies on the mechanical and rheological properties of the material in the course of the photoplastic effect has been conducted by considering the viscoelastic behavior of GeSe9 supporting the transient nature of the effect [81]. 9.7.2. Raman Spectroscopic Studies A systematic investigation of the photoductility effect in bulk glasses with particular emphasis on the microscopic origin of the

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effect commenced in our laboratory, almost 18 years ago, after the suggestion of the late Prof. H. Fritzsche who had that time proposed [82] a structural mechanism to account for the finding reported in [79]. Various binary As–S glasses were prepared in fiber form by drawing the viscous supercooled liquid and were studied by Raman scattering [83–87]. An early review summarizing this work can be found elsewhere [88]. Polarized Raman scattering was employed as a suitable tool to enlighten the structural mechanism underlying photoplastic effects by tracking both the creation and annihilation of certain species and monitor at the same time changes in the orientation of structural units at the short and intermediate length scales. A selection of these results is briefly summarized here. 9.7.2.1. Photoinduced Orientational Ordering An important finding emerging from analyzing polarized and depolarized Raman scattering measurements is that orientational ordering progresses in the stoichiometric As2 S3 glass as a result of the combined sub-bandgap (632.8 nm) illumination and mechanical (elongation) stress. The glass fibers retain the bulk glass structure whose atomic arrangement, vibrational modes, and polarization properties are accurately known, thus facilitating the analysis of the photo-processed material in terms of changes of the above properties. Representative polarized (VV) and depolarized (HV) Raman spectra recorded from an As2 S3 fiber subjected to uniaxial stress are shown in Fig. 9.12 (left) using a power density of ∼20 W cm−2 . The depolarized spectra exhibit monotonic increase and the depolarization ratio ρ = I HV /I V V saturates at sufficiently large values of the applied stress, S. As Fig. 9.12 (right) shows, this particular dependence of ρ on S was observed for several fibers of various diameters. Data from non-stoichiometric sulfur-rich glasses, which will be discussed below, are also shown. The analysis of a large body of experimental data demonstrated that the measured effect is well reproduced justifying the use of the depolarization ratio ρ as a reliable quantitative indicator of the structural changes that take place in the course of the illumination/stretching procedure. These results are obtained at ambient temperature using illumination

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λ0=647.1 nm

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250

300

350

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bulk

400

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450

0

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6 9 12 15 18 21 24 Stress [107 dyn cm-2]

Fig. 9.12. (Left) Representative polarized (VV) and depolarized (HV) Raman spectra of As2 S3 at various magnitudes of the applied elongation stress. The inset illustrates the morphic effect experienced by an optically processed fiber under elongation stress. (Right) Stress dependence of the depolarization ratio, IHV /IVV for As2 S3 and As25 S75 fibers of various diameters.

sources including sub-bandgap and near-bandgap conditions. No change in ρ was observed in the absence of the applied stress and vice versa, no fiber elongation takes place under stress, in dark. The structural changes leading to enhanced orientation remain unchanged after ceasing the illumination/stress stimuli, thus being permanent. Particularly, the form of the curves in Fig. 9.12 is historydependent. A sudden stress-jump step from the unprocessed state to a high value of the stress leads to a moderate change in the glass structure orientation. This finding implies that the final state is obtained through a hierarchy of structural mechanisms involved that become activated during the gradual application of the uniaxial stress.

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9.7.2.2. Anomalous Temperature Dependence — Analogy with the Photoviscous Effect It has been stressed in previous sections that the photoinduced effects sharing a common origin with the photoviscous effect exhibit striking similarities in the temperature dependence of some property of the effect. In all such cases, the effect under study showed counterintuitive behavior with increasing temperature, i.e., the effect became less noticeable at elevated temperature. Performing the experiment described in the previous section at temperatures higher than ambient, albeit appreciably lower than the Tg to avoid heat-induced effects, it was revealed that the PiS changes responsible for the photoplastic behavior into question, do also follow unexpected temperature dependence. The non-monotonic saturation value of the depolarization ratio is shown in Fig. 9.13 (left). This saturation value becomes systematically lower for 40◦ C and 60◦ C, while for higher temperature it reverts back to the room temperature value (at 90◦ C) and goes beyond that at 120◦ C, thus signifying anomalous temperature dependence. It should be stressed here that the maximum temperature of this experiment (120◦ C) is far below the Tg ≈ 210◦ C of As2 S3 ; hence, precluding thermal-induced changes of viscosity. The athermal nature of the effect was further confirmed by heating the fiber under stress in dark and measuring the depolarization ratio at ambient temperature. Neither bandgap narrowing at elevated temperatures is apt to induce heating-induced absorption of the laser light as the decrease of bandgap at 120◦ C is of about 3%. The overall behavior of the saturation value of ρ, which is a good indicator of the illumination-induced effect of viscosity, is shown in Fig. 9.13 (right, up). The values of ρ correspond to a constantstress value of 10 × 107 dyn cm−2 . The inverse of ρ is a measure of the rigidity of the glass structure or resistance to photoplastic changes. It is noteworthy that this anomalous temperature dependence, which is indirectly inferred from spectroscopic measurements, shares a striking similarity with the corresponding dependence of the viscosity measured upon illumination, as shown in Fig. 9.13 (right, down). Both curves exhibit maxima at about 60◦ C. A detailed explanation

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20 C (275 µm) o 20 C (225 µm) o Bulk glass at 20 C

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24

2.2

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Fig. 9.13. (Left) Stress dependence of the depolarization ratio for As2 S3 glassy fibers at various temperatures. Dashed and solid lines are guides to the eye. (Right, up) Temperature dependence of the inverse saturation value of ρ measured at a certain stress value. The data illustrate the anomalous characteristics of the photoviscous effect through the reversal of the temperature dependence above 60◦ C [86]. (Right, down) Temperature dependence of viscosity of As2 S3 ; (1) in dark, (2) upon illumination, (3) upon illumination using microindentation measurements. Data for curves (1) and (2) are from [35]; data for curve (3) are from [73].

considering two competing factors with opposing temperature dependence, leading to the trend shown in Fig. 9.12, has been presented elsewhere [86]. 9.7.2.3. Photoplastic Effects in Sulfur-Rich Glasses: As25 S75 The large body of experimental work on non-crystalline chalcogenides has shown that photostructural changes depend upon the glass stoichiometry, especially in families of glasses where the material exhibits nanoscale-sized structural heterogeneities, such as the

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binary Asx S100−x system [89, 90]. These heterogeneities depend on glass composition and hence different compositions behave in an individual way upon illumination. The structure of the stoichiometric composition As2 S3 is rigid, as it is composed of remnants of layers found in the crystalline counterpart. It also exhibits high chemical order and very limited heterogeneity at the nanoscale. The As25 S75 glass was explored to examine how photoplastic effects are expressed in glasses with flexible structures containing not only AsS3/2 pyramidal units, but also the chain-like and ring-like fragments characteristic of sulfur-rich compositions. The selected glass bears the advantage of exhibiting a rich variety of local bonding environments and a relatively high Tg ≈ 140◦ C, i.e., much above the room temperature. The response of this glass to photoplastic changes, using sub-bandgap (647.1 nm) and near-bandgap (514.5 nm) sources (Eg = 2.55 eV), is shown in Fig. 9.12 (right) in comparison to the stoichiometric glass data. The sub-bandgap light induced moderate orientation changes, while the near-bandgap one failed to induce any effect. The contrasting behavior between the As2 S3 and As25 S75 glasses has been discussed by addressing the role of three possible aspects: (i) differences in structure, (ii) the relation between incident light energy and band-gap energy, and (iii) the role of the glass transition temperature [87, 88]. 9.7.2.4. Atomistic Mechanisms Underlying Photoplastic Changes in As–S Glasses Various attempts have been provided to comprehend the atomistic origin of photoplastic phenomena in non-crystalline chalcogenides. However, in their vast majority such models invoke the ubiquitous STE mechanism without providing specific details to the short- and medium-range structural order of the material under study. Besides, and perhaps more important, such models do not pay attention to the simultaneous emergence of other photostructural changes that modify the structure and interfere with the mobility of the species responsible to photoplastic effect. Indeed, the role of atomic structure is among the most crucial factors, as it has been reported that near-bandgap light causes in sulfur-rich As–S glasses scission of

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S8 rings and polymerization of the formed diradicals to Sn chains [89, 90]. Such atomic-scale changes at the short- and medium-range structural order (from zero-dimensional units to arrangements of higher dimensionality) lead to a stiffer glass structure, which is less amenable to morphic changes. The contrasting behavior observed between the As2 S3 (As40 S60 ) and the non-stoichiometric As25 S75 glass calls for a deeper elucidation of the role of local atomic arrangement. Sulfur-rich glasses contain chain-like units that are expected to impede the photoplastic effect by reducing the facility of the structure to respond to an external mechanical stimulus. Two such possible scenarios can be envisaged are presented in the sketches of Fig. 9.14(a) and (b). In the former, possible entangled chain-like sulfur configurations will hinder the flow process. In the latter, such chain-like fragments can be reconfigured (relaxed), upon illumination and stressing, to directions other than that of the applied stress; hence not contributing to the fiber morphic changes. Evidently, structures with three-dimensional network structures will be less responsive to photoplastic changes owing to the over-constrained atomic arrangement and the lack of weak bonds, which are primarily susceptible to illumination. As a result, the specific structural characteristics and the concomitant softness of locally layered materials, such as As2 S3 , enhance the feasibility of structural changes that lead to the plastic deformation, Fig. 9.14(c). Fritzsche was among the first who proposed that intramolecular bond rupture can account for such effects [82]. He proposed that such atomic changes leading to photoplastic effects are common to any chalcogenide at any temperature, which was shown (see above discussion) that it is not entirely correct. Based on the spectroscopic data, an intramolecular model describing the opening and incorporation of As4 S4 cage-like species into the glass structure was proposed [87]. This model can partly offer a quantitative estimation of the fiber elongation upon illumination and stress, which amounts up to ∼30% of the observed effect. A schematic of this structural model is depicted in Fig. 9.14(e–g). The consideration of the specific role of the

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(a) (e)

:S h

h

(b)

(f) h

(c)

(g)

Fig. 9.14. (Left) Schematic representation of possible local structural arrangements in non-stoichiometric S-rich structurally flexible glasses (a) and (b) and in the As2 S3 glass. (c) The double-side arrow portrays the direction of a hypothetical external elongation stress. (Right). A possible way of a locally-planar morphogenesis. Highly symmetric realgar-type molecules (As4 S4 ) unfold, after the rupture of a homopolar (h) As–As bond, giving rise to planar-like configurations. c 2003, John Wiley and Sons. Reprinted from [88], Copyright 

As–As bonds in the photoinduced transformation of the As4 S4 cagelike species into orpiment-type configuration revealed that there exist in the glass sub-structures (of nanoscale extent), which could be “in resonance” with sub-bandgap light [87]. In accord to this reasoning, recent molecular orbital simulations on Se have shown sub-structures (curled and intersecting Se chains) with lower “bandgap” than the bulk can be easily affected by sub-bandgap light and thus have been envisaged as possible candidates facilitating photoplastic effects [91]. Last but not least, the proliferation of the structural changes from the short-range to the medium-range inevitably necessitates

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the adoption of intermolecular structural models to account for photoplastic effects. The buckling model, originally developed by Ihm [92], has frequently been considered to describe structural changes in chalcogenides. The model is grounded on the layered structure of chalcogenides and the weak interlayer interactions, i.e., van der Waals bonds, which are easily responsive to light. 9.7.3. Photoinduced Mass Transport: Relief Gratings and Healing Effects The first who reported and accounted for photoinduced effects related to mass transport, studying the kinetics of “healing” processes of scratches inscribed on the surface of chalcogenide films, was Kolomiets et al. [93]. The observed effect was manifested as an oscillating, reversible change — during illumination and annealing cycles — of the temperature needed to heal a channel scratched on a chalcogenide film. The optically field-induced mass transport resulting in giant relief modulations formed on the surface of a-As2 S3 upon intense (5 × 102 W cm−2 ) bandgap light illumination, was attributed to the photoinduced softening of the glass matrix leading to the formation of defects with enhanced polarizability [94]. To account for this effect, it was suggested that these defects experience diffusion under the optical field gradient force generating surface relief modulations. The effect is realized either by single- or two cross-polarized beam experiments and depends upon polarization of the electric field. Poborschii et al. [95] reported the emergence of relief deformations for a-Se under bandgap illumination at low temperature. This observation was assigned to photomelting taking place via an interchain bond breaking mechanism. Trunov and coworkers have systematically explored similar effects for a number of non-crystalline chalcogenides [96–100]. They demonstrated that similar mass transport effects can be achieved even at considerably lower power densities. This is a useful observation because such reduced light fluence is in the range of light intensities employed for the recording of holographic gratings in non-crystalline chalcogenides. Various details of the photoinduced mass transport were studied both experimentally and theoretically

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(to obtain photoinduced diffusion coefficients), including the inversion of the direction of the surface relief grating, kinetics of the effect at low temperature, and selective light-induced mass transport in amorphous Asx Se100−x tuned by composition see [101] and references therein. Some recent attempts are also focused in the formation of nanoscale structures in amorphous chalcogenide films [102]. This can be achieved by controlling appropriately the conditions by incorporating noble metal nanoparticles into the chalcogenide structure and using the excitation of the plasmon resonance of the nanoparticles. Finally, the expression of surface relief gratings using electron beams has also recently been emerged as an interesting phenomenon for manipulation the texture of non-crystalline chalcogenides at the nanoscale [103, 104]. 9.8. Athermal Photoinduced Changes of the Phase State Photoplastic or morphic effects, described in the previous section, are perhaps the most fascinating photoinduced phenomena as they emerge with spectacular changes in the shape of the material. However, photoinduced changes of the phase state can be even more intriguing as they seem to violate in certain cases the common wisdom. Their athermal nature and astonishing reversibility in some circumstances, entails prospects for captivating applications. Such effects are perhaps the most challenging to comprehend and explain from the wealth of photoinduced phenomena in non-crystalline chalcogenides. The current section is divided into two sub-sections. In the first, a brief overview of amorphous-to-amorphous transitions — the subject of which is quite limited — will be reviewed, while in the latter we will survey on the more extended literature on reversible amorphousto-crystal photoinduced transitions. 9.8.1. Reversible Amorphous-to-Amorphous Transitions (AAT) In analogy to the concept of polymorphism observed in crystalline solids upon changing the temperature (T) or the application of

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pressure (P), non-crystalline materials can also exhibit transitions to a distinct amorphous phase. While in crystals, T and P are parameters that are frequently used to drive and tune the phase transition, in amorphous solids, it is predominantly pressure that can drastically change the short (nearest neighbors) and medium (e.g. number of ring members) range structural order, leading to a new amorphous phase. Mishima et al. [105] was the first who pointed out that an amorphous-amorphous transitions exists in water. Several types of disordered solids experience such pressureinduced transitions, including also chalcogenide glasses, such as As2 S3 [106] and Ge–Se [107]. A “hidden” thermally-driven phase transition within the amorphous state of As50 Se50 was suggested to account for the findings of calorimetric studies, where two exothermic peaks, situated below and above Tg were observed [108]. The idea was based in the view that the glass and the parent crystal have similar short-range order. It was thus suggested that two different glassy structures can (co)exist in the As50 Se50 composition, each one related to the low- and high-temperature crystalline polymorphs. Under this situation, illumination could possibly induce transitions from one structural configuration state to the other [108]. Reports on well-documented optically-driven AATs are very rare [109]. Typically, an ATT cannot be considered as an actual phase change transition for two main reasons. First, an AAT is primarily related to subtle differences in the atomic structure of the two distinct meta-stable structures in the amorphous state. Second, the two distinct phases are not determined as in crystals by thermodynamics; they are both non-equilibrium states and the details of the stimulus (e.g. photons) employed to transform one phase to another strongly affects the kinetics of the transformation. It is worth-noting that whereas the atomic change can be moderate, an AAT can give rise to substantial changes in the optical properties, i.e. enhanced optical contrast between the two amorphous phases. This effect can endow new functionalities, possibly exploitable in next generation optical data recording, photonic bandgap tuning, and so on. Given that structural changes accompany practically any photoinduced effect, then a plausible question arises: what is the fraction of the atoms/bonds that must be affected in order to consider this

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structural change as an AAT? Typical photoinduced effects such as photodarkening or photobleaching have been considered to involve a limited fraction of the atoms in the illuminated volume, which does not exceeds ∼2% [26]. This small fraction does not justify the term AAT in this case. Notably, there are few cases where As–S binary chalcogenide glasses exhibit massive photo-induced bond reconfigurations. Detailed spectroscopic studies have shown that such Sulphur-rich binary glasses the fraction of bonds altered by illumination can be astoundingly high, ∼20%, i.e., almost one order of magnitude higher than the corresponding photo-induced reorganized bond fractions reported up to now in typical cases [89, 90]. The main structural transformation in these glasses involves the photoinduced scission of S8 rings and the polymerization of these diradicals to chain-like species. However, photoinduced polymerization is practically a transient effect and hence not classified as an AAT. Nanoscale phase separation was considered to be the key for this extraordinary behavior leading to massive PiS changes. Nanoscale phase separation can be envisaged as the situation where the composition of the particular system under study dictates a structure where local micro-environments of particular atomic configurations exist with comparable internal energies. Therefore, external stimuli can rather easily induce transformations from one local structure to another. The exploration of non-crystalline chalcogenides with high responsiveness in illumination and hence potential to applications, is a guide towards considering materials compositions which exhibit structural motifs that are able to withstand and proliferate the photoinduced changes into their volume, in a sustainable aspect. Evidently, this can be achieved in cases where the disorder characterizing the structure can afford certain relaxation routes which can lead to relaxation of the photoexcited bond to configurations different than the initial one. Given this context, disordered materials exhibiting nanoscale phase separation, as described above, are possible candidates for exhibiting structural transformations among two structural motifs, with alike bonding features, at low-cost of energy.

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Arsenic-rich, binary As–Se amorphous films grown by the pulsedlaser deposition technique were shown, using x-ray photoelectron spectroscopy (XPS), to exhibit strong nanoscale phase separation [110, 111]. This particular deposition method plays significant in the growth of amorphous chalcogenides with tailored-made functionalities owing to its advantage of maintaining quite well the composition of the target material, avoiding also the formation of structures and morphologies associated with irreversible processes. In brief, XPS data were interpreted in the context that the structure of Asx Se100−x PLD films (x > 40 at.%) consists primarily of AsAs3−m Sem pyramidal units. The units As4 (m = 0) and As3 Se (m = 1) are denoted as type-AsI environment. The As atoms in As3 Se pyramids have alike electronic properties with As4 units, hence, termed as elemental-like domains. Based on similar grounds, pyramids As2 Se2 (m = 2) and AsSe3 (m = 3) constitute the stoichiometric-like domains; type AsII environment. The fraction of As atoms participating in the elemental-like environment (AsI ) was found to be in range 15–20%. Exploring in detail structural and optical properties of As50 Se50 PLD and TE films it was found (see Fig. 9.15) that reversible switching takes place between two structurally distinct amorphous states, guided by exposure to near-bandgap light (increasing AsI ) and annealing (decreasing AsI ). This behavior justifies the use of the term AAT, especially in view of the large fraction of atoms involved and the concomitant change in the optical properties of the films. The oscillating effect does not depend on which external stimulus (light and annealing) is imposed first. Notably, only in PLD-prepared films the effect is observed repetitively, for several illumination/annealing cycles, while this does not hold for TE films. Another interesting outcome emerging from this study is that the PiS changes bear a rather strong transient character, as revealed by the film states “1” and “5” in Fig. 9.15 (left panel). As long as illumination is “on” the fraction of f (AsI ) reaches about 38–40%, while it decreases after ceasing illumination to ∼30%. In addition, annealing always causes considerable reduction in f (AsI ) to a value

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Fig. 9.15. (Left) Switching of fraction f (AsI ) = AsI /(AsI + AsII ) (%) in As50 Se50 thin films deposited by two different techniques. PLD (up) and TE (down) after imposing alternating external stimuli. The film states 1–8 correspond to cycling of irradiation followed by annealing or vice versa, where route (1) starts with irradiation and route (2) with annealing. The three lines of data points (up) shows the states: (i) transient (tr, laser ON), (ii) post irradiated (irr), and (iii) post annealed (ann). (Right) Correlation between changes in refractive index (n) at λ = 1500 nm (measured by ellipsometry) and f (AsI ) for as-deposited As50 Se50 PLD films after imposing external stimuli in the sequence irradiation → annealing (up) and annealing → irradiation (down). The inset shows a schematic of structural elemental-like (AsI ) and stoichiometric-like (AsII ) c 2012, John Wiley and Sons. pyramids. Reprinted from [91], Copyright 

near 10%, originating from the rupture of As–As bonds and the formation of As2 Se2 and AsSe3 pyramidal species. Figure 9.16 summarizes in a pictorial way the structural transformation of the AAT described above in the frame of an energy landscape representation of the involved steps. While in a typical reversible amorphous-to-crystal transition (exploited in optical data storage) the atomic arrangement oscillates between the crystal (state “1”) and the glassy state (obtained by melting and rapid quenching, state “2”), a richer phenomenology is offered in materials exhibiting nanoscale-phase separation which can drive the structure to amorphous states with alike, albeit discrete, bonding features.

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Fig. 9.16. Potential energy landscape representation of the photo- and heatinduced transitions in As50 Se50 PLD films. The deepest minimum “1” corresponds to the crystal which has been (depicted here as an idealized structure, not reflecting the accurate crystal structure). The amorphous as-deposited state “2” is built-up by both As–Se heteronuclear (black lines) and As–As homonuclear (red lines) bonds. Illumination guides the structure to minimum “3,” where the number of As–As bonds increases; the system is transiently trapped in a shallow minimum being prone to relaxation into the post-irradiated state “4,” characterized by a density of As–As bonds larger than “2” but lower than that of “3.” State “4” is thermally meta-stable; after annealing it relaxes to state “5” which is the amorphous state with the lowest density of homonuclear As–As bonds. Reversible switching in the structure and the optical properties of PLD films occurs between states “4” and “5.” State “5” can also be reached from state “2” after annealing. c 2012, John Wiley and Sons. Reprinted from [91], Copyright 

This type of AAT transitions could possibly be a more generic phenomenon in disordered materials, which however awaits to be studied. As discussed, the presence of necessary populations of structural species is a prerequisite enabling an external stimulus, such as light, to covert species athermally from one population to another. The refractive index contrast of As50 Se50 , under the condition of the current experiment amounts to Δn ≈ 0.04, is only a factor of two lower than the contrast in Ge2 Sb2 Te5 at λ = 633 nm (DVD operating wavelength), implying high potential for applications. Such structural rearrangements would entail low-energy consumption in

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potential devices as the ruptured and formed bond energies are comparable i.e. 200 kJ mol−1 (As–As) and 230 kJ mol−1 (As–Se). In comparison to crystal-amorphous transitions exploited in phasechange memories, the AAT entails negligible volume change and avoids films stress during crystallization which may suppress the growth rate. Exploitation of the diversity of distinct structural states in disordered structures could also provide possibilities for multilever data storage mechanisms. However, viable applications are still elusive as many details of AAT as processes for data storage are still unknown. 9.8.2. Athermal Transitions between Amorphous and Crystalline States 9.8.2.1. The Framework of Phase Changes by Electronic Excitation From a different perspective, irradiation-induced phase transitions in materials, or more generally stated, modifications of materials due to electronic excitation, is a generic effect observed not only in non-crystalline chalcogenides but, in principle, in any crystal [112]. Irradiation, by photons (laser annealing) and less commonly by electrons, has been used as a versatile means to modify the material’s surface to anneal damage created by various processes, such as implantation. For sufficiently intense beams a high density of photoexcited carrier are created, called electron-hole plasma. A key concept in understanding such phenomena is that the temperature of the excited electrons and ions is not necessarily the same [112]. Perhaps the first attempt to explain a non-thermal solid-liquid transition, a kind of athermal melting, traces back to the ideas developed by Van Vechten and coworkers based on the photoexcited electron-hole plasma [113, 114]. In an effort to account for critical observations, which had gone unnoticed in previous studies of the pulsed-laser annealing of crystalline Si, concepts for non-thermal transformation of the material’s surface from crystal to liquid were developed. In brief, it was postulated that if the density of photoexcited electrons, which is materials dependent, exceeds a

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certain threshold, then a second-order phase transition will take place. The depletion of bond charges causes instability of transverse acoustical phonon modes to the extent that the crystal cannot sustain shearing, hence passing to the “fluid” regime. In contrast to the normal thermal melting where the crystal undergoes a first-order transition and the atoms carry out long oscillations around the equilibrium positions, the athermally induced fluid retains its energy in the electrons, maintaining the atoms rather restful. The duration of the laser pulse is critical. For short durations, i.e. comparable or less than the vibrational period the effect in purely athermal as thermalization has not been settled. 9.8.2.2. Early Studies on Photocrystallization As thermal effects are practically unavoidable during illumination of a chalcogenide material, a great deal of confusion surrounds studies of photocrystallization. Literally speaking, photocrystallization arises solely from photoelectronic processes. Essentially, the sharp increase in the free carrier concentration upon illumination and the excitation of electrons across the mobility gap gives rise in a large density of broken bonds in the material. This process weakens the metastability of the amorphous state rendering the structure more amenable to crystallization. Dresner and Stringfellow were the first who studied the role of illumination in the characteristics of the phase change in elemental glassy Se [115]. They made reference to previous similar studies where illumination-enhanced crystallization rate of amorphous Se was interpreted based on thermal or combined photo- and thermal effects. Measuring the growth rate of the diameter of individual crystallites (spherulites) upon irradiation with a 100 W Hg lamp, they were able to obtain the crystallization kinetics. It was suggested that the effect of illumination on the rate of crystal growth is related to the generation of hole-electron pairs. Holes are the deeply trapped carriers that dictate the diffusion of the photoexcited pair, thus the flux of free holes are considered to control the growth rate of the crystal. The main contribution to the athermal mechanism of photocrystallization was ascribed to the energy released upon

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annihilation of the hole-electron pair, which could provide a means for reorientation of the Se chains disposing them in a crystalline configuration. Several other studies were focused on photocrystallization of various non-crystalline chalcogenides, i.e., Se [116], Gex –Se1−x [117], Se85 Te15 [118], and Se100−x Tex [119]. Ovshinsky and coworkers [120, 121] showed that msec long light pulses induce crystallization and re-amorphization of Gex Te1−x (x = 0.11, 0.66 and 0.72); however, they did not attempt to separate optical and thermal effects. Feinleib et al. [122] studied reversible light-induced crystallization of the amorphous Te81 Ge15 Sb2 S2 compound. This effect was considered as the optical analogue of the memory-type electrical switching discovered earlier in such compositions by S. R. Ovshinsky [123]. Feinleib et al. [122] suggested a model to interrelate the optical and electrical switching effects, proposing that the optically-induced reversible phase change does not solely originate from thermal effects but is also influenced by the generation of the photoexcited electron-hole carriers. Few more reports on the laser-assisted reversible crystallization of Te-rich alloys stated that the distinction of the role of optical and thermal effects was yet not clear [124, 125]. No progress in this field took place for a decade or more when athermal reversible quasicrystallization in GeSe2 glass studied by Raman scattering was reported by Griffiths et al. [126, 127]. The authors used various levels of the laser power interpreting the spectra as showing a transformation of the structure to a quasicrystalline configuration before it is converted to microcrystallites. They considered that photoinduced crystallization of the GeSe2 glass is reversible after keeping the glass in dark for several hours. The ambiguous interpretation of the Ge–Se Raman modes in that work made the elucidation of the mechanism underlying this photoinduced process dubious. In a more systematic experimental study by Haro et al. [128] light-induced crystallization of GeSe2 was slightly reconsidered. The “cluster” and “microcrystallites” approach interpretation employed by the authors led them to debatable interpretations of the experimental data, as strong Raman bands were erroneously assigned to Ge–Ge and Se–Se bonds in the stoichiometric glass. The use of above-bandgap light is another weak point which

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does not preclude the possibility for a significant influence of thermal effects. Indeed, the photocrystallization effect exhibited much slower kinetics with sub-bandgap light owing to the avoidance of heatinduced effects. Significant Raman line broadening is an additional solid evidence for thermal effects. On another front, quite a few studies were dedicated to elucidate the influence of light polarization on the photocrystallization of a-Se. Irradiation at T > Tg was found to induce anisotropy due to Se chain orientation [129]. Obviously, at such temperature, the effect has a strong thermal character in addition to the optical effect. Lyubin et al. [130, 131] studied the effect of laser polarization on the crystallization behavior of Se-containing amorphous chalcogenide films. It is not rare to meet contradictions in photocrystallization studies in the case of a-Se. As this material has its Tg at about room temperature, even small differences in the illumination power density can qualitatively and quantitatively change the features of the photocrystallization process, i.e. kinetics, preferred orientation, structure, and so on. For example, Roy et al. [132] explored the effect of illumination wavelength on the photocrystallization of a-Se using above- and sub-bandgap light. They observed a preferential growth of the crystal by sub-bandgap light (676.4 nm) illumination and non-preferential growth by the above-bandgap light (488.0 nm) using 120 W cm−2 . This observation contradicts the findings of Innami and Adachi [133] using 488 nm illumination at 20 W cm−2 who reported preferential orientation for this wavelength. 9.8.2.3. Early Studies on Photoamorphization A large number of articles have been published on the study of photocrystallization in amorphous chalcogenides, as discussed in the previous section. This effect is more feasibly realized as dictated by thermodynamics, since the crystal is the most energetically favored state. Besides, thermal effects can intervene — in parallel to light-induced effects — especially for low-Tg materials for which the supercooled regime (T > Tg ), where crystallization rate is maximized, is easy to attain. On the other side, photoamorphization, i.e. the light-assisted disordering of a crystal is a more uncommon

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effect. When observed, it inherently entails an athermal origin as there is no way of direct transformation of a crystal to an amorphous solid, unless melting (necessitating substantially high T’s) intervenes. Amorphization of a crystal can occur via high pressure, where the pressure quenched product can retain to a large extent the disorder induced under in situ pressure conditions [134]. Amorphization of materials, which can either form glasses [135] or not [136], can also take place under irradiation by energetic particles, such as neutrons. However, achieving a crystal-to-amorphous transformation by a “gentler” and more convenient stimulus, such as light, is more intriguing as this structural transition goes beyond our current understanding of disordered systems and deserves thorough consideration. Few studies have up until now focused on athermal phase change transitions of chalcogenides. Kolobov and Elliott reported that thermally evaporated amorphous films of As50 Se50 , after being thermally crystallized at 140◦ C, can be retrieved back in the amorphous form under low-intensity white light illumination for a duration of 150 minutes [137–141]. This is the sole composition of the binary system As–Se exhibiting the athermal transition. The amorphous-crystalamorphous cycle can be repeated consecutively. However, only the crystalline-to-amorphous transformation step (photoamorphization) is achieved optically. Partial amorphization was observed even in the case where the film was illuminated at high temperature (140◦ C). The kinetics of photoamorphization yielded an activation of 0.15 eV was estimated. Evidence for the intramolecular origin of the effect was provided by comparing the Raman spectra of the crystallized and amorphous films revealed that the molecular realgar-type As4 Se4 species found in the crystal, are not present in the amorphous phase, which implies a photo-polymerization reaction leading to a networklike solid. Another possible mechanism of intermolecular origin was envisaged according to which the cage-like molecules As4 Se4 are not destroyed, but these units just alter their relative orientation and spatial distribution upon illumination as a result of weakening of intermolecular interactions. This is a process resembling thermallyinduced orientational transitions in plastic crystals. Based on the disappearance of the sharp Raman band of As4 Se4 molecules in

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the amorphized film [139], the intermolecular model seems more plausible. Photoamorphization of orpiment, c-As2 S3 , was reported by Frumar et al. [142] Due to the extreme stability of supercooled As2 S3 and its inherent difficulty towards crystallization to the orpiment phase, the authors studied natural crystals, which are not free of contamination. Using near-bandgap light they observed partial only crystallization of the crystal at room temperature. Similar effects were observed at low temperature (36 K), confirming the athermal nature of the effect. Frumar, et al. [142] considered that the softness of the layered orpiment crystal can cause the generation of several defects under mechanical treatment. The presence of a high defect density can endow the metastable crystal with a Gibbs free energy higher than that of the amorphous state. Hence, light can provide the required energy needed to obtain the transition from the metastable (defected) crystal to the disordered state. 9.8.2.4. Recent Progress in Athermal, Optically-Driven, Reversible Amorphous-to-Crystal Transformations A recent detailed study of athermal photoinduced transitions between the amorphous and the crystalline states has been conducted by Benekou et al. [143] for the multicomponent bulk glass Ge25.0 Ga9.5 Sb0.5 S65.0 containing 0.5 at.% of Er3+ using abovebandgap laser illumination. Essentially, this the first study reporting an all-optical, truly reversible amorphous-to-crystal transformation where the complete cycle is achieved by illumination, without involving annealing steps. The benefit of the time-resolved Raman measurements (Fig. 9.17), which was employed, is that the photostructural changes were monitored in detail in the timescale of few seconds. The observed effects were purely athermal, as the temperature rise of the illuminated volume was estimated from Raman band shifts to be far below the Tg of this glass. A reliable assignment of the Raman bands is indispensable for the interpretation of the spectral changes generated in the course of illumination, which has been the main drawback in previous studies. Figure 9.17 (left) shows the Raman spectrum “1” of the well-equilibrated glass recorded at low light

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fluence unable to engender photostructural changes. The spectrum is fitted with various lines, each one assigned to particular species that can be found in the structure at reasonable concentrations for the glass composition under study [143]. CST and EST stand respectively for corner-sharing and edge-sharing tetrahedra. Bonding arrangements of such tetrahedra on medium-range order and beyond, develops structures of 3-D and 1-D topological character. The analysis of Raman spectra revealed that a three-stage mechanism of photostructural changes takes place at prolonged illumination. During the first stage of illumination significant photostructural changes were observed within the glassy state, prior to any

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photocrystallization effects. Spectrum “2” in Fig. 9.17 (left) Shows the significant enhancement of two new bands situated at ∼235 cm−1 and ∼375 cm−1 . The band at 235 cm−1 originates form Ge–Ge(Ga) ethane-like configurations. These units are formed as light ruptures CST and/or EST. The increase of the band at 375 cm−1 in spectrum “2” makes clear that illumination causes increase in the EST/CST ratio during this early illumination stage. These structural changes start immediately with illumination and saturate in about 1–3 minutes for P ∼ 104 W cm−2 . This transformation has an important outcome; it entails degradation of the 3-D network to structures of 1-D character (EST and ethanelike units). Hence, more available space or free volume is created, which is essential for triggering and facilitating atomic displacements towards the second stage, i.e. crystallization. Indeed, after this “incubation” first period, crystallites start growing as Raman spectra show. Spectrum “3” in Fig. 9.17 (left) stands for the final photocrystallized product. The very weak background in the spectra range 300–400 cm−1 shows that almost complete photocrystallization has been achieved. The kinetics of photocrystallization is quantified by evaluating the contribution of the Raman band at ∼340 cm−1 , which reflects the A1 of the low-temperature 3-D structure β-GeS2 crystal located at the same energy, Fig. 9.17 (right, (a)). Photocrystallization saturates in about 10 min. Changes in the Raman wavenumber (redshift by 1–2.5 cm−1 ) caused by laser heating are translated to temperature increase of about 60–150 K, i.e. much lower than the Tg of the glass under study. Perhaps, the most intriguing observation is that by lowering the illumination power by one order of magnitude (P ∼ 103 W cm−2 ) the photo-crystallized volume can be re-amorphized. The intensity of the Raman bands of the crystalline phase weaken progressively until the final stage, shown by spectrum “4” in Fig. 9.17 (left). The kinetics of the photoinduced re-amorphization is studied in detail (Fig. 9.17, right, (b)), revealing a timescale of ∼60 min. The re-amorphized product retains only a weak crystalline component. A quantitative aspect of the kinetics of the three steps involved in the photoinduced cycle glass-crystal-glass is presented in Fig. 9.17 (left).

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Details are given in the figure legend. It is worth-mentioning that the photo-crystallized product shows a weak tendency towards re-amorphization even in dark (laser-off). However, the kinetics in this situation is at least two orders of magnitude slower than the corresponding kinetics upon continuous illumination with low-fluence light. An interesting aspect of the observed fully reversible cycle (glasscrystal-reamorphized solid) is that this cycle can be repeated in a row for more than one time yielding similar results. The photocrystallization step is quantitative different for the various cycles, while the re-amorphizaiton process exhibits practically the same kinetics. In addition, the aforementioned reversible structural changes are accompanied by irreversible morphological changes reminiscent of those observed in the photoinduced mass transport phenomenon. Figure 9.18 (right) displays scanning electron microscopy (SEM) images during the photocrystallization process. Image (a) shows a faint imprint of the laser beam on the surface of the glass induced at low-fluence conditions which do not cause photostructural changes. Changes in surface morphology of the glass developed at high fluence are depicted in SEM images (b) and (c), which correspond to the early and final stages of photocrystallization, respectively. Mass transport results in the formation of columnar-like structures with dimensions of 1–1.5 μm. More systematic studies are currently underway in an effort to decipher the role of the Sb/Ga ratio in Ge25 Gax Sb10−x S65 glasses (x = 5, 7.5, 10) in the reversible athermal transition between the crystal and the glass [144]. Remarkably, the pure GeS2 glass does not exhibit this athermal photoinduced transformation, which manifests the crucial structural task of Ga/Sb in the glass. The creation of local (nanoscale) environments resulting from the different bonding requirement of the Ga/Sb atoms (3-fold coordination to S) is apparently a decisive factor for the responsiveness of the multicomponent glass to light. Despite quantitative differences, all glass of the above quaternary system demonstrated the athermal, reversible crystal-toamorphous transition.

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9.9. Summary and Perspectives In the preceding sections we have tried to delineate the particularities and microscopic origin of a number of photoinduced effects

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in non-crystalline chalcogenides. Emphasis was placed to categorize and sort effects of common origin. As a general perception, we should stress that the photoviscous effect, i.e. the athermal decrease of glass viscosity under illumination, stands as the cornerstone of a number of photoplastic effects. Macroscopic mass transport and any kind of deformation of the specimen under study appears rational, since electronic excitation under illumination emulates temperature rise above Tg . This athermal transformation of the solid viscosity to values corresponding to the supercooled liquid, renders relaxation processes fast enough, so as to fall within the observation experimental time. Delving into the archival literature, one frequently encounters reports which are simply descriptive, postponing a deeper apprehension of the measured effect. Despite that such works enrich the current phenomenology, bearing a hand-waving character they may add confusion towards our understanding of photoinduced effects. Indeed, several studies have been highly unmethodical reporting the occurrence of some type of photoinduced effect for a particular glass or amorphous film composition, eluding the temptation to consider important aspects of the effect in a more systematic approach. Besides, in several cases, the prosed “structural models” are simple handmade drawings, being highly irrelevant to real atomic arrangements of the structure in question. Understanding the microscopic origin of photoinduced phenomena is a tantalizing task. Although proposed universalities, established for a large number of materials explored, do indeed hold for few effects, it is not uncommon that exceptions to the rule are also frequently met in several cases. The fact that the very same amorphous chalcogenide prepared by a different method, frequently exhibits dissimilar response under illumination, has been an extra source of perplexity in the field. Research in amorphous chalcogenides is systematically diminishing worldwide over the last years, as other (nano)materials with (alleged) potential for applications emerge at a frantic pace. However, the interest in chalcogenide research will be continued since novel aspects of known effects will keep drawing our attention. Closing this review, we will refer to few such issues that may deserve further

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exploration as they could either provide better understanding of known effects or result in fascinating new findings. Computer simulations, such as ab initio molecular dynamics, being among the most accurate approaches, have provided instructive results on the structure of various non-crystalline chalcogenides, with emphasis on the last decade on the phase-change mechanisms in Ge-Sb-Te alloys [145, 146]. However, what is perhaps surprising is the lack of systematic computer simulations to guide and augment experiments on interpreting photoinduced effects. However, this is not unreasonable from the viewpoint that simulating the photoelectronic excitation process and the ensuing relaxation pathways, is a formidable task. Among the very few articles dealing with theoretical/simulation aspects we should refer to the modelling of the structure of As2 S3 clusters and their electronically excited states using ab initio quantum chemical calculations [147]. The existence of localized electronic states of amorphous semiconducting chalcogenides facilitates such an approach because the PiS changes can describe by the local nature of excited electrons at a good accuracy. More recently, modeling As2 S3 as an incompressible viscous fluid, mass transport and surface morphological changes were studied as the result of an optically induced pressure acting on induced dipoles [148]. Simulations towards this direction are expected to shed light on the origin of PiS changes and provide a quantitative means for a priori predictions. It might seem surprising that photoplastic effects were first reported and methodically explored for crystals (since 1957), as briefly surveyed in Section 9.6.1.1. A very recent report has revived the interest in such studies. While the role of light is considered to be positive — in the sense that it facilitates structural changes at the atomic level — Oshima et al. [149] presented findings that darkness can induce extraordinary plasticity of bulky ZnS crystals; hence, unsettling the widely accepted perception that inorganic semiconductors fail in a brittle manner under stress. The unexpected high plastic behavior of crystalline ZnS, withstanding deformation strain of ∼45%, observed at room temperature is the result of complete darkness, while under white or UV light irradiation the

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Fig. 9.19. (A) Stress-strain curves of ZnS single crystals. (B) An as-grown crystal. (C) and (D) ZnS crystals deformed under white and UV light. (E), (F), and (G) Crystals deformed at certain strains as shown in the solid curve in (A). c 2018. The Authors, some rights reserved; Reprinted from [149], Copyright  exclusive licensee American Association for the Advancement of Science.

crystals were fractured at few % of strain, as shown in Fig. 9.19. The role of dislocation motion is key to understanding the observed effects. The plastic deformation is accompanied by dramatic decrease of the optical bandgap from 3.52 for the undeformed crystal to 2.92 for the crystal deformed up to 35% plastic strain. Questing similar effects in bulk chalcogenide glasses would undoubtedly be a stimulating topic. Truly athermal, photoinduced phenomena have pervasively fascinated researchers working on non-crystalline chalcogenides as they form the ground of a number of potential applications in photonics and optoelectonics. On another front, it has always been challenging

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to demonstrate the purely athermal nature of the effect under study as irradiation can inevitably transfer some undesired amount of heat to the exposed material. Reversible, optically-driven athermal phase changes between a crystal and its disordered state have been demonstrated in a few cases. Recent findings [143] of an all-optical-based mechanism eliciting the reversible transition: glassy(amorphous) ↔ (metastable) crystalline ↔ re-amorphized solid, are of particular interest and certainly deserve more systematic studies. The interest particularly arises from our poor, yet, understanding of the second step of the transition stated above. Even scarcer are athermal light induced amorphous ↔ amorphous transformations, particularly when they are accompanied by strong changes in optical properties and can be induced in successive cycles [109]. The nature of polyamorphic transitions between two structurally distinct metastable amorphous phases driven solely by light, is a highly unexplored theme. The emerging field of 2D crystals such as transition metal dichalcogenides (TMDChs) of the form MX2 (M: Mo, W, . . . , X: S, Se, Te,) might open up new directions and possibilities for the demonstration of new potential functionalities arising from photostimulated effects. Despite that the demonstration of photoinduced effects in TMDChs materials is highly challenging due to the very poor glass-forming ability these materials exhibit, this is still an open field of research pervaded with opportunities and prospects. Benefiting from micro-fabrication capabilities arising from photoplastic effects, amorphous chalcogenides could apparently meet a number of applications in photonics. Counter to conventional heat methods which can be used to plastically deform or mold glassy/amorphous solids, the employment of light offers certain advantages. The avoidance of heat conduction and the precision targeting to the desired area for molding material’s shape, are amongst the most prominent. Even if the transition of such effects to commercial applications still seems remote or elusive, exploring the origin of photoinduced effects is of utmost interest in its own right. Undeniably, non-crystalline chalcogenides do not possess the exclusive privilege of being the sole light-responsive materials.

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However, they settle indeed atop this pyramid being the class of materials exhibiting the richest variety of photoinduced effects in comparison to other types. The systematic studies and the current understanding in this field of research might unlock the potential for clarifying similar effects in less explored areas.

Acknowledgments I want to thank a number of individuals who have contributed to the work presented in this chapter. At first, I would like to express my gratitude to Prof. G. N. Papatheodorou (my Ph.D. supervisor) for the guidance, advice and encouragement he provides constantly since 1991. His acquaintance with the (late now) Prof. H. Fritzsche (U. Chicago) was the trigger which initiated my exploration of photoplastic effects in chalcogenides almost 19 years ago. Since then, I have been cooperating on this research topic with a number a number of collaborators (Dr. D. Th. Kastrissios, Dr. K. S. Andrikopoulos, Dr. M. Kalyva, Dr. A. Siokou, Dr. F. Kyriazis, Ms. V. Benekou, Dr. J. Orava, and Prof. T. Wagner) whom I wish to thank. Illuminating discussions with Dr. R. O. Jones and A. V. Kolobov on specific aspects of this chapter, as well as the discussion and the assistance of Dr. M. L. Trunov with the Russian literature are highly appreciated. Finally, I want to thank my Ph.D. student Ms. A. Antonelou for her valuable help in sorting the references of the present document and the ICE-HT librarian Ms. M. Perivolari for managing the copyrighted material presented herein. Part of this work was financially supported by the Stavros Niarchos Foundation within the framework of the project ARCHERS (“Advancing Young Researchers’ Human Capital in Cutting Edge Technologies in the Preservation of Cultural Heritage and the Tackling of Societal Challenges”).

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104. Kaganovskii, Y., et al. (2014). Electron-beam induced variation of surface profile in amorphous As20 Se80 films, Journal of Applied Physics, 115, pp. 1–8. 105. Mishima, O., Calvert, L. D., and Whalley, E. (1985). An apparently first-order transition between two amorphous phases of ice induced by pressure, Nature, 314, pp. 76–78. 106. Vaccari, M., et al. (2009). High pressure transition in amorphous As2 S3 studied by EXAFS, Journal of Chemical Physics, 131, pp. 1–4. 107. Yildirim, C., et al. (2016). Universal amorphous-amorphous transition in Gex Se100−x glasses under pressure, Scientific Reports, 6, pp. 1–11. 108. Bershtein, V. A., Egorova, L. M., Kolobov, A.V., and Ryzhov, V. A. (1992). Investigation into structural transformations in thin films of As–Se system using method of differential scanning calorimetry, Soviet Journal of Glass Physics and Chemistry, 18, pp. 367–371. 109. Kalyva, M., et al. (2013). Reversible amorphous-to-amorphous transitions in chalcogenide films: Correlating changes in structure and optical properties, Advanced Functional Materials, 23, pp. 2052–2059. 110. Siokou, A., et al. (2006). Photoemission studies of Asx Se100−x (x: 0, 50, 100) films prepared by pulsed-laser deposition — the effect of annealing, Journal of Physics: Condensed Matter, 18, pp. 5525–5534. 111. Kalyva, M., et al. (2008). Soft x-ray induced Ag diffusion in amorphous pulse laser deposited As50 Se50 thin films: An x-ray photoelectron and secondary ion mass spectroscopy study, Journal of Applied Physics, 104, pp. 1–7. 112. Itoh, N., and Stoneham, A. M. (2001). Materials Modification by Electronic Excitation (Cambridge, England, Cambridge University Press). 113. Van Vechten, J. A., Tsu, R., Saris, F. W., and Hoonhout, D. (1979). Reasons to believe pulsed laser annealing of Si does not involve simple thermal melting, Physics Letters A, 74, pp. 417–421. 114. Van Vechten, J. A., Tsu, R., and Saris, F. W. (1979). Nonthermal pulsed laser annealing of Si; plasma annealing, Physics Letters A, 74, pp. 422–426. 115. Dresner, J., and Stringfellow, G. B. (1968). Electronic processes in the photo-crystallization of vitreous selenium, Journal of Physics and Chemistry of Solids, 29, pp. 303–311. 116. Clement, R., Carballes, J. C., and de Cremoux, B. (1974). The photocrystallization of amorphous selenium thin films, Journal of NonCrystalline Solids, 15, pp. 505–516. 117. Matsushita, T., Suzuki, A., Okuda, M., and Nang, T. T. (1979). Photocrystallization of amorphous Gex Se1−x thin films, Thin Solid Films, 58, pp. 413–417.

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118. Kumar, A., Agarwal, K., Goel, S., and Tripathi, S. K. (1990). Photocrystallization in amorphous thin films of Se85 Te15 , Journal of Materials Science Letters, 9, pp. 618–620. 119. Misra, R., Tripathi, S. K., Agnihotri, A. K., and Kumar, A. (1991). Photocrystallization in amorphous thin films of Se100−x Tex , Solid State Communications, 77, pp. 797–800. 120. Evans, E. J., Helbers, J. H., and Ovshinsky, S. R. (1970). Reversible conductivity transformations in chalcogenide alloy films, Journal of Non-Crystalline Solids, 2, pp. 334–346. 121. Bienenstock, A., Betts, F., and Ovshinsky, S. R. (1970). Structural studies of amorphous semiconductors, Journal of Non-Crystalline Solids, 2, pp. 347–357. 122. Feinleib, J., deNeufville, J., Moss, S. C., and Ovshinsky, S. R. (1971). Rapid reversible light-induced crystallization of amorphous semiconductors, Applied Physics Letters, 18, pp. 254–257. 123. Ovshinsky, S. R. (1968). Reversible electrical switching phenomena in disordered structures, Physical Review Letters, 21, pp. 1450–1453. 124. von Gutfeld, R. J. (1973). The extent of crystallization resulting from submicrosecond optical pulses on Te-based memory materials, Applied Physics Letters, 22, pp. 257–258. 125. Weiser, K., Gambino, R. J., and Reinhold, J. A. (1973). Laser-beam writing on amorphous chalcogenide films: Crystallization kinetics and analysis of amorphizing energy, Applied Physics Letters, 22, pp. 48–49. 126. Griffiths, J. E., Espinosa, G. P., Remeika, J. P., and Phillips, J. C. (1981). Reversible reconstruction and crystallization of GeSe2 glass, Solid State Communications, 40, pp. 1077–1080. 127. Griffiths, J. E., Espinosa, G. P., Remeika, J. P., and Phillips, J. C. (1982). Reversible quasicrystallization in GeSe2 glass, Physical Review B, 25, pp. 1272–1286. 128. Haro, E., et al. (1985). Laser-induced glass-crystallization phenomena of GeSe2 investigated by light scattering, Physical Review B, 32, pp. 969–979. 129. Tikhomirov, V. K., Hertogen, P., Glorieux, C., and Adriaenssens, G. J. (1997). Oriented crystallization of amorphous Se induced by linearly polarized light, Physica Status Solidi, 162, pp. R1–R2. 130. Lyubin, V., Klebanov, M., and Mitkova, M. (2000). Polarizationdependent laser crystallization of Se-containing amorphous chalcogenide films, Applied Surface Science, 154–155, pp. 135–139. 131. Lyubin, V., Klebanov, M., Mitkova, M., and Petkova, T. (1997). Polarization-dependent, laser-induced anisotropic photocrystallization of some amorphous chalcogenide films, Applied Physics Letters, 71, pp. 2118–2120.

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132. Roy, A., Kolobov, A. V., and Tanaka, K. (1998). Laser-induced suppression of photocrystallization rate in amorphous selenium films, Journal of Applied Physics, 83, pp. 4951–4956. 133. Innami, T., and Adachi, S. (1999). Structural and optical properties of photocrystallized Se films, Physical Review B, 60, pp. 8284–8249. 134. Tsuji, K., et al. (1993). Amorphization from quenched high-pressure phase in tetrahedrally bonded materials, Journal of Non-Crystalline Solids, 156–158, pp. 540–543. 135. Bonnet, J. P., Boissier, M., and Ait Gherbi, A. (1994). The amorphization process of neutron-irradiated crystalline quartz studied by Brillouin scattering, Journal of Non-Crystalline Solids, 167, pp. 199–204. 136. Snead, L. L., Zinkle, S. J., Hay, J. C., and Osborne, M. C. (1998). Amorphization of SiC under ion and neutron irradiation, Nuclear Instruments and Methods in Physics Research B, 141, pp. 123–132. 137. Elliott, S. R., and Kolobov, A. V. (1991). Athermal light-induced vitrification of As50 Se50 films, Journal of Non-Crystalline Solids, 128, pp. 216–220. 138. Kolobov, A. V., Bershtein, V. A., and Elliott, S. R. (1992). Athermal photo-amorphization of As50 Se50 films, Journal of Non-Crystalline Solids, 150, pp. 116–119. 139. Kolobov A. V., and Elliott, S. R. (1995). Reversible photoamorphization of crystalline films of As50 Se50 , Journal of NonCrystalline Solids, 189, pp. 297–300. 140. Kolobov, A. V., and Elliott, S. R. (1995). Reversible photoamorphization of a crystallized As50 Se50 alloy, Philosophical Magazine B, 71, pp. 1–10. 141. Prieto-Alc´on, R., et al. (1999). Reversible and athermal photovitrification of As50 Se50 thin films deposited onto silicon wafer and glass substrates, Applied Physics A, 68, pp. 653–661. 142. Frumar, M., Firth, A. P., and Owen, A. E. (1995). Optically induced crystal-to-amorphous-state transition in As2 S3 , Journal of NonCrystalline Solids, 192–193, pp. 447–450. 143. Benekou, V., et al. (2017). In-situ study of athermal reversible photocrystallization in a chalcogenide glass, Journal of Applied Physics, 122, pp. 1–7. 144. Benekou, V., et al. Unpublished results. 145. Akola, J., and Jones, R. O. (2007). Structural phase transitions on the nanoscale: The crucial pattern in the phase-change materials Ge2 Sb2 Te5 and GeTe, Physical Review B, 76, pp. 1–10. 146. Kalikka, J., Akola, J., and Jones, R. O. (2016). Crystallization processes in the phase change material Ge2 Sb2 Te5 : Unbiased density

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functional/molecular dynamics simulations, Physical Review B, 94, pp. 1–8. 147. Uchino, T., Clary, D. C., and Elliott, S. R. (2000). Mechanism of photoinduced changes in the structure and optical properties of amorphous As2 S3 , Physical Review Letters, 85, pp. 3305–3309. 148. Lu, C., Recht, D., and Arnold C. (2013). Generalized model for photoinduced surface structure in amorphous thin films, Physical Review Letters, 111, pp. 1–5. 149. Oshima, Yu., Nakamura, A., and Matsunaga, A. (2018). Extraordinary plasticity of an inorganic semiconductor in darkness, Science, 360, pp. 772–774.

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CHAPTER 10

Phase-Change Alloys: Structural Aspects Paul Fons∗,‡ and Alexander V. Kolobov∗,†,§ ∗

Keio University, Faculty of Science and Technology, Department of Electronics and Electrical Engineering 223-8522 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, Kanagawa 223-8522, Japan † Department of Physical Electronics, Herzen State Pedagogical University, Saint Petersburg, Russia ‡ [email protected] § [email protected]

In this chapter, after a brief introduction to phase-change alloys, the structures of the crystalline and amorphous phases are discussed starting with experimental results that demonstrated significant differences in the local order between the two states. This is followed by the description of extensive first-principles studies of the amorphous phase. The chapter proceeds to discuss the atomistic mechanism of the phase-change process. Finally, polyamorphism of the phase-change alloys is discussed.

10.1. Introduction Glasses are typically obtained from the melt upon quenching with a high cooling rate, while crystals result from slow cooling. What is fast and what is slow depends on the material in question. Thus, while it is very difficult to obtain crystalline As2 Se3 by cooling the melt (even at rates as slow as a few degrees per hour) at the same time it is also extremely difficult to form amorphous metals even with melts are quenched in fractions of a seconds. Amorphous solids are characterized by a lack of long-range order (crystallinity). At the same time, the short-range order, which includes coordination 323

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to the first-nearest neighbors as well as bond lengths and angles, usually remains similar to that of the corresponding crystal. Another characteristic attribute of amorphous solids is that due to potential anharmonicity, the bond lengths of the solid are somewhat longer than those in the crystalline phase. Due to the similarity in the local structure, the optical properties of the crystalline and amorphous phases are usually also rather similar. However, there is a particular class of materials, typically GeTebased alloys, that possess a very large optical contrast between the crystalline and amorphous phases. In the 1960s, S.R. Ovshinsky proposed to use such materials for memory applications [1]. It is this class of chalcogenides that is called phase-change alloys. In order to be suitable for memory applications, phase-change alloys have to possess simultaneously several properties, namely (i) a high speed of phase transformation, (ii) long thermal stability of the amorphous phase, (iii) large optical contrast, (iv) large cyclability (durability), and (v) chemical stability. Typically, to be of practical importance, the switching speed should be in the nanosecond range, thermal stability should be several decades at room temperature, and durability should exceed one million cycles. Hence only a very few materials have the unique property combination found in phase-change materials used for optical storage. Years of intensive research have singled out quasibinary alloys along the GeTe–Sb2 Te3 tie-line and, in particular, the Ge2 Sb2 Te5 composition. These Ge–Sb–Te alloys, usually referred to as GST, form the main body of this chapter. While this volume is dedicated to amorphous chalcogenides, the nature of phase-change alloys requires that the structure of the crystalline phase be also covered as well as the phase-change mechanism. 10.2. Structure of Phase-Change Alloys 10.2.1. Crystalline-Phase 10.2.1.1. Binary GeTe It is natural to start with binary GeTe, which is one of the end points and a phase-change material itself. GeTe is a narrow bandgap semiconductor and also a ferroelectric material with the

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Tc

0 collective atomic displacement

0 collective atomic displacement

Fig. 10.1. Schematics of a displacive (left) and order–disorder (right) transitions.

simplest structure that contains just two atoms in the primitive cell [2]. Recently, GeTe has attracted additional attention due to its large Rashba splitting [3]. At low temperature, GeTe possesses a rhombohedral structure with space group R3m, which can be viewed as a rock salt structure that is slightly distorted along the 111 direction along with a shear relaxation along the 111 direction. In this phase, Ge and Te atoms are six-fold coordinated to each other with subsets of three shorter (2.83 ˚ A) and three longer (3.15 ˚ A) bonds usually attributed to a Peierls distortion [4]. Based on diffraction studies [5], it was concluded that GeTe undergoes a displacive ferroelectric-to-paralectric transition at the Curie temperature, Tc , around 705 K when the structure changes to the rock salt structure (space group Fm¯3m) in a so-called displacive transition (Fig. 10.1, left panel). The displacive nature of the transitions was also suggested by Raman scattering [6]. Subsequent Extended X-ray absorption fine structure (EXAFS) studies [7] demonstrated that the structure remains distorted across Tc despite the change in global symmetry observed by Bragg diffraction. It was argued that the fact that GeTe becomes paraelectric macroscopically means that the local distortions become stochastic at Tc , that is, the ferroelectric-to-paraelectric transition is of the order– disorder type [8] as shown in Fig. 10.1 (right panel). This conclusion has been confirmed by a PDF analysis of total scattering [9, 10]. 10.2.1.2. Ge2 Sb2 T e5 and Related Materials The stable phase of GST possesses a hexagonal cell with the space group P¯ 3m1. Thin amorphous films, however, crystallize into a

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structure that is different from that of the stable trigonal phase [11–13]. Based on Bragg diffraction results, the metastable crystal structure of Ge2 Sb2 Te5 was identified as the rock salt (NaCl) structure (Fm3m) with a lattice constant of slightly above 6.00 ˚ A. From Rietveld refinement, it was concluded that the anion facecentered cubic (fcc) sublattice is fully occupied by Te atoms, while Ge and Sb atoms are randomly located on the cation sublattice. The stoichiometry of the structure requires the presence of vacancies on the Ge/Sb sites. It was subsequently shown that the rock salt structure is characteristic of a large range of GST alloys [14–17]. The rock salt like arrangement of atoms requires the formation of six bonds by each participating atom. At the same time, the number of valence electrons located on Ge and Sb atoms is lower. A way to ensure six bonds is by virtue of sharing the valence electrons among several bonds with less than two electrons per bond on the average through a process analogous of resonance bonding [18]. Recently, the term “metavalent bonding” was suggested to describe bonds in the crystalline phase of phase-change alloys [19]. Subsequent EXAFS studies [20, 21] demonstrated that the Ge–Te A, that is, bond length in metastable Ge2 Sb2 Te5 is 2.83 ± 0.01 ˚ significantly shorter than might be expected based on the rock salt structure as determined by X-ray diffraction (XRD) and the obtained lattice parameter of slightly over 6.00 ˚ A, that is, locally, the structure of metastable Ge2 Sb2 Te5 does not possess the rock salt symmetry but is very similar to that of the binary GeTe. At the same time, the obtained bond lengths are significantly longer than the sum of the corresponding covalent radii, which suggests that the bonds are not purely covalent in line with the proposed resonant bonding concept. Detailed analysis of the X-ray absorption near edge structure (XANES) spectra of crystalline Ge2 Sb2 Te5 demonstrated that the structure of the metastable cubic phase of GeTe-based phase-change alloys contains significant disorder with a large number of Ge atoms located off octahedral resonantly bonded sites [22].

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10.2.2. Amorphous Phase 10.2.2.1. Experimental Studies 10.2.2.1.1. Binary GeTe Despite years of studies, the structure of amorphous a-GeTe remains unresolved. X-ray diffraction studies [23] revealed that the interatomic distances and the coordination numbers of a-GeTe were in disagreement with those of crystalline c-GeTe, which led to the conclusion that a random covalent model with a 4(Ge):2(Te) local coordination was more appropriate to describe the amorphous phase. Similar radial distribution functions were obtained from electron diffraction studies [24, 25]. EXAFS measurements around both Ge and Te K-edges [26–28], Raman scattering and far-infrared absorption spectra for a-GeTe [29], as well as combined photoemission and inverse photoemission studies [30] were all interpreted in terms of the presence of GeTe4 tetrahedra, satisfying the 8-N rule [31]. On the other hand, Mossbauer spectrometry of 125 Te nuclei [32] and neutron scattering [33] studies suggested the preservation of the 3(Ge):3(Te)-coordinated local structure in the amorphous phase. 10.2.2.1.2. Quasibinary GeTe-Sb2 Te3 Alloys A drastic step forward in understanding the structure of the amorphous phase was the application of EXAFS to the structure of a-Ge2 Sb2 Te5 [20, 21, 34–36]. It was found that in the amorphous phase the Ge–Te and Sb–Te bonds became shorter and the structure possessed more local order than in the crystalline phase. The obtained Ge–Te and Sb–Te bond lengths were very close to the sum A, of the corresponding covalent radii for the elements (rGe = 1.22 ˚ A, rTe = 1.35 ˚ A [37]). The observation of bond shortening rSb = 1.38 ˚ and increased local order was unexpected: typically, for covalent solids, due to the anharmonicity of the interatomic potential, disorder usually results in longer and weaker bonds. Equally unexpected was the observed significant increase in bond order in the amorphous

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phase. These results were a clear experimental demonstration that the local structures in the two phases are significantly different. The decreased bond length in the amorphous state concomitant with the density decrease [38] is reminiscent of molecular solids, for example, selenium, when different kinds of bonding exist in a solid and their interplay determines the local structure. Thus, in the case of crystalline selenium, the covalently bonded atoms within helical chains are held together by weaker van der Waals interactions. Upon the loss of the long-range order, the inter-chain interaction decreases and the intra-chain forces dominate the local structure. It was also argued that due to weakening of the inter-chain bonds, local order determined by the intra-chain bonds increased [39]. The overall observed changes in XANES upon the phase transition were modelled by FEFF simulations [40] and the best agreement was obtained when Ge atoms were placed into tetrahedral symmetry sites [20] within the Te fcc lattice. The transition between the octahedral sites in the crystalline phase and tetrahedral sites in the amorphous phase led the authors to the proposal of an umbrella-flip model (Fig. 10.2). Shorter bonds in as-deposited amorphous phase of Ge2 Sb2 Te5 were also observed by high-energy X-ray scattering experiments [41]. The results were analyzed using the reverse Monte Carlo (RMC)

Fig. 10.2. The local change in the structure upon the transition from the crystalline (left) to amorphous (right) phase within the umbrella-flip model [20].

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technique and its was concluded that the Ge(Sb)-Te-Ge(Sb) and Te-Ge(Sb)-Te angles were close to 90◦ in disagreement with the tetrahedral coordination of the Ge atoms suggested from X-ray absorption fine structure (XAFS) analysis. 10.2.2.2. Ab-initio Simulations Welnic et al. [42] were the first to apply density functional theory to phase-change materials. Based on the results of experimental XAFS studies, these authors proposed to model the local structure of a-GST using the spinel structure1 with Ge atoms located on Mg sites, Sb atoms on Al sites, and Te atoms on O sites. It was found that the rock salt structure possesses a very similar energy to that of the spinel structure. The authors also found that the Ge–Te bond length in the spinel structure was shorter than that in the rock salt structure and band opening at the Γ point upon transformation from the octahedral Ge geometry in the rock salt phase to the tetrahedral geometry in the spinel phase was obtained in agreement with experiment [42]. A major step forward was in-silico generation of a melt-quenched amorphous phase-change materials — Such simulations were performed by several groups and the main results are reviewed below. The first simulation of the melt-quenched amorphous Ge2 Sb2 Te5 was reported by Caravati et al. [43]. The liquid structure (270 atoms) generated at 2300 K was equilibrated for 6 ps and then quenched in 16 ps and further equilibrated for 18 ps at 990 K. In order to generate a model of a-Ge2 Sb2 Te5 , the liquid was brought to 300 K in 18 ps. Subsequently these studies were extended [44]. Using a bonding cutoff distance chosen to be the outer edge of the appropriate partial pair correlation functions, the average coordination numbers of 3.8 (Ge), 4.0 (Sb), and 2.9 (Te) were obtained. Ge and Sb atoms were mostly four-fold coordinated and formed bonds preferentially with Te atoms. About 33% of Ge atoms were found to be tetrahedrally 1

The spinel is a ternary crystal with the composition of MgAl2 2O4 . In this structure, Mg ions are tetrahedrally coordinated and Al ions are octahedrally coordinated.

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coordinated, which was favored by the presence of Ge–Ge or Ge–Sb bonds. Akola and Jones [45, 46] performed similar simulations using significantly larger cells (460 atoms as opposed to 56 atoms of [43]) and also carried out molecular dynamics simulations of hundreds of picoseconds that is comparable to experimental amorphization times (ca. 1 ns). Their results were very similar. About 60% of Ge atoms in their simulations were four-fold coordinated, of which 34% were tetrahedrally bonded. Dihedral angles around Ge–Te (and Sb–Te) bonds showed pronounced maxima at 0, 90, and 180 that are consistent with octahedral bonding geometry and imply similarities between the amorphous and crystalline phases. This study also found the dominance of square fragments in the structure of the a-GST. Denoting Te atoms as “A” and Ge/Sb atoms as “B”, the authors introduced ABAB squares as building blocks for a-GST (Fig. 10.3). These authors subsequently studied the Ge8 Sb2 Te11 composition used in Blu-ray disks. The obtained total coordination numbers were found to be 4.0 (Ge), 3.7 (Sb), and 2.9 (Te) with 42% of Ge atoms being in tetrahedral configurations [47].

Fig. 10.3. The ABAB motifs in the amorphous phase [45].

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Heged¨ us and Elliott [48], using a model that contained 90 atoms, found four-membered rings (four-rings), analogous to ABAB blocks of [45], even at temperatures as high as 1073 K. The concentration of the four-rings increased as the temperature went down. The obtained bond angle distribution functions demonstrated the existence of both octahedrally and tetrahedrally coordinated Ge atoms while for Sb atoms the bond angle distribution had a single peak at 90o . The issue of the co-existence of distorted octahedral and tetrahedral Ge sites in amorphous GeTe-based alloys was further investigated by Micoulaut et al. It was found that the number of tetrahedral sites depended on details of simulations and, in particular, whether or not van der Waals interactions were included. The inclusion of van der Waals interactions resulted in a concentration of tetrahedrally coordinated Ge sites as high as 64% [49]. Krbal et al. [50] performed detailed Ge K-edge XANES analyses on the “melt-quenched” amorphous model by Heged¨ us an Elliott [48]. While XANES spectra calculated for each of the 20 Ge atoms in the cluster were all different, the average XANES spectrum was in very good agreement with experiment. The analysis revealed that the local structure around Ge atoms can be grouped into two characteristic groups, namely, (i) purely tetrahedral (Td ) configurations (7 sites) with bond lengths typically around 2.58 ˚ A and (ii) pyramids (Py ), with a Ge atom at the apex and with Te–Ge–Te angles very close to 90◦ (13 sites). There were three covalent Ge–Te bonds in this configuration with bond lengths in the range 2.6 to 2.8 ˚ A, with additional (one to three) neighbors located at distances around 3.0 to 3.5 ˚ A. A subgroup in this category (six sites) may be described as highly distorted octahedral (Oh ) structures with two or three nextnearest neighbors. The presence of three-fold and four-fold coordinated Ge sites shows that Ge species in GST are polyvalent. While the formation of Td coordinated Ge atoms and two-fold coordinated Te atoms in Ge(4):Te(2) configurations in the amorphous phase is not surprising considering the usual sp3 electronic configuration for Ge, the presence of the Py configurations with Ge atom forming three covalent bonds

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is less obvious and was explained by the formation of dative bonds, where lone pair electrons of Te interact with an empty p-orbital of Ge [51]. It should be noted that although the Ge(3):Te(3) local coordination apparently deviates from the 8-N rule typical of chalcogenide glasses, the situation is not so simple. The original Mott rule, proposed to account for insensitivity of amorphous chalcogenides to doping [52], actually only requires that atoms “use all their valence electrons in bonds with surrounding atoms or ions, modifying the local coordination to make this possible”, that is, it demands that the constituent elements have all saturated bonds, that is, the outer shells are complete. From this perspective, both the Ge(3):Te(3) and Ge(4):Te(2) configurations described above satisfy the requirements imposed by the Mott rule for ideal covalent glass networks.

10.3. Mechanism of Phase-Change The first atomistic mechanism of the phase-change process was proposed in [20] as an umbrella flip of Ge atoms between octahedral and tetrahedral sites within the Te fcc sublattice. Subsequent ab-initio studies of crystallization process could not confirm this idea and it was suggested that the crystallization process consists instead of ordering of four-membered rings [48] or ABAB fragments [46]. At the same time, it should be noted here that the ball-and-stick representation of the structure based on chosen bond length cut-off distances does not always correctly represent covalent bonds and arbitrarily depends on the chosen cut-off distance. Thus, nominally a four-fold coordinated distorted octahedral (or pyramidal) Ge atom in amorphous GST only forms three covalent bonds, as demonstrated by the increase in the interatomic electron density revealed by chargedensity difference (CDD) maps (Fig. 10.4) [50, 53]. The fourth “bond” in this configuration is always longer (same as the longer bonds in the crystalline phase) and significantly weaker. Based on the CDD representation, the amorphization process consists of the rupture of Ge–Te bonds, displacement of ABAB fragments, and

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Fig. 10.4. A slight elongation of a distance between Ge (blue) and Te (orange) atoms results in a drastic re-distribution of electron density (gray clouds). While both structures have four nearest neighbors as determined by the bond length offset corresponding to the crystalline phase, only three covalent bonds are formed in the amorphous state, the fourth bond being significantly weaker [53].

subsequent establishment of Ge–Ge bonds as illustrated in Fig. 10.5, resulting in some of Ge sites becoming tetrahedrally coordinated [54]. Since only one of the two atoms forming the Ge–Ge bonds is in tetrahedral geometry, the maximum concentration of tetrahedral Ge sites can be estimated as 50%. Vacancies are believed to facilitate the rearrangement of ABAB fragments. 10.4. Polyamorphysm In this subsection, we discuss differences in the amorphous structure of phase-change materials obtained through different pathways. First of all, it should be noted that optical reflectivity of the amorphous phase obtained after the from the crystalline phase is intermediate between those of the as-deposited and crystalline phases [55]. Second, it should be noted that the crystallization time is significantly shorter for the “recycled” amorphous phase [55, 56]. Direct structural evidence for the differences can be seen from comparison of XANES spectra of as-deposited and laser-amorphised samples [50] as shown in Fig. 10.6. This result may be compared with photodarkening in chalcogenide glasses when the absorption edge of

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Fig. 10.5. Schematics of the formation of Ge–Ge bonds in the amorphous phase [54].

annealed (i.e., equilibrated) films is located in between those for the as-deposited and illuminated states [58]. It is not unreasonable, that in the as-deposited film obtained from the vapor phase the atoms are more likely to possess the “ideal” amorphous coordination, such that Ge atoms form GeTe4 tetrahedra

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pressure-induced laser-induced

Energy (eV)

Fig. 10.6. X-ray absorption near edge structure (XANES) spectra of a-Ge2 Sb2 Te5 obtained by laser amorphization and application of hydrostatic pressure [57].

while Sb atoms are three-fold coordinated. The coordination numbers found from EXAFS analysis on as-deposited samples that satisfy the 8-N rule support this proposal. On the other hand, the amorphous phase obtained from the solid metastable cubic GST phase is more likely to preserve a certain number of Ge- and Sb-containing fragments with the valence angles close to those in octahedrally coordinated sites in the crystalline phase resulting in a larger concentration of distorted octahedral, or pyramidal, Ge sites. Similar conclusions were drawn from DFT simulations [50, 59] Metastable cubic GST can also be rendered amorphous by application of hydrostatic pressure [60]. XANES studies performed on a pressure-amorphised sample and in particular the observed lower white line and an appearance of a pronounced shoulder following the white line, suggest that a significant amount of Ge atoms become tetrahedrally coordinated after compression [60], which was interpreted as being due to a large amount of “wrong” Sb–Sb and Te– Te bonds that were not detected in laser-amorphised or as-deposited GST [61]. An amorphous–amorphous phase transition to a denser tetragonal framework at pressure exceeding 8-10 GPa was also reported from XRD measurements and simulations [61].

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Finally, the amorphous GST obtained by ion implantation was investigated [62, 63]. It was found that ion-irradiated samples crystallized significantly faster than the as-deposited samples. Raman scattering studies suggested that ion implantation ( Sb+ ions, 120 keV) leads to the destruction of tetrahedral Ge–Te bonds in the initial as-deposited phase [63]. From a comparative EXAFS study of as-deposited, re-amorphized (melt-quenched), and ion-implanted a-Ge2 Sb2 Te5 a larger concentration of Ge–Ge bonds in as-deposited samples was detected [64]. Somewhat related to polyamorphism is also the drift phenomenon (see a dedicated chapter), where the resistance of an amorphised film gradually increases with time. If the resistance change were simply linked to ordering of the structure as a prelude to crystallization, one would have expected the resistance to decrease. The experimentally observed opposite change suggests that the structural change within the amorphous phase is more complicated and may be associated with polyamorphism. 10.5. Applications of Phase-Change Alloys As mentioned at the beginning of this chapter, the idea to use phasechange materials for memory devices was first suggested by S.R. Ovshinsky. It was successfully implemented in optical memory such as compact, digital versatile, and BluRay discs and recently also in electrical non-volatile memory. Phase-change materials are also very promising for several photonics applications. The interested reader is referred to the corresponding chapters in this volume. Acknowledgements

References 1. Ovshinsky, S. (1968). Physical Review Letters, 21, p. 1450. 2. Goldak, J., Barrett, C., Innes, D., and Youdelis, W. (1966). Journal of Chemical Physics, 44, p. 3323. 3. Liebmann, M., et al. (2016). Advanced Materials, 28, p. 560.

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4. Gaspard, J.-P., Pellegatti, A., Marinelli, F., and Bichara, C. (1998). Philosophical Magazine B, 77, p. 727. 5. Chattopadhyay, T., Boucherle, J., and Von Schnering, H. (1987). Journal of Physics C, 20, p. 1431. 6. Steigmeier, E., and Harbeke, G. (1970). Solid State Communications, 8, p. 1275. 7. Fons, P., et al. (2010). Physical Review B, 82, p. 155209. 8. Stern, E., and Yacoby, Y. (1996). Journal of Physics and Chemistry of Solids, 57, p. 1449. 9. Fons, P., et al. (2012). Physica Status Solidi B, 249, p. 1919. 10. Matsunaga, T., et al. (2011). Applied Physics Letters, 99, p. 231907. 11. Yamada, N. (1996). MRS Bulletin, 21, p. 48, ISSN 0883-7694. 12. Nonaka, T., et al. (2000). Thin Solid Films, 370, p. 258. 13. Yamada, N., and Matsunaga, T. (2000). Journal of Applied Physics, 88, p. 7020. 14. Matsunaga, T., Kojima, R., Yamada, N., Kifune, K., Kubota, Y., Tabata, Y., and Takata, M. (2006). Inorg. Chem. 45, p. 2235. 15. Matsunaga, T., and Yamada, N. (2004). Physical Review B, 69, p. 104111. 16. Matsunaga, T., et al. (2007). Applied Physics Letters, 90, p. 161919 (pages 3). 17. Matsunaga, T., et al. (2008). Journal of Applied Physics, 103, p. 093511. 18. Pauling, L. (1960). The Nature of the Chemical Bond and the Structure of Molecules and Crystals: An Introduction to Modern Structural Chemistry (Cornell University Press). 19. Wuttig, M., et al. (2018). Advanced Materials, 30, p. 1803777. 20. Kolobov, A., et al. (2004). Nature Materials, 3, p. 703. 21. Hyot, B., Biquard, X., and Poupinet, L. (2001). Proceeding of EPCOS. 22. Krbal, M., et al. (2012). Physical Review B, 86, p. 045212. 23. Betts, F., Bienenstock, A., and Ovshinsky, S. R. (1970). Journal of Non-Crystalline Solids, 4, p. 554. 24. Dove, D., Heritage, M., Chopra, K., and Bahl, S. (1970). Applied Physics Letters, 16, p. 138. 25. Uemura, O., et al. (1979). Journal of Non-Crystalline Solids, 33, p. 71. 26. Wakagi, M., and Maeda, Y. (1994). Physical Review B, 50, p. 14090. 27. Kolobov, A., et al. (2004). Journal of Physics: Condensed Matter, 16, p. S5103. 28. Hirota, K., Nagino, K., and Ohbayashi, G. (1997). Journal of Applied Physics, 82, p. 65. 29. Fisher, G., Tauc, J., and Verhelle, Y. (1974). In: Amorphous and Liquid Semiconductors, edited by Stuke, J.

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30. Hosokawa, S., et al. (1998). Journal of Physics: Condensed Matter, 10, p. 1931. 31. Mott, N. F., and Davis, E. A. (1979). Electronic Processes in NonCrystalline Materials, 2nd Ed. (Clarendon Press Oxford). 32. Boolchand, P., Triplett, B. B., Hanna, S. S., and de Neufville, J. P. (1974). Mossbauer Effect Methodology (New York, NY, Plenum). 33. Pickart, S. J., Sharma, Y. P., and de Neufville, J. P. (1979). Journal of Non-Crystalline Solids, 34, p. 183. 34. Jovari, P., et al. (2008). Physical Review B, 77, p. 035202. 35. Baker, D., Paesler, M., Lucovsky, G., and Taylor, P. (2006). Journal of Non-Crystalline Solids, 352, p. 1621. 36. Paesler, M., et al. (2007). Journal of Physics and Chemistry of Solids, 68, p. 873. 37. Retrieved from http://www.webelements.com. 38. Njoroge, W. K., W¨ oltgens, H.-W., and Wuttig, M. (2002). Journal of Vacuum Science & Technology A, 20, p. 230. 39. Sayers, D. (1977). Amorphous and Liquid Semiconductors: Proceedings of the 7th International Conference on Amorphous and Liquid Semiconductors, edited by W. Spear, pp. 61–72. 40. Ankudinov, A. L., Ravel, B., Rehr, J. J., and Conradson, S. D. (1998). Physical Review B, 58, p. 7565. 41. Kohara, S., et al. (2006). Applied Physics Letters, 89, p. 201910. 42. Welnic, W., et al. (2005). Nature Materials, 5, p. 56. 43. Caravati, S., et al. (2007). Applied Physics Letters, 91, p. 171906. 44. Caravati, S., et al. (2009). Physical Review Letters, 102. 45. Akola, J., and Jones, R. (2007). Physical Review B, 76, p. 235201. 46. Akola, J., and Jones, R. (2008). Journal of Physics: Condensed Matter, 20, p. 465103. 47. Akola, J., and Jones, R. (2009). Physical Review B, 79, p. 134118. 48. J. Heged¨ us, and Elliott, S. (2008). Nature Materials, 7, p. 399. 49. Micoulaut, M., Gunasekera, K., Ravindren, S., and Boolchand, P. (2014). Physical Review B, 90, p. 094207. 50. Krbal, M., et al. (2011). Physical Review B, 83, p. 054203. 51. Xu, M., Cheng, Y., Sheng, H., and Ma, E. (2009). Physical Review Letters, 103, p. 195502. 52. Mott, N. F. (1967). Advances in Physics, 16, p. 49. 53. Kolobov, A. V., Fons, P., Tominaga, J., and Ovshinsky, S. R. (2013). Physical Review B, 87, p. 165206. 54. Kolobov, A. V., Fons, P., and Tominaga, J. (2015). Scientific Reports, 5, p. 13698.

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55. Khulbe, P. K., Hurst, T., Horie, M., and Mansuripur, M. (2002). Applied Optics, 41, p. 6220. 56. Raoux, S., et al. (2009). Applied Physics Letters, 95, p. 071910 (pages 3). 57. Kolobov, A. V., and Tominaga, J. (2012). Chalcogenides: Metastability and Phase Change Phenomena, vol. 164 (Springer). 58. Kolobov, A., and Adriaenssens, G. (1994). Philosophical Magazine Part B, 69, p. 21. 59. Akola, J., Larrucea, J., and Jones, R. (2011). E/PCOS 2010 Proceedings, September 6th-7th, 2010, Milano, Italy. 60. Kolobov, A. V., et al. (2006). Physical Review Letters, 97, p. 035701. 61. Krbal, M., et al. (2009). Physical Review Letters, 103, p. 115502. 62. Bastiani, R. D., et al. (2008). Applied Physics Letters, 92, p. 241925. 63. De Bastiani, R. (2008). Nuclear Instruments and Methods B, 26, p. 2511. 64. De Bastiani, R. (2008). Applied Physics Letters, 92.

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CHAPTER 11

Drift Phenomena in Phase Change Memories Daniele Ielmini Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano and IU.NET, Milano, Italy

Phase change memory (PCM) relies on the ability of a phase change material to exist in two distinct phases, namely the stable crystalline (or polycrystalline phase), and the metastable amorphous phase, to store digital data in non-volatile way. The metastability of the amorphous phase is the origin of a few reliability concerns, including thermally activated recrystallization of the amorphous phase, and thermally activated drift phenomena induced by structural relaxation of the shortrange order. This chapter will provide an overview of drift phenomena in PCM, addressing the physical and electrical characterization results, the physical interpretation, the modeling, and the impact on the device performance, especially for multi-level cell (MLC) operation and for the instability of the polycrystalline phase. Methodologies to alleviate the drift, such as innovative PCM device structures, will be finally discussed.

11.1. Introduction Phase change memory (PCM) is one of the most promising emerging memory technologies for storage class memory and embedded nonvolatile memory [1–5]. Thanks to the high-speed [6] and low-energy switching [7], the PCM device is also extremely attractive for in-memory computing applications, where the device complements or executes the data processing, rather than simply serving as storage

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cell [8–10]. Concepts such as Boolean logic [11], analogue computing [12], optical computing [13], and neuromorphic computing [14–18] have become indeed popular in the literature, in all cases exploiting the flexibility, reconfiguration, and energy efficiency of PCM. Despite the several achievements and application spaces, there are still many open issues regarding the reliability of PCM [19]. Many of these issues are related to the metastable structure of the amorphous phase, which is prone to thermally accelerated recrystallization [20, 21] and structural relaxation (SR) [22]. The latter phenomenon is generally interpreted as the root cause for the drift phenomenon, where the resistance increases with time immediately after programming even without any applied voltage [23–25]. SR has been generally observed in disordered material, such as amorphous Si [26, 27], amorphous SiC [28], amorphous Se [29], amorphous tetrahedral C [30], and several amorphous chalcogenide materials [19, 23–25]. SR can be characterized by several techniques, including differential scanning calorimetry (DSC) [27], high-resolution transmission electron microscopy (TEM) and electron diffraction [31], electron time-of-flight photocurrent measurements [29], and electrical measurements. The latter are most fruitful for electrical PCM, which are generally not suitable for physical studies due to the inherent structure of the cell and the nanoscale volume of the phase change material within the PCM. Several electrical parameters are affected in the PCM, including resistivity [23–25] and threshold voltage [32–34]. The time-dependent drift of electrical characteristics results in unstable resistance state, which is a challenge for single-bit and multi-level cell (MLC) PCM. This chapter provides an overview of drift phenomena in PCM, covering its impact on the cell characteristics, the physical understanding of the microscopic mechanisms, and the modeling at both single cell and statistical levels within the array. Reliability extrapolation techniques based on the Meyer–Neldel rule will be presented. Resistance drift on the polycrystalline PCM and its impact on singlebit cell reliability will be described and modeled. Cell structures and algorithms to improve the PCM robustness against drift will finally be discussed.

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11.2. Drift Characteristics Figure 11.1(a) shows the measured resistance for a PCM cell in the reset state, namely the amorphous phase, as a function of time after programming [35]. The PCM consists of a phase change material, generally Ge2 Sb2 Te5 (GST), connected to two electrodes for programming and reading the cell. The bottom electrode is generally confined to provide the sufficient current density and Joule heating that is necessary for the thermally induced phase transition in the memory cell, namely melting for the reset process, and crystallization for the set process. For this reason, the bottom electrode in these types of PCM is also called “heater.” The resistance in Fig. 11.1(a) increases with time according to the empirical power law: R = R0 (t/t0 )ν

(11.1)

where t0 is a reference time, R0 is the resistance at t0 , and ν is the exponent, also indicating the slope of drift on the bilogarithmic plot of Fig. 11.1(a). Drift has been explained as the gradual SR due to

EA

Energy

τ = τ0 e k B T

100

101

102

(a)

103

EA

Reaction coordinate

(b)

Fig. 11.1. Measured R as a function of time for a phase change memory (PCM) in the reset state at room temperature (a) and sketch of the defect annihilation in the structural relaxation (SR) process (b). A defect, such as a wrong bond or a dangling bond in the amorphous structure, is removed by thermal fluctuations, which can be described as the thermally activated transition between a metastable state and a stable state across an energy barrier. Reprinted with permission from [35], Copyright IEEE (2009).

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defect annihilation or defect evolution within the metastable structure of the amorphous phase. In fact, the amorphous chalcogenide volume has been obtained by non-equilibrium process of material quenching from the liquid phase during the reset operation. Within the short time of the quenching, which is typically in the range of 10 ns or below, atoms do not have enough time to find their minimumenergy configuration. As a result, the metastable amorphous structure evolves with time by several individual transition across variable energy barriers of amplitude EA , as indicated in Fig. 11.1(b). The transition time is dictated by the Arrhenius law: τ = τ0 exp(EA /kT ),

(11.2)

where τ0 is a characteristic time constant, k is the Boltzmann constant, and T is the local temperature. The change of the resistance is only one of the visible features of SR in PCM devices. Figure 11.2(a) shows the measured current– voltage (I–V) characteristics for a PCM cells in two programmed states for increasing times after the reset operation [32]. States A and B correspond to different volume of the amorphous material in the cell, which were obtained with different amplitude of the applied voltage pulse. A larger volume results in a lower current and a larger threshold voltage, VT [32]. Note that the I–V curves show a linear increase of current at low voltage, followed by an exponential increase of current at larger voltage, which is explained by the Poole–Frenkel (PF) conduction in the amorphous phase [36]. At the characteristic threshold voltage VT , the device displays a threshold switching, which is due to an electronic transition to the ON state with high conductivity [37, 38]. As the time increases, the I–V curves show a decreasing subthreshold current and an increasing VT . This is due to the general relationship between the sub-threshold current and VT , when parameters such as the thickness of the amorphous volumes, the phase change materials, and the temperature are changed in the experiment [38]. The decreasing current also leads to the increase of resistance as shown in Fig. 11.1.

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(b)

Fig. 11.2. Measured current–voltage (I–V) characteristics of a phase change memory (PCM) in two reset states A and B at increasing time (a) and measured threshold voltage (VT ) as a function of time from the programming pulse (b). The I–V curves show a decrease in the sub-threshold current and a corresponding drift of VT at increasing times. The VT displays a steep increase at early times below 30 ns, followed by a shallow but regular increase by about 50 mV per decade of time. Reprinted with permission from [24, 32], Copyright IEEE (2007, 2012).

Figure 11.2(b) shows the measured VT as a function of time in pulsed experiments, where the time range was spanned from 10−9 s to a few seconds [24]. There are two distinct response regimes, the first being the recovery transient in the first 30 ns from reset, which can be attributed to an electronic or thermal transition from the on state to the off state [24]. At longer times, VT increases according to a shallower slope on the semilog scale, of about 50 mV per decade of time, that is, similar to the one observed in the quasi-static characteristics of Fig. 11.2(a). 11.3. T-Accelerated Drift Figure 11.3(a) shows the measured R for a PCM cell as a function of annealing times for annealing temperature T from 90◦ C to 180◦ C. In these experiments, the cell was programmed each time in the reset state, annealed at temperature T for various time, and measured at room temperature between one annealing stage and the following one. As a result, the measured R only depends on the previous annealing T and time. The power law exponent in the figure increases

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(a)

(b)

Fig. 11.3. Measured R as a function of time for a phase change memory (PCM) in the reset state at increasing annealing (a) and Arrhenius plot of the structural relaxation (SR) times, measured as the time to reach a certain state resistance R∗ (b). The drift slope increases with T in (a) as also reported in the inset. The activation energy (slope in the Arrhenius plot) increases at increasing R∗ , which is summarized in the inset of (b). The crystallization time, τx , is also reported, in good agreement with SR times at large R∗ . Reprinted with permission from [39], Copyright AIP (2009).

with T , thus supporting the thermal acceleration model of Eq. (11.2). As T increases, the defects are annealed at faster times, thus resulting in a faster SR and steeper drift [40]. The inset shows the exponent ν as a function of annealing T , indicating a strong increase from a typical 0.1 at room temperature to almost 0.3 at 180◦ C. Figure 11.3(b) shows the Arrhenius plot of the characteristic times to reach a target resistance R∗ , collected from Fig. 11.3(a). The Arrhenius plot allows to extract the activation energy, EA for the drift process, which clearly appears to depend on R∗ (see the inset). This can be explained by considering SR as the superposition of several defect transition processes, each characterized by a different energy barrier, thus occurring at various times in Eq. (11.2). Each state R∗ of the PCM device thus corresponds to a certain maximum energy barrier EA of the SR processes. The time to reach a certain state, or a certain maximum energy barrier, decreases with T according the Arrhenius thermal acceleration [40]. Also note that the energy barrier for crystallization correspond to the maximum energy

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barriers for drift, as crystallization destroys the amorphous phase, thus serves as a cutoff energy to observe any possible SR dynamics in the amorphous phase. One should also note that all extrapolations to the Arrhenius lines in the figure cross at the same point, marked by a characteristic temperature TMN = 760 K. This result reveals a Meyer–Neldel rule, namely an exponential correlation between the pre-exponential time τ0 with the energy barrier EA in Eq. (11.2), which can be expressed by: τ0 = τ00 exp(−EA /kTMN ),

(11.3)

where τ00 is a time constant of about 1 μs in the figure and TMN is an isokinetic temperature, where the times to overcome various barriers are all equal to τ00 [40]. The Meyer–Neldel rule has been attributed to the fundamental concept of Gibbs free energy change ΔG controlling the SR transition in Fig. 11.1(b) [41]. The Gibbs free energy ΔG contains both enthalpy and entropy terms, where a larger barrier results in a larger entropy term associated to multiphonon capture. As a result, a larger barrier is compensated by an exponentially shorter pre-exponential time t0 in Eq. (11.3) thanks to the multiple configurations of collective phonon capture. From Eqs. (11.2) and (11.3), it is possible to develop a compact and accurate model for the T acceleration of the drift phenomena at various T . In fact, the drift behavior at room temperature, or any other relatively low temperature T1 , can be obtained by accelerated data obtained at a relatively high temperature T2 , by equating the energy barrier in Eq. (11.1) for T1 and T2 [42]. This leads to: T

1−β T2

t1 = τ00

1

T

β T2

t2

1

,

(11.4)

where t1 and t2 are the times to reach a certain state at T1 and T2 , respectively, while β = (TMN − T1 )/(TMN − T2 ) [42]. Figure 11.4 shows the same data of Fig. 11.3(a), but reported as a function of t1 corresponding to T1 = 300 K [42]. These data all overlap, thus supporting the acceleration model of Eq. (11.4). Also, the results suggest that extremely long drift times at low temperature, even

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10

o

90 C o 110 C o 130 C o 170 C o 180 C

8

R [Ω]

10

SR

7

10

Crystallization

6

10 2 10

4

10

6

8

10

12

14

10 10 10 10 10 Normalized time [s]

10

16

18

10

Fig. 11.4. Measured R as a function of normalized times according to Eq. (11.4) with T1 = 300 K. All data align on the same power law, thus supporting the Meyer–Neldel rule and the T -acceleration law of drift. Reprinted with permission from [42], Copyright Elsevier (2009).

in the range of 1015 , can be accelerated within 105 at elevated temperature, thus enormously decreasing the experimental time and cost. 11.4. Physical Mechanisms of Drift The increase of resistance and VT can be attributed to the decrease of the sub-threshold current in the amorphous PCM, which is generally attributed to an increase of the activation energy for conduction, EC . Due to the annealing of defects, such as wrong bonds and distorted bonds, the energy (mobility) gap increases during the SR [33, 34, 43], thus causing an increase of the energy barrier for electronic conduction, EC [32]. Figure 11.5(a) shows the measured EC at increasing annealing time at 120◦ C for various programmed states, corresponding to various thicknesses of the amorphous volume [44]. The increase of EC follows a logarithmic dependence on time given by [44]: EC (t) = EC0 (1 + γ log(t/t0 )),

(11.5)

where EC0 is the activation energy for conduction at t0 , and γ is approximately constant and equal to about 0.05 dec−1 for all

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(b)

Fig. 11.5. Measured activation energy of conduction for a phase change memory (PCM) in various programmed states (a) and measured change of the optical band gap from the Tauc plot for a thin film of amorphous Ge2 Sb2 Te5 (GST) as a function of time (b). Reprinted with permission from [43, 44], Copyright AIP (2012) and IEEE (2010).

programmed states (see the inset). By substituting Eq. (11.5) in the Arrhenius law for the resistance at low voltage given by [37]: R = R0C exp(EC /kT ),

(11.6)

where R0C is a constant, one obtains: R = R0C exp(EC0 /kT )(t/t0 )∧ (γEC0 /kT ),

(11.7)

which is equal to the power law of drift in Eq. (11.1) where ν = γEC0 /kT . This result highlights the physical origin of the drift exponent, which is linked to the time-dependence of the energy barrier for PF transport in the chalcogenide material. More extensive analysis has shown that the drift exponent is given by ν = ΔEC /ΔESR , where ΔEC and ΔESR are the variations of the energy barriers for conduction and for SR, respectively [45]. The increase of EC can be attributed to a change in the optical and mobility band gaps in the amorphous chalcogenide material as a function of time. Figure 11.5(b) shows the measured variation of the band gap as a function of time, obtained from ellipsometry experiments on thin films of amorphous GST [43]. The band gap increase might reflect

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(b)

(c)

(d)

Fig. 11.6. Coordination structures for Ge (dark blu) and Te (light blue) in GeTe, including octahedrally coordinated GeTe4 (a), octahedrally coordinated GeTe3 (b), tetrahedrally coordinated Ge2 Te2 with a wrong homopolar bond (c), and the calculated Tauc plot before and after removal of wrong bonds (d). Reprinted with permission from [46], Copyright APS (2015).

the SR of the amorphous structure, where wrong bonds, such as homopolar Ge–Ge within the GST structure, are replaced by stronger Ge–Sb and Ge–Te bonds with ionic contribution to the cohesive force of the material. Recent investigations by means of molecular dynamics and electronic structure calculations via the density functional theory have confirmed that drift arises from a widening of the band gap for prototypical phase change compound GeTe [46]. The drift originates from the broadening of the band gap and a reduction of the Urbach tails due to the removal of Ge–Ge homopolar bond chains during SR. Figure 11.6 shows various atomic short-range configurations in the GeTe structure, including octahedral coordination of Ge with four Te atoms (a), octahedral coordination of Ge with three Te atoms (b), tetrahedral coordination with one Ge–Ge bond (c) [46], and the Tauc plot (d), which allows to evaluate the band gap from the imaginary part of the dielectric function. Calculation results are compared before and after a metadynamics simulations, where homopolar Ge–Ge bonds were forcedly converted into GeTe bonds to mimic the effect of SR. The removal of the wrong bonds results in an increase of the band gap by about 20 meV, which is comparable to the increase of the optical band gap by 40 meV in GST during SR [43]. These results confirm the crucial importance of the atomistic structure in controlling SR and drift properties of phase change

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material, which was already pointed out by Ge K-edge X-ray absorption near-edge structure (XANES) spectra of GST [47]. Here, it was shown that drift is associated with a reduction of the preedge XANES spectra that is commonly attributed to tetrahedrally coordinated Ge atoms [48]. These results thus suggest that drift is due to a reduction of Ge in tetrahedral sites, which is also accompanied to Ge–Ge homopolar bonds as shown in Fig. 11.6(c). These results support the importance of a deep understanding of the short-range ordering, atomic bonds, and their evolution with time during SR, to accurately predict the physical and electrical transport properties of the PCM during the operation lifetime. Besides this intrinsic, atomistic-driven interpretation of drift, other proposed explanations include the impact of mechanical stress during the evolution of the phase change material in the PCM [25]. In fact, it has been pointed out that the crystalline phase is denser than the amorphous one by about 20%. As a result, the nanoscale phase change volume is subject to a compressive stress upon amorphization. The relaxation of the stress by viscous flow leads to an increase of the band gap at the origin of the resistance drift. Experiments on freestanding nanowire PCM have shown in fact that drift is very low in these types of structures, which is explained by amorphization not being confined by a surrounding material, therefore minimizing the compressive stress [49]. Although these experiments seem to support the mechanical interpretation of drift, the ubiquitous presence of drift in amorphous-deposited blanket films [26–31] suggests instead the interpretation based on atomistic SR in terms of thermally activated annihilation of defects, such as wrong bonds.

11.5. Drift Modeling Physically based models of drift are essential to predict the evolution of resistance at device and array level, thus providing tools to assess the reliability as a function of materials, process, and algorithms. Modeling of drift should include two aspects, namely (i) the thermally activated SR leading to the increase of the energy barrier for transport and (ii) the PF model of conduction, where the increase of the energy barrier leads to an increase of

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(a)

(b)

(c)

Fig. 11.7. Sketch of the energy barrier profile for Poole–Frenkel (PF) transport at zero applied voltage (a), PF transport with an applied voltage V inducing a barrier lowering (b), and increased effective barrier after structural relaxation (SR) due to defect annihilation (c). Reprinted with permission from [33], Copyright IEEE (2007).

resistance. Figure 11.7 illustrates the PF conduction model, where the current is controlled by the distance between the mobility edge, EC and the Fermi level, EF (a). Under an applied voltage, V , the barrier decreases linearly with V , thus resulting in an exponential increase of the current (b). This model is supported by observing the voltage-dependent lowering of the activation energy and the T-dependent sub-threshold slope in PCM devices [50]. Defects in the amorphous structure might be caused by localized states caused by disorder, according to the well-known model of Anderson localization [51]. The positive charge of the defect might be static, for example, similar to an ionized donor, or dynamic, that is, caused by the charge displacement induced by the electron trapping, according to the polaron concept [52]. Defect annihilation in the amorphous structure can be explained by the removal of wrong homopolar bonds, thus resulting in a more ideal amorphous structure with less localized states. Figure 11.7(c) attributes the increased mobility gap to the longer average distance among defects Δz  , although other physical explanation of the increases band gap might hold [46]. To account for the defect annihilation as a function of temperature and time, one can assume a simple rate equation given by: dN/dt = −N/τ (EA )

(11.8)

where N is the density of defects with energy barrier EA for their annihilation and τ is a characteristic time given by the Arrhenius law of Eq. (11.2). Assuming a uniform distribution of defects N (EA ) at

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time zero, one can calculate the remaining concentration of defects at any T for increasing time. Figure 11.8 shows the simulation results for N for T = 25◦ C (a) and 225◦ C (b) at increasing time. The results represent an “annealing front,” namely the boundary between annealed defects and remaining defects, moving toward higher EA at increasing times [40]. As T increases, the annealing front moves faster, thus resulting in an accelerated drift as experimentally observed (see, e.g., Fig. 11.3). The evolution of the front in Fig. 11.8 can be described by the value of EA , which marks the position for which the defect concentration has reduced to 50% of the initial distribution. From EA (t), one can assume a linear relationship with the effective energy barrier for conduction, namely EC –EF in Fig. 11.7, thus allowing to calculate the resistance according to Eq. (11.6), where EF = 0 (a)

(b)

Fig. 11.8. Calculated density of defects at increasing time for annealing temperature T = 25◦ C (a) and 225◦ C (b). The inset shows the remaining defect concentration as a function of time at increasing T , which highlights the T -accelerated defect annihilation dynamics. Reprinted with permission from [40], Copyright AIP (2008).

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Fig. 11.9. Measured and calculated R as a function of time for a phase change memory (PCM) in the reset state at T = 50◦ C and 100◦ C (a) and measured and calculated ν as a function of T at increasing reading current, Iread (b). Note the decrease of ν at increasing Iread , which is fruitful to mitigate drift effects in PCM. Reprinted with permission from [35], Copyright IEEE (2009).

was assumed. The results are shown in Fig. 11.9(a) for T = 50◦ C and 100◦ C as a function of time. The calculated energy barrier EC − EF , which is used to account for the experimental results is also shown. As the annealing temperature increases, the device shows a larger increase of EC − EF and, consequently, of R, which is consistent with the faster evolution of the annealing front in Fig. 11.8. Figure 11.9(b) shows the drift exponent n, obtained from the calculated I–V characteristics at increasing T and increasing read current Iread . The drift exponent increases with T because of the acceleration of the annealing process, while ν decreases at increasing Iread because of the exponential increase of the current according to the PF transport [53]. From these results, reading the PCM state at a relatively high constant current Iread can lead to a significant decrease of ν, from about 0.1 to below 0.04 at room temperature. These results are encouraging for the implementation of MLC PCM, which are most affected by drift [54]. Similar models were applied to the VT drift [32]. Here, the threshold voltage was evaluated as the voltage to reach a characteristic threshold current IT , which was assumed constant in reasonable agreement with experimental results (see, e.g., the small variations of IT at increasing time in Fig. 11.2(a)). Other similar models attribute

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the drift to a collective relaxation, where the energy barrier EA for defect relaxation increases after the transition [55]. As a result, SR causes the energy barrier for transition to increase with time. This is contrary to the model of a broad distribution of relaxation energy barriers, which is assumed in Fig. 11.8. 11.5.1. Statistical Drift Model While most works address the modeling of drift for individual cell, the study of PCM arrays and their statistics is most important for the understanding and predicting the product reliability. Figure 11.10(a) shows the measured resistance distribution of PCM cells at increasing time from the reset pulse [56]. Due to the resistance drift, the distribution shifts toward higher R, while the distribution slope remains approximately constant. However, the observation of individual cells within the distribution reveals significant variations in the drift slope: for instance, the selected cells a, b, and c all show a drift toward high resistance, however, their slope is different, as also reported in the inset. As a result, cells continuously change their relative position within the distribution. The drift slope is not a cell attribute, rather

(a)

(b)

Fig. 11.10. Cumulative distributions of R at increasing times for a phase change memory (PCM) array (a) and calculated resistance for five selected cells as a function of time. The drift fluctuations were obtained by a Monte Carlo model where the energy distribution of defects was randomized. The inset of (a) shows three selected cells displaying drift variations. Reprinted with permission from [56], Copyright IEEE (2010).

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it randomly changes from cycle to cycle, and can even change during time [56]. To account for the drift variations in the PCM array, a statistical drift model was developed by assuming the same physical picture of the rate equation of Eq. (11.8). The variation has been introduced by assuming a random energy distribution of the annihilating defects, instead of the uniform distribution in Fig. 11.8. Additionally, one may also assume a stochastic variation of the pre-exponential factor τ0 dictating the SR dynamics in Eq. (11.2). Figure 11.10(b) shows the simulation results for resistance drift in five selected cells, or the same cells observed in five successive cycles. Each cell displays a randomized resistance increase where the slope changes for each time, as a result of the random variation of the defect energy distribution [56]. The statistical drift model can also account for the time-dependent spread of ν, where the standard deviation of the drift exponent decreases with the observation time, due to the time averaging that smooths the stochastic variations of SR.

11.5.2. Drift of the Polycrystalline State One of the main strengths of the PCM is that its material can be engineered to match the desired functionality, for example, high speed, or extended endurance, or high retention. The latter case is most relevant for automotive and embedded PCM, where the nonvolatile memory must sustain elevated T during both packaging and operation. For instance, embedded memories for code storage must retain their state during the soldering reflow process for packaging, where the device can reach 260◦ C for few minutes. This temperature budget is excessive for conventional PCM with GST material, which normally crystallizes at 150◦ C. For this purpose, the PCM material must be engineered with dedicated composition, typically incorporating a relatively large amount of Ge [57, 58]. Although the Ge-rich GST displays crystallization temperatures above 300◦ C, thus satisfying the requisite of high stability of the amorphous state, it is also prone to drift in both the amorphous and polycrystalline state [59].

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(a)

(b)

Fig. 11.11. Measured and calculated R as a function of time for set and reset states at T = 85◦ C and 150◦ C (a), and set state data and calculations with rescaled R axis to highlight the drift and crystallization regimes (b). Reprinted with permission from [59], Copyright IEEE (2014).

Figure 11.11(a) shows the measured and calculated R as a function of time at T = 85◦ C and 150◦ C. Experiments were conducted by annealing the device at constant T , then measuring the resistance at room temperature for comparison. The reset state at about 10 MΩ shows a resistance drift at increasing time, which can be attributed by the SR process in the amorphous phase of the Ge-rich GST. However, also the set state with a polycrystalline phase shows an evolution with time, which is clearly displayed in Fig. 11.11(b). First, the resistance increases, similar to drift of the amorphous phase, where a higher T is reflected by a higher drift exponent. At relatively high temperature, however, a second regime occurs at about 105 s, where R start to decrease, similar to crystallization of the amorphous phase. The drift and crystallization dynamics in the figure can be explained by the evolution of the residual amorphous phase in the polycrystalline phase of the Ge-rich material. It can be assumed, in fact, that, a residual disordered phase remains in the polycrystalline phase, for example, at the grain boundaries between individual crystalline grains [59]. The low-resistance state of the GST, for instance, was observed to consist of polycrystalline phase with grains of random size depending on the annealing maximum temperature

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and ramp rate [60]. Alternatively, amorphous phase might exist because of the non-stoichiometric composition of the Ge-rich GST. As the residual amorphous phase undergoes SR during annealing, the resistance increases because of the band-gap widening, followed by crystallization, which causes the drop of resistance because of the barrier removal [59]. As a result, a single model can be developed to describe both drift and crystallization with the rate equation of Eq. (11.8). The model can be applied to both the set and the reset state, provided that parameters are changed accordingly. A statistical model for the set state was also developed by introducing random variations of the polycrystalline phase resistivity, the drift slope and the crystallization point, thus allowing to predict the reliability of the Ge-rich PCM at array level [61].

11.6. Mitigating Drift in PCM Cells Drift of the reset state is a minor problem for PCM, as the resistance window between set ad reset state generally increases. This is not the case for the Ge-rich GST cells, where the drift of the set state results in a window narrowing, thus jeopardizing the PCM reliability. Drift is also a significant problem for PCM cells with MLC storage, for example, 2 bits per cell [62] or 4 bits per cell [63]. In fact, when a certain level is programmed, for example, 01, its resistance increases, thus moving into the next level, for example, 10. The drift is therefore a major block in the development of MLC storage. Although the drift can be reduced by reading the PCM device at high read current (Fig. 11.9), this may also induce unwanted read disturb or even threshold switching effect when the read current is close to the thresholds current. Note that MLC PCM is extensively adopted in neural network aimed at accelerating deep learning and neuromorphic systems [9, 15, 18, 64–66]. Therefore, engineered materials and structures to minimize the drift are essential in the development of PCM-based memory and neuromorphic circuits. Figure 11.12(a) shows a novel memory cell, consisting of a nanowire of chalcogenide phase change material (core) surrounded by a surfactant metallic layer (shell), embedded within an insulating

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(c)

Fig. 11.12. Structure of the core-shell phase change memory (PCM) device (a), and measured R for four programmed states as a function of time for PCM cells without the surfactant layer (b) and with the surfactant layer (c). The drift exponent decreases by a factor 4 thanks to the deviation of the current from the amorphous phase to the surfactant metal layer. Reprinted with permission from [67], Copyright IEEE (2013).

material [67]. This type of pore cell is particularly effective to reduce the programming current, as the Joule heating is developed directly within the memory cell that needs to be transformed under the high temperature [68]. A planar version of the device of Fig. 11.12(a) was also presented and referred to as “projected memory cell” [69]. As the shell resistance is intermediate between the crystalline PCM and the amorphous PCM, the current flows mostly across the surfactant layer for the reset state, thus bypassing the amorphous phase where the SR causes resistance drift. As a result, the reset state and any intermediate state between set and reset states are almost immune to drift. This is shown in Fig. 11.12, comparing the measured resistance for MLC devices without surfactant layer (b) and with surfactant layer (c). The drift exponent decreases from about 0.05 to about 0.01 with the addition of the surfactant shell layer in the pore PCM structure, thus significantly alleviating the impact of drift on MLC operation. 11.7. Conclusions Drift is a major reliability issues for PCM devices, for MLC and even for single-bit cells in presence of SR of the polycrystalline phase of the phase change material. Drift results from SR, which is a fundamental thermodynamic process taking place in most amorphous materials.

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Given the widespread impact of drift on PCM, there has been an intense effort in characterizing, modeling, and mitigating drift in the past 20 years. Drift appears to originate from wrong bonds of chalcogenide materials, which are energetically unstable, thus tend to transform into more stable bonds. The higher band gap causes a measurable change of physical, optical, and electrical properties of the material, thus affecting the device behavior. While there are promising results in alleviating the drift by structural changes of the cell, there is still ample room for improvement by either material development, cell structural modifications, and system level optimization to allow for drift tolerant circuits for memory and neuromorphic computing. Acknowledgments This work has received funding from the European Research Council under the European Union’s Horizon 2020 research and innovation program (Grant Agreement 648635). References 1. Wuttig, M., and Yamada, N. (2007). Nature Materials, 6, p. 824. 2. Wong, H.-P., et al. (December, 2010). Phase change memory, Proceedings of the IEEE, 98(12), pp. 2201–2227, doi:10.1109/JPROC.2010. 2070050. 3. Raoux, S., Welnic, W., and Ielmini, D. (2010). Phase change materials and their application to non-volatile memories, Chemical Reviews, 110, pp. 240–267. 4. Ielmini, D., and Lacaita, A. L. (2011). Phase change materials in nonvolatile storage, Materials Today, 14, pp. 600–607. 5. Raoux, S., Ielmini, D., Wuttig, M., and Karpov, I. V. (2012). Phase change materials, MRS Bulletin, 37, p. 118–123. 6. Loke, D., et al. (2012). Breaking the speed limits of phase-change memory, Science, 336, pp. 1566–1569. 7. Xiong, F., Liao, A. D., Estrada, D., and Pop, E. (2011). Low-power switching of phase-change materials with carbon nanotube electrodes, Science, 332(6029), pp. 568–570. 8. Wong, H.-S. P., and Salahuddin, S. (2015). Memory leads the way to better computing, Nature Nanotechnology, 10, pp. 191–194.

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materials for brain-inspired computing, Nano Letters, 125, pp. 2179– 2186. Suri, M., et al. (2011). Phase change memory as synapse for ultradense neuromorphic systems: Application to complex visual pattern extraction, Proceedings of IEEE International Electron Devices Meeting (IEDM) (Washington, DC, IEEE), 4.4.1–4.4.4. Boybat, I., et al. (2018). Neuromorphic computing with multimemristive synapses, Nature Communications, 9, p. 2514. Kim, S., et al. (2013). A phase change memory cell with metallic surfactant layer as a resistance drift stabilizer. 2013 IEEE International Electron Devices Meetings (IEDM), (Washington, DC, IEEE), doi:10.1109/IEDM.2013.6724727. Boniardi, M., et al. (2013). Optimization metrics for phase change memory (PCM) cell architectures, IEDM Technical Digest (San Francisco, CA, IEEE), p. 681. Koelmans, W. W., et al. (2015). Projected phase-change memory devices, Nature Communications, 6, p. 8181.

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CHAPTER 12

Crystallization of Phase-Change Chalcogenides Jiri Orava∗ , Tae Hoon Lee† , Stephen R. Elliott† , and A. Lindsay Greer‡ ∗

IFW Dresden, Institute for Complex Materials, Dresden 010 69, Germany Department of Chemistry, University of Cambridge, Cambridge CB3 0FS, United Kingdom ‡ Department of Materials Science & Metallurgy, University of Cambridge, Cambridge CB3 0FS, United Kingdom †

12.1. Introduction Phase-change memory (PCM), using phase-change (PC) chalcogenides as the active layer, is a storage-class medium with the operating parameters balanced between a fast and volatile processor unit with minimal storage capacity and a non-volatile high capacity, but slow solid-state disk. The PC of interest is between crystalline and non-crystalline forms, termed glassy when prepared by cooling the liquid, of the same composition (congruent/polymorphic crystallization). PC data processing exploits the decrease in resistance, by ∼3 orders of magnitude in PCM induced by electrical pulsing, and the increase in optical reflectance, by 10%–15% in optical

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discs (DVD, Blu-ray) induced by optical pulsing, on reversible glassy-to-crystalline transitions. Crystallization, the SET (writing) operation in PCM, is the rate-limiting step. The switching time is short, typically 10–100 ns in PCM [1] and preferably it should be shorter than the switching time for volatile DRAM; sub-nanosecond switching times have been demonstrated in PCM [2, 3]. Melting of the crystalline phase, the RESET (erasing) operation in PCM, followed by rapid quenching to the glass — with a critical cooling rate of ∼108 –1012 K s−1 [4], is the most energy-consuming step. Here, the focus is on characterizing the crystallization mechanisms and dynamics in the liquid: (i) by newly emerging experimental techniques, allowing study of a wider temperature range of the existence of supercooled liquid, and measuring up to the maximum in the crystallization rate (mainly crystal-growth rate, U (T )) with high temporal resolution; and (ii) by computer simulations revealing the atomistic origin of the fast crystallization and able to probe the early stages of the nucleation processes, which are difficult to access experimentally. The variety of direct and indirect techniques used to measure U (T ) is shown in Fig. 12.1 and Table 12.1 with their typical measured ranges of U (T ) and the fragility-corrected reduced glass-transition temperature, Tgu = Trg − (m/505) [13], where Trg is the reduced glass-transition temperature (Trg = Tg /Tm ; Tg — glass-transition temperature, Tm — melting temperature) and m = [d(log10 η)/d(Tg /T )]T =Tg is the kinetic fragility of the liquid in Angell’s classification [29]. The combination of ultrafast (heating/cooling at ∼106 K s−1 [19]) and conventional calorimetry gives the widest range of dynamical processes over which indirect measurements of U (T ) can be made. The typical limitations and restrictions of each technique are given in Table 12.1 — details can be found in the cited references. The maximum in crystal-growth rate, Umax , spans ∼13 orders in magnitude. The principal differences between the glass-forming systems in Fig. 12.1 are kinetic and not so much thermodynamic [13] — the homologous temperature at which Umax occurs is a result of the interplay between the kinetics and thermodynamics. The typically studied PC systems are Ge–Sb–Te (where the Ge2 Sb2 Te5 composition has been the most thoroughly studied, and

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Fig. 12.1. Survey of the dependence of the maximum in polymorphic crystalgrowth rate, Umax , on the fragility-corrected reduced glass-transition temperature, Tgu , in a variety of glass-forming liquids. The highlighted regions show the typical ranges of dynamical processes being probed by the direct and the indirect techniques — details are listed in Table 12.1. The studies of liquid chalcogenides are, for example, conventional [5] and ultrafast [6] calorimetry of Ge2 Sb2 Te5 , optical microscopy of Te–Se [7], conventional (Te–Se) [8] and dynamic (a-Ge) [9] transition electron microscopy (TEM), optical excitations (Ag–In–Sb–Te) [10], electrical measurements (doped Ge2 Sb2 Te5 ) [11], and computer simulations (Ge2 Sb2 Te5 ) [12]. The temperature at which the rate has its maximum, Tmax , lies at Tmax /Tg = 1.48 ± 0.15 for the glass-forming systems [13]. Published with permission from [14].

is abbreviated as GST here and throughout the chapter) and Ag– In–Sb–Te (AIST) alloys. PC chalcogenides have liquids that, at relatively small supercooling, ΔT = Tm − T , the temperature range relevant for the SET operation, have viscosities η that are low, in the range of ∼10−3 Pa s, similar to those of pure liquid metals [30]. It has been thought that the fast-switching PC chalcogenides have liquids with high values of the kinetic “fragility,” m ≈ 90 for GST [6] and m ≈ 100 for GeTe from modeling [31] (recently, m ≈ 76 for GeTe was suggested by direct η measurements [32]), resulting in low η at high temperatures, which allows for the short crystallization times

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100 –103

0.1–0.3

1011 –1015 /1011 –1015

Conventional Differential Scanning Calorimetry (DSC) Ultrafast DSC Optical Excitations Electrical Measurements

1 could be obtained without degraded picture quality through an avalanchemultiplication effect when operating an a-Se photoconductive target having good charge-injection-blocking characteristics under a strong electric field >9 × 107 V/m [4]. The photoconductive target in this new operating scheme is called a High-gain Avalanche Rushing amorphous P hotoconductor (HARP). This target has since evolved into an ultra-high-sensitivity tube with η of about 600 (in the region

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where η > 1, this indicates the effective quantum efficiency). This tube, called the HARP pickup tube, was gathering attention as a novel technology for extending the scope of vision. It can be applied to a wide range of video applications, such as medical diagnostic research for early detection of cancer by high-sensitivity imaging. This paper presents a study on achieving high sensitivity in amorphous photoconductive targets and describes the basic structure and characteristics of the HARP target resulting from that study. 17.2. Achieving High Sensitivity in Photoconductive Targets Targets used in photoconductive pickup tubes can be divided into injection type and blocking type. The author conducted a study on the potential for achieving substantially high sensitivity (η >1) in these targets and on the feasibility of applying them to high-picturequality pickup tubes. 17.2.1. Injection-Type Target An injection-type target features a structure that allows for charge to be injected into the photoconductive layer from both the signal-electrode side and electron-beam-scanning side or from either one of these sides. Figure 17.1 illustrates the operating model of the injection-type target for the case that charge is injected from only the beam-scanning side. In the figure, one photoexcited hole stored on the scanning side will eventually disappear by recombining with an electron. Before this happens, however, N number of electrons from the scanning beam will sequentially pass through the electroninjection/recombination layer and move to the signal electrode. As a consequence, the number of electrons made to flow from the signal electrode into an external circuit with respect to one hole will be N + 1. This electron-injection-type target therefore has an amplification effect with a gain of N + 1, which means that high sensitivity with η in excess of unity becomes possible. Denoting electron transit time in the electron-injection/recombination layer as τt and lifetime of a photoexcited hole as τl , gain G is expressed

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Fig. 17.1. Operating model of the electron-injection-type target.

by the following equation: G=

τl =N +1 τt

(17.1)

In addition, the following condition must be satisfied so that gain G exceeds 1 and stored holes are deleted every scan to prevent the occurrence of photoconductive lag. τ t < τ l ≤ te

(17.2)

Here, te is the time taken by the scanning beam to scan one pixel. In this target, however, the number of scanning-beam electrons needed to make stored holes disappear is N + 1 times that number of holes even under ideal operating conditions that satisfy Eq. (17.2). This presents a problem, as the effective target storage capacitance increases proportionally to sensitivity raising the fear that capacitive lag will increase significantly. To clarify this problem, the author studied the relationship between gain G and lag by calculating capacitive lag. Given an electron-injection-type target featuring 4-μm-thick a-Se film (relative permittivity: 6) and a scanning size of 6.6 × 8.8 mm (scanning size of a 2/3-inch tube), Fig. 17.2 shows the relationship between gain G and calculated capacitive lag of the third field after

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Fig. 17.2. Capacitive lag versus gain G of injection-type target.

cutoff of incident light. The calculations were performed for a beam temperature Tb of 3000 K, a beam current Ib of 600 nA, and a signal current Is of 200 nA, and for three different values of dark current Id as shown. Here, stored capacitance C of the target must be treated as effective target storage capacitance, and is therefore taken to be G times the value of about 800 pF as determined by the abovementioned target dimensions. Referring to the figure, we see that capacitive lag increases dramatically with increase in G, and that a sufficient reduction effect in capacitive lag cannot be obtained even for large dark current Id of 20 nA (equivalent to large bias-light current). As described earlier, an electron-injection-type target can obtain high sensitivity with η > 1. It suffers, however, from poor lag characteristics during high-sensitivity operation in theory, and from a drop in the S/N ratio since dark current is large compared to the blocking-type target described as follows. As a result, it is difficult to achieve a pickup tube that requires both high-sensitivity and high quality by an injection-type target.

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17.2.2. Blocking-Type Target The blocking-type target has a structure that blocks the injection of external charge from both the signal-electrode side and electron-beam-scanning side. As an example, Fig. 17.3 shows the structure and band model of a SATICON target [1, 5]. In the figure, the injection of holes is blocked by the junction formed between the signal-electrode/CeO 2 -film and the photoconductive film consisting mostly of a-Se. At the same time, the injection of electrons is blocked by an Sb2 S3 layer. Pickup tubes using a blocking-type target of

(a)

(b)

Fig. 17.3. Structure (a) and band model (b) of a SATICON target.

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this kind have excellent low-lag and low-dark-current characteristics, and they had been widely used in cameras requiring high picture quality. On the other hand, the band model in the figure tells us that a blocking-type target is characterized by only one scanningbeam electron on the target per one photoexcited hole stored on the scanning side. In principle, therefore, electrons beyond the number of incident photons are not removed by an external circuit and sensitivity is limited at η = 1. Figure 17.4 shows the dependency of η on incident-light wavelength in a SATICON tube (from actual measurements). It can be seen that η is maximum at about 0.7 in the short-wavelength region. Thus, considering the theoretical limit of 1 for η, sensitivity can be increased by no more than 1.4 times this maximum measured value by enhancing the structure, such as by making the second layer into a sensitization layer. For the reasons described earlier, a conventional blocking-type target is not applicable in principle to raising the sensitivity of a HD camera by about six times.

Fig. 17.4. SATICON spectral-sensitivity characteristics.

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17.3. Increased Sensitivity in an a-Se Photoconductive Target Operating in a Strong Electric Field As we saw in the last section, it is not easy to satisfy the requirements of high-sensitivity and high-picture quality at the same time. This prompted me to perform new studies and experiments on target materials, structure, operating method, and so on. In one particular study, we constructed a prototype pickup tube with an a-Se target having exceedingly favorable charge-injection-blocking characteristics (high-voltage resistance) and examined its characteristics under a very strong electric field that could not be attempted in past targets due to a dramatic rise in dark current. It was found that this pickup tube exhibits a significant increase in sensitivity when the target’s electric field is made larger than a certain value. This tube is referred to as “Experimental Tube I.” Its target structure, sensitivityincrease phenomenon, and other characteristics are described in detail as follows. 17.3.1. Experiment on Operating an a-Se Photoconductive Target in a Strong Electric Field (i) Target Structure of Experimental Tube I Figure 17.5 shows an external view of Experimental Tube I and Fig. 17.6 shows its target structure. Experimental Tube I is a

Fig. 17.5. External view of Experimental Tube I.

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Fig. 17.6. Target structure of Experimental Tube I.

2/3-inch tube using an electromagnetic-focusing and electromagneticdeflection (MM-type) electron gun. The photoconductive film in this target is a 2-μm-thick a-Se film formed by vacuum deposition (vacuum: 1 × 10−6 Torr). The target is of the blocking type. Like the SATICON, it blocks the injection of holes at the junction formed between the a-Se film and the transparent-signal-electrode and CeO2 layers, and blocks the injection of electrons through the use of an Sb2 S3 layer. But, in contrast to the SATICON, it does not include high-concentration Te- and As-doped layers to concentrate an electric field near the signal–electrode interface, which means that even better hole-injection-blocking characteristics can be expected. Also, for the Sb2 S3 layer, inert-gas (Ar) pressure at the time of deposition was set to 2.4×10−1 Torr considering the porous-film fabrication conditions that would suppress the emission of secondary electrons even when target voltage is exceptionally high and promote stable low-velocity beam scanning. The thicknesses of the CeO2 and Sb2 S3 films in the target are 20 and 100 nm, respectively, indicating that these two films are considerably thinner than the Se layer. Target thickness can therefore be regarded as essentially the same as that of the Se layer. (ii) Current–Voltage Characteristics Figure 17.7 shows target current–voltage characteristics of Experimental Tube I. Blue light (center wavelength: 440 nm) is used here as incident light. From the figure, we see that signal current increases rapidly as target voltage increases from 0 V but comes to saturate,

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at least temporarily, starting at about 20 V. This saturation region is thought to correspond to the state where most electron–hole pairs excited in the Se film by incident light have come to separate under a strong electric field within the film becoming signal current as a result. As target voltage continues to increase, however, we see the phenomenon of signal current again rising dramatically beyond this saturated region. Quantum efficiency η with respect to blue light in a-Se film is estimated to be 0.9 for an operating electric field of 8 × 107 V/m [6]. In Experimental Tube I, this electric-field strength corresponds to a target voltage of 160 V, and this fact enables us to establish a scale for η on the right vertical axis in Fig. 17.7. This scale tells us that η exceeds 1 at a target voltage of 180 V and reaches 10 at 240 V. Furthermore, at a target voltage of 260 V, η is 40 and extremely high sensitivity occurs in Experimental Tube I. As for dark current, it also becomes large in the high-voltage region, but it is nevertheless quite small at 0.2 nA under target-voltage operating conditions of 240 V (η = 10). As described earlier, the phenomenon of increased sensitivity with η exceeding 1 has been

Fig. 17.7. Current–voltage characteristics.

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observed when operating an a-Se photoconductive target with a blocking-type structure in a very strong electric field. 17.3.2. Investigation of Increased-Sensitivity Phenomenon The relation between current–voltage characteristics and an a-Se photoconductive target with and without an electron-injection blocking layer has already been reported by Maruyama [5]. This relation is shown in Figs. 17.8(a) and 17.8(b). Target No. 2, whose structure features the blocking of both holes and electrons, exhibits a signal current that tends to saturate with increase in target voltage. Target No. 1, on the other hand, whose structure features no blocking of electrons (i.e., the electron-injection-type target described in Section 17.2.1), exhibits a dramatic increase in signal current above a certain voltage. Thus, considering that the behavior of signal current of the Target No. 1 shown in Fig. 17.8(b) is similar to that shown in Fig. 17.7, and that η exceeds 1 when charge injection from an external electrode occurs in photoconductive film, we can offer an interpretation as to why η in Experimental Tube I achieves a value much > 1. Specifically, a blocking-type target cannot maintain its blocking characteristics in the presence of a strong electric field, and

(a)

(b)

Fig. 17.8. Relation between target structure and current–voltage characteristics.

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it consequently operates as an injection-type target at this time. This interpretation, though, does not adequately explain why dark current here is extremely small and why lag characteristics (to be discussed below) are favorable. For this reason, the author decided to investigate the operation mechanism behind increased-sensitivity phenomenon based on the following experimental results. (1) Voltage Dependency of Effective Target Storage Capacitance The author measured capacitance of the target by the cathode modulation method [7] to find out how effective target storage capacitance in Experimental Tube I depends on target voltage. This method begins by performing beam scanning while shutting out incident light to the pickup tube and by balancing target surface potential with cathode potential. The system then applies a modulating pulse to the cathode and momentarily lowers cathode potential. As a result, target surface potential as seen from the cathode rises by the amount of pulse amplitude and, for the time until a balance with the cathode potential is again reached, target current flows as scanning-beam electrons become attached to the target. Thus, denoting the amplitude of the cathode modulation pulse as ΔVk , the effective scanning coefficient as s, target current as It , and field time as tf , effective target storage capacitance CE can be determined by the following equation. CE = sIt tf /ΔVk

(17.3)

Figure 17.9 shows waveform photos of target current in Experimental Tube I for different values of target voltage VT with ΔVk set to 1 V. Change in current waveform due to target voltage cannot be observed. This means that if we extract current values from these observed waveforms and apply them to Eq. (17.3), effective target storage capacity CE will always be the same, as shown in Fig. 17.10. The value of CE obtained from these measurements is about 1600 pF. This value is nearly the same as the target storage capacitance calculated for a 2/3-inch tube having a scanning area

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Fig. 17.9. Target current waveforms during cathode modulation in Experimental Tube I (vertical: 33.3 nA/division; horizontal spot interval: 1/60 s).

Fig. 17.10. Effective target storage capacitance.

of 58.1 mm2 (6.6 × 8.8 mm), a-Se relative permittivity εs = 6, and a film thickness of 2 μm. In addition, to perform the same kind of measurements for an electron-injection type of pickup tube, we constructed a tube having the target structure shown in Fig. 17.11. This target features a

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Fig. 17.11. Structure of experimental electron-injection-type target.

2-μm-thick a-Se layer and a 60-nm-thick electron-injection/recombination layer composed of Se film doped with In2 O3 . Storage capacity per unit area can therefore be treated as being nearly equal to that of Experimental Tube I. Figure 17.12 shows target current waveforms for ΔVk of 1 V in the constructed tube using this target. Since this tube has no electron-injection blocking layer, measured target voltages are lower, and in contrast to Experimental Tube I, current values are observed to increase with voltage. In these measurements, scanning area was set to about 1/2 (29 mm2 ) that of Experimental Tube I, as increase in current values due to electron injection was predicted. These experimental results suggest that, at the least, the phenomenon of η exceeding 1 in Experimental Tube I is not attributable to an amplification effect based on electron injection. (2) Dependency of Current–Voltage Characteristics on Direction of Incident Light Figure 17.13 shows current–voltage characteristics for blue light incident on the target of Experimental Tube I from the faceplate side (front incidence) and from the beam-scanning side (rear incidence). Here, to obtain a clear understanding of the difference in characteristics between these two types of incidence, the author adjusted the amount of incident light so that signal current for front incidence and rear incidence is equal at a target voltage of 60 V.

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Fig. 17.12. Target current waveforms during cathode modulation in an electroninjection-type pickup tube (vertical: 33.3 nA/division; horizontal spot interval: 1/60 s).

The results shown in the figure demonstrate that current–voltage characteristics do indeed depend on the direction of incident light: voltage corresponding to an increase in sensitivity is higher for rear incidence than for front incidence. We point out here, however, that light absorption coefficient a of a-Se takes on larger values as wavelength becomes shorter. It increases from 7 × 103 per centimeter for red light (wavelength: 620 nm) to 8.5 × 104 per centimeter for green light (540 nm) and a very large value of 2 × 105 per centimeter for blue light (440 nm) [8]. Consequently, most incident light in the abovementioned experiment using blue light will be absorbed near the surface of the Se film. In addition, considering that the camera tube’s target voltage is applied so that the signal-electrode side takes on a positive potential with respect to the scanning side, holes and electrons can be treated

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Fig. 17.13. Dependency of current–voltage characteristics on direction of incident light.

as main transit carriers within the film for front incidence and rear incidence, respectively. Accordingly, Fig. 17.13 shows that increase in sensitivity differs between hole and electron transit carriers. It is thought that this phenomenon does not occur in an electroninjection-type target since its gain is determined by Eq. (17.1). To confirm this, I performed the same type of experiment as the one above for of Experimental Tube I on the tube that we constructed for the target structure shown in Fig. 17.11. Figure 17.14 shows the results of this experiment. These results reveal no dependency of current–voltage characteristics on the direction of incident light, and can therefore be said to refute electron-injection operation in Experimental Tube I. (3) Dependency of Current-Field Characteristics on Se Film Thickness We next constructed two tubes named Experimental Tube II and Experimental Tube III having the same target configuration as

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Fig. 17.14. Current–voltage characteristics of an electron-injection-type target (dependency on direction of incident light).

Experimental Tube I but featuring a-Se films having thickness values of 1 and 3 μm, respectively. Figure 17.15 shows signal current for blue light versus target electric field for all three of these tubes. In all cases, we can observe sensitivity-increase phenomenon starting at an electric field of about 0.9 × 108 V/m, although sensitivity for the same electric field increases as the film becomes thicker in this region of increased sensitivity. For an injection-type target, whose gain is determined by Eq. (17.1) as mentioned earlier, there is little chance of increasing its gain by increasing film thickness in this way. Thus, the results of this experiment also indicate that sensitivityincrease phenomenon is not attributable to an injection-amplification effect. Based on the results of the experiments described earlier, the author can make a conclusion as to the source of sensitivity-increase phenomenon in Experimental Tube I where η attains a value much >1. This phenomenon is due to an avalanche-multiplication effect within a-Se film and not to charge injection from an external

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Fig. 17.15. Current-field characteristics.

electrode, the latter of which has been traditionally known to be the only technique for achieving high sensitivity in a photoconductive target. In other words, this phenomenon can be explained by an amplification effect brought on when electron–hole pairs created by incident light are accelerated by a strong electric field to create new electron–hole pairs through impact ionization, which then become the source of further impact ionization continuing the process. Figure 17.16 schematically illustrates the operating principle of this target. The experimental results of Fig. 17.13, moreover, suggest that the ionization coefficient in a-Se avalanche multiplication is greater for holes than for electrons. This property turns out to be very convenient for achieving high sensitivity, since holes in photoexcited electron–hole pairs happen to be the main transit carriers in film within an ordinary pickup target. In the following, an amorphous photoconductive target having an avalanche-multiplication effect is called a “HARP target.”

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Fig. 17.16. Operational representation of the HARP tube.

17.4. Main Characteristics of a HARP Target To clarify the main characteristics of a HARP target, the author measured and analyzed various characteristics of Experimental Tube I at a target voltage VT of 240 V, that is, under operating conditions in which η = 10 with respect to blue light (avalanche mode). 17.4.1. Lag Characteristics Figure 17.17(a) shows lag characteristics for a signal current of 200 nA, a beam current of 600 nA, and no bias light, while Fig. 17.17(b) shows, for comparison purposes, lag characteristics for a target voltage VT of 160 V (η = 0.9) at which avalanche multiplication does not occur (non-avalanche mode). The interval represented by each spot in these figures is 1 field or 1/60 of a second. In both cases, lag at the third field after cutoff of incident light is about 4.6%, and no deterioration in lag characteristics due to avalanche multiplication can be observed. This measured value of lag agrees well with the 4.6% theoretical value of capacitive lag calculated for a target storage capacity of 1600 pF and an electron-gun beam temperature of 3000 K in Experimental Tube I. Accordingly, lag in this tube consists only of capacitive lag; it does not include photoconductive lag caused by shallow-level trapping in

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Fig. 17.17. Lag characteristics in Experimental Tube I (spot interval: 1/60 s).

photoconductive film. This result suggests that lag in a tube with a HARP target (HARP tube) can be made small by adopting bias light to make dark current equivalently large, by decreasing storage capacity through a thicker target film, and by using an electron gun with a low-beam temperature. To verify the effects of bias light in Experimental Tube I, the author investigated the relationship between bias-light current and the third-field lag value. The results of this study are shown in Fig. 17.18. It can be seen that lag decreases with increase in biaslight current and that measured lag agrees well with calculated capacitive lag. Next, to confirm the lag-reduction effect of thickening the target film, we constructed an experimental tube with an a-Se film thickness of 6 μm and measured lag characteristics. In this case, target voltage was set to 640 V where η = 10 with respect to blue light. Figure 17.19 shows the lag characteristics that we obtained with this tube. Compared to the characteristics of Experimental Tube I shown in Fig. 17.17(a), we can see that lag decreases significantly. In addition, the lag value of 1.7% measured at the third field in the figure agrees with calculated capacitive lag for a target storage capacity of 530 pF. Figure 17.20 shows lag characteristics when applying a bias-light current of 5 nA to this experimental tube with a thick-film target. We see that lag at the third field has dropped to 0.6%, which

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Fig. 17.18. Change in lag due to bias-light current.

Fig. 17.19. Lag characteristics in an experimental tube with a 6-µm target film.

nearly agrees with the 0.7% value of capacitive lag determined from calculations. In short, we have found that lag in a HARP pickup tube can be decreased by the method described earlier and that the value of this decrease can be predicted with good accuracy by calculations.

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Fig. 17.20. Lag characteristics in an experimental tube with a 6-µm target film with a bias-light current of 5 nA.

Fig. 17.21. Resolution characteristics (blue light).

17.4.2. Resolution Characteristics Figure 17.21 shows resolution characteristics of Experimental Tube I measured under blue light. The figure also shows characteristics in non-avalanche mode for purposes of comparison. Examining these results, we see no differences in characteristics between these two modes indicating that operation by avalanche multiplication has no effect on resolution characteristics. Figure 17.22 shows the results of performing the same measurements under red light. The same resolution characteristics as

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Fig. 17.22. Resolution characteristics (red light).

those shown in Fig. 17.21 for blue light are obtained. We point out here that red light is absorbed throughout the 2-μm thick Se layer in contrast to the situation with blue light, this in accordance with the relationship described earlier between wavelength and the light absorption coefficient of a-Se. Nevertheless, despite this large difference in absorption according to wavelength, no drop in resolution can be observed under red light. The reason for this is thought to be that no light scattering occurs in an amorphous semiconductor target. Figure 17.23 shows an example of a resolution chart image (blue light) picked up by Experimental Tube I. We can see from this image that a limiting resolution of more than 800 TV lines can be obtained. Superior resolution characteristics have been obtained by an experimental tube that combines a target having nearly the same structure as the target of Experimental Tube I with a 2/3-inch electromagnetic-focusing and electrostatic-deflection (MS-type) electron gun having an even sharper scanning-electron beam for HDTV use. This experimental tube achieves an amplitude modulation factor of 33% at 800 TV lines and a limiting resolution of more than 1400 TV lines. We therefore see that a HARP target can achieve exceedingly high resolution capable of supporting HDTV [2], and at the same time, that resolution characteristics of a HARP tube are influenced by the characteristics of the electron-beam system.

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Fig. 17.23. Example of a resolution chartimage.

17.4.3. Photoelectric Conversion Characteristics Figure 17.24 compares photoelectric conversion characteristics between avalanche and non-avalanche modes. It can be seen that while the γ value of avalanche mode becomes gradually smaller as signal current becomes larger, it is about the same as that of nonavalanche mode at 0.95 up to about the 300-nA region. The reason for this gradual decrease in γ is given as follows. When the amount of incident light increases, the amount of charge stored on the scanningside surface of the target likewise increases resulting in a large change in surface potential. This, in turn, leads to a drop in effective target voltage by that amount of change and a smaller avalanche multiplication factor. In non-avalanche mode, effective target voltage also drops with an increase in incident light. In this case, though, there is almost no drop in sensitivity as long as incident light does not greatly increase since, as shown in Fig. 17.7, operation at a target voltage of 160 V lies in the saturation region. The γ value of nonavalanche mode is therefore constant in the operation range shown in Fig. 17.24. The photoelectric conversion characteristics observed in avalanche mode whereby γ decreases gradually with increase in

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Fig. 17.24. Photoelectric conversion characteristics.

incident light are considered practical in terms of expanding the effective dynamic range of a camera. Maximum output signal current ISmax of a HARP target is given by the following equation. ISmax = CVT /stf

(17.4)

From this equation, we get ISmax = 29.5 μA for target storage capacity C = 1600 pF, VT = 240 V, effective scanning coefficient s = 0.78, and field time tf = 1/60 s. Considering that the maximum output signal current of a SATICON tube (2/3 inch) is 2.5 μA [9], it would be no exaggeration to say that the dynamic range of a HARP target itself is extremely large. On the other hand, the maximum beam current of practical electron guns is currently several μA in value, and the maximum output signal current of a HARP tube is restricted by this value. 17.4.4. Excess Noise Figure 17.25 shows line-select waveforms when capturing ITE Grayscale chart I in blue light. First, Fig. 17.25(a) shows the

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(b)

(c)

Fig. 17.25. Grayscalechart captured waveforms: (a) Non-avalanche mode VT = 160 V, (b) Non-avalanche mode VT = 160 V with incident light intensity at 1/11 of (a), (c)Avalanche mode VT = 240 V with incident light intensity same as (b).

waveform captured at VT = 160 V (non-avalanche mode) when adjusting the amount of incident light so that signal-current peak is 200 nA. Next, Fig. 17.25(b) shows the waveform captured while maintaining the same VT of (a) but decreasing incident light to 1/11 its value in (a). Finally, Fig. 17.25(c) shows the waveform captured while maintaining the same amount of incident light as (b) but increasing VT to 240 V to increase signal current by avalanche multiplication to 200 nA, the same as that of (a). A 4.5-MHz low-pass filter is used in all of the abovementioned cases. Figure 17.25(c) corresponds to a state of high-sensitivity operation in which η reaches 10 by avalanche multiplication. Here, if we focus our attention on the noise superimposed on the step waveform, we can see that its increase from that of (a) and (b) in the same figure is very small. This leads me to predict that the excess noise coefficient representing the amount of noise added by avalanche multiplication will be extremely small in Experimental Tube I. The following investigates this excess noise coefficient. 2 The mean-square value of Schott noise current Ins in avalanche mode of Experimental Tube I is given by the following relation. 2

Ins = 2eIp M 2 BF

(17.5)

Here, e is electron charge, Ip is primary photocurrent, M is avalanche multiplication factor, B is frequency bandwidth, and F is the excess

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noise coefficient. Thus, if we denote the mean-square value of input2 conversion noise current of the camera’s pre-amplifier as Ina , the S/N ratio in video output of a camera using Experimental Tube I can be given by the following equation. S/N = 

IP M 2 2eIP M 2 BF + I¯na

(17.6)

2

In the earlier, Ina is given as follows, where Boltzmann’s constant is denoted by k, temperature by T , output capacitance of the camera tube by Co , input capacitance of the pre-amplifier’s junction field effect transistor (JFET) by Ci , the JFET equivalent noise resistance by Req , and load resistance by RL .   1 4 2 2 2 2 Ina = 4kT B + π B (Co + Ci ) Req (17.7) RL 3 2

The correct value of Ina in an actual camera is obtained by measuring the S/N ratio with the electron beam of the camera tube cut off. Excess noise coefficient F at a target voltage VT = 240 V in Experimental Tube I can therefore be determined from Eq. (17.6) by measuring the S/N ratio of the video signal at the time of incident light, where noise includes both optical Schott noise and amplifier noise. To this end, we need to know the value of M , the avalanche multiplication factor, but for the reason given below, we may consider that M = η. As shown by 17.7, the current–voltage characteristics of Experimental Tube I for blue light exhibit saturation in a certain range of target voltage. Current, however, still increases in this region, if only slightly, as voltage rises. In addition, η has a value of 0.9 at VT = 160 V. On the basis of the above, the author considers that the quantum efficiency of primary carriers generated by blue light is nearly 1 at VT = 240 V. Accordingly, the value 10 of η at VT = 240 V can be said to be equal to the avalanche multiplication factor M at that time. The S/N ratio of video output from experimental test equipment incorporating Experimental Tube I was measured using a noise meter

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with a built-in 4.2-MHz low-pass filter. The results are given below (in dB) for two cases. (i) Electron beam of camera tube is cut off: 42.9 dB (at a reference signal current of 200 nA) (ii) VT is set to 240 V and signal current (Ip M ) to 200 nA: 39.9 dB (Ip = 20 nA, M = 10) 2

From these measured values, the author get Ina of 2.05 × 10−18 and a S/N ratio from Eq. (17.6) of 98.9. Thus, if frequency bandwidth B is 4.2 MHz, excess noise coefficient F becomes 0.76 from the relation of Eq. (17.6). In relation to the above, the excess noise coefficient measured for an avalanche photodiode is known to agree well with values calculated from McIntyre’s equation [10], as follows:      1 2 α 1− (17.8) F =M 1− 1− β M Here, α and β are the ionization coefficients of electrons and holes, respectively. Tsuji et al. [11] have reported the following equations for α and β of a-Se based on measurements made with a sandwich-type cell. α = 3.8 × 107 exp(−1.5 × 107 /E) cm−1

(17.9)

β = 1.7 × 107 exp(−9.3 × 106 /E) cm−1

(17.10)

Here, E is electric field (V/cm). Incidentally, avalanche multiplication factor M can be given by the following equation where d is the thickness of the multiplication layer [12]. M=

(β − α) exp{(β − α)d} β − α exp{(β − α)d}

(17.11)

Thus, for a cell with an a-Se film thickness of 2 μm and E equal to about 1.263 × 106 V/cm, M is 10, the same as that of Experimental Tube I. In this electric field, F from Eq. (17.8) is 2.1. In an a-Se sandwich-type cell, this calculated value agrees well with the measured value [13]. Furthermore, as can be understood from Eq. (17.8),

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F takes on a minimum value when α/β = 0 but is still as high as 1.9 for operating conditions of M = 10. In light of the above, the fact that the excess noise coefficient of 0.76 obtained for Experimental Tube I is < 1 (corresponding to no noise multiplication) suggests that some kind of noise-reduction effect exists in the operation of an avalanche-multiplication type of pickup tube. Although there are still some points that are not sufficiently clear in that operation mechanism, I do know that the electricfield dependency of the avalanche multiplication factor is extremely strong. Thus, in a pickup tube that employs stored-charge operation, a type of negative feedback effect can be considered whereby the multiplication factor is modulated inversely to stored charge so that noise becomes smaller than the theoretical value. In summary, the small increase in noise shown in Figure 17.25(c) even for a multiplication factor of 10 in Experimental Tube I can be attributed to an excess noise coefficient having a value 8 μm, however, we found that it was no longer possible to simply extrapolate from the techniques developed previously. We therefore had to undertake new research to make any further developments. In the following, we will provide a fairly detailed description of the research and development of a HARP pickup tube with a target film thickness of 25 μm, whose sensitivity exceeds that of the naked eye. 17.8. Development of the Ultra-High-Sensitivity HARP Pickup Tube To achieve a further increase in the sensitivity of HARP pickup tubes, they basically have to be designed with a greater target film thickness as described earlier. But various problems arise if the target film thickness is simply increased without making any changes to the basic structure of Fig. 17.31. For example, increasing the target film thickness causes a proportional increase in the tendency for the sensitivity of the target to vary with time, and leads to increased geometric distortion and spurious images at the peripheral parts of the screen. These phenomena become particularly noticeable when the film thickness exceeds 8 μm, and can make the camera tube unusable. Consequently, to achieve ultra-high-sensitivity HARP pickup tubes with a target film thickness >8 μm, we made two new studies as described below. 17.8.1. Research into Suppressing the Temporal Variation of Sensitivity As can be seen from the basic principles shown in Fig. 17.16, when the target gets thicker, the distance traveled by electrons and holes increases. The Se layer is doped with As (arsenic) to prevent it from crystallizing, but the As in the Se layer produces electron trapping levels (traps), which have the side effect of seriously impairing the electron transport properties. So when the target layer is made

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thicker, it becomes easier for traveling electrons to get caught in these traps. The captured electrons affect the distribution of electric field inside the target, and as a result they increase the variation of sensitivity with time. We therefore made a detailed study of targets with film thicknesses ranging from 8 to 30 μm in terms of the relationship between the density distribution of As in the film thickness direction and the crystallization-prevention effect and the suppression of changes in sensitivity. As a result, we discovered a density distribution that satisfies both of these conditions, and solved the problem of the sensitivity varying with time. Consequently, the As density distribution in the target with a film thickness of 25 μm differs greatly from that of the target originally developed. 17.8.2. Research into Desensitizing Parts Outside the Scanning Region Since the target in a HARP pickup tube requires an electric field of about 108 V/m, thicker target films must be subjected to very high voltages — about 2000 V for a 20 μm film, and about 3000 V for a 30 μm film — while the target surface on the electron-beamscanning side should have a positive potential in the scanning region of roughly 0–20 V with respect to the cathode (electron-beam source) during normal operation. In the parts outside the scanning region, the accumulated positive holes continue to build up because they are not scanned by the electron beam, and the potential of these parts rises to a value almost equal to the voltage applied to the target. Consequently, when a potential of 2000 V is applied to the target, for example, the potential difference between the parts inside and outside the scanning region becomes very large (about 2000 V), giving rise to the following problems: (i) At the edges of the scanning region, the electron-beam curves outward due to this large potential, causing a large amount of geometric distortion at the edges of the picture. (ii) The curved electron-beam impinges on the target with a greater angle of incidence, leading to increased emission of secondary

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Fig. 17.35. Spurious images caused by secondary electron emission.

electrons from the target that gives rise to spurious images as shown in Fig. 17.35. With regard to (ii) above, since the target voltage is very high, this problem cannot even be dealt with by optimizing the fabrication conditions of the porous Sb2 S3 layer as described earlier to suppress the emission of secondary electrons. Consequently, we investigated the development of a target with a new structure in which the increase in the potential of these parts is prevented by eliminating the sensitivity of the target outside the scanning region. This target is referred to below as a desensitized target. We studied ways of making a desensitized target, and derived the following design guidelines: (i) The target should consist of a light-absorbing layer and a hole transit layer. (ii) The electric field in the light-absorbing layer should be close to zero, so that excited electron–hole pairs are eliminated by recombination. (iii) The electric field in the hole transit layer should be kept to a value at which avalanche multiplication does not occur.

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An important point here is that the desensitized target must be configured using the same materials as the target shown in Fig. 17.31. This is due to production-related problems, whereby the use of other new materials causes contamination of the vacuum vapor deposition equipment and can result in the basic characteristics of the HARP target, such as high sensitivity, not being exhibited within the scanning region. In other words, we had to form a film with no sensitivity using the same materials as those selected for implementing high sensitivity. Figure 17.36 shows the structure of the HARP target we devised within these constraints based on the earlier guidelines. The desensitized target is basically formed by using vapor deposition to overlay an a-Se film doped with As on a target with the same structure as the scanning region, and doping the region close to the interface of the bond between the two with LiF. The thickness of this overlaid part is taken to be about 30% greater than the target film thickness in the scanning region. A band model of the desensitized target is shown in Fig. 17.37. Close to the interface between the optical-absorption layer and the hole transit layer, hole trapping levels are formed by the LiF. In the initial state, the electric field

(a)

(b)

Fig. 17.36. Structure of the newly developed HARP target: (a) Inside beam scanning area and (b) Outside beam scanning area.

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Fig. 17.37. Band model of the insensitive target.

is applied more or less uniformly across the optical-absorption layer and hole transit layer as shown by the dotted line in this Figure. But once light hits the target, holes are generated and trapped at the trapping levels, thereby forming a positive space charge so that in the steady state the electric field in the optical-absorption layer becomes almost zero. Consequently, after this state has been reached, even when light strikes this region and generates electron–hole pairs, they are extinguished by recombination. On the other hand, the electric field due to the target voltage is applied only across the hole transit layer, but due to the relationship with film thickness (the hole transit layer being designed with a thickness about 30% greater than that of the scanning region), the magnitude of this field is kept below 8 × 107 V/m, where avalanche multiplication does not take place. Based on these principles, the desensitized target eliminates almost all of the charge produced by the incident light, and any charges that are left behind without recombining do not undergo avalanche multiplication, so it has virtually no sensitivity. As a result of actual measurements, it has been confirmed that the sensitivity outside the scanning region is reduced by a factor of several million compared with inside the scanning region. By using this desensitized target in the parts outside the scanning region, the abovementioned increase in potential at the electron-beam-scanning surface was suppressed, and it became possible to suppress the generation of geometric distortion and spurious images even when a high target voltage of about 3000 V

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is applied. The research into developing this desensitized target was essential for implementing ultra-high-sensitivity HARP pickup tubes by increasing the film thickness. When the target film thickness is increased in order to achieve ultra-high sensitivity, it is also necessary to consider what voltage should be applied to the target. The voltage required for a given film thickness was discussed earlier. Incidentally, the breakdown voltage of capacitors that can be incorporated into the small circuit boards of handheld cameras is at most around 3000 V. Accordingly, the applied voltage must be made less than this value. We therefore decided to use a target film thickness of 25 μm in the ultra-highsensitivity HARP pickup tube target (maximum applied voltage: ∼2500 V). 17.9. Sensitivity, Resolution, and Lag Characteristics of the HARP Pickup Tube with a Target Film Thickness of 25 µm An external view of this ultra-high-sensitivity HARP pickup tube is the same as the Experimental Tube I shown in Fig. 17.5. Figure 17.38 shows signal current and dark current versus target voltage in the HARP pickup tube with a selenium target 25-μm thick. The signal current rapidly increased at target voltages of more than 1800 V. This phenomenon resulted from avalanche multiplication in the selenium layer of the target as already mentioned in the previous section. The figure shows that an avalanche multiplication factor of several hundred can be obtained at a target voltage of 2500 V. The sensitivity of the tube rises in proportion to a rise in the multiplication factor because the signal current is proportional to the multiplication factor in the avalanche-mode region. The dark current also increases in the avalanche-mode region. However, at a target voltage of 2500 V, the dark current is as little as ∼2 nA. The limiting resolution, limited size of the beam, was more than 800 TV lines. With regard to the lag characteristics, the decay lag in the third field after the incident light was turned off was negligible. This is because the target of the tube has a very small storage

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Fig. 17.38. Signal current and dark current versus target voltage.

capacitance of about 130 pF due to the increased thickness. A thicker target provides a great improvement not only in sensitivity but also in lag. 17.10. Ultra-High-Sensitivity HARP Cameras and Their Applications An ultra-high-sensitivity HARP camera equipped with the new tubes has been developed. The camera is for broadcasting and its appearance is shown in Fig. 17.39. The target voltages of the camera were adjusted to about 2500 V for each channel. Figure 17.40(a) shows a monitor picture produced by the three-tube HARP camera. The illumination is 0.3 lx and the lens iris is at F1.7. To illustrate the big difference in sensitivity between the HARP camera and a CCD camera, Fig. 17.40(b) shows a picture taken under the same conditions with a three-CCD camera (+18 dB). In spite of the dim lighting, the picture produced by the HARP camera is very clear, but a doll in the picture taken with the CCD camera looks like

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Fig. 17.39. Ultra-high-sensitivity HARP color camera equipped with the newly developed tubes (Maximum sensitivity: 11 lx , F8).

(a)

(b)

Fig. 17.40. Monitor pictures produced by color cameras with HARP tubes and CCDs. Illumination is 0.3lx and lens irises are at F1.7: (a) Image taken with the HARP (25-m thick) camera and (b) Image taken with a charge-coupled device (CCD) camera (+18 dB).

a ghost because of lack of sensitivity. It was confirmed that the HARP camera has a maximum sensitivity of 11 lx at F8. This means that the HARP camera is about 100 times as sensitive as the CCD camera. This new HARP camera can take color pictures of objects under conditions so dark that the objects are imperceptible to the naked human eye. As an example of nighttime emergency reporting, Fig. 17.41 presents an image from an NHK news video on the All Nippon Airways hijacking incident that was broadcast on June 22, 1995. The image was captured at 3:40 a.m. at the Hakodate Airport

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Fig. 17.41. Example of a picture of reporting breaking news at night taken with a HARP camera (Hijacking incident).

in Japan. In darkness where the human eye can barely see, a team poised beneath the jumbo jet, ready to raid the hijacked aircraft is captured clearly by the HARP camera. It goes without saying that the sensitivity of the camera can be decreased by decreasing the target voltage, so that the camera is capable of producing excellent picture quality over a wide range of shooting conditions from daylight to moonlight. The high-sensitivity and superior picture quality of HARP cameras has also led to a considerable amount of interest from medical and scientific fields. The author describes how it is applied to research into X-ray medical diagnosis here. A notable example is the potential use of HARP cameras in next-generation X-ray medical diagnosis systems. This research has been done in cooperation with other organizations such as the Tokai University Medical Faculty group (Prof. Hidezo Mori) and the High Energy Accelerator Research Organization (Dr. Kazuyuki Hyodo) in Japan. The X-ray equipment currently used in hospitals is only able to see large blood vessels with a diameter of at least 0.2–0.5 mm, but this study aims to make it possible to obtain clear images of blood vessels that are several times smaller. It has been said that if narrow blood vessels with a diameter of 0.1 mm or less can be imaged, then it should be possible to detect cancer earlier and make better diagnosis of conditions such as heart attacks and cerebrovascular disorders.

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For this purpose, it is necessary to have a special variety of X-rays that are absorbed well by a tiny quantity of contrast medium inside the narrow blood vessels to be imaged, and a TV camera that can clearly reproduce the image formed on a fluorescent screen (placed behind the subject being viewed) due to this absorption. For the special X-rays, we are using monochromatic X-rays with a specific energy obtained from synchrotron radiation. The TV camera is required to have superior sensitivity and resolution. This is because the image on the fluorescent plate is finely detailed and very dark (so as to restrict the exposure of the subject to X-rays). We have therefore conducted experiments involving the use of an ultra-high sensitivity and high-resolution HD HARP camera in the imaging section of a next-generation X-ray medical analysis system. Figure 17.42 shows a photograph (obtained using this system) of tiny blood vessels called tumor angiogenesis that developed in cancerous parts of a mouse. This image shows narrow blood vessels of a characteristic shape with a diameter of 0.1 mm or less, which it has not been possible to see hitherto. This technology is attracting interest as an X-ray diagnosis technique that can lead to the early detection of cancer. Researchers at the School of Medicine at Stony Brook University have been researching solid-state HARP for X-ray medical diagnosis with the aim of early cancer discovery, and in 2016, they successfully

Fig. 17.42. Image of minute blood vessels (mouse cancer).

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developed a large-area solid-state HARP imager (SHARP-AMFPI: Scintillator High-Gain Avalanche Rushing Photoconductor–Active Matrix Flat Panel Imager) that uses a thin-film-transistor (TFT) array in the signal read-out circuit [19, 20]. In addition, since a-Se can convert X-rays into electrons directly, it should be possible to exploit this capability to produce X-ray imaging devices with unparalleled levels of resolution and sensitivity [21]. Consequently, HARP technology is attracting high levels of interest for applications such as X-ray area detectors for protein crystallographic analyses and medical diagnoses.

17.11. Conclusion The author described a study on materials and operation methods for a photoconductive target that could realize a high-sensitivity and high-picture-quality pickup tube with a quantum efficiency η higher than 1. It was found that operating an a-Se photoconductive target having good charge-injection blocking characteristics in a strong electric field could achieve high sensitivity of η > 1 through an avalanche multiplication effect within the target without lag and resolution characteristics degrading. It was also found that this target, which we named “HARP,” could provide all the characteristics needed for obtaining high-quality pictures, including low burn-in, low dark current, low noise, and wide dynamic range in addition to no generation of photoconductive lag. The appearance of this HARP target featuring both high-sensitivity and high-picture quality makes it possible to obtain very high sensitivity at a level >100 times that of CCD color cameras for broadcasting. The high-sensitivity and superior picture quality of HARP targets has also led to a considerable amount of interest from the fields of X-ray medical diagnosis. The research and development on the HARP pickup tube and its camera was conducted in joint research with NHK Science & Technology Research Laboratories, Hitachi Ltd., Hamamatsu Photonics K. K. and Hitachi Kokusai Electric Inc. The author would

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like to thank many researchers who helped to develop the HARP pickup tube and HARP camera, for suggestions and cooperation.

References 1. Shidara, K., et al. (1981). The advanced composition of SATICON photoconductive target, IEEE Electron Device Letters, EDL-2(4), pp. 101–102. 2. Okano, F., Kumada, J., and Tanioka, K. (1990). The HARP highsensitivity handheld HDTV camera, SMPTE Journal, 99(8), pp. 612– 619. 3. Neuhauser, R. (1987). Photoconductors utilized in TV camera tubes, SMPTE Journal, 96(5), pp. 473–484. 4. Tanioka, K., et al. (1987). An avalanche-mode amorphous selenium photoconductive layer for use as a camera tube target, IEEE Electron Device Letters, EDL-8(9), pp. 392–394. 5. Maruyama, E. (1982). Amorphous built-in-field effect photoreceptors, Japanese Journal of Applied Physics, 21(2), pp. 213–223. 6. Pai, D., and Enck, R. (1975). Onsager mechanism of photogeneration in amorphous selenium, Physical Review B, 11, pp. 5163–5174. 7. Goto, N. (1964). The lag characteristics of the 11/2 in Vidicon, ITE, 18(3), pp. 11–18 (in Japanese). 8. Hagen, S. H., and Derks, P. J. A. (1984). Photogeneration and optical absorption in amorphous Se–Te alloys, Journal of Non-Crystalline Solids, 65, pp. 241–259. 9. Tanioka, K., Shidara, K., and Hirai, T. (1981). Highlight lag characteristics of photoconductive camera tube and its improvement, ITE, ED-603, 5(22), 73–78 (in Japanese). 10. McIntyre, R. J. (1966). Multiplication noise in uniform avalanche diodes, IEEE Transactions on Electron Devices, ED-13, pp. 164–168. 11. Tsuji, K., et al. (1991). Ultra-high- sensitive image pickup tubes using avalanche multiplication in a-Se, Materials Research Society Symposium Proceedings, 219, pp. 507–518. 12. Moll, J. L. (1981). Physics of Semiconductor Devices, 2nd Ed., (New York, NY, Wiley), Chapter 1. 13. Ohoshima, T., et al. (1991). Excess noise in amorphous selenium avalanche photodiodes, Japanese Journal of Applied Physics, 30(6B), pp. L1071–L1074. 14. Tanioka, K., et al. (1986). Development of new SATICON photoconductive target, ITE, ED980, 10(22), pp. 1–6 (in Japanese).

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15. Fujita, T., Sakai, H., Maruyama, E., and Goto, N. (1976). Newly developed camera tube SATICON, IEICE, ED75-83, pp. 39–46 (in Japanese). 16. Kubota, M., et al. (1996). Ultrahigh-sensitivity new super-HARP camera, IEEE Trans., Broadcasting, 42 (3), pp. 251–258. 17. Tanioka, K., et al. (2003). Ultra-high-sensitivity new super-harp pickup tube and its camera, IEICE Transactions on Electronics, 86-C(9), pp. 1790–1795. 18. Tanioka, K. (2007). The ultra sensitive TV pickup tube from conception to recent development, Journal of Materials Science: Materials in Electronics, 18, pp. S321–S325. 19. Scheuermann, J. R., et al. (2018). Solid-state flat panel imager with avalanche amorphous selenium, Proceedings of SPIE, 9783, 978317-1978317-9. 20. Scheuermann, J. R., et al. (2018). Toward scintillator high-gain avalanche rushing photoconductor active matrix flat panel imager (SHARP-AMFPI): Initial fabrication and characterization, Medical Physics, 45(2), pp. 794–802. 21. Goldan, A. H., and Zhao, W. (2013). A field-shaping multi-well avalanche detector for direct conversion amorphous selenium, Medical Physics, 40(1), 010702-1-010702-3.

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CHAPTER 18

Metal-Doped Chalcogenides∗ Tomas Wagner, Bo Zhang, Max Fraenkl, Silvya Valkova, Radim Vala, and Tomas Hrbek Department of General and Inorganic Chemistry, University of Pardubice, Pardubice, Czech Republic

18.1. Introduction Metal-doped chalcogenide bulk glasses and their thin films have become attractive materials for fundamental research because of their structure, properties, and preparation. They have many current and potential applications in optics, optoelectronics, electronics, chemistry, and biology (optical elements, gratings, microlenses, waveguides, bio- and chemical sensors, solid electrolytes, batteries, memories, light sources, etc.). Some aspects of their structure, properties, and applications have already been reviewed [1–11]. A wide range of photo-induced phenomena exhibited by chalcogenide thin

∗

The paper is dedicated to Professor Miloslav Frumar. 593

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films enables them to be utilized in a variety of optical applications [12–15]. The aim of the current text is mainly a unique process of formation of ionic conductive amorphous chalcogenide films by opticallyinduced solid-state chemical reaction published by M.T. Kostyshin first time in 1966 [16]. Potential applications of this process in memory switching were originally envisaged by Hiroshi [17] 10 years later. Kozicki [18] extensively reviewed what has been done during the following 40 years up to now in ionic memory switching and defined current terminology this type of memory, i.e., the electrochemical metallization (ECM) memories. In chalcogenide ternaries or quaternaries, several tens of atomic percent of the mobile metal, Ag or Cu, is usually added to binary base glasses involving a group IV or group V atom, such as As–S, Ge–S, or Ge–Se, thus forming the active layer (electrolyte) of the memory device. The metal can be incorporated during the formation of the source material, during fabrication, or even during the initial stages of device operation in a process known as forming or conditioning. In general, these ternary glasses are more rigid than organic polymers, but more flexible than a typical oxide glass and their other physical properties follow the same tendency. This structural flexibility allows the formation of voids through which ions can easily move from one equilibrium position to another and also allows the formation of electrodeposits within the electrolyte. Adding Ag to a chalcogenide base glass can be achieved by diffusing the metal from a thin surface film via the process of optically-induced diffusion and dissolution (OIDD). This technique uses light energy greater than the optical gap of the glass to create charged defects near the interface between the metal or metal-rich and unreacted chalcogenide layers [19]. The holes created are trapped by the metal to form ions, while the electrons move into the chalcogenide film. The electric field so formed is sufficient to allow the ions to overcome the energy barrier at the interface and move into the chalcogenide [20]. For convenience, the ultraviolet (UV) or visible light is used for photodissolution. Exposition wavelength is used in dependence of the film thickness and penetration depth of the actinic light in the film [21].

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(a)

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(b)

Fig. 18.1. A schematic cross section through a sample of an Ag-chalcogenide during the optically-induced diffusion and dissolution (OIDD) process [27].

The OIDD, also known in literature as photodoping or photodissolution, of some metals (Ag, Cu, Zn, Cd) in a wide range of compositions in glassy chalcogenide films [22–27]. In the bilayer or multilayer metal/chalcogenide structure, light illumination induces a fast migration of metal atoms into chalcogenides, as Fig. 18.1 shows. Amorphous Ag/As33 S67 and Ag/Ge30 S70 films have proved useful materials for the fabrication of phase gratings and other diffractive optical elements [21, 28] with relief nanostructures. There are also other related phenomena in Ag-rich chalcogenide glasses, e.g., in ternary Ag–As–Se, Ag–As–S, Ag–Ge–S systems, which exhibit a so-called photo-induced surface deposition of metallic Ag, i.e., the photo-induced segregation of fine particles on a glass surface [29, 30]. A similar effect is known in some minerals, e.g., Ag3 AsS3 or Ag3 SbS3 , during their exposure to light. Furthermore, silver-containing chalcogenide films were found to exhibit reversibility in optical writing and thermal erasing of Ag patterns [31, 32].

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Another potential option in the optical recording of information is to make use of glasses or their films with stoichiometric composition, such as AgAsS2 [33]. Such glasses, e.g., from the AgInSbTe quaternary system, are potentially applicable in phase change optical recording based on a phase transition between the amorphous and crystalline states [34, 35]. Generally, such a transition can be induced by light exposure to a different energy to perform irreversible or reversible recording. The glasses of the Ag–Ge–S, Ag–Ge–Se, Ag–As–S, and Ag–As–Se systems belong to so-called ionic conductors [36], and this quality has been demonstrated to be beneficial, e.g., in reversible (opto) electrical switching, which can be applied in ECM memory [18, 24, 37] as a nonvolatile memory. To consider further development of such applications, in our current text mainly ECM memory materials, it is essential to understand the physical principles of OIDD. It is also important to know a definite and reproducible way of the preparation of silver-containing chalcogenide glass films and their physicochemical properties, especially the optical, thermal, and structural ones, since they are closely related to the mechanism of the above-described phenomena. This text focuses on the amorphous bulks and their film’s synthesis and preparation, their chemical, structural, and physicochemical properties, description of the physicochemical origin of the process of silver (optically-, thermally-, electrically-induced) dissolution and diffusion into thin amorphous films, such as As33 S67 , Sb33 S67 , Ge30 S70 , Ge10 Sb30 S60 , As30 Se70 , Ge20 Se80 , and GeGaS, their physicochemical properties and their potential applications in ECM memories.

18.2. Bulk Glasses and Thin Film Preparation Glasses doped with silver (Ag) can be prepared by the classic methods of synthesis for chalcogenide glasses (a direct synthesis from elements or compounds in ampoules and their melt-quenching), or by the doping of chalcogenide glasses by silver or silver compounds including AgX (X = Cl, Br, I), Ag2 Ch (Ch = S, Se, Te), or by other methods. In all cases, either homogeneous or

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phase-separated (composite) [9, 38–41], or nanoparticles containing glasses are obtained (see e.g., [42]). In many Ag–containing glasses, two glass-forming regions can be found, e.g., in the glassy systems Ag–As–S, Ag–As–Se [27, 38, 43], and Ag2 Se–Ga2 Se3 –GeSe2 [44]. By the heating of a phase Ag9 (As0.4 Se0.6 )91 glass to 120◦ C, the samples became homogeneous, as can be judged from impedance spectroscopy [38]. This fact is in accordance with the higher solubility of Ag in chalcogenides at higher temperature. The glasses of the Ge–Se–AgI system containing higher Se content also appear to be phase separated; while glasses of this system containing lower Se content based on Ge–Se face sharing tetrahedral units are homogeneous [45]. Ag-doped glasses and thick films can be also prepared by the sol– gel method, or by a silver ion exchange from solutions or melts [46]. Thick films can be prepared by the spin-coating technique, e.g., from the n-propylamine, n-butylamine solutions of bulk glasses and inorganic salts [49–53], or from organometallic precursors [54]. In such a case, the prepared films might contain excess solvent, which can be removed by the vacuum heating of the film. Thin amorphous films of Ag-containing glasses have mainly been prepared by thermal vacuum evaporation [55–57], sputtering [58–61], chemical or electrochemical deposition from solutions, by flashevaporation [62–64], and recently by the pulsed laser deposition method [65–73]. In addition, Ag-containing films can be prepared by a socalled photodoping of chalcogenides, where a bilayer (Ag or Ag compound)/chalcogenide is illuminated by light [e.g., [24, 52, 57] or exposed to an e-beam, or X-rays [74] as Fig. 18.1 shows. Silver is then dissolved in a chalcogenide, forming the systems of Ag– As–S, Ag2 S–GeS–GeS2 , Ag2 S–GeS2 , Ag2 Se–Ga2 Se3 –GeSe2 , Ag–As– Te, Ag–B–Si–S, Ag–Se–Te, Ag–GeSex , Ag–Ge–Sb–Se, AgI–As2 Se3 , etc. [1–8, 75]. Ag chalcogenides can also be prepared by chemical plating [76], when a chalcogenide film (e.g., GeSe4 ) is treated by a soluble Ag+ salt (e.g., by AgNO3 or [Ag(CN)2 ]− ) solution. A thin Ag2 Se (Ag2 S) layer is formed on the surface by a chemical reaction, with thickness

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growing with dipping time [76]. The exposure of such a film to light or even an electron beam causes the photodoping of Ag. The area exposed to the e-beam cannot only be doped; it can become a metallic conductor. A negatively charged e-beam spot attracts Ag+ ions. They flow from the surrounding unexposed regions, even from the distances in the order of millimeters, into the exposed spots, where they are reduced by the e− beam illumination (Ag+ + e− = Ag0 ). The unexposed area becomes an insulator-like conductor with a greater gap energy, while the Ag clusters are formed on the exposed areas giving them metallic properties [76]. All deposition techniques allow for obtaining films with a uniform thickness in the range 0.1–2 μm. Silver layers are typically evaporated on the top of amorphous chalcogenide films either in full thickness (typically between 80 and 150 nm of silver) [77, 78] for kinetic measurements, or in portions (∼10 nm of silver) for the step-bystep optically-induced dissolution technique [77], which allows for preparing Ag–chalcogenide films with the desired composition and silver concentration. We succeeded in the depositing of thin Ag–As–S amorphous films also directly from a mixture of organic solutions using the spin-coating method [49]. Using step-by-step solid-state reactions, the composition of the doped films can be tailored, and an exact content of Ag is obtained. Single-phase samples of Ag content from 1 to 27 at% and thickness up to 2.5 μm were demonstrated by such a method in the Ag–As–S system [79, 80]. All deposition techniques of chalcogenide glasses were summarized and reviewed in our chapter, in the book edited by Zhang and Adam [81].

18.3. Photodoping (OIDD) This effect was discovered more than 50 years ago and reviewed several times, e.g. [1–8, 82]. Photodoping, or photo-induced dissolution, is the effect when a film of an Ag or Ag compound is illuminated (UV, VIS, electrons) in contact with a chalcogenide layer or a bulk glass, and the silver is dissolved in the chalcogenide by a photochemical reaction. This way, we doped many materials, e.g., As–S, As–Se, Sb2 S3 , Ge–S, Ge–Se, As–Te, Si–S, Se–Te, Ge–Se, Ge–S,

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Ge–Sb–S (As0.33 Te0.67 )x Te100−x , and others [1–8, 38, 49, 51, 82–92]. The sensitivity to radiation is relatively high, but it is lower than the sensitivity of silver halides in the photographic process. A number of models have been proposed to explain this phenomenon [1–5, 39, 86, 93]. The composition of photo-doped layers depends on the conditions of their preparation (thickness and composition of chalcogenide, thickness of Ag, temperature, conditions of exposure, etc.). The dissolved silver diffuses into the volume of chalcogenide and thus the photodoping gives relatively thin Ag-doped films. Deeper Ag-doped patterns can be prepared by the illumination of multilayers of alternating Ag–chalcogenide–Ag–chalcogenide, etc. [75]. The optically-induced dissolution and diffusion of metals in a-chalcogenides has several typical features: — The dissolution and diffusion of metals can proceed even in the dark; their rates are much lower without illumination. The concentration profile of a photo-doped metal not only follows Fick’s law; it is often of a step-like form with a sharp diffusion front (Fig. 18.2) [24, 39, 93, 94].

Fig. 18.2. The Ag concentration depth profiles obtained for the Ag/a–As30 S70 sample during photo-induced dissolution from the corresponding Rutherford backscattering spectroscopy (RBS) spectra [27].

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— Large amounts of Ag can be dissolved in amorphous chalcogenide layers, in general up to 30–40 at% [87, 93, 95, 96], and in the case of GeSe3 up to 57 at% [97]. — The diffusion of Ag follows the direction of light and very sharp edges between the doped (exposed) and undoped (non-exposed) areas can be obtained. As a result, optical gratings, waveguides, and high-resolution photo resists can be prepared and produced. — The optical transmittance of the doped parts decreases, and the absorption edge shifts toward the long-wavelengths part of the spectrum by doping. — Diffusion is much quicker when the dielectric substrate is covered with a conductive film [39] or when the chalcogenide is deposited on an electrically conductive substrate; the lateral diffusion (perpendicular to the direction of light) is much quicker [19, 98]. In this case, the electrical Coulomb potential, formed on the interface doped–undoped part of chalcogenide, is apparently lowered by the conductivity of the substrate [19] and the diffusion of metal ions can also proceed in the lateral direction. — The rate of the Ag dissolution depends strongly on the chalcogenide composition [39]. The photo-induced dissolution and diffusion of Ag proceeds more quickly in films with an excess of sulfur [19], which suggests that the excess chalcogen plays an important role in the reaction with silver. The mechanism of silver photodoping is yet to be fully understood [1–7]. The whole process of the photo-induced dissolution and diffusion of metals in a-chalcogenides apparently consists of several steps. At the interface between silver and a silver-doped chalcogenide, it proceeds through the ionization of Ag Ag + h+ = Ag + ,

or

Ag = Ag+ + e− ,

(18.1)

in which a silver atom captures a prevailing free carrier from the chalcogenide (hole) or loses its electron. As a result, very mobile Ag ions are formed. The Ag metal can also react with the excess sulfur

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of the chalcogenide, e.g.: Ag + S = Ag + + −S − ,

(18.2)

2Ag + S = 2Ag + + S 2− ,

(18.3)

or

or reduce the chalcogenide, e.g. Ag + 2As2 S3 = As4 S4 + 4Ag 2 S.

(18.4)

Ag is oxidized to an Ag+ ion (Eqs. 18.1–18.4). The reduction of As2 S3 in the Ag–As–S system goes to As4 S4 , but not to the formation of free As–As bonds as determined from Raman spectra, because the Raman band near 234 cm−1 corresponding to As–As vibrations does not change its amplitude during the photodoping. The products of reactions (18.1)–(18.4) remain dissolved in the amorphous matrix. The increased content of the As4 S4 structural units was found in the thin film Raman spectra. Similar effects as in the Ag–As–(S, Se) systems were found in the Ag–GeSe3 system. Photo-doped Ag+ ions form at first a phase close to Ag2 Se. GeSe2 and Ag2 Se have very close heat of formation: −10.8 and −9 kcal/mol and further Ge–Ge bonds are formed [43]. The schematic Equations (18.1)–(18.4) describing the dissolution of silver in amorphous chalcogenides are in fact parts of chemical reactions, which can be described for selenides, e.g., by 2Ag + Se = Ag 2 Se; ΔG0298 = −25.13

kJ , mol

(18.5)

4Ag + 2As2 Se3 = 2Ag 2 Se + As4 Se4 ; ΔG0298 = −12.365 kJ/mol, (18.6) 6Ag + As2 Se3 = 3Ag 2 Se + 2As;

ΔG0298

= −8.155 kJ/mol. (18.7)

During the photodoping process, all resulting compound Equations (18.5)–(18.7) do not usually crystallize and remain dissolved in an

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amorphous matrix. The ΔG of reactions (18.5)–(18.7) is negative; these reactions can thus proceed spontaneously even without illumination, as already mentioned. The values of ΔG of reactions (18.5)– (18.7) are further decreased by the mixing entropy part (−T ΔSm ) due to the dissolution of the resulting compounds in the glassy matrix. At higher Ag content, the Ag-rich phase can be separated, as shown by electrical conductivity measurements [39]. The exposure of the interface of the metal/chalcogenide or of the interface of the doped/undoped part to light of energy close to the band gap of chalcogenide creates electron–hole pairs, and the process of photodoping is quicker. When the interface of the doped/undoped part of the chalcogenide is exposed, the free holes, which prevail, and charge carriers in the undoped amorphous chalcogenides, diffuse together with mobile Ag ions into the undoped part of the chalcogenide. The free electrons are captured more quickly. Due to this process, the Coulomb potential is formed on the interface of the doped/undoped part of the a-chalcogenide [19, 39, 88, 98]. This potential slows down, and eventually, stops a further movement of the Agdoped front. When the chalcogenide is illuminated, newly created electrons and holes lower this Coulomb potential; Ag ions can then move (diffuse) further. Generally, the free electrons and holes are created mainly in the illuminated part. Due to the extremely short diffusion length of free carriers in a highly disordered amorphous solid, their lateral diffusion (perpendicular to the direction of light) is extremely small. Very sharp concentration edges can be received between the illuminated and unilluminated parts of the a-chalcogenide [75]. In the Ag–As–S and Ag–As–Se systems, the step-like form of the Ag+ diffusion profile can also be explained by the diffusion in a two-phase system [39, 98], because two glass-forming regions divided by a relatively large immiscibility region exist in the Ag–As–S, Ag– As–Se systems and also in the Ag–Ge–S(Se) system . The step-like profile of the diffusion edge of Ag+ in chalcogenide films [98] was also confirmed by Rutherford backscattering spectroscopy (RBS) (Fig. 18.2, [27]). The possibility of reaching an Ag-content from 1% to 27 at.% contradicts the model of a twophase-system diffusion [94, 98].

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Fig. 18.3. The optical band gap and the refractive index dependence on the silver content at different wavelengths of the prepared Ag–As–S films [96].

The amorphous films are further from the equilibrium than glasses, and the formation of a new phase (phase separation) could be very slow. Many non-equilibrium states can thus be formed. The kinetics of Ag dissolution fits the model with two stages with different diffusion rates, with exponential dependence in the early stages of the diffusion, and linear dependence in further stages, (f (t) = −aexp(−bt)+ct +d). The two-stage (exponential and linear) dependence of diffusion depths was found not only for vacuumevaporated films, but also for thick films prepared by spin-coating. It is surprising that contrary to significant changes in composition, the optical constants of pure and doped films change only slightly (Fig. 18.3 [96]). 18.4. Kinetics 18.4.1. Kinetic Measurement Methods and OIDD Process Kinetics The OIDD reaction kinetics have been studied using various techniques, e.g., the measurement of the optical transmittance [99] or X-ray diffraction of the Ag (111) peak [100]. The most convenient and reliable is the reflectivity technique, which was first developed

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by Firth [23], and later modified by Ewen et al. [101], by us [77, 102] and Marquez et al. [103, 104]. The modified computer-controlled reflectivity technique [102] was used to measure the kinetics of the OIDD of silver (d = 80 nm) in As30 S70 , Sb33 S67 , and Ge30 S70 (d = 800 nm) films by monitoring the change in thickness of an undoped chalcogenide. The measurement of the rate of OIDD is based on periodic variations of the reflectivity of a weakly absorbing film with its thickness, due to the interference between the light reflected from the top and bottom surfaces of the film. A typical plot of reflectivity as a function of exposure time during one of these experiments is shown in Fig. 18.4. The time between successive maxima or minima on the curve corresponds to decrease in the thickness of the undoped layer by λ/2n, or to increase in the thickness of the doped layer by zλ/2n, where λ is the wavelength of the detected light (λ = 550 nm), n is the refractive index of the undoped As30 S70 , Sb33 S67 , and Ge30 S70 layer at this wavelength (n = 2.3, 2.65, and 1.9, respectively), and z is a constant relating the thickness of the doped layer to the thickness of the undoped material consumed (z = 1.07).

Fig. 18.4. A typical reflectivity curve as a function of the illumination time, for the Ag/As30 S70 bilayer system during the optically-induced diffusion and dissolution (OIDD) process [27].

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Spectral elipsometry is also a method of the choice to measure silver depth profiles after every illumination step [105–107] in the films of the Ag–Ge–S and Ag–Ge–GaS system. The silver layer thickness during the course of the reaction was also determined following the technique proposed by Goldschmidt and Rudman [108], and later improved by Fernandez-Pena et al. [99], which is based on the measurement of the variation of the electrical resistance of the silver film during the OIDD process. Simultaneous measurements of optical transmittance (or reflectivity) and electrical resistance [80, 109] allow for the measuring of the OIDD kinetics with good accuracy. 18.4.2. OIDD Kinetics The kinetics of OIDD in, e.g., Ag/As33 S67 bilayer was monitored using two independent techniques (reflectivity and resistance measurements) simultaneously at room temperature using an Ar ion laser beam (λ = 514 nm) for the sample exposure [109]. The monitoring of the electrical resistance of the silver layer is certainly a very important tool to accurately establish the time when the entire elemental silver source is completely consumed during OIDD. The monitoring of electrical resistance change during the OIDD process helped us to calculate the initial silver-consumption rate υAg (υAg = 1.26 nm/s), which was exactly the same as the rate of the Agdoped/undoped boundary movement obtained from the reflectivity technique [109]. The reflectivity oscillation curve (i.e., the position of the maxima and minima) shown in Fig. 18.4 was used to derive the experimental points for the kinetic curves (Fig. 18.5). As the reflectivity curve shows, the amplitude of oscillations decreases gradually with time and, at a certain point they die out, and then the value of the reflectivity increases monotonically to a new level. The intensity change in the reflectivity curve during the OIDD process was attributed to the changing refractive index value of the reflecting layer, from that of the initial, elemental Ag layer, to that of an As33 S67 layer doped with different levels of Ag. The final increase in the reflectivity at the end of the OIDD effect is certainly due to

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Fig. 18.5. A typical kinetic curve for optically-induced diffusion and dissolution (OIDD) of Ag into an As33 S67 glass film. The solid line is a fit to the experimental points [109].

the leading edge of the boundary (doped/undoped) region, reaching the top surface of the film, so that the Ag concentration at this surface then gradually increases up to a constant value. The electrical resistance and optical reflectivity kinetic curves demonstrate that the OIDD process continues, very efficiently, even after the elemental Ag layer is used up, i.e., the Ag exhaustion had no effect on the OIDD kinetic curve [109]. To find the best physical model to describe and interpret such experimental kinetic data corresponding to the metal-dissolution kinetic measurements, four different fitting functions were tested [109]. It is clear that the measured kinetic curve (i.e., doped layer thickness vs. exposure time), shown in Fig. 18.5, has got a more complex character than was usually reported. It cannot be fitted, as it was suggested in earlier works, by a simple linear term [20] or a square root function [23, 25, 110–113]. A more complex character of kinetic curves during the OIDD process of silver was observed in many chalcogenide systems (As–S, Sb–S, Ge–S [21, 102]) depending on the silver-doped chalcogenide film thickness. The kinetics can be fitted using a composite function consisting of a single exponential and steady-state terms [21, 102], or a single exponential and square root terms described in [109]. The

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Table 18.1. The comparison of the results of kinetic parameters of opticallyinduced diffusion and dissolution (OIDD) obtained in Ag/As30 S70 and Ag/ Ge30 S70 systems [86].

Conditions

kexp (s−1 ) klin (s−1 ) Ea,exp Ea,lin Sample T = 120◦ C T = 120◦ C (kJ mol−1 /eV) (kJ mol−1 /eV)

k = f (T ) As30 S70 3.4 × 10−2 6.1 × 10−3 I = 90 mW/cm Ge30 S70 1.2 × 10−2 4.6 × 10−4 k = f (I) T = 120◦ C

As30 S70 1.7 × 10−2 (I = 70%) Ge30 S70 1.1 × 10−2 (I = 70%)

22.5/0.21 20.5/0.19

33.3/0.31 40.2/0.37

3.0 × 10−3 0.102/9 × 10−4 0.108/1 × 10−3 (I = 70%) 1.0 × 10−3 0.094/8 × 10−4 0.096/9 × 10−4 (I = 70%)

latter function is appropriate when the thickness of the chalcogenide exceeds 1500 nm [109]. The former two-stage exponential/linear function, f (t) = −a exp(−bt) + ct + d, where b and c are the rate coefficients, and a and d are two constants, seems to be appropriate for films with a thickness d < 1500 nm. The parameters b and c are reaction rate coefficients (a = kexp , b = klin in units of s−1 ). The parameters a and d correspond to the photo-doped layer thickness at the end of stage 1 and at the beginning of stage 2, respectively. The kinetic curve showed that there are two stages of OIDD. The first stage is characterized by the rate coefficient kexp and the second stage by klin , where kexp > klin . The OIDD rate, as expressed by two rate coefficients (kexp and klin ), depends strongly on temperature [21, 102], chalcogenide film thickness [26], exposure light energy [114, 115], and light intensity [86, 116–118]. The values of the activation energies during the two stages (Eexp and Elin ) calculated from typical Arrhenius plots (ln k vs. T −1 or ln k vs. I −1 ) are shown in Table 18.1. 18.4.3. OIDD Process Mechanism The OIDD process is generally considered to be a solid-state chemical reaction [27]. The detailed physical or physicochemical interpretation of the process can be found in models [39, 127, 190]. The understanding of the OIDD process is still far from complete, and, e.g., the kinetics of the process require further study.

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The measured kinetic curves and different activation energies in different stages of OIDD show the complex character of the process [102, 109]. The composite mathematical functions needed to be applied to find the best fit to experimental kinetic data and then the physicochemical mechanism of the OIDD process was suggested. The kinetic curves characterize two different velocity constants (the exponential and linear stages or the exponential and square root stages for different thicknesses of the reaction products), which support the idea of two or three consequent physicochemical processes, depending on the OIDD product thickness (Fig. 18.6), described also in other systems by Schmalzried [128]. It was suggested that during the first stage, when a very thin film of a reaction product is formed, the OIDD process rate was determined by space charge at the Ag/Ag-doped/undoped

Fig. 18.6. A schematic diagram of the proposed model for the optically-induced diffusion and dissolution (OIDD) process in an Ag/chalcogenide system.

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chalcogenide boundary, which is built in after the originally twolayer system Ag/chalcogenide is exposed to light. The light with the energy higher than the optical gap of the chalcogenide Eg,opt is absorbed in close vicinity of the chalcogenide surface or of the metaldoped/undoped boundary, and electron-hole pairs are excited. The electrons are likely to be trapped within a short distance and form negatively charged centers located at the chalcogen sites, while the holes can migrate in much longer distances, e.g., 10 μm [129]. The accumulation of the holes at the Ag/chalcogenide boundary leads to the formation of pairs of Ag+ ions and electrons. The holes and Ag+ ions are introduced into the chalcogenide, leaving behind a part of silver species bonded to the chalcogen sites, and a part of free unbonded Ag+ ions, which are able to move forward and neutralize the electrons. The electron tunneling from the metallic Ag into the chalcogenide can speed up the overall process. The described process refers to a silver-containing thin chalcogenide film formed during the exponential stage of OIDD. The silver-doped film thickness increases and influences the boundary space charge. At the same time, the electron tunneling diminishes. The rate of the Ag-doped film formation goes through a linear stage, when the supply of ions and charged particles (electrons, holes) is sufficient. When a silver-doped film is formed, holes have to migrate through the silver-doped part toward the “Ag/Agdoped film” boundary, and the Ag+ ions need to migrate in the opposite direction. The slowest part and the driving force of OIDD is the chemical reaction at the “Ag-doped/undoped chalcogenide” boundary (e.g., 2Ag + S = Ag2 S). The difference between silver chemical potential ΔμAg and silver isothermal activity aAg in the doped part and on the boundary between the doped and undoped parts of the film is the measure of the reaction rate in the studied solid-state system. The silver activity aAg depends on the silver solubility in an amorphous chalcogenide and the phase in which it is present [128]. The source of silver or silver ions is changing during the course of OIDD. At the beginning, the source is the elemental Ag, it then changes to a solid solution of silver in a chalcogenide, but the kinetics is not influenced by this fact [109]. The linear

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rate (linear reaction law) applies to the product film thickness of 1–1.5 μm [21, 109]. When the thickness of an Ag-doped chalcogenide becomes greater than 1–1.5 μm, the reaction rate slows down. Gradually, a change to a parabolic rate of OIDD is observed. This means that OIDD is no longer determined by the reaction rate (e.g., 2Ag + S = Ag2 S), but by the diffusion of silver ions and other charged particles through the increasing thickness of the reaction-product film (an Ag-doped chalcogenide). The overall process rate becomes diffusion limited. The diffusion coefficient calculated from such kinetic curves [21, 109] was DAg+ , optical = 1.16 × 10−11 cm2 /s (the light intensity used in the experiment was 200 mW/cm2 ). The value of thermal diffusion coefficient DAg+ , thermal = 4 × 10−14 cm2 /s for the Ag+ ion selfdiffusion in darkness was obtained [130]. A similar result, namely that DAg+ , optical > DAg+ , thermal by three orders of magnitude, was also obtained in [94]. The values and origin of the activation energies at the two stages (Eexp and Elin ) were discussed by Dale et al. [7] and us (Wagner and Dale) [21]. The activation energy of OIDD (Ea ∼ 0.1–0.3 eV, the temperature range 20–120◦ C) decreases by one order of magnitude compared with thermally-activated silver diffusion and dissolution (Ea ∼ 1.3 eV, in the temperature range 20–120◦ C) in the dark [21, 131, 132]. The activation energies of two Ag/chalcogenide systems for stages 1 and 2 (Ea,exp , Ea,lin ) described earlier are shown in Table 10.1. Their values are close to those characteristic of the activation energy of the diffusion process of Ag+ ions in ionconducting chalcogenide glasses, namely, in sulfides Ea = 0.23 eV and in selenides Ea = 0.14 eV [130] at T = 175◦ C. To explain the differences in activation energies between optically and thermally activated diffusion, the activation energies of ionic conductivity and self-diffusion of Ag+ ions [133] and the Anderson-Stuart model of strong electrolytes [134] have to be considered. The Anderson-Stuart model correlates the activation energy with the energy needed for the metal ion transition between bridging and non-bridging chalcogen atoms [132]. The absorbed light energy generates valence alternation pairs (VAPs), which could contribute to decrease in the activation energy [126] of OIDD.

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The chemical kinetic theory also claims that processes with activation energies Ea > 10 kJ/mol ∼ 0.1 eV can be connected with chemical processes. Ongoing chemical processes during OIDD and the resulting structure changes of the optically-doped films were proved, e.g., by EXAFS [134–137], IR spectroscopy [77, 138], Raman spectroscopy [97, 139], and photo differential scanning calorimetry (DSC) [140]. A number of models were proposed to describe OIDD taking into account different kinetics. The models described the kinetics according to where the actinic light was absorbed. We believe that the light most effective for OIDD is absorbed in close vicinity of the metaldoped/undoped boundary [24, 25]. The role of the light is to excite the holes (the majority carriers in most chalcogenide glasses) and to enable their diffusion through the boundary. However, on the basis of the observation — that the light that is hardly absorbed in the doped or undoped chalcogenide film can also cause, to some extent, silver diffusion and dissolution effects [84, 109, 140]. It was concluded that photon absorption in the metal layer could also contribute to OIDD. Within the frame of those observations, Goldschmidt and Rudman [108] and Lis and Lavine [141] concluded that the absorption of light in the silver layer generates hot electrons, which overcome the energetic barrier between a metal and chalcogenide films leaving behind Ag+ ions. The generated electrons are trapped in the chalcogenide. This process produces electrostatic attraction and starts an enhanced transfer of Ag+ ions into the host chalcogenide film. Recent experiments on the Ag/Sb2 S3 bilayer films by Lee et al. [84] shed some light on such a mechanism using two different light wavelengths, one absorbed by the silver layer, and the other one not absorbed in a 10-nm film of Ag deposited on the top of the chalcogenide film. It was demonstrated [84] that the more effective light for the OIDD process was the light absorbed by the Ag film. In our opinion, however, the question remains open, because immediately after a silver-doped chalcogenide is formed, the absorption in it cannot be avoided. In fact, the OIDD process can be activated with light in a wide energy range from X-ray [142, 143] through UV [141] and visible [21] to near-infrared (IR) [144], which also determines the light penetration depth and the number of electron-hole pairs excited.

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The silver diffusion and dissolution process of metals in chalcogenides was induced by the exposure to light of different energy levels, or at elevated temperature without light, or to a combination of both light and elevated temperature. The OIDD process rates, e.g., in the Ag/As30 S70 [94, 95] bilayer system (Fig. 18.7(a) and (b)), showed typical kinetic curves, from which reaction rates were calculated according to the model discussed earlier. The OIDD process rate

Fig. 18.7. Kinetic curves of optically-induced diffusion and dissolution (OIDD) Ag in an As30 S70 film (a) and of TIDD Ag in an As30 S70 film. The Ag concentration depth profiles (c) obtained for the Ag/a–As30 S70 sample during OIDD from the corresponding Rutherford backscattering spectroscopy (RBS) spectra and Ag concentration depth profiles (d) obtained from the Ag/a–As30 S70 sample during thermally-induced diffusion and dissolution (TIDD) from the corresponding RBS spectra [94].

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is 2–3 orders of magnitude higher than the rate of thermally-induced diffusion and dissolution (TIDD) [94, 95]. 18.5. Diffusion Profiles Silver diffusion profiles during OIDD was measured by different techniques, such as the tracing of the 107 Ag and 109 Ag isotopes during the process [144, 145] or by RBS [21, 86, 145, 146], using α particles or carbon ions (e.g., C+ ) as projectiles. RBS is the only method enabling a practically non-destructive qualitative and quantitative analysis of the films during OIDD. The depth resolution of the method is from 10 nm to a few micrometers and the accuracy (in the range 2%–5%) depends on the knowledge of stopping powers, which enables one to evaluate the depth dependence due to the energy loss of the projectiles. Typical RBS spectra (Fig. 18.8(a), (b) and (c)) were converted into the depth-concentration profiles of present elements (e.g., Fig. 18.7(c), (d) and Fig. 18.8(d), (e), (f)) using the GISA program [146]. The depth profiles of silver in chalcogenide films exhibit steplike profiles, which could not be fitted by standard error or Gaussian functions usually used to describe diffusion. The step-like silver profile is a unique feature found in several systems such as Ag/As–S [21, 102, 133, 147, 148], Ag/Ge–S [86] and Ag/Ge–Se [145, 149, 150] during OIDD. Its origin is still a subject of discussion. We suggested that it is due to the presence of two immiscible glass-forming regions in Ag-chalcogenide glass systems [20, 77]. Alternatively, the step-like profile may be due to the space charge [129] formed at the Ag-doped chalcogenide/undoped chalcogenide boundary, because the holes (being majority carriers) can migrate a longer distance after the excitation, while electrons are trapped and localized in the undoped part of film [129], as Fig. 18.6 shows. The step-like silver profiles were found in samples during both OIDD and TIDD. The RBS spectra corresponding to these experimental conditions show similar Ag-diffusion profile development as shown in Fig. 18.7(c) and (d). The final product of OIDD or TIDD of silver in chalcogenide films has, according to RBS measurements, a constant value of the silver depth profile [21].

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(d)

(b)

(e)

(c)

(f)

Fig. 18.8. Typical Rutherford backscattering spectroscopy (RBS) spectra are shown in (a)–(c), obtained in an Ag/a–As30 S70 sample after different illumination times (0, 2000, and 6000 seconds, respectively). The Ag, As, and S concentration depth profiles, shown in (d)–(f), were obtained from the corresponding RBS spectra (a)–(c) [79].

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Table 18.2. The limits of the silver concentration obtained by optically-induced diffusion and dissolution (OIDD) in different chalcogenide systems. Composition CAg,OIDD limit (at.%)

As33 S70 As30 S70 As30 Se70 Ge30 S70 Sb33 S67 Ge10 Sb30 S60 30

31

20

25

10

7

18.6. Reaction Products and Their Properties The silver diffusion and dissolution process led to homogeneous products (Fig. 18.8) in a wide range of compositions based on the dissolution limits of silver in different chalcogenide compositions [3, 21, 86, 87, 108, 151–155]. Silver dissolution limits in different chalcogenide films given in Table 18.2 were obtained using a step-bystep OIDD, which allows one to prepare films with a wide range of silver concentration. Silver concentration in chalcogenide films strongly influences their physicochemical properties. 18.7. Glass Structure of Silver-Doped Bulks and Films The optically-induced diffusion and dissolution of metals resulted in structure changes of optically-doped chalcogenide films. Such structure changes were identified by several methods, e.g., EXAFS [135–137]. The four-fold coordination of Cu atoms was found in the As2 Se3 glass [156] and also in the As2 S3 glass [157] with a low Ag concentration. For a higher concentration of Ag in chalcogenide glasses, silver atoms were found to be three-fold coordinated in Ag– As–S [157], Ag–As–Se [158], and Ag–Ge–Se. Our results using new approach in structure measurement and its modelling are discussed later in this text. Far-IR spectroscopy of optically-doped materials [77, 138] also proves the existence of Ag–S or Ag–Se bonds. Raman spectroscopy results described in [139] and applied to our Raman measurements for the films of the Ag–As–S, Ag–As–Se, Ag–Ge–S, and Ag–Sb–S systems [79, 96, 153, 154] verified and expanded the knowledge about the structure changes due to OIDD (Fig. 18.9). The spectra of Ag–As–S films [79, 153] were interpreted using references [159–161]. The illuminated As30 S70 film (Fig. 18.9(a), x = 0)

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Fig. 18.9. The Raman spectra of Ag–As–S films (a) and Ag–Ge–S (b) prepared by the optically-induced diffusion and dissolution (OIDD) process [79, 86].

contains strong bands at 333, 344 (AsS2/3 units), and 364 cm−1 (As4 S4 units), and also weak bands at 474 and 496 cm−1 (S8 rings or S ring fragments), respectively. The consequent step-by-step silver photodoping leads to the appearance of a new strong band at 376 cm−1 (the AsS3 pyramids connected by an S–Ag–S linkage), and to decrease in the intensity of the main bands and weak bands

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described for As30 S70 film, S8 rings, or S ring fragments included (Fig. 18.9(a), curves from x = 0 to x = 27 at.%). The Raman spectra measured in the Ag–Ge–S [86] films are shown in Fig. 18.9(b). The spectra were interpreted using references [162–165]. The Ge30 S70 films (Fig. 18.9(b)) contain strong bands at 343 cm−1 (units GeS4/2 , the corner sharing type [164]), 374 cm−1 and 436 cm−1 (GeS4/2 units, the edge sharing type [164]), and also a weak band at 250 cm−1 (GeS4/2 units, the ethane-like type “ETH” [164]), and at 485, 218, and 155 cm−1 (S8 rings or S ring fragments), respectively. The consequent step-by-step silver photodoping leads to increase in the intensity of the Raman band at 250 cm−1 (GeS4 , the ETS units), and to decrease in the intensity of the main bands 374 and 436 cm−1 (GeS4/2 , the edge-sharing units), and disappearance of the weak bands 485, 218, and 155 cm−1 assigned to the S–S bonds (Fig. 18.9(b), curves from x = 0 to x = 31 at.%). The introduction of Ag to the chalcogenides of As, Sb, or Ge also causes the formation of the As–As, Sb–Sb, or Ge–Ge bonds. Such bonds can be easily formed, because their energies are not far from the energies of the hetero-bonds among these atoms, and sulfur or selenium, e.g., of As–S, As–Se, Ge–S, Ge–Se, etc. [5, 166]. The Ag–Ag, Ge–S, Ag–S, Ag–Ge, and Ge–Ge interactions were found in Ag–Ge–S [167, 168] and Ag–As–S [137, 169–172] systems. The combination of chemical modelling based on results of experimental techniques, such as Raman spectroscopy, nanoindentation, synchtrotron X-ray diffraction, neutron diffraction in combination with computational methods based on reverse Monte-Carlo (RMC) simulation techniques and the ab-initio density functional theory (DFT), or a so-called experimentally constrained DFT. Since the Ge–S–Ag and As–S–Ag glasses have similar potential applications, it is interesting to compare the environment of silver atoms and the changes of the host covalent matrices induced by alloying. The structure of glassy AsS2 –25Ag was investigated by diffraction techniques and EXAFS in a similar way [137]. It was found that the mean Ag–S coordination number was 3.34 ± 0.4, while the Ag–Ag coordination number was 0.78 ± 0.4. On average, the total coordination number of Ag was close to 4. The Ag–S distance was

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practically the same in the two glasses, but the first peak was more A, pronounced in AsS2 –25Ag. The Ag–Ag distance was 2.92 ± 0.03 ˚ ˚ which is close to the value found in GeS3 –25Ag (∼2.96–3.01 A). The coordination number of As was close to 3 in AsS2 –25Ag, and no As–As bonds had to be allowed to get reasonable fits. The S–As coordination number was around 1.5, while the S–S coordination number was not higher than the sensitivity of our approach (∼0.3). Thus, while the Ge–Ge bonds were formed in GeS3 –25Ag, the AsS3/2 units remained intact in AsS2 –25Ag. The other important difference between the two glasses was that due to the non-vanishing S–S bonding, each sulfur atom participated in ∼2 covalent bonds in GeS3 –25Ag. The same number was around 1.5 in AsS2 –25Ag. It can be concluded that even if the chemical short range order was changed (due to the formation of the Ge–Ge bonds), the connectivity of the covalent network of the Ge and S atoms was not altered by the addition of Ag. The structure of Ag photo-doped films is similar to the structure of glasses [27], in Ag–As–S glasses, Ag is three-fold coordinated by a chalcogen, the As atoms remain three-fold coordinated by chalcogens. The (As0.33 S0.67 )100−x Agx (0 ≤ x ≤ 28) bulk glasses showed with x from 4 up to 24 at.% Ag, and with x = 28 at.% Ag, a microphase separation using scanning electron microscopy (SEM), and Raman studies [170, 171]. The (As0.33 S0.67 )100−x Agx (0 ≤ x ≤ 28) in a wide concentration range were studied by simultaneous X-ray diffraction, neutron diffraction, and extended X-ray absorption fine structure measurements [169]. The AsAgS2 composition, which forms a homogeneous glass, was modeled with the RMC simulation technique, which enabled the construction of large three-dimensional structural models, compatible with a set of available experimental information (XRD, ND, and EXAFS data in our case). Partial pair distribution functions (PDFs), most probable interatomic distances, and coordination numbers can be extracted from a model atomic configuration. The simulation box contained 16,000 atoms. It was established that Ag preferred the environment of S; the Ag–As bonding could not be observed. Similarly to the AsAgS2 crystalline modifications smithite and trechmannite, the main structural units

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of the glass are AsS3 pyramids. The covalent network of As and S atoms became fragmented in the glassy AsAgS2 , unlike in the glassy AsS2 . The environment of Ag atoms in the AsAgS2 glass differed from that in the crystalline state. In average, each Ag atom had four nearest neighbors, three of them being S and one being Ag. The results are summarized in Table 18.3. Some selected bond angle distributions in the glassy AsAgS2 as obtained from the RMC final atomic configuration are shown in Fig. 18.10. The rather well-defined As–S–As bond angle centered at about 103◦ corresponded to the AsS3 pyramids. The Ag–S–Ag bond angle distribution was much more diffuse. The main peak was at 95◦ , but the usual “contact peak” close to 60◦ (triangular coordination) could also be found. The latter is due to the first neighbor Ag pairs sharing the same S atom, while the second neighbor Ag pairs, separated by 3.5–3.8 ˚ A, contribute to the main peak. The S–Ag–S bond angle distribution is characterized by a peak at about 82◦ and a long tail extending to higher angles. The position of the main peak and the small rise close to 180◦ indicates that in spite of NAg being

Table 18.3. The nearest neighbor distances rij (within the first coordination shell) and coordination numbers Nij for amorphous AsAgS2 . The A. The uncertainty of Nij is about 0.4 [169]. uncertainty of rij is 0.02–0.03 ˚ AsAgS2 [169] Pairs As–As As–S As–Ag S–As S–S S–Ag Ag–As Ag–S Ag–Ag As–X S–X Ag–X

AgAsS2 [157]

rij (˚ A)

Nij

rij (˚ A)

Nij

— 2.26 — 2.26 — 2.55 — 2.55 2.92 — — —

0 2.99 0 1.49 0 1.67 0 3.34 0.78 2.99 3.16 4.12

— 2.27 — 2.27 — 2.54 — 2.54 — — — —

— 3.0 — 1.5 — 1.6–1.65 — 3.2–3.3 — 3.0 3.1–3.15 3.2–3.3

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Fig. 18.10. As–S–Ag, Ag–S–Ag and S–Ag–S bond angle distribution in an AsAgS2 glass [169].

close to 4, the local order around Ag is not tetrahedral, but slightly resembles the octahedral arrangement. It is interesting to compare the local atomic order in the AsAgS2 glass with the structure of its crystalline counterparts. The AsAgS2 compound exists in two crystalline modifications: smithite [173] and trechmannite [174]. In both smithite and trechmannite, each As atom is bonded to three S atoms in a trigonal pyramid; three such pyramids form an As3 S6 molecule by sharing S atoms; the As3 S6 molecules are connected via Ag atoms. The length of the As–S bonds varies between 2.21 and 2.36 ˚ A in smithite, and between 2.21 and 2.30 ˚ A in trechmannite. In both AsAgS2 crystal modifications, one Ag is coordinated by four S atoms in a distorted tetrahedron. The distortion is greater in smithite, where the Ag–S bond length A in varies from 2.51 to 3.03 ˚ A, while rAgS changes from 2.59 to 2.73 ˚ trechmannite. The existence of many nonequivalent bonds is reflected in a series of bands on the IR spectrum, as shown, e.g., in smithite by Golovach et al. [175]. The IR spectrum of the glassy AsAgS2 is essentially smeared, which was explained by the irregular packing of the AsS3 structural units [175]. Our study confirms that, similar to smithite and trechmannite, the AsS3 pyramids exist in the glassy AsAgS2 . However, in contrast to the crystalline phases, the As–S bond length was well defined — there was a distinct peak at 2.26 ˚ A on the As–S partial PDF of the glassy AsAgS2 . The environment of

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Ag atoms in the glass differed from that in the crystalline state. In the glassy state, each Ag atom had about three S nearest neighbors A and (NAgS = 3.34 ± 0.4) at the average distance of 2.55 ± 0.02 ˚ about one Ag neighbor (NAgAg = 0.78 ± 0.4) at the average distance of 2.92 ± 0.03 ˚ A. This finding suggests that in the glassy AsAgS2 , silver is predominantly four-fold coordinated, but instead of bonding to four S atoms — as in the crystalline state — Ag has an Ag neighbor in the glass. Further density functional/molecular dynamics simulations and experimental data (X-ray and neutron diffraction, extended X-ray absorption fine structure) were combined to determine structural and other properties of amorphous AsS2 and AgAsS2 [172]. These semiconductors represent the two small regions of the Ag–As–S ternary diagram, where homogeneous glasses form, and they have quite different properties, including ionic conductivity. We found excellent agreement between the experimental results and large-scale (over 500 atoms) simulations, and we compare and contrast the structures of AsS2 and AgAsS2 . The calculated electronic structures, vibrational densities of states, ionic mobilities, and cavity distributions of the amorphous materials are discussed and compared with the data on crystalline phases where available. The high mobility of Ag in solidstate electrolyte applications is coupled to the large cavity volume in AsS2 , and local modifications of the covalent As–S network in the presence of Ag is presented in Fig. 18.11. The presence of cavities (vacancies, voids) and their distribution have significant effects on the properties of materials and have not yet been discussed in AsS2 and AgAsS2 . We show the corresponding distributions in Fig. 18.12, calculated using a cutoff of 2.5 ˚ A. AsS2 had a much lower density and a much larger cavity volume (37.8%) than AgAsS2 (4.8%), and was clearly porous at the atomistic level. The cavity volume of a-SiO2 was 31.9% with the same parameter set [176]. The trechmannite structure may be viewed as a defective PbS (galena) structure. The defects are vacancies: one on the Ag site surrounded by six S atoms, the other one on the S site surrounded by six As atoms. To test whether this effect occurs in the amorphous

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(a)

(b)

(c)

(d)

(e)

(f)

Fig. 18.11. (Color online) The structures of (a) and (b) a-AgAsS2 and (c) and A) and 540 atoms (d) a-AsS2 . The simulation boxes comprise 560 (side 23.1 ˚ (24.1 ˚ A), respectively. (e) Ag atoms and (f) As and S atoms in a-AgAsS2 . Ag: gray, As: magenta, S: yellow [172].

state, we calculated the partial PDF involving cavity centers. All atom types had comparable PDF weights near the cavities, but the cavity-S coordination number was the highest (2.4). The overall cavity coordination was close to six-fold as in trechmannite, but the nearest neighbors were mixed in a-AgAsS2 . In spite of the relatively high Ag concentration, many Ag cations (∼40%) were adjacent to cavities, which would increase their mobility in the As/S matrix. The low cavity–cavity coordination number (100◦ C. In fact, the value of Tc depends on the heating rate and the thermal history of the material leading to Tc being a dynamic property. Therefore, not only Tc itself, but the activation energy of crystallization is important. Once the activation energy, Ea , is reached, the time, t, which is required for crystallization to occur at a given temperature, T , can be estimated using the Arrhenius formula, t = A exp(−Ea /RT ),

(20.3)

where A is a frequency factor and R is the gas constant [22]. The amorphous phase of a prototypical PCM, Ge2 Sb2 Te5 (GST), has a Tc of about 150◦ C and has been proven to be stable for 10 years at 110◦ C (the upper-left to upper-right panels of Fig. 20.6) [23]. In other words, from a practical perspective the amorphous phase of GST will remain in the disordered phase unless a laser write pulse is applied. The stability of amorphous phases is not rare, for example, amorphous-Si (a-Si), can remain in an amorphous state indefinitely at room temperature. However, at the same time, to be viable as a recording medium, the amorphous phase must be switchable into the crystalline phase on a time scale of tens of nanoseconds (ns) when irradiated by an appropriate laser pulse (upper-left to lower-left panels of Fig. 20.6). To summarize, PCM should possess apparently contradictory properties, namely, the amorphous phase should exhibit stability on a time scale of years, but must switch on nanosecond time scales; this contrast in terms of time reaches the surprisingly large ratio of about ∼ 1017 . On the other hand, materials such as a-Si and other sulfide- or selenide-based chalcogenides are nearly impossible to transform into the crystalline phase on such short-time scales with relatively low laser power (the laser power should not be so large as to lead to damage of the substrate or surrounding layers that are usually organic materials). Generally, since the strength of covalent bonds becomes stronger as the atomic number decreases for a given column of the periodic table,

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only tellurides satisfy the requirements, while chalcogenides lighter than tellurides are too strongly bonded to switch reversibly under moderate laser conditions. Indeed, all available PCMs used to date for optical discs have been tellurides such as Ge–Sb–Te (GST) [24] and Ag–In–Sb–Te (AIST) [25]. The reason why tellurides are the best materials among the vast range of inorganic materials as well of the history of phase change has been detailed elsewhere [26]. For practical applications, an additional crucial physical property is required. Even if a material can be reversibly switched between two phases on nanoseconds time scales, unless the difference in optical reflectivity contrast is sufficient, the material would be useless for optical disc applications as data would not be able to be recorded via structure. The optical reflectivity of a material is determined by the dielectric function that determines the optical constants, which describes light–matter interaction. It should be noted that a-Si or a-Ge have essentially the same optical constants as those of their crystalline counterparts, which also makes these materials difficult for use as optical recording materials [27]. On the other hand, typical PCMs exhibit large differences in optical constants between the two phases resulting in a large optical contrast in the visible light range (the upper-right and lower-left panels of Fig. 20.6). This attribute has been explained in terms of the different nature of chemical bonding in the two phases, namely, the amorphous phase satisfies Mott’s 8-N rule (Octet rule) with covalent bonds, where N represents the number of valence electrons, while in the crystalline phase, a smaller number of valence electrons are available than the coordination number leading to the crystalline phase being highly polarizable or so-called resonantly bonded; this property, in turn, results in large changes in the optical constants between the two phases [28, 29]. More recently bonding in the crystalline phase has been referred to as “metavalent bonding” [30]. It is this contrast in the dielectric behavior that occurs as a result of the unique bonding properties of each phase that makes the PCMs useful for optical disc applications. A large number of chalcogenides have been proposed as possible PCMs, and most of the candidate compounds have been tellurides. Figure 20.7 represents a schematic ternary phase diagram of some

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Fig. 20.7. Ternary phase diagram showing different important phase change materials [4].

of the most important PCM families [4]. A breakthrough in PCMs development was the discovery of the GST ternary system, in particular, the GeTe–Sb2 Te3 pseudobinary tie-line [24]. This is the reason why ternary phase diagrams are often used to describe PCMs, and the cation elements (Ge, Sb) are sometimes replaced with different elements, while the anion remains Te as shown in Fig. 20.7. The GeTe–Sb2 Te3 tie-line includes several ternary stoichiometric compounds such as Ge2 Sb2 Te5 , GeSb2 Te4 , and GeSb4 Te7 , often referred to as GST225, GST124, and GST147, respectively. These compounds satisfy all the aforementioned physical properties required for rewritable optical discs. Another important family of PCMs is the AIST system [25]. More specifically, the AIST system can be described as Ag- and In-doped Sb70 Te30 as shown in Fig. 20.7. These two alloys have been successfully utilized for CDRW, DVD-RAM, and Blu-ray discs. This implies that tellurium, Te, the heaviest element in the chalcogen family except for the unstable isotope Po, exists in almost every home in the world, regardless of whether the occupants know it. A remarkable difference between GST and AIST is the crystallization mechanism of the amorphous phases. As discussed in the previous section, in optical discs, the matrix is a crystalline background

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Fig. 20.8. Schematic pictures of nucleation- and growth-dominated crystallization processes.

in which amorphous marks are written. Therefore, erasure of data implies crystallization of amorphous marks. For this process, there are two distinct material classes. For one class, represented by GST, crystallization is a nucleation-dominated process as shown in the left panel of Fig. 20.8, where the crystalline portion is shown in orange with the amorphous component colored blue. Nucleation-dominated materials are characterized by having higher nucleation than growth rates resulting in random nucleation within the amorphous mark. It should be noted that both nucleation and growth rates are functions of temperature. The relative difference between these two rates determines whether the materials exhibit nucleation- or growthdominated behavior. The nucleation rate of growth-dominated materials is typically so small that nucleation events within the amorphous mark rarely occur. Instead, growth of the crystalline domain from the amorphous/crystal phase boundary dominates the crystallization process as shown in the right panel of Fig. 20.8. AIST is an example of a growth-dominated material [31, 32]. The most important difference between these mechanisms is scalability. Since the full area of the amorphous mark must be crystallized by randomly nucleated crystal grains, nucleation-dominated materials show a small dependence on mark size. On the other hand, for growth-dominated materials, as the crystallization process is complete when the growth from

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the boundary reaches the center of the amorphous mark, growthdominated material exhibit size dependence, namely, the smaller the mark size, the faster the crystallization speed. This scalability has an advantage for the realization of denser optical discs. A detailed crystallization mechanisms of PCMs can be found in Chapter 12 and the literature [33–35]. 20.3. Displays 20.3.1. Basic Principle of Phase Change Displays Here, we move on to a different application of PCMs. Historically, PCMs have been developed for use as rewritable optical discs. As mentioned earlier, PCMs must necessarily possess the ability to switch between two phases with different optical properties. In other words, if a material possesses this characteristic, its application is not limited only to optical disc applications, but different applications that require similar traits are also feasible. One of the newest applications is non-volatile electrical memory in which contrast is given by electrical resistivity in phase change random access memory (PCRAM). This application is discussed in Chapter 21. In the current chapter, the focus is on applications based on the optical properties of PCMs. One example is display technology. Displays are essential in modern society and seem omnipresent as exemplified from watch faces and smartphones to TV monitors and large outdoor display advertising. Several technologies coexist, but in the current chapter the relative merits and demerits of each will not be explored, but instead a newcomer to the field will be introduced. The concept was first proposed and demonstrated in 2014 by Hosseini, Wright, and Bhaskaran from groups at the University of Oxford and the University of Exeter [36]. Figure 20.9 schematically demonstrates the basic principles of phase change display technology. The reflective type of display utilized a GST film. Figure 20.9(a) shows a cross-sectional schematic of a reflective device, where ITO/ GST/ITO multi-layers are deposited onto a metal film. The indium tin oxide (ITO) is a well-known transparent conductive oxide, and the metal layer acts as a mirror. In general, the color is determined

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Fig. 20.9. (a) A schematic cross-section image of an ITO/GST/ITO multilayer structure. (b) Simulated and measured optical reflectivity spectra of the amorphous and crystalline films. (c) Change in reflectivity as a function of GST thickness simulated for visible wavelengths with three different ITO thicknesses. (d) Four different thicknesses and two different phase states enable eight different colors [36].

by the light reflected from the object, thus when light passes through the dielectric multi-layer and is reflected at the surface of mirror layer, the appearance of the display is strongly dependent on interference effects occurring in the multi-layer. This optical

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structure is referred to as a Fabry–Perot-type interferometer. In this case, the interference effects are dominated by the thicknesses of the constituent layers as well as the optical constants of the dielectric layers. Conventionally, once a dielectric material has been grown on a reflective substrate, the thickness and the dielectric constants are fixed. A good example is a SiO2 film on a Si substrate. The SiO2 layer itself is transparent to visible light due to its large band gap, but if 300-nm-thick SiO2 layer is grown on a polished Si substrate, it appears purple. This phenomena is known as the creation of colored reflections from transparent and highly absorbing dielectric films deposited onto a metallic substrate due to strong interference effects [37]. However, of course, such constant and unchangeable color is not useful for display applications as a display element must be able to switch between ON and OFF states. The key point here is the tunability of appearance based on “phase change” technology. As already described in this chapter, a reversible change of the phase and the concomitant modulation in the optical constants of PCMs allow them to be used in controllable color-change applications. Simulated and experimentally measured reflectivity spectra of amorphous and crystalline GST films are shown in Fig. 20.9(b). In both phases, the simulated spectra reproduce well the experimental results. It should be noted that the reflectivity spectra vary dramatically depending on the bottom ITO thickness, t, from 50 to 180 nm, offering direct evidence that the different appearances are due to interference effects. Not only the ITO thickness, but the thickness of the GST film also can serve to alter the apparent color of the display element as simulated in Fig. 20.9(c), where the GST thickness is varied from 5 to 95 nm with three different ITO films thicknesses. This suggests that tailoring the thicknesses of the constituent layers can be used to enhance the reflectivity at a specific wavelength. Note that the vertical axes of Fig. 20.9(c) represent a change in the optical reflectivity between the amorphous and crystalline states. This suggests that the crystallization of the GST film in the device results in a color change in the entire film and that reamorphization can revert the color to the original color demonstrating

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Fig. 20.10. Collections of phase change displays (a) [36], (b) [38], (c) [39], (d) [40], (e) [42], (f) [43], (g) [44], (h) [2], (i) [45].

the possibility of reversible color modulation. Fig. 20.9(d) clearly demonstrates the color variation of a multi-layer structure with different ITO thicknesses as well as with different phases of GST (ITO (10 nm)/GST (7 nm, amorphous or crystalline)/ITO (t nm)/Pt (100 nm)/SiO2 /Si). After the successful demonstration of the phase change display, several groups around the world have reported beautiful color images as shown in Fig. 20.10 [2, 36, 38–45]. Depending on the thicknesses of the PCM and/or ITO layers, mirror metal layer composition, and annealing temperatures, a variety of colors have been realized. Furthermore, since the thickness of the total structure is very thin, these multi-layered films are amenable to the fabrication of flexible devices, promising flexible display applications as well. So far, the optical properties of multi-layer in blanket films have been discussed. In order to exploit the intriguing properties

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of PCMs, fabrication of small devices on a large scale is necessary. Furthermore, it is necessary to realize controllable switching of a single cell to realize a high-resolution display. But how? The answer is to switch a local area electrically. We would like to remind readers that typical PCMs can be switched between two states reversibly by an optical or electrical stimulus. Laser irradiation is used in optical discs to locally heat PCMs. This is applicable as the optical discs rotate in a disc recorder and a laser mounted on a radially moving armature is directed toward the disc surface. However, to use PCM-based optical devices as a display, laser-induced phase change is not practical. Instead, it has been proposed that the electrical switching of individual cell elements is viable analogous to PCRAM. Therefore, phase change display applications can be regarded as a hybrid of optical disc and PCRAM technologies where the optical properties of electrically switched PCMs are utilized. Figure 20.11 (a)

(c)

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Fig. 20.11. (a) Schematic image of electrically induced color changes. (b) An original picture of the Oxford Radcliffe Camera. Reproduced patterns on different structures with ITO thickness of (c) 50, (d) 70, and (e) 180 nm [36].

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shows the first demonstration of a phase change display device [36]. A good reason to use ITO for the dielectric layers is that the same layers can serve as top and bottom electrodes due to ITO’s conductive properties. To realize electrically induced color change, the authors made patterns using the nanometer scale conductive tip of an atomic force microscope (CAFM). Figure 20.11(b) shows a rendition of the famous Oxford Radcliffe Camera. Initially, the GST layer was in the as-deposited amorphous phase, and an electrical stimulus from a CAFM tip transformed a nanoscale local area into the crystalline phase. This approach mimics nanoscale pixilation. Figure 20.11(c), (d), and (e) represent drawings with three different bottom ITO thicknesses of 50, 70, and 180 nm, respectively. The clear color contrast as well as the ability to tune the color with ITO thickness demonstrates the technological feasibility of phase change displays. It should be noted that the scale bars seen in the figure are 10 μm suggesting surprisingly high resolution. A cross-section of a state-of-the-art phase change display device is schematically illustrated in Fig. 20.12 in conjunction with a topview optical microscope image. The technology has been coined a solid-state reflective display (SRD ) [2]. A SRD consists of capping (ITO), PCM (GST), spacer (ITO), and mirror layers (metal). A useful feature is that the mirror layer also plays the role of a heater. The heater/mirror layer is connected with the electrodes on both sides and applied voltage pulses are converted to a uniform and controlled thermal response, which heats up the PCM layer. In PCM layers filamentary switching can occur when current flows and once a

Fig. 20.12. Schematic image of a solid-state reflective display (SRD) and an optical microscope image [2].

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filament structure is created, subsequent current preferentially flows through the newly created low-resistance filament region preventing complete crystallization of an amorphous area. Since the SRD design allows for the spatial separation of the PCM layer from the heater element, no current flows through the PCM and instead uniform heating allows for crystallization of the entire film homogeneously. The right panel of Fig. 20.12 shows an optical microscope image of three SRD pixels, where the as-deposited amorphous state (left), crystallized state (center), and reamorphized state (right) show a clear color contrast underscoring the high potential of the novel display device. 20.3.2. Chalcogenide Materials for Displays The chalcogenides compounds used for display applications are similar to those used for optical discs, namely, PCMs, as the display requires reversible switching and a sharp contrast in optical constants between the two phases. This is why a Ge–Sb–Te alloy, one of the best known PCMs, was employed for the first generation of PCM-based display. AIST is another well-known PCM that is used in CD-RW optical discs. R´ıos et al. reported that AIST also exhibits strong phase change display performance as can be seen in Fig. 20.13 [42]. The authors observed a very similar color gamut for the amorphous phase of both AIST and GST. Furthermore, AIST presents a similar but broader color gamut than GST for a device in which the PCM layer is 6 nm thick or thicker in the crystalline state. The excellent color controllability underscores the strong potential for the realization of phase change displays by optimization of the material used. As discussed earlier in this Chapter, two categories of PCMs exist, nucleation-dominated materials as represented by GST and growth-dominated materials such as AIST. Figure 20.13 and the paper by R´ıos et al. demonstrates that growth-dominated PCMs are useful for phase change display applications. Moreover, it was reported that AIST can be used as an active material for obtaining off-line color modulation [42]. A significant difference between optical discs and display applications is the size of the active area. In optical discs, the switched region

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Fig. 20.13. Comparison of color gamut for GST and AIST based displays with different PCM thicknesses [42].

is several tens of nanometer depending on the laser spot size as well as the numerical aperture, while a single display cell pixels is typically several tens of microns. The cell size of the display pixel shown in Fig. 20.12 is 56 × 56 μm [2]. Therefore, the electrical switching of these large pixels elements is a key challenge for commercialization of SRD. On the other hand, the requirement for ultrafast nanosecond order switching, which is a prerequisite for optical discs and PCRAM applications, is unnecessary for display PCMs as the human eye cannot keep pace with such high-speed changes. In other words, there may exist numerous chalcogenide materials that have been overlooked in the development of PCMs for optical discs applications

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that are appropriate for SRD applications. Therefore, even though there are common features required for both, the criteria for materials exploration is not identical, and consequently, there still remains a large realm of possible materials for the development of novel PCMs optimized for the display applications. 20.4. Outlook In this Chapter, two applications utilizing the reversible change of optical properties in chalcogenides PCMs were introduced. One was the area of rewritable optical discs as represented by DVD-RAM and Blu-ray discs, a mature technology in common use. Another is a newcomer driving innovation in display technology by the use of PCMs. It should be noted that a startup, Bodle Technologies, was founded in 2015 to undertake the commercial development of phase change display technology [46]. This is a remarkable in that after the industrialization of PCMs for optical discs, there have been few mass-produced products based upon functional chalcogenides realized except for non-volatile electrical memory. Even though the optical properties of PCMs recently have attracted revived attention for photonic applications [47], most work is still at a fundamental research level and further breakthroughs are required to enable practical application. The history of chalcogenide-based PCMs dates back more than a half century since the first report by Ovshinsky [48], and while some mature technologies exist, at the same time, there are also growing areas of research that employ PCMs. Typically these applications rely on the unique properties of chalcogenides, and it will be necessary to watch for further developments of PCMs in the future. References 1. https://www.panasonic.com/uk/consumer/home-entertainment/acces sories/lm-bes25we25.html 2. Broughton, B., et al. (2017). Solid-state reflective displays (SRD ) utilizing ultrathin phase-change materials, SID Symposium Digest of Technical Papers, 48(1), pp. 546–549.

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3. Clemens, P. C. (1983). Reversible optical storage on a low-doped Te-based chalcogenide film with a capping layer, Applied Optics, 22, pp. 3165–3168. 4. Wuttig, M., and Yamada, N. (2007). Phase-change materials for rewriteable data storage, Nature Materials, 6(11), pp. 824–832. 5. Ohta, T., Birukawa, M., Yamada, N., and Hirao, K. (2002). Optical recording, phase-change and magneto-optical recording, Journal of Magnetism and Magnetic Materials, 242–245, pp. 108–115. 6. Nakamura, S., et al. (1996). InGaN multi-quantum-well-structure laser diodes with cleaved mirror cavity facets, Japanese Journal of Applied Physics, 35, pp. L217–L220. 7. Nakamura, S. (2000). Current status and future prospects of InGaNbased laser diodes, JSAP International, 1, pp. 5–17. 8. Yamada, N. (2012). Origin, secret, and application of the ideal phasechange material GeSbTe, Physica Status Solidi B, 249, pp. 1837–1842. 9. Asahi, H., Kawamura, Y., and Nagai, H. (1983). Molecular beam epitaxial growth of InGaAlP visible laser diodes operating at 0.66–0.68 μm at room temperatures, Journal of Applied Physics, 54, p. 6958. 10. Hino, I., et al. (1983). Room-temperature pulsed operation of AlGaInP/GaInP/AlGaInP double heterostructure visible light laser diodes grown by metalorganic chemical vapor deposition, Applied Physics Letters, 43, p. 987. 11. Horimai, H., Lim, P. B., Hesselink, L., and Inoue, M. (2002). Volumetric optical disk Storage with collinear polarized holography, International Symposium Optical Memory & Optical Data Storage (ISOM/ODS’02). 12. Betzig, E., et al. (1992). Near field magneto optics and high density data storage, Applied Physics Letters, 161, pp. 142–144. 13. Ash, E. A., and Nichols, G. (1972). Super-resolution aperture scanning microscope, Nature, 237, pp. 510–512. 14. Ash, E. A., and Nichols, G. (1999). Nanometric aperture arrays fabricated by wet and dry etching of silicon for near-field optical storage application, Journal of Vacuum Science & Technology B, 17, pp. 2462– 2466. 15. Ichimura, I., Hayashi, S., and Kino, G. S. (1997). High density optical recording using a solid immersion lens, Applied Optics, 36, pp. 4348– 4348. 16. Matsumoto T., Shimano, T., and Osaka, S. H. (2000). An efficient probe with a plannar metallic pattern for high density near field, 6th International Conference on Near Field Optics and Related Technologies (NFO 6), p. 55.

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17. Oesterschultz, E. (2001). Transmission line probe based on a bow-tie antenna, Journal of Microscopy, 202, p. 39. 18. Tominaga, J., Nakano, T., and Atoda, N. (1998). An approach for recording and readout beyond the diffraction limit with an Sb thin film, Applied Physics Letters, 73, pp. 2078–2080. 19. Kikukawa, T., Nakano, T., Shima, T., and Tominaga, J. (2002). Rigid bubble pit formation and huge signal enhancement in super-resolution near-field structure disk with platinum-oxide layer, Applied Physics Letters, 81(25), pp. 4697–4699. 20. Tominaga, J., et al. (2000). The characteristics and the potential of super resolution near-field structure, Japanese Journal of Applied Physics, 39 (2S), p. 957. 21. Kikukawa, T., Fukuzawa, N., and Kobayashi, T. (2005). Properties of super-resolution near-field structure with platinum-oxide layer in Blu-ray Disc system, Japanese Journal of Applied Physics, 44, pp. 3596–3597. 22. Ozawa, T. (1970). Kinetic analysis of derivative curves in thermal analysis, Journal of Thermal Analysis, 2(3), pp. 301–324. 23. Lacaita, A. (2006). Phase change memories: State-of-the-art, challenges and perspectives, Journal of Solid State Electrochemistry, 50(1), pp. 24–31. 24. Yamada, N., et al. (1991). Rapid-phase transitions of GeTe–Sb2 Te3 pseudobinary amorphous thin films for an optical disk memory, Journal of Applied Physics, 69(5), pp. 2849–2856. 25. Kageyama, Y., Iwasaki, H., Harigaya, M., and Ide, Y. (1996). Compact disc erasable (CD-E) with Ag–In–Sb–Te phase-change recording material, Japanese Journal of Applied Physics, 35 (Part 1, No. 1B), pp. 500–501. 26. Raoux, S., and Wuttig, M. (2009). Development of materials for third generation optical storage media, Phase Change Materials Science and Applications (New York, NY, Springer), Chapter 10. 27. Baldus-Jeursen, C., Tarighat, R. S., and Sivoththaman, S. (2016). Optical and electrical characterization of crystalline silicon films formed by rapid thermal annealing of amorphous silicon, Thin Solid Films, 603, pp. 212–217. 28. Shportko, K., et al. (2008). Resonant bonding in crystalline phasechange materials, Nature Materials, 7(8), pp. 653–658. 29. Huang, B., and Robertson, J. (2010). Bonding origin of optical contrast in phase-change memory materials, Physical Review B, 81, p. 081204.

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30. Zhu, M., et al. (2018). Unique bond breaking in crystalline phase change materials and the quest for metavalent bonding, Advanced Materials, 30(18), p. 1706735. 31. van Pieterson, L., et al. (2005). Phase-change recording materials with a growth-dominated crystallization mechanism: A materials overview, Journal of Applied Physics, 97(8), p. 083520. 32. Matsunaga, T., et al. (2011). From local structure to nanosecond recrystallization dynamics in AgInSbTe phase-change materials, Nature Materials, 10(2), pp. 129–134, 02. 33. Zhou, G. F., Borg, H. J., Rijpers, J. C. N., and Lankhorst, M. (2000). Crystallization behavior of phase change materials: Comparison between nucleation- and growth-dominated crystallization, 2000 Optical Data Storage, Conference Digest, pp. 74–76. 34. Raoux, S., and Wuttig, M. (2009). Experimental methods for material selection in phase-change recording; Crystallization kinetics, Phase Change Materials Science and Applications (New York, NY, Springer), Chapters 5, 7. 35. Orava, J., et al. (2012). Characterization of supercooled liquid Ge2Sb2Te5 and its crystallization by ultrafast-heating calorimetry, Nature Materials, 11(4), pp. 279–283. 36. Hosseini, P., Wright, C. D., and Bhaskaran, H. (2014). An optoelectronic framework enabled by low-dimensional phase-change films, Nature, 511(7508), pp. 206–211. 37. Kats, M. A., Blanchard, R., Genevet, P., and Capasso, F. (2013). Nanometre optical coatings based on strong interference effects in highly absorbing media, Nature Materials, 12, p. 20. 38. Hosseini, P., and Bhaskaran, H. (2015). Colour performance and stack optimisation in phase change material based nano-displays, Proceedings of SPIE, 9520, pp. 9520–9527. 39. Bakan, G., et al. (2016). Ultrathin phase-change coatings on metals for electrothermally tunable colors, Applied Physics Letters, 109(7), p. 071109. 40. Ji, H.-K., et al. (2016). Non-binary colour modulation for display device based on phase change materials, Scientific Reports, 6, p. 39206-1-7. 41. Lyu, Y., et al. (2016). Multi-color modulation in solid-state display based on phase changing materials, 13th IEEE International Conference on Solid-State and Integrated Circuit Technology (ICSICT), pp. 165–167. 42. R´ıos, C., Hosseini, P., Taylor, R. A., and Bhaskaran, H. Color depth modulation and resolution in phase-change material nanodisplays, Advanced Materials, 28(23), pp. 4720–4726.

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43. Yoo, S., et al. (2016). Multicolor changeable optical coating by adopting multiple layers of ultrathin phase change material film, ACS Photo, 3(7), pp. 1265–1270. 44. Lyu, Y., et al. (2017). Multi-color modulation of solid-state display based on thermally induced color changes of indium tin oxide and phase changing materials, Optics Express, 25(2), pp. 1405–1412. 45. Talagrand, C., et al. (2018). Solid-state reflective displays (SRD ) for video-rate, full color, outdoor readable displays, Journal of the Society for Information Display, 26, pp. 619–624. 46. http://bodletechnologies.com/ 47. Wuttig, M., Bhaskaran, H., and Taubner, T. (2017). Phase-change materials for non-volatile photonic applications, Nature Photonics, 11(8), pp. 465–476. 48. Ovshinsky, S. R. (1968). Reversible electrical switching phenomena in disordered structures, Physical Review Letters, 21, pp. 1450–1453.

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CHAPTER 21

Non-Volatile Memory Paolo Fantini TD Department, Micron Technology, Vimercate, Italy

21.1. Introduction The aim of this chapter is to show how the peculiar properties of some chalcogenide-based glasses, specifically the class of phase change materials, can be employed in the field of non-volatile memory (NVM) applications. A general introduction on the fundamentals of phase change memory (PCM) device physics and architecture will be provided to the reader. The main issues of PCM technology to challenge conventional NVMs solutions will be also addressed. In addition, starting from a historical outlook on the potential applications of the PCM technology, the opportunities of PCM for future applications in the actual ecosystem of memories will be illustrated. 21.2. PCM Working Principle and Technology In part II of the present book, the peculiar property of some chalcogenide alloys to reversibly toggle between the amorphous and the crystalline phase has been widely discussed. In the previous chapter, it has been highlighted as the pronounced optical contrast between 713

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the amorphous and the crystalline phase gives these chalcogenide materials suitable for technological applications in the field of optical media and memories. In addition to the optical contrast, the amorphous and crystalline phases also present a strong electric contrast: being the disordered amorphous network insulating, while the crystalline phase is conductive. The abrupt resistivity change between the two phases (∼3 orders of magnitudes!) can be employed as the basis of electrically programmable and reading data storage. Hereto, the idea at the basis of the PCM is to electrically induce the phase transition of a chalcogenide-based thin film and to measure the device resistance as the logic state of the cell. Since both states are stable, no energy is required to keep data stored and PCM results in an inherently NVM technology. The PCM cell architecture is essentially a resistor constituted by a thin film of chalcogenide material with a low-field resistance that changes by orders of magnitudes, depending on the phase state of the chalcogenide alloy in a possibly thinner layer than the total film thickness that is called active region of the cell. A prototypical architectural example of a PCM device, in its mushroom-type fashion because of the shape of the active region coupled with the heater, is shown in Fig. 21.1(a). The switching between the two states of the active region is temperature activated. The glassy state of the material in the active region can crystallize when it reaches a critical temperature (Tc ) and crystal nucleation and growth can occur (Set operation). To bring the chalcogenide alloy back to the amorphous state (Reset operation), the temperature must be increased above the melting point of hundreds of degree Celsius and then very quickly quenched down to prevent any ability of the glass to crystallize, leaving the cell in the amorphous state (Fig. 21.1(b)). The very small heater/phase change contact area that characterizes this kind of PCM architecture is the key feature to develop, thru the proper setting of voltage/current pulses, a sufficient Joule heating effect to locally reach both the critical temperatures, Tc and TM , thanks to the current crowding. Figure 21.2 illustrates the electrical characteristics of the PCM cell. Depending on the chalcogenide material phase, the memory

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Fig. 21.1. (a) Sketch of the prototypical mushroom-like phase change memory (PCM) cell where the current crowding thru the small heater-phase change material contact gives rise to the active area of the cell with mushroom boundary. (b) Temperature–time scheme of the pulses used to program the PCM cell in the Reset and Set states and to readout the state of the cell. Electrical pulses change the temperature in the active region of the cell, accordingly.

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Fig. 21.2. (a) Current-voltage characteristics of the phase change memory (PCM) cell with the chalcogenide alloy in the crystalline and amorphous phase and in (b) the R-I “U-shaped” programming curve of a PCM cell together with the R-I programming curve starting from the Set state.

device features one of the two electrical characteristics depicted in Fig. 21.2(a). The crystalline phase behaves as a resistor with a slope mainly dominated by the heater resistance itself. The amorphous phase shows an S-shape negative differential resistance (SNDR), that starts from a high resistive off-state and collapses,

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with a decreased bias on the cell, into a high-conductive on-state through the so-called threshold switching effect [1]. Figure 21.2(b) shows a typical programming curve of a PCM cell where the x-axis reports the programming current intensity of squared pulses of 100 ns duration and the y-axis the measured resistance as a function of the programming stimulus. Both types of state transitions are shown in the figure. For the reset to set transition, the cell was always prepared in the reset state (correspondingly to R ≈1.5 MΩ) prior to the application of the programming pulse. In this case, the programmed resistance steeply decreases for programming currents >100 µA, due to the crystallization of amorphous chalcogenide film in the active region. The figure also shows the opposite (set-to-reset) transition, where the cell is prepared in the low-resistance crystalline state (R ≈ 3 kΩ). Here, the cell resistance remains unchanged for moderately small programming currents, then abruptly increases for current values >500 µA. This current value marks the chalcogenide melting temperature within the active region. In fact, rapid cooling of the melted chalcogenide along the falling edge of the program pulse results in a final amorphous phase, increasing the cell resistance. Note that the falling edge is a critical parameter in the set-to-reset transition: if the falling edge is not fast enough, the melted glass may re-crystallize leading to a final state with lower resistance. As already noticed, since both the crystalline and the amorphous state are stable, the two phases could be used to store binary information in an NVM device, where the bit “1” corresponds to the conductive state and the bit “0” to the insulating one. This electrically induced structural and electronic change has been thus named memory switching. It is worth noting that the threshold switching effect is required to get the memory switching mechanism, but not vice versa. In fact, an amorphous chalcogenide has to be driven in a highly conductive electrical state through threshold switching to get the transition temperatures without enormous electrical fields [1, 2]. The minimization of the reset programming current, in addition with the power consumption control, addresses many performance implications enabling the PCM technology: the thermal cross talk between adjacent cells, the need of a selector device able to drive

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high current in the programming ON-state and to inhibit the current flow in the OFF-state, the IR drop management with large memory arrays and the cell endurance with programming cycling. Several PCM architectures have been proposed to minimize the reset current. Schematically, the various PCM cell architectures reported in literature can be classified accordingly into two main categories following this taxonomy and philosophy of the cell architecture: (i) Built-in heater architecture where a dedicated element, hence named “heater,” generates the heating necessary for the phase transition inside the PCM cell (ii) Self-heating architecture that relies on the Joule heating generated inside the chalcogenide itself to increase the temperature and promote the phase transition and both, obviously, present advantages and weaknesses. The above presented mushroom-type PCM cell is the prototype of the first class, that has been realized following different process embodiments and seize features [3–6]. In [6], the synopsis of the process integration of one of them, so-called Wall structure, that demonstrated its manufacturability at the 45-nm technology node as a 1 Gb PCM product operating at 1.8 V and exploiting a reset current as low as 200 µA can be found. At variance, an example of self-heating-based cell in its extremely scaled version where the PCM cell constitutes the conformal connection between carbon nanotube electrodes with few nanometers diameter size is reported in [7]. This is an academic work that demonstrated both the phase transition on the nanometerscaled device and the reset current scalability as low as 5 µA. In addition to architectural approaches, mostly related to the programming current minimization, a lot of efforts have been devoted to other areas of improvement of the PCM to sublimate its performances, namely (i) The thermal engineering (ii) The material exploration (iii) The drift minimization and management for Multi-Level PCM

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21.2.1. Thermal Engineering Being the PCM technology inherently based on the ability to convert the current across the device in temperature, any heat generation and dissipation mechanism is vital for the success of PCM. Thus, a successful PCM architecture requires to be coupled with an optimized thermal design of the cell. In fact, in many thermally unoptimized devices, >99% of the heat is lost to the surrounding structure at the expense of the write current and the programming disturb between adjacent cells [8, 9]. This means that most of the heat generated inside the cell heats up the nearby dielectrics and metal lines (see Fig. 21.3). A lot of works to reduce power consumption by increasing the thermal resistances of the structure has been done in the last decades leading to these strategies as guidelines to address the optimization of the thermal engineering of the PCM: (i) Increase the thermal resistance of surrounding dielectrics, also considering the air gap option

(a)

(b)

Fig. 21.3. (a) Schematic of the typical mushroom cell where the melted dome during the programming operation is highlighted and the arrows represent the heat loss paths that need to be interrupted for a more efficient energy consumption. (b) Transmission electron microscopy (TEM) section that highlights as the aggressor cell (dashed-line dome on the left) can thermally disturb the adjacent cell (dashed-line dome on the right) promoting the partial crystallization of the amorphous Ge–Sb–Te (GST) dome, eroding part of it [9].

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(ii) Increase the interfacial thermal boundaries, also increasing the number of interfaces This last point is crucial in the technology scaling perspective since the surface/volume ratio increases with the scaling down of cell dimensions and interfaces between layers constitute the larger component of the total thermal resistance [9]. For the development of energy-efficient PCM devices, metrology techniques to characterize the heat generation and dissipation in the nanoscale regime, both spatially and temporally, are required. Thus, a lot of efforts have been addressed in this direction in the last decades for a better control of the heat flow in non-equilibrium conditions and when the device dimensions and the thickness of the layers become smaller than the scattering lengths of phonons [9–12]. 21.2.2. Material Exploration Till now we indicated the phase change material as a generic chalcogenide alloy. Indeed, the best chalcogenide alloys for PCM applications belong to the class of GeSbTe compounds, which follow a pseudo-binary composition (between GeTe and Sb2 Te3 , also including the GeTe and Sb2 Te3 corners). Among them, the Ge2 Sb2 Te5 (usually referred as GST) is the mostly used since it provides a good compromise between its speed of transformation, from the disordered to the crystalline structure, and the stability of the amorphous phase able to meet retention product requirements like 10 years at 85◦ C [13]. Ge2 Sb2 Te5 also became the reference for the comparison of all the different materials explored. A ternary diagram as map for material exploration of the Ge–Sb–Te stoichiometries is shown in Fig. 21.4. Indeed, a wide variety of materials has been explored, which aim at tailoring the desired phase change properties accordingly to the specific applications. In general, using phase change materials with high crystallization temperatures results in higher retention of the reset state at the cost of slower set times, since the bonds are harder to be both formed and broken [16, 17]. A strong

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(a)

(b)

Fig. 21.4. (a) Ternary diagram for Ge, Sb, and Te. The GeTe–Sb2 Te3 tie line, where the Ge2 Sb2 Te5 is located can be distinguished. In addition, directions toward more Sb-rich, more Ge-rich and Te-rich with respect to the Ge2 Sb2 Te5 composition to optimize the alloy properties accordingly with the feature that need to be prioritized, from an application point of view, have been highlighted. (b) Schematic representation of the possible ring size transformation in the amorphous-crystal phase change. The 4-fould rings in the amorphous phase that act as nuclei for crystallization (which resembling to) are highlighted. The statistics of 4-fould rings in the disordered phase becomes a crucial parameter for a fast nucleation and it can be manipulated by means of the Ge–Sb–Te (GST) stoichiometry modulation [14, 15].

retention is mandatory for automotive applications involving highoperating temperatures [18]. Devices that were able to maintain a stable stoichiometry, even after multiple cycles showed excellent endurance, still switchable after 2 × 1012 of programming cycles [19]. Improving the speed and endurance of PCM will open up several new opportunities to operate at DRAM levels of write frequency and be useful for a memory-type Storage Class Memory (SCM) as it will be better illustrated later on. GST optimization thru doping represents the general strategy for tailoring PCM devices matching the best features versus specific applications for which it has been developed for. The result of using bi-doped GeTe (