OPTICAL AND ELECTRICAL PROPERTIES PHYSICS AND CHEMISTRY OF MATERIALS WITH LAYERED STRUCTURES Managing Editor E. MOOSER, Laboratoire de Physique Appliquee, CH -1003, Lausanne, Switzerland Advisory Board E. J. ARLMAN, Bussum, The Netherlands F. BASSANI, Physics Institute of the University of Rome, Italy J. L. B REBNER, Department of Physics, University of Montreal, Montreal, Canada F. JELLINEK, Chemische Laboratoria der Rijksuniversiteit, Groningen, The Netherlands R. NITSCHE, Kristallographisches Institut der Universitat Freiburg, West Germany A. D. Y OFFE, Department of Physics, University of Cambridge, Cambridge, U.K. VOLUME 4 OPTICAL AND ELECTRICAL PROPERTIES Edited by P. A. LEE Brighton Polytechnic, England D. REIDEL PUBLISHING COMPANY DORDRECHT-HOLLAND/BOSTON -U.S.A. Library of Congress Cataloging in Publication Data Main entry under title: Optical and electrical properties. (Physics and chemistry of materials with layered structures; v. 4) Includes bibliographies and indexes. 1. Solids-Optical properties. 2. Solids-Electric properties. 3. Layer structure (Solids). 1. Lee, Peter A., 1926- II. Series. QD478.P47 vol. 4 lQC176.8.06J 530.4'1s [530.4'1) ISBN-13: 978-94-010-1480-9 e-ISBN-13: 978-94-010-1478-6 001: 10.1007/978-94-010-1478-6 Published by D. Reidel Publishing Company P.O. Box 17, Dordrecht, Holland Sold and distributed in the U.S.A., Canada, and Mexico by D. Reidel Publishing Company, Inc. Lincoln Building, 160 Old Derby Street, Hingham, Mass. 02043, U.S.A. All Rights Reserved Copyright © 1976 by D. Reidel Publishing Company, Dordrecht, Holland Softcover reprint of the hardcover I st edition 1976 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means electronic or mechanical, including photocopying, recording or by any informational storage and retrieval system, without written permission from the copyright owner TABLE OF CONTENTS PREFACE Vll B. L. EVANS / Optical Properties of Layer Compounds 1 J. BORDAS / Some Aspects of Modulation Spectroscopy in Layer Materials 145 R. ZALLEN and D. F. BLOSSEY / The Optical Properties, Electronic Structure and Photoconductivity of Arsenic -Chalcogenide Layer Crystals 231 P. M. WILLIAMS / Photoemission Studies of Materials with Layered Struc- tures 273 R. c. FIV AZ and PH. E. SCHMID / Transport Properties of Layered Semicon- ductors 343 D. J. HUNTLEY and R. F. FRINDT /Transport Properties of Layered Struc- ture .I'v~etals 385 R. F. FRINDT and D. J. HUNTLEY / Experimental Aspects of Superconductiv- ity in Layered Structures 403 J. M. VANDENBERG-VOORHOEVE / Structural and Magnetic Properties of Layered Chalcogenides of the Transition Elements 423 INDEX OF NAMES 459 INDEX OF SUBJECTS 461 PREFACE This fourth volume in the series 'Physics and Chemistry of Materials with Layered Structures' is concerned with providing a critical review of the significant optical and electrical properties by established authors who have themselves made many significant contributions to these fields. Research into these materials has recently gained a new impetus and their fascinating properties have attracted many new research workers. These people should find much of value in the reviews contained in this volume and the editor is very much indebted for the painstaking and hard work put into the preparation of the various chapters by the authors. The optical properties provide useful information for deriving the band struc tures, a knowledge of which is required for an interpretation of measurements on the electronic properties. The chapters by Dr Evans, Dr Williams and Dr Bordas describe different techniques which have provided much detailed data on this subject. An interesting property of these materials is the comparative ease with which thin specimens may be prepared for these measurements and this is highlighted in the super conducting experiments outlined by Professor Frindt and Dr Huntley. These authors together with Dr Vandenberg's chapter on the magnetic properties also describe the interesting and significant intercalation mechanisms whereby a wide range of organic compounds and alkali metals may be incorporated in the lattice. This provides an additional parameter for varying the properties of these materials and may yet be seen to provide eventual possible applications of layer compounds. The arsenic chalcogenides have been extensively studied for their photoconduc tive properties and Dr Zallen and Dr Blossey have written a useful and extensive review of this subject. These particular materials have analogous amorphous or glassy structures and a comparison is made with this equally rapidly growing field of research. The transport properties have been reviewed from both the semiconducting point of view (Dr Fivaz and Dr Schmid) and the metallic properties (Dr Huntley and Professor Frindt). These show quite clearly the increasing understanding we now have of the electrical properties of these materials. In the preparation of a book of this kind there is inevitably a time lag before publication and in what has now become a rapidly expanding field of research much new data is continually becoming available. However, the extensive data provided by the various authors should give the necessary platform and informa tion source for workers in this field. VIII PREFACE I would like to thank the authors for their co-operation and forbearance in the preparation of this volume, and to Professor E. Mooser, the General Editor of this series of volumes, for his encouragement and invaluable advice. I am also indebted to Dr A. B. Yoffe for his helpful suggestions and discussions in the initial composition of this volume. Criticisms due to shortcomings or omissions in the preparation of this volume should be levelled at the editor alone, but with recent developments in this rapidly expanding field there is much scope for further contributions to future volumes in this series. Brighton Polytechnic, England DR P. A. LEE OPTICAL PROPERTIES OF LAYER COMPOUNDS B. L. EVANS Physics Department, University of Reading, England 1. INTRODUCTION 2 2. INTERBAND ABSORPTION THEORY 3 2.1 Direct Interband Transitions 3 2.2 Indirect Interhand Transitions 13 3. EXCITON THEORY OF ABSORPTION 14 3.1 Delocalized (Wannier) Excitons 15 3.2 Delocalized (Mo) Excitons: Optical Selection Rules 20 3.3 Delocalized Hyperbolic (Mlo M2) Excitons 23 3.4 Exciton Effects at an M3 Critical Point 25 3.5 Intermediate Excitons 25 3.6 Indirect Exciton Transitions 26 3.7 Exciton Line Broadening 27 4. FREE CARRIER ABSORPTION 28 4.1 Classical Model 29 4.2 Electron Energy Band Model 29 5. THE EFFECT OF AN APPLIED ELECTRIC FIELD ON THE CRYSTAL DIELECTRIC FUNCTION 30 5.1 Effective Mass Approximation (EMA) 30 5.2 Forbidden Interband Transitions 36 5.3 Indirect Transitions 37 5.4 Excitonic Transitions 38 5.5 Symmetry Analysis of Electro Reflectance Spectra 41 6. THE EFFECT OF AN APPLIED MAGNETIC FIELD ON THE CRYSTAL DIELECTRIC FUNCTION 41 6.1 Simple Energy Bands 42 6.2 Complex Energy Bands 43 6.3 Delocalized Excitons in a Magnetic Field 43 6.3.1 Parabolic (Mo) Excitons 43 6.3.2 Hyperbolic Excitons 45 6.4 Intra and Interband Magneto Absorption in Semiconductors 47 6.5 Exciton Absorption in a Magnetic Field 49 6.5.1 Parabolic Excitons 49 6.5.2 Hyperbolic Excitons 51 7. COMBINED ELECTRIC AND MAGNETIC FIELDS 51 51 7.1 Semiconductor Having Simple Energy Bands 7.2 Semiconductors Having Compiex Energy Bands 52 52 7.3 Indirect Transitions 53 7.4 Exciton Transitions 8. STRESS MODULATED SPECTRA 9. THE EFFECT OF TEMPERATURE ON THE CRYSTAL DIELECTRIC FUNCTION 54 54 9.1 Temperature Modulated Indirect Transition Spectra 9.2 Temperature Modulated Direct Transition Spectra 55 9.3 Temperature Modulated Plasma Resonance Spectra 56 P. A. Lee (ed.), Optical and Electrical Properties, 1-144. All Rights Reserved. Copyright © 1976 by D. Reidel Publishing Company, Dordrecht-Holland. 2 B. L. EVANS 10. THE MEASURED OPTICAL PROPERTIES OF LAYER COMPOUNDS 58 10.1 Group II Dihalides 58 10.2 Group IV Halides ·64 10.3 Group V Halides 70 lOA Transition Metal Halides 73 10.5 Group III Chalcogenides 76 10.6 Group IV Dichalcogenides 87 10.7 Group V Chalcogenides 90 10.8 Transition Metal Dichalcogenides 103 10.9 Graphite 131 REFERENCES 134 143 ACKNOWLEDGEMENTS 1. Introduction This chapter is primarily concerned with the ways in which optical absorption/reflection measurements can give information about the electron energy band structure of layer crystals. Infra-red measurements of the atomic vibration spectra are given at the end of the chapter. Layer crystals, as the name implies, are built up from crystalline layers stacked in a regularly repeating sequence. The layer thickness, defining a unit cell dimension, is typically 10 A whereas the lateral dimension of the layer are those of the crystal. Two limiting cases can be envisaged. (1) The bonding between the layers is comparable with the intra layer bonding resulting in an anisotropic 'three dimensional' crystal. (2) The interlayer bonding is comparatively weak, in this case the properties of the crystal are those of the individual layer. In practice the interlayer bonding is such that the two dimensional model is never strictly valid although some features of this model have been employed to describe the properties of a few types of layer crystal. One important consequence of the layer· like nature is that many of these crystals show interlayer cleavage. As a result it is possible, by repeated cleaving using transparent adhesive tape, to prepare very thin crystals on which optical transmission measurements can be made even in the intrinsic absorption region. For the same reason these cleaved crystal surfaces are optically flat with the result that the normal incidence transmissivity and reflectivity of a crystal slice have the theoretical values predicted from the measured bulk crystal dielectric constant [1]. An exception occurs in the case of very thin crystals where surface effects modify the crystal dielectric constant [2]. In principle the one-electron energy band structure of a crystal is established by matching the calculated joint density of states, lev, with the measured absorption spectrum of the crystal. Singularities in the joint density of states at critical points, see Section 2, give rise to a characteristic structure which, when identified in the measured absorption spectrum, allow the specific critical point transition energies to be determined. In practice some degree of electron-hole interaction exists which not only introduces an additional exciton absorption but also modifies the interband absorption structure, Section 3, so that direct identification of the OPTICAL PROPERTIES OF LAYER COMPOUNDS 3 relevant critical point transition energy is impossible. Further information about the critical point type is gained from electric, magnetic and stress field measure ments, Sections 4, 5, 6 and 7. 2. Interband Absorption Theory This resume of intrinsic absorption processes begins with the expression [3] for the transition probability per unit time Wml if the absorbed incident radiation is monochromatic and transitions can occur to any of a group of closely spaced or continuously distributed final states m Wml = 2h7T p(Em) IH~,12 (1) p(E",) is the density of final states (energies approx. Em) H~" as derived by first order perturbation theory, is given by J * H~l = -ieh I/Jm exp (iq ·r)A· VI/Jl dT (2) me where A(r, t)=Aoexp[i(q·r-wt)]+ee (3) is the vector potential representation of the electromagnetic field and I/J" I/Jm are the initial and final state wave functions. The initial state may be a discrete state or one of a continuous range of states. 2.1. DIRECT INTERBAND TRANSITIONS Equations (1-3) can be applied to semiconductors and insulators having a full valence band (v.b) and empty conduction band (c.b) since such a system conforms to the requirement that there is a continuous range of final (empty c.b) states available. The wave function I/Juk,(r) of a v.b state can be written (4) where N is the number of unit cells in crystal volume V and uVkl(r) is a Bloch function. Substituting (4) and a similar expression for the c.b wave function I/Jck (r) 2 in (2) gives (5) where, because of the cell periodicity of UVk" Uck, the integral has been replaced by a sum over the N unit cells of the crystal, R is a lattice vector determining the j jth cell. The summation in (5) is zero unless kl - k2 +q = K, a reciprocal lattice vector, or, on the reduced zone scheme (6)