Disordered Solids structures and Processes ETTORE MAJORANA INTERNATIONAL SCIENCE SERIES Series Editor: Antonino Zichichi European Physical Society Geneva, Switzerland (PHYSICAL SCIENCES) Recent volumes in the series: Volume 36 NEW TECHNIQUES FOR FUTURE ACCELERATORS II: RF and Microwave Systems Edited by M. Puglisi, S. Stipcich, and G. Torelli Volume 37 SPECTROSCOPY OF LIGHT AND HEAVY QUARKS Edited by Ugo Gastaldi, Robert Klapisch, and Frank Close Volume 38 MONTE CARLO TRANSPORT OF ELECTRONS AND PHOTONS Edited by Theodore M. Jenkins, Walter R. Nelson, and Alessandro Rindi Volume 39 NEW ASPECTS OF HIGH-ENERGY PROTON-PROTON COLLISIONS Edited by A. Ali Volume 40 DATA ANALYSIS IN ASTRONOMY III Edited by V. Oi Gesli, L. Scarsi, P. Crane, J. H. Friedman, S. Levialdi, and M. C. Maccarone Volume 41 PROGRESS IN MICROEMULSIONS Edited by S. Martellucci and A. N. Chester Volume 42 DIGITAL SEISMOLOGY AND FINE MODELING OF THE LITHOSPHERE Edited by R. Cassinis, G. Nolet, and G. F. Panza Volume 43 NONSMOOTH OPTIMIZATION AND RELATED TOPICS Edited by F. H. Clarke, V. F. Oem'yanov, and F. Giannessi Volume 44 HEAVY FLAVOURS AND HIGH·ENERGY COLLISIONS IN THE 1-100 TeV RANGE Edited by A. Ali and L. Cifarelli Volume45 FRACTALS' PHYSICAL ORIGIN AND PROPERTIES Edited by Luciano Pietronero Volume 46 DISORDERED SOLIDS: Structures and Processes Edited by Baldassare Oi Bartolo A Continuation Order Plan is available for this series. A continuation order will bring delivery of each new volume immediately upon publication. Volumes are billed only upon actual shipment. For further information please contact the publisher. Disordered Solids structures and Processes Edited by Baldassare Di Bartolo Boston College Chestnut Hill, Massachusetts Assltant Editors Gonul Ozen and John M. Collins Boston College Chestnut Hill, Massachusetts Plenum Press • New York and london Library of Congress Catalog1ng-1n-Publlcatlon Data Disordered solids: structures and processes / edited by Baldassare Di Bartolo. p. cm. -- (Ettore Majorana international science series. Physical sciences; v. 46) Includes bibliographical references. ISBN-13: 978-1-4684-5477-2 e-ISBN-13: 978-1-4684-5475-8 DOl: 10.1007/978-1-4684-5475-8 1. Order-disorder models. 2. Solids--Optical properties. 3. Semiconductors--Optical properties. 4. Glass--Optical properties. I. Di Bartolo, Baldassare. II. Series. OC173.4.073D56 1990 530.4' 1--dc20 89-49260 CIP Proceedings of a course on Disordered Solids: Structures and Processes, held June 15-29, 1987, in Erice, Sicily, Italy © 1989 Plenum Press, New York Softcover reprint of the hardcover 1s t edition 1 989 A Division of Plenum Publishing Corporation 233 Spring Street, New York, N.Y. 10013 All rights reserved No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher "Has science promised happiness? I do not think so. It has promised the truth, and the question is to know if with truth we can achieve happiness." Emile Zola (Discourse to the students of Paris, 18 May, 1893) v PREFACE This book presents an account of the course "Disordered Solids: Structures and Processes" held in Erice, Italy, from June 15 to 29, 1987. This meeting was organized by the International School of Atomic and Molecular Spectroscopy of the "Ettore Majorana" Centre for Scientific Culture. The objective of this course was to present the advances in physical modelling, mathematical formalism and experimental techniques relevant to the interpretation of the structures of disordered solids and of the physical processes occurring therein. Traditional solid-state physics treats solids as perfect crystals and takes great advantage of their symmetry, by means of such mathematical formalisms as the reciprocal lattice, the Brillouin zone, and the powerful tools of group theory. Even if in reality no solid is a perfect crystal, this theoretical approach has been of great usefulness in describing solids: deviations from perfect order have been treated as perturbations of the ideal model. A new situation arises with truly disordered solids where any vestige of long range order has disappeared. The basic problem is that of describing these systems and gaining a scientific understanding of their physical properties without the mathematical formalism of traditional solid state physics. While some of the old approaches may occasionally remain valid (e.g. chemical bonding approach for amorphous solids), the old ways will not do. Disorder is not a perturbation: with disorder, something basically new may be expected to appear. The challenge to theoretical physicists and to those who have to formulate and present these problems in didactical terms is evident: we must enlarge our view of the Solid State in order to encompass in its treatment disordered as well as periodic structures. This course was a response to such a challenge. A total of 63 participants came from 40 laboratories and 17 different countries (Austria, Bangladesh, F.R. of Germany, France, India, Israel, Italy, Morocco, The Netherlands, P.R. of China, Poland, Portugal, Spain, Turkey, United Kingdom, U.S.A. and U.S.S.R.). The secretaries of the course were Dr. J. Collins for the scientific aspects and Mr. J. ,Di Bartolo for the administrative aspects of the meeting. Forty-seven lectures divided into 11 series were given. In addition 7 (one- or two-hour) "long" seminars and 19 "short" seminars were pre sented. Nine problem sessions were organized; the purpose of these ses sions was to create a closer interaction between participants and lectures. During a problem session a lecturer did not introduce any new material, but vii explained in greater detail some points of the theory already presented, answered more questions, presented examples, etc. A topic of general and great interest to physicists was also treated in a special session: "Elementary Particles: Discoveries and'Perspectives." Several participants presented overviews of the research projects of their laboratories and universities. Two round table discussions were held. The first round-table dis cussion took place the third day of the meeting and had as subjects an evaluation of the work done in the first days of the course and the consideration of suggestions and proposals regarding the format of the lectures, the level of the presentations, etc. The second round-table discussion was held at the end of the course: the attendees had the opportunity of evaluating the work done during the entire meeting and to discuss various proposals for the next course of the International School of Atomic and Molecular Spectroscopy. During the final session A. Ritter and L. McNeil presented a summary of the meeting and identified the major themes which appeared in various degrees throughout the course. I wish to express my sincere gratitude to Drs. Gabriele and Savalli and to all the personnel of the "Ettore Majorana" Centre who contributed so much to create a congenial atmosphere for our meeting. I wish to acknowledge the sponsorship of the meeting by the Italian Ministry of Public Education, the Italian Ministry of Scientific and Technological Research, the Italian National Research Council, the Sicilian Regional Government, the European Physical Society and the Department of Physics of Boston College. I would like to thank the members of the organlzlng committee (Professors Klingshirn and Silbey), the secretaries of the course (Dr. John Collins and Mr. John Di Bartolo), Ms. Gonul Ozen, Dr. Guzin Armagan and Mr. Daniel Di Bartolo who helped a lot with various aspects of the meeting. A warm "thank you" to Antonino La Francesca, "Nino"! I would like to thank Ms. Patricia Vann of the Plenum Publishing Corporation for her encouragement and assistance during the preparation of this book. I wish to acknowledge the very patient and careful work done by the assistant editors of this book, Gonul Ozen and John Collins. It was a privilege to direct this school and to meet so many fine people who came from many distant places to work together in the very friendly ambience provided by the Ettore Majorana Centre. It is always a pleasure to return to my native Sicily, and to enjoy the warm hospitality of Erice. This is a magic place, made even more pleasurable by the scientific encounters that occur in the congenial atmosphere of this ancient village. We always long for these events and we look forward to many meetings in years to come. B. Di Bartolo Editor and Director of the International School of Atomic and Molecular Spectroscopy of the Ettore Majorana Centre Erice, June 1987 viii CONTENTS THE EVOLVING NOTION OF ORDER 1 G. Careri ABSTRACT --------------------------------------------------------- 1 I. INTRODUCTION ---------------------------------------------- 1 II. ORDER AND DISORDER IN MATTER ------------------------------ 2 III. CONCLUDING REMARKS 3 REFERENCES ------------------------------------------------------- 4 PROBABILISTIC METHODS IN PHYSICS --------------------------------- 9 N.G. van Kampen ABSTRACT --------------------------------------------------------- 9 I. PROBABILITY THEORY ---------------------------------------- 10 II. STOCHASTIC PROCESSES -------------------------------------- 14 III. MARKOV PROCESSES ------------------------------------------ 16 IV. THE MASTER EQUATION --------------------------------------- 18 V. FOKKER-PLANCK AND LANGEVIN -------------------------------- 20 VI. THE LANGEVIN APPROACH ------------------------------------- ,21 VII. EXPANSION OF THE MASTER EQUATION -------------------------- 23 VIII. HOPPING IN AN INHOMOGENEOUS MEDIUM ------------------------ 26 REFERENCES ------------------------------------------------------- 28 DYNAMICAL PROCESSES IN DISORDERED SYSTEMS ------------------------ 31 R. Silbey ABSTRACT --------------------------------------------------------- 31 I. INTRODUCTION ---------------------------------------------- 31 II. FORSTER TRANSFER ------------------------------------------ 32 III,. EXCITATION OR PARTICLE TRANSPORT -------------------------- 34 ix III.A. Formal Manipulations ------------------------------ 34 III.B. Effective Medium Approximation -------------------- 38 III.C. CTRW Approximations ------------------------------- 39 III.D. Anomalous Diffusion and Trapping ------------------ 41 IV. OPTICAL LINE SHAPES IN DISORDERED SOLIDS 43 IV.A. Optical Line Shape: Weak Disorder ------------------ 44 IV.B. Homogeneous Line Widths of Molecular Transitions in Glasses ----------------------------------------- 46 V. FRACTALS AS MODELS OF DISORDERED SYSTEMS ------------------ 47 V.A. Description of Fractal Structure ------------------- 47 V.B. Transport on Fractals ------------------------------ 50 VI. CONCLUSIONS ----------------------------------------------- 51 ACKNOWLEDGEMENTS ------------------------------------------------- 52 REFERENCES ------------------------------------------------------- 52 SHARP SPECTRAL LINES OF LUMINESCENT CENTERS IN SOLIDS ------------ 55 B. Di Bartolo ABSTRACT --------------------------------------------------------- 55 I. SPECTROSCOPY OF LUMINESCENT SOLIDS ------------------------ 56 I.A. Systems and Interactions --------------------------- 56 I.B. Basic Concepts of Spectroscopy --------------------- 56 1. Classical Bound and Radiating Electron --------- 56 2. Quantum Mechanical Radiative Decay ------------- 58 3. Absorption and Induced Emission ---------------- 61 4. Absorption Coefficient and Absorption Cross Section ---------------------------------------- 63 I.C. Saturation ----------------------------------------- 64 I.D. Line Broadening ------------------------------------ 69 I.E. Lifetime-Broadening Mechanism. Lorentzian Lineshape ------------------------------------------ 70 I.F. Time-Independent Random Perturbations. Gaussian Lineshape ------------------------------------------ 74 I.G. Superposition of Probability Densities: Lorentzian, Guassian, and Voigt Lineshapes --------------------- 75 I.H. Fluorescence Line Narrowing ------------------------ 79 x II. SPECTRAL LINES OF LUMINESCENT CENTERS IN ORDERED SOLIDS --- 82 II.A. Systems -------------------------------------------- 82 II.B. Vibrations of Solids ------------------------------- 82 II.C. Eigenstates and Eigenfunctions of Vibrations ------- 84 II.D. The Ion-Vibration Interaction ---------------------- 87 II.E. Thermal Line Broadening ---------------------------- 90 II.F. Thermal Line Shift 94 II.G. The Optical Analog of the Thermal Line Shift ------- 98 II.H. About Sharp Lines: Facts and Examples -------------- 100 REFERENCES ------------------------------------------------------- 108 LOCALIZATION AND PERCOLATION IN ALLOY SEMICONDUCTORS ------------- 111 C. Klingshirn ABSTRACT 111 I. A PEDESTRIAN APPROACH TO LOCALIZATION AND PERCOLATION ----- 111 I.A. Simple Classical Aspects --------------------------- 112 I.B. What is Different in Quantum Mechanics? ------------ 113 I.C. Concepts of Localization --------------------------- 115 1. Weak Localization ------------------------------ 115 2. Anderson Localization -------------------------- 117 3. Percolation ------------------------------------ 122 4. Scaling Theory --------------------------------- 123 II. OPTICAL PROPERTIES OF (ALMOST) PERFECT SEMICONDUCTORS ----- 125 II.A. Bank Structure and Excitons ------------------------ 126 II.B. Some Optical Properties of Semiconductors ---------- 127 II.C. Some Proofs for Thermal Exciton Motion ------------- 128 III. WHAT CAN WE LEARN FROM OPTICAL SPECTROSCOPY ABOUT LOCALIZATION IN ALLOY SEMICONDUCTORS? --------------------- 130 III.A. Some Properties of Alloy Semiconductors ------------ 131 III.B. A Review of the Optical Properties ----------------- 131 III.C. The Concept of Alloy Disorder ---------------------- 132 III.D. Experimental Proofs for the Existence of Localized Excitons in CdS1_xSex ------------------------------ 136 1. Site Selective Spectroscopy -------------------- 137 xi