Linear and Nonlinear Electron Transport in Solids

Transcription

1 Linear and Nonlinear Electron Transport in Solids

2 NATO ADVANCED STUDY INSTITUTES SERIES A series of edited volumes comprising multifaceted studies of contemporary scientific issues by some of the best scientific minds in the world, assembled in cooperation with NATO Scientific Affairs Division. Series B: Physics RECENT VOLUMES IN THIS SERIES Volume 10 - Progress in Electro-Optics edited by Ezio Camatini Volume 11 - Volume 12 - Fluctuations, Instabilities, and Phase Transitions edited by Tormod Riste Spectroscopy of the Excited State edited by Baldassare Di Bartolo Volume 13- Weak and Electromagnetic Interactions at High Energies (Parts A and B) edited by Maurice Levy, Jean-Louis Basdevant, David Speiser, and Raymond Gastmans Volume 14- Physics of Nonmetallic Thin Films edited by C.H.S. Dupuy and A. Cachard Volume 15- Nuclear and Particle Physics at Intermediate Energies edited by J. B. Warren Volume 16- Electronic Structure and Reactivity of Metal Surfaces edited by E. G. Derouane and A. A. Lucas Volume 17- Linear and Nonlinear Electron Transport in Solids edited by 1. T. Devreese and V. E. van Doren Volume 18- Photoionization and Other Probes of Many-Electron Interactions edited by F. 1. Wuilleumier Volume 19 - Point Defects and Their Structure in Nonmetallic Solids edited by B. Henderson and A. E. Hughes Volume 20- Physics of Structurally Disordered Solids Edited by Shashanka S. Mitra The series is published by an international board of publishers in conjunction with NATO Scientific Affairs Division A Life Sciences Plenum Publishing Corporation B Physics New York and London c Mathematical and D. Reidel Pub1ishing Company Physical Sciences Dordrecht and Boston D Behavioral and Sijthoff International Publishing Company Social Sciences Leiden E Applied Sciences Noordhoff International Publishing Leiden

3 Linear and Nonlinear Electron Transport in Solids Edited by 1. T. Devreese State University of Antwerp ( R UCA) and U!A Antwerp, Belgium and V. E. van Doren State University of Antwerp (RUCA) Antwerp, Belgium SPRINGER SCIENCE+BUSINESS MEDIA, LLC

4 Library of Congress Cataloging in Publication Data Nato Advanced Study Institute on Linear and Nonlinear Electronic Transport in Solids, Rijksuniversitair Centrum Antwerpen, Linear and nonlinear electron transport in solids. (NATO advanced study institutes series: Series B, physics; v. 17) Includes indexes. 1. Electron transport-addresses, essays, lectures. 2. Semiconductors-Addresses, essays, lectures. I. Devreese, JozefT. Il. Doren, V. E. van. III. Title. IV. Series. QC176.8.E4N ISBN ISBN (ebook) DOI / Lectures presented at the NATO Advance Study Institute on Linear and Nonlinear Electronic Transport in Solids held at the State University of Antwerp (RUCA), Antwerp, Belgium, July 21-August 2, Springer Science+Business Media New York Originally published by Plenum Press, New York in 1976 Ali 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

5 Preface The Advanced Study Institute on "Linear and Nonlinear Electronic Transport in Solids" was held at the Riiksuniversitair Centrum Antwerpen (R.U.C.A.) with its nice surroundings and excellent facilities, from July 21 till August 2, The Institute was sponsored by N.A.T.O. Co-sponsors were: Bell Telephone Mfg. Co. N. V. (Belgium), Esso Belgium N. V. (Belgium), Generale Bankmaatschappij (Belgium), Kredietbank (Belgium), Metallurgie Hoboken Overpelt N. V. (Belgium) and the National Science Foundation (USA). A total of 90 participants including the lecturers attended the Institute. In recent years several important developments took place in the understanding of the electronic conduction in solids. Purely phenomenological approaches are now complemented by basic theories which provide a more exact description of the transport properties. The experimental studies produced also better results and raised several questions which need further studies for interpretation. One of the aims of the summer school has been to develop a better understanding of the conduction problem both theoretically and experimentally, starting from an elementary level and proceeding to topics of increased complexity. In the main the summer school dealt with general theories of transport phenomena in solids and the study of electronic properties of metals and semiconductors. As far as the general theory is concerned, the Boltzmann equation, the relaxation time concept and the inverse transport coefficients approach have been developed; these constitute the basic tools of the various investigations. In the applications have been included a variety of topics covering the field of both crystalline and amorphous materials. The thermodynamical aspect of the electron gas in metals, of the electron-hole plasmas and of the charge carriers in liquid metals has been treated. The conductivity of small gap and disordered semiconductor~ was studied. The models of the polaron, and transv

6 PREFACE port by hopping, have been used for the evaluation of transport quantities, including linear and nonlinear phenomena over a wide range of fields. The transport properties of trans1t1on metal ion compounds, chalcogenide glasses and amorphous semiconductors were the main experimental results, presented together with their respective interpretations. In addition to the lectures a variety of seminars, covering a wide range of topics, were given by members of the school which not only helped to supplement the programme, but also contributed to a more active participation. The present volume covers the proceedings of the Summer School which are contained under the headings: General Theory, Metals and Semiconductors, Amorphous Semiconductors and Seminars. I should like to thank the lecturers for their collaboration in preparing the manuscripts in time which enabled the participants to attend the lectures comfortably and more beneficially. The invited speaker for the opening session of the Institute was Professor Grosse of Physikalisches Institut der Rheinisch Westfalischen Technischen Hochschule Aachen, whom I should like, taking this opportunity, to thank from this position once again. My thanks are also due to the members of the International Advisory Committee: Professors J. Bok, M. H. Cohen, J. Friedel, J. Hodby, S. Lundqvist, N. H. March, N. Mott, K. S. Singwi, and K. K. Thornber. It gives me great pleasure to thank the Rector of the Rijksuniversitair Centrum Antwerpen (R.U.C.A.), Professor Dr. L. Massart, for his warm and continuous interest in the Institute, and for making available so promptly and effectively the university facilities. I should also like to thank Mr. A. Drubbel, Chief Administrator of the University, and through him his staff, for their coordinated effort which so greatly contributed to the success of the Institute. Finally, I wish to thank Drs. V. Van Doren and J. Van Royen, and Miss H. Evans for their dedication in carrying out the enormous secretarial task which enabled the smooth operation of the Summer School. My thanks are also due to Dr. F. Brosens, Dr. L. Lemmens, Drs. P. Van Camp and J. Van Royen for reading the proofs, and Miss H. Evans for preparing the author index. March 1976 Jozef T. Devreese Professor of Theoretical Physics, University of Antwerp (R.U.C.A. and U.I.A.) Director of the Advanced Study Institute

7 Contents Part I GENERAL THEORY Linear and Nonlinear Response Theory with Applications... 3 D. Langreth Conductivity via Nonequilibrium Statistical Physics G. J. Papadopoulos Aspects of Linear and Nonlinear Electronic Conduction in Dissipative Media K. K. Thornber On the Electronic Transport in Polar Solids J. T. Devreese and R. Evrard Theory and Application of Inverse Transport Coefficients N. H. March Part II METALS AND SEMICONDUCTORS Interacting Electron Gas in Metals K. S. Singwi Effects of Correlations on the Conductivity of Electron-Hole Plasmas..... N. Tzoar and P. M. Platzman Aspects of Transport in Liquid Metals M. P. Tosi vii

8 viii Structural Effects on Superconductivity K. L. Ngai Classical Transport in Small-Gap Semiconductors W. Zawadzki CONTENTS Part III AMORPHOUS SEMICONDUCTORS Solved and Unsolved Problems for Non-Crystalline Materials N. F. Mott Theory of Hopping Conductivity in Disordered Semiconductors P. N. Butcher Hopping Transport in High Electric Fields I. G. Austin The Formation and Motion of Small Polarons D. Emin Electronic Properties of Amorphous Semiconductors P. Nagels 435 Part IV SEMINARS Functional Integrals. G. J. Papadopoulos Some Recent Findings in Noise Theory and Their Implications for Transport Processes K. K. Thornber Low Frequency Fluctuations in Electronic Transport Phenomena P. Handel Electron-Hole Liquid Condensation in Semiconductors T. L. Reinecke and S. C. Ying

9 CONTENTS Thermodynamic and Transport Properties in the Hubbard Model E. N. Economou Optical Determination of Hot Carrier Distribution Functions.... G. Bauer ix Part V SPECIAL SEMINAR Softons, Softarons, and Bisoftarons in Amorphous Solids..... E. N. Economou, K. L. Ngai, and T. L. Reinecke 595 List of Lecturers 613 Author Index Subject Index 625