Electronic Processes in Non-Crystalline Materials PDF
Preview Electronic Processes in Non-Crystalline Materials
THE INTERNATIONAL SERIES OF MONOGRAPHS ON PHYSICS GENERAL EDITORS W. MARSHALL D. H. WILKINSON A dangling bond in a random network simulating the structure of amorphous germanium or silicon. ELECTRONIC PROCESSES IN NON-CRYSTALLINE MATERIALS BY N. F. MOTT Emeritus Cavendish Professor of Physics in the University of Cambridge AND E. A. DAVIS Lecturer in Physics in the University of Cambridge SECOND EDITION CLARENDON PRESS • OXFORD OXFORD UNIVERSITY PRESS Great Clarendon Street, Oxford 0x2 6Dp Oxford University Press is a department of the University of Oxford. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide in Oxford New York Auckland Cape Town Dar es Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto With offices in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore South Korea Switzerland Thailand Turkey Ukraine Vietnam Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries Published in the United States by Oxford University Press Inc., New York © Oxford University Press 1971, 1979 The moral rights of the authors have been asserted Database right Oxford University Press (maker) First published 1971 Second Edition 1979 First published in paperback 2012 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this book in any other binding or cover and you must impose the same condition on any acquirer British Library Cataloguing in Publication Data Data available Library of Congress Cataloging in Publication Data Data available Printed in Great Britain on acid-free paper by Clays Ltd, St Ives plc ISBN 978-0-19-964533-6 (pbk) 13579108642 TO RUTH AND CHRISTINE This page intentionally left blank PREFACE TO SECOND EDITION IN THE seven years since we completed our first edition, there have been very substantial advances in our knowledge of non-crystalline materials based on experiment and in their theoretical interpretation, and we have therefore found it necessary to rewrite the greater part of this book. Many review articles now exist, and because of these and so as to keep the book within a reasonable size we have not attempted as full a review of the literature as we did in the first edition. Our purpose, however, remains the same: to present a theoretical framework and to relate it to the experimental material. Some of the outstanding advances since our first edition seem to us to be the following: the very detailed understanding of the electrical properties of glow-discharge-deposited silicon obtained notably at Dundee and Marburg, and in particular the realization that this material can be doped; experiments on conduction in an inversion layer at the interface between silicon and silicon oxide, which combined with numerical calculations of the minimum metallic conductivity in two dimensions provides strong evidence for the existence of this quantity; real-space calculations of the energy spectra of both electronic and vibrational states from model struc- tures, and increasing realization for chalcogenide and silicate glasses of the importance of the polaron concept and of the distortion produced by a trapped carrier, leading to Anderson's concept of a 'negative Hubbard U' and to detailed models of photoluminescence, states in the gap, and other properties of these materials. These are some highlights; many other advances may be of comparable importance Finally, it is a pleasure to thank many colleagues who have helped us in the writing of this book, Dr S. R. Elliott for reading the galley proofs, and Miss Shirley Fieldhouse for her invaluable work in the preparation of the bibliography. Cambridge N.F.M. August 1977 E.A.D. This page intentionally left blank PREFACE TO FIRST EDITION TEN YEARS ago our theoretical understanding of electrons in non-crys- talline materials was rudimentary. The classification of materials into metals, semiconductors, and insulators was based on band theory, and band theory starts from the assumption that the material is crystalline. According to band theory, an insulator is a material with an energy gap between the conduction and valence bands, and a transparent insulator is one in which the gap is greater than the quantum energy of visible light. Ordinary soda glass is an insulator and transparent; a gap seemed to exist but we did not know how to describe the gap. Even now we do not know how to calculate it, but the concepts that we have to use are fairly clear. A milestone in the development of the subject was Ziman's quantitative explanation of the electrical properties of liquid metals, put forward in 1960. This was a weak-interaction theory, the effect of each atom being treated as small. The success of this theory prompted investigations of what happens when the interaction is large, as it must be when an energy gap exists. The keys to our present understanding have been the principle of loffe and Regel (1960) that the mean free path cannot be less than the distance between atoms, and the concept of localization introduced by Anderson in his paper 'Absence of diffusion in certain random lattices', published in 1958. In a sense, our book is written around these two themes. We have built a theoretical edifice on them, and since mathematical rigour is anything but easy in this subject we have not hesitated to guess at the approximate solutions of problems that at present are unsolved. Our aim is to suggest models that can be compared with experiment. We have chosen the experimental material, too, with a view to comparing it with our theory and our conjectures. Thus we have given a rather full account of what is known in October 1970 about the electrical and optical properties of certain amorphous semiconductors, in particular silicon, germanium, chal- cogenide glasses, and selenium, which we think relevant. We have said much less about conduction in glasses containing transition-metal ions as they would in our view fit better into a book about polarons. Our chapter on impurity conduction is not meant to be exhaustive; we include it because impurity conduction is the most fully understood process of conduction in a random field. We have said rather little about the phenomenon of switching, fearing that anything we could-write would be out of date too quickly. Finally it is a pleasure to thank our many colleagues who are interested in non-crystalline materials and who have helped us to write this book. We
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