Table Of ContentExcitation Energy
Transfer Processes in
Condensed Matter
Theory and Applications
PHYSICS OF SOLIDS AND LIQUIDS
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Excitation Energy
Transfer Processes in
Condensed Matter
Theory and Applications
Jai Singh
Northern Territory University
Darwin, Northern Territory, Australia
Springer Science+Business Media, LLC
Library of Congress Cataloging-in-Publication Data
On file
ISBN 978-1-4899-0998-5 ISBN 978-1-4899-0996-1 (eBook)
DOI 10.1007/978-1-4899-0996-1
© 1994 Springer Science+Business Media New York
Orgiginally published by Plenum Press, New York in 1994
Softcover reprint of the hardcover1 st edition 1994
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
To My Family
Preface
The theory of excitons was first put forward by Frenkel more than
half a century ago, and the subsequent pioneering developments
of Peierls, Wannier, and Mott followed soon afterward. Since then
there have been tremendous advances in the excitonic spectroscopy
of condensed matter both experimentally as well as theoretically.
The last two decades particularly have seen remarkable develop
ments in excitonic research in fundamental and applied spheres.
On the fundamental side, interest has been generated in the
areas of dynamics of excitons, such as recombination kinetics, exci
tonic polarons, self-trapping, polaritons, energy transport pro
cesses in crystalline, disordered and charge transfer solids, excitonic
luminescence, superradiance, and biexcitons and excitonic con
densation. On the applied side, developments have been in the
areas of femtosecond spectroscopy leading to the understanding
of excitons in ID, 2D, and 3D (or even OD) systems; excitonic
processes in heterojunction or quantum-well-structure solids,
superlattices (which have numerous industrial applications), and
excitonic processes in device applications and high-T materials.
c
There have also been significant developments in nonlinearity,
bistability and solitons.
Some topics in the applied research areas noted above are new
and still developing. It is therefore quite timely and desirable to
produce a volume with updated theory and its applications in the
area of excitonic research.
The aim of this book is to present a unified approach to theo
retical developments in the excitation energy transfer processes in
condensed matter. Earlier volumes published on excitons, such as
those by Knox, Davydov, and Craig and Walmsley, cover the initial
independent developments in excitonic processes. A more recent
book by Veta, Kanzaki, Kobayashi, Toyozawa, and Hanamura
vii
viii Preface
entitled Excitonic Processes in Solids is an extensive source of exci
tonic properties in various solids. The present book follows a
unified approach to develop an advanced theory of both the Wan
nier and the Frenkel excitonic processes, including the new topics
of exciton dynamics, laser sputtering, and polymer ablation.
Chapters 1 and 2 dealing with a unified basic theory of Frenkel
and Wannier excitons and their interaction with phonons will
acquaint readers with most of the theoretical approaches used in
condensed matter theory to the problem of the excited state
employing the method of second quantization. Chapters 3 and 4
deal with the theory of polarons and excitonic polarons, and self
trapping, respectively. In addition to presenting both polarons and
self-trapping through a unified approach, both processes are
described for various kinds of electron-phonon and exciton
phonon interactions; and the application of theory to experiment
is also included. Chapter 5 reviews the theory of the various exciton
recombination and dissociation reactions observed in many solids.
Chapter 6 offers a microscopic approach to understand the
mechanism of laser sputtering in semiconductors and polymer
ablation.
It is expected that this book can provide a deeper and
advanced understanding of the electronic properties of the excited
state in crystalline solids. Although it will be useful to anyone
working on condensed matter, graduate students and researchers
in the field are expected to benefit most.
I have a long list of colleagues, co-workers, and friends whose
encouragement and support have helped in the completion of this
volume. In particular I would like to acknowledge support from
Lisa Bernstein, Christian von de Broeck, David Brown, M.
Georgiev, Choy Heng Lai, Katja Lindenberg, Leonardo N. Itoh,
A. Matsui, Samir Raut, Michael Schreiber, Linda Seitz, A. Thila
gam, and Furong Zhu. I would also like to thank Eike Burningham
for typing the manuscript with great patience over a long period
of time. Finally, I would like to acknowledge the patience and
understanding of my wife, Tara, throughout the course of prep ara
tion of the manuscript.
Jai Singh
Darwin
Contents
Chapter 1
Theory of Excitons
1.1. Introduction..................................... 1
1.2. Quantum Approaches to Crystalline Solids .......... 2
1.2.1. Bloch Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.2. Tight-Binding Functions. . . . . . . . . . . . . . . . . . . . . 6
1.3. Wannier Excitons ................................ 7
1.3.1. The Hamiltonian in the Second Quantization. . . 8
1.3.2. Energy Eigenvalues and Eigenfunctions of a
Wannier Exciton ........................... 12
1.3.3. Determination of Coefficients C~(JJ, K - f/) ..... 28
1.3.4. The Hamiltonian for Wannier Excitons . . . . . . . . 28
1.3.5. Summary.................................. 30
1.4. Frenkel Excitons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
1.4.1. Eigenvector of Frenkel Excitons . . . . . . . . . . . . . . 32
1.4.2. Energy of a Frenkel Exciton ................. 34
1.4.3. An Alternative Expression for the Energy
of a Frenkel Exciton . . . . . . . . . . . . . . . . . . . . . . . . 39
1.4.4. The Frenkel Exciton Hamiltonian. . . . . . . . . . . . . 40
1.5. Comparative Comments on Wannier and Frenkel
Excitons ........................................ 41
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Chapter 2
Exciton-Phonon Interactions
2.1. Introduction..................................... 47
2.2. The Wannier Exciton-Phonon Interaction. . . . . . . . . . . 48
2.3. The Frenkel Exciton-Phonon Interaction. . . . . . . . . . . . 52
2.4. The Exciton-Phonon Interaction in Polar Crystals . . . . 57
ix
x Contents
2.5. The Exciton-Phonon Interaction due to the
Deformation Potential ............................ 62
2.5.1. The Deformation Potential Wannier Exciton-
Phonon Interaction ....... . . . . . . . . . . . . . . . . . . 64
2.5.2. The Deformation Potential Frenkel Exciton-
Phonon Interaction .. . . . . . . . . . . . . . . . . . . . . . . . 65
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Chapter 3
Polarons and Excitonic Polarons
3.1. Introduction..................................... 69
3.2. Energy of Polarons in Polar Crystals. . . . . . . . . . . . . . . . 71
3.3. Polarons in Nonpolar Crystals. . . . . . . . . . . . . . . . . . . . . 78
3.3.1. Energy of Acoustic Polarons in Nonpolar
Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.3.2. Energy of Optical Polarons in Nonpolar
Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.4. Polaron States Arising from the Deformation Potential 86
3.5. An Alternative Approach to the Theory of Polarons .., 87
3.6. Wannier Excitonic Polarons ...... ,................ 93
3.7. Frenkel Excitonic Polarons ........................ 97
3.8. Alternative Approximate Method of Diagonalization .. 102
3.9. Energy of a Frenkel Excitonic Polaron. . . . . . . . . . . . .. 107
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 110
Chapter 4
Self-Trapping
4.1. Introduction..................................... 111
4.2. Electron Self-Trapping . . . . . . . . . . . . . . . . . . . . . . . . . . .. 113
4.2.1. The Weak Coupling Limit (Polaron State) . . . .. 119
4.2.2. The Strong Coupling Limit (Localized State) . .. 120
4.2.3. The Intermediate Coupling Limit. . . . . . . . . . . .. 122
4.2.4. The Coupling Coefficient g . . . . . . . . . . . . . . . . . .. 134
4.3. Exciton Self-Trapping. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 135
4.3.1. Self-Trapping of Frenkel Excitons ............ 138
4.3.2. Self-Trapping of Wannier Excitons . . . . . . . . . . .. 148
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 150
