The Physics of the Two-Dimensional Electron Gas

444 Pages·1987·19.359 MB·English

by  Klaus von Klitzing (auth.), J. T. Devreese, F. M. Peeters (eds.)

The Physics of the
Two-Dimensional
Electron Gas
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Volume 157-The Physics of the Two-Dimensional Electron Gas
edited by J. T. Devreese and F. M. Peeters
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edited by P. Jena, B. K. Rao, and S. N. Khanna
Volume 159-Lattice Gauge Theory '86
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Sefles B: PhysIcs
The Physics of the
Two-Dimensional
Electron Gas
Edited by
J. T. Devreese
and
F. M. Peeters
University of Antwerp
Antwerp, Belgium
Plenum Press
New York and London
Published in cooperation with NATO Scientific Affairs Division
Proceedings of a NATO Advanced Study Institute on
The Physics of the Two-Dimensional Electron Gas,
held June 2-14, 1986,
in Oostduinkerke, Belgium
Library of Congress Cataloging in Publication Data
NATO Advanced Institute on the Physics of the Two-Dimensional Electron Gas
(1986: Oostduinkerke, Belgium)
The physics of two-dimensional electron gas.
(NATO ASI series. Series B, vol. 157)
"Proceedings of a NATO Advanced Study Institute on the Physics of the
Two-Dimensional Electron Gas, held June 2-14, 1966, in Oostduinkerke, Bel
gium"-T.p. verso.
"Published in cooperation with NATO Scientific Affairs Division."
Bibliography: p.
Includes index.
1. Electron gas-Congresses. 2. Energy-band theory of solids-Congresses.
3. Semiconductors-Congresses. 4. Hall effect-Congresses. 5. Electron
phonon interactions-Congresses. I. Devreese, J. T. (Jozef T.) II. Peeters, F. III.
North Atlantic Treaty Organization. Scientific Affairs Division. IV. Title. V. Ti
tle: Two-dimensional electron gas. VI. Series: NATO advanced science in
stitutes series. Series B, Physics; v. 157.
QC176.8.E4N38 1986 530.4'1 87-13983
ISBN-13: 978-1-4612-9061-2 e-ISBN-13: 978-1-4613-1907-8
001: 10.1007/978-1-4613-1907-8
© 1987 Plenum Press, New York
Softcover reprint of the hardcover 1s t edition 1987
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
PREFACE
The 1986 Advanced Study Institute on "The Physics of the two-Dimen
sional Electron Gas" took place at the Conference Centre liTer Helme", close
to Oostende (Belgium), from June 2 till 16, 1986.
We were motivated to organize this Advanced Study Institute in view
of the recent experimental and theoretical progress in the study of the
two-dimensional electron gas. An additional motivation was our own theore
tical interest in cyclotron resonance in two-dimensional electron systems
at our institute.
It is my pleasure to thank several instances and people who made this
Advanced Study Institute possible. First of all, the sponsor of the Advanced
Study Institute, the NATO Scientific Committee. Furthermore, the co
sponsors: Agfa Gevaert, Bell Telephone Mfg. Co. N.V., Burroughs Belgium.
Control Data. Digital Equipment Corporation, Esso Belgium. European
Research Office (USA). Kredietbank. National Science Foundation (USA).
Special thanks are due to the members of the Program Committee and
the members of the Organizing Committee.
I would also like to thank Mrs. H. Evans for typing assistance.
J.T. Devreese
Professor of Theoretical Physics
February 26, 1987
v
CONTENTS
THE INTEGER AND THE FRACTIONAL QUANTUM HALL EFFECT
The Quantum Hall Effect 1
K. von Klitzing
Theory of the Integer Quantum Hall Effect - an Introductory
Survey •••••••••••• 27
J. Hajdu
1. Klaus von Klitzing's discovery 27
2. The Hall effect ••.••••• 28
3. Quantum mechanics of an electron in a magnetic field 31
4. Different ways of calculating the Hall conductivity 33
5. Disordered systems 36
6. High field limit 39
7. The gauge argument 42
8. Topological approach 44
9. Scattering theoretical approach 47
10. Field theoretical approach 49
11. Conclusions 49
References 50
Experimental Aspects of the Fractional Quantum Hall Effect 51
G.S. Boebinger
1. Introduction •••••••• 51
2. Theoretical background • • . 56
3. Experimental configurations 60
4. Experimental results 66
5. Other experiments and conclusions 90
Acknowledgments 93
References • . • • • • • • 93
Interactions in 2D Electron Systems 97
P.M. Platzman
1. Some qualitative aspects of itinerant 2D systems 97
2. Excitations in the Fractional Quantum Hall Effect -
magneto-rotons • • • • • • • • • • • • • • • • • • • 108
3. Transport and impurity effects in the magneto-roton
picture 127
References • • • . • • . • . • • • • • • • • • • • • • 129
vii
ELECTRON-PHONON INTERACTION
Electron-Phonon Interaction in Two-Dimensional Systems:
Polaron Effects and Screening • • • • • ••••• • 131
J.T. Devreese and F.M. Peeters
Introduction • • • • • • • • • • • • • 131
1. The free polaron in two dimensions - singe particle
approximation • • • • • • • • •• •••••• 132
2. Many-particle problem in two dimensions - effect of
screening of the electron-phonon interaction • • • • • 138
3. The 2D polaron system subjected to a static magnetic
field . . . . . . . . . . . . . . . . . . . . . . . 145
References 153
Appendix A: Theory of the cyclotron resonance spectrum
of a polaron in two dimensions • • • • • • 155
Appendix B: Influence of many-body effects on the cyclotron
resonance mass of two-dimensional polarons with
application to GaAs-AIGaAs heterostructures 169
Hot Carrier Effects in Quasi-2D ~olar Semiconductors • • • • • 183
J. Shah
1. Introduction • • • • • • • • • • • • • • • • • 183
2. Basic concepts • • • • • • • • • • • • • • • 184
3. Electron-phonon interactions in 3D • • • • • 185
4. Theoretical investigations in quasi-2D systems • 197
5. Experimental investigations • • • • 203
6. S\1llDD8ry • • • • • • • • • • • • 217
Acknowledgments • • • • • • • • • • • • • • 218
References • • • • 218
Anomalous Current Oscillations in Semiconductor-Insulator
Semiconductor Structures and Related Devices • • • • • 227
J.P. Leburton
1. Introduction and historical background 227
2. Experiments • • • • • • 228
3. Theoretical models • • • • • • 236
4. Conclusions • • • • • • • • • • 254
Acknowledgments • • • • • • 255
References 255
BAND STRUCTURE
k.p Theory for Two-Dimensional Systems 259
R. Lassnig
1. Introduction ••••••• 259
2. Fundamentals - 3D theory • • 261
3. k.p theory for 2D systems 271
4. Heterostructures • • • • 274
5. Wave function matching 277
6. Variational solution • 278
7. Numerical results 280
8. Spin splitting • • • • • 282
9. Tunneling through semiconductor barriers • 284
Acknowledgments •••• 291
References •••••••••••••••• 291
Inversion Electrons in 1nSb in Crossed Electric and Magnetic
Fields 293
U. Merkt
1. Introduction 294
viii
2. Classical trajectories of inversion electrons in
crossed fields • • • . • • . • • • • . • • • • • 295
3. One-band model for crossed fields: energy levels and
transition probabilities . • • . . • • • • . • . 298
4. Experiments: diamagnetically shifted intersubband
resonance vs cyclotron resonance • • • • • • • • • • 311
5. Two-band model in crossed fields: analogy to relati-
vistic electrons • • . • • . • • • . . . • • • • • 320
6. Experiments: destruction of Landau quantization in
strong electric fields 333
Acknowledgments • 339
References • . • • • . . 339
Electric Properties of II-VI Compound Super lattices 341
J.M. Berroir and M. Voos
1. Introduction. • • • . • • . • • . . . 341
2. Band structure of bulk HgTe and CdTe • 345
3. Growth of II-VI compound super lattices 345
4. Magneto-optical investigations of HgTe-CdTe superl attices 347
5. Optical absorption studies • . • • • • . • • • 356
6. HgTe-CdTe superlattices as infrared materials 359
7. Some aspects of CdTe-Cd1_xMnxTe super lattices 360
8. Some prospects about Cdl_xMnxTe-Cdl_1MnyTe hetero-
structures • 360
9. Conclusion . 362
Acknowledgments • 363
References 363
SPECIAL TOPICS
Density of States of Two-Dimensional Systems in High Magnetic
Fields 365
E. Gornik
Abstract 365
1. Introduction 366
2. Specific heat 367
3. Magnetization 375
4. Activated resistivity 376
5. Magnetocapacitance • . • 381
6. Cyclotron resonance spectroscopy 383
7. Conclusions 390
Acknowledgments 391
References 391
Electrons on Liquid Helium 393
F.M. Peeters
1. Introduction .. 393
2. Surface state electrons on liquid helium 394
3. Wigner crystal 399
4. Self-trapping 406
Acknowledgments 419
References 419
Author index 421
Material Index 431
Subject Index • 433
*
THE QUANTUM HALL EFFECT
Klaus von Klitzing
Max-Planck Institut fur Festkorperforschung, Heisenberg
strasse I, Postfach 80 06 65, D-7000 Stuttgart 80, F.R.G.
Ladies and Gentlemen:
First of all thank you very much for the invitation and for the possi
bility to give this opening lecture at this meeting of the Advanced Study
Institute with the title "The Phys ics of the T"W'o
DiIIlensional Electron Gas".
Now this subject "The Two-Dimensional Electron Gas" has been a hot
topic in semiconductor physics for about twenty years and since 1975 we
have every two years an International Conference just with this title "The
Physics of Two-Dimensional Systems", but during the last three or four
years there has really been an explosion in this field. A large number of
publications, a large number of groups are now working in this field and
the reason is that this physics of two-dimensional systems is not only a
very interesting subject for basic research, there are also a lot of appli
cations and therefore a large number of industrial laboratories are inte
rested in this field. Today I will give you more or less an introduction.
It is very difficult to give a lecture for specialists and simultaneously
for non-specialists, so I will speak at the beginning a little bit about
the t"W'o - diIIlens ional systeIIls in general
and about some applications. After this I will give an introdu.ct
ion to the Qu.antu.JIl Hall Effect, including
some applications and at the end I will point out the problems
in connection with the question ho"W' to u.nderstand the
Qu.antu.IIl Hall Effect in detail and this will
be the subject of a large number of talks during this Conference. I am
quite sure that in the near future a large number of groups will work on
these two-dimensional systems and the quantized Hall effect is one reason
for this.
In Fig. 1 I list some typical structures which are related to two
dimensional systems. If you hear words like quantum wells, NIP! which
means differently doped semiconductors or HEMT; all these structures are
*
This text is ba~ed on a tape recording of the opening lecture by Prof.
K. von Klitzing.
2D-SYSTEMS:
- Quantum Wells
- NIPI
- HEMT, TEGFET, MODFET, SDHT
- Quantum Hall Device
tD-SYSTEMS:
- Quantum Well Wires
- Transport perpendicular to
quantum wells (tunneling
structures, superl attices, nipi, ... )
Fig. 1. Examples of two (20)- and one-dimensional (10) systems.
related to two-dimensional systems and 1 have already the title of the
next Conference for Professor Devreese: "One - d imens ional
systems". If you are going to smaller and smaller structures you
reach this situation where you have the one-dimensional systems, not
quantum wells but quantum wires or if you are discussing electronic trans
port for very thin layers: tunneling structures, superlattices and so on,
you have problems connected to one-dimensional systems'and this will be the
direction of future research.
Now, if you are speaking about two-dimensional systems, I think we
should have the followin8 picture in mind (see Fig. 2). You have electrons
confined within very narrow potential layers. If this potential layer is
Th' mk' ; ,
E = E;. kll=K• • ~y
El-Eo> kT, r. EF ~ 2 DEG
Fig. 2. Schematic view of a two-dimensional system (20EG).
2