Semiconductor Physics: An Introduction

534 Pages·1999·11.465 MB·English

by  Professor Karlheinz Seeger (auth.)

Semiconductor Physics
Springer-Verlag Berlin Heidelberg GmbH
Karlheinz Seeger
Semiconductor
Physics
An Introduction
Seventh Edition
With 321 Figures
, Springer
Professor Karlheinz Seeger
Am Modenapark 13/5
A-1030 Vienna, Austria
and
Institut für Materialphysik der Universität
Boltzmanngasse 5
A-1090 Vienna, Austria
The sixth edition appeared in Springer Series in Solid-State Sciences, Vol. 40
Library of Congress Cataloging-in-Publication Data applied for.
Die Deutsche Bibliothek - CIP Einheitsaufnahme
Seeger, Karlheinz:
Semiconductor physics: an introduction/Karlheinz Seeger. - 7. ed. - Berlin; Heidelberg; New York;
Barcelona; Hong Kong; London; Milan; Paris; Singapore; Tokyo: Springer
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ISBN 978-3-662-03799-7 ISBN 978-3-662-03797-3 (eBook)
DOI 10.1007/978-3-662-03797-3
© Springer-Verlag Berlin Heidelberg 1973, 1982, 1985, 1989, 1991, 1997, and 1999
Original1y published by Springer-Verlag Berlin Heide1berg New York in 1999.
Softcover reprint of the hardcover 7th edition 1999
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To Lotte
and to Julia and Monika
Preface
This book is the seventh edition of an introductory text on semiconductor
physics for senior undergraduate and beginning graduate students of physical
science and electrical engineering. It is an updated and improved version of the
previous editions, which appeared both in English and in many translations,
and includes recent developments in the field, in particular, new insight into the
fractional quantum Hall effect, the discoverers of which have been honored by
the 1998 Nobel Prize for Physics. In addition, the section on the optical
properties of superlattices has been rewritten featuring the compositional type
which has an advantage over the doping type because of the reduced scattering
by impurities. The experimental technique of four-wave mixing of laser ra
diation applied to a superlattice is discussed extensively. In the chapter on
quantum transport, the section on the theory of the Bloch oscillation and the
Wannier-Stark ladder of energy levels in a strong electric field has been en
riched by a simplified calculation of the density-of-states function. Last but not
least, the recently invented gallium-nitride-type laser emitting violet light has
been included in the section concerning semiconductor lasers. This laser might
revolutionize the CD player, which, in terms of sales, is the most prominent
laser application at present.
The reader will probably be aware that the recent development of devices
on a nanometer scale requires a theoretical treatment that can no longer be
based on the semiclassical Boltzmann transport equation, which relies on the
assumption that the distribution function of carriers varies little over the de
Broglie wavelength. Advanced theoretical treatments of the subject apply
second quantization, the Kubo formalism, for nonequilibrium phenomena the
Green's function technique, and for ultrafast dynamics, the density-matrix
theory. These advanced quantum-mechanical approaches may be studied
e.g. in the book by G.D. Mahan: Many-Particle Physics, Plenum, New York
1983 (1003 pages!). They are applied to semiconductor nanostructures e.g. in a
compilation of articles by E. Schöll: Theory 0/ Transport Properties 0/ Semi
conductor Nanostructures, Chapman and Hall, London 1997, wh ich is re
commended as "further reading", whereas here the experimental results on
nanostructure devices including quantum wires and dots are in the foreground
of the presentation. The nearly nine-hundred references, mostly to journal
publications, will be particularly appreciated by researchers in the field.
VIII Preface
A final word about the system of units and the syntax is in order. For an
experimentalist, only the SI system of units is useful. Therefore the CGS
Gaussian notation preferred by theoreticians has not been used. Vectors are
characterized by boldface types. The notation (5.7.7,8) refers to both equation
(5.7.7) and equation (5.7.8) while the notation [5.7] refers to the reference [5.7].
Corrections and suggestions will be gratefully received and may be ad
dressed to the author at "Am Modenapark 13/5, A-I030 Vienna, Austria".
A basic prerequisite for the existence of this book is (and always was) the
excellent co operation with Hofrat Dr. Wolfgang Kerber and his team at the
"Zentralbibliothek für Physik" located at our Physics Department. They, as
well as Dr. Claus Ascheron of Springer-Verlag, deserve my heartfelt thanks.
Vienna, Austria K. Seeger
May 1999
To Instructors who have adopted the text for classroom use, a solutions
manual is available free of charge by request on departmental letterhead
to Dr. C. Ascheron, Springer-Verlag, Tiergartenstr. 17, D-69121 Heidelberg,
Germany.
Contents
1. Elementary Properties of Semiconductors ................. .
1.1 Insulator - Semiconductor - Semimetal - Metal ........ 1
1.2 The Positive Hole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Conduction Processes, Compensation, Law of Mass Action 4
Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2. Energy Band Structure ............................... 10
2.1 Single and Periodically Repeated Potential Weil ........ 10
2.2 Energy Bands by Tight Binding of Electrons to Atoms ... 17
2.3 The Brillouin Zone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.4 Constant Energy Surfaces. . . . . . . . . . . . . . . . . . . . . . . . . 32
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3. Semiconductor Statistics .............................. 34
3.1 Fermi Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2 Occupation Probabilities of Impurity Levels. . . . . . . . . . . . 40
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4. Charge and Energy Transport in a Nondegenerate Electron Gas 47
4.1 Electrical Conductivity and Its Temperature Dependence 47
4.2 HaH Effect in a Transverse Magnetic Field ............ 53
4.3 HaH Techniques ............................... 63
4.4 Magnetoresistance.............................. 65
4.5 Corbino Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.6 Transport in Inhomogeneous Samples . . . . . . . . . . . . . . . . 72
4.7 Planar Hall Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.8 Thermal Conductivity, Lorenz Number,
Comparison with Metals . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.9 Thermoelectric (Seebeck) Effect .................... 82
4.10 Thomson and Peltier Effects ...................... 89
4.11 Thermomagnetic Effects . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.12 Piezoresistance ................................ 10 1
4.13 Hot Electrons and Energy Relaxation Time ........... 105
X Contents
4.14 High-Frequency Conductivity . . . . . . . . . . . . . . . . . . . . . . 111
4.15 Noise....................................... 115
Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5. Carrier Diffusion Processes ............................ 120
5.1 Injection and Recombination . . . . . . . . . . . . . . . . . . . . . . 120
5.2 Diffusion and the Einstein Relation. . . . . . . . . . . . . . . . . . 122
5.3 The p-n Junction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
5.4 Quasi-Fermi Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
5.5 The Bipolar Transistor. . . . . . . . . . . . . . . . . . . . . . . . . . . 140
5.6 The Metal-Semiconductor Contact . . . . . . . . . . . . . . . . . . 145
5.7 Various Types of Transistors Including MOSFET . . . . . . . 147
5.8 Dember Effect and PEM Effect. . . . . . . . . . . . . . . . . . . . . 153
5.9 Photovoltaic Effect ............................. 156
Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
6. Scattering Processes in a Spherical One-Valley Model ......... 161
6.1 Neutral Impurity Scattering . . . . . . . . . . . . . . . . . . . . . . . 161
6.2 Elastic Scattering Processes ....................... 165
6.3 Ionized Impurity Scattering . . . . . . . . . . . . . . . . . . . . . . . 168
6.4 Acoustic Deformation Potential Scattering
of Thermal Carriers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
6.5 Acoustic Deformation Potential Scattering
of Hot Carriers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
6.6 Combined Ionized Impurity
and Acoustic Deformation Potential Scattering ..... . . . . 183
6.7 Piezoelectric Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
6.8 The Phonon Spectrum of a Crystal . . . . . . . . . . . . . . . . . . 190
6.9 Inelastic Scattering Processes ...... . . . . . . . . . . . . . . . . 195
6.10 The Momentum Balance Equation
and the Shifted Maxwellian . . . . . . . . . . . . . . . . . . . . . . . 199
6.11 Optical Deformation Potential Scattering . . . . . . . . . . . . .. 203
6.12 Polar Optical Scattering . . . . . . . . . . . . . . . . . . . . . . . . .. 208
6.13 Carrier-Carrier Scattering . . . . . . . . . . . . . . . . . . . . . . . . . 217
6.14 Impurity Conduction and Hopping Processes . . . . . . . . . .. 218
6.15 Dislocation Scattering . . . . . . . . . . . . . . . . . . . . . . . . . .. 221
Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
7. Charge Transport and Scattering Processes
in the Many-V alley Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
7.1 The Deformation Potential Tensor . . . . . . . . . . . . . . . . .. 226
7.2 Electrical Conductivity . . . . . . . . . . . . . . . . . . . . . . . . . .. 230
7.3 Hall Effect in a Weak Magnetic Field . . . . . . . . . . . . . . .. 234
7.4 The W eak- Field Magnetoresistance . . . . . . . . . . . . . . . . . . 236