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Survey of Semiconductor
Physics
Surveyof Semiconductor
Physics Volume II
Barriers, Junctions, Surfaces, and Devices
Karl w. Boer University of Delaware
~SPRINGER SCIENCE+ BUSINESS MEDIA, LLC
Copyright © 1992 by Springer Science+Business Media New York Originally published by Van Nostrand Reinhold in 1992 Softcover reprint of the hardcover Ist edition 1992 Library of Congress Catalog Card Number 89-21473 ISBN 978-94-010-5293-1
AII rights reserved. No part of this work covered by the copyright hereon may be reproduced or used in any fonn or by any means.-graphic, electronic, or mechanical, including photocopying, recording, taping, or infonnation storage and retrieval systems-without written permis sion of the publisher.
Library of Congress Cataloging-in-Publication Data (Revised for voI. 2)
Boer, K. W, (Karl Wolfgang), 1926-Survey ofsemiconductor physics.
Contents: v. 1. Electrons and other particles in bulk semiconductors-v. 2. Barriers, junctions, surfaces, and devices.
Includes bibliographical references and indexes. 1. Semiconductors. II. ritle.
QC611,B64 1990 537,6'22 89-21473 ISBN 978-94-010-5293-1 ISBN 978-94-011-2912-1 (eBook) DOI 1O.1007/978-94-011-2912-1
v
To my students,
who are endeavering to further unravel the exciting puzzles of nature, and who are helping to create the foundation for the development of new and better semiconductor devices.
Preface
Any book that covers a large variety of subjects and is written by one author lacks by necessity the depth provided by an expert in his or her own field of specialization. This book is no exception.
It has been written with the encouragement of my students and colleagues, who felt that an extensive card file I had accumulated over the years of teaching solid state and semiconductor physics would be helpful to more than just a few of us. This file, updated from time to time, contained lecture notes and other entries that were useful in my research and permitted me to give to my students a broader spectrum of information than is available in typical textbooks.
When assembling this material into a book, I divided the topics into material dealing with the homogeneous semiconductor, the subject of the previously published Volume 1, and the inhomogeneous semiconductor, the subject of this Volume 2. In order to keep the book to a manageable size, sections of tutorial character which can be used as text for a graduate level class had to be interwoven with others written in shorter, reference style. The pointers at the right-hand page header will assist in distinguishing the more difficult reference parts of the book (with the pointer to the right) from the more easy-to-read basic educational sections (with the pointer tending to the left). In Part II of this volume, however, I have deviated from the style of the book and included more extensive material that is not published elsewhere in such comprehensive form. Since
> the topic of this part, carrier transport through space-charge regions, is of such central importance to the inhomogeneous semiconductor, this somewhat unusual shift of emphasis toward tutorial completeness, including an atlas of solutions, seems to be justified.
For reference purposes, I included more tables and figures than are necessary for a text, and have added several footnotes that will be helpful in reminding the reader of facts which are often difficult to locate.
The necessity of keeping the volume to a size that can easily be handled required a stringent selection of the material. Any such selection is subjective. I apologize to my colleagues who may not find their own subject of specialization represented in sufficient detail. I also apologize for my selection of references in the text. They cannot
vii
viii Preface
be comprehensive. The given references are meant as examples, and in a rapidly progressing field may not remain best choices. The reader should be aware of this fact, and after gaining entry into the field should search for more recent literature.
The book is organized around the most important semiconductors Si and GaAs, but I have extended this discussion at times to other materials of interest, including Ge, III-V and II-VI compounds and amorphous Si:H.
When similar topics have to be covered in different parts of the book, a progressively advanced description is used, including more model details or a more sophisticated mathematical approach. The search for interconnecting sections is eased by cross-referencing, an extended Table of Contents, and a comprehensive word index. For a brief scan of topics, however, the short version of the Table of Contents and the List of Tables may be consulted. A List of Symbols is included to assist in identifying the terms used. Multiple use of the same symbols was permitted (in order to avoid excessive subscripts) where confusion is 'unlikely. Conventional use of symbols was given preference whenever possible.
The sentence at the beginning of each chapter and the Summary and Emphasis at its end provides a quick overview.
The homework problems are collected from a wide variety of topics. Some are of review (r) character to enhance retention. Other topics require mathematical solutions to connect partially presented material. When elementary in nature, such topics are identified by (e). There are topics (*) which require independent thinking and provide various degrees of challenge to the student. Some of the 't#>pics require additional literature (1), and are designed to familiarize the student with literature searches.
Many figures have been relabeled or redrawn from the original, omitting nonessential features or less important curves of a family. Some figures were transposed into a coordinate system that permits easy comparison with other figures in the text. Tables included without source citations were compiled from data published in LandoldtBornstein (1955 and 1982). The author appreciates the permission received from publishers and authors to use their material for tables and figures. Copyright lines have been added when requested.
The book has many contributors; foremost are the active students who took up the challenge of extensively commenting upon the material. They helped to point out difficult passages, and assisted in several iterations of editing. The book, however, could not have been
Preface ix
written without extensive assistance from many of my colleagues and the large number of specialists and referees employed by the publisher. I appreciate especially the constructive comments and assistance I received from my collegues A. M. Barnett, L. J. Brillson, J. 1. Cowley, G. Higashi, L. Daweritz, R. Enderlein, E. Jahne, J. Kolodzey, A. H. Marshak, 1. S. Papadimitriou, J. Piprek and J. E. Phillips.
It is impossible to recall all the names of students and colleagues who gave invaluable advice and criticism, not only at the University of Delaware, but also during several extended visits to Stuttgart, Berlin, New Delhi, Osaka, and Sydney.
The assistance I have received from the Material Science Program of the University of Delaware is gratefully acknowledged. The very extensive computational work was done to a large extent by several of my graduate students, most prominently by Mauricio Garcia, Ahmed Y. Ali and Fu-Hsing Lu.
The dedicated work of S. Pruitt, D. Willette, A. Hoover, 1. Abrantes, K. Papadimitriou, D. Brzoska, and J. Holowka of bringing the rough manuscript into a camera-ready form is gratefully acknowledged.
I also wish to acknowledge with gratitude the special assistance I received from the editors and staff of Van Nostrand Reinhold.
Finally, a special word of thanks is due to my family who supported me throughout this work and surrounded me with an environment of peace, love, and understanding.
Contents
PART I: SURFACE PROPERTIES
Chapter 1 Introduction
1.1 The Inhomogeneous Semiconductor 1.1.1 Surfaces, Interfaces, and Inhomogeneous Doping
1.1.2 Space-Charge Effects
1.2 Technical Relevance (History and Outlook)
1.2.1 Point Contact Rectifiers
1.2.2 Plate Rectifiers 1.2.3 Schottky Barriers and Ohmic Contacts 1.2.4 Homo- and Heterojunction Devices
1.2.5 Device Surfaces
Chapter 2 Crystal Surfaces, An Introduction
2.1 The Ideal Crystal Surface 2.1.1 Crystallographic Aspects, Surface Structures
2.1.1A Surface Relaxation
1
3
3 3 5
6
6 7 7 9
12
15
15 16 16
2.2 The Reconstructed Surface 17 2.2.1 Surface Reconstruction 17
2.2.1A Reconstructed Surface Denotation 18 2.2.1B Examples of Reconstructed Surfaces 18
2.2.2 Surface Steps and Facets 19 2.3 Surface Energy 20
2.3.1 Energy of Reconstructed Surfaces 23 2.3.2 Phononic Surface States 25
2.3.2A Surface-Phonon Spectrum 25 2.3.3 Electronic Surface States 28
2.3.3A Surface States in a One-Dimensional Model 28 2.3.3B Surface States in Three-Dimensional Models 29
2.3.3B.l Two-Dimensional Brillouin Zones and Band
Structures 31 2.3.3B.2 Electron States from Ideal Si Surfaces 31 2.3.3B.3 Electron States from GaAs Surfaces 34
xi
xii Content"
2.4 The Surface with Adsorbates 2.4.1 Physisorbed or Chemisorbed Layers
2.4.2 Surface States of Adsorbates
Chapter 3 Surface Analysis
34
35 35
41
3.1 Diffraction Analysis of Surfaces 42 3.1.1 Low-Energy Electron Diffraction (LEED) 43
3.1.1A Detection of Terraces with LEED 48 3.1.1B Experimental LEED Setup 48
3.1.1B.1 Mirror-Electron Microscope LEED (MEM-LEED) 48
3.1.1C Analysis of LEED Patterns 3.1.1D Reliability Factors
3.1.2 Medium-Energy Electron Diffraction (MEED)
3.1.3 Reflection High-Energy Electron Diffraction
49 51 51
(RHEED) 51 3.1.3A Kikuchi Lines 53
3.1.4 Other Diffraction Methods 54 3.1.4A Transmission High-Energy Electron Diffraction
~HU~ M 3.1.4B Spin-Polarized LEED (SPLEED) 56 3.1.4C Low-Energy Positron Diffraction 56 3.1.4D Neutron Diffraction 56 3.1.4E X-Ray Diffraction 56
3.1.5 Low-Energy Atomic Scattering 57 3.2 Methods Involving Electron Excitation 57
3.2.1 Auger Electron Spectroscopy (AES) 57 3.2.1A Angle-Resolved Auger Spectroscopy (ARAES) 60 3.2.1B Spin-Polarized Secondary Electrons 60
3.2.2 Ultraviolet and X-Ray Photoelectron Spectroscopy
(UPS, XPS) 60 3.2.2A Angle-Resolved XPS and UPS (ARXPS and
ARUPS) 62 3.2.3 Ion Neutralization Spectroscopy (INS) 63 3.2.4 Surface Penning Ionization (SPI) 63 3.2.5 Soft X-Ray Emission Spectra 64 3.2.6 Extended X-Ray Absorption Fine Structure and
(EXAFS)-Related Methods 64 3.2.6A Near-Edge X-Ray Fine Structure (NEXAFS or
XANES) 65
Contents xiii
3.2.6B X-Ray Absorption Resonance Spectroscopy
(XARS) 65 3.2.6C Surface-Extended X-Ray Absorption Fine Struc-
ture (SEXAFS) 65 3.2.7 Appearance Potential Spectroscopy (APS) 66
3.2.7A Soft X-Ray, or Auger-Appearance Potential
Spectroscopy (SXAPS, AEAPS) 66 3.2.7B Surface-Extended Energy Loss Fine Structure
(SEELFS) 66 3.2.8 Proton-Induced X-Rays 67
3.3 Methods Involving Phonon Excitation 68 3.3.1 Infrared Reflection-Absorption Spectroscopy (IRAS) 68 3.3.2 Methods Involving Inelastic Electron Scattering 68
3.3.2A Electron Energy Loss Spectroscopy (EELS) 69 3.3.3 High-Resolution Electron Energy Loss Spectroscopy
(HREELS) 70 3.3.4 Comparison of Methods Using Fine Structures in
Electron Yield 71 3.3.5 Comparison of Sensitivity and Resolution of Several
Methods 71
3.4 Methods for Direct Surface Observation 72
3.4.1 Field-Ion Microscopy (FIM) 72 3.4.2 Classical Electron Microscopy (EM) 75
3.4.2A Scanning Electron Microscopy (SEM) 77 3.4.2B Transmission Electron Microscopy 78 3.4.2C High-Resolution Electron Microscopy (HREM) 78 3.4.2D Reflection Electron Microscopy 80
3.4.2D.1 Various Types of High-Resolution Electron
Microscopy 81 3.4.2E Emission Electron Microscopy (EEM) 81
3.4.2E.1 Low-Energy Electron Microscopy (LEEM)
82 3.4.3 Scanning Tunnel Microscopy (STM)
3.4.3A Surface Influence on Workfunction
3.4.4 Electron Holography
3.5 Methods Involving Atomic Emission and Scattering
3.5.1 Individual Atom-Desorption Using FIM
3.S.1A Time-of-Flight Atom-Probe
3.S.1B Magnetic Sector Atom-Probe
83 86 87
88
88 88 88
xiv Contents
3.S.1C Imaging Atom-Probe and Other Methods 89 3.S.1D Use of Atom-Probes to Sample Thin Layer
Interfaces 89 3.S.2 Methods to Employ Globa.! Desorption of Species from
the Surface 90 3.S.2A Secondary Ion Mass Spectroscopy (SIMS) 90 3.S.2B Electron-Stimulated Desorption of Ions Measured
in Angular Distribution (ESDIAD) 91 3.S.2C Thermal Desorption Mass Spectroscopy (TDMS)
92 3.S.3 Ion-Scattering Spectroscopy (ISS) 92
3.S.3A Low-Energy Ion Scattering 93 3.S.3B Medium- and High-Energy Ion Scattering (MEIS,
HEm) 93 3.S.3C Rutherford Backscattering Spectroscopy (RBS or
HEIS) 93
Chapter 4 Surface Structures 99
4.1 Clean Reconstructed Surfaces 99 4.1.1 Silicon Surfaces 100
4.1.1A Si(lOO) Surface 100 4.1.1B Si(111) Surface 102
4.l.lB.1 Si(l11) 1 X 1 Surface 103 4.l.lB.2 Si(l11) 2 X 1 Surface 104 4.1.1B.3 Si(l11) 7 X 7 Surface 106
4.l.lC The Si(llO) Surface 108 4.1.2 Germanium Surfaces 108
4.1.2A Ge(111) Surface 109 4.1.2B Other Ge Surfaces 110
4.1.3 III-V Compound Surfaces 111 4.1.3A The GaAs Surfaces 111
4.1.3A.1 GaAs(llO) Surface 112 4.1.3A.2 GaAs(100) and (111) Surfaces 113
4.1.4 Surfaces of Other Zincblende Semiconductors 117 4.1.S Surfaces of Wurtzite Semiconductors 119
4.2 Surfaces with Adsorbates 121
4.2.1 Surface Coating by Molecular Beam Epitaxy (MBE) 123 4.2.1A Overlayers 124 4.2.1B Island Formation on Clean Surfaces
4.2.1B.1 Ag on Si(l11) 7X7
125 125
Contents xv
4.2.1B.2 Surface Phase Transition Induced by
Adsorbates 126
4.2.1B.3 Pd- and In-Coating of Si(111)7 X 7 128 4.2.1C Chemical Reaction With Metal Layers 129
4.2.1C.l Smooth Transparent Metal Coating 129
4.3 Surface Reactions 129
4.3.1 Chemistry at the Surface 130
4.3.1A Catalytic Reactions 130
4.3.1B Chemistry of H20 on Si(lOO) Surfaces 131
4.3.2 Chemisorption 131
4.3.2A Chemisorption of Oxygen 132
4.3.2B Hydrogen Termination of Si(111) Surfaces 135
4.3.3 Chemisorption on Binary Compounds 136
4.3.3A Enhancement of Chemisorption 136
Chapter 5 Crystal Growth, Epitaxy 141
5.1 Nucleation, Crystal Seed Formation 141
5.1.1 Supersaturation, Overcritical Size Nucleus 142
5.1.1A Nucleation from Melt 142
5.1.1B Seed Selection for Single Crystal Growth 145
5.1.1C Nucleation from Solution 145
5.1.2 Artificial Nucleation 146
5.2 Theory of Crystal Growth 146
5.2.1 The Kossel-Stranski Theory 147
5.2.1A Screw Dislocation and Crystal Growth 149
5.2.1B Whisker Growth 149
5.3 Processes Limiting Crystal Growth Rates 149
5.4 Classical Methods of Crystal Growth 151
5.4.1 The Bridgeman Technique
5.4.1A Horizontal Solidification, Zone Refining
5.4.2 The Czochralski Method
5.4.2A Crystal Growth through an Aperture
5.4.2B Dendrite Methods
5.4.3 The Verneuil Process
5.4.4 Low-Temperature Solution Growth
5.4.4A Electrodeposition
5.4.5 High-Temperature Solution Growth
5.4.6 Hydrothermal Growth
5.4.7 Vapor Transport Controlled Crystal Growth
152
152
156
159
160
160
161
162
163
163
163
XVI Contents
5.4.7 A Chemical Vapor Transport
5.4.8 Growth from the Solid Phase
5.5 Epitaxial Growth of Layers
5.5.1 Evaporation for Producing Thin Films
5.5.2 Molecular Beam Epitaxy (MBE)
5.5.2A Substrate Preparation
5.5.2B Epilayer Deposition
5.5.2C Substrate Dependence of Epigrowth
5.5.2D Delta-Function Doping
5.5.3 Atomic Layer Epitaxy (ALE)
5.5.4 Migration Enhanced Epitaxy (ME E)
5.5.5 Liquid Phase Epitaxy (LPE)
5.5.5A Substrate Preparation for LPE
5.5.5B Growth Techniques
5.5.6 Chemical Vapor Deposition (CVD)
5.5.6A Metalorganic CVD (MOCVD)
Chapter 6 Phononic Effects at Surfaces
6.1 Acoustic Surface Vibrations, Surface Waves
164 165 165
167 169 175 176 178 179 180 182 182 183 183 185 186
192
193 6.1.1 Elasticity Theory, Wave Equations 193
6.1.1A Soundwave Reflections at Semiconductor Sur-
faces
6.1.1B Rayleigh Waves
6.1.2 Modes of Surface Oscillation
6.2 Lattice Dynamics at the Surface 6.2.1 Surface Vibrational Amplitudes
6.2.1A Adsorbate Vibrational Amplitudes
6.2.2 Surface Debye Temperatures
6.2.2A Temperature Effect on LEED
6.2.2A.1 Debye-Waller Factor
6.2.2B Surface Expansion
6.2.2C Surface Melting
6.2.2D Phonon-Distribution and Surface Debye Temper
ature
196 197 200 201 202 202 204 204 205 207 207
208 6.3 Brillouin Scattering on Acoustic Surface Phonons 209
6.3.1 Surface Ripple Effect 211
6.4 Interaction of Light with Optical Surface Phonons 211 6.4.1 Surface Phonon Polaritons 212
Contents XVll
6A.1A Measurements of Surface Polariton Spectra 216 6A.1A.1 Coupling through a Surface Grating 216 6A.1A.2 Attenuated Total Reflection (ATR) 216
604.2 Surface Infrared Spectroscopy to Identify Adsorbates
219 6A.2A The Si(100) 2 X 1 Surface with Adsorbed Hydro-
gen 220 6A.2B Raman Spectroscopy of Surface Waves 223 6A.2C Electron Energy Loss Spectroscopy for Surface
Waves
6A.2C.1 EELS to Identify Adsorbates
6A.2C.2 Vibrational Modes of Adsorbates
604.3 Inelastic Atomic Scattering for Surface Phonon
Detection
6.5 Technical Applications of Surface Waves
224 225 227
227 229
6.5.1 Surface Wave Attenuation 230 6.5.2 Applications of Surface Ultrasound 231
6.5.2A Surface Ultrasound for Testing of Material
Properties 233
Chapter 7 Electronic Surface and Interface States 236
7.1 Electronic States at Clean Surfaces 237 7.1.1 General Features of Electron-Surface Interaction 238
7.1.1A Image Force-Induced Surface States 239 7.1.1B Short-Range Electron-Surface Interaction 240
7.1.1B.l Electron Density Profile 242 7.1.1B.2 Localization Behavior of Surface States 243 7.1.1B.3 Relaxed and Unrelaxed Surfaces 246 7.1.1BA Surface Bonding 247
7.1.1C Dissipative Part of Surface Interaction 249 7.1.1D Electron Levels of Clean Surfaces in the Band
Gap 249 7.1.2 Intrinsic Surface Defects 250 7.1.3 Examples of Surface States 252
7.2 Surface States Induced by Adsorbates 253
7.2.1 Hydrogen Adsorbates on Si(100) and Si(l11)
7.2.2 Monolayer of Homologous Atoms
7.2.3 Surface States with Nonmetallic Adsorbates
7.2.3A Oxidation of Si Surfaces
7.2.3B Oxidation of GaAs(llO) Surfaces
254 255 258 258 259
xviii Contents
7.2.4 Natural Surfaces 260 7.3 Interface States Between Two Semiconductors 261
7.3.1 Interface Band Structure 261 7.3.1A The GaAs-Gao.sAlo.sAs Interface 261 7.3.1B The Ge-GaAs Interface 263
7.3.2 Defects at Heterojunction Interfaces 265 7.4 Interface States at Metal-Semiconductor Boundaries
269 7.4.1 Interface States Between Semiconductors and Metals
269 7.4.2 Interface State Models 269 7.4.3 Interface States with Metals Forming Compounds 270
7.4.3A Metal Silicide Interfaces 270 7.4.3B Interlayers and Chemical Reactions 271
7.4.4 Surface States and Degree of Surface Coverage 272 7.5 Fermi-Level Pinning by Surface Defects 273
7.5.1 Unified Defect Model 274 7.5.2 Induced Density of Interface State Model 275
Chapter 8 Semiconductor Interfaces and Contacts 280
8.1 Interfaces and Space-Charge Regions 281 8.1.1 Classification of Interfaces and Contacts 284
8.1.1A Classification Disregarding Space Charges 284 8.1.1B Classification Including Space-Charge Regions 286
8.1.2 Canonical Interface Potential Steps 288 8.1.2A The Schottky-Mott Barrier 288 8.1.2B The Anderson Model of Heterojunctions 289 8.1.2C The Bardeen Model 290 8.1.2D Heterojunctions with a Modifying Interface
Dipole 292
8.2 Experimental Evidence on Band Alignment 294
8.2.1 Experimental Results for Metal-Semiconductor
Interfaces 294 8.2.1A Methods to Measure the Barrier Height 295
8.2.1A.1 Current-Voltage Characteristics 295 8.2.1A.2 Capacitance-Voltage Characteristics 296 8.2.1A.3 Internal Photo emission 298 8.2.1A.4 Photoelectron Spectroscopy 298
Contents xix
8.2.1A.S Ballistic Electron Emission Spectroscopy 300 8.2.1B Basic Results for Schottky Barriers 300 8.2.1C Experimental Trends in Schottky Barriers 302
8.2.2 Experimental Results on Band Offsets in Hetero-
junctions 304 8.2.2A Methods to Measure Band Offsets 306
8.2.2A.1 Photoelectron Spectroscopy 306 8.2.2A.2 Electron Energy Loss Spectroscopy 308 8.2.2A.3 Internal Photoemission of Electron 308 8.2.2A.4 Capacitance-Voltage and Current-Voltage
Characteristics 308 8.2.2B Experimental Results for Heterojunctions 310 8.2.2C The Polar Ge-GaAs Interface 312
8.3 Band Offset Models 315 8.3.1 Band Edge Offset and Linear Models
8.3.1A The Harrison Valence Band Offsets
8.3.1B Empirical Valence Band Offset Assuming Transitivity
8.3.1C
8.3.1D
Transition Metal Levels as Reference
The Frensley-Kroemer Model
8.3.2 Theories That Include Interface Properties
8.3.2A Interface Induced States
8.3.2A.1 Similarity to MIG-States Responsible for
Schottky Barriers
8.3.2B Interface Dipole via Charge Neutrality Levels
8.3.2B.1 Disorder-Induced Gap States in Semicon
ductors
8.3.2C Interface Dipoles
8.3.2D Surface States and Vacancy Levels
8.3.3 Ab Initio Calculation of Valence Band Offset
8.3.3A The Model Solid Approach
Chapter 9 Electron Penetration through Surfaces
9.1 The Electron Workfunction
9.1.1 Surface Dependence of the Workfunction
9.2 Emission of Electrons through Surfaces
9.2.1 Thermionic Emission
9.2.2 Photoemission (External Photoeffect)
9.2.2A Carrier Transport to the Surface
9.2.2B The Photoelectric Yield
315 319
319 319 321 323 324
324 324
326 326 328 330 330
335
336
337 338
339 341 343 344
xx Contents
9.2.2C Influence of Space-Charge Regions 345 9.2.2D Negative Electron Affinity 348
9.2.3 Secondary Electron Emission 349 9.2.3A Energy Distribution of Secondary Electrons 350 9.2.3B Universal Yield Curves 350 9.2.3C Microscopic Aspects of Emission Yield 353
9.2.4 Field Emission 356 9.2.4A Cold Field Emission through Surface Barrier 358 9.2.4B Influence of Thermal Electron Distribution 359
9.2.5 Field Emission from Semiconductors 363 9.2.6 Origins of Tunneling Electrons 364
9.2.6A Saturation Effects in Semiconductors 367 9.2.6B Field Emission, Wide-Gap Semiconductors 369
9.2.7 Photo-Assisted Field Emission 370
9.3 More Detailed Analysis of the Workfunction 370 9.3.1 Workfunction and Surface Reconstruction 371 9.3.2 Interface Barriers 371
9.3.2A The Metal-Semiconductor Interface 372 9.3.2B The Heterojunction Interface 374
9.3.3 Surface and Interface Penetration 375 9.3.3A Interference Effects from Interface Reflection 376
Chapter 10 Photon Penetration through Surfaces 381
10.1 Reflection and Transmission in Maxwell '8 Theory
10.1.1 Transmission and Reflection at an Interface of Two
Media
10.1.1A Reflection and Transmission in Nonabsorbing
382
385
Dielectrics 387 10.1.1B Reflection and Transmission in Semiconductors
388 10.1.2 Maximize or Minimize Photon Transfer
10.1.2A Antireflecting Coating
10.1.2B Graded Index Coating (GRIN)
10.1.2C Textured Surfaces
10.1.2D Light Trapping in Semiconductors
10.1.3 The Dielectric Function
10.2 Exciton Influence on Reflectance
10.2.1 Additional Boundary Conditions (ABC's)
389 389 394 395 396 397 400
401
Contents xxi
Chapter 11 Surface Influence on Bulk Properties 405
11.1 Surface-Induced Mobility Effects 405 11.1.1 Specular and Diffuse Surface Scattering 406 11.1.2 Carrier Mobility in Surface Inversion Channels 408
11.1.2A Impurity Scattering 409 11.1.2A.l Mobility in Heterojunction Quantum Well
409 11.1.2B Surface Roughness Scattering
11.1.2C Phonon Scattering
11.1.2D Mobilities Near Vicinal Surfaces
11.1.2E Field-Dependence of the Mobility
11.2 Surface and Interface Recombination
11.2.1 Recombination Traffic within the Bulk
11.2.1A The Hall-Shockley-Read Center
11.2.1B The Generation/Recombination Current
11.2.2 Recombination in a Sheet or at the Surface
11.2.3 Surface and Interface Recombination Centers
PART II: SPACE-CHARGE EFFECTS IN SEMI-
410 410 412 413 414 415 417 420 421 423
CONDUCTORS ~7
Chapter 12 Space Charges in Insulators 429
12.1 Basic Electrostatic Relations 12.1.1 The Poisson Equation
12.2 Fixed Space-Charge Distributions
12.2.1
12.2.2
12.2.3
12.2.4
12.2.5
12.2.6
Chapter 13
Sinusoidal Continuous Space-Charge Distribution
Abruptly Changing Space-Charge Distribution
Space-Charge Double Layer with Neutral Interlayer
Asymmetric Space Charge Double Layer
Single Space-Charge Layer
Space-Charge Double Layer, Nonvanishing
Net Charge
Creation of Space-Charge Regions in Solids
13.1 One Carrier Abrupt Step-Junction
429 430 433 433 435 438 439 440
441
444
446 13.1.1 Electron Density, Space Charge, Field Distribution 447
13.1.1A Electrode-Surface Charges 449 13.1.1B Field Distribution 450 13.1.1C Electrostatic and Fermi Potentials 451
xxii Contents
13.1.1D Currents
13.1.1E Current-Voltage Characteristics
13.1.1E.1 Current Rectification
13.1.1F Dependence on the Doping Step-size
13.2 Significance of Basic Barrier or Junction Variables
13.2.1 Interdependence of Carrier Densities, Fields and
Currents
13.2.2 Potentials and Currents
13.2.2A Dependence on Other Parameters
13.3 Space-Ch~rge Limited Current 13.3.1
13.3.2
13.3.3
Chapter 14
Majority C~rier Injection
Minority Carrier Injection
Trap-Controlled Space-Charge-Limited Currents
The Schottky Barrier
14.1 The Classical Schottky Barrier 14.1.1 Schottky Approximation: Field and Potential Distribu
tions
454 457 458 459
461
461 461 463 465 467 468 469
472
472
474 14.1.2 Zero Current Solution of the Electron Distribution 477
14.1.2A Diffusion Potential, Junction Field 478 14.1.2B Debye Length and Barrier Width 479 14.1.2C The Accuracy of the Schottky Approximation 480
14.1.3 Nonvanishing Currents 481 14.1.3A The Electron Density Distribution 483
14.1.4 Current-Voltage Characteristics 488 14.2 Modified Schottky Barrier 489
14.2.1 The Schottky Barrier with Current-Dependent Inter-
face Density 490 14.2.1A Metal/Semiconductor Boundary Condition 490 14.2.1B Current-Voltage Characteristic in a Modified
Schottky Barrier 492 14.2.1B.1 The Shape Factor 494 14.2.1B.2 Modified Boltzmann Range 495 14.2.1B.3 DRO-Range 496 14.2.1B.4 Electrostatic and Electrochemical Poten-
tials in a Schottky
Barrier 498 14.2.2 Schottky Barrier with Two or More Donor Levels 498
14.2.2A Junction Field in Double-Donor Barrier 500
Contents xxiii
14.2.2B Gradual Depletion of Deep Donors 500 ·14.2.2C Exact Solutions of Double-Donor Barriers 502 14.2.2D Current-Voltage Characteristics for Double-Donor
Barriers 502 14.2.2E The Exponential A-Factor 506
14.2.2E.1 A-Factor in Junctions with Donor Distribu-
tions 508 14.2.3 Schottky Barriers with Multiple Donors, Field Excita-
tion 509
14.3 Schottky Barrier with Optical Excitation 510
14.3.1 Partially Compensated Schottky Barrier 511 14.3.2 Compensated Barrier with Optical Excitation 511 14.3.3 Schottky Barrier with Field Quenching 513
14.3.3A Compensated Barrier with Optical Excitation
and Field Quenching 514
14.4 Schottky Barrier as Part of a Heterojunction 514
14.4.1 Electron Boundary Condition at the Heterojunction
Interface 517 14.4.2 Current-Voltage Characteristics 519
14.4.2A Magnitude of the Effective Diffusion Velocity 520 14.4.3 Heterojunction with Interface Recombination 521
14.4.3A Non-Ideal Heterojunction Characteristics 521
Chapter 15 Minority Carriers
15.1 Carrier Generation and Recombination 15.1.1 Thermal Excitation
15.1.2 Optical Excitation
15.1.3 Field Ionization
15.2 Trapping and Recombination
15.2.1 Electron and Hole Traps
15.2.2 Recombination Centers
15.3 Quasi-Fermi Levels, Demarcation Lines
15.3.1 Thermal Equilibrium and Steady State
15.3.1A Zero Net-Current, Thermal Equilibrium
15.3.1B Nonvanishing Current, Steady State
15.3.2 Current Continuity
15.4 Carrier Lifetimes
15.4.1 Large Generation, Optical Excitation
526
527 528 529 531
533 534 535
535
538 538 539 542
544
548
xxiv Contents
Chapter 16 Minority Carrier Currents 552
16.1 Minority Carrier Currents in the Bulk 553 16.1.1 Thermal Excitation GR-Currents 555
16.1.1A The Diffusion Equation and 'its Solution 555 16.1.1B Maximum GR-Currents 558 I6.1.1C Pure Generation or Recombination Currents 559
16.2 GR-Current with Surface Recombination 560 16.2.1 Thermal GR-Current with Surface Recombination 561
16.2.1A The Effective Diffusion Velocity 563 16.2.2 Optical Excitation GR-Currents with Surface Recom-
bination 565 16.2.2A Currents in Short and Long Devices 568 16.2.2B Collection Efficiency of Minority Carriers 570
16.2.3 Effective Diffusion Velocity for Optical Excitation 572 16.2.4 Optical vs. Thermal Carrier Generation 572
16.3 Drift-Assisted GR-Currents 573 16.3.1 Field-Influence in the Bulk 573 16.3.2 Analytical Solution of Diffusion with Constant Field 573
16.3.2A Justification for the Separation of Injection and
Generation Currents 578
Chapter 17 Schottky Barrier in Two-Carrier Model 582
17.1 Electron and Hole Currents in Barriers 582 17.1.1 Divergency-Free Electron and Hole Currents 583 17.1.2 GR-Currents in Schottky Barrier Devices 583
17.1.2A GR-Currents in the Space-Charge Regions 584 17.1.2B Field Influence in the Barrier Layer 588 17.1.2C The Definition of the Carrier Density at the
Splicing Boundary 589 17.1.2D Minority Carrier Density at the Metal/Semicon-
ductor Interface 589 17.2 Schottky Barrier with Two Carriers 590
17.2.1 The Governing Set of Equations 590 17.2.1A Example Set of Parameters 592 17.2.1B Boundary Conditions 592
17.2.2 Example Solutions for a Thin Device 594 17.2.2A Carrier Distributions 596
17.2.2A.l Boltzmann Region for Minority Carriers 597 17.2.2B Generation and Recombination Rates 599
Contents xxv
17.2.2C Currents in the Schottky Barrier 600 17.2.2D Quasi-Fermi Levels and Demarcation Lines 604
17.2.2D.1 Electron and Hole Density Crossings 605 17.2.2D.2 Carrier Inversion Layer with Consequences
on the Space Charge 606 17.2.3 Schottky Barrier Device 607
17.2.3A Medium Width Device, Boundary Conditions 607 17.2.3A.1 General Solution Behavior 607
17.2.3B Wider Device Example Solutions 609 17.2.3B.1 Splicing of Solution Curves in Barrier and
Diffusion Regions 610 17.2.3C Solution Behavior of Thick Devices 610
17.2.3C.1 Fermi Levels and Currents 612
Chapter 18 pn-Homojunctions 617
18.1 Simplified pn-Junction Model 617 18.1.1 Basic Features of the Simplified Model 618 18.1.2 Simplified Junction Model in Steady State 620 18.1.3 Junction Capacitance 621 18.1.4 The Current-Voltage Characteristic of the Simplified
Junction
18.1.5 Relevance to Actual pn-Junctions
18.2 Abrupt pn-Junction 18.2.1 Governing Set of Equations and Example
622 625
625
Parameters 625 18.2.2 Solution Curves for Thin Germanium pn-Junction 626
18.2.2A The Position of the pn-Junction 627 18.2.2B Junction Field and Potential Distribution 627 18.2.2C Quasi-Fermi Level and Current Distributions in
the pn-Junction 629 18.2.2C.1 Boltzmann-, DRO- and DO-Ranges 630
18.2.2D Carrier Heating in pn-Junctions 630 18.2.2E GR-Currents and Divergency-Free Currents 632 18.2.2F Contributions to the Current-Voltage Character-
istic
18.3 Thick pn-Junction Device (Ge)
18.3.1 Shift in Current Contributions With Device
Thickness
18.3.2 The Solution Curves of the Thicker Device
635
636
636 640
xxvi Contents
18.4 p-Type n-Type Back-to-Back Barriers 642 18.4.1 The Solution Curves for the Back-to-Back Barrier 643 18.4.2 Currents in the Back-to-Back Barrier 646
18.5 Si-Homojunction
18.5.1 The Solution Curves of a Si-Diode
18.5.2 Current Contributions in a Si-Diode
18.5.2A The Current-Voltage Characteristics
18.6 More Complex Homojunctions
18.6.1 Linearly Doped Junction
18.6.2 High Minority Carrier Injection
18.6.3 Series Resistance Limitation
18.6.4 Position-Dependent Material Parameters
18.6.4A Generalized Transport Equations
18.6.4B Modified Poisson Equation
18.6.4C Continuity Equation
Chapter 19 Carrier Velocity Limitation
647 648 650 651
653
654 655 655 656 656 657 658
661
19.1 Drift Velocity Saturation 661
19.1.1 The External Field Component 663 19.2 Diffusion Velocity Limitation 665
19.2.1 Carrier Heating in Space Charge Regions 666 19.2.2 Built-in Field Region 666
19.3 Field-Dependent Mobility in pn-Junction 667 19.3.1 Solution Curves with Field-Dependent Mobility 668
Chapter 20 Semiconductor Heterojunctions 676
20.1 Interconnection of Bands 677 20.1.1 Sloping Bands in Graded Heterojunctions 680
20.2 Examples of CdS-Related Hetero-junctions 681
20.2.1 d-Type High/Low pn-Heterojunction; CU2S/CdS 681 20.2.1A Boundary Condition at the Interface of the
Abrupt Heterojunction 682 20.2.1B Solution Curves in d-Type Heterojunctions 684 20.2.1C Electrostatic and Electrochemical Potential Distri-
butions 686 20.2.1D Currents in the CU2S/CdS Heterojunction 688
20.2.2 d-Type Low/High pn-Heterojunction; CulnSe2/CdS 690
Contents xxvii
20.2.2A Solution Curves of the d-Type Low/High Hetero-
junction 691 20.2.2B Frozen-in Steady State in Wide-Gap Material 692 20.2.2C Solution Curves for Nonvanishing Bias 695
Chapter 21 The Photovoltaic Effect 701
21.1 Enhanced Generation and Recombination with Light 701
21.1.1 Semiconductors or Photoconductors 703 21.1.2 Photo-emf and Photocurrents 704 21.1.3 Quasi-Equilibrium Approximation 705
21.2 Reaction Kinetic, Balance 706 21.2.1 Trap-Controlled Carrier Densities 708
21.3 Simple Model of the Photodiode 710 21.3.1 Derived Photodiode Parameters 712 21.3.2 Resistive Network Influence on the Diode Characteris-
tics 714
Chapter 22 The Schottky Barrier Photodiode 720
22.1 A Thin Schottky-Barrier Photodiode 22.1.1 Zero Total Current
22.1.1A Zero Recombination at Outer Surfaces
22.1.1B The Device without Light 22.1.1C The Device with Stepwise Increased Constant
720 721 721 722
Optical Generation 723 22.1.1D Influence of Interface Recombination 724
22.2 Thin Device at High Optical Generation Rates 725 22.2.1 Adjustment of Quasi-Fermi Levels at Electrode Inter-
face 725 22.2.1A Field Changes at High Generation Rates 727
22.2.2 Complete Schottky Barrier Device with Two Elec-
trodes 727 22.2.2A The Open Circuit Voltage 728 22.2.2B Nonvanishing Bias 731 22.2.2C Current-Voltage Characteristic 732
22.2.3 Lessons Learned from a Thin Schottky-Barrier
Photodiode 733
22.3 Thicker Schottky Barrier Device 733
xxviii Contents
Chapter 23 The pn-Junction with Light
23.1 Open Circuit Conditions
739
739 23.1.1 Thin, Symmetric Si-Diode with Abrupt Junction 740
23.1.1A Current Distribution in a Symmetric pn-Junction
740 23.1.1B Solution Curves for Symmetric pn-Junction 742 23.1.1C Influence of Device Thickness and Surface Re-
23.1.1D
23.1.1E
23.1.1F
23.1.1G
combination
Influence of Recombination Center Density
Influence of the Generation Rate
Influence of the Doping Density
Parameter Dependence of Voc for Insufficient
Minority Carrier Supply
23.1.1H Influence of the Energy of the Recombination
746 748 750 751
751
Center 752 23.1.2 Thin Asymmetric Si Diodes with Abrupt Junction 753
23.1.2A Recombination through Charged Recombination
Centers
23.1.2B Inhomogeneous Optical Generation
23.1.2C Thin Asymmetric Junction Design
23.1.2C.1 Asymmetric Bulk Thickness
23.1.2C.2 Asymmetric Recombination
23.1.2C.3 Asymmetric Generation
23.1.2CA Asymmetric Doping
23.1.3 Thick Asymmetric Devices, Si Solar Cells
23.2 Nonvanishing Bias
23.2.1 Thin Symmetrical pn-Junction Device
23.2.1A Thin Asymmetric Si pn-Junction Device
23.2.1B Si-Solar Cell with Nonvanishing Bias
Chapter 24 The Heterojunction with Light
24.1 The CU2S/CdS Solar Cell
24.1.1 The Current-Voltage Characteristics
24.1.2 Space Charge Effects in the Junction
24.1.2A Influence of Electron Traps
24.1.2B Influence of a Compensated Layer near the
754 756 759 760 762 762 763 764 767 767 771 771
778
779 781 782 782
Hetero-Interface 784 24.1.2C Influence of a Field-Induced Depletion of Hole
Traps 786 24.1.2D Influence of Field Quenching 787
Contents xxix
24.1.3 Kinetic Effects of Solar Cell Characteristics 789 24.1.3A Voltage Drop Kinetics Method 790
24.1.4 Influence of Interface Recombination 794 24.1,4A Boundary Condition at the Interface 795
24.1.5 Information from the Exponential A-Factor 796 24.1.6 Lessons Learned from the CdS/CU2S Solar Cell 800
24.2 The CdS/CuInSe2 Solar Cell 801
24.2.1 Homogeneous Optical Generation in CuInSe2 801 24.2.2 Inhomogeneous Optical Generation 802
24.2.2A Recombination Overshoot and Outdiffusion 806 24.2.2B Functional Parameter Dependence, Open Circuit
Voltage 809 24.2.2C Device Width Dependency 812 24.2.2D Influence on the jV-Characteristics 813
24.2.3 Heterostructure CdS/CuInSe2 Solar Cell 816 24.2,4 Minority Carrier Mirror Near Electrodes 817
Chapter 25 The pin Junction with Light 820
25.1 The CdS/CuInSe2 nip-Heterostructure 820
25.1.1 Drift-Field Enhanced Collection 821 25.1.2 Doping Density Dependence in the i-Region 823
25.2 The a-Si nip-Homostructure Solar Cell 826
25.2.1 The nnp Versus nip Q-Si Solar Cell Operation 829 25.3 The Pros and Cons of an i-Layer 832
Chapter 26 High-Field Domains
26.1 Inhomogeneous Field or Current Distributions
26.1.1 Negative Differential Conductance
26.2 Field-of-Direction (Phase-Space) Analysis
26.2.1 Decrease of Carrier Density with Field
26.2.1A Field Quenching
26.2.1B
26.2.1C
Cathode- and Anode-Adjacent Domains
Franz-Keldysh Effect to Directly Observe High
Field Domains
26.2.1D Drift Velocity Saturation
26.2.1D.1 Incomplete Drift Saturation
26.2.1E Pseudo-Cathodes and the Field of Directions
836
836
838
839 845 845 846
850 852 853 855
xxx Content8
26.2.1F Workfunction Dependence on Photoconductivity
857 26.3 Stationary and Moving High-Field
Domains 859 26.3.1 Moving Subdomains 863 26.3.2 Stability Criteria and Moving Domains 863
26.3.2A Trap-Controlled Domain Kinetics 865 26.3.2A.1 Singular Point Analysis 866 26.3.2A.2 Field of Direction for Kinetic Solutions 868 26.3.2A.3 Periodic Solutions for Trap-Controlled
Domains
26.4 Decrease of Carrier Mobility with Field
26.4.1 The Gunn Effect
26.4.2 Field-of-Direction Analysis of Gunn-Domains
26.4.2A Moving Domain-Type Solutions
26.4.2B Current Oscillations
26.4.3 Other Types of Moving High-Field Domains
Chapter 27 Current Channels
27.1 Current Channel Formation 27.1.1
27.1.2 27.1.3 27.1.4
Initiation of Current Channels
Current Channels in Dielectrics and Devices Thermo-Optical Method to View Current Channels
Channel Modelling
PART III: MATERIALS AND FABRICATION TECH-
870 871
873 873 874 876 877
881
881 882 882 884 886
NOLOGY 893
Chapter 28 Purification of Semiconductor Materials 895
28.1 Preparation of the Raw Materials
28.2 Preparation of Semiconductor Grade Silicon
28.2.1 Chemical Reactions for Purification
28.2.1A The Dupont Process of Si-Purification
28.2.1B The Siemens Process of Si-Purification
28.2.1B.1 The Union Carbide Modification
28.2.1B.2 The Boron Problem
28.2.1B.3 The Hemlock Process
28.3 Preparation of Semiconductor Grade Ge
896
897
897 897 899 900 900 900 900
Contents XXXI
28.4 Preparation of Electronic Grade GaAs 28.4.1 Compensation of GaAs and Use of Cr
28.5 Zone Refining
28.5.1 Normal Freezing
28.5.1A Kinetic Effects in Normal Freezing
28.5.2 Zone Melting
28.5.2A Multiple Zone Passage
28.5.2B Zone Refining and Volatile Components
28.5.2C Floating Zone, Avoiding Contamination
28.5.2C.1 Stability of the Floating Zone
28.5.2D Floating Zone Refining
901
903
903
903 908 909 910 911 912 912 914
Chapter 29 Crystallization and Device Shaping 919
29.1 Crystalline Silicon
29.1.1 Czochralski-Grown Silicon
29.1.1A Controlling Thermal Parameters
29.1.2 Floating Zone Purification
29.1.3 Shaping Processes
29.1.3A Wafer Cutting
29.1.3B Lapping, Polishing and Etching
29.1.3C Direct Growth of Si Sheets
29.1.3C.1 Horizontal Ribbon Growth
29.1.3C.2 Ceramic Support-Stabilized Meniscus
Pickup
29.1.3C.3
29.1.3C.4
29.1.3C.5
29.1.3C.6
29.1.3C.7
29.1.3C.8
29.1.3C.9
Ribbon-to-Ribbon Technique
Web Dendrite Growth
Web Growth Between Foreign Filaments
Edge-Defined Film-Fed Growth (EFG)
The Inverted Stepanov Process
Silicon Sheets from Powder
Thin-Film Polycrystalline Si on Ceramic
919
919 921 922 922 922 923 925 925
926 928 928 929 930 931 931
Substrates 931 29.1.4 Polycrystalline Silicon 932
29.1.4A Heat Exchanges Method (HEM) 932 29.1.4B Bridgeman Growth 933 29.1.4C Mold Casting 933 29.1.4D Meniscus Formation and Sheet Growing Speed 933
29.1.5 Quality and Material Throughput 934 29.1.5A Swirl-Defect and Carrier Lifetime 935 29.1.5B Si Wafer Throughput 936
xxxii Contents
29.2 Amorphous Silicon Deposition 936
29.2.1 Glow Discharge for a-Si Deposition 940 29.2.1A Types and Parameters of ac Glow Discharges 940 29.2.1B Reactors and Deposition Systems 942 29.2.1C dc Glow Discharge 944
29.2.2 Reactive Sputter Deposition 944 29.2.3 Ionized-Cluster Beam Deposition 946 29.2.4 Chemical Vapor Deposition 946
29.2.4A Low Temperature CVD 947 29.2.4B Photo CVD 948 29.2.4C CVD with Postdeposition Hydrogeneration 948 29.2.4D Homogeneous CVD 949
29.2.5 Properties of the a-Si:H 950
29.3 Crystalline GaAs 951
29.3.1 Czochralski-Grown GaAs 951 29.3.1A Wafer Preparation 952 29.3.1B The Cleaving Film Technique (CLEFT) 953
29.4 Crystalline CdS 954
29.4.1 CdS Bulk Crystals
29.4.1A Growth by Kyropoulos or Zone Melting
29.4.1B Bulk Crystal Growth from the Solutions
29.4.2 CdS Platelets
29.4.3 Evaporated Polycrystalline CdS
29.4.3A Slow Evaporation from Elements
29.4.3B Recrystallized Evaporated CdS
29.4.4 Sintered CdS Layers
29.4.4A Layer Preparation before Sintering
29.4.5 Chemical Vapor Deposition
29.4.5A Sprayed CdS-Films
29.4.5B Organometallic Vapor Deposition
Chapter 30 Doping and Junction Formation
30.1 Diffusion
30.1.1 The Diffusion Coefficient
30.1.2 Boundary Conditions for Diffusion
30.1.2A Finite Dopant Supply
30.1.2B Diffusion from Infinite Dopant Reservoir
30.1.2C Comparison of Both Diffusion Modes
30.1.3 Diffusion Depth and Junction Depth
30.1.4 Concentration-Dependent Diffusion
954 954 955 955 957 957 957 959 959 959 959 959
963
963
964 965 965 966 967 968 969
Contents XXXlll
30.2 Doping of Semiconductors 30.2.1 Dopants in Si and GaAs
30.2.1A Solubility of Dopants
30.2.1B Concentration-Dependence of Dopant Profiles in
971 972 975
~ 9ro 30.2.1C Concentrationa Dependence of Dopant Profiles in
GaAs 978
30.3
30.4
30.5
Doping by Ion Implantation
30.3.1 The Ion Implantation System
30.3.2 Ion Implantation
30.3.2A Deviations from the Gaussian Profile
30.3.2B Limitations of Ion Implantation
30.3.2C Annealing of Implantation Defects
30.3.2D Lateral Doping Profile
Multiple Junction Generation
Homogeneous Background Doping
30.5.1 Doping by Zone Melting
30.5.2 Doping by Transmutation
Chapter 31 Electrodes
31.1 Electrodes on Silicon
31.1.1 Ohmic Contacts
31.1.1A Aluminum as Gate Contact and Lead
31.1.1B Silicides as Contacts
31.1.1C Aluminide Formation
31.1.1D Diffusion Barriers
31.1.2 Schottky Barriers
31.2 Electrodes on GaAs 31.2.1 Ohmic Contacts
31.2.1A Ohmic Contact on n-type GaAs
31.2.1B Ohmic Contacts to p-type GaAs
31.2.2 Schottky Barriers on GaAs
31.3 Electrodes to Other Semiconductors
31.4 Phase Diagrams
31.4.1 The AI/Si and Pt/Si Systems
31.4.2 Ternary Phase Diagram Si/Ti/O
31.4.3 The GaAs/Metal System
31.5 Vacuum Deposition for Metallization
978
979 980 986 986 988 991
991
992
993 994
998
999
1000 1001 1002 1004 1005 1006 1007 1007 1008 1010 1010
1011
1011
1011 1013 1014
1018
xxxiv Contents
31.5.1 Evaporation
Chapter 32 Integrated Circuit Processing
1018
1022
32.1 Insulating Layer Deposition 1025 32.1.1 Si02 Layer Growth 1025
32.1.1A Thermal Oxidation 1025 32.1.1B Electrochemical Oxidation 1026 32.1.1C Si02 and Si3N4 Deposition 1026
32.2 Lithography and Masking 1028 32.2.1 Masks and Alignment 1030
32.2.1A Projection and Stepper Printing 1031 32.2.1B Optical Resolution 1031 32.2.1C Resist Application and Resist Systems 1032
32.3 Pattern Etching 1033 32.3.1 Wet Chemical Etching 1035
32.3.1A Si Etchants 1035 32.3.1A.l Electrolytic Etching 1037 32.3.1A.2 Defect-Sensitive Etches 1037
32.3.1B Selective Etchants on Si Integrated Circuits 1037 32.3.1B.l Silicon Dioxide Etchants 1038 32.3.1B.2 Silicon Nitride Etchant 1039 32.3.1B.3 Metal Etchants 1039
32.3.2 Plas~a Etching 1039 32.4 Etching of Gallium Arsenide 1040
32.4.1 GaAs Undercutting 1043 32.4.2 Dry Etching of GaAs 1044
32.5 Integrated Circuit Process Sequence 1045 32.5.1 Simple Passive Elements of an IC 1046
32.S.1A Metal Contacts 1046 32.S.1B Resistors 1048 32.S.1C Capacitors and Inductors 1049
32.5.2 Active Devices 1052 32.5.3 Three-Dimensional Integration 1054
32.6 Assembly and Packaging 1055
PART IV: SEMICONDUCTOR DEVICES 1061
Chapter33 Schottky Barriers and Diodes
33.1 Schottky Barrier Devices
1063
1064
Contents xxxv
33.1.1 Electrical Properties of Schottky Barrier Devices 1065 33.1.1A The Image Force 1066 33.1.1B Thermally Assisted Tunneling 1070 33.1.1C Carrier Recombination 1072 33.1.1D Tunneling through an Interface Layer 1073
33.1.1D.1 Image Force Effects, Insulating Layer 1075 33.1.1D.2 Pseudo-Interface Layers with Silicides 1076
33.1.1E Minority Carrier Injection 1076 33.1.1F The Contact Resistance 1077 33.1.1G Spatial Inhomogeneities 1077 33.1.1H Contact Stability 1081
33.1.2 Schottky Barriers to Si 1081 33.1.2A Doping Dependence 1082
33.1.3 Schottky Barriers to GaAs 1083 33.1.3A Schottky Barrier Device Fabrication 1085
33.1.4 Schottky Barriers to Other III-V Compounds 1086 33.1.5 Schottky Barriers on Other Semiconductors 1087
33.2 Device Application of Schottky Barriers 1087
33.2.1 Microwave Schottky Barrier Diode 1089 33.2.2 Metal-Semiconductor Field Effect Transistor 1090
33.2.2A Charge-Coupled Devices 1095 33.2.3 Schottky Barrier Photodiodes 1097
33.2.3A Metal-Insulator-Semiconductor Detectors 1097 33.2.4 Light-Emitting Diodes 1100
33.3 pn-Junction Diodes 1101 33.3.1 pn-Junction Diodes for Rectification 1101
33.3.1A Power Junction Device 1103 33.3.2 Variable Resistance Utilization 1105 33.3.3 Variable Capacitance Utilization 1106 33.3.4 High-Field Effect Diodes 1107
33.3.4A The Tunnel Diode 1108 33.3.4B The IMPATT Diode 1110
33.3.4B.1 The BARITT Diode 1111 33.3.4C The Transferred-Electron Device (TED) 1112
Chapter 34 Solar Cells 1119
34.1 The Solar Spectrum
34.1.1
34.1.2
Influence of the Earth's Atmosphere
Solar Cell Efficiency Limits in Sunlight
1120 1120 1124
xxxvi Contents
34.2 The Single Crystal Si Solar Cell 1128
34.2.1 Production of the Si solar Cell 1128 34.2.1A Improved Si Solar Cells 1132 34.2.1B Polka-Dot Electrodes 1136 34.2.1C Radiation-Resistant Si Solar Cells 1138
34.3 Low-Cost Si Solar Cells 1139 34.3.1 Solar Grade Si 1139 34.3.2 Polycrystalline Si Solar Cells 1139
34.3.2A Thin-Film Polycrystalline Si Solar Cells 1141
34.4 The Amorphous Si:H Solar Cell 1142
34.4.1 Cell Degradation 1144 34.4.2 Stacked and Tandem Solar Cells 1145
34.5 High-Efficiency 111-V Solar Cells 1150
34.5.1 The GaAs Solar Cell 1150 34.5.1A Thin-Film GaAs Cells 1151
34.5.2 The InP Solar Cell 1152 34.5.3 Hetero- and Multijunction III-V Solar Cells 1153
34.5.3A Stacked and Cascade GaAs-Based Cells 1153 34.6 Polycrystalline Thin-Film Cells 1153
34.6.1 The CdTe Solar Cell 1154 34.7 Polycrystalline Heterojunction Solar
Cells 1157 34.7.1 The CdS/Cu:cS Solar Cell 1157
34.7.1A The Pros and Cons for CdS/Cu:cS 1160 34.7.2 The CdS/CuInSe2 Solar Cell 1162
Chapter 35 Light Emitting Devices 1171
35.1 Minority Carrier Generation 1172
35.2 Luminescent Transitions 1173
35.2.1 Light Emission Efficiency 1177 35.2.1A External Efficiency of LEOs 1180 35.2.1B LED Degradation 1181
35.2.2 Design of Efficient LEOs 1183 35.2.3 LED Frequency Response 1184
35.3 Semiconductor Lasers 1186 35.3.1 Cavity, Threshold and Spectral Purity 1187 35.3.2 LED Laser Design 1192 35.3.3 LED Laser Degradation 1193
35.3.3A High-Power Lasers
35.3.4 Dimensional Confinement
35.4 LED Applications
Contents xxxvii
1195 1196 1197
35.4.1 Ultra-Short LED-Laser Pulses 1198
Chapter 36 Transistors and Multiterminal Devices 1202
36.1 The Bipolar Transistor and its Operation 1204 36.1.1 Modes of Operation 1205
36.1.1A Static Characteristics 1207 36.1.1B Voltage and Power Gain 1210 36.1.1C High-Frequency Performance 1214 36.1.1D High-Field Effects and Breakdown 1216
36.1.2 Special Use Transistors 1218 36.1.2A Power Transistors 1218 36.1.2B Switching Transistor 1218
36.1.3 The Thyristor 1220 36.1.3A Bidirectional Thyristors 1223 36.1.3B High Voltage Rating Thyristors 1223
36.1.4 Modern Development of Bipolar Transistors 1224 36.1.4A The New Planar Bipolar Transistor 1225 36.1.4B Heterojunction Bipolar Transistor (HBT) 1226
36.2 Unipolar Transistors 1226 36.2.1 Junction Field-Effect Transistors (JFET) 1228 36.2.2 The Metal-Semiconductor Field-Effect Transistor
(MESFET) 1232 36.2.2A Short Channel Devices 1233
36.2.2A.1 Field-Dependent Mobility 1233 36.2.2A.2 High-Frequency Behavior 1235
36.2.2B The Permeable Base Transistor (PBT) 1236 36.2.3 The Metal-Oxide Field-Effect Transistor (MOSFET) 1237
36.2.3A The Fourth Electrode in MOSFETs 1239 36.2.3B Device Scaling 1240
36.2.4 Other Types of MOSFETs 1240 36.2.4A Buried Channel MOSFET 1240 36.2.4B High-Performance MOSFETs (HMOS) 1241 36.2.4C Double Diffused MOSFETs (DMOS, DIMOS) 1242 36.2.4D VMOS and UMOS Structures 1242 36.2.4E MOSFETs for Nonvolatile Memory 1243 36.2.4F Silicon-on-Insulator Devices (SOl) 1244
36.2.5 Heterostructure Field-Effect Transistor (HFET) 1245
xxxviii Contents
36.2.6 Hot-Electron Transistors
36.2.7 Quantum-Effect Devices
36.2.7 A Materials and Basic Principles
36.2.7B Multiwell Transistor Structures
36.2.7C Superlattice-Base Transistor
Chapter 37 Semiconductors and Devices: An Epi-
1247 1251 1251 1252 1252
logue 1257
37.1 Desired Properties of New Materials
37.2 Trends and Future Potential 37.2.1 Trends in Transistor Technology
37.2.2 Trends in Solar Cell Technology
PART V:
Appendix Computation Routines and Tables
A.l Numerical Methods A.Ll The Kutta-Merson Integration Routine
A.l.lA Runge-Kutta Part
A.LlB Kutta-Merson Part
A.1.2 The Finite Element Numerical Method
A.L3 The Pros and Cons of the Two Methods
A.2 Some Mathematical Tools A.2.l Series
A.2.2 Coordinate Systems
A.2.3 The Wave Equation
A.3 List of Acronyms
AA Symbols Used
A.5 Important Derived Parameters
A.6 Summary of Important Equations
A.6.l Space Charge Related
A.6.lA Constant Space Charge Distributions
A.6.lB
A.6.lC
A.6.lD
A.6.lE
A.6.lF
Majority Carrier Injection (Space Charge Lim
ited Current)
Classical Schottky Barrier
Modified Schottky Barrier
Two-Level Schottky Barriers
Heterojunction Quasi-Schottky Barrier
1258
1262 1263 1267
1275
1275
1275 1275 1275 1277 1278 1280 1281 1281 1282 1283 1285
1294
1302
1303 1303 1303
1303 1303 1304 1304 1304
Content8 xxxix
A.7
A.6.lG Quasi-Schottky Barrier with Interface Recombi
nation
A.6.lH
A.6.1I
A.6.1J
A.6.lK
A.6.lL
A.6.lM
A.6.lN
A.6.1O
A.6.lP
A.6.lQ
A.6.lR
Carrier Generation and Recombination
Diffusion Currents
Drift-Enhanced Diffusion Current
Tunneling Current
Majority Carrier Distribution Near Junction
Carrier Velocity Saturation
pn-Homojunctions
Surface Recombination Current
Surface Conditions with Light
pn-Junction with Light
Classical Solar Cell Diode Model
A.6.2 Vacuum Related
A.6.3 Phonon Related
A.6.4 Photon Related
A.6.4A Reflection and Transmission of Light
Tables
Bibliography
Word Index
1304 1305 1305 1305 1306 1306 1306 1306 1306 1306 1307 1307 1307 1308 1308 1308 1309
1337
1389
List of Tables
Chapter 1 1.1 Properties of Some Semiconductors for Junctions .......... 11
Chapter 2 2.1 Relation Between Higher Index Surfaces and their
Step-Construction .................................... 21 2.2 Configuration and Heat of Formation of Chemisorbed Oxygen
on Si ................................................. 36
Chapter 4 4.1 Bond Length for 1r-Bonded Chain Model of
Si(111) 1x1 Surface .................................. 107 4.2 Displacement, Dimension, and Angle Parameter of
GaAs Surface ......................................... 114 4.3 Relaxation Parameters for (110) Surfaces of Zincblende
Semiconductors ....................................... 119 A.1 Si Surface Structure, Induced by Metal Deposition ......... 1309
Chapter 5 5.1 Segregation Coefficient for Impurities in Si and GaAs 155 5.2 Organometallic Feedstock Gases for MOCVD .............. 188
Chapter 6 6.1 Adatom Stretching Modes ................................. 228
Chapter 7 7.1 Energy of Acceptor and Donor States for Si Surfaces ....... 253 7.2 Transition Metals and Rare Earths that form Metal Silicides 271 7.3 Schottky Barrier Height of Transition Metals and Silicides
on n-type Si .......................................... 272 7.4 Canonical Schottky Barrier Height and Pinned
Fermi Level Position .................................. 276
Chapter 8 8.1 Workfunctions for Different Metal Surfaces ................ 305 8.2 Band Edge Offset of Heterojunctions ...................... 317
xli
xlii List of Tables
8.3 Position of Valence Band Edge Relative to Ge ............. 321 8.4 Midgap Energies after Tersoff ........... . . . . . . . . . . . . . . . . . .. 325 8.5 Band Edges and Deformation Potential .................... 331
Chapter 10 10.1 Index of Refraction and Transmittance for
Antireflection Coating ................................ 394
Chapter 13 13.1 Junction Parameters ...................................... 448 13.2 Interdependence of Barrier Variables ....................... 462
Chapter 14 14.1 Semiconductor Parameters ................................ 474
Chapter 17 17.1 Parameters of Ge Barrier .................................. 592
Chapter 18 18.2 Parameters for Si Diode ................................... 648
Chapter 20 20.1 Parameters for CdSjCu2S Heterojunction .................. 684 20.2 Parameters for CdSjCulnSe2 Heterojunction .............. 692
Chapter 23 23.1 Parameters for Thin Symmetric Si Diode .................. 740 23.2 Derived Parameters for Symmetric Si Diode ............... 746 23.3 Capture Coefficient for Si Diode ........................... 755
Chapter 24 24.1 Optical Generation-Related Parameters for CdSjCulnSe2
Solar Cell ............................................. 805 24.2 Changes in Parameters for Computation ................... 806 24.3 Diffusion Voltage and Characteristic Lengths for
CdSjCulnSe2 Solar Cell .............................. 810 24.4 Computed Changes in Open Circuit Voltage ............... 810
Chapter 25 25.1 Parameters for a-Si:H Solar Cell ........................... 827
List of Tables xliii
Chapter 28 28.1 Segregation Coefficient for Impurities in Semiconductors ... 906 29.1 Thermal Parameters for Si ................................ 934 29.2 Parameters for Four Sheet-Growth Technologies ........... 937 29.3 Parameters for Four Ingot-Growth Technologies ............ 938 29.4 Flatbed Deposition Parameters for a-Si:H ................. 943 29.5 Properties of a-Si:H Layer ................................. 950
Chapter 30 30.1 Diffusion Parameters of Dopants in Si ..................... 973 30.2 Diffusion Parameters of Dopants in GaAs and InP ......... 974 30.3 Diffusion Sources for Dopants in Si and GaAs .............. 975 30.4 Energy Loss of Fast Ions in Si ............................. 983 30.5 Maximum Energy Loss Due to Nuclei Scattering ........... 983
Chapter 31 31.1 Barrier Height of Metals to Si ............................. 1000 31.2 Material Properties for Electrodes on Si ................... 1003 31.3 Barrier Height of Metals to GaAs .......................... 1008 31.4 Metallization Techniques for Producing Ohmic Contacts 1009
Chapter 32 32.1 Negative and Positive Resist for Lithography .............. 1029 32.2 Plasma Etchants with Resulting Anisotropy and Selectivity 1043 32.3 Etchants to GaAs ......................................... 1044 32.4 Gases for Dry Etching of GaAs ............................ 1046 32.5 Process Flow Chart for Integrated Circuit ................. 1051
Chapter 33 33.1 Fabrication of Schottky Barriers ........................... 1088 33.2 Schottky Barrier Photodiodes ............................. 1099 33.3 Negative Differential Conductivity Parameters of
GaAs and InP ........................................ 1114
Chapter 34 34.1 Clear Day Total and Partial Radiances .................... 1123 34.2 Components of Radiances of Clear Days ................... 1124 34.3 Parameters of Violet-Type Si Solar Cell .................... 1133 34.4 Radiation Damage of Si Solar Cells ........................ 1139 34.5 Maximum Theoretical Efficiency of Tandem Solar Cells .... 1149
xliv List of Tables
Chapter 35 35.1 Photometric Brightness of Light Sources ................... 1180 35.2 Heterojunction Laser Diodes using Alloys .................. 1180
Chapter 36 36.1 Cutoff Frequency of Heterojunction Bipolar Transistors 1227 36.2 Electronic Parameters of II 1-V Semiconductors ............. 1247
Chapter 37 37.1 World Photovoltaic Shipments ............................. 1268 37.2 Emerging Markets for Solar Panels ........................ 1269
Appendix A.l Greek Alphabet ........................................... 1309 A.2 Periodic System of Elements ............................... 1309 A.3 Atomic Numbers, Masses and Abudances of Most
Abundant Isotopes .................................... 1311 AA Abundance of Semiconductor Constuents in Earth's Crust . 1312 A.5 Radioisotopes of Dopants in Semiconductors ............... 1312 A.6 Mechanical and Thermal Properties of Semiconductors
and Metals ........................................... 1313 A.7 Diffusion Coefficient for Dopants in Si and GaAs ........... 1313 A.8 Electron Effective Masses in Specified Conduction Bands ... 1314 A.9 Hole Effective Masses and Valence Band Parameters ....... 1315 A.I0 Band Gaps with Temperature and Pressure Coefficients .... 1316 A.ll Extensive Listing of Properties of Ge, Si, and GaAs ........ 1318 A.12 Nomogram for Uniformely Doped Si ....................... 1319 A.13 Nomogram for Uniformely Doped GaAs ................... 1320 A.14 Thermal and Mechanical Parameters of Semiconductors .... 1321 A.15 Intrinsic Workfunctions of Semiconductors ................. 1321 A.16 Heterojunction Lattice Mismatch and Dislocations ......... 1322 A.17 Workfunctions of Metals ................................... 1323 A.18 Workfunctions of Silicides ................................. 1323 A.19 Ohmic Contacts to Ge and Si .............................. 1324 A.20 Ohmic Contacts to Si ..................................... 1325 A.21 Ohmic Contacts to GaAs .................................. 1326 A.22 Ohmic Contacts to GaAs, GaAsP, GaInAsP, and GaP ..... 1327 A.23 Ohmic Contacts to Various III-V Compounds.: ............ 1328 A.24 Ohmic Contacts to Various II-VI Compounds .............. 1329 A.24 Ohmic Contacts to Various Semiconductors ................ 1330 A.26 Phonon Energies at Characteristic Points in Semiconductors 1331
List of Tables xlv
A.27 Static and Optical Dielectric Constant of Semiconductors .. 1332 A.28 Absorption Constant and Reflectance of Semiconductors ... 1333 A.29 Optical Constants of Semiconductors ...................... 1334
Survey of Semiconductor
Physics
