Semiconductor
`Optoelectronic
`Devices
`
`PALLAB BHATIACHARYA
`
`Vizio EX1016 Page 0001
`
`

`
`lill
`
`LIBRARY OF CONGRESS
`
`l~ll~l~llm~~~m~wml~mmm
`0 015 993 914 5
`
`Semiconductor
`Optoelectronic Devices
`
`PALLAB BHAITACHARYA
`
`This book provides a comprehensive view of compound semiconductors and their applications in
`phoronic devices. The material is well presented and can be used as either a textbook or as a
`reference source.
`-Professor Ben Streetman, The University of Texas at Austin
`
`In the past decade, there has been remarkable innovation in optoelectronic devices, components,
`and circuits. They have moved out of the laboratory and into a wide variety of systems and
`applications. To help readers take advantage of these advances, author Pallab Bhattacharya
`offers an in-depth, accessible inll·oduction to the principles of these devices with a unique
`tutorial/reference approach.
`The first real, comprehensive text/reference book on the subject, Semicondul1or Optoelectronic
`Devices:
`• Describes the basic properties of semiconductors and hetcrojunctions, and epitaxial techniques
`used to grow them.
`• Carefully presents the basic optical processes of absorption and recombination in bulk and
`quantum well structures.
`• Analyzes and describes light-emitting diodes, lasers, photodetectors, solar cells, and light-
`modulators.
`• Reviews the emerging, important topic of optoelectronics integrated circuits (OEJC).
`The principles of the devices are presented with appropriate analyses and derivations,
`measurement techniques, and recent experimental results. The author introduces new concepts
`such as pseudomorphic materials, quantum well, distributed-feedback and surface-emitting
`lasers, modulated barrier photodiodes, coherent and wavelength selective detection, and
`quantum well modulation devices.
`
`About the Author
`Pallab Bhattacharya received his Ph.D. degree in Electronic and Electrical Engineering from
`the University of Sheffield, U.K., in 1978.
`Dr. Bhattacharya is Professor of Electrical Engineering and Computer Science at the University
`of Michigan at Ann Arbor. He was invited Professor at the Ecole Polytechnique federale de
`Lausanne, Switzerland, during 1981-1982. He is Associate Editor of the IEEE Transactions on
`Electron Devices and serves on the advisory board of the Electrical and Communications
`Systems Division at the National Science Foundation.
`His research has focused on liquid phase and molecular
`beam epitaxy, electronic and optoelectronic properties
`of semiconductors, optoelectronic devices, and
`optoelectronic integrated circuits.
`
`ISBN 0-13-805748-6
`90000
`
`PRENTICE HALL
`Englewood Cliffs, NJ 07632
`
`9
`
`Vizio EX1016 Page 0002
`
`

`
`UIJrm~· of Congress Cotologing·in·Publicotion Daw
`Olmnnchurya, Pallab.
`Semiconductor optocle<:lronic devices I Pullab Bhanacharya.
`p. em.
`Includes bibliographical references and index.
`ISBN 0-13-805748-6
`I. Optoelectronic devices. 2. Semicooductors.
`TK8320.B52 1994
`621.3815 • 2- dc20
`
`!. 'Iitle.
`
`93-38501
`"
`C1P
`
`"~-t 'I'J
`
`Publisher: Alan Apt
`Production Editor: M ona PompiJi
`Co~er Designer: Pallab Bhallacharya
`Copy Editor: llrcnda Melissnracos
`Preprcss Buyer: Linda Behrens
`Mnnufuccuring Buyer: Dave Dickey
`Supplemencs Editor: Alice Dworkin
`Editorial Asslscnnc: Shirley McGuire
`Cover llluscracion: Oproeleccronic integrated circuit shown on cover is part of a 4-channel transmitter array
`(councsy of 0. Wodn. PujitSu Limited. Atusgi. Japan).
`
`~~ @) 1994 by Prcniice-1-loll, Inc.
`=:-
`A Parnmounl Communicncions Compnny
`Englewood Cliffs. New Jersey 07632
`
`The auchor and publisher of chis book h:wc used rheir bcsr err on~ in ptc{>aring chis book. ·n1cse effons include
`the development, rcsenrch. nnd ce.~ting of the lheorie.~ nnd programs ot determine their effectiveness. The author
`and publisher shall not be linblc in ony event for incidental or consequential dumagcs in connection with, or
`arising out of. the furnishing. pcrfonnnnce. or usc of these programs.
`
`All righ1s reserved. No part of !his book may be reproduced, in any form or by ony means, without permission
`in writing from the publisher.
`
`Printed in the United States of America
`
`10 9 8 7 6 5 4 3 2
`
`ISBN 0-13-805748-6
`
`PRENTICE-HAI..L 1NTERNAT10Nt\L (UK) LIMITED, London
`PRilNTICE- HAl.L OF AUSTR,\UA PrY. LIMITED, Sydney
`PRP.NTtCE·HAL.L CANADA, I NC., Toronto
`PRilNTtCil·HAU.. HtsrANOAMF.JUCANA, S.A., Mexico
`PREN11CE·HALI. OP INDIA PRIVATI! LiMl'rEO, New Delhi
`PRt:NTICE· HAU.. OP JAt'AN, INC., Tokyo
`SIMON & SCHUSTER ASIA i>rE. LTD., Singapore
`EDITORA PRENTICE-HALL DO BRASIL, LTDA., Rio de Janeiro
`
`Vizio EX1016 Page 0003
`
`

`
`Semiconductor
`Optoelectronic
`Devices
`
`..
`PALLAB BHATTACHARYA
`Department of Ele<;;frical Engineering
`and Computer Science
`University of Michigan, Ann Arbor
`
`..
`
`\
`
`Prentice Hall, Englewood Cliffs, New Jersey 07632
`
`~
`
`Vizio EX1016 Page 0004
`
`

`
`Dedicated to the
`cherished memory
`of my father.
`
`I
`
`Vizio EX1016 Page 0005
`
`

`
`F
`
`Preface
`
`SCOPE
`
`Since the demonstration of the first light-emitting diode (LED) and junction laser, op(cid:173)
`toelectronics has made remarkable progress. The developments in this field have been
`driven by the needs of lightwave communication systems, alternate energy sources,
`and optical or optoelectronic counterparts of electronic switching and logic elements.
`Optical devices and components and optical fibers are selectively replacing electronic
`devices and circuits, offering unique advantages. In fact, optoelectronic devices and
`circuits have unobtrusively and efficiently made their way into our daily lives. In the
`ught of this enormous progress in the field, it is hoped that this book will reflect these
`dramatic changes in the field and serve two main purposes: (1) to formally introduce
`senior-level undergraduate and graduate students to optoelectronics, thereby helping
`them to guide their studies and career developments, and (2) to provide, in an acces(cid:173)
`sible textbook format, a good and well-focused reference/tutorial book for practicing
`engineers and physicists.
`
`PRESENTATION
`
`The text has been developed at two levels, to benefit both the seniors and graduate
`students. The book is intended to be self-sufficient and extensive reference work should
`not be necessary. A background of a fhst course in semiconductors is assumed.
`The first four chapters lay the foundations for the optoelectronic devices. The
`first chapter describes compound semiconductor materials and their epitaxy. Much
`of the present-day device concepts would not be realized without sophisticated and
`matured epitaxial techniques. Semiconductor statistics and carrier transport properties
`are described in Chapter 2. The basic optical processes of absorption and recombi(cid:173)
`nation in bulk and quantum well structures are analyzed and described in Chapter 3.
`Here, detailed quantum mechanical calculations are excluded, since these are found
`in at least half-a-dozen texts. However, appropriate references are provided as foot-
`
`vii
`
`Vizio EX1016 Page 0006
`
`

`
`viii
`
`Preface
`
`note":s. Chapter 4 describes junction theory, including metal-semiconductor junctions
`and heterojunctions. The case of high-level injection, which becomes important for
`laser operation, is emphasized in this chapter.
`The devices themselves are described in Chapters 5- 11 in the following order:
`light-emitting diodes, lasers, photodetectors, solar cells, and light-modulators. Lasers
`and photodetectors, which are perhaps the more important and common optoelectronic
`devices, are each described in two chapters.
`The principles of the devices are presented with appropriate analyses and deriva(cid:173)
`tions. Measurement techniques and recent experimental results are also included to
`give the reader a feel for real parameter values.
`The organization of the device chapters should provide the instructor the flexibility
`to present material to both undergraduate and graduate students. In discussing the
`different devices, 1 have introduced new concepts, within the scope of the text. For
`example, pseudomorphic materials, quantum wells, distributed-feedback and surface(cid:173)
`emitting lasers, modulated barrier photodiodes, coherent and wavelength selective
`detection, and quantum well modulation devices are all described and analyzed in
`various levels of detail. Finally, the text is concluded in Chapter 12 with a review of
`optoelectronic integrated circuits (OEICs), an emerging and important subject.
`
`HOW TO USE THIS BOOK
`
`This book is flexible and can be adapted to your local curriculum and course needs.
`An example of a one-term senior undergraduate course thar could be taught ti·om the
`book would cover chapters l, 2. and 4 as review; chapters 3, 5, 6, parL of 7, 8, and
`part of J 1 should be treated as essentiaJ; and chapter 1 0 could be treated as optional.
`The rest of chapters 7 and 11. and chapters 9 and 12 T consider advanced material
`that you can teach in a graduate level course or material that you can choose from
`selectively to tailor the course to your desired emphasis and objectives.
`
`READING LIST AND PROBLEMS
`
`Suggested texts for more extensive reading and key articles from journals and period(cid:173)
`icals are listed at the end of each chapter and as footnotes. These will help the more
`inquisitive students to go beyond the confines of the text and course and to enhance
`their knowledge and understanding. Also included are a set of problems at the end
`of each chapter, in addition to a few worked-out examples. The purpose of these
`problems is twofold: ( l) to enhance the understanding of the different devices and
`underlying concepts and (2) to get a feel for practical values of different device and
`material parameters and their units.
`
`UNITS
`
`The rationalized MKS system of units has been mostly fo llowed, with convenient
`changes. For example em is more often used as the unit of length, and the electron
`
`Vizio EX1016 Page 0007
`
`

`
`volt (eV) is used in place of joule (J) as the unit of energy. The cgs system is
`sometimes used to keep in line with common use.
`
`Preface
`
`ix
`
`ACKNOWLEDGMENTS
`
`It is a pleasure to acknowledge all those who have provided help, inspiration, and
`encouragement as I proceeded with this arduous task.
`I would like to thank Pro(cid:173)
`fessor Ben Streetman for providing invaluable suggestions and warning me of the
`many pilfalls before l got started. Discussions with Dr. Niloy Dutta are gratefully
`acknowledged. I am indebted to my colleagues, Professor George Haddad for his
`encouragement and Professor Jasprit Singh for his many valuable comments and sug(cid:173)
`gestions. The text has greatly benefited from the help and comments of many of
`my present and Fonner graduate students. Special thanks are due to Latry Davis,
`Augusto Gutierrez-Aitken, Yeeloy Lam, Sanjay Sethi, and Hsiang-Chi Sun, and Drs.
`Yaochung Chen, Subrata Goswami, Shantanu Gupta, Weiqi Li, and Doyle Nichols.
`I would like to thank my professional colleagues who have generously contributed
`data and photographs. They are J. Goldman (RIB ER SA) and Drs. G. A. Antypas
`(Crystacomm Jnc.), S. N. G. Chu (AT&T Bell Laboratories), 1. Hayashi (Optoelectron(cid:173)
`ics Technology Research Laboratory), J. L. Jewell (Photonics Research Incorporated),
`J. Loehr (Wright Laboratories, WPAFB), D. A. B. Miller (AT&T Bell Laboratories),
`D. Pooladdej (Laser Diode, Inc.), R. Sahai (Rockwell International), J. Singh (Uni(cid:173)
`versity of Michigan), S. Swirhun (Bandgap Technology Corporation), W. T. Tsang
`(AT&T Bell Laboratories), 0. Wada (Fujitsu Limited), I. Weinberg (NASA, Lewis Re(cid:173)
`search Center), and E. Woelk (AJXTRON Gmbii). This book would not have seen the
`light of day without the hard work of three persons: Christina Baydl, who transformed
`my hieroglyphics into a readable form, and Mary Ann Pruder and Mina Hale, who
`did all the artwork. The help of Alan Apt and Mona Pompi li is greatly appreciated.
`I will remain indebted to all of you.
`Last, and by no means the least, I am indebted to my mother for her support
`and to my family for their understanding, support, and willingness to sacrifice many
`evenings, weekends, and holidays.
`
`Paflab Bhattacharya
`Ann Arbor, Michigan
`
`Vizio EX1016 Page 0008
`
`

`
`Contents
`
`1 ELEMENTAL AND COMPOUND SEMICONDUCTORS
`
`1.1
`
`1.2
`
`1.3
`
`1.4
`
`1.5
`
`1.6
`
`1.7
`
`Introduction 2
`
`Bonding in Solids 5
`
`Crystalline Nature of Solids 9
`
`1.3.1 Directions and Planes, 13
`1.3.2 Reciprocal Lattice Vectors, 15
`
`Alloy Semiconductors 17
`
`Lattice-Mismatched and Pseudomorphic Materials 21
`
`Transmission Media and Choice of Materials 29
`
`Crystal Growlh 35
`
`lnti'Oduction, 35
`I. 7.1
`I. 7.2 Bulk Crystal Growth, 35
`1.7.3 Epiwxial Material Growth, 37
`1.7.4 Factors Controlling Heterointerface Quality. 49
`1.7.5 Doping of Semiconductors, 50
`
`1.8
`
`Device Processing 53
`
`Problems 56
`
`Reading List 58
`
`2 ELECTRONIC PROPERTIES OF SEMICONDUCTORS
`
`59
`
`2. 1
`
`2.2
`
`Introduction 60
`
`Can·ier Effective Masses and Bandstructure 60
`
`xi
`
`Vizio EX1016 Page 0009
`
`

`
`xii
`
`Contents
`
`2.3
`
`2.4
`
`2.5
`
`2.6
`
`2.7
`
`Effect of Temperature and Pressure on Bandgap 65
`
`Carrier Scattering Phenomena 68
`
`Semiconductor Statistics 74
`
`2.5.1 Energy Distribution Functions, 74
`2.5.2 Density of States Function, 76
`2.5.3 Density of Carriers in Intrinsic and Extrinsic Semiconductors, 8/
`2.5.4 Compensation in Semiconductors, 86
`2.5.5 Consequences of Heavy Doping: Bandtail States, 90
`
`Conduction Processes in Semiconductors 95
`
`Bulk and Surface Recombination Phenomena 102
`
`Introduction, 102
`2.7.1
`2. 7.2 Recombination-Generation via Defects or Levels in the Bandgap. 102
`2. 7.3
`Swface Recombination, I 05
`
`Problems 107
`
`Reading List 111
`
`3 OPTICAL PROCESSES IN SEMICONDUCTORS
`
`112
`
`3.1
`
`Electron-Hole Pair Formation and Recombination 113
`
`3. 1. I Radiative and Non-Radiative Recombination, 116
`3.1.2 Band-to-Band Recombination, I 18
`
`3.2
`
`Absorption in Semiconductors 119
`
`3.2. I Matrix Elements and Oscillator Strettgth for Band-to-Band
`Transitions, I 19
`Indirect Intrinsic Transitions, 126
`3.2.2
`3.2.3 Exciton Absotption, 126
`3.2.4 Donor-Acceptor and lmpurit)'-Band Absotption, 127
`3. 2.5 Low-Energy (Long-Wavelength) Absorption, 129
`
`Effect of Electric Field on Absorption: Franz-Keldysb and Stark
`Effects 131
`
`Absorption in Quantum Wells and the Quantum-Confined Stark
`Effect 133
`
`The Kramer-Kronig Relations 137
`
`Radiation in Semiconductors 139
`
`3.6.1 Relation between Absorption and Emission Spectra, /39
`3.6.2 Stokes Shift in Optical Transitions. 141
`3.6.3 Near-Bandgap Radiative Transitions, 142
`
`3.3
`
`3.4
`
`3.5
`
`3.6
`
`3.7
`
`Deep-Level Transitions 145
`
`Vizio EX1016 Page 0010
`
`

`
`Contents
`
`xiii
`
`156
`
`3.8
`
`3.9
`
`3.10
`
`3. 1 J
`
`Auger Recombination 146
`
`Luminescence from Quantum Wells 147
`
`Measurement of Absorption and Luminescence Spectra 147
`
`Time-Resolved Photoluminescence 150
`
`Problems 153
`
`Reading List 154
`
`4 JUNCTION THEORY
`
`4.1
`
`4.2
`
`Introduction 157
`
`P-N Junctions 157
`
`Junction Formation, /57
`4.2./
`4.2.2 Electrostatics of the p-n junction: Contact Potential and Space
`Charge. 163
`4.2.3 Current-Voltage Relationship, I 72
`4.2.4 Quasi-Fermi Levels and High-Level Injection, 178
`4.2.5 Graded Junctions, 181
`4.2.6 AC Operation of Diodes: Dijfusio11 Capacitance, 183
`4.2.7 Breakdown Phenomena in Junction Diodes, 183
`
`4.3
`
`Schotlky Barriers and Ohmic Contacts 186
`
`Introduction, 186
`4.3.1
`4.3.2 Schottky Barriers, 187
`4.3.3 Ohmic Contacts, 191
`
`4.4
`
`Semiconductor 1-leterojunctions 193
`
`Introduction, 193
`4.4.1
`4.4.2 The Ideal HeterojuncLion, 194
`4.4.3 Curre/11-Voltage Characteristics, 197
`4.4.4 Real Heterojunction Band Offsets, /98
`4.4.5 Application of Heterojunctions to Bipolar Tmnsistors, 199
`
`Problems 202
`
`Reading List 204
`
`5 LIGHT EMITTING DIODES
`
`205
`
`5.1
`
`5.2
`
`5.3
`
`5.4
`
`Introduction 206
`
`The Electroluminescent Process 206
`
`Choice of LED Materials 208
`
`Device Configuration and Efficiency 210
`
`Vizio EX1016 Page 0011
`
`

`
`xiv
`
`Contents
`
`Injection. Efficiency, 210
`5.4.1
`5.4.2 Recombination Efficiency, 212
`5.4.3 Extraction Efficiency and External Conversion Efficiency, 213
`5.4.4 Coupling Loss, 217
`
`5.5
`
`5.6
`
`Light Output from LED 218
`
`LED Structures 220
`
`5.6.1 Heterojunction LED, 220
`5.6.2 Burrus Surface-Emifling LED. 222
`5.6.3 Guided Wave or Edge-Emilling LED. 223
`5.6.4 Drive Circuifly, 225
`
`5.7
`
`Device Performance Characteristics 226
`
`5.7./ Spectral Response, 226
`5.7.2 Output Power-Time Characteristics, 227
`5.7.3 Ligl!t(Power)-Current Characteristics, 228
`5. 7.4 Diode Current-Voltage Clwracteristics, 228
`
`5.8
`
`5.9
`
`Frequency Response and Modulation Bandwidth 229
`
`Manufacturing Process and Applications 231
`
`5.10
`
`Defects and Device ReHability 233
`
`Problems 234
`
`Reading List 235
`
`6 LASERS: OPERATING PRINCIPLES
`
`237
`
`6.1
`
`6.2
`
`Introduction 238
`
`Guided Waves 238
`
`6.2.1 Waveguide Modes, 238
`6.2.2 Propagming Modes in a Symmetric Slab Waveguide, 241
`6.2.3 Asymmetric and Three-Dimensional Waveguides, 242
`
`Emission and Absorption of Radiation in a Two-Level Systems 244
`
`The Einstein Relations and Population Inversion 245
`
`Gain in a Two-Level Lasing Medium 248
`
`Lasing Condition and Gain in a Sem iconductor 250
`
`Selective Amplification and Coherence-Need for Laser Cavity 254
`
`6.7.1 Threshold Condition for Lasing, 255
`
`Lineshape Function and Line-Broadening Mechanisms 259
`
`Lasing Threshold Condition in a Two-Level System 260
`
`6.3
`
`6.4
`
`6.5
`
`6.6
`
`6.7
`
`6.8
`
`6.9
`
`Vizio EX1016 Page 0012
`
`

`
`Contents
`
`xv
`
`6.10
`
`Axial and Transverse Laser Modes 261
`
`Problems 263
`
`Reading List 264
`
`7 LASERS: STRUCTURES AND PROPERTIES
`
`265
`
`7. 1
`
`7.2
`
`Junction Laser Operating Principles 266
`
`Threshold Current 270
`
`7.2.1 Threshold Current Density of a Semiconductor Laser Treated as a
`Two-Level System, 270
`7.2.2 Threshold Current Density from the Spontaneous Emission Rate, 271
`7.2.3 Power Output, 275
`7.2.4 Temperature Dependence of Threshold Current, 276
`
`7.3
`
`Heterojunction Lasers 277
`
`Losses in Heterostructure Lasers, 283
`7.3.1
`7.3.2 Heterostrucwre l.L1ser Materials, 284
`
`7.4
`
`Distributed Feedback Lasers 285
`
`Introduction, 285
`7.4.1
`7.4.2 Coupled-Mode Theory, 286
`
`7.5
`
`The Cleaved-Coupled-Cavity (C3) Laser: A Technique for Obtaining
`Narrow Spectral Linewidth 292
`
`7.6
`
`Quantum Well Lasers 294
`
`7.6. I
`
`Strained Quwlfum Welll.L1sers, 296
`
`Surface-Emitting Lasers 300
`
`Rare-Earth Doped Lasers 302
`
`Alternate Pumping Techniques 304
`
`Device Fabrication 305
`
`Measurement of Laser Characteristics 307
`
`Laser Mounling and Fiber Coup! ing 308
`
`Modulation of Lasers: Rate Equations 311
`
`7.13. 1 Steady-State Solution or Static Characteristics, 312
`7.1 3.2 Transient Phenomena and Frequency Response, 3/4
`
`Mode Locking of Semiconductor Lasers 322
`
`Anomalous Behavior and Device Reliability 323
`
`7.7
`
`7.8
`
`7.9
`
`7 . I 0
`
`7. I I
`
`7.12
`
`7. 13
`
`7.14
`
`7.15
`
`Vizio EX1016 Page 0013
`
`

`
`xvi
`
`Contents
`
`7.16
`
`Long-Wavelength Semiconductor Lasers 325
`
`Problems 326
`
`Reading List 328
`
`8 PHOTODETECTORS
`
`8. J
`
`8.2
`
`Introduction 330
`
`Photoconductors 332
`
`8.2.1 DC Photoconductor, 336
`8.2.2 1\C Photoconducror, 338
`8.2.3 Gain and Bandwidth, 339
`8.2.4 Noise in Photoconductors, 340
`
`8.3
`
`Junction Photodiodes 342
`
`lwroduction, 342
`8.3.1
`8.3.2 p-i-n (PIN) Photodiodes, 343
`1-/eterojunction Diodes, 355
`8.3.3
`
`8.4
`
`Avalanche Photodiodes 358
`
`329
`
`Introduction, 358
`8.4.1
`8.4.2 Avalanche Multiplication: Ionization Threshold Energies, 359
`8.4.3 Multiplication and Ionization Coefficients in p-i-11 mul p-n Jtwction
`Diodes, 361
`8.4.4 Measurement of Multiplication Factors and Impact Ionization
`Coefficients, 365
`8.4.5 Noise Pe1jormance of Avalanche Photodiodes, 368
`8.4.6 Practiced Avalanche Photodiodes, 369
`8.4. 7 Super/a/lice Avalanche Plwtodiodes, 372
`
`8.5
`
`High-Speed Measurements 375
`
`Impulse Response Measuremems. 375
`8.5.1
`8.5.2 OptiCttl Heterodyning, 376
`8.5.3 Electro-optic Measurement Technique. 377
`8.5.4 Fiber Coupling, 378
`
`8.6
`
`Comparison of Different Detectors 380
`
`Problems 381
`
`Reading List 382
`
`9 SPECIAL DETECTION SCHEMES
`
`384
`
`9. 1
`
`9.2
`
`Introduction 385
`
`Phototransistor 385
`
`Vizio EX1016 Page 0014
`
`

`
`Contents
`
`xvii
`
`9.3
`
`9.4
`
`9.5
`
`9.6
`
`9.7
`
`9.8
`
`9.9
`
`Modulated Barrier Photodiode 388
`
`Metal-Semiconductor (Schottky Barrier) Photodiode 395
`
`Metal-Semiconductor-Metal (MSM) Photodiode 396
`
`Detectors for Long-Wavelength Operation 400
`
`Wavelength Selective Detection 402
`
`Coherent Detection 406
`
`Microcavity Photodiodes 409
`
`Problems 411
`
`Reading List 412
`
`10 SOLAR CELLS
`
`413
`
`10.1
`
`I 0.2
`
`10.3
`
`10.4
`
`I 0.5
`
`I 0.6
`
`Introduction 414
`
`Basic Principles: Current-Voltage Characteristics 415
`
`Spectral Response 420
`
`Heterojunction and Cascaded Solar Cells 422
`
`Schottky Barrier Cells 425
`
`Materials and Design Considerations 426
`
`10.6. 1 Materials Require111ents, 426
`10.6.2 Solar Cell Design, 427
`10.6.3 p+ -11-11+ versus n+ -p-p+ Cells. 428
`10.6.4 Dependence o.f Cell Performance on Extenwl Factors, 428
`
`Problems 430
`
`Reading List 431
`
`11 OPTOELECTRONIC MODULATION AND SWITCHING DEVICES
`
`432
`
`11.1
`
`l l.2
`
`11.3
`
`11.4
`
`11.5
`
`Introduction 433
`
`Analog and Digital Modulation 435
`
`Franz-Keldysh and Stark Effect Modulators 436
`
`Quantum Well Electro-Absorption Modulators 436
`
`Electro-Optic Modulators 439
`
`11.5.1 Birefriugence and the Electro-Optic Effect: Applicatiou to Phase
`Modulation, 439
`11.5.2 Electro-Optic Amplitude Modulation, 443
`
`Vizio EX1016 Page 0015
`
`

`
`xvlii
`
`Contents
`
`11.5.3 The Quadratic Electro-Optic Effect: Quantum Well Modullllors, 448
`1/.5.4 Modulation by Carrier Injection, 450
`
`11.6
`
`Optical Switching and Logic Devices 451
`
`11.6.1 Introduction, 45/
`11.6.2 Self-Electro-Optic Device. 451
`1/.6.3 The Bipolar Comroller-Modulator, 454
`11.6.4 Switching Speed and Energy, 460
`
`Problems 463
`
`Reading List 464
`
`12 OPTOELECTRONIC INTEGRATED CIRCUITS
`
`465
`
`12.1
`
`12.2
`
`12.3
`
`12.4
`
`12.5
`
`lntroduction 466
`
`Need for Integration: Hybrid and Monolithic Integration 466
`
`Applications of Optoelectronic Integrated Circ uits 468
`
`Materials and Processing for OEICs 471
`
`Integrated Transmitters and Receivers 473
`
`12.5.1 From-End Photoreceivers, 474
`12.5.2 OEJC Transmitters. 481
`12.5.3 Complex Circuits and Arrays, 485
`
`12.6
`
`Guided Wave Devices 487
`
`1 2.6.1 Waveguides and Couplers, 487
`12.6.2 Active Guided Wave Devices, 491
`
`12.7
`
`Prospects for Optical Interconnects 491
`
`Problems 495
`
`Reading List 495
`
`LIST OF SYMBOLS
`
`APPENDICES
`
`1
`
`IMPORTANT PROPERTIES OF COMMON SEMICONDUCTORS
`
`2 DISPERSION RELATION OF A DIATOMIC LATTICE
`
`3 THE FERMI INTEGRAL AND CARRIER CONCENTRATION IN
`DEGENERATE SEMICONDUCTORS
`
`496
`
`501
`
`503
`
`507
`
`Vizio EX1016 Page 0016
`
`

`
`Contents
`
`xix
`
`4 RADIATION DENSITY AND PHOTON DENSITY
`
`5 PARAMETERS FOR UNIFORMLY DOPED ABRUPT GaAs JUNCTION
`AT 300°K
`
`6 FREQUENCY RESPONSE OF LIGHT-EMITIING DIODE
`
`7 PROPAGATION MODES IN A SYMMETRIC PLANAR SLAB
`WAVEGUIDE
`
`8 MODES IN AN ASYMMETRIC SLAB WAVEGUIDE
`
`9 SIGNAL-TO-NOISE RATIO IN BALANCED DETECTION SYSTEM
`
`10 ELECTROABSORPTION IN BIAXIALLY STRAINED QUANTUM WELLS
`
`11 POWER FLOW IN DUAL-CHANNEL DIRECTIONAL COUPLER
`
`INDEX
`
`509
`
`511
`
`513
`
`515
`
`517
`
`518
`
`521
`
`523
`
`525
`
`Vizio EX1016 Page 0017
`
`

`
`3
`
`Optical Processes in
`Semiconductors
`
`\
`
`-Lwninescence from Quanfuiil
`Wells
`
`A:bsorption in Quantum WellS
`and the Quantum-<9onfutell $tark
`Effect
`
`112
`
`Vizio EX1016 Page 0018
`
`

`
`Sec. 3.1
`
`Electron-Hole Pair Formation and Recombination
`
`113
`
`ELECTRON-HOLE PAIR FORMATION AND RECOMaiNATION
`
`The operation of almost all optoelectronic devices is based on the creation or annihi(cid:173)
`lation of electron-hole pairs. Pair formation essentially involves raising an electron in
`energy from the valence band to the conduction band, thereby leaving a hole behind
`in the valence band. In principle, any energetic particle incident on a semiconductor,
`which can impart an energy at least equal to the bandgap energy to a valence band
`electron, will create pairs. With respect to the bonding in the lattice, this process
`is equivalent ~o prealcing a covalent bond. The simplest way to create electron-hole
`pairs is to irradia~e the semiconductor. Photons with sufficient energy are absorbed,
`and these impart their energy to the va.J~nce band electrons and raise them to th~
`conduction band. This process is, therefore, also called absorption. The reverse pro(cid:173)
`~ess, that of electron and hole recombination, is associated with tj:le pair giving up its
`excess energy. Recortbination may be radiative or nonradiative. In a nonradiative
`transition, the excess energy due to recombin~tion is usually imparted to phonons and
`dissipated as heat. In a radiative transition, the excess energy is dissipated as photons,
`U$U&lly having energy equal to the bandgap (i.e., hw = £8 ). This is the luminescent
`process, which is classified according to the method by which the electron-hole pairs
`are created. Photoluminescence involves the radiative recombination of electron-hole
`pairs created by injection of photons. Cathodoluminescence is the process of radiative
`recombination of electron-hQle pairs created by electron bombardment. Electrolumi(cid:173)
`nescence is the process of radiative recombination following injection with a p-n
`junction or s4n.ilar device.
`· In a semiconductor in equilibrium (i.e., without any incident photons or injection
`of electrons), the carrier densities can be calculated from an equilibrium Fermi level by
`using Fermi-Dirac or Boltzmann statistics outlined in Sec. 2.5.3. When excess carriers
`arc created by one of the techniques described above, nonequilibrium conditions are
`generated and the concept of a Fermi level is no longer valid. One can, however,
`define ponequilibrium distribution functions for electrons and holes as
`1
`)
`(
`1 + exp &~'in
`
`h~) =
`
`(3.1)
`
`/p (£) = -
`----:----:-
`1 + exp ( t:~'le)
`
`(3.2)
`
`These distribution fqnctions define £/'! and £!P• the quasi-Fermi levels for electrons
`and holes, respectively. In some tex~s they are referred to as IMREFs (Fermi spelleq
`backward). Wlien the excitation source creating excess carriers is removed, £111 =
`£1p =£F. The difference (Etn- Etp) is a measure of the deviation from equilibrium.
`As with equilibrium statistics, we obtain for H1e nondegener~te case
`
`(3.3)
`
`Vizio EX1016 Page 0019
`
`

`
`114
`
`CHAPTER 3 Optical Processes in Semiconductors
`
`and the nonequilibrium carrier concentrations are given by
`
`11 = Nc exp (
`
`E.rn - Ec)
`
`ku T
`
`p = Nv cxp
`(
`
`&v -Er )
`, P
`ku1
`
`(3.4)
`
`(3.5)
`
`(3.6)
`
`The concept of quasi-Fermi levels is extremely useful, since it provides a means
`to take into account changes of canier concentration as a function of position in a
`semiconductor. As we shall see in Chapter 4, in a p-n junction under forward bias a
`large density of excess carriers exist in the depletion region and close to it on either
`side. The concentration of these carriers can be detennined from tbe appropriate
`quasi-Femu levels. A junction laser is operated under such forward bias injection
`conditions to create population inversion. To consider a simple example, assume that
`an n-type semiconductor with an equilibrium electron density n0 (= N D, the donot;.
`density) is uniformly irradiated with intrinsic photoexcitation (above-bandgap light)'
`so as to produce l;;.n electron-hole pairs with a generation rate G. The nonequilibrium
`electron and hole concentrations are given by
`n = l;;.n + n0
`p = l;;.n +ntfno
`
`(3.7)
`
`(3.8)
`
`Using Eqs. 3.3-3.8, Fig. 3.1 illustrates the change in the energy position of the quasi
`Ferrni levels in GaAs as the generation rate changes.
`
`2.0..---- -- - - - - - -- - - - ,
`
`trn
`
`~ 1.51_ £""-c---- - - -- - - ----;
`"' ~
`~ 1.0
`-~
`~
`·~
`&
`
`Electron-hole pair density (em -J)
`
`Figure 3.1 Energy position of the
`electron and hole quasi-Fenni levels
`as a function of pair generation
`rate in GaAs at room temperature.
`It is assumed that the sample is
`n-type with No= 1015 cm-3 (from
`M: Sbur, Physics of Semiconductor
`Devices, @1990. Reprinted
`by permission of Prentice-Hall,
`Englewood Cliffs, New Jersey).
`
`Vizio EX1016 Page 0020
`
`

`
`Sec. 3.1
`
`Electron-Hole Pair Formation and Recombination
`
`115
`
`The excess carriers created in a semiconductor must eventually recombine. In fact,
`under steady-state conditions the recombination rate must be equal to the generation
`rate:
`
`G=R
`
`(3.9)
`
`:r
`
`Generation and recombination processes involve transition of carriers across the energy
`bandgap and are therefore different for direct and indirect bandgap semiconductors,
`as illustrated in Fig. 3.2. In a direct bandgap semiconductor, as shown in Fig. 3.2(a),
`the valence band maximum and the conduction band minimum occur at the zone
`center (k = 0) and an upward or downward transition of electrons does not require a
`change in momentum or the involvement of a phonon. Therefore, in direct bandgap
`semiconductors such as GaAs, an electron raised to the conduction band, say, by
`photon absorption, will dwell there for a very short time and recombine again with
`a valence band hole to emit light of energy equal to the bandgap. Thus, the proba(cid:173)
`bility of radiative recombination is very high in direct bandgap semiconductors. The
`processes are quite different in an indirect bandgap semiconductor. Considering the
`band diagrams shown in Fig. 3.2(b) and (c), since the conduction band minima are not
`at k = 0, upward or downward transition of carriers require a change in momentum,
`or the involvement of a phonon. Thus, an electron dwelling in the conduction band
`minimum, at k =/: 0, cannot recombine with a hole at k = 0 until a phonon with
`the right energy and momentum is available. Both phonon emission or absorption
`processes can assist the downward transition. In order for the right phonon collision
`to occur, the dweU time of the electron in the conduction band increases. Since no
`crystal is perfect, there are impurities and defects in the lattice that manifest them(cid:173)
`selves as traps and recombination centers. It is most likely that the electron and hole
`will recombine nonradiatively through such a defect center, and the excess energy is
`dissipated into the lattice as heat. The competing nonradiative processes reduce the
`probability of radiative recombination in indirect bandgap materials such as Si, Ge, or
`
`i I·
`I
`
`t
`I
`
`lllustration of
`Figure 3.2(a)
`band-to-band of absorption
`and recombination processes in
`(a) direct bandgap semiconductor
`and (b) and (c) indirect bandgap
`semiconductor.
`
`'·
`
`(a)
`
`.•·
`
`Vizio EX1016 Page 0021
`
`

`
`116
`
`CHAPTER 3 Optical Processes in Semiconductors
`c
`
`(b)
`
`(c)
`
`Figure 3.2 (continued)
`
`GaP. These semiconductors ate therefore, in general, not suitable for the realization
`of light sources such as light-emitting diodes and lasers.
`
`3.1.1 Radiative and Nonradiative Beconibination
`For continuous carrier generation by optical excitation or injection, a quasi equilibrium
`or steady state is produced. Electrons and holes are created and ariililiilated in pairs
`and, depending on the injection level, a steady-state excess density 11n· = D..p is
`established in the crystal. This equality is also necessary for the maintenance of overall
`charge neutrality. When the excitation source is removed, the density of excess carriers
`returns to the equilibrium values, n0 and ~o. The decay of excess carriers usually
`follows an exponential law with respect to time "" exp ( - tlr), where r is defined as
`
`Vizio EX1016 Page 0022
`
`

`
`Sec. 3.1
`
`Electron-Hole Pair Formation and Recombination
`
`117
`
`the lifetime of excess carriers. The lifetime is determined by a combination of intrinsic
`and extrinsic parameters, and the performance characteristics of most optoelectronic
`devices depend on it. In the discussion that follows, we will be concerned mainly
`with bulk recombination processes. It is imp01tant to remember that, depending on the
`semiconductor sample and itc; surface, there can be a very strong suiface recombination
`component which depends on the density of surface states.
`In general, the excess carriers decay by radiative and/or nomadiative recombina(cid:173)
`tion, in which the excess e~ergy is dissipated by photons and phonons. The former is
`of importance for the operation of luminescent devices. Nonradiative recombination
`usually takes place via sw"face or bulk defects and traps (Fig. 3.3), as discussed in
`Chapter 2, and reduces the radiative efficiency of the material. Therefore the tota