Physics of Optoelectronic Devices

730 Pages·2009·23.75 MB·English

by  Shun Lien Chuang

physics of
Op toelectronic Devices

SHUN LIEN CMUA.NG
Professor of Electrical and Computer Engineering
t'riiversi ty of Illinois at Urbana-Chazpzizn

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Physics of optoel~atronic devices / S.L. Chunng.
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"Wilzy-Interscience publication."
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I. Title'.
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I.'rinteJ i n the IIniteJ Stares ot't~.1!1*:riit:

Physics of Optoelectronic Devices

Preface

This textbook is intended for graduate students and advanced undergraduate
students in electrical engineering. physics, and materials science. It also pro-
vides an overview of the theoretica1 background for professional researchers
in optoelectronic industries and research organizations. The book deals with
the fundamental principles in semiconductor electronics, physics, and elec-
tromagnetic~, and then systematically presents practical optoelectronic de-
vices, including semiconductor lasers, optical waveguides, directional
couplers, optical modulators, and photodetectors. Both bulk and quantum-
well semico~lductor devices are discussed. Rigorous derivations are presented
and the author attempts to make the theories self-contained.
Research on optoelectronic devices has been advancing rapidly. To keep up
with the progress in optoelectronic devices, it is important to grasp the fun-
danle~ltal physical principles. Only through a solid understanding of fun-
damental physics are we able to develop new concepts and design novel
devices with superior performances. The physics ofoptoelectronic devices is a
broad field with interesting applications based on electromagnetics, sen~ico~i-
d~lctor physics, and quantum meclianics.
I have developed this book fbr a course 011 optoelectronic devices which 1,
have taught at the University of Illinois at ' rbana-Champaign for the past ten
years. Many of our students are stiin~.~lated
by the practical applications of
quantum mechanics in sen~iconductor optoelectronic devices because many
.#
quantum phenomena can be observed directly using artifical materials such
as quantum-,well heterostnlctures with absorption or emission wavelengths
determined by the quantized energy levels.

Scope

This book emphasizes the theory of' semiconductor optoelectror~ic devices.
Comparisons between theoretical and experimental results are also shown.
The book starts with the fundanlentals, including Maxwell's equations, the
continuity equation, ar.d the basic semiconductor equations of solidLstate
slcctronics. These equations are 'essetltial in learning scn,icond~ictor physics
applied to optoclectronics, We then disoass t'r~t.p/*ti,r~lg~ltiolz.
yc.rzt*ratiouz, inod~l-
Intion, curd rl~~tecriotl
~,J'li,ght. which z.1 re tllr keys to .ii nclerstanding the p11 ysics
behind the operation cf optoelect.ronic rlevict:~. Fc~r~xanlpl.ct,
knowledge of the
ceneration anti propng:;ition of 1ii~Ilt is (:ri!ci;:il for -u~~derstar;ciing
how a semi-
L.
r. . .
concl~iciur laser t,pci-ntrs. 1 11;: t h c o r ~ vf' ga.i:.! ~(jzfiicieitl
r j f scrujconductor-

r . -
1
lvsers shows hotv Iicrl.lt
Cc
is ii1~1i3jj [ic~;,
; i i k i wi1;'t"giii~1? theory shows how light is
.
-

confincd to the w:~veeuicle in a laser cavi ly. An undel-standing of the modula-
tion of light is useful in designing optical switches and nlodulators. The
absorption coefficient or bulk and cliianturn-well se~niconcluctors dernon-
strates how light is detected and leads to a discussion on the operating prin-
ciples of photodetectors.

Features

lnlportant topics such as semiconductor heterojunctions and band struc-
ture calculations near the band edges for both bulk and quantum-well
senliconductors are presented. Both Kane's model, assuming parabolic
bands and-Luttinger-Kohn's model, with valence-band mixingeffects in
quailtun] wells, are presented.
Optical dielectric waveguide theo~y
is discussed and applied to semicon-
ductor lasers, dil-ectional couplers, and electrooptic modulators.
Basic optical transitions. absorption, and gain are discussed with the
tinle-dependent perturbation theory. The general theory for gain and
absorption is then applied to studying interband and intersubband tran-
sitions in bulk and quantum-well semicondtictors.
Inlportant se~niconductor lasers such as double-heterostructure, stripe-
geometry gain-guided sernicond~ictor lasers. quantum-well lasers, dis-
tributed feedback lasers, coupled laser arrays, and s~lrfiice-emittinglasers
are discussed in great detail.
High-speed modulation of semiconductor lasers using both linear and
nonlinear gains is investigated systen:atically. The analytical theory for
the laser spectral linewidth enhancenlerlt factor is derived.
New subjects such as theories on the band structures ofstrained semicon-
ductors and strained quantum-well lasers are investigated.
The electroabsorptions, in bulk (Franz-Keldysh effccts) and quantum-
well sen~iconductors (quantum confined Starkeffects). are discussed sys-
ten~aticalty including exciton effects. Both the bound and continuum
states of escitons ilsing the hydrogen atom model are disc~~ssed.
Intersubband transitions in quantum wells, in addition to conventional
interband absorptions for fc.r-infrared photodetector applications, are
presented.

Courses

A few possibie courses for thz use of this book are listed. Some backgl-oiind in
unciergruduate electrornagnetics anci ~~~~~~~11 physics is assumed. A back-
zrouncl in cluantuln mechanics will be I?tlprt~I but is not required, since all of
-
the essentials are coverrcl i l l rile chapt-rs on Fundiirnental:;.

* Oveniesv of Optoelectronic Devi.crs: Chapter 1. Chapter- 2, Chapter 3 (3.1,

? 3 5 '1.7). Chapter -i (7. ! -7.-?.
7.6). CI-lapt$r 3, Chapter 9 (9. I-9.6), Chap-
.3 . -, - . . . .-

(-1:
.> ,.- r... .- '?
t<i- !() (1(;.!-1[>.3*;. .- , , t . k , l - s
!
:l:>J
C'!~:IJJ!L.I.
14.

Optoelectronic Device Physics: Chapters 1-4, Chapter 7 (7.1, 7.5, 7.6),
Chapters 9-14.
Electrornagnetics and Optical Device Applications: Chapter 2 (2.1-2.4),
Chapters 5-8, Chapter 9 (9.1-9.3, 9.5, 9.6), Chapter 10 (10.1-10.3, 10.5-
10.7), Chapter 12, Chapter 14.

The entire book (except for some advanced sections) can also be used for a
two-semester course.

Acknowledgments

After receiving a rigorous training in my Pl1.D. work on electromag~letics at
Massachusetts Institute of Technology, I became interested in semiconductor
optoelectronics because of recent developments in quantum-well devices with
many applications in wave mechanics. I thank J. A. Kong, my Ph.D. thesis
adviser, and many of my professors for their inspiration and insight.
Because of the sigilificant ilun~ber of research results appearing in the
literature, it is difiicult to list all ofthe irnport-tant contributions in the field. For
a textbook. only the f~lndamental principles are emphasized. I thank those
colleagues who granted nle pern~ission to reproduce their figures. I apologize
to all of my colleagues whose important corltributions have not been cited. I
atn grateful to many colleagues and friends in the field, especially D. A. B.
Miller, W. H. K~lox, M. C. Nuss, A. F. J. Levi. J. O'Gorman, D. S. Chemla, and
the late S. Schmitt-Rink, with whom I had many stimulating discussions on
quantum-well physics during and afte;. my sabbatical leave at AT&T Bell
Laboratories. I would also like to thank many of my students who provided
valuable comments, especially .C. S. Chang and W. Fang, who proofread the
~naiiuscript. I tha~~kmanyofmyresearch
assistants, especially D. Ahn, C. Y. P
chao, and S. P. Wn, for their interaction on research siibjecb related to this
book. The support of my research on quantum-well optoelectronic devices by
the Office ofNaval Research during the past years is greatly appreciated. I am
!
grateful to L. Beck for reading the whole nlanuscript and K. C. Voyles for typ-
ing many revisions of the nlanuscript in the past years. The constant support
and encouragement of my wife. Shu-Jung, are deeply appreciated. Teaching
and cond~icting research have beell the stimulus for writing this book; it was
an enjoyable learning experience.

Contents

Chapter 1. Introduction

1.1 Basic Concepts
1.2 Overview
Problems
References
Bibliography

PART I FUNDAMENTALS
-..

Chapter 2. Basic Semiconductor Electronics
21

2.1
Maxwell's Equations and Boundary Conditions
2.2 Semicondilctor Electronics Equations
2.3
Generation and Recombination in Set-niconductors
3.4
Examples and Applications to Optoelectronic Devices
2.5
Semiconductor p-N and 12-P Heteroj~inutions
2.6
Semiconductor n-N Heter0junf:tion.s and
Metal-Semiconductor Junctic-.
. .s
Problems
References

chapter 3. . Basic Quan turn Mechanics

3.1
Schrodinger Equation
! 3.2 The Square Well
3.3 The Harmonic Oscillator
3.4 The Hydrogen Atom (3D and 2 0 Exciton Bound and
Continuum States)
3.5 Time-Independent Perturbation Theory
3.6 Lowdin's Renormalization Method
3.7 Tinle-Dependent Perturbation Theory
Problems
References

Chapter 4.
Theory a j f FI:iechrt!!.;ic Band 5trncfures i a ~
Semiconductors
124

4.1
'The Bloch '-Yhec-;lt-c:ni ;~.!:d tl~c,
b . p T~,lsthod hi-
Simple Bands
I24
4.2
Kanc's TvI~dc:! Gir Btir~ii Str~icture:
3r . p Flettlod
. -
).i{i tll [I3:t: c; !.> l l 4 . i ~ 1 3
1 1. fi ! :? iSi,icij
(1)
!,.I.
1 29

xii
CONTENTS

4.3 Luttinger-Kohn's Model: The k p Method for Degenerate
Bands
137
4.4 The Effective Mass 'Tlleory for a S i n ~ l c
Band and
Degenerate Bands
141
4.5
Strain Effects on Band Structures
1 44
4.6 Electronic States in an Arbitrary One-Dimensiox~al
Potential
157
4.7 Kronig-Penney Model for a Superlattice
166
4.8 Band Stntctures of Sen~iconductor Quantum Wells
175
4.9 Band Structures of Strained Semiconcluctor
Quantum Wells
185
Problems
1 90
References
195

Chapter 5. Electromagnetics
200

5.1 General Solutions to Maxwell's Equations and Gauge
Transbr~mations
-" 200
5.2 Time-Harmonic Fields and Duality Principle
203
5.3
Plane Wave Reflection From a Layered Medium
205
5.4 Radiation and Far-Field Pattern
214
Problems
219
References
220

PART I1 PROPAGATION OF LIGHT

Chapter 6. Light Propagation in Various Media

6.1 Plane Wave ~olutiqns for Maxwell's Equations in
Homogeneous Media
6.2 Light Propagation in Isotropic Media
6.3
Light Propagation in Uniaxial Media
Problems
References

Chapter 7. Optical Waveguide Theory

7.1 Symmetric Dielectric Slab Wavesuides
7.2 ~ s ~ n ~ l n e t r i c
Dielectric Slab Waveguides
7.3
Ray Optics Approach to the Waveguide Problems
7.4 Rectangular Dielectric Waveg~liclcs
7.5 The Effective Index Method
7.6 Wiive Guiclance in a Lossy or- Gain Pvlediurn
Problenls
Rekrences

I."OI\ITENTS
xiii

Chapter 8. kVaveguidc Couplers and Coup1,ed-Mode Theory
253

8.1 bVaveguidc Couplers
8.2 Coupling of Modes in the Time Domain
8.3 Coupled Optical Waveguides
8.4 Improved Coupled-Mode Theory and Its Applications
8.5 Applications of Optical Waveguide.Coup1ers
8.6 Distributed Feedback Structures
Problems
References

PART 111 GENERATION OF LIGHT

Chapter 9. Optical Processes in Semiconductors
337

9.1 Optical Transitions Using Fermi's Golden Rule
9.2 Spontaneous and Stimulated Emissions
9.3 Interband Absorption and Gain
9.4 Interband Absorption and Gain in a Quantum-Well
Structure
9.5 Momentum Matrix Elements o.f Bulk and
Quantum-Well Semiconductors
9.6 Intersubband Absorption
9.7 Gain Spectrum in a Quantum-Well LAaser with
Valence-Band-Mixing Effects
Problems
References

Chapter 10. Semiconductor Lasers

10.1 Double Hcterojunction Semiconductor Lasers
3 95
10.2 Gain-Guided and Index-Guided Semiconductor Lasers
412
10.3 Quantu m-Well Lasers
42i
10.4 Strained Quantum-Well Lasers
437
10.5 Co~lpled Laser Arrays
449
10.6 Distributed Feedback Lasers
; 457
10.7 Surface-Emitting Lasers
444
Problems
,:
47 1
References
4'7 3

Chapter I I. Direct Wlodnla ti:,!]
of Semicond~etor Lasers

1 1.1
Rate Equatict~s :incl Linear G;rin Analysis

A.
TIlc Hydrogen Atom (3D and 2D Exciton Bound and
Continuum States)

B.
Proof of the Effective Mass Theory

C.
Derivations of the Pikus-Bir Harniltonian for a Strained
Semiconductor

D.
Semiconductor Heterojunction Band Lineups in the
Model-Solid Theory

E.
Kramers-Mronig Relations

F.
Poynting's Theorem and Reciprocity Theorem

G . Light Yn~pagation in Gyro tropic Media-Magnetoop tic

-,..
Effects
W. Formulation of the Improved Coupled-Mode Theory

]I.
Density-Matrix Formulation of Optical Susceptibility

J.
Optical Constants of GaAs and InP

K.
Electronic Properties of Si, Ge, and a Few 'Binary, Ternary,
and Quarternary Compounds

Introduction

Semiconductor optoelectronic devices, such as laser diodes, light-emitting
diodes, optical waveguides, directional couplers, electrooptic modulators, and
photodetectors, have important applications in optical communication sys-
tems. To understand the physics and the operational characteristics of these
optoeIectronic devices, we have to understand the fundamental principIes. In
this chapter, we discuss some of the basic concepts of optoelectronic devices,
then present the overview of this book.

I
BASIC CONCEPTS

?'he basic idea is that for a semiconductor, such as GaA.s or InP, many
interesting optical properties occur near the band edges. For example,
Table 1.1 shows part of the periodic tabIe with many of the elements that are
important for semiconductors [I, 21, including group IV, 111-V, and 11-VI
compounds. For a 111-V compound semicon 'rlctor mlch as GaAs, the gal-
lium (Ga) and arsenic (As) atoms form a zinc-biei;de structure, which consisls
of two interpenetrating face-centered cubic Iattices, one made of gallium
atoms and the other made of arsenic atoms (Fig. 1.1). The Ga atom h+"an
atomic nun-tber 31, which has an [Ar] 3d1"s'-tp1
configuration, i.e., three
valence electrons on the outermost shell. (Here [Ar] denotes the configbra-
tion of Ar, which has an atomic nu~nber 18, and the 15 electrons are
clistribrlted as ls22s22p63s23p6.)
The As atom has an atomic number 33 with
an [Ar] 3d104s24p3 configuration or five valence electrons in the outermost
shell. For a simplified view, we show a planar bonding diagram [3, 41 in Fig.
1.2a, where each bond between two nearby atoms is indicated rvith two dots
representing two valence electrons. These valence electrons are contributed
by either Ga or As atoms. The bonding diagram shows that each atom, such
as Ga, is connected to four nearby As atoms by four valence bonds. If we
assume that none of the bonds is broken, tve have all of the electrons in the
valence band and no free electrons in the concf~.rction band. 'The energy
band diagram as a function of positiog is shown in Fig. 1.2b, where E, is
the band edge of the cor~cluc:irjn b:in.(:i 3.11~1
I?!, is the band edge of the valerrcc
band.
When a light with an, optic;~i entcgv hrj abirve theh;~ndgap E , is inciderrt
on the semicvnductor. c;ptical nbsorptior: is significmt. Here / I Is tl~e. Planck

Table 1.1 Part of the Periodic Table Containing Group I1 to VI Elements

I [Ne] 3 ~ ~ 3 ~ '
I [Ne] 3s'?p3
[ [Ne] 3 ~ ~ 3 ~ '
I

-

32 Ge

[Ar] 3d1'

4s24p'

33 As

[Ar] 3d1"

3 ~ ~ 4 ~ "

Group VI

A
B 1

34 Se

[Ar] 36'"

4s'4p4

Group V
A
B
Group I I
A
B

I
48 Cd
49 In
1
50 ~n
51 Sb
52 Te

[Kr] 46'''
[l<r] 4d"'
1
[KT] 4d1('
[Kr] 4d "
[k]
4d1?

56 Ba

[Xe] 6s'

Group I11
A
B

-
80 Hg

[Xe] 4f I"

5dI06s2

Group IV
A
B

Note: [Ne] = 1
~
~
2
~
~
2
~
~

[Ar] = [Ne] 3s'3ph
[Kr] = [Ar] 3d'04s'4p6

[Xe] = [Kr] 4d'05s25p6