optical nonlinearities in bulk, multiple- quantum-well and ...€¦ · entitled optical...
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Optical nonlinearities in bulk, multiple-quantum-well and doping superlattice
gallium-arsenide with device applications.
Item Type text; Dissertation-Reproduction (electronic)
Authors Chavez-Pirson, Arturo.
Publisher The University of Arizona.
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Optical nonlinearities in bulk, multiple-quantum-well and doping superlattice GaAs with device applications
Chavez-Pirson, Arturo, Ph.D.
The University of Arizona, 1989
Copyright @1989 by Chavez-Pirson, Arturo. All rights reserved.
V·M·I 300 N. Zecb Rd. Ann Arbor, MI 48106
OPTICAL NONLINEARITIES IN BULK,
MUL TIPLE-QUANTUM-WELL AND DOPING SUPERLA TTICE GaAs
WITH DEVICE APPLICATIONS
by
Arturo Chavez-Pirson
Copyright © Arturo ChaveZ-Pirson 1989
A Dissertation Submitted to the Faculty of the
COMMITTEE ON OPTICAL SCIENCES (GRADUATE)
In Partial Fulfillment of the Requirements For the Degree of
DOCTOR OF PHILOSOPHY
In the Graduate College
THE UNIVERSITY OF f RIZONA
1 989
THE UNIVERSiTY OF' ARIZONA GRADUATE COLLEGE
2
As members of the Final Examination Committee, we certify that we have read
the dissertation prepared by Arturo Chavez-Pirson
entitled Optical Nonlinearities in Bulk, Multiple-Quantum-Well and Doping
Superlattice GaAs with Device Applications
and recommend that it be accepted as fulfilling the dissertation requirement
for the Degree of Doctor of Philosophy.
Date
Date
Date
Date
Final approval and acceptance of this dissertation is contingent upon the candidate's submission of the final copy of the dissertation to the Graduate College.
I hereby certify that I have read this dissertation prepared under my direction and recommend that it be accepted as fulfilling the dissertation requirement.
Date
3
STATEMENT BY THE AUTHOR
This dissertation has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library.
Brief quotations from this dissertation are allowable without special permission. provided that accurate acknowledgement of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the copyright holder.
SIGNED :-I-1}~~=,,~~~04~27---12~,----
4
ACKNOWLEDGEMENTS
I would like to thank my advisor Professor Hyatt Gibbs for the many exciting opportunities he has given me in the time that I have been at the Optical Sciences Center. As an undergraduate at MIT. I heard Hyatt give a talk on nonlinear optics and optical computing. It was his vision that brought me to the University of Arizona. and it was his inspiration that enabled me to find my way as a scientist. I also wish to thank Professors Nasser Peyghambarian and Stephan Koch not only for their careful review of this dissertation. but also for their enthusiasm and invaluable guidance during many collaborative research efforts. I wish to thank the faculty of the Optical Sciences Center. especially Professor Stephen Jacobs for his generous friendship on and off the tennis court.
I wish to acknowledge the assistance of many collaborators outside the University including Professor Gottfried DOhler of the University of Erlangen. Sam McCall of AT&T. Masahiro Ojima of Hitachi. Keiro Komatsu of NEC. and Rich Tiberio of the Nanofabrication Facility. I would like to thank the MBE crystal growers who have supplied the GaAs samples for these studies. especially Arthur Gossard of AT&T and Keith Evans of Wright-Patterson Air Force Base.
I would like to thank my friends and colleagues in the lab for sharing their experience and for making my research more fun. Without them I would not have been able to complete this work. Thanks to Yong Lee. Mial Warren. Chih-li Chuang. Victor Esch. Ruxiang Jin. Russell Pon. Seung-Han Park. and Brian McGinnis.
As I look back on my years of education. I recall those special influences that have motivated me to pursue a career in science. I thank my teachers. especially Mr. Friedman. Dr. Pavel Litvinov. and Professor Shaoul Ezekiel of MIT. Most importantly. I wish to express my gratitude and love to my family who throughout the years have loved me and encouraged me to do my best. And to Cathy I extend my most special thanks and love. In times of challenge and happiness you were with me. supporting and loving. It was your faith in me that gave me the confidence to persevere.
5
TABLE OF CONTENTS
LIST OF ILLUSTRATIONS ....................................... 7
ABSTRACT ................................................ 10
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12
1. OPTICAL NONLINEARITIES OF BULK GaAs ..................... 16
Plasma Theory of Optical Nonlinearities in GaAs . . . . . . . . . . . . . .. 16 Experimental Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 23 Sample Preparation and Experimental Techniques . . . . . . . . . . . . . . . 23 Experimental Results: Nonlinear Absorption ................... 27 Experimental Results: Nonlinear Refractive Index . . . . . . . . . . . . . . . 29 Comparison of Theory with Experiment. . . . . . . . . . . . . . . . . . . . .. 34
2. OPTICAL NONLINEARITIES OF MULTIPLE-QUANTUM-WELL GaAs .... 40
Theory of Optical Properties in MQW Structures . . . . . . . . . . . . . . . 41 Experimental Conditions and Techniques ..................... 43 Nonlinear Absorption and Refractive Index . . . . . . . . . . . . . . . . . .. 45 Carrier Lifetime Measurements. . . . . . . . . . . . . . . . . . . . . . . . . . .. 49 Comparison of MQW and Bulk GaAs . . . . . . . . . . . . . . . . . . . . . .. 52
3. OPTICAL NONLINEARITIES OF DOPING SUPERLATTICES ........... 57
Carrier Lifetime in a Doping Superlattice. . . . . . . . . . . . . . . . . . . .. 60 Optical Nonlinearities of a Hetero N-I-P-I Structure ............. 65
4. OPTICAL PROPERTIES OF QUANTUM WIRES AND QUANTUM DOTS .. 72
Fabrication of Quantum Wires and Quantum Dots in GaAs/AIGaAs .. 74 Photoluminescence Spectrum and Lifetime Properties . . . . . . . . . . . .. 77 Passivation of GaAs Surfaces ............................ 83 CdS Quantum Dots in Glass ............................. 87
5. NONLINEAR OPTICAL BEHAVIOR OF A GaAs/AIGaAs DISTRIBUTED FEEDBACK STRUCiURE ......................... 95
Properties of a DFB Structure-Theoretical Treatment . . . . . . . . . . . .. 96 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 100 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 103
6
TABLE OF CONTENTS-Continued
6. INTEGRATED GaAs/AIGaAs FABRY-PEROT ETALON FOR OPTICAL BIST ABILITY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 107
Design of Fabry-Perot Etalon . . . . . . . . . . . . . . . . . . . . . . . . . . .. 107 Nonlinear Optical Performance .......................... : 113 Reduction in Thermal Sensitivity . . . . . . . . . . . . . . . . . . . . . . . .. 119
7. OPTICAL NOR GATE USING DIODE LASER SOURCES. . . . . . . . . . . .. 122
Experimental Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 123 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 124 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 126
REFERENCES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 131
7
LIST OF ILLUSTRATIONS
I-I. Band structure of bulk GaAs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 13
I-I. Schematic representation of the bulk GaAs linear absorption spectrum. . . .. 22
1-2. Experimental set-up for pump-and-probe measurement ............... 26
1-3. Experimental and theoretical nonlinear optical absorption spectra for bulk GaAs at room temperature ......................... 28
1-4. Experimental ar.d theoretical nonlinear optical refractive index spectra for bulk GaAs at room temperature . . . . . . . . . . . . . . . . . . . . . . . .. 31
o 1-5. Fabry-Perot transmission spectra for a 299-1\. MQW at low and high
pumping intensities .................................... 33
1-6. Comparison of transmission peak shift measurement with the experimental nonline¥ absorption and refractive index spectra of 299-A MQW GaAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 35
1-7. Refractive indGx changes due to thermal effects in a Fabry-Perot etalon with 299-A MQW GaAs as nonlinear material . . . . . . . . . . . . . . . . .. 36
1-8. Relative contribution of the different nonlinear effects as determined by the plasma theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 38
2-1. Schematic representation of the energy band structure for a MQW superlattice ................................. 41
2-2. Density of states function in two and three dimensions . . . . . . . . . . . . . .. 42
2-3. Experimental nonlinear absorption spectra for MQW and bulk GaAs at room temperature . . . . . . . . . . . . . . . . . . . . . . . . . 46
2-4. Experimental nonlinear refractive index spectra for MQW and bulk GaAs at room temperature . . . . . . . . . . . . . . . . . . . . . . . . . 48
2-5. Experimental set-up for the measurement of the time dynamics of the carrier population in MQW and bulk GaAs . . . . . . . . . . . . . . . . . . .. 50
2-6. Time evolution of the absorption-recovery in MQW and bulk GaAs at room temperature . . . . . . . . . . . . . . . . . . . . . . . .. 51
2-7. Results of the carrier lifetime measurements for MQW and bulk GaAs at room temperature . . . . . . . . . . . . . . . . . . . . . . . .. 53
8
LIST OF ILLUSTRATIONS-Continued
2-8. Maximum refractive index change as a function of carrier density for MQW and bulk GaAs .................................. 54
2-9. Maximum refractive index change per carrier as a function of carrier density for MQW and bulk GaAs. . . . . . . . . . . . . . . . . . . . . . . . . .. 56
3-1. Schematic representation of the band structure of a doping super lattice 58
3-2. Linear absorption spectrum of a GaAs n-i-p-i structure at room temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 62
3-3. Differential transmission spectra of a GaAs n-i-p-i structure at room temperature for different pumping intensities ............. 63
3-4. Experimental and theoretical intensity-dependent carrier build-up dynamics for a GaAs n-i-p-i structure at room temperature . . . . . . . . . . . . . . . . 64
3-5. Room temperature linear absorption spectrum of a GaAs hetero n-i-p-i structure . . . . . . . . . . . . . . . . . . . . . . . . . . .. 68
3-6. Experimental nonlinear absorption and refractive index spectra for a GaAs hetero n-i-p-i measured at room temperature . . . . . . . . . . . . . .. 69
4-1. Density of states function in zero, one, two, and three dimensions. . . . . . .. 73
4-2. Fabrication steps used to pattern quantum dots and quantum wires in GaAs SQW structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 76
4-3. SEM photograph of a GaAs quantum dot array . . . . . . . . . . . . . . . . . . .. 78
4-4. SEM photographs of a single GaAs quantum dot and single GaAs quantum wire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 79
4-5. Transmissi(}n and photoluminescence spectra of a 250-A SQW measured at 17K . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4-6. Photoluminescence spectrum of a GaAs quantum wire array measured at 77K ...................................... 82
4-7. Results of the Na2S passivation treatment on GaAs surfaces ............ 85
4-8. Absorption spectra of CdS quantum dots of various sizes measured at 8K .. 88
4-9. Band structure of bulk and quantum dot CdS ..................... 90
4-10. Temperature-dependent shift of the CdS quantum dot absorption edge away from its value at 8K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 92
9
LIST OF ILLUSTRATIONS-Continued
4-11. Photoluminescence spectrum of CdS quantum dots measured at 8K . . . . . .. 93
5-1. Schematic representation of the forward and backward going waves propagating through a distributed feedback structure. . . . . . . . . . . . .. 97
5-2. Theoretical reflection spectra for GaAs-Alo•30Gaa.7aAs quarter wave stacks with varying numbers of periods . . . . . . . . . . . . . . . . . . . . . . . . . .. 99
5-3. Experimental reflection spectra of a GaAs DFB structure at high and low intensity ............................... 101
5-4. Experimental and theoretical nonlinear pulse reshaping in a GaAs DFB structure ............................... 102
5-5. Optical limiting in a GaAs DFB structure . . . . . . . . . . . . . . . . . . . . . .. 104
5-6. Thermal effects in a GaAs DFB structure induced by a long input pulse.. 105
6-1. Maximum reflectivity of a GaAs-AIGaAs DFB structure as function of the aluminum content and number of periods in the structure. . . . . . . . .. 109
6-2. Design of an integrated Fabry-Perot etalon using GaAs and AlAs. . . . . .. III
6-3. Reflection spectra of integrated Fabry-Perot etalons taken froin different portions of the same wafer. . . . . . . . . . . . . . . . . . . . . . .. 112
6-4. SEM photograph of an array of integrated Fabry-Perot devices. . . . . . . .. 114
6-5. Reflection spectrum of the base mirror in the integrated Fabry-Perot etalon 115
6-6. Optical bistability in the integrated Fabry-Perot etalon .... . . . . . . . . .. 116
6-7. NOR gate response in the integrated Fabry-Perot etalon. . . . . . . . . . . . .. 118
6-8. Optical bistability in the integrated Fabry-Perot etalon using 400 JL-sec pulses ..................................... 120
7-1. Configurations for optical NOR gate operation with two diode laser sources . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 124
7-2. Optical NOR gate output signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 126
7-3. Probe diode laser spectra with and without pump injection 128
7-4. Actual set-up for optical NOR gate with two diode lasel's and a Faraday isolator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 130
10
ABSTRACT
The linear and nonlinear optical properties of bulk. multiple-quantum-well. and
doping superlattice GaAs are investigated experimentally and theoretically. and their
properties are discussed in terms of their applicability to optical bistable devices and
optical logic gates. A systematic study of the room temperature. frequency-dependent
optical nonlinearities of bulk and multiple-quantum-well GaAs is reported and
discussed. The results of the bulk GaAs experiments are in good agreement with a
recently developed plasma theory. The carrier lifetime and the optical nonlinearities of
multiple-quantum-well structures of varying well sizes are measured and compared to
bulk GaAs. The prospect of lowering the power threshold for nonlinear action is
explored in GaAs doping superlattices. The ability to increase the carrier lifetime
with internal space charge fields is demonstrated experimentally in a doping superlat
tice structure. The possibility of using these long lifetimes to lower the power
requirements of optical bistability is discussed. The linear optic~l properties of
quantum-confined structures are studied both in GaAs/ AIGaAs quantum wires as well
as in CdS quantum dots. The enhanced confinement of the carriers shifts the absorp
tion band-edge to higher energies relative to bulk. The techniques used to fabricate
these nanometer-sized features are outlined.
Several optical device structures are fabricated and tested. The nonlinear ref
lection properties of a distributed feedback structure consisting of a GaAs/AIGaAs
quarter wave stack are evaluated experimentally both from the physics and device
point of view. Such a structure is used to monolithically grow a nonlinear Fabry
Perot etalon for optical bistability and optical logic gating. This integrated Fabry
Perot device is uniform over a I cm2 area with switching characteristics comparable to
11
the best devices previously obtained and with improved thermal stability. The fact
that diode lasers can be used as light sources makes GaAs optical logic gates more
attractive for optical signal processing. An all-optical NOR gate using GaAs as
nonlinear optical material and diode laser as optical source is demonstrated for this
purpose.
12
INTRODUCTION
The possibility of using nonlinear optical materials for nonlinear optical signal
processing has aroused a great deal of interest [Gibbs (1985)]. Since the first observa
tions of optical bistability in GaAs [Gibbs et ai. (1 979a.b)]. there has developed a
strong. multi-faceted research effort to study the nonlinear optical properties of GaAs
and related GaAs compounds as well as to develop new GaAs-based optical devices
for optical computing and optical switching. This has resulted in the observation of
new physical effects such as the quantum-confined Stark (QCSE) effect [Miller et ai.
(1985)]. the quantum well envelope state transition (QWES1) effect [West. Eglash
(1985)]. and the ac-Stark effect [Mysyrowicz et at. (1986); Von Lehmen et ai. (1986)].
These effects have been incorporated into optical devices. the most celebrated being the
self electro-optic device (SEED) [Miller et al. (1984)]. GaAs nonlinear Fabry-Perot
etalons were the first devices which directly exploited the large optical nonlinearities
near the band-edge to perform optical bistability and all-optical logic gating [Gibbs et
at. (1979c); Jewell et at. (1985)]. In this work we extend the experimental and theoret
ical understanding of the nonlinear properties of GaAs as well as improve certain
aspects of the performance of GaAs nonlinear Fabry-Perot etaJon devices.
There are two main parts to this dissertation. The first part deals with the
linear and nonlinear optical properties of GaAs and related GaAs compounds. The
band structure of bulk GaAs is shown in Fig. I-I. In direct gap semiconductors such
as GaAs each photon absorbed by the crystal results in the creation of an electron in
the conduction band and a hole in the valence band. It is the number of these photo
generated carriers which determine the nonlinear optical properties of the crystal.
Chapter one details the linear and nonlinear optical properties of bulk GaAs at room
'-----k' WAVEVECTOR
VAL.ENCE BANOS
CONDUCTION BAND
EL.ECTRONS
~I.IGHT
I.IGHT HOI.E BAND
Fig. 1-1. Band structure of bulk OaAs [Agrawal. Dutta (1986)].
13
14
temperature. The absorptive and dispersive properties of GaAs arE! studied experi
mentally and theoretically as a function of the photo-generated electron-hole concentra
tion. In bulk crystals electrons and holes are naturally free to move in all three
dimensions of real space. In multiple-quantum-well (MQW) structures the electrons
and holes are physically confined to move in only two dimensions. This modifies the
absorptive and dispersive properties of the material. In chapter two the room tempera
ture linear and nonlinear optical properties of MQW crystals are studied experimen
tally. This chapter includes a systematic study of the well size dependence on the
nonlinear optical properties. Applying an electric field to a bulk or MQW structure
also modifies its absorption properties. The electric field can be applied externally or
it could be built into the structure. In doping superlattices the built-in fields tend to
spatially separate electrons and holes and lead to novel optical and electrical effects
such as long carrier lifetimes. These doping superlattices are studied in chapter three.
In chapter four the optical properties of one dimensional and zero dimensional struc
tures are studied. These are called quantum wires and quantum dots. respectively.
We present the fabrication techniques used to produce these structures in GaAs. the
problems associated with this method. and show some luminesence results for quantum
wires. In addition we also study the optical properties of CdS microcrystallites in
glass. a material system in which the quantum confinement effects are most pro
nounced.
The second part of the dissertation concentrates on nonlinear optical device
structures and performance. In chapter five we study reflection properties of a distri
buted feedback (DFB) structure composed of GaAs and AIGaAs. Inserting nonlinear
optical material in a periodic structure results in nonlinear optical functions. one of
which is optical limiting. We use the DFB idea to monolithically grow high reflecting
mirrors for a nonlinear Fabry-Perot etalon. In chapter six we describe the design and
15
performance of the etalon. We observe optical bistability and optical logic gating in
this device. In the final chapter an all-optical NOR gate using GaAs as nonlinear
optical material and diode laser as optical source is demonstrated. This demonstration
shows some of the advantages of using GaAs Fabry-Perot etalons for nonlinear optical
processing as well as its limitations.
16
CHAPTER ONE
OPTICAL NONLINEARITIES OF BULK GaAs
Interest in understanding the character and microscopic origin of the nonlinear
optical properties of semiconductors has been increasing. both because of the underly
ing physics and the potential application to all-optical and opto-electronic devices.
GaAs is an especially attractive semiconductor since GaAs nonlinear optical devices
could conceivably be integrated with existing GaAs high speed electronics and diode
laser sources. In this chapter the nonlinear optical properties of bulk GaAs are
studied experimentally and compared with a recently developed plasma theory [Lee.
Chavez-Pirson et al. (1986a)].
Plasma Theory of Optical Nonlinearities in GaAs
The nonlinear optical properties of a semiconductor stem from the interaction
of photo-generated electrons and holes. Any theory which attempts to describe the
nonlinear optical effects must incorporate these many-body interactions. Recently. a
quantum mechanical Green's function theory has been developed to calculate the
optical dielectric function [Haug. Schmitt-Rink (1984)]. A Green's function approach
is a non-perturbative technique used to solve a many-body problem. This theory is
parametrized by N. the electron-hole pair density. It takes a quasi-equilibrium
approach in which the electronic excitations are in a therma! quasi-equilibrium state.
Unfortunately. this particular formalism involves integral equations which can only be
17
solved numerically. For the purposes of simplicity and ease of calculation. a partly
phenomenological plasma theory has been developed to more easily analyze the
nonlinear optical properties of GaAs [Banyai. Koch (l986a)].
The simplified theory assumes that a linear response function [Kubo (I 957)].
calculated from the full Hamiltonian. can be used to parametrically include density-
dependent terms and temperature effects. In this way the many-body effects are
contained in renormalized temperature-dependent quantities. The Hamiltonian used to
describe the relative motion of the electron-hole pair in the semiconductor crystal
satisfies a modified Wannier equation.
{- .lo2 e2 e-"r ~ } -"- V2 - - - - E}. (h (r) .. 0 2m fo r
(1.1)
~
where E}. are the eigenvalues of the modified Wannier Hamiltonian. m is the effective
mass. e is the electric charge. fo is the static dielectric constant. and cp}. (r) are the eig-
enfunctions which describe the relative motion of the electron and hole. A screened
Coulomb potential (Yukawa potential) is used to account for the density-dependent
plasma screening of the Coulomb interaction; the screening is characterized by K.. the
density-dependent inverse screening length. The bound states of the Wannier HamiIto-
nian are called excitons. In the absorption spectrum. exciton transitions appear as a
hydrogen-like series of lines below the inter band absorption edge and with a
continuum at the band-edge.
At zero temperature and for zero density of electron-hole pairs. one can obtain
the linear optical response function for the system. This is given by the Elliot formula
[Elliot (1957)]
1m X(w) - 2 rr rev 2 L lIP" (r..Q) 12 0 (fl w - E" _ EgO)
X
18
(1.2)
where X(w) is the frequency-dependent optical susceptibility. rev is the valence band to
conduction band dipole matrix element. and EgO is the unrenormalized band-gap.
When the carrier-dependent terms are included. the Elliot formula is generalized and
becomes
1m X(w) = 2 rr rev 2 A(w) 2:= lIP" (r=O) 12 Or (fl w - E" - Eg) (1.3)
X
where A(w)::tanh[ ~f] is the band filling factor.IL(N) '" lLe (N) + ILh (N) is the sum of
the quasichemical potentials of electrons and holes. IP" (r) is the wave function for the
relative motion of a (bound or unbound) electron-hole pair which is computed as an "-
eigenfunction of the Wannier equation with the screened Coulomb potential. E" is the
corresponding energy eigenvalue. and Eg .. EgO + oEg is the density-dependent renor
malized band-gap energy. Also.
(1.4)
is the line-shape function which approximates the Urbach tail of the excitons. ER is
the Rydberg exciton energy. and f .. fo + fiN is a broadening factor. The Urbach tail
is the exponential fall-off of the absorption coefficient with decreasing photon energy
[Urbach (1953)]. The exciton Rydberg energy. which characterizes the strength of the
binding energy. is given by
19
(1.5)
fl 2e where 110 .. ~ is the Bohr radius. The phenomenological broadening factor takes
me
into account scattering between quasi-particles as well as between quasi-particles and
lattice imperfections and impurities.
The absorption cofficient can be derived from the optical susceptibility by
using the relation
O/(w) E!!! 47TW 1m x(w)
cfo
so that the absorption coefficient for the generalized Elliot equation becomes
O/(W) = % A(w) L 1r,6~ (r=O) 12 6r (fl w - E~ - Eg)
X
where 0/0= 87T
2W r 2 cy
cfo
(1.6)
(1.7)
Unfortunately. the Hamiltonian in (1.1) with the Yukawa potential cannot be
solved analytically. Instead a Hulthen potential. which can be solved exactly. is used
to apPl"Oximate the Yukawa potential.
(1.8)
where g is chosen so that the number of bound states for the Yukawa and Hulthen
20
potentials are the same. This yields g .. -JL. This brief discussion outlines the basic IT lloI'
structure of the plasma theory. Even though the theoretical approach of the plasma
theory is different from the Green's function technique. the nonlinear optical properties
calculated with the simplified plasma theory are in good agreement with the much
more complicated Green's function theory [Banyai. Koch (I986a)]. It has the advantage
of being simpler to calculate and easier to use in device simulations.
The microscopic origins of the electronic nonlinearity in bulk GaAs are
explained by many-body effects which include plasma screening of the long-range
Coulomb interaction. bandgap renormalization. and band filling [Haug. Schmitt-Rink
(1985); Banyai. Koch (I 986a); Lee. Chavez-Pirson et al. (I 986a)]. These nonlinear
effects are included in the plasma theory outlined above. A short physical interpreta-
tion of these effects is given here.
Plasma screening of the Coulomb interaction is a weakening of the effective
Coulomb interaction between charged carriers because of the presence of other charged
carriers nearby. This decreases the effective attraction between electron-hole pairs
and reduces the exciton binding energy. In the plasma theory. the screening is charac-
terized by It. When this screening reaches a critical level (Mott density). the screened
Coulomb potential is not strong enough to support any bound exciton states. The Mott
density roughly corresponds to t.he density at which there is one electron for each
3 exciton volume au.
The screening also suppresses the Coulomb enhancement factor of the
continuum states. The Coulomb enhancement factor IrP>. (r=O) 12. also known as the
Sommerfeld factor. can be understood in the following way. If there was no Coulomb
interaction between charged carriers. then the wavefunctions associated with oppositely
charged carriers would have a smaller probability of overlapping than if there was a
net attraction. The absorption coefficient (and the luminescence efficiency) is prop or-
21
tional to the wavefunction overlap. As electron and hole wavefunctions of the
different bound and quasi-continuum states overlap more readily. the absorption value
near the band-gap increases. When screening becomes important the Coulomb attrac
tion is reduced and the enhancement factor is suppressed. This results in an overall
reduction in the absorption coefficient near and above the band-gap. A schematic
representation of the GaAs absorption spectrum with and without Coulomb effects is
shown in Fig. 1-1.
Band-gap renormalization c5Eg is a consequence of the fact that the single
particle energy of electrons and holes changes with increasing plasma density. The
two mechanisms which govern the renormalization are the screening of the intra band
Coulomb interaction between similarly charged particles and the screened exchange in
teraction between identical particles. These two mechanisms describe the overall
reduction in electron correlation since each factor effectively reduces the probability of
two electrons occupying the same phase space. The sum of the corresponding energy
terms represents the energy that the particles gain by avoiding each other. As the
carrier density increases. the electrons and holes are forced closer together and conse
quently suffer a loss in their free particle energies. The energy loss is reflected as the
band-gap reduction.
Band filling A(w) results from the occupation of quantum states in the conduc
tion and valence bands. As electrons and holes fill the individual states in the bottom
of the conduction band and the top of the valence band. those states are no longer
available for other carriers to occupy. As a result of the Pauli exclusion principle. the
band-filling effect reduces the valence band to conduction band transition probability.
In the optical spectrum the band-filling effect appears as a reduction in absorption
and. at sufficiently high carrier densities. even inversion (gain) energetically above the
unrenormalized band-edge.
22
n-1
- n-2 :i .!.
n .. 3
--
Fig. 1-1. Schematic representation of the GaAs absorption spectrum with (solid lines) and without (dotted lines) the Coulomb interaction [Bassani (1975)].
23
Experimental Conditions
In studying the optical nonlinearities of bulk GaAs. there are several relevant
temperature and time regimes to consider. At low temperature (2 K). the exciton
feature dominates the absorption spectrum in bulk crystals. At this temperature
excitonic effects are the major contribution to the nonlinearity [Shah. Leheny (1977);
Gibbs et ai. (l979c); Lowenau et ai. (1982); Fehrenbach et ai. (1982)]. As the tempera
ture increases. scattering with LO phonons broadens the exciton resonance. At room
temperature the bulk-exciton feature is barely resolvable in the spectrum. The time
regimes associated with the nonlinearity are broken down in the following way.
Excitons at room temperature are thermally ionized in less than a picosecond. It is in
this way that a photo-generated exciton gas decays into an electron-hole plasma
[Chemla et ai. (1984)]. Because of fast « psec) intra-band relaxation processes. the
electron-hole plasma quickly reaches a quasi-equilibrium distribution within the band.
At much later times (nsec) the carriers recombine radiatively or nonradiatively and the
refractive index and absorption return to their values prior to optical excitation.
Sample Preparation and Experimental Techniques
To perform transmission measurements on samples with bulk GaAs substrates
requires the removal of the substrate. This is done to isolate the optical characteristics
of the structure of interest from the unwanted absorption of the substrate. There are
reports of attempts at growing lower band-gap material using a higher band-gap
material as a substrate; for example. GaAs on GaP [Lee et ai. (1987)]. In this case the
24
substrate is optically transparent and optical transmission measurements can be
performed without the complication of removing the substrate. In our samples.
however. GaAs substrates are used. The removal of the substrate is a two step
process. First. the sample is mechanically ground with a polishing tool to a total
thickness of approximately 25 microns. The remaining material is chemically etched
using a solution of NH40H:H20 2 [LePore (1980)]. This wet chemical etch removes
GaAs at a rate twenty times faster than Alo.30Gao.7oAs. Our samples contain an o
Alo.30Gao.7oAs etch stop layer of approximately 2000-A so that the chemical etch
proceeds through the substrate but stops etching before reaching the structure of
interest. The bulk sample investigated consisted of a 2.05-micron layer capped on
both sides with Alo.30Gao.7oAs. Optical transmission measurements on the sample
reveal Fabry-Perot interference fringes in the optical spectrum. The 30% reflectivity
due to GaAs-air interfaces produces wavy oscillations in the spectrum which
sometimes distort the true absorption characteristics of the sample. To eliminate these
effects an anti-reflection coating is applied to the front and back surfaces.
The anti-reflection (AR) coating consists of a single quarter wave layer of
material with refractive index n~ where ns is the index of the substrate. The ref-
ractive index of GaAs is 3.6 near the band-edge. Silicon monoxide (SiO) and silicon
nitride (SisN4) were chosen for coating materials because their indices could be
adjusted to be approximately 1.85. SiO was thermally evaporated on the surfaces of
the GaAs samples. The resulting AR coating was much poorer than expected (Re!7%)
primarily because the index of the coating was much lower than 1.85. This occurs
because both SiO and SiOz are evaporated in the coating process. Since the index of
the Si02 is 1.52. the average index of the coating is lower than required. Better AR
coatings were eventually obtained with SiO (R<2%). However. because of the strong
temperature dependence on the stoichiometry of the evaporant material. the refractive
25
index of the coating was not reproducible.
The second AR coating process investigated involved the deposition of nonstoi-
chiometric silicon nitride by chemical vapor deposition based on the combination of
silane and nitrogen gases [Salik (1988)]. The refractive index of SisN4 is approxi-o
mately 1.98 at a wavelength of 6300-A or longer. However. the index of the deposited
material can vary depending on the partial pressure of the nitrogen gas. For this
application the index is 1.85. Once specified. the index is reproducible to well within
3%. Since our deposition system had no in situ thickness monitoring. the most difficult
parameter to control was the film thickness. However. after preliminary thickness cal-
ibration. AR coatings were reliably produced with a residual reflection of less than 2%
per surface. Even better silicon nitride anti-reflection coatings (R<lxlO-4 over a
narrow spectral region) have been applied to the facets of diode lasers for the pro duc-
tion of optical amplifiers [Eisenstein. Stultz (1984)].
The experimental configuration was a pump-and-probe scheme utilizing an
optical multichannel analyzer (OMA). The experimental set-up is shown in Fig. 1-2.
The pump was tuned to 1.51 eV throughout the experiment and a broad band o
(1.38-1.51 eV) probe source was obtained from photoluminescence of a 299-A
multiple-Quantum-well (MQW) GaAs platelet pumped by an argon-laser beam. The
pump and probe beams were synchronously modulated by acousto-optic modulators to
produce I-JLsec and 0.8-JLsec rectangular pulse trains. respectively. at 10 kHz. These
pulse widths are much longer than the carrier lifetime assuring a quasi steady-state
throughout the duration of the pulse. Under these pumping conditions. thermal effects
are observed to be negligible. The transmitted probe pulses are collected and inte-
grated by the OMA. The pump and probe beams are focused to a 15-micron-diameter
spot size. but because of carrier diffusion the effective pump spot is 20 mkrons; in
this way. the probe spot area is uniformly excited.
Fig. 1-2. Experimental set-up for pump-and-probe measurement.
IBM PC
26
27
Experimental Results: Nonlinear Absorption
The nonlinear absorption spectrum of bulk GaAs as a function of the input
pump power is shown in Fig. 1-3. The corresponding carrier densities are indicated.
The top curve in the set represents the linear absorption spectrum of bulk GaAs and
shows a small exciton feature. As the pumping intensity increases. the absorption
feature changes. At small pumping intensities. most of the negative absorption change
comes from the exciton saturation. but the net effect is small. As the pumping
intensity increases further. broad absorption changes in the band begin to appear and
become dominant. The wavy structures in the absorption spectrum at the highest
pumping intensity are due to the interference fringes arising from the incomplete anti-
reflection coating. These features are more pronounced at the high pumping intensities
because the material has become more transparent.
To properly describe the nonlinear effects requires knowledge of the underlying
mechanism driving these absorption changes. Photons incident on the sample are
absorbed and produce electron-hole pairs in the ma~erial. It is the number of these
charged carriers which directly affects the optical properties of the material. This or i-
ginates from the experimental fact that resonant or nonresonant excitation produces the
same nonlinear effects as long as the total carrier density is the same. The relationship
between pumping intensity. I. and carrier density. N. is described via a rate equation
approximation.
dN N -"'--+ dt T (1. 9)
where T is the electron-hole lifetime. w is the pump radial frequency. and Ot!(w) is the
1.50,-----------------.
CI 0.60 = ,5Z a ~ ~ 0.30
o~~-~~~-----------~
1.40 1.45 Energy (eVI
1.50
1.50,------------------,
120
10.0 20.0
Fig. 1-3. Room-temperature bulk GaAs optical nonlinearities: experiment and theory. (a) Experimental absorption spectra for different excitation powers P: (1) O. (2) 0.2, (3) 0.5, (4) 1.3, (5) 3.2, (6) 8, (7) 20, (8) 50 mW on a 15-!.Lm diameter spot. (b) Calculated absorption spectra for different electron hole pair densities N: (1) 1015, (2) 8xl016 (3) 2xl017, (4) 5xl017• (5) 8xl017, (6) 1018, (7) 1.5xl018•
28
29
absorption coefficient measured at the pump frequency. In steady-state (dN/dt - 0).
the carrier density can be calculated. All the parameters in the equation are directly
measured from this experiment except for the carrier lifetime. For bulk GaAs at room
temperature the carrier lifetime is measured to be 32 nanoseconds. The details of this
carrier lifetime measurement are described in chapter two. The rate equation approxi
mation used here assumes that the carrier lifetime does not change appreciably with
carrier density (r(N) ... r) and that the single exponential decay originates from radiative
and nonradiative decay processes. Higher order decay terms (r(N) 5!! ~N-2) correspond
ing to Auger recombination are neglected. These assumptions are valid for bulk and
multiple-quantum-well GaAs at these pumping intensities. however doping superlat
tices require a carrier "lifetime" that is density-dependent (see chapter three).
Experimental Results: Nonlinear Refractive Index
Associated with the nonlinear absorption changes are nonlinear refractive index
changes. These dispersive optical nonlinearities are essential for the operation of
optical NOR gates and optical bistable devices. Two methods of experimentally deter
mining the nonlinear refractive index changes are used here. The Kramers-Kronig
transformation is an analytic expression following directly from Cauchy's theorem
which relates the imaginary and real parts of a complex-valued function [Kittel (1976)].
In this case the absorptive and dispersive components of the complex refractive index
function can be related by the Kramers-Kronig transformation.
30
(1.10)
where ~n(E). ~O!(E) are the refractive index and absorption changes ~ function of
photon energy. respectively. Although this relation is analytically correct. it may not
always give an accurate representation of ~n(E). To be correct ~O!(E) needs to be
known over all values of E. Since this condition can never be satisfied experimentally.
finite integration limits are introduced. The validity of the Kramers-Kronig transfor-
mation with finite limits will depend on the shape of the function and the integration
limits chosen. If ~O!(E) is approximately zero at both limits of the integration range.
then the integral will be accurate to within some small error «5%).
The nonlinear refractive index changes calculated from the Kramers-Kronig
transformation are shown in Fig. 1-4. The spectral shape of the nonlinear refractive
index changes is characterized by a band-gap resonant dip at which the index change
is maximum followed by a slowly decreasing fall off for longer wavelengths. The
applicability of this analytic relationship to these experimental conditions was verified
by a direct interferometric technique [Lee. Chavez-Pirson et ai. (l986b)]. In this
experiment the nonlinear refractive index changes are measured by monitoring
nonlinear Fabry-Perot transmission peak shifts due to dispersive nonlinearities.
This method relies on the measurement of the nonlinear optical phase in a
Fabry-Perot resonator. If the material had no dispersion. then the round trip phase
change ~cp in the cavity would be
(l.ll)
0.060.---------------.--,
1.40 1.45 EnefllY (eV)
1.50
0.04,-------------------,
GaAs T'300K
Fig. 1-4. Room-temperature bulk GaAs optical nonlinearities: experiment and theory. (a) Nonlinear refractive index changes corresponding to the measured absorption spectra. Curves a-g are obtained by the Kramers-Kronig transformation of the corresponding experimental data (2)-(8) in Fig. 1-3(a). (b) Calculated nonlinear index changes. Curves a-I are obtained from curves (2)-(7) in Fig. 1-3(b), respectively.
31
FSR(X) .. __ X:.:.,.2 __
2"'"" n· L· L 1 1
32
(1.12)
where ax is the Fabry-Perot transmission peak shift in wavelength. FSR(X) is the free
spectral range. and ni and Li are the index and thickness of each of the materials in
the resonator. As the refractive index changes with increasing intensity the phase
changes and the resonant wavelength of the Fabry-Perot is shifted. By measuring the
shift of the resonance peak we can explicitly determine the index change.
M.. an ... X 4ITL
where L is the length of the active material.
(1.13)
Accurately monitoring the transmission peak could be a problem if the mea-
surement relied on a pump-and-probe technique. Since this Fabry-Perot etalon is
spatially nonuniform on a IS-micron scale. a proper overlap of the pump and probe
beams is not trivial. However. in this case the pump and probe are derived from the
same source. The incident pump not only generates the carriers responsible for the
nonlinearity. but also provides the probe via radiative decay of the photo-generated
carriers. The photoluminescence from the excited sample acts as the probe. and the
light exiting the cavity satisfies the resonances of the Fabry-Perot. By measuring the
Olltput of the resonator at different pumping levels we can follow the transmission
peak shift as a function of the pump intensity.
The high and low intensity Fabry-Perot spectrum is shown in Fig. 1-5. In the
high pumping cases the transmission peak is shifted to the shorter wavelengths cons is-
tent with a refractive index decreasing with increasing pump intensity. Of course the
850
· · · ·
~ .'
. :..........-- Low intensity
High intensity
Wavelength (nm) 910
Fig. 1-5. ;;rypical Fabry-Perot transmission peaks seen by the photoluminescence of the 299-A MQW at low and high pump intensities after normalization.
33
34
material does have dispersion and this must be taken into account in the phase
o function. The sample for the peak shift experiment is a 299-A multiple-quantum-well.
The results of the peak shift method are superimposed on the results of a Kramers-
Kronig transformation in Fig. 1-6. From these experiments. we can conclude that the
Kramers-Kronig transformation of the nonlinear absorption changes produces valid
index results under these pumping conditions.
The main disadvantage of the peak shift technique is that it gives only one
nonlinear refractive index value for a given resonance wavelength. In most cases we
are interested in knowing the entire spectral dependence. This is easily done with the
Kramers-Kronig transformation since the absorption spectrum can be quickly and effi-
ciently obtained with the OMA. To obtain the nonlinear refractive index spectrum
with the peak shift method requires a measurement at each resonance wavelength
provided the Fabry-Perot cavity supports a resonance at that particular wavelength.
The peak shift method can also be used to measure refractive index changes
due to thermal effects. In this case the Fabry-Perot is heated. and the temperature-
dependent peak shift is measured. Thermal effects produce positive index changes.
The results of these measurements shown in Fig. 1-7 demonstrate that temperature
increases of only a few degrees celsius produce index changes comparable. but of
opposite sign. to index changes of electronic origin. This has important consequences
for the operation of nonlinear Fabry-Perot devices since heating due to optical
pumping may severely restrict their operating conditions in a system.
Comparison of Theory with Experiment
Using the generalized Elliot formula (1.7) with material parameters consistent
-e ~ ~ o -lIIC -c: .2 -c:a.. ... o en ..Q <C
= <l
1.44 Energy (eV)
1.50
o Fig. 1-6. Nonlinear absorption spectra of 299-A MQW GaAs for excitation powers P: (1) 0, (2) 1.1, (3) 2.8 (4) 7.0 (5) 17.6 (6) 44 mW on a l5-JLm diameter spot. Curves a-e in (b) are obtained from curves (2)-(6) in (a), respectively. Dots in (b) are the data obtained by measurement of the blue shifts of the Fabry-Perot transmission peaks.
35
36
0.04
0 Room femp. 20°C - 30°C A
0 40°C 0 0
~ 0.02 I-A
All. 00
0 o 0 0 0 -
A A A A A All.
0 I I I 880 890 900
Wavelength (nm)
o Fig. 1-7. Refractive index changes in the 299-A MQW due to thermal effects.
37
with GaAs at room temperature (me - O.0665mo. mh '" O.52mo. fa .. 12.35. au .. 1.24
10-6 cm. ER - 4.2 meV. ro - 1.25ER and r 1 - (2xlO-18cm3)ER ) yields the results shown
in Fig. 1-3(b) and Fig. 1-4(b). From this theoretical construction one can determine the
relative contribution of each of the nonlinear effects simply by observing how each
affects the shape of the density-dependent absorption and refractive index spectra.
Figure 1-8 shows theoretically generated absorption and refractive index spectra
derived by artificially turning off (a, b) excitonic (bound state) contributions. (c. d)
band-filling. and (e. f) band-gap renormalization during the calculation. Without off
setting contributions from the saturation of bound states (a). the absorption spectra at
low carrier densities experience a pronounced red shift due to band-gap renormaliza
tion. Without band-filling (c). the absorption spectra seems to pivot at the band-edge
while strongly increasing the absorption at the low photon frequencies. Finally
without band-gap renormalization (e). the absorption spectra shifts strongly to the blue.
From this analysis. one can conclude that the absorption changes due to the bleaching
of bound states via exciton ionization are largely compensated by the red shift of the
continuum states caused by band-gap renormalization.
Depending on the frequency regime. the band-filling and the screening of the
continuum-state Coulomb enhancement dominate the nonlinear dispersive changes. The
band filling is responsible for the broad low frequency tails of an. whereas the
screening mainly causes the sharp structure in the vicinity of the band gap. It is also
important to note that the negative an from the exciton saturation is largely offset by
the positive an from the band gap reduction at low intensities. More significantly. the
nonlinearities responsible for a total an large enough for optical bistability and optical
NOR gating are band-filling and screening of the Coulomb enhancement of the
continuum states.
O~~~~~~------------~ -~~.CO~=---~~O~~-----~~------~~
(n..-~)/E.
1..~------------------------~
Nobaodlllllft9
lQO zoo
QO~--------------.--------____ ~
20.0
No _fllllnq
IQO ZQO
0.090·..--------------...,
-M!
-OD4ll
Ol~--~~~~~----------~ ·~fuo~~~=-~O~~----~IQO~------~ZQO·QO~no~~--~~o~-------I~OD~------~~
11100.~"E. 1n...~)/E.
Fig. 1-8. The relative contribution of different nonlinear effects from the plasma theory; labelling of the curves is as in Fig. 1-3(b).
38
CHAPTER TWO
OPTICAL NONLINEARITIES OF
MULTIPLE-QUANTUM-WELL GaAs/AIGaAs
39
With the advent of crystal growth techniques such as molecular beam epitaxy
(MBE) and metalorganic chemical vapor deposition (MOCYD), growth of high quality
bulk and multiple-quantum-well (MQW) crystals of precise layer thickness is now
possible. When the GaAs layer thickness is less than or on the order of the electron o
de Broglie wavelength (a!300-A), we call the structure a quantum well. Interestingly,
the optical properties of MQW GaAs/AIGaAs are qualitatively different from bulk
GaAs. The quasi-two-dimensional nature of MQWs changes the shape of the density
of states at the fundamental absorption edge. In addition, the physical confinement of
electron-hole pairs in MQW structures enhances excitonic effects relative to bulk. The
increased binding energy of the exciton makes possible the observation of the exciton
resonance even at room temperature [Miller et af. (1982)]. In this chapter we study
experimentally the room-temperature, frequency-dependent optical absorptive and dis-
persive nonlinearities of MQW GaAs/AIGaAs [Chavez-Pirson et af. (1988)] and
compare them with bulk GaAs. We directly measure the carrier lifetime of MQW
structures of varying well sizes. We also explicitly compare the magnitude of the
MQW nonlinear refractive index changes as a function of well size. Finally, we
evaluate whether or not MQW material is better than bulk for applications such as
optical bistability.
40
Theory of Optical Properties in MQW Structures
A MQW crystal is a compositional superlattice consisting of alternating layers
of two different semiconductor materials. In GaAs/AlGaAs MQWs. each period in
the superlattice contains a small band-gap material (GaAs) sandwiched between high
band-gap material (AIGaAs). Electrons and holes are confined to the GaAs layers
because of the potential barrier they encounter at the GaAs-AlGaAs interface. Since
the thickness of the GaAs layer is on the order of the de Broglie wavelength of the
electron. the energy levels assochted with motion perpendicular to the boundary are
split into discrete bands. A schematic representation is shown in Fig. 2-1.
The theoretical treatment that describes the optical properties of multiple-
quantum-wells must take into account the quasi-two-dimensional nature of the
electron-hole interaction. This is done by changing the potential in the single particle
Hamiltonian (I. I) from a three dimensional to a two dimensional Coulomb interaction
[Shingada. Sugano (1966)]. In the absence of many-body effects. a linear response
function can be constructed exactly like the Elliot formula (1.7) where the wavefunc-
tions used are the solutions to the two-dimensional unscreened Coulomb potential.
There are several important differences between the 2-D and 3-D results. The
density of states in 2-D is step-like where as in 3-D it is proportional to .Jllw-Eg (Fig.
2-2). The exciton bound states are more tightly bound in 2-D. Specifically, the
binding energy of the first (Is) exciton is four times larger in 2-D and the 2-D Bohr
radius [a20 CIt ~] is two times smaller than the corresponding 3-D value where ao is
the 3-D Bohr radius. Furthermore. the absorption enhancement near the band gap (I rp
(r=O) 12) is stronger in 2-D. This is because both the Is excitonic enhancement term
and the electron-hole correlations from the quasi-continuum and scattering states are
larger in 2-D than 3-D [Schmitt-Rink et al. (1988)]. A final difference is that in 2-D
---
E g.1
-
~
I
i
E 9.2
I
I I
, I i
I d~
Direction of Periodicity, Z
-1· Vo.c.
~
~ I
I VO.V. ... t
Fig. 2-1. Schematic representation of a multiple-quantum-well structure. The electron and hole energy levels are quantized. The optical transitions are shifted to higher energies relative to the bulk band-gap Eg• l .
41 .
en L&J I-
~ en L&.. o >t: en z L&J Q
42
----------P3D~ ------"".....-.....-."."" -,' ,,/
"" 3ml1TLZ ~/ I -- 2m/7TLz
/ 1 m/7TLZ , ,
ENERGY
Fig. 2-2. Density of s'tates function in two and three dimensions [Schmitt-Rink et ai, (1989)].
43
the light- and heavy-hole valence subbands are split at the r point. In 3-D these
subbands are degenerate. After including all these effects the quantum well absorp
tion spectrum consists of two series of steps corresponding to the heavy-hole and light
hole transitions from the valence subbands to the conduction subbands. Exciton peaks
appear at each transition with a correlation enhanced continuum in between.
The dominant nonlinearities in MQWs are phase space filling. screening. and
exchange effects [Schmitt-Rink et al. (1985); Chemla et ai. (1988)]. These effects
combine to saturate the exciton resonance. As the number of photo-generated electrons
and holes increases. they begin to fill the states from which excitons are formed. Since
only transitions into unoccupied final states are allowed by the Pauli exclusion
principle. fewer exciton states are available. This blocking mechanism is known as
phase-space filling. With increasing carrier density. charged carriers are forced closer
together. As in bulk. this changes the effective correlation and exchange interactions.
decreases the single particle energies. and shrinks the band-gap. These reductions in
the band-gap energy are exactly compensated by decreases in the exciton binding
energy. The resulting increase of the exciton diameter reduces the exciton oscillator
strength. Screening modifies the Coulomb interaction by weakening the electron-hole
attraction. This decreases the overlap of electron and hole wavefunctions and
suppresses the absorption enhancement from electron-hole correlations. At the highest
carrier densities. the exciton resonance is completely saturated leaving the step-like
density of state feature characteristic of a two-dimensional system.
Experimental Conditions and Techniques
The temperature and time regimes associated with the opticalnonIinearities of
44
MQW structures are approximately the same as in bulk GaAs. At low temperature (2
K). the exciton feature dominates the absorption spectrum in MQW crystals. As the
temperature increases. scattering with LO phonons broadens the exciton resonance.
However. unlike bulk GaAs. the exciton feature in the absorption spectrum is clearly
intact at room temperature. As in the bulk GaAs experiments. the nonlinear optical
effects are described by N. the electron-hole density.
We study the nonlinear effects using a pump-and-probe technique coupled with
an optical multichannel analyzer (OMA). The experimental set-up is identical to the
one in chapter one (Fig. 1-2). The pump beam originates from a cw tunable dye laser
(Styrl 9) pumped by an argon-ion laser. The infra-red pump laser wavelength is tuned
o well inside the band-gap (600-A) of each sample in order to efficiently generate
o electrons and holes. A broad band (700-A) probe beam is derived from the photolumi-
nescence of a MQW sample pumped by 100 mW from the argon laser. Depending on
the MQW sample to be studied. a separate MQW platelet is selected whose photolumi-
nescence best covers the spectrum of interest. The pulse widths of the pump and
probe beams. 1.0- and 0.8-JlSec. respectively. are much longer than the carrier lifetime
assuring a quasi steady-state throughout the duration of the pulse. Thermal effects are
observed to be negligible at the pumping rate of 20-kHz. The transmitted probe pulses
are collected and integrated by the OMA. The pump and probe beams are focused to
a 15-micron-diameter spot size. but because of carrier diffusion the effective pump
spot is 20 microns. o
Four different MBE-grown samples were used in this work: 76-. 152-. 299-A
GaAs/AIGaAs MQWs and bulk GaAs. These samples were grown in the same MBE
chamber in order to minimize the variability of sample quality. The first MQW
o 0 contains 63 periods. each period consisting of a 76-A GaAs layer followed by 81-A of
Alo.37Gao.63As. for a total GaAs thickness of 0.45 micron. The second sample contains
45
o 0 100 periods. each period consisting of a 152-A GaAs layer followed by 104-A of
Alo.33Gao.67As. for a total GaAs thickness of 1.52 microns. The third sample contains o 0
61 periods. each period consisting of a 299-A GaAs layer followed by 98-A of
Alo.s6Gao.64As. for a total GaAs thickness of 1.8 micron. The bulk sample consisted of
a 2.05-micron layer capped on both sides with Alo.30Gao.7oAs. Each sample required
that the GaAs substrate be removed and that an anti-reflection coating be applied to
the front and back surfaces of the samples. Complete details of the process are
described in chapter one in the sample preparation section.
Nonlinear Absorption and Refractive Index
The room temperature nonlinear absorption spectra of the MQWs as a
function of carrier density are shown in Fig. 2-3. For reference the nonlinear
absorption spectrum of bulk GaAs is also included. In contrast to the bulk crystal. all
the MQW structures have a prominent exciton feature in the absorption spectrum.
The lowest energy exciton transition moves to higher energies and the MQW band-edge
is shifted to shorter wavelengths relative to bulk. The amount of the blue-shift
depends on the degree of confinement; i.e. large wells with a small degree of confine-
ment are shifted less than narrow wells. The separation between energy levels also
increases with increasing confinement. The wavelength difference between the nz=1
o 0 and Dz=2 excitons is larger for the 152-A sample than for the 299-A sample. The
o 0 nz·2 exciton for the 76-A sample is shifted off the scale. The 76-A sample even
shows the splitting of the light- and heavy-hole transitions. It is important to note that
the linear absorption coefficient increases as the well size decreases. This is because
of the absorption enhancement due to greater overlap of electrons and holes in narrow
46
1.5 299 A
-'::1.. -c: .2 -Q. ~
~ ~ 0.5 0.5
Yb-~~~~~~~~900 &~0~~o~~--~~~890
-'::1.. -c: .2 1.0 -Q.. ~ o (J')
~ 0.5
76A 2.0
1.5
1.0
0.5
O~~~~~~~ __ ~ O~~ __ ~~ __ ~~~~ 820 900 810 870
Wavelength (nm) Wavelength (nm)
Fig. 2-3. Nonlinear absorption spectra for MQW and bulk GaAs. Curve 0 in e':lch set represents the un pumped (linear) absorption spectrum. The highest number curve in each set c0rtesponds to a carrier density N of 4.5xlO'8 cm-3 for bul1f,. 3.8xlO'8 cm-3 for 299-A. 2.8xlO'8 cm-3 for I 52-A. and 9.6xlO'7 cm-3 for 76-A. Each lower numbered curve within a set represents a 40% reduction in N from the higher numbered curve.
47
wells.
At low carrier densities excitonic saturation is the dominant feature in the
nonlinear absorption of MQWs. The lowest order (Oz-I) exciton saturates at a faster
rate than higher order exciton transitions. This is because the Oz-l exciton is affected
by both the exclusion principle and screening. whereas the Oz-2.3.. excitons are only
affected by screening. This demonstrates the relative weakness of screening as a
nonlinear mechanism in comparison to phase-space filling in quasi-two dimensional
o systems. Similarly. in the 76-A sample the heavy-hole exciton saturates at a faster
rate than the light-hole exciton. In quasi-equilibrium the thermalized population of
light holes will always be less than heavy holes. Therefore. the heavy-hole exciton
will experience more saturation per injected electron-hole pair. As the carrier density
increases further the exciton disappears leaving the step-like shape of the density of
states. At even larger densities the absorption at the plateaus between the steps is sup-
pressed as the elp.ctrons and holes lose correlation .
. fhe nonlinear refractive index changes associated with each sample (Fig. 2-4)
are obtained by a Kramers-Kronig transformation of the corresponding absorption
changes. The spectral shape of the nonlinear refractive index changes for all the
samples is characterized by a bandgap resonant dip at which the index change is
maximum followed by a slowly decreasing fall off for longer wavelengths. In order to
produce large off-resonant index changes (~n > 0.01). saturation of the exciton feature
alone is not sufficient. A more complete saturation of the band-edge is needed.
0.02
-c: <l - 0 Ql 0' c: 0
..c: U x -0.0 -0.02 Ql
"'0 c: 0 - 299 A
-0.04 900 830
0.0 -c: <l -Ql 0' c: 0
..c: U x Ql
"'0 c: - 0 0
152A 76A -0.06 -0.08
830 890 810 Wavelength (nm) Wavelength (nm)
Fig. 2-4. Nonlinear refractive index changes for MQW and bulk GaAs. The curve numbers in each set correspond to the same carrier densities as described in Fig. 2-3.
48
900
870
49
Carrier Lifetim(~ Measurements
The electron-hole carrier concentration for the different pumping intensities. I.
is determined through a rate equation approximation (eqn 1.9) in the steady state limit
(dN/dt om 0).
(2.2)
where T is the electron-hole lifetime. w is the pump radial frequency. and ct(w) is the
absorption coefficient measured at the pump frequency. All the parameters in the
equation are directly measured from the experiment except for the carrier lifetime. To
determine the lifetime for each sample. the experimental set-up was modified to
measure the time dynamics of the carrier population.
A sub-nanosecond pump source (0.5 nsec) from a nitrogen-pumped dye laser
generates the carriers. The pump source is peaked at 817 nm with a spectral width of
2 nm. The output of a cw dye laser modulated by an acousto-optic modulator acts as
the probe source. The probe pulse length is 4 p.sec. The probe is tuned to the wave-
length which displays the largest absorption change in the sample; this corresponds to
the exciton resonance in the MQW samples. A fast risetime (100 psec) avalanche pho-
todiode and fast oscilloscope (l GHz) monitor the transmitted probe pUlse. The pump
and probe spots are 280- and 10-microns in diameter. respectively. A large pump spot
is used to minimize the effects of carrier diffusion. The experimental set-up is shown
in the Fig. 2-5. The temporal impulse response of the entire system is 0.5 nanose-
conds. As soon as the pump pulse energy is absorbed by the sample. the probe
transmission increases indicating a decrease in the absorption coefficient. The energy
per pump pulse is 100 nJ at the sample. As the carriers recombine the absorption
I AR ~a •• r I-I---flov• ~ .. rll-----1BI----p-ro-b-.-'\~1"_
I. Pul •• O.n. Z. Trig. Sourc.
Optical Oot.ct.
J1J1. Plnhol.
-T11mlnal. Zero Ord.r
Pump 'l..----I-I-~--.,r.-~a .. r (2Hz)
Fig. 2-5. Experimental set-up for the measurement of the time dynamics of the carrier population in MQW and bulk GaAs.
50
Fig. 2-6. Time evolution of the absorption-recovery. Fr~m left to righ~ and top to bq}tom the time traGrS correspond to bulk GaAs. 299-A MQW. 152-A MQW. IOO-A MQW. and 76-A MQW. The top trace in each picture shows the probe transmission through the sample before and after the pump pulse. The bottom trace shows the residual pump pulse transmission through the sample with no probe pulse incident.
51
52
recovers to its original level. The absorption-recovery traces for all the samples are
o shown in Fig. 2-6. The properties of a IOO-A MQW are included. Even though the
o IOO-A MQW was not grown in the same MBE chamber as the other samples. it is a
high quality MQW sample. Figure 2-7 presents the singie-exponential decay time asso-
ciated with each sample. These are the lifetime values inserted in the rate equation
approximation to calculate the electron-hole density.
The lifetime results indicate a systematic reduction in the carrier lifetime with
decreasing well size. This can be attributed to two possible factors. The increased
overlap of the electrons and holes in a quantum well may enhance the radiative recom-
bination probability. In this case the luminescence efficiency would increase even
though the lifetime was decreasing. The second factor involves the increased probabil-
ity that a carrier will interact with the GaAs-AIGaAs interface. In this case nonradi-
ative recombination due to interface imperfections would determine the total lifetime.
Since the interfaces are relatively more important in narrow wells than in large wells.
the carrier lifetime and the luminescence efficiency would be smaller in narrow wells.
Photoluminescence experiments on all the samples indicate that the luminescence effi-
ciency decreases with decreasing well size. Therefore. we suspect that nonradiative
rather than radiative processes are shortening the lifetime in narrow wells.
Comparison of MQW and Bulk GaAs
We pick the maximum index change for each sample and plot it as function of
carrier density (Fig. 2-8). The band-gap resonant nonlinearity is primarily due to
plasma screening and band-filling in bulk GaAs and excitonic saturation in MQW.
From these curves we see that larger total index changes are associated with the
53
Carrier Lifetime in Bulk and MQW GaAs
Sample Lifetime
1. Bulk (2.05 micron) 32 nsec
0
2. 299A MQW 24 nsec
0
3. 152A MQW 18 nsec
0
4. 100A MQW 10 nsec
0
5. 76A MQW 3 nsec
Fig. 2-7. Numerical results of the carrier lifetime measurement for various MQWs and bulk GaAs samples.
c: <l
54
0~08'--------------""""
o 152A
o 299A
0.02
o~ ____ ~~~ __ ~~~~~~~~ __ ~~~ 10'5 10'6 1017 1018 10'9
N (cm-3)
Fig. 2-8. The maximum refractive index change ~n as a function of carrier density N for MQW and bulk GaAs.
55
narrower wells. To compare the size of the nonlinearities of the different samples. the
peak nonlinear refractive index change per carrier was calculated as a function of
carrier density. These curves are plotted in Fig. 2-9. showing that MQWs with
narrow wells have a higher nonlinearity than those with thick wells at all carrier
densities. The graph also shows that each MQW has a higher nonlinearity than bulk.
o The 76-A sample has three times the nonlinearity of bulk at high carrier densities but
has ten times at low carrier densities. These results indicate that MQWs with thin
wells have larger nonlinearities than the other samples. Park et aI. obtained similar
~n/N results in a pump-probe experiment using nanosecond pulses [Park et at. (I 988)].
However. they did not explore the low carrier density regime where the difference in
~n/N is largest nor did they explicitly take into account the variation of carrier
lifetime with well size.
Although the peak value of ~n/N is higher for the MQW. the MQW's shorter
lifetime demands a stronger pumping rate (higher intensity) to generate the same carrier
density as that in the longer-lifetime bulk sample. This is an important trade-off
when operating these samples in the quasi-steady state regime. Also. the nonlinear
refractive index changes scale with the enhanced linear absorption of the narrow
wells. Therefore. although larger index changes are available. they are accompanied
by larger absorption. The larger peak absorption in MQWs means that the detuning
from the band-gap must be greater for the same intracavity loss and carrier generation
absorption. Since the index changes decrease with increasing detuning. the large
excitonic nonlinearity of the MQW may not be completely accessible. These factors
may explain the experimental fact that the threshold power for optical bistability is
nearly constant for both MQWs and bulk.
.." E (,,) -en -b ->C -
12~----------------------------~ o 76A
Fig. 2-9. The maximum refractive index change per carrier ~n/N as a function of carrier density for MQW and bulk GaAs.
56
57
CHAPTER THREE
OPTICAL NONLINEARITIES OF GaAs DOPING SUPERLA TTICES
Artificially layered structures of GaAs can produce interesting changes in the
optical properties of the material. Among these. doping superlattices. also known as n
i-p-i super lattices. exhibit optical and electrical properties such as a tunable photolumi
nescence spectrum [Dohler et ai. (1981)]. tunable electroabsorption [Chang-Hasnain et
ai. (1987)]. and variable carrier lifetime [Rehm et al. (1983)] that are not observed in
bulk GaAs. Most significantly. the intensity levels required to obtain nonlinear
transmission changes in GaAs n-i-p-i structures are orders of magnitude smaller than
in bulk or multiple-quantum-well GaAs [DOhler. Ruden (1984)]. In this chapter we
measure the carrier lifetime in a photo-excited n-i-p-i crystal [Chavez-Pirson et ai.
(1989)] as well as the optical nonlinearities of n-i-p-i and hetero n-i-p-i structures
[Chavez-Pirson et. al. (1987)].
Dohler first proposed the idea of a doping super lattice [DOhler (1972)]. Doping
super lattices are periodic arrays of n- and p- doped layers interspersed with undoped
(i-) layers. The intrinsic layer could be of the same composition as the doped material.
or it could be another material altogether. In the n-i-p-i structure. a space charge
potential of ionized impurities in the doping layers periodically modulates the valence
and conduction bands. The motion of the charged carriers along the doping direction
is quantized into subbands by the space charge potential. A schematic representation
is shown in Fig. 3-1. The strength of this modulation. 2ta. V. from Poisson's equation
is
n -
ground state
Eotf.n Eeff.n
f .~_J~ _____ ..... -- :_",--- -... ~ . - - - - - --
direction ot plDriodieity
Fig. 3-1. Schematic representation of the band structure of a doping superiattice. The doping profile modulates the bands such that the electton and hole wavefunctions are spatially separated. [Dohler (1985)]
58
59
(3.1)
where e is the electron charge. f is the static dielectric constant. no and nA are the
doping levels of n- and p-doped material. respectively. and dn' dp • and d j are the
layer thicknesses for the n-doped. p-doped. and intrinsic materials. respectively. We
assume that the impurity space charge is exactly neutralized such that
(3.2)
The built-in potential from the space charge creates an internal electric field which
tends to spatially separate the electrons and holes. The reduced overlap of the electron
and hole wavefunctions enhances the carrier lifetime by several orders of magnitude
[Rehm et at. (1983)]. The built-in electric field also changes the shape of the absorp
tion spectrum of the GaAs via the Franz-Keldysh effect [Franz (1958); Keldysh (1958)].
The Franz-Keldysh effect produces a uniform shift of the absorption edge to lower
energy.
Nonlinear optical effects in n-i-p-i structures are produced by injected free
carriers which tend to screen the electric fields built up by the dopants and decrease
the depth of the space charge potential. Reducing the optical power threshold for
nonlinear action is desirable in certain optical device applications. especially for
multiple pixel switching. Because of the long carrier lifetime available in doping sup
erlattices. it might be possible to integrate over time the carriers produced by a low
power optical pulse and. in effect. trade-off low power operation with long lifetime
response. One of the motivations for studying n-i-p-i structures is to characterize the
quality and limit of the lifetime vs. power trade-off with special emphasis on lowering
60
the power required for optical bistability.
Carrier Lifetime in a Doping Superlattice
Although doping superlattices can have long carrier lifetimes under some con
ditions. to be useful in low power devices they must simultaneously maintain a long
carrier lifetime and produce large absorptive and dispersive changes. We measure
both the carrier lifetime and the nonlinear transmission modulation of a n-i-p-i
structure as a function of the incident intensity.
The structure is grown by metalorganic chemical vapor deposition (MOCYD)
and consists of 10 periods of alternating layers of n- and p- doped GaAs 130 nm thick
with a doping concentration of 2 x 1017cm-3; no intrinsic layers are included. With no
excess carriers injected. the built-in potential is approximately 1.32 eV corresponding
to a maximum electric field of approximately 1.95 x 105 V fcm in the depletion regions.
For the optical transmission experiments. the GaAs substrate is removed.
In the experiment we directly measure the nonlinear transmission changes
through the sample by a pump-and-probe technique. The pump beam from a cw dye
laser is tuned to a wavelength (800 nm) above the band-gap of the GaAs for efficient
generation of free carriers. The pump and a broadband probe are synchronously
modulated by acousto-optic modulators; the pump and probe pulse widths are 100 and
1 microseconds. respectively. The separation time between pump pulses (typically 300
microseconds) is chosen so that the excess carriers have a chance to decay. The
arrival time of the probe pulse relative to the rising edge of the pump pulse can vary
continuously. even probing times after the pump is turned off. The probe passes
through the sample under different pumping intensities and time delays and is
61
collected by the optical multichannel analyzer (OMA).
The linear absorption spectrum of the sample is shown in Fig. 3-2. The
absorption band-edge is significantly broadened relative to bulk and the band tail
extends to the long wavelengths. consistent with the Franz-Keldysh effect. The
subband structure is not observable because of the strong broadening of the subband
levels. The differential transmission spectrum (aT rn at various pump intensities is
shown in Fig. 3-3. As photocarriers accumulate and neutralize the space charge. the
internal electric fields are suppressed. and the absorption edge pivots to sharper slopes.
This enhances the transmission at long wavelengths while increasing the absorption in
the band-edge region. Figure 3-4(a) shows the build-up time required to obtain the
maximum modulation for a given intensity. For the higher intensity (12 W /cm2) the
maximum modulation reaches steady state in 3 microseconds. However. this build-up
time is increased to 40 microseconds for a lower intensity (1.2 W /cm2) pump. This
lifetime is three orders of magnitude longer than bulk. In general. increasing the
injection rate (input intensity) by orders of magnitude does not change the carrier
density proportionally nor at the same rate.
We also measure the intensity-dependent decay dynamics by delaying the probe
relative to the falling edge of the pump pulse. Both the build-up and decay dynamics
can be effectively modelled with a rate equation whose carrier decay time depends
exponentially on c~rrier density. N [DOhler (1983)].
dN .. _E.. + ct(w)l dt T(N) IIw
(3.3)
T(N) .. To e-kN (3.4)
where N is the carrier density. I is the input intensity. ct(w) is the absorption coeffi-
1. 500-1 ~-----.---.-.---... -I
--------, 1
Fig. 3-2. Linear absorption spectrum for a n-i-p-i structure at room temperature.
62
0.3 r-------------~--
-0.3 0.83
25 mW/crr(1. 100 mW/cm2 200 mW/cm2
800 mW/Cm2 3.4 W/crn2
Wavalansth ,in microns 0.90
Fig. 3-3. Differentia! transmission spectra C:l at room temperature for different
pump intensity values. The intensity values from highest to lowest are 3.4 W /cm2,
800 mW/cm2, 200 mW/cm2, 100 mW/cm2, 25 mW/cm2
,
63
- 30.0 9-I
32 ~
~ 20.0
"C
~ as
! 10.0
CIJ
15 ,Q o~
0.0
~o. b I
9 :::> cc
~ " a: I-
~ <II -I- C,) I-a u C
~
~ C,) 0.0
0.0
a
.'. & • • •
• Q
• • ..
0.0
• •
•
..
Intensity-Depondent Build-up Dynamics
• •
.. ..
12.3 W/cm 6.:1 W/cm 2.7 W/.cm 1.2 W/cm
•
D
..
20.0 40.0 TIME {microsecond)
60.0
I ·3
I • 1.5
I ·0.66
I •
TIME (microsecond) 2.0
Fig. 3-4. Intensity-dependent carrier build-up dynamics. (a) The maximum
modulation tll available at the given intensity is plotted as a function of time.
(b) The results from a rate equation model using a carrier-dependent lifetime are plotted. dN/dt .. -N/'r(N) + I; T(N) - Toexp(-kN). To .. 1. k - 10. and I - ( 3. 1.5. 0.66. 0.3 ).
64
65
cient at the pump frequency. ilw is the photon energy. and r(N) is the carrier
dependent lifetime. The numerical solution to this differential equation is shown in
Fig. 3-4(b). The time dynamics of the carrier density build-up agree with the experi
mental curves. This density-dependent carrier lifetime is quite different from pure
bulk or multiple-quantum-well GaAs and is part of the reason why n-i-p-i structures
can show sizeable nonlinear effects with very low intensities.
Unfortunately. although the nonlinear transmission modulation is relatively
large at intensities of 12 W /cm2• the corresponding absorption changes are small (.6.ct <
0.2 jl-Im). It is possible to obtain larger absorption changes. but at the expense of
shortening the carrier lifetime to bulk-like values. At that point n-i-p-i structures no
longer offer any advantage over bulk. Furthermore. the nonlinear index changes are
not large enough for optical bistability. This is because the corresponding absorption
changes are small and they are spread out over a large spectral region. Therefore.
although GaAs doping superlattices have interesting tunable optical properties. they do
not produce the large index changes required for optical bistability at low optical
powers.
Optical Nonlinearities of a Hetero N-I-P-I Structure
Hetero n-i-p-i crystals are periodic arrays of n- and p- doped layers inter
spersed with undoped (i-) layers of a different. smaller band-gap semiconductor
[DOhler. Ruden (1984)]. Hetero n-i-p-i crystals come in two types. Type I structures
sandwich a quantum well between the n-doped regions. In this way the combined
absorption from the n-i-p-i and quantum well generates free carriers capable of over
saturating the quantum well absorption [DOhler. Ruden (1984)]. Type II structures
66
position the intrinsic. lower band-gap quantum well between the n- and p-doped
regions. in such a way as to maintain a permanent electric field across the quantum
wells [Street et ai. (1986)]. Inserting more than one quantum well between the p- and
n- doped layers can also be done [Kost et ai. (1988); Ando et ai. (1989)]. This
structure has the advantage that fewer photons are needed to screen the built-in fields.
Electrons and holes from many quantum wells are added together to compensate the
internal space charge field. In general. hetero n-i-p-i structures may be able to
combine the long lifetime effects associated with a n-i-p-i structure with the sharp
excitonic resonances of the multiple-quantum-well. In this section. we study the room
temperature nonlinear optical properties of a GaAs/AIGaAs Type I hetero n-i-p-i
structure [Chavez-Pirson et ai. (1987)].
The sample was grown by MBE on an undoped GaAs substrate. It consists of
50 periods of alternating n-i-p-i layers. Each period has the following pattern: p-n-i-
i-i-n. where all the doped layers are Alo.30Gllo.70As and only the the central intrinsic
layer is GaAs. The p-doped (Be) layers are 320-A thick and doped to 6x I 018 cm-3.
o The n-doped (Si) layers are 160-A and doped to 2xl018 cm-3. The intrinsic GaAs is
o 0 200-A thick and is surrounded by 50-A thick Alo.30Gllo.7oAs on each side. For the
experiment. the GaAs substrate is removed by mechanically grinding followed by
chemically etching to an intrinsic Alo.30Gllo.7oAs stop layer 0.5 micron thick.
In the experiment we directly measure the nonlinear transmission changes
through the sample by a pump and probe technique using an optical multichannel
analyzer (OMA). The pump beam from the dye laser is tuned well inside the the band
(1.54 eV) to efficiently generate the free carriers which are responsible for the nonline-o
arities. The probe source is obtained from the photoluminescence of a 152-A MQW
sample pumped by an argon laser. The broad band probe and pump beams are syn-
chronously modulated by acousto-optic modulators to produce one microsecond rectan-
67
gular pulses of variable repetition rates. The orthogonally polarized pump and probe
beams are overlapped in time and space on the sample. The spot diameters of the
beams are 20 microns. The probe passes through the sample under different pumping
intensities and is collected by a spectrometer equipped with an OMA.
Figure 3-5 shows the the linear absorption spectrum at room temperature. To
obtain data free from reflection losses due to the GaAs-air interface. the sample was
anti-reflection coated with a quarter wave layer of silicon nitride. The residual ref
lection of less than 2% per surface produces the wavy interference pattern at the lower
photon energies. The knee in the absorption spectrum can be identified as the band
edge (1.50 eV). The band-edge is shifted to higher energies in comparison to a pure
MQW sample of equal well size. The band-edge absorption is spectrally broader (80
me V) than both bulk and multiple quantum well (typically lOme V). Figure 3-6(a)
shows the nonlinear absorption changes for different pump intensities. The intensities
required to obtain the largest nonlinear changes are on the order of several kW fcm'}..
Nonlinear changes extend over more than 100 meY. The optically modulated transmis
sion change (aT IT) is as large as 50% at the higher photon energies and at these
incident intensities. However. one should note that optically induced absorption modu
lation in the n-i-p-i structure of the previous section is obtained at substantially lower
incident intensities (l.5 W fcm'}.).
The lifetime of the carriers has a direct bearing on the amount of power
needed to generate a given carrier density and nonlinear change. Using a simple rate
equation approximation. the power requirements at stel:ldy-state scale inversely with the
lifetime. If by increasing the pump pulse repetition rate. the transmission modulation
decreases. then we can infer that the carriers cannot respond to changes on that time
scale. i.e lifetime is longer than the time between pUlses. We increased the repetition
rate to the point where thermal broadening became important (15 kHz) and noticed no
1.5001~--------------------~
EnQrgy In QV 1. 53
Fig. 3-5. Linear absorption spectrum of a hetero n-i-p-i structure at room temperature.
68
1~--------------------------~
(a)
- 7 -, E :::l. - 6 0
<J 5
4 3 2
0 1
1.41 1.52 0.04
(b)
-0.04 I--L--..I._..L.--J.._I...--I-.....I._..i--J..---I
1.42 E . V 1.52 -nergy In e
Fig. 3-6. Room temperature hetero n-i-p-i optical nonlinearities. (a) Experimental absorption changes for different excitation powers P: (1) 0.2, (2) 0.6, (3) 1.5. (4) 3.8. (5) 9.6, (6) 24. (7) 60 mW on a 20-JLm diameter spot. (b) Experimental nonlinear refractive index changes. The.6.n curves are obtained by a KramersKronig transformation of the corresponding experimental data (1)-(7) in (a).
69
70
modulation decrease. Modulation did decrease to zero. however. when the probe pulse
was delayed from the pump by 5 microseconds. In addition. the photoluminescence
spot due to the pump pulse diffused only to 30 microns in diameter. These facts
indicate that the carrier lifetime is at most 70 microseconds (15 kHztl and probably
less than I microsecond at this pump level. This is much shorter than the lifetimes
observed in the n-i-p-i structure of the previous section and also shorter than previous
lifetime results [Simpson et ai. (1986)].
We calculate the nonlinear dispersive changes (an) by performing a Kramers-
Kronig transformation on the experimental nonlinear absorption changes. Figure 3-6(b)
shows the result. To cross-check this result. we directly measure the optically induced
index changes [Lee. Chavez-Pirson et. ai. (I 986b)]. For this. the hetero n-i-p-i sample
is placed inside a Fabry-Perot cavity with mirror reflectivities of 90%. We measure a o 0
peak shift (ah) of lO-A at 8670-A corresponding to an index change of (.6.n = -.03)
which agrees with the Kramers-Kronig calculation. With the same Fabry-Perot used to
measure the peak shifts. we also observe optical bistability. The switch up power is
20 mW and the wavelength of operation is 866 nm (1.43 eV).
Although large index changes are available in this hetero n-i-p-i. they are
obtained at relatively high input powers. The somewhat disappointing results associ-
ated with the hetero n-i-p-i sample can be explained. The shortened carrier lifetime
does not allow the accumulation of carriers at low input intensities. Furthermore. the
absorption spectrum shows no sign of an excitonic transition. In chapter two we
observed that in MQWs the excitonic transition saturates only at large carrier densities.
We believe that electrons from the overly doped Alo.30Gao.7oAs layers populate the
GaAs quantum wells even in the absence of injected carriers. The excess carriers
change the optical properties in much the same way that photo-generated carriers
modify the characteristics of a MQW. The exciton transition is saturated and the
71
absorption feature is spectrally broadened. We believe that an appropriately doped
sample with no free electrons in the quantum wells should preserve the integrity of the
exciton peak and display the low power nonlinearities theoretically expected in these
types of samples.
72
CHAPTER FOUR
OPTICAL PROPERTIES OF QUANTUM WIRES AND QUANTUM DOTS
The optical properties of a semiconductor can be modified by reducing the
dimensionality of the carrier confinement. The interesting properties of multiple
quantum-well crystals. discussed in chapter two. are the result of restricting electron
hole pairs to two dimensions. Further confinement of the carriers to one dimension
(I-D). quantum wires. and zero dimension (0-0). quantum dots. may exhibit equally in
teresting and novel properties. One of the motivations for studying these structures
comes from the possibility of engineering the strength and spectral position of the
excitonic resonance by varying the particle size. The linear and nonlinear optical pro
perties of quantum-confined structures have been studied theoretically by several
authors [Efros. Efros (1982); Banyai. Koch (I 986b); Brus (1986); Schmitt-Rink et al.
(1987); Banyai et 'll. (1988)]. Enhanced dimensional confinement of the carriers tends
to concentrate the density of states into narrow spectral regions. A schematic
representation of the density of states for different dimensions is shown in Fig. 4-1.
The concentration of oscillator strength in the lower dimensional structures should
produce strong excitonic resonances with isolated absorption peaks.
Recent experiments in III-V semiconductors have attempted to observe the
enhanced confinement using optical techniques [Kash et al. (1986); Cibert et al. (1986);
Temkin et al. (1987); Kubena et al. (1987)]. but the spectra do not dramatically show
the characteristic structure of an electron-hole pair confined in all three dimensions.
This may be partly due to the inhomogeneous broadening of the quantum dot transi
tion caused by the nonuniformity of the particle sizes. Unless fabrication tolerances
I I
10 (WIRE)
ENERGY
00 (BOX)
&-ft
2D Step-ft
Fig. 4-1. Density of states function for 0-. 1-. 2-. and 3-dimensions [Temkin et al. (1987)].
73
74
are tightly controlled. the absorption features of the quantum dots will be substantially
broadened [Vahala (1988)]. Recently. a laterally confined resonant-tunnelling heteros
tructure has shown electrical conduction consistent with enhanced confinement [Reed
et ai. (1988)].
Experiments using II-VI semiconductors have been more successful. Colloidal
suspensions of small ZnS and CdS crystallites in solution have been synthesized which
show enhanced quantum-confinement in the optical spectrum [Rossetti (I 985)].
Quantum-confinement has also been observed in microcrystallites of CuCI and CdS
grown in a glass matrix [Ekimov. Onushchenko (I 982.1 984)]. In this chapter we study
the linear optical properties of quantum wires in the GaAs/ AlGaAs system and
quantum dots in CdS microcrystallites in borosilicate glass [Esch. Chavez-Pirson et ai.
(1989)].
Fabrication of Quantum Wires and Quantum Dots in GaAs/ AIGaAs
Quantum wires and quantum dots require physical confinement in two and
three dimensions. respectively. Recent advances in microfabrication techniques now
permit lateral confinement of carriers on the nanometer scale such that quantum
confined structures can be physically realized [Craighead (I 984)]. We use these micro
electronic techniques to define quantum wires and quantum dots in a GaAs/ AIGaAs
single-quantum-well. GaAs microstructures of nanometer dimensions have been called
quantum wires and quantum dots in the literature. even though the lateral dimensions
of the structures are not less than the de Broglie wavelength of the electron. This
loose nomenclature is tolerated because it is still not clear at what specific size regime
quantum-confined effects become important. We use the terms quantum wires and
75
quantum dots to denote the nanometer-size structures that we have fabricated.
A schematic representation of the process is shown in the Fig. 4-2. We begin
with a single-quantum-well (SQW) structure grown by MBE. o •
The 250-A SQW IS
° sandwiched between a 200-A Alo.soG30.7oAs cover layer and a I-micron Alo.30G30.7oAs
base. The thick base layer has two functions. It serves as a chemical etch stop layer
for the GaAs substrate removal process described in chapter one. It also provides
mechanical support to the sample when the substrate is removed. The substrate is
removed only after the quantum wires and dots are fabricated.
° A thin (IOOO-A) layer of poly(methyl methacrylate). also called PMMA. is spun
onto the top surface of the wafer and then baked for one hour at 170oC. PMMA is an
electron-beam photoresist material. A JEOL-JBX 5DII U electron-beam lithography
system is used to expose the PMMA and define the quantum wire and dot patterns.
Several different dosages (typically 60.000 /-tCoulomb/cm2) of the electron beam flux are
used in order to determine the dosage which produces the smallest features in the
developed PMMA. The PMMA is developed in I: 1 solution of methyl isobutyl ketone
and isopropanol for one minute and rinsed with isopropanol such that the material
exposed by the e-beam is removed from the surface and only unexposed PMMA
remains. Metal is then thermally evaporated onto the surface. Several different metals
of varying thicknesses were attempted (Ni.AI-Cu.Cr). but nickel was chosen because of
its good lift-off characteristics and its resistance to etching. In the "lift-off" process.
the sample is vigorously shaken in a solution of boiling methylene chloride for seven
minutes. This dissolves the PMMA unexposed by the e-beam and removes the metal
attached to it. The metal that adhered to the GaAs wafer through the holes in the
PMMA remains on the wafer reproducing the original e-beam pattern. The metal on
the wafer now acts like an etch mask. The etching process removes GaAs material
from every where on the wafer except for the regions covered with metal. Two
1)
2)
3)
4)
5)
6)
SQW~////~ o
1000A
E-beo.m
~
Photoresist (PMMA) coating .
Photoresist exposure using focused E-beam (JEOL)
Photoresist development
Metal Film deposition different metals/ different thickness
Lift-off
Etching
~ ~ Qduotantum A) chemically assisted
C:"":==:::"..:::J ion beam etching CAIBE
B) reactive ion etching RlE
Fig. 4-2. Fabrication steps used to pattern quantum dots and quantum wires in a GaAs SQW structure.
76
17
etching processes were used: a chlorine-based chemically assisted ion-beam etching
method and a boron-trichloride reactive ion etching method. The etch depth is
o approximately lOOO-A. A Hitachi scanning electron beam (SEM) microscope is used to
evaluate the size and uniformity of the quantum wires and dots. A SEM picture of a
finished quantum dot array is shown in Fig. 4-3. At the top of each dot one can
observe the residual nickel that served as the etch mask. The diameter of the dot near
• 0 the top of the column IS 600-A. Quantum wire and quantum dot arrays as well as
single wires and single dots were fabricated (Fig. 4-4).
Photoluminescence Spectrum and Lifetime Properties
The absorption and photoluminesence properties of the SQW material was
studied in order to determine the quality of the MBE sample and to have good
reference properties from which to compare the quantum wire results. The transmis-o
sion spectrum of the 250-A SQW at 17K is shown in Fig. 4-5. The ryhotoluminesence
spectrum for the same sample at the same temperature is also indicated. The sinusoi-
dal shape of the transmission spectrum is a result of interference effects in the micron-
thick sample. Superimposed on the Fabry-Perot fringe is the absorption dip from the
Is exciton transition.
The photoluminescence (PL) properties of the wire structures are studied. The
GaAs substrate is removed from the quantum-confined structures in order to eliminate
the unwanted photoluminescence originating from the substrate. The pump source is
the 514 nm line from an argon-ion laser. The pump intensity is 60 W /cm2• The beam
is modulated by an acousto-optic modulator to produce microsecond pulses at a 10kHz
rate. The pump is focused to a lO-micron spot on the sample with a microscope
Fig. 4-3. Oblique SEM photograph of an etched array of posts in GaAs. The posts are approximately SOO-nm tall. The remaining nickel mask can be seen at the tips of each of the posts.
78
79
Fig. 4-4. SEM photograph of (a) a single GaAs quantum dot and (b) a single GaAs quantum wire.
c o -tJ) tJ) -E tJ) C o t.. +J
1. ODD, I
f. I I
~ i
I r I
I r I
I
I i I I
I i r
80
0.0°8.79 o. 86
o Fig. 4-5. Transmission and photoluminescence spectra of a 250-A single-quantum-well measured at 17K. The small dip in the transmission spectrum (top curve) corresponds to the absorption band-edge of the SQW material.
81
objective. The sample is mounted in a MMR microrefrigerator capable of cooling the
sample to liquid nitrogen temperatures. The photoluminescence from the sample is
collected by the focusing objective and imaged onto the slit of a spectrometer equipped
with an optical multichannel analyzer (OMA). The OMA detector array is cooled to
-20°C in order to reduce the dark noise from the detector head and improve the signal
to noise ratio of the measurement. The dark noise level in each detector element is
105 counts/sec/diode while the readout noise in the detector array is 33
counts/diode/scan.
The PL signal from a quantum wire array is shown in Fig. 4-6. The PL
signal from the unpatterned SQW is shown for comparison purposes. There are
severals points to note. The number of PL counts collected from the quantum wire
array is a factor of 103 less than the un patterned areas. The reduced PL efficiency of
the quantum wire array is due to a reduction in the available area to excite (10% fill
factor) and a faster carrier lifetime in the quantum wires. The nominal width of the
° smallest wire structures is 600-A. By measuring the PL efficiency we can determine
the lifetime of the carriers in the quantum wire. As the wire width decreases. the
effects due to surface atoms become increasingly important. Photo-excited electrons
and holes generated inside the wire diffuse a short distance before interacting with a
surface. These surfaces are excellent sites for nonradiative recombination. We
estimate a lifetime reduction factor of 100 in the smallest wire arrays. Assuming a
lifetime of approximately 10 nanoseconds for the unpatterned SQW. we deduce that the
carrier lifetime in the wires is 100 picoseconds.
Interestingly. the peak wavelength of the PL signal from the quantum wires is
blue-shifted relative to the PL peak of the un patterned SQW. The origin of this blue-
shift is tentatively attributed to an enhancement of the quantum-confinement due to the
lateral confinement of the carriers. We observed the blue-shift only in the narrowest
82
40~--------------------------------~3x104
-c:: .-E
Cis -c:: :::I o (J --oJ c..
(b)
2
(a) -<lii--lIr
1
-50~--~~~--~--~--~--~~~--~0
0.78 0.86 Wavelength in microns
Fig. 4-6. (a) Photoluminescence (PL count rate) spectrum of a quantum wire array measured at 17K. (b) The PL spectrum of the unpatterned SQW measured at 17K.
83
wires. However. more mundane effects may also explain this kind of shift. For
instance. strain induced by the nickel etch mask may also blue-shift the band-gap
under certain conditions. Furthermore. the amount of strain may be wire size
dependent such that the strain is strongest for the smallest wire sizes. These ancillary
effects prevent an unambiguous determination of the origin of the blue-shift in these
samples.
We have recently developed a new etch mask material (polystyrene spheres)
that can be dissolved in acetone after the etching process. This technique has the
advantage that the quantum-confined structures are free-standing with no metal on the
top surface to induce strain effects. The polystyrene process. although still not
optimized. may offer a new method of patterning quantum dots in GaAs. It may also
clarify the origin of the blue-shift in these etched microstructures.
Passivation of GaAs Surfaces
The reduced luminescence efficiency from etched microstructures seriously
limits the ability to measure the PL intensity from small numbers of quantum wires or
dots. We have developed a sodium sulfide (Na2S) passivation treatment which reduces
the surface recombination velocity of the GaAs-air interface. A similar Na2S
treatment was first reported by Sandroff [Sandroff et al. (1987)]. There has been
interest in developing better ways of passivating GaAs surfaces [Nelson et. al (1980);
Offsey et. al (1986)]. Our N~S passivation treatment restores the carrier lifetime in
thin GaAs layers. directly exposed to air. to bulk-like values. Since the lifetime
enhancement is directly reflected in an enhanced luminescence efficiency. we hope to
apply this passivation treatment to increase the PL efficiency of the etched GaAs
84
quantum wires.
The quality of the passivation treatment was tested with an epilayer of (100)
bulk GaAs 2-microns thick sandwiched between O.S-micron Alo•30Gllo.7oAs layers.
The carrier lifetime and photoluminescence intensity of the structure are measured
first with both AIGaAs covers and then with the top AIGaAs cover removed. In the
latter case one side of the GaAs layer is directly exposed to air. The high quality
GaAs-AIGaAs interface has the relatively low surface recombination velocity (SRV) of
450 em/sec [Nelson. Sobers (1978)]. Electrons and holes that encounter the interface
have a low probability of being captured. However. the GaAs-air interface has a
SRV several orders of magnitude higher which is an indication of a much poorer
interface. The carrier lifetime and photoluminescence intensity drop by a factor of
100 after the top AIGaAs window is removed.
The passivation treatment requires that the starting GaAs surface be free of
any oxide layer. Therefore the exposed GaAs layer is rinsed with a GaAs etching
solution (NH40H:H20 2 1:100). This removes the oxide layer and exposes a clean GaAs
surface. The sample is immersed in a I M aqueous solution of Na2S for seven
minutes. The excess liquid is spun off. leaving a thin. crusty white layer of sodium
sulfide. The lifetime and PL measurements are repeated under the same pumping con
ditions. After the passivation treatment the carrier lifetime and PL intensity return to
their initial values before the top AIGaAs cover was removed. The results of these
experiments are shown in the Fig. 4-7. It is important to note that we have experi
mentally confirmed that the improved luminescence efficiency is directly correlated
with a longer carrier lifetime. Also. we observe that the passivation can be rinsed
away with H20. If desired. the coating can then be re-applied. This process can be
repeated several times without degrading the quality of the passivation treatment.
The physical mech:mism which explains the properties of the passivation are
!! 5
! ?: ~ CD
S CD g CD U U) CD C
~ ~ .c a.
85
PASSIVATION OF GaAs SURFACE WITH Na2S
10
8
6
4 t-
r r 80th Top window Mild
AIGaAs windows ROfllOVed Etch Inlact
NaS Appl'od
Top Window ~ AIGaAs BaAs
AIGaAs
!i.O Ne.S Rlnso Ro-appll~
Fig. 4-7. The photoluminescence intensity of a bulk GaAs epilayer before and after the N~S passivation treatment.
86
not completely understood. However. it is believed that ridding the GaAs surface of
oxides and arsenic can result in dramatically improved surface properties [Sandroff et
ai. (1987)]. In fact. we observe that the photoluminescence intensity of a GaAs
epilayer exposed to air increased substantially after being rinsed with a wet etching
solution. even though the improved surface properties lasted for only a few minutes.
The NazS passivation treatment had much longer lasting effects. We suspect that the
sulfur atoms chemically bond to the surface gallium atoms and tie up the dangling
bonds normally present at the surface. This reduces the number of surface states and
blocks certain nonradiative recombination channels. Over time these sulfur bonds are
broken. the surface reoxidizes. and the surface properties deteriorate.
When the passivation was applied to the quantum wire structures. the PL effi
ciency of the wires did not increase. This disappointing result is partly due to the
crystallographic dependence of the NazS treatment. Applying the passivation to GaAs
surfaces other than the (100) surface did not appear to result in improved PL effi
ciency. We also observed that the adherence of the passivation to the side walls of
waveguides and quantum wire structures was poor. Furthermore. the crusty. white
crystals that are the residue of the treatment scatter the input pump light and. conse
quently. reduce the coupling efficiency into the microstructures. Even when the passi
vation was successful. the good effects of the treatment are short-lived. After 24
hours the GaAs surface returns to its pre-passivation condition. Therefore. although
this simple chemical treatment can produce impressive reductions in the surface recom
bination velocity in certain situations. it does not solve the problem of the poor lumi
nescence efficiency from etched microstructures. Perhaps. the best method of
enhancing the PL efficiency is re-growth of AlGaAs material on top of the etched
quantum wires or quantum dots.
87
CdS Quantum Dots in Glass
Other semiconductor material may also show quantum-confined effects. We
have recently developed a fabrication process in which we can reproducibly grow
nanometer-size microcrystallites of cadmium sulfide (CdS) embedded in a glass matrix
° [Liu (1988)]. Since the exciton diameter in bulk CdS is 60-A. these micro crystallites
are true quantum dots.
Optimal quantum dot growth is produced with a glass composition (weight%) of
Si02 56%. ~03 8%. K20 24%. CaO 3%. BaO 9%. The amount of CdS added is rela-
tively small. 0.5% CdS by weight. The mixture is heated to 14300C such that the glass
is in a molten state. The melt is stirred at 20 rpm for 1.5 hours at this temperature.
It is then rapidly quenched to room temperature and annealed at 590°C for several
minutes to reduce the glass strain. The original sample is divided into several pieces.
These fragments undergo different secondary heat treatments with temperatures in the
range from 590°C to 770°C for time periods of IS. minutes (high temperature) to 140
hours (low temperature). The exact temperature and time of the heat treatment
determine the particle size. The size dependence on the time and temperature of the
heat treatment can be described by a recondensation mechanism proceeding via a
diffusive phase decomposition of a supersaturated solid solution [Lifshitz. Slezov
(1959)].
We measure the linear absorption spectra corresponding to the different heat
treatments to assess the particle size and size distribution. We use a scanning mono-
chromator equipped with a photon-counting photomultiplier to measure both the
absorption and photoluminescence spectra. The absorption spectra for different treat-
ments is shown in Fig. 4-8. Judging from the blue-shift of the band-edge and shape
of the lowest quantum-confined absorption peak. low-temperature/long-time heat
7.0r-----------------------,
i E E
0)
0~~~~~_2~====~~
7.0r-------------------__ ~
-I e e
b)
88
0.32 Wavelength (I'm) 0.50 Wavelength (I'm) 0.50
7.0 r--------------....., 7.0 r------.--------.....,
i
c)
Wavelength (I'm) 0.50
I
E e
d)
Wavelength (I'm) 0.50
Fig. 4-8. Absorption spectra of CdS quantum dots with different heat treatments measured at 8K. From left to right and top to bottom (a) 590°C for 140 hours (b) 640°C for 4 hours (c) 670°C for 0.25 hours (d) 770°C for 40 hours.
89
treatments produced the best quantum-confined absorption features. In fact the CdS
microcrystallites produced by this technique display the highest quality quantum-
confined absorption peaks yet reported in CdS material. High temperature heat treat-
ments yielded microcrystallites with bulk-like properties indicating that the particle
size is larger than the bulk-exciton diameter.
The spectral width of the lowest quantum-confined absorption peak is much
broader than the bulk-exciton resonance. This broadening could be caused by inho-
mogeneous broadening due to a wide distribution of particle sizes or by homogeneous
broadening of the fundamental transition due to a shortened lifetime. The linear
absorption measurement alone could not determine this unambiguously. A hole-
burning experiment revealed that the IS transition is primarily homogeneously
broadened [Park (1988); Esch (1989)].
The blue-shift of the band-edge can be explained by the increasing confinement
of the carriers. The band structure of bulk CdS is shown in Fig. 4-9(a). For small
particle sizes we model the situation as an electron in a three dimensional potential
well. This is schematically represented in Fig. 4-9(b). Ignoring the Coulomb interac-
tion. we can describe the spectral position of the absorption band-edge by the
following expression.
(4.1)
where me is the electron effective mass. and rPnl are the roots of the Bessel function
(rPlS .. 3.14. rPIP -=4.49. rPlD .. 5.76). From this simple expression we can calculate how
much the band-edge shifts as function of the particle size. The higher energy absorp-
tion peaks in Fig. 4-8 correspond to higher energy allowed transitions (lP.ID). The
measured blue-shift of the band-edge can be compared with this simple theory to
I i
(a) ~ __ I
j I i i
2.582eV i . A I
1-~o.o16ev O.057eV _~ ___ B
(b) 1D
1P
1S
/ i \c k=O
n=l.
n=l.
n=l.
----r E gap
__ J -.
1=2
1=1
1=0
Fig. 4-9. (a) Band structure of bulk CdS. (b) schematic representation of the three dimensional confinement of the electron in the quantum dot potential.
90
91
deduce the size of the microcrystallites. In this way we deduce that the radius of the
° particles for the 590oC/140 hour heat-treatment is 12-A.
There has been some speculation that the electron-phonon coupling in semicon-
ductor quantum dots might be different from bulk. The small size of the quantum dot
might limit the available phonon frequencies, in essence cutting off the long-wave-
length phonon modes. To verify this we measure the temperature-dependence of the
absorption band-gap. The shift of the absorption edge away from its value at 8K is
shown in Fig. 4-10 for various samples with the different heat treatments. From the
figure we can conclude that the band-gap shift is essentially identical to that of bulk
CdS. This indicates that the thermal gap reduction is confinement independent and
suggests that the electron-phonon coupling in the dots is like bulk.
The photoluminescence (PL) spectra of the quantum dot samples reveal some
unexpected characteristics. The PL spectrum for the smallest quantum dots is shown
in Fig. 4-11. We pump with the 365-nm line of the argon laser. The absorption
spectrum is superimposed on the PL spectrum. The sharp line near the absorption
peak is from the pump laser. The two smaller features on the red side of the pump
are from the argon laser. These features are artifacts of the measurement. The
dominant feature in the quantum dot PL spectrum is the long wavelength emission.
The broad emission is much stronger than any radiative recombination at the band-
edge. We suspect that the strong luminescence is due to long-lived surface and/or
impurity states in the microcrystallites. These long-lived states may also be important
in explaining the recently measured nonlinear absorption characteristics of the CdS
quantum dots.
In summary, we have observed the quantum-confined effects in a CdS semi-
conductor crystal. The blue-shift of the fundamental absorption edge is caused by the
enhanced confinement of the electron in the three dimensional potential well of the
0.02
0.00 • • • • • • • ..-.. ! • ~ -0.02 • • • • 1 ........" • • I
t -0.04 • • :2 t 1
(J1 • -o.ca t ~ « .. l.i.J -0.08 0
a.
-0.10 •
-0.12 0.00 50.00 100.00 130.00 200.00 2~.00 300.00
TEMPERATURE (K)
Fig. 4-10. Shift of the absorption edge away from its value at 8K for various heat treatments. "A," 590De for 140 hours (peak at 377.5nm at 8K); "+" 640De for 4 hours (peak at 400 nm at 8K); "x" 670De for 0.25 hours (peak at 428.5nm at 8K); ""',, 770De for 40 hours (peak at 478nm at 8K).
92
7.0~--~------------------------~
-en +-l
Photoluminescence .~
~ ~
,.c ..--. $..4 ~ C'j I -S . S ~
.~
'-' S ~ ~ .......
0 +-l 0 ~
0 ~
0.3 Wavelength (fLm) 0.7
Fig. 4-11. Photoluminescence and absorption spt~ctra of the 640oC/4 hour CdS quantum dot sample measured at SK.
93
94
microcrystallite. We measure the temperature-dependence of the absorption band-gap
and conclude that the temperature shift is confinement independp.nt. We also measure
the photoluminescence spectrum of the quantum dots. The PL spectrum is dominated
by efficient long-wavelength emission due to surface-dependent effects.
CHAPTER FIVE
NONLINEAR OPTICAL BEHAVIOR OF A GaAs/ AIGaAs
DISTRIBUTED FEEDBACK. STRUCTURE
95
The study of wave propagation in periodic structures has a long history in
physics [Brillouin (1953)]. In fields from acoustics to solid state physics to electro
magnetism. the phenomena associated with periodic structures are explained by the
same mathematics. In optics periodic structures can be used as mirrors. couplers. and
wavelength selectors. The linear optical properties of a sinusoidally-varying index
perturbation has been studied by Kogelnick with a coupled mode analysis [Kogel nick
(1969)]. This treatment has been extended to explain the lasing action in a distributed
feedback laser [Kogelnick (1972)]. More recently. there has been interest in studying
the properties of a periodic structure consisting of nonlinear optical material. An
exact solution to the nonlinear properties of a distributed feedback structure (DFB)
with a Kerr nonlinearity (An=n2I) has been determined [Winful et ai. (1979)].
In this chapter we study the nonlinear properties of a DFB structure with
GaAs as the nonlinear medium. We study the experimental characteristics of the
structure and compare it with the results from a numerical simulation [Chavez-Pirson
et ai. (1986)]. Unlike the exact theoretical treatment of Winful. the nonlinear optical
properties of GaAs cannot be described by a Kerr nonlinearity. Therefore. in the the
oretical modelling of the structure. we numerically solve for the transmission and ref
lection coefficients including the nonlinear absorption and refractive index changes in
the GaAs layers.
96
Properties of a DFB Structure-Theoretical Treatment
A distributed fP.edback (DFB) structure is composed of a periodic spatial distri
bution of the refractive index. For this study two materials having different indices
(GaAs and AIGaAs) are grown in a stack of quarter-wave layers. Because of the
index mismatch at the interfaces. light propagating through the structure is reflected at
each interface. If the reflected fields add in phase. then a large reflected output field
results. Since the GaAs layers have an intensity-dependent index. the DFB structure
has nonlinear characteristics.
We calculate the transmission and reflection properties of the DFB structure by
propagating a forward and backward wave through the structure and self-consistently
matching the boundary conditions at each interface. Since the nonlinear transmitted
and reflected beams are not single-valued functions of the input. we self-consistently
calculate the input and reflected beams as a function of the transmitted beam. This
method has been used to calculate the steady-state optical bistable performance of a
Fabry-Perot etalon [McCall (1974)]. It is extended to take into account the fact that
the feedback is distributed throughout the structure and not localized at the input and
output faces.
A schematic representation of each boundary is shown in Fig. 5-1. The
complex electric field components corresponding to the forward and backward waves
are shown. Using Maxwell equations. the boundary conditions relating the fields on
either side of the boundary are
(5.1)
--
-E--1·°--Gll!£OO!II!eo--
12 --.......-= -=-=--- ---- ...............
Region 1 Region
E new F -=E--
E new B
-2
-
Fig. 5-1. The forward and backward travelling electric field components at the boundaries of each interface in a distributed feedback structure.
97
I Err'" "2
I EB + "2
98
(5.2)
where £1 and £2 are the complex dielectric functions for the material in region I and 2.
respectively. The electric field components Err and Ebb are propagated to the
preceding interface such that
E new J<' _ old -ik1l212 F .. ""fr e (5.3)
E new E old +ikn212 B ... bb e (5.4)
where k=21T/Ao is the free space propagation constant. n2 is the complex index of ref-
raction in medium 2. and 12 is the physical distance between the interfaces. This
process is repeated throughout the structure. This calculation is quite general. For
instance. it allows arbitrary thicknesses for the materials as well as arbitrary wave-
length-dependent optical constants. The nonlinear character of the GaAs material is
included in the complex dielectric function by making the refractive index and absorp-
tion coefficient wavelength- and intensity-dependent. The total electric field is
computed by summing the complex electric field components at each point in the
structure and readjusting the index and absorption values of the material accordingly.
We calculate the reflection spectra of quarter wave stacks of GaAs and
Alo.30Gan.7oAs with different numbers of periods. The results are shown in Fig. 5-2.
The resonance wavelength is determined by the quarter wave condition Xo/4=nL. where
n is the index of the material and L is the thickness of the material in each quarter
wave layer. At the resonance wavelength the reflectivity is maximum in each case.
1. OOO---~-------,----------, i \
1. OO.o~r--- -_._------- -------.
! I ~ i
i !
vJ I
~ .. > I ;
i r f\
\Af~ .. l
~VVVi Fig. 5-2. Theoretical reflection spectra for GaAs-Alo.30Gao.7oAs quarter wave stack with varying numbers of periods. (a) 5 periods (b) 20 periods (c) 40 periods.
99 .
100
As the number of periods in the stack increases. the maximum peak reflectivity
increases and the width of the high reflection zone spectrally broadens. Off-resonance
the reflectivity decreases and undergoes oscillations.
Experimental Results
The structure was grown by molecular beam epitaxy (MBE) and consists of 35
periods of alternating layers of GaAs and Alo.30Gao.7oAs. Each layer is nominally a o 0
quarter wave in optical thickness (580-A for GaAs and 620-A for Alo.30Gao.7oAs). o
Each GaAs layer consists of two 260-A GaAs quantum wells separated by a thin o
60-A Alo.soGao.7oAs barrier. The sample has a wedge such that one end has propor-
tionally thinner layers than the other end. Because of this wedge. translation across
the sample from the thick to the thin end tunes the wavelength of peak reflectivity
from long to short wavelengths.
The experimental set-up consists of an argon-pumped Coherent CR-590 dye
laser using LDS 821 dye. The light is modulated by an acousto-optic modulator and
then focused onto the sample. An experimental reflectivity spectrum at high and low
intensity is shown in Fig. 5-3. The peak power on the sample is approximately 40
mW focused to a 20-micron spot for all the experimental results to follow. The
nonlinear mechanism is of electronic origin under these conditions and reduces the ref-
ractive index of the GaAs at high intensity; these processes are fast « I picosecond).
A smaller index in the GaAs layers corresponds to optically thinner layers and blue-
shifts the original spectrum.
The nonlinear characteristics of the reflected beam for different input wave-
lengths is shown in the Fig. 5-4. Accompanying each experimental result is the cor-
--Co) Q.) --Q.)
a::
o.5or--------------
"-*'><\ 1\ Low Intensity
~x \
\ \
o 85~5~O~~~~-8~68-0~~~~-8~810 o
Wavelength (A)
Fig. 5-3. Experimental reflection spectra for a GaAs-Alo.30Gllo.7oAs distributed feedback structure at high and low intensity.
101
0.03.._-------...,.., (a)
!C (Ill -....... l1li -o~ ______________ ~
o 2 ~NI'IsAT
0.01~--------------__
l-e (Ill -....... I: -
(b)
o~ ____________ ~~ 036
IIN/IsAT 0.02~-------__
(0)
Fig. 5-4. Nonlinear reflection response of a distributed feedback structure as function of the input wavelength. X. The pump power at the sample is 40 m W in a 20-micron spot. For each experimental curve on the right there is a cqrresponding thrretical curve oto the left. From top to bottom (a) X .. 8744-A (b) X .. 8·735-A (c) X .. 8728-A.
102
103
responding result from the theoretical calculation. The laser wavelength is tuned to
the blue side of the low intensity reflection minimum. As the input intensity
increases. the original spectrum blue-shifts. and the ret1ectivity at the given wavelength
decreases. When the spectrum shifts through its reflectivity minimum. the reflected
light experiences a pronounced dip. As the spectrum shifts further. the reflectivity
begins to increase again. This qualitatively explains the characteristic dips in the
figures. Optical limiting action is seen Fig. 5-5. In this case since the wavelength of
the input light is blue-shifted even with respect to the high intensity spectrum. it never
shifts through the reflection minimum and therefore never experiences a reflection dip.
As the laser power increases. the blue-shift of the spectrum reduces the reflectivity to
exactly compensate for the increased input. The reflectivity at the knee of limiting is
20%.
Red-shifting of the spectrum due to thermal effects is observed with longer
pulses (> 5 p,sec). Part of the energy from a long optical pulse heats the sample. The
heating builds-up over the time. The effects of heating are shown in Fig. 5-6. For
the long input pulse the temperature rises and the refractive index of the structure
increases (opposite to electronic effect). This has the tendency of red-shifting the ref
lectivity spectrum. From the figure. we can observe that the reflected light monotoni
cally increases over time even though the input light level is constant.
Conclusions
In summary a pure etalon-like DFB structure shows nonlinear behavior because
of the nonlinear GaAs material in the structure. This DFB geometry should be distin
guished from DFB waveguides and is interesting for several reasons. DFB nonlinear
Fig. 5-5. Optical limiting in a distributed feedback structure. The pownr at the sample is 40 m W in a 20-micron spot and the input wavelength A .. 8713-A.
104
Fig. 5-6. Thermal effects in a DFB structure with long input pulse. The input power at the sample is 60 mW. The top time trace shows the response for a I-lLsec input pulse. The bottom trace shows a long input pulse (7-lLsec) producing thermal changes.
105
106
operations such as optical limiting and switching may be applied to optical parallel
processing. In addition. the MBE-grown quarter-wave stack offers designers great
flexibilty in tailoring a spectrally specific optical characteristic. According to the
model desc:-ibed. optical bistability should not be observed at room temperature in this
structure. but a DFB structure with more feedback (two times as many layers) should
exhibit bistable switching and high contrast optical logic operation. Pure DFB has
been emphasized here to clarify the physics. but the optimum etalon device may
employ DFB sections between the Fabry-Perot mirrors.
CHAPTER SIX
INTEGRATED GaAs/AIGaAs FABRY-PEROT ET ALON
FOR OPTICAL BIST ABILITY
107
Since the initial observations of optical bistability in the GaAs system [Gibbs et
ai. (1979a.b)]. there have been continuous efforts to improve the device performance.
Single device characteristics that have undergone improvement are the threshold power
for optical bistability. switching speeds of operation. and throughput of the device
[Gibbs (1985)]. Of course. nonlinear optical signal processors will require many
devices operating together. Other issues such as device uniformity. cascadibility of
operation. interconnection considerations. and system architecture become important.
To make nonlinear switching devices practical. these issues must be addressed and
solved. In this chapter we stress the design and fabrication of highly uniform devices
through MBE growth. We study the characteristics of the devices and compare them
to previous devices.
Design of Fabry-Perot Etalon
The optical properties of distributed feedback structures offer interesting possi
bilities as interferometric devices [van der Ziel. Ilegem (1975); Thornton et ai. (1984);
Gourley. Drummond (1986)]. The ability to produce high reflectors with
GaAs/ AIGaAs quarter wave stacks is essential for the implementation of a monolithi
cally grown Fabry-Perot etalon. We use the quarter wave stack structure to grow
108
high reflecting mirrors on each side of a GaAs spacer layer [Jewell et ai. (1987);
Kuszelewicz et al. (1988)]. In the past. Fabry-Perot etalons were constructed by
sandwiching external dielectric mirrors to a I-micron thick GaAs layer. This
procedure yielded devices that were highly nonuniform. either due to wedges produced
in the GaAs as a result of the etching process and/or due to the nonparallel alignment
of the external mirrors. For instance. the Fabry-Perot resonance wavelength could
vary by several free spectral ranges in an area as small as 50-microns. Although
portions of such a sample might yield good nonlinear optical performance. it is
difficult to imagine how an array of these devices m:r;ht work.
The integrated Fabry-Perot concept solves the uniformity problem and produces
devices of comparable quality to the best past devices with highly improved heat
sinking capabilities in reflection. The design of the device involves two main steps.
First. one determines the reflectivity. spectral bandwidth and center wavelength of the
high refl~ctors. Second. one chooses the spacer layer such that the resonance wave
length of the structure has the proper detuning from the optical absorption band-gap to
yield a high finesse cavity with large enough nonlinear index changes to produce
optical bistability.
The reflector design consists of alternating layers of GaAs and AIGaAs. By
growing materials with dissimilar indices of refraction one can obtain optical reflec
tions from the surfaces of the index mismatch. Ideally. one would like two materials
with an index contrast as large as possible. For this reason we choose GaAs and
AlAs. The index mismatch is .6.n=O.6. In Fig. 6-1 we show the results of calculations
indicating how the reflectivity of a quarter wave stack of GaAs and AIGaAs with
varying amounts of aluminium changes with the number of periods in the stack. One
can see that above 10 periods the reflectivity gain becomes smaller and smaller. To
obtain a reflectivity of 90% over a spectral range tens of nanometers wide requires at
1.00 I ~
I
0.90 ~ !
~ O.BO ~ > 0.70 ~ I- ~ U 0.60 ...; W . --l ., LL 0.50 -; W ... IX 0.40 ~ ~ "'1
« 0.30 -; W "'1
D... 0.20 ~ i ~
I
0.10 -1
x = X = X = X =
1.0 O.B 0.6 0.4
0.00 4--r-..... 1 ---'--'--_0r-T-' 0_0 ,-- I --1--'- -. ·....-r-' 0.00 5.00 10.00 15.00
PERIODS
Fig. 6-1. Maximum reflectivity of a GaAs-AIGaAs DFB structure as function of the aluminum content and number of periods in the structure.
109
110
least 7 periods using AlAs material.
Determination of the proper detuning requires some analysis with the modelling
program discussed in chapter five. The main criterion for the design was high
contrast switching operation in the reflection mode. Since the modelling program
included the nonlinear absorption and nonlinear refractive index. realistic parameters
could easily be evaluated. The spacer layer itself had to be a multiple of Ao/2n where
>"0 is the resonance wavelength and n is the refractive index of the spacer material.
An intensive study of the performance of a nonlinear Fabry-Perot etalon including the
results from the full GaAs plasma theory has been done [Warren (1988)].
The final design is shown in Fig. 6-2. The sample is grown entirely by MBE.
During the growth the substrate is rotated in order to enhance the growth uniformity.
A short period superlattice is grown immediately on the top of the substrate to
improve the surface morphology so that subsequent layers will grow more smoothly.
The success of this fabrication process relies not only on the uniformity of the growth
process but also on the accuracy of the layer thicknesses. For instance a 5% error in
the calibration thickness degrades the performance of the device substantially. The
Fabry-Perot resonance wavelength could be spectrally shifted into the high absorption
region of the GaAs resulting in a poor finesse structure.
The experimental reflection spectra at different positions of a I cm x I cm
section of the wafer is shown in Fig. 6-3. The theoretical performance of the
structure is also shown. The target resonance wavelength is close to the designed
value. More importantly. the resonance wavelength deviates less than three linewidths
over the entire I cm2 region; this is by far the most uniform performance of these
devices to date. The finesse of the structure is approximately 18. which again is the
highest to date in an etalon capable of optical bistability.
We etched a 100 x 100 array of 5-micron by 5-micron square pixels in the
Integrated M8E-Grown Fabry-Perot Etalons in GaAs
GaAs 575 A } x1 High Reflector /
795 A AlAs
GsAs 1.5975/1 Spacer
AlAs 795 ..\
GsAs 575..\ } x9 High Reflector
AlAs 795..\
A/ ••• Gao.sAs 100 A } x38
AI •• 1Ga..sA9 100 ..\
AI."Ga..sAs 500 A
Semi-Insulating GsA!! substrata
GROWl1-f: WRIGHT -PA "l"'1'ERSON AFS
Fig. 6-2. Design of an integrated Fabry-Perot etalon using GaAs and AlAs quarter wave layers with a bulk GaAs spacer layer.
III
Predicted (8891.4)
Ol~~--~~--~~~~ __ ----~~-~----~ 0.84 Wavelength (p.m) Q91 0.84 Wavelength (jJJ1l)' 0.91
e)
6 5 0.0- x x
(micrometer yl 2 1 2.62- x )(
1.0~ If)' (
0.0 2.5 5.0 (micrometer xl O'=" ________ --:~ l-0.5in-j 0.87 Wavelength (p.m) 0.94
Fig. 6-3. (a)-(d) linear reflection spectra of integrated Fabry-Perot etalons taken from different portions of the same wafer. (e) schematic representation of the wafer where the spectra in a.h,c,d. correspond to positions 104.3.6. (f) theoretical linear reflection spectrum for the structure.
112
113
structure. This is done using contact photolithography and reactive ion etching. The
surface of the structure is coated with a I-micron thick layer of a UV sensitive photo
resist. The UV light passes through a mask physically attached to the surface of the
sample. In this way the array pattern from the mask is transferred to the photoresist
material. The photoresist is developed leaving behind an array of pixels in photoresist.
We use a boron-trichloride reactive ion etching process to define the pixels in the
GaAs structure. An SEM photograph is shown in the Fig. 6-4. From the profile of a
single pixel we can observe a periodic contrast variation near the top of a pixel. This
corresponds to the top quarter wave stack high reflector. The etch depth was chosen
to be 3 microns such that the base surface after the etching would expose the bottom
high reflector. The reflectivity of the bottom reflector is 90% over a wide spectral
range and its spectral dependence agrees well with the predicted performance of the
mirror. The experimental reflection spectrum is shown in Fig. 6-5.
Nonlinear Optical Performance
The nonlinear optical performance of the device is characterized by the quality
of the optical bistability and optical NOR-gate response. A typical optical bistability
trace in reflection is shown in the Fig. 6-6. The dye laser is modulated by acousto
optic modulators to produce triangular pulses at a 10 kHz rate. The inverted input
pulse is shown in the oscilloscope trace along with the reflected signal. The output is
plotted as a function of the input to reveal the bistability loop. Bistable switching can
be understood in the following qualitative way. The input wavelength is tuned to the
short wavelength side of the Fabry-Perot resonance. As the intensity in the cavity
builds-up the refractive index in the spacer layer decreases. This shifts the resonance
Fig. 6-4. SEM photograph of an array of integrated Fabry-Perot devices. Each pixel is 5 x 5 microns with a center to center separation of 20-microns. The bottom picture is a magnified view of a single pixel. Note the integrated mirror at the top of the pixel.
114
1. 0001
I ~ I
r I
; I
I
I I I
O. 0 0 ~ I .-1._-J..-_-J..----I._....I--_~_j ~. WavQlgns'th 1n m1cI"'ons o. 9 1
Fig. 6-5. Reflection spectrum of base mirror in the intebTated Fabry-Perot etalon after pixellation via reactive-ion etching.
115
Fig. 6-6. Optical bistability in the integrated Fabry-Perot etalon. The . input wavelength is X ... 887 nm and the peak input power is 30 mW. The top trace is the inverted triangular input pulse and the bottom trace is the reflected signal. The curve to the right displays the reflected intensity as a function of the input intensity.
116
117
to shorter wavelengths such that more light from the input enters the cavity and
decreases the index even further.
switching behavior in the etalon.
This process avalanches and produces the sharp
The peak power on the etalon is lO mW focused
into a 20-micron spot. Tighter focusing of the input with higher power microscope
objectives has the undesirable feature that the Fabry-Perot resonance broadens. This
occurs because each angle incident on the etalon sees an effectively different
resonance. When the input cone of light is large (for stronger focusing). the different
resonances are convolved together. The optical power requirements for nonlinear
switching did not decrease with higher power microscope objectives. However. if an
optical fiber is butt-coupled to the input face of the resonator. better performance can
be obtained. This is because the light exiting the fiber is a spatially filtered plane
wave. The light reflected from the etalon is collected by the same fiber and detected
with a partially reflecting mirror. This method can reduce the power requirements by
a factor of 2 when using a single-mode optical fiber with guiding diameter of
IO-microns. This configuration was used to implement a fiber-etalon-fiber optical
bistable fiber link [Jin et ai. (1989)].
The results of an optical NOR-gate operation is shown in the Fig. 6-7. The
experimental set-up is identical to the one used in the lifetime measurements of chapter
two. In this case. the probe wavelength is tuned to the transmission resonance of the
etalon. We remove the substrate from the integrated Fabry-Perot (F-P) etalon in order
to perform transmission measurements. The sub-nanosecond pump pulse (88 nJ) is
tuned to 817 nm for efficient carrier generation and focused to a 260-micron spot
diametp.r. As soon as the pump is absorbed. the refractive index of the spacer
decreases and the resonance is shifted to shorter wavelengths. The probe transmission
decreases as the Fabry-Perot shifts since the probe wavelength is no longer resonant
with the device. As the carriers recombine. the index returns to its original value and
Fig. 6-7. NOR gate response of the integrated Fabry-Perot etalon in transmission. The probe wavelength is X .. 888 nm. The pump pulse is 0.5 nanosecond full width half maximum.
118
119
the Fabry-Perot returns to its original resonance wavelength. The probe transmission
increases as the Fabry-Perot returns to its inital resonance. The lIe lifetime associated
with the NOR-gate operation is 12 nanoseconds. Faster NOR-gate operation has been
reported [Lee et ai. (l986c)]. By exposing more of the GaAs surface to nonradiative
recombination. the carrier lifetime can be shortened. As was the case with the
quantum wires. more exposed surface leads to faster lifetimes. We also explored this
possibility in the pixellated integrated F-P devices. In this case. only sidewall recom
bination contributed to the faster recombination and yet we still observe a faster NOR
gate recovery (I nanosecond). Smaller pixels (I-micron) should speed up the device
even further.
Reduction in Thermal Sensitivity
The operation of closely-spaced bistable devices can introduce undesirable
thermal effects. Thermal nonlinearities produce positive refractive index changes
which compensate the electronic nonlinearities. Unless energy can be effectively
removed from the devices. these thermal effects can degrade the performance as well
as produce thermal gradients in the wafer. The integrated Fabry-Perot structure
operating in reflection solves some of this thermal loading problem. The heat conduc
tion from the etalon into the GaAs substrate is very efficient. This allowed the obser
vation of nonlinear optical gating with millisecond pulses.
Without any heat-sinking in the etalon. thermal effects are observed with
pulses as short as 5-/1sec. In this monolithic etalon we observe optical bistability with
400-flsec pulses (Fig. 6-8). Other methods of heat sinking Fabry-Perot etalons have
also been reported [Jewell (1984); Olin. Sahlen (1989)]. However. these methods require
Fig. 6-8. Optical bistability in reflection in the integrated Fabry-Perot etalon using 400 fl.-sec triangular pulses. The peak input power is 40 mW and the input wavelength is A ... 887 nm. The top trace shows the time response of the switching. The bottom trace shows the narrow bistable loop.
120
121
additional processing steps. The integrated F-P structure experiences a reduced
thermal sensitivity simply from the fact that excess heat can be conducted away into
the OaAs substrate and dissipated in a much larger thermal mass.
122
CHAPTER SEVEN
OPTICAL NOR GATE USING LASER DIODE SOURCES
Optical logic elements. especially in the form of 2-D arrays. can possibly be
applied to massively parallel signal processing. GaAs/ AIGaAs multiple-quantum-well
etalons have previously shown optical bistability [Gibbs et al. (1982)] and various
types of logic-gate operations [Jewell et al. (1985)] at room temperature. Most of these
experiments have used a dye laser. which is large in size and expensive. One attrac
tive feature of these devices is that a GaAs/AIGaAs diode laser can be used as a light
source making the total system more practical. Not only are solid-state light sources
compatible with these devices. but so is the entire optoelectronic technology base of
detectors and GaAs electronics. For this reason GaAs enjoys a strong advantage
relative to any other material and may signal the direction of optical signal processing
in the near term. Use of a diode laser to observe optical bistability in a
GaAs/AIGaAs etalon has been reported [Tarng et ai. (1984)]. but the mode-hopping
noise induced by optical feedback was a major problem. A long separation (> 2m)
between the diode laser and etalon device was necessary for stable operation.
The present chapter demonstrates a stable optical NOR gate using two diode
lasers [Ojima. Chavez-Pirson et ai. (1986)]. Furthermore. the length of the optical
system is relatively short (30 em). This chapter also invesigates the influence of a
pump diode laser on a probe diode laser in terms of longitudinal-mode frequency in
stability.
123
Experimental Apparatus
Figure 7-1 shows the two optical configurations that were tested to demonstrate
an optical NOR gate using two diode laser sources. The main difference between the
two is that a Faraday isolator is used in Fig. 7-1(a). while a quarterwave plate (plus a
polarization beam spIi,~er) serves as an isolator in Fig. 7-I(b). The Faraday isolator
(Hoya Glass M500) has an isolation ratio of 32 dB at 830 nm. The aperture of the
isolator is 2 rom in diameter. and the beam diameter from the probe laser is 5 mm.
Thus only 20% of the beam is transmitted through the isolator with optics used. The
diode lasers (Hitachi HL8314E) have a typical maximum output at the emitting facet of
30 m Wand a wavelength of 830 ± 20 nm. The wavelength of the diode lasers can be
temperature tuned (0.3 nm/oq so that the emission wavelength of the lasers matches
the spectral requirements of the Fabry-Perot etalon. One diode laser is operating cw
for probing the optical gate. The other diode laser is pulsed for pumping the gate and
has a pulse width of 200 nsec and a repetition rate of ~ 0.1 MHz. Laser power on the
gate is I mW on the average for the probe and 15 mW at the peak for the pump in
Fig. 7-1(a). The pump and probe beams on the gate are linearly polarized and orthogo-
nal to each other in the configuration of Fig. 7-1(a). while they are circularly polarized
and have opposite senses in Fig. 7-I(b). All three lenses. two for collimating the diode
lase beams and one for focusing the beam onto the gate. are Asahi-Pentax PLH-12.
They were originally designed for optical disk recording applications and have a
numerical aperture of 0.28.
The optical gate consists of a GaAs/ AIGaAs multiple-quantum-well crystal
sandwiched between two dielectric mirrors. The multiple quantum well consists of
° ° 180 periods of 58-A thick GaAs wells and 96-A thick Alo.4Gao.sAs barriers. The
free-exciton absorption peak was observed at 825 nm at room temperature. and a diode
GaAs/AIGaAs MQW Detector Fabry- prot Etalon PBS
Faraday II
-P.~M~~====t=a: Polarizer
Fabry- Perot ).14 Plate PBS
Fig. 7-1. Configurations for optical NOR gate operation with two diode laser sources. The optical isolator is either (a) a Faraday rotator or (b) a quarterwave plate plus polarization beam splitter (PBS).
124
125
laser with 825-nm peak wavelength was selected for the pump. The front mirror was
specially designed to have low reflectivity (30%) at the pump laser wavelength (825 nm)
and high reflectivity (97%) at the probe laser wavelength (850 nm). The rear mirror
has high reflectivity (94%) at both wavelengths. This combination of mirrors allows
efficient pumping and high finesse at the probe wavelength [Jewell et ai. (1985)].
A PIN detector placed behind the gate detects the transmitted probe beam from
the gate. A film polarizer was inserted between the detector and gate in Fig. l(a) to
reject the vertically polarized pump laser light. When adjusting the positions of the
two light spots on the gate to overlap exactly. the detector was replaced with a TV
camera system. To observe the frequency of the probe diode laser. a glass plate was
inserted just after the probe-beam collimating lens to reflect light into a grating spec
trometer equipped with an optical multichannel analyzer (OMA).
Results and Discussion
Figure 7-2 is a typical output signal of the optical NOR gate depicted in Fig.
7-l(a). When the pump light pulse is absorbed. the gate's transmission at the probe
wavelength is driven low. This yields an optical NOR logic. When the input signal
light is on. the output light from the gate is off and vice versa with a second input
signal being off (although how to input other signal beams is a nontrivial problem).
The operating principle has been explained as follows [Gibbs et ai. (l979b)]. The
transmission peak wavelength of the nonlinear Fabry-Perot etalon is initially set to the
probe laser wavelength so that transmission is high without the pump. The pump light
creates a high density of carriers. so that the free exciton absorption is saturated and
the index of refraction is decreased at the probe wavelength. This shifts the Fabry-
Fig. 7-2. Optical NOR gate output signal. Bottom line: zero output. Time scale: 5 /ls/div.
126
127
Perot transmission peak to shorter wavelengths and decreases its transmission at the
probe wavelength provided the frequency spectrum of the probe diode laser does not
change. For NOR-gate operation with the setup of Fig. 7-1(a) it was verified that that
the probe diode laser oscillates in a single longitudinal mode as shown in Fig. 7-3(a);
i.e. the spectrum does not change at all, with or without the pump laser.
However, in the configuration of Fig. 7-1(b), the spectrum of the probe laser
was found to change due to the pump laser. Figure 7-3(b) shows an example of the
pump-laser effect on the probe laser. The spectrum dotted in Fig. 7-3(b) was obtained
by widening the pump pulse width so that the duty factor of the pump was more than
90%. In this extreme example, a signal similar to that of Fig. 7-2 was observed even
without GaAs nonlinear material in. the Fabry-Perot etalon. This apparent but false
NOR gate signal occurs because the transmission of the Fabry-Perot etalon is low for
the changed probe-laser spectrum. This sensitivity of the probe-laser frequency to
weak injection from the pump laser was not the property of one particular laser.
Three diode lasers were tested as a probe in Fig. 7-1(b), and they all showed spectrum
changes due to the pump-laser injection, although the changes were different from one
diode laser to another.
In the configuration of Fig. 7-1(b), most (95%) of the pump light reflected from
the gate is injected into the probe laser diode laser. On the other hand, in Fig. 7-1(a),
99% of the reflected pump light goes bac.:k to the pump diode laser; the remainder (1 %)
is further rejected by the Faraday isolator by more than 99%. Therefore, the amount
of pump light injected into the probe is more than 104 times smaller in Fig. 7-I(a) than
in Fig. 7-I(b).
Even with the pump laser off. mode-hopping noise can be induced by feedback
of the probe-laser light reflected from the gate. This situation is similar to the
feedback-induced noise in an optical disk system [Ojima et al (1986)]. Mode-hopping
(0)
(b)
WITH PUMP ~ I, II 'I .. II I , I I I I t' ,
I , ~
./
{WITHOUT PUMP WITH PUMP
WITHOUT PUMP
Fig. 7-3. Typical probe diode laser specta: (a) for configuration of Fig. 7-1(a) and (b) for configuration of Fig. 7-1(a).
128
129
noise occurs at particular driving currents and temperatures. However. it is easy to
adjust the driving current and/or the temperature to obtain stable oscillation indefin
itely [Chinone et al. (1985)]. Such noise is often enhanced by the wavelength depen
dence of the gate's transmission. The configuration using the Faraday rotator was
found to give much better isolation against the feedback than the configuration using
the quarterwave plate.
Figure 7-4 is a photograph of an actual setup used to demonstrate an optical
NOR gate operation corresponding to Fig. 7-I(a). The length of the setup was E!!! 30
cm. This demonstration is far from an actual signal processing system in terms of
cascadability. power dissipation. and 2-D array. However. it obtains the answer to a
logic question using an all-optical gate and diode lasers. As such. it is one step
toward optical signal processing.
Conclusion
Optical NOR gate operation has been successfully demonstrated using two
diode lasers and a GaAs/ AIGaAs multiple-quantum-well etalon. The essential
component in the apparatus is a Faraday isolator that eliminates probe-laser frequency
shifts caused by unintentional pump-beam injection and probe-beam feedback. The
fact that diode lasers can be used as light sources makes GaAs optical logic gates
much more attractive for optical signal processing.
Fig. 7-4. isolator.
Setup for optical NOR gate with two diode lasers and a Faraday
130
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