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Optical studies of semiconductor heterostructures: measurements of tunneling times, and studies of strained superlattices
Citation
Jackson, Michael Kevin
(1991)
Optical studies of semiconductor heterostructures: measurements of tunneling times, and studies of strained superlattices.
Dissertation (Ph.D.), California Institute of Technology.
doi:10.7907/2c3x-qn71.
Abstract
This thesis describes experimental studies of semiconductor heterostructures, using optical techniques. The work presented concerns two topics in the study of semiconductor heterostructures: the escape of confined electrons and holes by tunneling, and the accommodation of lattice mismatch by strain. Time-resolved photoluminescence techniques have been used to measure the times required for electrons and holes to escape by tunneling through the A1As barriers of GaAs/A1As/GaAs/A1As/GaAs double barrier heterostructures. The effect of the indirect (X-point) levels in the AlAs barriers upon escape of confined electrons has been investigated using continuous (CW) photoluminescence. Time-resolved studies of electrically biased double-barrier heterostructures have been made, using both photoluminescence and photocurrent techniques. Finally, the accommodation of the large (6%) lattice mismatch in CdTe/ZnTe superlattices has been studied using Raman scattering.

In Chapter 2 we describe the measurement of tunneling escape times for electrons and holes confined in the quantum well of undoped GaAs/A1As/GaAs/A1As/GaAs double-barrier heterostructures. Photoluminescence from carriers photoexcited in the quantum well by short optical pulses was used to study escape from the quantum well. By using the two-beam technique of photoluminescence excitation correlation spectroscopy (PECS), the first experimental measurements of the tunneling escape times for both the electrons and the holes were obtained. The tunneling escape times were seen to be exponentially dependent upon the barrier thickness for barriers between 16 and 34 A. Escape times for both electrons and holes were found to be fast, and were as short as 12 ps in structures with 16 A (6 monolayer) A1As barriers. The rapid escape of heavy holes that was observed experimentally was in disagreement with simple calculations of the heavy-hole tunneling escape times, which indicated that the heavy holes should escape on a time scale many orders of magnitude longer than the times observed experimentally. This drastic difference can be explained theoretically by considering a four-band model for holes in confined systems. For finite carrier densities and temperatures, mixing of the quantum well heavy hole levels with light hole levels, due to dispersion perpendicular to the growth direction, can explain the experimental observations. This observation that heavy holes can escape rapidly by tunneling is quite general, and is applicable to a wide variety of problems involving tunneling of holes in semiconductor heterostructures.

Chapter 3 describes a study of the effect of indirect (X-point) levels in the A1As barriers on the tunneling escape of electrons in undoped GaAs/AlAs/GaAs/AlAs/GaAs double-barrier heterostructures. The X-point levels, thought to be important in the electrical characteristics of double-barrier heterostructures, were found to affect the escape of photoexcited electrons in devices where the energy of the electron state confined in the GaAs quantum well is nearly equal to, or higher than, that of the X-point levels in the AlAs barriers.

In Chapter 4, we present time-resolved photoluminescence and photocurrent studies of tunneling in doped devices under electrical bias, in which current is flowing. Studies of the photoluminescence decay indicate that significant transport of photoexcited carriers from the electrodes into the quantum well occurs. This transport of photoexcited carriers constitutes a photocurrent, and the two-beam PECS technique for photoluminescence has been extended to a study of photocurrents in these devices. This technique may be useful for the study of tunneling in devices not amenable to photoluminescence techniques.

Chapter 5 describes a study of the accommodation of lattice mismatch in CdTe/ZnTe strained layer superlattices. Using resonance Raman scattering, the energies of the ZnTe-like phonons were determined in a series of superlattices of varying average CdTe content. The ZnTe-like phonon energies decrease with increasing average CdTe content, indicative of the increasing strain of the ZnTe layers. The observed energies agree well with calculations of the strain shift of the phonons. The results indicate that the superlattice layers adopt a lattice constant independent of the buffer layer on which they are grown, and are coherently strained to a lattice constant that minimizes the strain energy of the superlattice.

Finally, the Appendix describes operation of the colliding pulse mode-locked (CPM) dye laser used in the time-resolved photoluminescence and photocurrent experiments. Alignment of the laser, and routine operation are documented.
Item Type:
Thesis (Dissertation (Ph.D.))
Subject Keywords:
Applied Physics
Degree Grantor:
California Institute of Technology
Division:
Engineering and Applied Science
Major Option:
Applied Physics
Thesis Availability:
Public (worldwide access)
Research Advisor(s):
McGill, Thomas C.
Thesis Committee:
McGill, Thomas C. (chair)
Yariv, Amnon
Miles, Richard Henry
Defense Date:
23 July 1990
Record Number:
CaltechETD:etd-07022007-134108
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DOI:
10.7907/2c3x-qn71
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OPTICAL STUDIES OF SEMICONDUCTOR
HETEROSTRUCTURES:

MEASUREMENTS OF TUNNELING
TIMES,

AND STUDIES OF STRAINED
SUPERLATTICES

Thesis by

Michael Kevin Jackson

In Partial Fulfillment of the Requirements
for the Degree of
Doctor of Philosophy

California Institute of Technology

Pasadena, California

1991
(Submitted July 23, 1990)

To my parents, Helen, Alan, and Tasha

Acknowledgements

I would like to thank my advisor, Dr. T.C. McGill, for the opportunity to work
in the exciting and friendly research group that he has assembled. His ceaseless
efforts to keep the group well-equipped and working on interesting problems are
greatly appreciated.

In the course of working in Dr. McGill’s research group, I have had the plea-
sure, both personally and professionally, of working with a great number of en-
thusiastic and talented people. I would especially like to thank those who have
had the greatest impact on my time as a graduate student, in both work-related
and personal matters: Dr. Richard Miles, whose patient introduction to optical
experiments, keen insight, and steady encouragement have helped me tremen-
dously; Dr. David Chow, whose unfailing good nature and concern for others
made our years of sharing an office very enjoyable; and Dr. David Ting, whose
friendly manner, and sound advice are greatly appreciated. I would like to thank
Dr. Matthew Johnson for his patience in teaching me laboratory techniques, in
particular regarding the CPM laser, and for his stubborn insistence on quality
and honesty; without Matthew’s help, little of the work presented in this thesis
would ever have been done. I have also enjoyed many discussions with my class-
mate, Yasantha Rajakarunanayake, whose energy, enthusiasm, and optimism are
a source of constant amazement and inspiration. I have enjoyed many discussions
with Ed Yu, and am grateful for having had the benefit of his insight. I would
particularly like to thank Ed for his role in the work presented in Chapter 2. I
have enjoyed working with Jan Soderstrom during his brief time spent at Caltech,
and would like to acknowledge his help in the work presented in Chapter 4. The
exceptional efforts in MBE growth by Doug Collins during our collaboration on

the work presented in Chapter 3 are greatly appreciated. I have also enjoyed

many discussions with Ed Croke, Mark Phillips, and Todd Rossi, and would like
to acknowledge Todd’s help with the autocorrelator described in Appendix A. I
would like to acknowledge the encouragement of Dr. Alice Bonnefoi, who made
my adjustment to Caltech much easier. It is a pleasure to acknowledge discus-
sions with Drs. J.O. McCaldin, George Wu, Bob Hauenstein, Ted Woodward, and
Wesley Boudville. I have also benefited from my contacts with Pete Zampardi,
Yixin Liu, Johanes Schwenberg, Mike Wang, Ron Marquardt, Harold Levy, Rob
Miles, and Tracey Fu. I would also like to thank all those who helped me by
critical reading of this thesis; their efforts have greatly improved the content.

I would like to thank Marcia Hudson and Carol McCollum, for their excellent
support on administrative matters, and for many interesting conversations. Vere
Snell, whose professional and friendly manner helped shape the research group
when I joined, is greatly missed.

I have also benefited greatly from my interactions with Dr. A. Yariv. I would
like to acknowledge helpful conversations with Dr. Darryl Smith, of Los Alamos
National Laboratory, and Dr. Ogden Marsh, of Hughes Research Laboratories.
I would also like to acknowledge the tremendous help I received regarding the
CPM laser from a number of people: Dr. Janis Valdmanis, of the University of
Michigan, who gave very freely of his time to talk to me about the laser; Marcos
Dantus and Bob Bowman at Caltech were also very helpful. The appendix on the
CPM laser is largely a result of conversations with these people. I would also like
to thank Dr. C.W. Nieh, of Caltech, for providing TEM data; Dr. J.-P. Faurie,
of the University of Illinois, for providing CdTe/ZnTe superlattice samples; and
Bobby Weikle for help with electron-beam evaporations.

During my time at Caltech I have enjoyed talking with Vicki Arriola, Jana
Mercado, Laura Rodriguez, Ali Ghaffari, and Rosalie Rowe. I would also like to

acknowledge the staff in all of the shops, stockrooms, and administrative capaci-

ties for making my stay at Caltech more enjoyable.

I would like to acknowledge financial support, in the form of fellowships,
from the Natural Sciences and Engineering Research Council of Canada, and the
California Institute of Technology.

Finally, I would like to thank Lionel Laroche, and Dr. Hal Zarem, for their
friendship and support. I also owe thanks to Peter Leigh-Spencer, of Edmonton,
who taught me about racing cars and, without realizing it, about doing exper-
iments. I would like to thank my family for their unfailing encouragement and
support; in particular, I would like to thank my parents for the high value they
placed upon education. Finally, I would like to thank Tasha for her love and

support; without her, I surely would have given this up long ago.

vi
Abstract

This thesis describes experimental studies of semiconductor heterostructures,
using optical techniques. The work presented concerns two topics in the study
of semiconductor heterostructures: the escape of confined electrons and holes by
tunneling, and the accomodation of lattice mismatch by strain. Time-resolved
photoluminescence techniques have been used to measure the times required for
electrons and holes to escape by tunneling through the AlAs barriers of GaAs/-
AlAs/GaAs/AlAs/GaAs double barrier heterostructures. The effect of the in-
direct (X-point) levels in the AlAs barriers upon escape of confined electrons
has been investigated using continuous (CW) photoluminescence. Time-resolved
studies of electrically biased double-barrier heterostructures have been made, us-
ing both photoluminescence and photocurrent techniques. Finally, the accomo-
dation of the large (6%) lattice mismatch in CdTe/ZnTe superlattices has been
studied using Raman scattering.

In Chapter 2 we describe the measurement of tunneling escape times for elec-
trons and holes confined in the quantum well of undoped GaAs/AlAs/GaAs/-
AlAs/GaAs double-barrier heterostructures. Photoluminescence from carriers
photoexcited in the quantum well by short optical pulses was used to study escape
from the quantum well. By using the two-beam technique of photoluminescence
excitation correlation spectroscopy (PECS), the first experimental measurements
of the tunneling escape times for both the electrons and the holes were obtained.
The tunneling escape times were seen to be exponentially dependent upon the
barrier thickness for barriers between 16 and 34A. Escape times for both elec-
trons and holes were found to be fast, and were as short as 12ps in structures
with 16A (6 monolayer) AlAs barriers. The rapid escape of heavy holes that

was observed experimentally was in disagreement with simple calculations of the

vii

heavy-hole tunneling escape times, which indicated that the heavy holes should
escape on a time scale many orders of magnitude longer than the times observed
experimentally. This drastic difference can be explained theoretically by consid-
ering a four-band model for holes in confined systems. For finite carrier densities
and temperatures, mixing of the quantum well heavy hole levels with light hole
levels, due to dispersion perpendicular to the growth direction, can explain the
experimental observations. This observation that heavy holes can escape rapidly
by tunneling is quite general, and is applicable to a wide variety of problems
involving tunneling of holes in semiconductor heterostructures.

Chapter 3 describes a study of the effect of indirect (X-point) levels in the AlAs
barriers on the tunneling escape of electrons in undoped GaAs/AlAs/GaAs/-
AlAs/GaAs double-barrier heterostructures. The X-point levels, thought to be
important in the electrical characteristics of double-barrier heterostructures, were
found to affect the escape of photoexcited electrons in devices where the energy
of the electron state confined in the GaAs quantum well is nearly equal to, or
higher than, that of the X-point levels in the AlAs barriers.

In Chapter 4, we present time-resolved photoluminescence and photocurrent
studies of tunneling in doped devices under electrical bias, in which current is
flowing. Studies of the photoluminescence decay indicate that significant trans-
port of photoexcited carriers from the electrodes into the quantum well occurs.
This transport of photoexcited carriers constitutes a photocurrent, and the two-
beam PECS technique for photoluminescence has been extended to a study of
photocurrents in these devices. This technique may be useful for the study of
tunneling in devices not amenable to photoluminescence techniques.

Chapter 5 describes a study of the accomodation of lattice mismatch in CdTe/-
ZnTe strained layer superlattices. Using resonance Raman scattering, the energies

of the ZnTe-like phonons were determined in a series of superlattices of varying

vill

average CdTe content. The ZnTe-like phonon energies decrease with increasing
average CdTe content, indicative of the increasing strain of the ZnTe layers. The
observed energies agree well with calculations of the strain shift of the phonons.
The results indicate that the superlattice layers adopt a lattice constant indepen-
dent of the buffer layer on which they are grown, and are coherently strained to
a lattice constant that minimizes the strain energy of the superlattice.

Finally, the Appendix describes operation of the colliding pulse mode-locked
(CPM) dye laser used in the time-resolved photoluminescence and photocurrent

experiments. Alignment of the laser, and routine operation are documented.

List of Publications

Parts of this thesis have been, or will be, published under the following titles:

Chapter 2:
Electron Tunneling Time Measured by Photoluminescence Exci-
tation Correlation Spectroscopy,
M.K. Jackson, M.B. Johnson, D.H. Chow, T.C. McGill, and C.W. Nieh,
Appl. Phys. Lett. 54, 552 (1989).

Electron Tunneling Time Measured by Photoluminescence Exci-
tation Correlation Spectroscopy,

M.K. Jackson, M.B. Johnson, D.H. Chow, J. Soderstrom, T.C. McGill, and
C.W. Nieh, in Proceedings of the OSA Topical Meeting on Picosecond Elec-
tronics and Optoelectronics, Salt Lake City, Utah, March 8-10, 1989, edited
by T.C.L.G. Sollner and D.M. Bloom, p. 124.

Hole Tunneling Times in GaAs/AlAs Double Barrier Structures,
E.T. Yu, M.K. Jackson, and T.C. McGill, Appl. Phys. Lett. 55, 744 (1989).

Chapter 3:
X-point tunneling in AlAs/GaAs double barrier heterostructures,
D.Z.-Y. Ting, M.K. Jackson, D.H. Chow, J.R. Soderstrom, D.A. Collins,
and T.C. McGill, Solid-State Electronics 32, 1513 (1989).

X-point Escape of Electrons from the Quantum Well of a Double-
Barrier Heterostructure, .
M.K. Jackson, D. Z.-Y. Ting, D.H. Chow, D.A. Collins, J.R. Soderstrom,

and T.C. McGill, in preparation.

Chapter 4:
Time-Resolved Photoluminescence and Photocurrent Studies of
GaAs/AlAs Double-Barrier Heterostructures,
M.K. Jackson, D.H. Chow, J.R. Séderstrom, and T.C. McGill, in prepara-

tion.

Chapter 5:
Raman Scattering Determination of Strain in CdTe/ZnTe Super-
lattices,
M.K. Jackson, R.H. Miles, T.C. McGill and J.P. Faurie, Appl. Phys. Lett.
55, 786 (1989).

Contents

Acknowledgements

Abstract

List of Publications

List of Figures

List of Tables

1 Introduction

1.1 Introduction to Thesis ............2..... 0-0-0004

1.2

1.3

1.1.1 Overview 2.0... 2. ee
1.1.2 Summary of Results ..................0..
1.1.3 Outline of Chapter... 2... ..0.....0...0-.0..
Background and Motivation ..................0.0..
1.2.1 Semiconductor Heterostructures...............
1.2.2 Tunneling: High-Speed Device Applications ........
1.2.3 The Characteristic Time for Tunneling ...........
1.2.4 Strained-Layer Superlattices ...............0.4.
Experimental Studies of Tunneling Times. .............

1.3.1 Techniques for Studies of Tunneling Times .........

iil

Xvi

XvVill

xii

1.3.2 Tunneling Time Measurements in Undoped Double- Barrier

Heterostructures 2... 0.0... ee ee 29

1.3.3 X-point Escape of Electrons ...............0.4. 30
1.3.4 Tunneling in Biased Structures ............... 32

1.4 Raman Scattering Studies of Strained-Layer Superlattices.... . 32
1.5 Outline of Thesis ............ 0.02.00. 0 2.02000 00,4 36
References... 0. 39

2 Tunneling Time Measurements in Undoped Double-Barrier Het-

erostructures 45
2.1 Introduction... 2... 0.0.00 45
2.1.1 Background .........00.0.2. 020000505005, 45
2.1.2 Summary of Results ..............2..0-0.0. 46
2.1.3 Outline of Chapter ............2.-..02.008. 47

2.2 Time-Resolved Luminescence Technique .............. 48
2.2.1 Background ........... 0.0.00 000000004 48
2.2.2 Experimental Setup... ............-..2.00. 49
2.2.3 Theory... 2... 0. 52

2.3 Samples... 2.2... 0.2.00 0. pe ee 61
24 Results... 0... 63
2.4.1 Time-resolved Measurements at 80K ............ 63
2.4.2 Dependence upon Barrier Thickness... .......... 67
2.4.3 Temperature-Dependent Measurements........... 69

2.5 Discussion... 2... 0-2 ee 69
2.6 Comparison with Results in Other Systems. ............ 77
2.7 Conclusions .. 2... 80

References... 0... ee 81

3 X-point Escape of Electrons from the Quantum Well of a Double-

Barrier Heterostructure 85
3.1 Introduction... 0... 0... 85
3.1.1 Background .........0..0..0.. 2.00. .045. 85

3.1.2 Summary of Results .......0....0....2.....048. 91

3.1.3 Outline of Chapter... . 0.0.2.0... ...0...04. 92

3.2 Experimental Techniques. ........-.....-.0.02.04. 92
3.3 Results and Discussion .. 2... 0.22. ee 95
3.4 Conclusions .. 2... 0.0... ce 103
References... 2... 105

4 Studies of Electrically Biased Double-Barrier Heterostructures 108

4.1 Introduction... 2... 0... ee ee 108
4.1.1 Motivation and Background ...............04. 108
4.1.2 Summary of Results ...............-.00.. 110
4.1.38 Outline of Chapter... ...........-.. 02.000. 111

4.2 Time-Resolved Photoluminescence................-.. 112
4.2.1 Device Preparation ............-.-0..0-000,4 112
4.2.2 Experimental Arrangement ................. 114
4.23 Results... 0.2.0... 20. 0.20... 00.2 eee eee 114
4.2.4 Discussion. ......-. 0,-0.2. 0 0-0. eee eee 118

4.3 Photocurrent Measurements ..................00.- 119

4.3.1 Device Preparation and Current-Voltage Characteristics . 119

4.3.2 Experimental Apparatus .................0.4. 122
433 Results. .....0.00202.00.. 000.0000 eee ees 124
4.3.4 Discussion ........02..00.0.. 000 pee ee eee 129

44 Conclusions .........0.0. 2.0 00 ee ee ee es 135

References .........-.2.-..8005 ke ee 137

5 Raman Scattering Determination of Strain in CdTe/ZnTe Su-

perlattices 139
5.1 Introduction... 2... .. 0. 2 139
5.1.1 Background .................. 000-0000. 139
5.1.2 Summary of Results ............2......2.-. 140
5.1.3 Outline of Chapter ............--..0....00-. 141
5.2 Samples ........ 0... 0. eee ee 141
5.3 Experimental Setup... ....-............20004 ‘2. 141
5.4 Results... 2... . 144
5.5 Discussion... . 2... 0... 146
5.6 Conclusions .... 2... 20.0.0. 2 151
References... 2... 152
Appendices 154.
A Colliding Pulse Mode-Locked Laser 155
A.l Introduction... 2... 0. 2 ee 155
A.l.l Background ...........-......0.2.2.-.0004. 155
A.1.2 Outline of Appendix .................2004 160
A.2 Operating Principles ..........- 0.2.0... . 00000. 160
A.3 Design Considerations ............ eee 164
A.4 Diagnostic Equipment ........-.......2. 0.000004 167
A.5 Alignment Procedure. ..............02--.00-02004 169
A.5.1 Linear Cavity, Gain Only... .............00.. 170

A.5.2 Linear Cavity, Gain and Absorber.............. 174

A.5.3 Ring Cavity... 22. ee 175
A.5.4 Achieving Mode-Locking ................... 176
A.6 Routine Maintenance of Laser... .........0....0.0.. 176
A.7 Performance of Laser... .......... 02000000200 e 177

References... 2.20.00. ee kk ee eee 179

XV1

List of Figures

1.1

1.2
1.3
1.4
1.5
1.6
1.7
1.8

2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8

3.1

Energy gap versus lattice constant for some zincblende semicon-

ductors. 2... 6
Band diagram for a double-barrier heterostructure. ........ 9
Tunneling processes: single and double barrier... ........ 13
Schematic diagram of a superlattice... ............0.4. 17
Accomodation of lattice mismatch. ...............0.. 20
Coherently strained and free-standing superlattices ........ 22
Tunneling escape time versus barrier thickness ........... 31

Typical Raman scattering spectrum for a CdTe/ZnTe superlattice 35

Experimental setup for time-resolved photoluminescence .... . 50
Processes involved during photoexcitation of double barrier... . 54
Calculated sum-frequency delay scans................, 59
Typical correlation photoluminescence spectra ........... 64
Typical photoluminescence delay scans ............... 66
Decay times at 80K as a function of barrier thickness ....... 68
Calculated valence subband dispersion ..............., 73
Calculated average heavy-hole tunneling escape times ...... . 75

Schematic diagram of the X-point in double-barrier heterostructures 88

xvil
3.2 Calculated decay of the probability density for an electron initially
localized in the quantum well of a double-barrier heterostructure .
3.3 Typical photoluminescence spectraat5K..............,
3.4 Photoluminescence peak energiesat5K...............,

3.5 Integrated photoluminescence intensity under identical conditions,

at5K 2... ee,

4.1 Current-voltage characteristic for sample IIJ-082 ..........
4.2 Sum frequency photoluminescence spectrum under bias ......
4.3 Sum frequency photoluminescence delay scans under bias .... .
4.4 Current-voltage characteristics for III-083, III-221, and II]-222 . .
4.5 Experimental arrangement for photocurrent experiment... .. .
4.6 Typical sum-frequency photocurrent delay scan ..........
4.7 Sum-frequency photocurrent delay scans as a function of bias. . .
4.8 Comparative sum-frequency photocurrent delay scans for three

samples .. 2.2... .

4.9 Conduction band profile for double-barrier under bias ...... .

5.1 Experimental setup for Raman scattering..............
5.2 Representative Raman spectra in the range of single optical phonon
scattering 2... ee

5.3 Comparison of theoretical with experimental phonon energies. . .

A.1 Diagram of the CPM laser layout... 2...

A.2 CPM configuration during alignment ................

XVill

List of Tables

2.1

3.1

5.1

Sample parameters.....................00-00, 62

Summary of sample parameters and observed photoluminescence

peak energiesat 5K. 2. ......0..0.0...0 0.00004, 93

CdTe/ZnTe superlattice sample parameters. ............ 143

Chapter 1

Introduction

1.1 Introduction to Thesis

1.1.1 Overview

This thesis describes experimental studies of semiconductor heterostructures,
using optical techniques. Recent advances in semiconductor epitaxial growth
techniques have resulted in a wealth of new electrical, optical, and optoelectronic
device applications, and have also allowed us to study a variety of fundamental
issues in physics. The work described in this thesis concerns two major topics in
the study of such semiconductor heterostructures: the time required for escape
of confined electrons and holes by tunneling, and the accomodation of lattice
mismatch by strain. The first part, concerning tunneling, describes studies of
carriers confined in GaAs/AlAs/GaAs/AlAs/GaAs double-barrier heterostruc-
tures. Time-resolved photoluminescence techniques have been used to measure
the times required for electrons and holes to escape by tunneling through the
AlAs barriers. The tunneling time results have implications for high-speed de-

vices based on tunneling of electrons or holes. The final chapter of the thesis

describes a study of the accomodation of lattice mismatch in CdTe/ZnTe super-
lattices. The lattice mismatch between CdTe and ZnTe is large (6%) and makes
the growth of these superlattices difficult. A series of these superlattices has been
studied, using resonance Raman scattering; measurements of the phonon ener-
gies in these structures are used to determine the extent of accomodation of the

lattice mismatch by strain in the layers composing the superlattice.

1.1.2 Summary of Results

One of the major results of this thesis is the measurement of tunneling es-
cape times for electrons and holes confined in the quantum well of undoped
GaAs/AlAs/GaAs/AlAs/GaAs double-barrier heterostructures. Photolumines-
cence from carriers photoexcited in the quantum well by short optical pulses was
used to study escape from the quantum well. By using the two-beam technique of
photoluminescence excitation correlation spectroscopy (PECS), the first experi-
mental measurements of the tunneling escape times for both the electrons and the
holes were obtained. The tunneling escape times were seen to be exponentially
dependent upon the barrier thickness for barriers between 16 and 34A. Escape
times for both electrons and holes were found to be fast, and were as short as
12 ps in structures with 16A (6 monolayer) AlAs barriers. The rapid escape of
heavy holes that was observed experimentally was in disagreement with simple
calculations of the heavy-hole tunneling escape times, which indicated that the
heavy holes should escape on a time scale many orders of magnitude longer than
the times observed experimentally. This drastic difference can be explained the-
oretically by considering a four-band model for holes in confined systems. For
finite carrier densities and temperatures, mixing of the quantum well heavy hole

levels with light hole levels, due to dispersion perpendicular to the growth di-

rection, can explain the experimental observations. This observation that heavy
holes can escape rapidly by tunneling is quite general, and should be applica-
ble to a wide variety of problems involving tunneling of holes in semiconductor
heterostructures.

This thesis also describes a study of the effect of indirect (X-point) levels in
the AlAs barriers on the tunneling escape of electrons in undoped GaAs/AlAs/-
GaAs/AlAs/GaAs double-barrier heterostructures. The X-point levels, thought
to be important in the electrical characteristics of double-barrier heterostructures,
were found to affect the escape of photoexcited electrons in devices where the
energy of the electron state confined in the GaAs quantum well is nearly equal
to, or higher than, that of the X-point levels in the AlAs barriers.

Photoluminescence studies of tunneling in undoped double barriers have also
been extended to doped devices under electrical bias, in which current is flow-
ing. Studies of the photoluminescence decay indicate that significant transport
of photoexcited carriers from the electrodes into the quantum well occurs. This
transport of photoexcited carriers constitutes a photocurrent, and the two-beam
PECS technique for photoluminescence has been extended to a study of photocur-
rents in these devices. This technique may be useful for the study of tunneling
in devices not amenable to photoluminescence techniques.

The final result described in this thesis is a study of the accomodation of lattice
mismatch in CdTe/ZnTe strained layer superlattices. Using resonance Raman
scattering, the energies of the ZnTe-like phonons were determined in a series of
superlattices of varying average CdTe content. The ZnTe-like phonon energies
decrease with increasing average CdTe content, indicative of the increasing strain
of the ZnTe layers. The observed energies agree well with calculations of the strain
shift of the phonons. The results indicate that the superlattice layers adopt a

lattice constant independent of the buffer layer on which they are grown, and are

coherently strained to a lattice constant that minimizes the strain energy of the

superlattice.

1.1.3 Outline of Chapter

The purpose of Chapter 1 is to introduce the topics to be discussed in the
remainder of the thesis, provide background information that will allow the re-
sults that will be presented to be viewed in the context of previous work in this
field, and outline the rest of the thesis. Section 1.2 describes the motivation
for our studies of semiconductor heterostructures; in particular, applications to
high-speed devices, including background on studies of the characteristic time
for tunneling, and applications of strained layer superlattices are discussed. In
Section 1.3, experimental techniques applied to the study of tunneling times are
described. Section 1.4 describes studies of strained layer superlattices using Ra-
man scattering. Finally, Section 1.5 describes the organization of the remainder

of the thesis.

1.2 Background and Motivation

1.2.1 Semiconductor Heterostructures

The ability to grow the semiconductor heterostructures studied in this thesis is
based upon great advances in the last decade in epitaxial” growth techniques such
as molecular beam epitaxy (MBE) and metalorganic chemical vapor deposition
(MOCVD). The ability to grow epitaxial films with abrupt interfaces between

different semiconductors has resulted in a huge variety of device applications,

“In the current context, epitaxial means that the film has a crystallographic structure related

to that of the substrate.

some of which will be described in the following sections. These heterostructure
systems also offer an ideal test of some of our conceptions of basic physics, in
devices that can be studied in the laboratory. An example of such a topic is the
time required for tunneling escape of confined electrons and holes, which can be
studied in semiconductor heterostructure devices.

Epitaxial growth techniques have been used to grow a wide variety of semi-
conductor materials. Figure 1.1 shows the energy gap versus the lattice constant
for a variety of III-V and II-VI zincblende semiconductors that have been grown
with these techniques. Epitaxial growth techniques were first perfected for het-
erostructures composed of materials whose lattice constants are quite close, such
as GaAs and AlAs. As can be seen in Figure 1.1, the lattice mismatch in the
GaAs/AIAs system is a small fraction of a percent, which has greatly facilitated
development of epitaxial growth techniques in this system. Largely as a conse-
quence of the growth techniques being in a fairly advanced state of development,
the GaAs/ AlAs system has seen the greatest success in application to novel elec-
tronic, optical, and optoelectronic applications. The application of this material
system to high-speed tunneling devices will be considered in Section 1.2.2.

In addition to the relatively small number of lattice-matched semiconductor
systems, it is also possible to grow high quality strained heterostructures of ma-
terials with lattice mismatches as high as 7%. The freedom to combine a wider
variety of materials greatly increases the possible heterostructure combinations,
allowing a greater ability to tailor material properties. It is also possible to take
advantage of the strain to control energy levels and nonlinear optical properties
in ways not possible by other means [1, 2]. Recent advances in the understanding
of the influence of growth conditions, such as substrate temperature, upon the
formation of defects and the relaxation of strain [3], and demonstrations of long-

lived InGaAs strained quantum well lasers [4] indicate that strained systems hold

3 T
e Znse
GaPe 8 ZnTe
@ AlAs
ae a
> CdSe@_ AlSb
w r
a. CaAse © CdTe
oy @ InP
f=,
jaa)
1 F- “
GaSb
InAs InSb
O 1 L 1
5 6 7

Lattice constant (A)

Figure 1.1: Energy gap at 4.2K versus lattice constant for some zincblende semi-
conductors. The dark shaded circles are III-V semiconductors, and the lighter

shaded circles are II-VI semiconductors.

great promise for further development and device applications. Some specific

applications of strained II-VI superlattices will be considered in Section 1.2.4.

1.2.2 Tunneling: High-Speed Device Applications

Solid-state devices based on tunneling have been of interest since the pioneer-
ing work of Esaki [5]. Tunnel diodes, also known as Esaki diodes, are based on
homojunctions of heavily doped p-type and n-type materials such as GaAs. The
essential feature of these devices is a current-voltage characteristic that shows
an initial increase in current with increasing voltage, followed by a decreasing
current with further increase in voltage. This region of decreasing current with
increasing voltage, known as negative differential resistance (NDR), is of use in
high frequency oscillators. By placing the device in a waveguide resonator and
applying a voltage sufficient to bias the diode into the NDR region, oscillation can
be sustained [6]. Early work on Esaki diodes, based on point contacts of zinc with
heavily doped n-type GaAs, showed oscillation at frequencies up to 103 GHz [6].
One of the main reasons for interest in oscillators based on tunnel devices is that
there are very few compact sources of radiation in the 100 to 1000 GHz frequency
range. This frequency range is of interest for atmospheric monitoring [7], and for
millimeter wave astronomy [8]. Sources of radiation in this region allow the use
of heterodyne detectors, such as superconductor-insulator-superconductor (SIS)
tunnel junctions, which are advantageous for narrow bandwidth operation in the
millimeter wave region [9]. Sources based on multiplication of lower frequency
Gunn oscillators have been demonstrated at up to 500 GHz [10], but there are few
solid state devices capable of fundamental oscillation at such high frequencies.
Devices based on tunneling present a possible solution to the lack of sources in

this frequency range.

New concepts for tunnel devices based on heterostructure materials were pro-
posed in 1973 by Tsu and Esaki [11] and have stimulated a resurgence of interest
in this field. Figure 1.2 shows a diagram of the conduction band edge versus po-
sition for one such device, known as a double-barrier heterostructure. The device
consists of two heavily doped electrodes surrounding the three layer region in the
center. This central region consists of two thin layers of a large bandgap mate-
tial, which act as barriers, surrounding a single thin layer of a smaller bandgap
material. The electron states in the thin central region, called the quantum well,
are affected by confinement of the electrons by the large bandgap barriers on
the scale of their deBroglie wavelength. Typical quantum well widths are on the
order of 50 A and lead to to an increase in the lowest allowed energy for electrons
in the quantum well on the order of 100 meV. The position of the lowest allowed
energy level in the quantum well is indicated in Figure 1.2 by a dashed line.
When electrical bias is applied to the device, the current increases, reaching a
peak when the electrons in the negatively biased electrode are at an energy equal
to that of the lowest electron state in the quantum well. At this bias condition,
illustrated in Figure 1.2(b), the device is said to be at resonance. Further increase
in the bias results in the electrons in the negatively biased region having an en-
ergy above that of the lowest quantum well state, and results in a decrease in the
current. The region of decreased current past the resonance voltage is referred
to as the valley, and negative differential resistance devices are often character-
ized in terms of their peak-to-valley current ratio. Further increase in bias past
the valley eventually results in an increase in the current through the device due
to nonresonant mechanisms, or transport through higher excited states in the
quantum well.

Double-barrier heterostructure devices were first demonstrated in the GaAs/-

/ AlGaAs system by Chang et al. [12]. Subsequent development of this material

(a) Zero Bias

(b) At Resonance

Figure 1.2: Conduction band versus position for a double-barrier heterostructure,

(a) at zero bias, and (b) at resonance. The two

outermost layers are doped n-type,

indicated by the shaded region, and act as electrodes. The two large-bandgap

layers act as barriers, and surround the quantum well in the center of the device.

The dashed line in the quantum well indicates the energy of the lowest allowed

electron state in the well.

system has progressed to the point where room temperature current densities
can be as high as 1.3 x 10°A/cm? in devices with peak-to-valley current ratios
of approximately 2 [13]. Higher peak-to-valley current ratios are possible at the
expense of decreased peak current density, and can be as high as 5.1:1 at room
temperature for peak current densities of 10*A/cm? [14]. The high current density
devices have been used in oscillators at frequencies as high as 420 GHz [15], and
mixing action has been observed at frequencies up to 2.5 THz [16].

Recent efforts in this field have centered on the demonstration of double-
barrier devices with superior performance, using other material systems. Work-
ing devices have been demonstrated in the InGaAs/GaAs/AIAs system (17], and
the InAs/AISb system [18]. The InAs/AlSb system shows the highest peak
current densities observed to date, with maximum room temperature values of
4x 105A/cm? and peak-to-valley current ratios of 4:1 (18, 19]. These devices have
recently been demonstrated to oscillate at frequencies up to 675 GHz [19], and
are predicted to be capable of oscillation at up to 1.3 THz.

This frequency of 675 GHz represents the highest frequency of fundamental
oscillation for any solid-state device, and demonstrates very clearly the suitability
of tunneling devices for high-frequency operation. Recent proposals and demon-
strations of three-terminal tunnel structures [20, 21, 22, 23, 24, 25, 26] suggest
that the high-frequency application of the two-terminal devices described above
may be followed by three-terminal devices based on tunneling. These devices
could have application in high-frequency analog or digital circuits, and may aid
in the development of multilevel digital logic (21, 23].

Although high-frequency tunneling devices are affected by conventional con-
siderations of stray capacitances and transit times across the depletion region, the
ultimate speed of operation is expected to be limited by the tunneling time. Re-

cently, Brown [27] has been able to quantify the dependence of the power output

of the double-barrier oscillators on these three factors. The lifetime of electrons
confined in the quantum well was found to be an important limitation on the
output power of the oscillators at high frequency. The importance of the speed
of tunneling to the performance of these devices has been a major motivation for

the time-resolved studies of tunneling reported in this thesis.

1.2.3 The Characteristic Time for Tunneling

As discussed in the previous section, there is currently great technological in-
terest in the speed of tunneling. There is, however, a more fundamental reason for
the interest in the characteristic time for tunneling, related to our understanding
of basic quantum mechanics. The question of the characteristic time for tunnel-
ing remains unanswered even after 50 years of study. As will be discussed in this
section, there are many differing definitions of tunneling times; the measurements
described in Chapter 2 are, strictly speaking, measurements of tunneling escape
times. The relationships between the various tunneling times, and experiments
intended to measure them, are not clear. It is not the purpose of the work in
this thesis to attempt to resolve this issue; however, this section is intended as
background to our study of tunneling escape times in double-barrier heterostruc-
tures. First discussed in 1931 by Condon [28], the time scale for the tunneling
process has many important implications. For example, during tunneling, the
motion of the electronic charge could be expected to cause polarization of the
material through which the tunneling is occurring, or induce image charges in
the surrounding electrodes. This image charge effect would be negligible if the
time for tunneling were fast with respect to the time required for the electron
plasma to respond (given by the plasma frequency). This issue is of current in-

terest in the field of scanning tunneling microscopy (STM), in which the extent

of the image charge effect on the tunneling current is thought to be important in
understanding the results of STM experiments [29].

In this section, we will briefly outline the basic questions in this field, and try
to give a feel for the origin of the controversy. The various competing theories for
tunneling times have recently been reviewed by Collins et al. [30] and by Hauge
and Stgvneng [31]. In passing it is important to note that even these review
articles are controversial, as seen by the comment [32] and reply [33] concerning
Ref. [30]. The purpose of this section is not to duplicate these two extensive
reviews, but to give a brief survey of the open questions in this area, and to suggest
that the only satisfactory resolution of the debate will derive from comparison
of the various theories with new experimental data. The reader interested in
the details of the various theories, and the various arguments relating to their
relative merit, is referred to Refs. [30, 31] and the references therein. The various
experimental approaches to measurements of tunneling times will be discussed
in Section 1.3.1, and the experimental results pertaining to tunneling obtained
during the course of this thesis will be described in Chapters 2, 3, and 4.

The question which has generated so much debate, simply phrased, is: what is
the time scale relevant for the tunneling of an electron from one side of a barrier
to another? This situation is schematically illustrated in Fig. 1.3(a), which shows
an electron tunneling across a single barrier. A related question, and one that
is more directly addressed by the experiments in this thesis, is: what is the
characteristic time for escape from a metastable state, and are there other time
scales in addition to this escape time? This situation is illustrated in Fig. 1.3(b),
in which an electron, initially confined in the quantum well of a double-barrier
heterostructure, is shown tunneling through the barriers.

Thornber et al. [34], in their work on single-barrier tunneling (as illustrated

in Fig. 1.3(a)), have suggested that there is a single time scale for the entire tun-

(a) (b)

Figure 1.3: Schematic diagram of an electron (a) tunneling through a single

barrier (b) escaping from the quantum well of a double-barrier heterostructure.

neling process, and that the relevant time is given by the inverse of the transition
rate for incoming electrons to tunnel through the device. They argued that be-
cause the electron wavefunction in tunneling has a finite tail in the barrier during
the entire process, that it was essentially interacting with the barrier during the
entire time. Applied to the case of escape from a metastable state, illustrated in
Fig. 1.3(b), this approach implies that the relevant time scale for the process is
the quasi-bound state lifetime for the state in the quantum well.

In another approach, Buttiker and Landauer [35] have used semiclassical ar-
guments to suggest that in single-barrier tunneling, as illustrated in Fig. 1.3(a),
it is possible to define a traversal time for an electron to cross the barrier region,
given by

= om
TBL = [ in(a)

where z, and x2 define the classical turning points, and m is the mass. «(z) =

(2m(Vo(z) — E)/h is the decay constant in the classically forbidden region,
where Vo(x) is the potential energy as a function of position, and £ is the en-
ergy of the incoming electron. This time appears to be simply an integral of the
distance divided by an effective velocity, where the standard expression for the
velocity of a particle in a classically allowed region is extended to the forbidden
region, ignoring the fact that such a velocity is imaginary. In the extension of
this semi-classical approach to the escape from a metastable state illustrated in
Fig. 1.3(b), it is claimed [36] that it is possible to separately and unambiguously
identify a traversal time, related to the tunneling through the barrier, and that
this time is different from the lifetime of the metastable state. This idea seems to
imply that it is possible to identify a time at which a particle starts tunneling, and
make some measurement of the time of interaction with the barrier starting when
the particle “decides” to tunnel, and ending when the particle has completed tun-
neling. Although there is no obvious reason that this semiclassical approach is
valid in the quantum mechanical problem, it has had some support in the results
of some experiments regarding tunneling in single barriers and Josephson junc-
tions, which will be briefly described in Section 1.3.1. Biittiker has suggested [37]
that the photoluminescence decay measurements described in Chapter 2 of this
thesis constitute measurements of the lifetime of the metastable state, but do not
contain information regarding the traversal time.

As can be concluded from the above discussion, and from inspection of the
other literature in which various workers have proposed tunneling times that
are independent of the barrier thickness [38], or go to zero in the limit of zero
incident kinetic energy [39], that there are a wide variety of procedures for calcu-
lating quantities in the tunneling problem that have the dimensions of time. The

difficulty in defining and measuring a tunneling time originates in the fact that

time is not an observable in quantum mechanics. The only procedure at our dis-
posal is to follow the time evolution of other observable quantities, such as charge
densities, and from the evolution of these quantities, infer information about the
relevant time scale for tunneling. Nevertheless, the work in the last 50 years does
not seem to have addressed this aspect of the problem seriously, i.e., the need to
define the observables that can be measured experimentally. The original work of
Condon [28] and MacColl [40] advocated the use of wave packets, in solutions of
the time-dependent Schrodinger equation, as a method for making this connec-
tion. Their approach, which depends upon identification of the peak positions or
the center of gravity of the wavepacket, has been criticized on the grounds that
there is no physical basis for identification of the peak of the wavepacket [35]. On
the other hand, the semiclassical approach advanced by Bittiker and Landauer,
among others, clearly seeks to extend the results of classical mechanics to the
quantum mechanical regime. Some of the impetus to pursue the semiclassical
approach may derive from the fact that the quantum mechanical expression for
the escape rate of a particle from a metastable state in a quantum well can be
factored into an attempt frequency, and a transmission probability per attempt
[41]. This picture of escape from a metastable state allows one to view the escape
process as the motion of a particle back and forth between the classical turning
points, with a small probability of transmission at each arrival at a turning point.
When it is possible, as in this case, to view a quantum mechanical result in a
semiclassical way, the semiclassical analogy often aids in forming an intuitively
appealing understanding of the quantum mechanical process. There does not
appear, however, to be any a prior justification for direct extension of classical
concepts to the quantum mechanical regime.

In summary, attempts to identify a characteristic time for tunneling have

been highly controversial, and difficult to verify experimentally. It would seem

that the main problem in the theories is their inability to make the connection
to experimentally verifiable quantities. Experimental techniques available for
the measurement of tunneling times will be described in Section 1.3.1, and the
results of time-resolved photoluminesce studies will be given in later chapters of

this thesis.

1.2.4 Strained-Layer Superlattices

This section introduces the subject of strained II-VI superlattices, including
their potential applications, and serves as background for the Raman scattering
studies of CdTe/ZnTe superlattices that will be introduced in Section 1.4, and
described in Chapter 5. Originally proposed by Esaki and Tsu [42] in 1970,
superlattices have attracted a great deal of interest because of the ability to tailor
the electrical and optical properties in ways not available with conventional bulk
semiconductors. A superlattice consists of many thin layers of one semiconductor
interleaved with thin layers of another semiconductor. A CdTe/ZnTe superlattice
is schematically illustrated in Fig. 1.4. The alternating layer structure is typically
repeated for many periods, to form a structure that is on the order of a micron
thick, with individual layers carefully controlled in composition and thickness.
The superlattice is grown on a thick substrate, and normally some form of buffer
layer or layers is grown between the substrate and the superlattice. The buffer
layer can serve several purposes: its most important function is to provide a
clean, abrupt surface upon which to grow the superlattice. The buffer layer can
also serve to force dislocations from the substrate to bend parallel to the surface
of the buffer layer, and not propagate into the overlying film, thus providing
a more perfect surface on which to grow the superlattice. The buffer may, in

certain circumstances, be able to affect the lattice constant of the superlattice

Figure 1.4: Schematic diagram of a CdTe/ZnTe superlattice. The superlattice
consists of many repeated thin layers of CdTe and ZnTe, grown on top of a buffer

layer which is deposited on a relatively thick substrate.

that is subsequently grown. In this case, the buffer layer is seen as a template
for subsequent growth of the superlattice.

Superlattices were first studied in lattice-matched systems. However, as men-
tioned in Section 1.2.1, there has been great progress in the epitaxial growth of
strained-layer structures. In 1983, Osbourn [43] suggested the growth of strained-
layer superlattices, in which the lattice constants of the two materials are not
exactly equal. The CdTe/ZnTe superlattice illustrated in Fig. 1.4 is a strained-
layer superlattice; the lattice mismatch between CdTe and ZnTe is 6%. The
greater variety of materials available once the constraint of close lattice match is
removed allows growth of a large number of new heterostructures. Normally in
such superlattices, it is desirable that the lattice mismatch be accomodated by
elastic strain of the superlattice layers. Then, in addition to the increased vari-
ety of materials available, strain effects can be manipulated to produce changes

in the electronic and optical properties that cannot be effected by other means,

e.g., the strain-induced shifts and splittings of the electronic levels in a super-
lattice. This has recently been proposed [1] as a means of producing infrared
detectors for the 8-12 wm region with InAs/Ga,In;_,Sb superlattices. In these
superlattices, the strain allows the bandgap of the superlattice to be decreased
while still allowing strong optical absorption [1]. Another example of the unique
possibilities available with strain are the nonlinear optical properties of strained
superlattices grown in the [111] direction. The strain fields in these superlattices
result in electric fields in the superlattice layers through the piezoelectric effect,
and are predicted to result in very strong nonlinear optical effects [2].

II-VI strained-layer superlattices are of interest for use as visible light emitters
in the blue-green portion of the visible spectrum [44]. Although direct bandgap
II-VI semiconductors with bandgaps in this spectral region exist, p-n junctions for
light emitters have not been successfully fabricated. The main reason for this lack
of success is due to the difficulties in doping wide-bandgap II-VI semiconductors.
Although it is possible to dope these materials, there are none with wide bandgaps
in which it is possible to dope both n-type and p-type to high densities [44]. The
interest in II-VI superlattices is based on the fact that some materials can be
doped heavily n-type, and some p-type. By combining a heterojunction of two
materials, one of which can be doped n-type and one p-type, it has been proposed
that it would be possible to make a p-n junction. CdTe and ZnTe are one such
pair, where ZnTe can only be doped p-type, and CdTe can be doped n-type
or p-type. Although the resulting superlattices have bandgaps in the red, they
represent a system in which to study the issues that will be important in other
wider-bandgap superlattices.

In strained superlattices, the lattice mismatch between the layers can be acco-
modated either by elastic strain or by the formation of strain-relieving defects. It

is normally desired, for device quality and uniformity, that the lattice mismatch

be accomodated entirely by uniform elastic strain. Such a structure is said to
be coherently strained. One of the central problems in the study of strained su-
perlattices is the determination of the extent to which lattice mismatch can be
accommodated by strain of the layers. It has been observed in the growth of indi-
vidual thin films on lattice-mismatched substrates that for film thicknesses below
a value known as the critical thickness, lattice mismatch can be accomodated by
elastic strain without the formation of significant densities of defects. Beyond
this critical thickness, the effect of increasing film thickness is the formation of
dislocations.

The same ideas of critical thickness that are applicable to growth of thin
films also apply to strained layer superlattices, but the situation is slightly more
complicated. In superlattices, there is a critical layer thickness, beyond which
misfits will be formed at the interface between individual layers of the superlattice.
The situations possible for the accomodation of mismatch between superlattice
layers are schematically illustrated in Fig. 1.5. The unstrained bulk materials are
shown in Fig. 1.5(a). In the superlattice, the mismatch may be accomodated
entirely by elastic strain, as shown in (b), with the formation of a tetragonal unit
cell. If the strain energies are too large, the situation in (c) results, in which
misfit dislocations relieve the strain.

In superlattices, even for individual layer thicknesses below the critical layer
thickness limit, there is another critical thickness related to the total thickness
of the superlattice. If the superlattice has a free-standing lattice constant in the
plane of the layers that is different from that of the buffer layer, and the total
superlattice thickness is too great, dislocations will be formed at the interface
between the superlattice and the buffer layer, and in the first superlattice layers.
Below this critical superlattice thickness, the superlattice will adopt a lattice con-

stant equal to that of the buffer on which it is grown. The two possible situations

(a) Unstrained bulk materials

ZnTe

(b) Coherently strained layers

Figure 1.5: Schematic illustration of accomodation of lattice mismatch in super-
lattice layers. (a) The unstrained bulk materials. (b) Coherently strained layers,
in which lattice mismatch is accomodated by elastic strain. (c) Unstrained lay-
ers, with misfit dislocations at the interface. The difference between the lattice

constants of the two materials has been exaggerated for clarity.

for total superlattice thicknesses, i.e., below and above the critical thickness, are
illustrated in Figs. 1.6 (a) and (b), respectively. The superlattice shown in Fig.
1.6(a) is coherently strained to the buffer layer. In the case illustrated in Fig.
1.6(b), a network of dislocations has relieved the strain near the buffer layer,
and the superlattice has adopted an in-plane lattice constant different from that
of the substrate. Experimental studies of a number of materials systems have
indicated that the portion of the superlattice beyond the dislocation network can
adopt a uniform lattice constant that minimizes the strain energy of the super-
lattice. This configuration is referred to as a free-standing superlattice, because
the superlattice adopts a lattice constant that is essentially independent of the
buffer layer on which it is grown.

The experimental techniques used to resolve these issues related to the acco-
modation of lattice mismatch will briefly be described in Section 1.4. Progress in
the characterization of strained layer superlattices will be essential in the devel-
opment of the growth techniques for such systems, and will be important in the

eventual use of strained-layer superlattices in practical applications.

1.3. Experimental Studies of Tunneling Times

In this section we will introduce the subject of experimental studies of tunnel-
ing times. Section 1.3.1 is devoted to a brief review of the experimental techniques
available for such studies. The following sections then describe the three problems
related to tunneling times in GaAs/AlAs double-barrier heterostructures stud-
ied in this thesis. Section 1.3.2 introduces the time-resolved photoluminescence
measurements of tunneling times in undoped double-barrier heterostructures that
will be presented in Chapter 2. Section 1.3.3 discusses the use of continuous wave

(CW) photoluminescence in the study of the effect of the X-point on the escape

(a) superlattice coherently strained to buffer

buffer

(b) free-standing superlattice

buffer

dislocations free-standing
superlattice

Figure 1.6: Superlattices with total thickness below and above the critical thick-
ness. (a) Below critical thickness the superlattice is coherently strained to the
buffer layer. (b) Beyond the critical thickness, a network of dislocations forms at
the buffer layer-superlattice interface, and the superlattice adopts a free-standing
lattice constant (independent of the buffer layer). Superlattice layers near the

interface with the buffer are dislocated to accomodate the lattice mismatch.

of electrons from the quantum well, serving as an introduction to the work that
will be described in Chapter 3. Finally Section 1.3.4 introduces the use of time-
resolved photoluminescence and time-resolved correlation photocurrent studies of

biased double-barrier heterostructures, which will be described in Chapter 4.

1.3.1 Techniques for Studies of Tunneling Times

In this section we will give an overview of the experimental techniques that
can be used for studies of tunneling times. The techniques to be discussed are
mostly based on the use of ultrafast optical pulses from mode-locked lasers. Gen-
eration of these optical pulses will not be discussed here, but will be described
in Appendix A. The techniques based on optical methods are divided into three
main categories: electrooptic sampling, photoluminescence, and photocurrent.
At the end of this section, low-frequency electrical studies applied to the mea-
surement of tunneling times are described, and finally there is a brief mention of
other techniques that have been proposed, but have not yet been demonstrated
for the study of tunneling times.

The first experimental technique to be described is that of electrooptic sam-
pling. This technique, pioneered by Valdmanis et al. [45], takes advantage of the
electrooptic effect, in which an electric field in certain materials affects the in-
dex of refraction. In this technique, an electrical device such as a double-barrier
heterostructure is mounted in a stripline environment, where at least part of the
stripline is fabricated on an electrooptic substrate. Ultrafast electrical pulses,
generated by illumination of a photoconductive circuit element [46, 47], can be
introduced onto the stripline and allowed to interact with the device. The sig-
nals propagating at later times can be determined by measuring the polarization

change of a suitably delayed optical pulse transmitted through the electrooptic

material next to the stripline conductor. Since the change of polarization is pro-
portional to the electric field, the voltage on the stripline can be determined as
a function of time by varying the delay of the sampling pulse with respect to
the pulse used to generate the initial electrical pulse. This technique has been
applied to the study of GaAs/AlAs double-barrier heterostructures by Whitaker
and coworkers [48], and more recently by Diamond et al. [49]. These studies
require the devices to be in a stripline environment, where they are susceptible to
stray capacitances and other effects unrelated to tunneling. As such, they repre-
sent appropriate measurements of devices intended for practical application, but
may not be the best way to measure the ultimate speed of the tunneling process.

The second main technique to be described is that of photoluminescence (PL),
which can be divided into three different approaches: conventional continuous
wave (CW) PL, direct time-resolved PL, and photoluminescence excitation cor-
relation spectroscopy (PECS). Photoluminescence is the study of the photons
emitted by recombining electron-hole pairs that are created by photoexcitation.
The ability to use PL to obtain information regarding the electron and hole pop-
ulations derives from the fact that free-carrier photoluminescence is proportional

to the density of electrons and holes, i.e.,
Ipy(t) = Bn(t) p(t) (1.1)

where B is a constant, characteristic of the material. In CW photoluminescence,
a CW laser is used to excite electron-hole pairs above the bandgap. The carriers
created quickly thermalize to the lowest electron and hole states. These carriers
can then recombine and emit photons, which are detected and integrated over
time. If the carriers can also tunnel to other states not detected in the PL
experiment, then the densities of the recombining carriers are reduced, and so

is the PL signal. Thus, the intensity of the CW PL signal is a measure of the

tunneling decay times, or in general, the nonradiative decay times, relative to the
recombination time. This technique as applied to the study of the effect of indirect
levels in the AlAs barriers of GaAs/ AlAs double-barrier heterostructures will be
introduced in Section 1.3.3, and the results of such a study will be described in
Chapter 3.

The second main photoluminescence technique requires the use of ultrafast
pulses from a mode-locked laser. Since the PL signal is described by Eq. 1.1
above, the decay of the populations can be probed if the photoluminescence
signal can be monitored as a function of time. In such experiments, a single
ultrafast optical pulse is used to excite electron-hole pairs on a time scale short
with respect to the tunneling process of interest. Then the PL signal is directly
monitored by a streak camera [50], microchannel plate photomultiplier tube [51],
parametric upconversion [52], or Kerr effect gating [53]. These techniques have
been applied to the study of tunneling by Deveaud [54], Tsuchiya (55], and others.
The direct detection technique suffers from the problem, apparent in Eq. 1.1, that
it is the product of the electron and hole densities that governs the evolution of
the PL signal. Therefore, if the PL signal decays, it is impossible to discern which
population decrease was responsible for the decay, and thus which tunneling time
is being observed. If the responses of the populations n(t) and p(t) are dominated
by tunneling, with exponential decay times 7, and 7, respectively, then the PL
signal of Eq. 1.1 is seen to decay according to

Ipz(t) = B no po exp lt (= + -)|

Te Th
where no and po are the initial carrier densities created by photoexcitation, and
are presumably equal. The above equation clearly shows that it is the reduced
time (1/7. + 1/1,)~' that is observed. This inability to distinguish between the

decay of electron and hole carrier densities led to misinterpretation of early studies

of tunneling in GaAs/AlAs double-barrier heterostructures. The experimental
observations that revealed this oversight are described in Chapter 2 of this thesis,
and required the use of the PECS technique that will be described next.

The third photoluminescence technique available in addition to the CW and
direct time-resolved techniques already described is photoluminescence excitation
correlation spectroscopy (PECS). This technique, originated by von der Linde
[56], will be described in detail in Section 2.2. Here we will give only a very brief
description of the principle. PECS is a form of pump-probe technique, in which
the response to photoexcitation by two optical pulses, delayed with respect to
one another by time 7, is measured using synchronous detection techniques. The
PL signal detected in this experiment depends on the delay +, and is given by

IBECS(t) = a lex (-2!) + exp (-2!)] (2)
The power of the PECS technique is evident in the above equation: the signal
is the sum of two equal amplitude exponentials, containing the two individually
recoverable time constants. If, for example, the hole time tT, is much longer than
the delay times y accessed experimentally, then the signal will be proportional
to 1+ exp(—|y|/7-). This technique allowed the measurements of both electron
and hole tunneling escape times described in Chapter 2.

The third main experimental technique for the direct determination of tunnel-
ing times involves time-resolved measurements of photocurrents. Conventional
time-resolved photocurrent techniques are similar to the direct time-resolved PL
techniques described above. In a time-resolved photocurrent experiment, an ul-
trafast optical pulse excites electron-hole pairs, and the subsequent behavior of
the photocurrent signal is measured as a function of time. This technique has
been applied to the study of tunneling times (57, 58], but has been limited to

times on the order of nanoseconds. A new time-resolved photocurrent technique

analogous to the PECS photoluminescence described above will be presented
in Chapter 4. Using photoexcitation by two optical pulses, and recovering the
time-averaged photocurrent as a function of relative delay y, measurements of
times related to the tunneling of photoexcited carriers may be observable. This
techique is very new, and the details of its interpretation are still quite uncertain.
However, it holds promise as a technique for study of structures not amenable to
study with other techniques such as photoluminescence.

We will now discuss a very different group of experimental techniques for the
study of tunneling times, based upon low frequency electrical measurements of
tunneling currents. Instead of direct measurement of tunneling times, these tech-
niques rely on the use of time scales for processes unrelated to tunneling, such
as the plasma frequency, as a sort of clock for the study of tunneling. Although
somewhat indirect, they represent an important approach to the experimental
study of tunneling times. Because of space limitations, these techniques, repre-
sented by the work of Guéret [59, 60] and Esteve [61] will not all be described
in detail. One representative experiment, that of Ref. [60] will be described,
and the interested reader is referred to Refs. [59] and [61] for discussions of the
other approaches. Guéret [60] studied single-barrier tunneling in a wide range
of GaAs/ Al,Ga,_-As/GaAs single barriers. For thin barriers, the measured tun-
neling current could be accurately calculated by a theory neglecting any image
charge effects from the n-type electrodes. For thicker barriers, however, signifi-
cant deviations from this theory were observed, and were attributed to dynamic
rearrangement of the electron plasma in the electrodes during the course of tun-
neling. The crossover between the two regions was found to be characterized
by the product wprp, © 3 , where wp is the plasma frequency for the electron
density in the electrodes, and rpy is the Buttiker-Landauer traversal time de-

scribed in Section 1.2.3. In this experiment, the inverse of the plasma frequency,

a known quantity, is used as a reference against which to measure the tunneling
time. Other similar approaches have used the cyclotron frequency for an elec-
tron in a magnetic field [59], and the propagation delay along a stripline (61].
Although these low frequency techniques provide valuable information regarding
tunneling times, they are quite indirect, and rely upon theories describing the
effect upon tunneling of other unrelated processes. In view of the great variety of
contradictory theories concerning the simple question of the characteristic time
for tunneling, it would seem somewhat risky to rely on these more complicated
theories to provide evidence on the subject of tunneling times.

Finally, we will briefly discuss some techniques that have not yet been demon-
strated, but that hold potential for application to the study of tunneling times.
Cutler et al. have proposed the use of a scanning tunneling microscope to measure
a tunneling time [62]. Another technique that could be applied to measurements
of tunneling times is active-layer photomixing [63]. Developed for study of the
frequency response of laser diodes, the photomixing technique relies on the inter-
ference of two CW lasers to provide a perturbation of the electron-hole density
in a semiconductor at the difference frequency dw = w, — wo. If the lasers are
relatively close in frequency, and stable, difference frequencies in the GHz to THz
range can be obtained. It may be possible to use such a technique to study the
devices described in Chapter 4, in which optical excitation can be used in devices
that show negative differential resisistance. The DC photocurrent may show fea-
tures as a function of the difference frequency related to the response time of the
device. Finally, the technique of phase-space absorption quenching [64], based
on the decrease of absorption caused by Fermi-filling of electron and hole bands,
may be useful for future studies of tunneling times.

In summary, there are several experimental techniques that can be used for

studies of tunneling times. The technique of electrooptic sampling has the ad-

vantage of being quite direct, but is sensitive to all of the considerations such as
stray capacitances, etc., that limit the speed of a tunneling device, in addition to
the tunneling time of interest. Photoluminescence techniques, including CW, di-
rect time-resolved, and the two-beam technique of photoluminescence excitation
correlation spectroscopy (PECS), can be used, and PECS measures the decay of
both electron and hole populations. Time-resolved photocurrent techniques can
be used, including a recently developed extension of the PECS photoluminescence
technique to the study of photocurrents. Finally, low frequency measurements of
tunneling currents in single barriers and Josephson junctions have been used to
make indirect measurements of tunneling times. Other experimental techniques,
using scanning tunneling microscopes, active layer photomixing, and phase space
absorption quenching may lead to development of new methods by which to mea-

sure tunneling times.

1.3.2 Tunneling Time Measurements in Undoped Double-

Barrier Heterostructures

The first measurements of tunneling escape times in GaAs/AlAs double-
barrier heterostructures were performed by Tsuchiya et al. using direct time-
resolved photoluminescence [55]. The samples studied were a series of undoped
GaAs/AlAs/GaAs/AlAs/GaAs heterostructures in which the final GaAs cap
layer thickness was 300 A.

This work was followed by our study, to be described in Chapter 2, of similar
samples using the photoluminescence excitation correlation (PECS) technique.
The experimental measurements of the electron and hole escape times obtained
constitute one of the most important results presented in this thesis. The tun-

neling escape times for electrons and holes were found to be very similar, and are

plotted in Fig. 1.7 as a function of the AlAs barrier thickness. The exponential
dependence of the observed decay time on barrier thickness for barriers ranging
from 16 to 34A is indicative of tunneling escape, which occurs on a time scale
as short as 12 ps in the fastest sample measured. The experimental techniques

used, and the interpretation of these results, will be presented in Chapter 2.

1.3.3 X-point Escape of Electrons

Many of the tunneling properties of heterostructures can be understood simply
by characterizing each of the constituent materials by a potential energy and an
effective mass. However, in certain situations it is important to account for a
more detailed picture of the band structure of the materials. One such situation
is related to the indirect nature of the AlAs material used as the barrier material in
many double-barrier heterostructure devices. The minimum energy for electrons
in the conduction band in AlAs occurs not at the zone center, but in the [001]
direction at or near the edge of the Brillouin zone. This point in the zone, known
as the X-point, is thought to be important in the valley currents in GaAs/AlAs
double-barrier heterostructures [65], and limits room temperature peak-to-valley
current ratios to a maximum of approximately 5:1. Chapter 3 describes a study
of the effect of the X-point in such devices. A series of GaAs/AlAs/GaAs/AlAs/-
GaAs heterostructures with varying well thickness was studied. For wide wells,
the quantum well state lies lower in energy than the X-point levels in the barriers.
By decreasing the well thickness, and thereby increasing the confinement energy,
the quantum well state can be raised in energy until it is above the X-point levels
in the barriers. By studying CW photoluminescence in these structures, evidence
for rapid escape of electrons via the X-point was obtained. This study will be

described in detail in Chapter 3.

10 E T T T T T T T
10* 5 | 1
F 10°; — a E
> 10°F 7
CG " I 5 | 3
1 l i ! l ! i |

O 10 20 30 40 50 60 70 80
Barrier Thickness (A)

Figure 1.7: Experimentally observed tunneling escape time in GaAs/AlAs/-
GaAs/AlAs/GaAs heterostructures. The escape time for electrons and heavy

holes is very similar, and is plotted as a function of the barrier thickness.

32
1.3.4 Tunneling in Biased Structures

The time-resolved studies of tunneling described in Sections 1.3.2 and 1.3.3
were performed in the absence of electric fields in the devices. Since the double-
barrier devices are electrically biased during operation, it is desirable to make
measurements of tunneling times in the presence of electric fields. Norris et al.
[66] have used direct time-resolved photoluminescence in biased heterostructures,
in which their device was embedded in a p—i—n structure. Although this allowed
the application of an electric field, the device studied did not show negative
differential resistance. The only studies of tunneling times in working negative
differential resistance devices were made using electrooptic sampling (48, 49].

The work described in Chapter 4 concerns studies of operational double-
barrier heterostructures. Structures were fabricated with thin electrodes on the
surface side of the device, and either thin gold contacts, or annular contacts were
made. The devices showed negative differential resistance, while simultaneously
allowing photoexcitation of the quantum well and observation of the photolumi-
nescence from the quantum well. These devices were studied, using the PECS
time-resolved photoluminescence technique. Evidence from the photolumines-
cence measurements indicated that study of photocurrents in these devices using
techniques analagous to the PECS PL technique could prove interesting. Results

of these studies will be described in Chapter 4.

1.4 Raman Scattering Studies of Strained-Layer
Superlattices

As described in Section 1.2.4, one of the central issues in the study of strained-

layer superlattices is the determination of the extent to which lattice mismatch

is accomodated by elastic strain. This section begins with a brief description
of experimental techniques that can be used to determine strain, and then de-
scribes the use of Raman scattering for this purpose in the study of strained-layer
superlattices.

Several techniques can be used to make experimental determinations of strain
in superlattices, each having different advantages. One of the simplest techniques
is that of photoluminescence (PL), which gives information about the lowest elec-
tronic levels in the superlattices, which are sensitive to strain. Unfortunately, the
interpretation of PL data is complicated by the fact that the electronic energies
are also affected by confinement, and the extent of confinement is strongly af-
fected by the values of the band offset* between the two materials composing the
superlattice. Unfortunately the values of band offsets are difficult to measure,
and are not known very precisely. An additional complication in PL is that the
effects of strain and confinement can produce opposite effects of similar mag-
nitude, and it can be impossible with certain choices of sample parameters to
determine the difference between strained and unstrained structures. Another
powerful technique that has been used to determine the accomodation of strain
is x-ray scattering. This technique can measure the lattice constant of the super-
lattice to great accuracy. An experimental complication is that x-ray scattering
probes a depth on the order of 10m. Since typical superlattice and buffer layer
thicknesses are on the order of a few microns, signals from all of the buffer layers
and the substrate are observed, which can complicate the interpretation of x-ray
data.

A complementary technique for the determination of strain in superlattices,

and the one used for the CdTe/ZnTe superlattices studied in this thesis, is Raman

“The change in the energy of the valence band edge in traversing a heterointerface of one

material with another is known as the valence band offset.

scattering. First predicted in 1923 by Smekal, and observed by Sir C.V. Raman
in 1928, Raman scattering is the inelastic scattering of photons by excitations
in the material being studied. Experimentally, photons, typically from a laser,
are incident upon the sample to be studied, and the scattered light is collected
and spectrally resolved. In addition to a very large signal at the exciting laser
energy, scattered photons with energies equal to the exciting laser energy plus or
minus the energy of the excitation being studied can be seen, corresponding to the
absorption (anti-Stokes process) or emission (Stokes process) of a quantum of the
excitation. Higher order processes are also possible, in which several potentially
different excitations can be simultaneously excited or absorbed. In semiconductor
superlattices, the excitations most often studied possible include electronic, and
vibrational (phonon) modes.

In the study described in Chapter 5, the energies of the longitudinal optical
phonons in the superlattices will be studied. Fig. 1.8 shows a typical Raman
scattering scan for a CdTe/ZnTe superlattice. The intensity of the scattered
light is shown as a function of the energy loss from the exciting laser. Because
the energy shifts from the exciting laser are typically quite small, the energy
loss in Raman studies have historically been shown in units of wavenumbers,
or inverse centimeters, a convention that will be followed in this thesis.| The
scan shown in Fig. 1.8 shows three main phonon features near 200, 400, and 600
cm’, corresponding to one, two, and three phonon scattering. The structure of
the phonon peaks indicates that more than one particular phonon is involved in
the process. The laser energy for this scan was just above the bandgap of the
superlattice, and the rising edge at the highest energy losses seen in Fig. 1.8 is

the beginning of the photoluminescence signal, which is much larger than the

'The wavenumber & for a photon of wavelength A is defined as k = 1/X. The conversion to

energy units is 1cm7! = 0.124 meV.

1000

500 +

Counts (photons/s)

100 200 300 400 500 600 700

Energy Loss (cm *')

Figure 1.8: Typical Raman scattering spectrum at 5K for a CdTe/ZnTe super-
lattice with 26A CdTe and 32A ZnTe layers, collected in the backscattering
geometry. Scattering from one, two, or three phonons can be seen, near 200, 400,
and 600 cm™', respectively. Structure in the various phonon peaks indicates that
several different phonons are involved. The rising edge at high energy loss is the
onset of the photoluminescence signal, visible because the laser energy for this

scan was just above the bandgap.

Raman signal. Because the signals observed in Raman scattering are very weak,
and must be detected with energy resolution on the order of 0.1 meV at energies
on the order of 1.5eV in the presence of huge signals from scattered laser light,
the experimental difficulties in completing these studies are considerable. The
experimental considerations for such experiments will be described in Section
5.3.

In order to use measurements of phonon energies to determine strain in super-
lattices, it is necessary to consider the effect of strain upon the phonon energies.
This topic will be considered in detail in Section 5.5, where calculations of the

phonon energies in CdTe/ZnTe superlattices will be described.

1.5 Outline of Thesis

Chapters 2, 3, and 4, describe experimental studies of tunneling times in
GaAs/AlAs double-barrier heterostructures. Chapter 2 describes a study, using
time-resolved photoluminescence, of the times required for carriers confined in
the quantum well of GaAs/AlAs/GaAs/AlAs/GaAs heterostructures to escape
by tunneling through the AlAs barriers. The theoretical analysis of the two-beam
photoluminescence excitation correlation spectroscopy (PECS) technique used in
these measurements is discussed, incorporating numerical solutions that extend
previous analyses of limiting cases to a much more general situation, more appro-
priate to the experimental conditions. The experimental study of the dependence
of the tunneling escape times for electrons and holes upon the thickness of the
AlAs barriers is then described. The surprising experimental result that heavy
holes escape much more rapidly than initially expected is explained in terms of
the mixing of light- and heavy-hole bands in the quantum well, important for the

understanding of experiments necessarily conducted at finite temperature and

with finite photoexcited carrier densities.

Chapter 3 describes a study of the effect of indirect X-point levels on the es-
cape of electrons from the quantum well. A series of undoped double-barrier het-
erostructures with varying quantum well widths was studied using conventional
photoluminescence. The results of a study of the dependence of the photolumi-
nescence intensity upon the position of the quantum well energy level relative to
the X-point levels in the barriers is described, and used to determine the effect
of the X-point levels on the escape of electrons.

Chapter 4 describes the study of time-resolved photoluminescence and pho-
tocurrents in biased double-barrier heterostructures. A description is given of the
preparation of devices that show negative differential resistance, while simultane-
ously allowing the photoexcitation of carriers in the quantum well and collection
of the photoluminescence. Results of photoluminescence decay studies of these
structures while under bias are shown, indicating that investigations of the pho-
tocurrents flowing in these biased devices could prove interesting. A technique
for time-resolved photocurrent, analagous to the PECS time-resolved photolu-
minescence technique, is described. Time-resolved photocurrent results for three
double-barrier heterostructures are presented.

Chapter 5 addresses the accomodation of lattice mismatch in strained CdTe/-
ZnTe superlattices, and describes a resonance Raman scattering study of four
superlattices. The dependence of the observed phonon energies upon the compo-
sition of the superlattice is investigated. The experimental results are compared
with various theories of the accomodation of lattice mismatch in this system, and
used to determine the distribution of strain in the superlattice layers.

Appendix A contains a description of the colliding pulse mode-locked (CPM)
dye laser used in the time-resolved experiments described in this thesis. Mod-

ifications to the laser undertaken during the course of this work are described,

along with descriptions of the design considerations and motivations for these
changes. Routine operation and characterization of the performance of the laser

is also described.

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Chapter 2

Tunneling Time Measurements
in Undoped Double-Barrier

Heterostructures

2.1 Introduction

2.1.1 Background

As mentioned in Chapter 1, the electrical properties of the double-barrier
heterostructure, and in particular the properties at high frequencies, have been
of great interest since its proposal by Tsu and Esaki [1]. The desire to char-
acterize the high-frequency behavior of the double-barrier heterostructure stems
from interest in its use as an oscillator [2, 3, 4] and as a switching element [5, 6].
However, the time associated with tunneling has been the subject of many years
of discussion [7]. Recently there have been several experimental studies of the
temporal response of double barrier heterostructures. Whitaker and coworkers [8]

and Diamond et al. [9] have used electrooptic sampling measurements to study

single tunnel devices. Tsuchiya et al. [10] used direct time-resolved detection of
the photoluminescence from carriers in the quasi-bound states in the quantum
wells of undoped double-barrier heterostructures. They studied the decay of the
photoluminescence from carriers in the quantum well, and, by assuming that es-
cape of heavy holes was negligible, claimed to measure the electron population
in the quantum well as a function of the barrier thickness. In this chapter we de-
scribe time-resolved photoluminescence studies of undoped GaAs/AlAs/GaAs/-
AlAs/GaAs double-barrier heterostructures using the two-beam technique of
photoluminescence excitation correlation spectroscopy (PECS). Using this differ-
ent technique, we have extended the experiments of Ref. [10], which were limited
to times greater than 60 ps, to significantly shorter times. In addition, our exper-
imental results indicate that the analysis of the experimental data of Ref. [10],
which ignored the effect of hole tunneling, is incomplete, and we discuss a new

model of the tunneling of holes in confined structures.

2.1.2 Summary of Results

We report a study of the decay of photoexcited carriers in GaAs/AlAs/GaAs/-
AlAs/GaAs double-barrier heterostructures, using photoluminescence excitation
correlation spectroscopy (PECS). An analysis of the PECS experimental tech-
nique is presented using numerical integration of the rate equations governing
the PECS signals. This extends previous analyses of the experimental signals,
which were limited to certain special cases, to a more general class of problems.
The tunneling time for electrons to escape from the lowest quasi-bound state in
the quantum wells of double-barrier heterostructures with barriers between 16
and 62A has been measured at 80K. The decay time for samples with barrier

thicknesses from 16 A (+12 ps) to 34 A (+800 ps) depends exponentially on bar-

rier thickness, in reasonable agreement with calculations of electron tunneling
time derived from the energy width of the quasi-bound state resonance. Elec-
tron and heavy-hole carrier densities are observed to decay at the same rate, in
contrast to resonance-width calculations that indicate that heavy-hole tunnel-
ing times should be much longer than those for electrons. The rapid escape of
heavy holes can be explained by considering the effects of mixing of light- and
heavy-hole bands in the quantum well confined hole states. We also studied an
undoped double-barrier heterostructure with superlattice barriers, and observed
a decay time of 350+60 ps at 80K. Finally we studied a double barrier with pure
AlAs barriers and a narrower quantum well, in which two time constants could

be extracted from the time-resolved data.

2.1.3 Outline of Chapter

The photoluminescence excitation correlation technique used for time-resolved
studies of photoluminescence is described in Section 2.2, which also includes a
description of the experimental setup, and numerical analysis of the experimental
signals. The samples studied are described in Section 2.3. Section 2.4 describes
experimental results at 80 K and as a function of temperature from 80 to 5K.
The experimental results are discussed in Section 2.5. Section 2.6 compares the
present work with results from other workers using complementary techniques.

Finally, conclusions are summarized in Section 2.7.

2.2 Time-Resolved Luminescence Technique

2.2.1 Background

The time-resolved luminescence technique used in this chapter depends upon
nonlinearity in the photoluminescence process as a mechanism to generate an
integrated photoluminescence signal, in response to excitation by two optical
pulses, that depends upon the delay between the two pulses. This technique
was developed by several groups, who took advantage of different nonlineari-
ties to achieve similar ends. Mahr and coworkers [11, 12] took advantage of
absorption saturation in organic dyes. Using the bimolecular recombination of
photogenerated carriers, Rosen et al. [13] and von der Linde et al. [14] indepen-
dently developed the technique that has been variously referred to as population
mixing, picosecond excitation correlation, or photoluminescence excitation cor-
relation spectroscopy, the term that we shall use. This technique, which is quite
simple experimentally, measures a correlation function related to the evolution
of the photoluminescence, rather than the exact temporal response of the pho-
toluminescence emission. Various workers have used this technique for studies
of hot carrier relaxation and cooling [14], recombination in p-type GaAs [13],
spatial diffusion profiles [15], lifetimes near defects in GaAs substrates [16], and
nonradiative decay times in intentionally radiation-damaged GaAs [17]. Simi-
lar experimental techniques have been used for transmission measurements, and
allowed demonstrations of quantum beats in large organic molecules [18, 19].

The photoluminescence excitation correlation spectroscopy technique has been
used in the present work for studies of tunneling escape from double-barrier het-
erostructures. The most complete analysis of this technique to date was by

Johnson et al. [16], who derived analytical expressions for the experimentally

observed signals in certain limiting cases. They found that, for the case where
radiative recombination dominates the population evolution, the experimentally
observed correlation signal is zero, and also derived analytical expressions for the
situation where nonradiative recombination dominates. In Section 2.2.3 we will
present a more general analysis that reduces to the results of Johnson et al. [16]
for limiting cases, but allows numerical calculations of the signals in cases where
both radiative and nonradiative decay processes are important in the evolution

of the carrier densities.

2.2.2 Experimental Setup

The experimental setup is shown in Fig. 2.1. A dispersion compensated collid-
ing pulse mode-locked (CPM) ring dye laser is used to generate a train of pulses
200 to 300 fs full width at half maximum (FWHM), at a repetition frequency of
120 MHz. The operation of the laser, alignment procedures, and routine main-
tenance are described in Appendix A. The laser output is centered at 6200 A,
corresponding to an energy of 2eV, and has a spectral width of approximately 20
to 50 A FWHM, depending upon the pulse width. One of the two output pulse
trains from the CPM laser is equally divided into two separate beams which are
independently chopped at f; =1600 and f.=2000 Hz, and delayed with respect
to one another by time y (—500 <7 <500ps). Metal-coated reflective retrore-
flectors (Newport BBR) were used in the two arms, one of which was mounted
on a Klinger stepper motor that allowed motion of approximately 30 cm. Af
ter chopping and relative delay, the two beams are recombined and focused to
a 25m diameter spot on the surface of the sample. The typical average power
used was 0.5 mW per beam after chopping. The photoluminescence is spectrally

resolved with a double pass spectrometer, and then detected by a GaAs pho-

Lockin

PMT

Spectrometer

Argon Laser

Colliding Pulse
Dye Laser

Rove

Figure 2.1: Experimental setup for time-resolved photoluminescence. The
source of ultrafast optical pulses is the dispersion-compensated colliding pulse
mode-locked (CPM) dye laser. The laser output is split into two beams of equal
amplitude, which are mechanically chopped by C1 and C2, and then recombined
and focused on the sample. Photoluminescence is imaged from the sample into

a spectrometer, and detected with a GaAs photomultiplier tube (PMT), and a

lock-in amplifier.

tomultiplier tube (PMT). After amplification, the PMT signal is synchronously
detected by a lock-in amplifier at either the fundamental frequency f, or the sum
frequency feum=fit+fe. It has recently been suggested [20] that detection using
two lock-in amplifiers, connected in series, and referenced separately to f, and
fz, has improved noise reduction properties compared to the scheme used in the
present work, where a reference signal generated directly at fgum is used for a
single lock-in. This possibility was not investigated in the present work. All data
recording, control, and display functions were performed with a Hewlett Packard
HP9836 computer. All of the results reported here were taken with the sample
mounted in a helium immersion dewar, at a temperature between 80 and 5K.
In order to guarantee reliable results, the interferometer must be carefully
aligned to ensure that no walk-off (movement perpendicular to the direction of
the beam) of the variably delayed beam occurs when the delay is changed. A
misalignment of the interferometer is evident in data collected for positive and
negative delays y. The symmetry of the experimental apparatus requires the
photoluminescence scans with delay to be symmetrical about zero delay, and any
departure from this behavior is evidence of some asymmetry in the setup, which
is usually related to the interferometer alignment. Therefore, we always present
scans taken for both positive and negative delay, and these scans are expected to
be symmetrical with respect to zero delay. Although active stabilization methods
have been used for this purpose [21], it was found to be sufficient to use the
following procedure to align the beam splitter and the retroreflector mounted
on the stepper motor. With the CPM laser running, the retroreflector is moved
to the end of its travel closest to the beam splitter. The retroreflector is then
moved in the two directions perpendicular to the motion of the stepper motor
until the laser spot is exactly in the center of the retroreflector, at the corner of

the three reflective surfaces. This condition can be very accurately determined

by placing the chopper C2 in the path of the beam, and viewing the interference
pattern caused by the reflection of the laser beam, which is symmetric when
properly aligned. Then the retroflector is moved to the opposite end of its travel
on the stepper, and the beam splitter is again adjusted so that the laser beam
hits exactly the center of the retroflector. The above procedure is repeated until
the beam is correctly positioned at both ends of the stepper motor travel. Then
the retroflector is translated approximately 0.5 cm so that the laser beam strikes
flat areas, and not the edges, of the reflective surfaces in the retroreflector. This
procedure ensures that the laser beam and the motion of the stepper motor
are collinear, thus eliminating any beam walkoff as the delay is varied. It was
also found with certain configurations of the CPM cavity that the output beam
diverged sufficiently that the differing path length in the interferometer resulted
in differing spot sizes. This was corrected by a pair of lenses just outside the

CPM laser that collimated the beam.

2.2.3 Theory

The use of photoluminescence as a probe of the tunneling escape rates for
carriers photoexcited in the quantum well of a double-barrier heterostructure,
originated by Tsuchiya et al. [10], relies on photoexcitation by a short optical
pulse. Whereas Tsuchiya et al. [10], used direct detection of the photolumines-
cence with a streak camera, in the present work we have used the photolumi-
nescence excitation correlation spectroscopy (PECS) technique for time-resolved
measurements. In this section we will present an analysis of the PECS technique
that is more general than that obtained by previous workers [16], and present
numerical calculations of the expected experimental signals for situations similar

to those studied experimentally in the following sections.

In Fig. 2.2, we present a schematic diagram of the carrier processes in the
quantum well that are relevant during the experiment. The conduction and
valence bands are shown as a function of position, and the lowest electron and
hole energy levels in the quantum well are indicated by dashed lines. Because of
the higher heavy hole effective mass, the lowest hole level in the quantum well
is a heavy hole state. The processes of excitation of electron-hole pairs by the
incoming laser, tunneling of electrons and holes from the quantum well, and the
radiative recombination of carriers between the lowest electron and heavy-hole
states within the well are all shown in Fig. 2.2. It is the luminescence from the
recombination of electrons and heavy holes in the lowest quantum well states that
is detected in the experimental measurements of tunneling times.

In our experiments, the photoexcitation energy of the CPM laser is 2eV, which
is considerably higher than the 1.6 to 1.8 eV quantum well transition observed
in photoluminescence in the structures studied. However, recent estimates of
the times for thermalization of electrons between subbands in GaAs/Al,Ga,_,As
multiple quantum wells have given times less than 200 fs [22]. This is consistent
with the fact that we do not observe photoluminescence from the excited state
transitions. We will therefore assume the thermalization of both electrons and
holes to the lowest subband to be fast compared to the times of interest here,
so that the effect of photoexcitation by an optical pulse is to instantaneously
increase the carrier densities in the lowest electron and heavy hole quantum well
states. The effects of the excess excitation energy on the carrier distribution
functions, and in particular upon the carrier temperature, will be discussed in
Section 2.5.

Measurements of the tunneling escape times for electrons and heavy holes are
derived from the variation of the photoluminescence signal Ijum, detected at the

sum chopping frequency, with delay y. The sum-frequency signal is monitored at

Figure 2.2: Schematic diagram of relevant carrier processes occurring in the dou-
ble-barrier samples during photoluminescence. The conduction and valence band
edges are shown as a function of position. Also shown are photoexcitation of
electron-hole pairs by the laser, tunneling of electrons and holes out of the well,
and recombination of carriers confined in the lowest quasi-bound electron and

heavy-hole states in the quantum well.

a wavelength corresponding to the lowest confined electron to heavy-hole transi-
tion. If the lowest-energy confined electron and heavy-hole carrier densities are n
and p, respectively, then the photoluminescence detected by the photomultiplier
tube is Ip, « fnpdt, where the integration is over times long compared to the
tunneling processes of interest here, but short compared to the chopping periods.
Since the laser excitation is periodic with period T,.p it is natural to consider
the sum-frequency component of the photoluminescence, I,..,(7), in terms of the
integrated photoluminescence detected in one period T,.,. Assuming that each
optical pulse creates an equal density g of electron and holes, the chopped optical
generation function is given by
+00
Gerop(t,7)=9 D [Sp(t)(t — MT rep) + S4(t)6(t — 7 — mT rep)],
where 5;,(t) and S,,(¢) are unit amplitude square waves at the chopping frequen-
cies f; and f2, respectively, 6(t) is the Dirac-delta function, and ¥ is the relative
delay between the two arms of the interferometer. Because of the chopping, dur-
ing the experiment the sample is exposed to zero, one, or two optical pulse trains
at various times, depending upon the instantaneous values of S;,(t) and 5;,(t).
We will assume that the populations, and thus the photoluminescence signal,
achieve a steady state value in a time short compared to the chopping periods.
Then the sum-frequency signal, Jsun(7), can be simply expressed in terms of the
integrated photoluminescence detected in these three cases of exposure to zero,
one, or two unchopped pulse trains. The integrated photoluminescence intensity
detected in one period T,., is proportional to prep npdt. For excitation by the
unchopped one-pulse-train optical generation function
+00
Gilt)=9 DS) d(t-mT rp),
m=—00

the luminescence is defined to be J;, which is obviously independent of delay

, since there is only one pulse train. Similarly, J,(7) is the integrated photo-
luminescence intensity corresponding to the unchopped two-pulse-train optical
generation function

Galt) =9 So [6(t— mTup) + (7 — mT xp)

By considering the component of the photoluminescence response at the sum

chopping frequency, it can be shown that Ijum(7) is simply given by

Teum(¥) « [o(y) — 2h]. (2.1)

Eq. 2.1 is very general, depending only on the nature of the synchronous detection,
and the assumption that the populations reach steady state quickly compared to
the chopping periods. This simple relation allows the calculation of the sum-
frequency signal in any case in which the populations n(t) and p(t) are known.
It can be seen from Eq. 2.1 that Ijum reflects the departure from linearity of the
response of the photoluminescence with excitation intensity, because it measures
the difference between the photoluminescence detected during excitation by two
pulses, and twice the luminescence detected during excitation by one pulse.

For the present case, considering radiative recombination and tunneling, the
evolution of the electron and hole populations in the quantum well can be de-

scribed by simple rate equations,

dn n
dp = G(t,7) - a Bnp. (2.3)
dt , Thh

In Eqs. 2.2 and 2.3, B is a constant related to the radiative recombination rate
[23], and G(t, 7) is the appropriate optical generation function. The two times 7,
and 7p, are the tunneling escape times for the electrons and heavy holes, respec-

tively. Eqs. 2.2 and 2.3 can be solved numerically for the case G(t, 7) = Gi(t)

to obtain J; = for? np dt, and similarly for G(t,y) = G2(t,y) to obtain I2(7).
Igum(7) can then be found using Eq. 2.1. The advantage of this approach over
that used in previous analyses [16] of this experimental technique is that the
nonlinearity in the rate equations can be handled easily, and it is not necessary
to make assumptions regarding the radiative or nonradiative nature of the pop-
ulation evolution. This analysis can easily be extended to other experimental
situations where, for example, the populations of excitons or other levels are
important.

Eqs. 2.1-2.3 can also be solved analytically in certain simple cases [16]. If
the electron and hole population evolutions are dominated by tunneling, the
responses to a single optical pulse are n,(t) and p,(t), the population responses to
two optical pulses are independent, and n;(Tyrep) and p;(Trep) are small compared

to g, the sum-frequency signal is proportional to the cross correlation [16]

Tmum(¥) & l” [ns(t)p(t—7) + m(t—7)pa(t)] (2.4)

This expression, which is responsible for the name “correlation spectroscopy,”
shows that the sum-frequency signal is due to the recombination of electrons
created by the first pulse with holes created by the second pulse, and vice versa.
The first term corresponds to recombination of the electrons created by the first
pulse at time ¢ = 0, with holes created by the pulse at t = y. The second term
is due to recombination of the electrons created by the pulse at time ¢ = 7, with
holes created by the pulse at time t = 0. The fact that the sum-frequency signal
is composed of two terms is a major advantage of this technique, because it allows
access to information regarding both the electron and hole decay times, 7, and
Thh, aS will be shown next. This distinguishes the PECS technique from direct,
time-resolved detection of the photoluminescence. Use of the PECS technique

enabled the measurements presented in this chapter, which were the first to obtain

information regarding the escape of both electrons and heavy holes.

In the tunneling-dominated case, i.e., when the evolutions of the electron
and hole populations are dominated by tunneling, the electron and heavy-hole
densities decay exponentially with time constants 7, and Tyy, respectively. In this
case, substitution into Eq. 2.4 shows that the sum-frequency signal is proportional

to the sum of two exponentials of equal amplitude,

Teum(7) o [exp (—ly|/te) + exp (—l7|/Tmn)]- (2.5)

In the radiative recombination dominated case, i.e., when the population evolu-
tion is not significantly affected by tunneling, the assumptions leading to Eqs. 2.4
and 2.5 are not valid. In this case, the sum-frequency component of the photolu-
minescence is zero [16]. This is because when radiative recombination dominates
the population evolution, every photon absorbed produces a photon out. Thus
photoluminescence intensity is linearly dependent upon the photoexcitation in-
tensity, and the sum-frequency component of the photoluminescence is zero, ac-
cording to Kq. 2.1.

To determine the applicability of Eq. 2.5 to the intermediate region between
the radiative-recombination-dominated and tunneling-dominated cases, Eqs. 2.1-
2.3 have been numerically integrated for various values of 7, Ty,, and B. In
Fig. 2.3 we show as solid lines the sum-frequency photoluminescence signal as a
function of delay calculated by numerically integrating Eqs. 2.1-2.3. Also shown
in Fig. 2.3 as dashed lines are curves calculated from the simple result of Eq. 2.5.
The curves shown in Fig. 2.3 were calculated for experimentally realistic pa-
rameters: the electron tunneling escape time 7 was 100 ps, and the heavy-hole
tunneling escape time 7}, was 1000 ps. The excitation density per optical pulse
gis 10''cm~?, and the repetition period of the laser T,.p is 8 ns. Matsusue et al.

[23] have measured the radiative recombination constant B in 90 A GaAs quan-

n Isyum (arbitrary units)

— 5 . T T T T 7
~S (c)
4.5 - rn 4
4k ae _
3.5 F 4
0 200 400 600 800 1000

Delay (ps)

Figure 2.3: Calculated sum-frequency delay scans for three values of B, the
radiative recombination constant. (a) B = 107-*cm?/s, the value from Ref. [23]
at 80K, (b) B = 10-?cm?/s, (c) B = 107'cm?/s. The solid line shows the signal
calculated by integrating the rate equations, and the dashed line shows the simple
expression given in Eq. 2.5. It can be seen that the simple expression from Eq. 2.5
is very accurate in all three cases. The electron and heavy-hole tunneling decay
times 7, and Typ, are 100 and 1000ps, respectively, the excitation density per

optical pulse g is 10*'cm~?, and the repetition period of the laser T,., is 8 ns.

tum wells, and found a value of 10~3cm?/s at 80 K, and we show in Fig. 2.3(a) the
behavior for this value of B. In Figs. 2.3(b) and (c), we show the same calculation
for progressively more radiative-recombination-dominated cases, where the values
of B were 10~? and 10~*cm?/s, respectively. Comparing the exactly integrated
curves shown as solid lines, and the simple expression, shown as dashed lines,
in Fig. 2.3, it can be seen that the simple expression is very accurate even in
the extreme case shown in Fig. 2.3(c), where the radiative recombination process
dominates the evolution of the carrier densities.

The case of extreme recombination-dominated population evolution was also
studied, where the tunneling escape times were much longer than the radiative
recombination time. It was found that that the sum-frequency signal calcuated
for this case is independent of delay. Thus in the case where tunneling becomes
negligible, we still do not expect to see Igum(7y) decay with the radiative lifetime.
In this case, where the tunneling escape times are very long, some other pro-
cess such as nonradiative recombination may become important, and the rate
equations 2.2 and 2.3 will have to be modified accordingly.

In summary, we have numerically solved for the behavior of the sum-frequency
signal detected in the PECS experiment as a function of delay for realistic ex-
perimental conditions. Our results indicate that the simple expression of Eq. 2.5
is valid in the cases studied, and we will use this equation as the basis for inter-
preting our data. We also pointed out that in the case where tunneling becomes
negligible, the sum-frequency signal does not decay with the radiative recombi-
nation lifetime, and this technique is therefore insensitive to the exact magnitude

of the radiative recombination time.

61
2.3 Samples

Double-barrier heterostructures were grown on (100) GaAs substrates by
molecular beam epitaxy in a Perkin-Elmer 430 system at 600°C. All layers were
nominally undoped with an estimated residual carbon acceptor concentration of
10'*cm~*. Three sample series were studied, labelled A, B, and C, and sample
parameters are summarized in Table 2.1. Sample series A, with a constant quan-
tum well width of 58A and pure AlAs barriers of varying thicknesses, consisted
of 7 samples with barrier thicknesses ranging from 16 to 62 A. All samples in this
series were grown on the following buffer layers: 0.5m of GaAs, a superlattice
buffer layer consisting of 5 periods of (50A Alo.ssGaogsAs, 500A GaAs), and a
0.7 pm layer of GaAs. This was to provide a high quality layer on which to grow
the double-barrier heterostructure; the final GaAs layer eliminates any optical ef-
fects from the superlattice. Then a symmetrical GaAs/AlAs/GaAs/AlAs/GaAs
double-barrier heterostructure was grown, with a well thickness of 58 A, and a
final GaAs layer thickness of 300 A, which served as a cap. Seven samples were
studied, with bulk growth rate information predicting barrier thicknesses of 16,
22, 28, 34, 34, 48, and 62A. High resolution transmission electron microscopy
confirmed the barrier thicknesses of the 16 A sample and one of the 34A samples,
within an uncertainty of 2 monolayers. We estimate an absolute uncertainty in
barrier thickness of +2 monolayers for all of the samples, although control of the
relative barrier thickness between samples appears to be better than 1 monolayer.
The single sample B1 had undoped superlattice barriers, and corresponded to the
doped structure with a peak-to-valley current ratio of 21.7:1 at 77K [24], one of
the highest values ever reported for a pure GaAs/AlAs heterostructure tunnel
device. This sample was grown on a 0.5m undoped GaAs buffer grown directly

on the GaAs substrate, and had a GaAs well of width 49A. The superlattice

Sample Growth Number Well Width Barrier Thickness

(A) (A)
Al ITI-069 58 16
A2 IIJ-064 58 22
A3 ITI-062 58 28
A4 III-059 58 34
A5 III-066 58 34
A6 III-070 58 48
AT III-063 58 62
Bl III-088 49 (see text)
Cl IIJ-329 45 37

Table 2.1: Parameters for the samples studied. Series A, consisting of seven sam-
ples, all had constant well thickness and varying AlAs barrier thickness. Sample
Bi had superlattice barriers which were each composed of three 8.5 A AlAs lay-
ers, separated by two 8.5A GaAs layers. Sample C1 was similar to sample A4,

but had a narrower 45 A quantum well.

barriers were each composed of three 8.5A AlAs layers, separated by two 8.5A
GaAs layers. Again, the final layer was a 300 A GaAs cap. The final sample, Cl,
was similar to sample A4, but had a narrower quantum well width of 45 A, which
increased the confinement energy of states in the well. This sample was grown

directly on a 0.5m GaAs buffer layer.

2.4 Results

2.4.1 Time-resolved Measurements at 80K

In Fig. 2.4, we present typical photoluminescence spectra taken at 80K at
the fundamental and sum chopping frequencies, for the 28 A barrier sample A3.
The spectrum at the fundamental frequency consists of a single feature centered
at 7650A. The wavelength of the feature in the fundamental frequency spec-
trum is in reasonable agreement with the calculated position of 7730A for the
transition from the lowest electron subband to the lowest heavy-hole subband in
a 58A quantum well. The width of the fundamental frequency photolumines-
cence is consistent with broadening by monolayer fluctuations of the quantum
well width, which indicates the samples are of high quality. The peak of the
corresponding feature in the sum-frequency spectrum is shifted slightly to longer
wavelengths; the reason for this shift is not clear. The sum-frequency peak is
lower in amplitude by a factor of 0.28 compared to the peak in the fundamental
frequency photoluminescence. This compares well with the tunneling-dominated
case, where the ratio of the sum-frequency signal to the fundamental signal is
expected to be 0.27:1 [16].

In Fig. 2.5, we present several semilogarithmic plots of typical peak photo-

luminescence intensity at the sum chopping frequency, as a function of the time

Amplitude (a. u.)

O Ea | l I ~~-4
7000 7600 7650 7700 7700

Wavelength (A)

Figure 2.4: Typical correlation photoluminescence spectra for 28 A barrier sam-
ple A3 at 80K. Shown are luminescence signals at the fundamental chopping
frequency (solid line) and the sum-frequency (dashed line). Both scans were

taken with delay y = 0. The sum-frequency spectrum has been multiplied by 2.

delay y between the two pulses, taken at 80K. All three scans show a coher-
ence peak at exactly zero delay, which is due to the optical interference of the
two incident pulses on the sample, in combination with the nonlinearity of the
photoluminescence with pump intensity. Instabilities in the interferometer, due
to vibrations, prevent stable fringes from being formed on the sample when the
two pulses overlap in time, and result in fluctuations of the intensity from zero to
twice the incident average intensity. Because luminescence is a nonlinear function
of the excitation intensity, this results in a greater photoluminescence signal. The
width of this coherent artifact, if resolved, was confirmed to be equal to the au-
tocorrelation width of the laser pulses, and serves both as a measure of the pulse
width at the sample, and also as a convenient and precise alignment of the zero
of the relative delay in the interferometer. However, the coherence peak is com-
pletely unrelated to the decay of the electron and heavy hole populations. The
scan shown in Fig. 2.5(a) for sample A3, which has 28 A barriers, was taken at
a wavelength of 7665 A, the peak of the sum-frequency photoluminescence spec-
trum shown in Fig. 2.4. This delay scan consists of the coherence peak at zero
delay discussed above, with wings extending to much longer times. The wings in
the sum-frequency delay scan shown in Fig. 2.5(a) show a dependence upon delay
well described by a single exponential, over range of more than 2 in the logarithm
of the amplitude. Fits to this sum-frequency delay data using a single exponential
are shown as dashed lines in Fig. 2.5(a), where the negative and positive delay
portions of the scans were fitted separately, and the two time constants fitted are
combined to yield a best fit value for the decay time. For the 28 A barrier sample
A3 shown in Fig. 2.5(a), this single decay time was 236 + 20 ps. In Fig. 2.5(b), we
show the decay scan for the 22 A barrier sample, A2, again taken at the peak of
the sum-frequency photoluminescence spectrum. The decay is again fitted quite

well by a single exponential, although the increased tunneling rates in this sam-

ty " (a) |
oe *e, 4
ae ww Nee
-1/ . aww "ae
—2 E 1 l L al
=~ —500 —250 0 250 500
bo
3 er T T T rn
~ b
co) 1+ —“ ee ( ) 7
oe] e ee” “ey °
3 ee” Aa ~ e
a 0 r ea” Tete . |
& -1 a ws
<< a 1 oon ae L 2
a —-100 -50 0 50 100
3.2 i T ; qT ) =
r Cc
2.8 + ( 4
” »%,
2.4 + — me 4
a a
er weereee Meas e 4
: iad ° 1 n L ofee
-~500 —250 6) 290 500

Delay y (ps)

Figure 2.5: Semilogarithmic plots of the variation of the sum-frequency lumines-
cence signal with delay y at 80K. All three scans show the coherent artifact at
+ = 0 due to interference of the two optical pulses. (a) Sample A3 (28A bar-
riers) is described well by a single decay time of 236 + 20ps, derived from the
fits indicated by dashed lines to the negative and positive portions of the scan.
(b) Sample A2 (22A barriers) is described by a single decay time of 47 + 5 ps.
(c) Sample C1, which has a narrower quantum well, shows double exponential
behavior, and the fit shown by a dashed line gives time constants of 150 and

3500 ps. Note the differing time scales for the three plots.

ple reduce the photoluminescence intensity and result in poorer signal-to-noise
in the data shown. The single decay time for this scan was 47 + 5ps, based on
the fits shown as dashed lines. Finally, in Fig. 2.5(c), we show the decay scan
for sample Cl, which had a narrower 45 A quantum well, taken at the peak of
the sum-frequency photoluminescence, which was at 7375A. The decay in this
sample is not well described by a single exponential. We show in the same figure
a dashed line, which is a best-fit of the sum of two exponentials with equal ampli-
tude, the functional form expected according to Eq. 2.5. The double exponential
fits the data very well, and gives time constants of 130 and 3500 ps. Although the
data are not shown, the superlattice-barrier structure sample C1 showed single

exponential decay at 80K, with a time constant of 350-60 ps.

2.4.2 Dependence upon Barrier Thickness

The samples in series A described above were studied under similar conditions,
and all showed delay scans that could be fitted well by a single exponential decay.
In Fig. 2.6, we have plotted the exponential decay time at 80K. The decay time
depends exponentially on barrier thickness for barriers up to approximately 34 A.
Over this range of exponential dependence, the decay time varies by two orders of
magnitude, ranging from a time of approximately 12 ps at 16 A, to approximately
800 ps at 34 A. The two samples A4 and A5 that are nominally identical show very
similar decay times, indicating excellent sample reproducibility. Given the rapid
variation of the decay times with barrier thickness seen in Fig. 2.6, this indicates
that the barrier thickness repeatability between samples is considerably better
than the +2 monolayer uncertainty estimated in the absolute barrier thickness.
For barriers thicker than 34A, the decay time seems to approach a value that

is independent of the barrier thickness. This is probably due to some some

Decay Time (ps)

1 1 | 1 l ! l i
O 10 20 30 40 50 60 70 80

Barrier Thickness (A)

Figure 2.6: Measured decay times at 80K as a function of barrier thickness for
sample series A, where the quantum well thickness is 58 A. The data points are
the measured decay times, with error bars on the thickness based on absolute
uncertainty in the barrier thickness, and error bars on the decay times from
uncertainties in the fits to the delay scans. The solid, dashed, and dot-dashed
lines are the electron, heavy-hole, and light-hole tunneling times, respectively,

calculated from the widths of the lowest-energy transmission resonances.

nonradiative process unrelated to tunneling that becomes more important as the
barriers become thicker and the tunneling escape rates decrease. Due to the
120 MHz repetition rate of the excitation pulses, and the limited —500 to 500 ps
range for the delay, 7, there is an upper limit on the order of 2ns to the decay
times that can be measured accurately with our technique. Consequently, the
result for the sample with a barrier thickness of 62 A should be viewed with some
caution. Our measurements extend the previous work of Tsuchiya et al. [10] to
significantly shorter times, and our measured decay times are about a factor of 4

longer than those of Tsuchiya et al. [10].

2.4.3 Temperature-Dependent Measurements

The dependence of decay time upon temperature was studied for the 28A
sample A3, at temperatures from 80 to 5K. The laser power for this experiment
was reduced to an average power per beam of 0.3mW before chopping, and one
measurement was taken at 5K at an average power per beam of 0.16mW. The
laser pulsewidth for these measurements was 300fs FWHM. Over this range the
sum-frequency signal dependence on delay was exponential, with a single decay

time, and the decay time increased slightly with decreasing temperature.

2.5 Discussion

The exponential dependence of the decay times seen in Fig. 2.6 for barrier
thicknesses between 16 and 34 A is characteristic of a decay time related to tun-
neling. To allow comparison with theory, in Fig. 2.6 we have also plotted the
theoretical times for electrons, heavy holes, and light holes to tunnel out of the
quantum well, calculated using the energy widths of the transmission resonances

and the uncertainty principle. The solid, dashed, and dot-dashed lines are the cal-

culated electron, heavy-hole, and light-hole tunneling times, respectively. From
Ref. [25], the time for a particle to tunnel out of a quasi-bound state in the quan-
tum well is related to the energy width AE,,,,.,, of the corresponding resonance

in the transmission probability by r=h/AE The transmission probability

FWHM"
is calculated using the transfer matrix approach of Kane [26], modified to account
for the different effective masses of the particle in the quantum well and in the
barrier.

For electrons, we have considered only I-point barriers. It is appropriate
to use a simple one-band expression for the wave vector in the well, given by
k=(2m*m,E/h’)'/? , where m*, is the effective mass in the GaAs well, m, is the
free electron mass, and E is the energy of the particle with respect to the GaAs
band edge. However, with the pure AlAs barriers in our samples, the lowest
quasi-bound electron state has an energy far from the band edge in the AlAs
barriers, and the one-band model overestimates the wave vector in the barriers.
Thus, we have used a two-band model [27] to calculate the electron wave vector
in the barriers. The conduction band barrier height used in these calculations
was 1.07 eV, corresponding to a valence band offset of 0.55 eV [28], and an AlAs
band gap of 3.13 eV. The effective masses in the well and the barriers were taken
to be 0.067 and 0.15, for the electrons, 0.087 and 0.15 for the light holes, and
0.62 and 0.76 for the heavy holes, respectively [29]. For the light holes, we also
use a two-band model for the barrier wave vector, and for the heavy holes, we
use a one-band expression to estimate the wave vector in the barriers. From the
theoretical curves in Fig. 2.6, we can see that the tunneling time for electrons
is much shorter than that for heavy holes, and the light-hole tunneling time is
shorter than that for the electrons.

Comparing these theoretical estimates of the tunneling times with the decay

times observed experimentally, we note that the decay times agree well with the

calculated tunneling time of the electrons. However, if we expected Eq. 2.5 to
explain the data, then we should observe two decay times, a short one near zero
delay and a longer time at much longer delays. We might expect the longer decay
time to be that for the heavy holes, and perhaps suspect that a much shorter
decay time for the electrons is present in the curves of Figs. 2.5(a) and (b), but
is not resolved experimentally. This is not the case, and there is no evidence of
a faster decay in more detailed scans at smaller delays. In addition, the direct
time-resolved photoluminescence data of Tsuchiya et al. [10] show significant pho-
toluminescence intensity at time delays similar to ours, which shows that both
the electron and heavy hole densities are still significant after the decay times
we measured. Therefore, we conclude that the delay scans we show in Fig. 2.5
are correctly described by Eq. 2.5, but that the electrons and heavy holes escape
from the quantum well by tunneling at very similar rates. The tunneling escape
times for both electrons and heavy holes are thus given by the decay times shown
in Fig. 2.6. The simply-calculated heavy-hole tunneling escape times shown by
the dashed line in Fig. 2.6 differ from the experimentally observed heavy hole
tunneling escape times by a large factor, which varies from approximately 100
for 16 A barriers to more than 10° for 34 A barriers. This surprising experimental
observation provides an answer to the problem of charge accumulation due to a
buildup of holes in the quantum well. If rapidly escaping electrons were to leave
the photoexcited holes behind in the quantum well, a net positive charge would
accumulate in the well. With the estimated density of approximately 10!!cm~?
carriers created per pulse, and a laser repetition time T,., of 8 ns, the simply-
calculated heavy-hole times shown in Fig. 2.6 would predict enormous accumu-
lations of carriers. Such an accumulation of positive charge would greatly affect
the photoluminescence linewidth, and no such broadening is observed. Thus the

rapid escape of heavy holes that is experimentally observed resolves the prob-

lem of the escape of photoexcited holes, and the hole accumulation that would
accompany slow escape of the holes.

This surprising observation of the rapid escape of heavy holes could qualita-
tively be explained by several phenomena. The most obvious possibility is the
effect of accumulated holes on the band profile. An accumulation of heavy holes
would result in band bending that would tend to reduce the escape rate for elec-
trons, and increase the escape rate for holes. However, simple estimates of the
magnitude of this effect indicate that it is too weak to change the heavy-hole
tunneling escape times by the many orders of magnitude required to explain the
experimental data. Similarly, transport of accumulated heavy holes due to dif-
fusion in the plane of the quantum well is insufficient to reduce the heavy hole
densities by the huge factors required. A physically reasonable explanation for
the rapid escape of heavy holes has recently been developed by Yu, Jackson, and
McGill [30]. They considered the mixing of the light-hole and heavy-hole bands
due to confinement in the quantum well, in order to estimate an average heavy
hole tunneling escape time. A simple picture of holes in confined systems shows
that heavy- and light-hole subbands are created by confinement in the quantum
well, and that their confinement energies can be calculated simply by consider-
ing the valence band offset and the appropriate effective masses in the well and
the barrier regions. While this approach correctly predicts the maxima of the
valence subbands, it neglects the free-particle behavior of the holes in the plane
of the quantum well. In Fig. 2.7 we show the valence bands in the quantum
well as a function of parallel wavevector ki, calculated using the 4-band Kohn-
Luttinger model [31] of the valence bands, in the spherical approximation. The
nonparabolicity of the subbands with increasing parallel wavevector results from
interaction between the various subbands. The result of the interaction is that

the wavefunctions at nonzero parallel wavevector ky for the band labelled “hh,”

ray)

Energy (meV)
ae ©

—100

0 0.01 0.02 0.03 0.04 0.05
K , (n/a)

-120

Figure 2.7: Valence subband dispersion in the plane of the quantum well layers,
calculated with the Kohn-Luttinger model. Nonparabolicity of the subbands
is due to interation among the bands, which results in mixed heavy-hole and

light-hole components of the bands for nonzero ky. After Ref. [30].

and identified as the lowest “heavy-hole-like” subband, consist of components of
both light-hole and heavy-hole character.

For any finite population of holes, the lowest heavy-hole-like subband hh1 will
be filled to some nonzero parallel wavevector, and therefore holes with nonzero
parallel wavevector will have mixed light-hole and heavy-hole character. The
wavefunction | ( ky) > at a particular ky can be decomposed as a sum of the

zone-center wavefunctions |p? > as

|¥ (Ry) > = Yo alk) |¢8? >, (2.6)

where the sum over 1 denotes sum over light- and heavy-hole bands, as well as
the sum over subband indices. The values of the coefficients a:( ky) are calculated
using the Kohn-Luttinger model for the valence bands. To estimate the effect
that this mixing has on the heavy hole tunneling escape time, Yu et al. [30]
calculated an average heavy hole escape time by averaging the escape rates over
the entire hole distribution, which was characterized by a total density, and a
temperature. The escape rate for a given parallel wavevector was calculated by

combining the weighted rates for the constituent wavefunctions from
1/7 (hy) = Yosh) [1/707], (2.7)

where [1 [7 is the escape rate for the i’th zone-center hole level, calculated
using the simple transmission resonance approach described earlier. An average
heavy hole tunneling escape time was calculated by averaging Eq. 2.7 over parallel
wavevector, assuming a hole distribution characterized by Fermi-Dirac statistics,
and a particular total heavy hole density and temperature.

The results of calculations of the average heavy hole tunneling escape time
using this approach are shown in Fig. 2.8 for the samples Al through A5 that

showed clear evidence that the decay was dominated by tunneling escape. The

“t

gp holes (theoretical) L,=16A

107 !11< expt. 1

gp electrons (theoretical

jori2beseecseczsson==-Foue sons ro = ore

101° 101! 101% 1018

Average tunneling time (s)

io to 10 ~~
Hole population (em~*)

Figure 2.8: Calculated average heavy hole tunneling escape times, for samples
Al, A2, A3, and A4, which had barrier thicknesses of 16, 22, 28, and 34 A,
respectively. The average tunneling escape time is shown as a solid line, as a
function of the total heavy hole subband occupation density. Also shown for
comparison are the calculated electron escape times, shown as dashed lines, and
the experimentally observed decay times, which are indicated by the arrows. The

estimated heavy hole density in the experiment is approximately 10''cm~?. After

Ref. [30].

results shown in Fig. 2.8 were calculated assuming a temperature of 80K. From
Fig. 2.8 it can be seen that the heavy hole escape time decreases with increasing
hole density, as the heavy hole band becomes filled to larger parallel wavevector,
where mixing with the light hole bands is more important. Because the light
hole escape is much faster than the heavy hole escape, the result is a significant
decrease in the tunneling escape time, even though the magnitude of the light hole
component of the wavefunction is only a few percent. The estimated densities
of electrons and heavy holes produced by each optical pulse in our experiment
are of the order of 10*'cm~?. To allow comparison, we also show in Fig. 2.8 the
calculated electron escape times, shown as dashed lines, and the experimentally
observed decay times, which are indicated by the arrows.

Comparing the results in Fig. 2.8, we can see that for the experimentally
estimated excitation density of approximately 10''cm~?, the calculated heavy
hole, calculated electron, and experimentally observed decay times are all within
an order of magnitude of each other. The success of this simple model is striking
in view of the fact that it contains no adjustable parameters, and explains the
overestimate by a factor of 100 to 10° of the heavy hole tunneling escape times
obtained from the simple transmission resonance calculation.

As the hole band-mixing effect is expected to be less pronounced for lower tem-
peratures, and lower carrier densities, the results described in Section 2.4.3 might
be expected to show the long lifetime of the zone-center heavy holes. The failure
to observe the long zone-center heavy hole tunneling time may be attributable
to the large excess energy per photoexcited carrier created by the CPM laser
excitation at 2eV. This results in carriers that have initial temperatures well
in excess of the lattice temperature, which dominates any effect of changing the
sample temperature. However, the observation of the long zone-center heavy hole

tunneling time should be possible using a tunable pulsed laser source, operated

at an energy sufficiently close to the photoluminescence bandgap that the pho-
toexcited carriers are created with low excess energy. The delay scan shown in
Fig. 2.5(c) shows double exponential decay, which may be due to the fact that the
sample, C1, has a wider photoluminescence gap due to the increased confinement
of electrons and holes in this structure. The excess energy with which the carriers

are created is therefore less, which may explain why the two times are observed.

2.6 Comparison with Results in Other Systems

The results of our measurements of tunneling escape times in GaAs/AlAs/-
GaAs/AlAs/GaAs double-barrier heterostructures are complementary to other
time-resolved studies of double-barrier devices using techniques such as electro-
optic sampling or the use of these devices in oscillator circuits. In addition, there
have been investigations of tunneling in other structures, such as double quantum
wells, using time-resolved photoluminescence. In this section, the results of the
various investigations will be compared, to summarize the state of the field at
the time of writing.

Tsuchiya et al. [10] were the first to use photoluminescence to study tunneling
escape from double-barrier heterostructures. The devices they studied were very
similar to those studied in the present work. As mentioned previously, the times
we measure at 80K are a factor of approximately four longer than those found
by Tuchiya et al. [10]. However, in Ref. [10] it was assumed that the heavy
hole escape was negligible, and that the direct time-resolved photoluminescence
decay was only due to escape of electrons from the quantum well. In view of
the present work, this assumption is not valid. If, as we found, the escape of
electrons and heavy holes occurs at the same rate, then the photoluminescence

decay times measured in Ref. [10] should be multiplied by a factor of 2 to obtain

the electron and heavy hole escape times. The remaining discrepancy of a factor
of approximately 2 between the results of the present work and that of Ref. [10]
can be attributed to experimental uncertainty in the barrier thicknesses.

Whitaker et al. were the first to use electrooptic sampling to study GaAs/-
AlAs/GaAs/AlAs/GaAs double-barrier heterostructures [8]. They studied a de-
vice with a 45A quantum well and 15A barriers, and obtained a large-signal
switching time of 2ps, although they only measured the transition time in one
direction. In a similar study of a double barrier with a 45 A quantum well and
17A barriers, Diamond et al. [9] measured a switching time of 8+2ps. The
difference between the two measurements by electrooptic sampling has not been
accounted for, but may be attributable to uncertainties in sample parameters.
For the 16 A barrier sample Al studied in the present work, a tunneling time of
12 +3 ps was obtained. The well width in sample Al is 58 A, which is estimated
to increase the tunneling escape time for electrons by a factor of 2 compared to an
identical sample with a well width of 45 A. Therefore, we can estimate from the
present work that the tunneling escape time in a sample with 16A barriers and
a 45 A quantum well would be 6ps. Thus the time-resolved photoluminescence
results in the present work are in reasonable agreement with the electro-optic
sampling measurements of Refs. [8] and [9].

Brown et al. (3, 32] have fabricated oscillator circuits using GaAs/AlAs/-
GaAs/AlAs/GaAs double barrier heterostructures mounted in waveguides. They
observed oscillation at up to 200 GHz for structures with a 45 A quantum well and
17 A barriers, and oscillation at up to 420 GHz with 11 A barriers. The oscillation
frequencies for the 17 and 11 A barrier samples of 200 and 420 GHz correspond to
periods of 5 and 2.4ps, respectively. These times compare well with the times of
6 and 3 ps estimated from the time-resolved photoluminescence measurements in

the present work. The exact relationship of the maximum oscillation frequency

to the tunneling escape time is not completely clear, however. Brown et al. [33]
have suggested a model for the effect of the quasi-bound state lifetime upon the
oscillation power that they claim yields quantitative agreement with experiment,
using the lifetimes calculated as in Fig. 2.6. However, as can be seen from Fig. 2.6,
the calculated electron escape time is faster than the observed decay time by a
factor of approximately 10 for the thin barrier samples used in the high-frequency
oscillators. This discrepancy between the tunneling times used to accurately
predict maximum oscillation power and those measured by photoluminescence
has not yet been explained.

Finally, there have been measurements of tunneling in double quantum well
structures, using time-resolved photoluminescence (34, 35, 36, 37]. These struc-
tures consist of two quantum wells, of differing well widths, separated by barrier
layers. Bastard et al. [35] have studied the transfer of photoexcited electrons and
holes from one quantum well to another, using a variable electric field to vary the
alignment of the confined states in the two wells. They observed resonances in
the tunneling due to crossings of the heavy hole level in the narrower quantum
well with both the heavy hole and the light hole levels in the wider well. They
have suggested that the effects of light and heavy hole mixing are important in
the hole transfer in the double quantum well systems. The results of Bastard
et al. [35] are in qualitative agreement with the results of the present work, and
suggest that the phenomenon of light- and heavy-hole mixing is important in a
general class of tunneling problems, as one would expect. However, the results of
Ref. [35] have recently been contradicted by Shah et al. [36], who claim that they
did not observe any evidence of heavy hole tunneling upon alignment with light
hole levels. This result, which directly contradicts the observations of Ref. [35],
could be due to a difference in the experimental electron and heavy hole carrier

densities. As pointed out by Yu et al. [30] the strength of the light- and heavy-hole

mixing is dependent upon the density of heavy holes, and becomes unimportant
for sufficiently low carrier densities. Further work on this subject will be required
to determine the cause of the discrepancy. Finally we point out that Nido et al.
[37] observed hole tunneling times in double quantum well structures that were
intermediate to calculations of heavy- and light-hole tunneling times, which is in

qualitative agreement with the results of the present work.

2.7 Conclusions

In summary, the tunneling times for electrons and heavy holes to escape from
the lowest quasi-bound state in the quantum wells of GaAs/AlAs/GaAs/AIlAs/-
GaAs double-barrier heterostructures have been measured using photolumines-
cence excitation correlation spectroscopy (PECS). The electrons and heavy holes
are observed to escape at the same rate, at rates similar to the calculated elec-
tron escape times, but many orders of magnitude faster than the calculated heavy
hole times. The rapid escape of heavy holes can be explained by considering the
mixing between light- and heavy-hole bands in the quantum well, which results
in much more rapid escape of heavy holes from the quantum well. A detailed
understanding of the escape of the photo-excited holes from the quantum well is
important to understand the results of all of the measurements reported to date

that are based on optical excitation.

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Chapter 3

X-point Escape of Electrons
from the Quantum Well of a

Double-Barrier Heterostructure

3.1 Introduction

3.1.1 Background

In this chapter we will consider the effect of the indirect conduction band
minima in AlAs upon the escape of photoexcited electrons from the quantum
well of a double-barrier heterostructure. At a GaAs/AlAs interface the valence
band edge in GaAs is approximately 0.55 eV higher than the valence band edge
in AlAs [1]. In both materials, the valence band maximum occurs at the Bril-
louin zone center, which is referred to as the [-point. The low temperature direct
bandgaps of 1.52 and 3.13 eV for GaAs and AlAs, respectively [2], place the I-
point conduction band edge in the GaAs approximately 1.07 eV below that in

AlAs. Since this confines electrons to the GaAs layers, the lowest energy electron

states in GaAs/AlAs heterostructures will normally be derived mainly from the
bulk GaAs T-point wavefunctions. This justifies use of a simple effective mass
model of the GaAs bulk conduction band structure in calculations of heterostruc-
ture properties. However, the appropriate model in a heterostructure for the bulk
AlAs is not as obvious; the band structure of bulk AlAs is indirect. The AlAs
conduction band has multiple minima, located at the X-point, which is a point
on the edge of the Brillouin zone in the (001) and equivalent directions. Despite
the fact that AlAs is an indirect material, much of the work on tunneling in the
GaAs/AlAs material system has ignored the indirect nature of AlAs, character-
izing the conduction band only by the zone center (I-point) effective mass and
potential energy [3]. This approach has been successful in describing many of
the physical effects observed in heterostructures fabricated with the GaAs/AlAs
system, particularly when the effects of confinement on the electrons are not
great [3]. However, the X-point conduction band minima play an important or
dominant role in several heterostructures. We will discuss examples of some of
these devices in the following paragraph.

The first example of a structure in which the X-point conduction band minima
are important is the short period GaAs/AlAs superlattice, a structure that has
been extensively studied both theoretically [4]-[7] and experimentally [8]-[14] as
a possible alternative to Al,Ga,_,As alloys. In these short period superlattices,
localization of the electrons at the I-point in the GaAs layers can cause confine-
ment energies large enough to result in interaction with the AlAs X-point, and
it is possible, with sufficient confinement, to obtain a superlattice whose lowest
conduction band states are derived mainly from the AlAs X-point [5]. Another
structure in which the indirect nature of AlAs is important is the double quan-
tum well, where the X-point levels can contribute to nonresonant tunneling from

one well to another [15]. In GaAs/AlAs double-barrier heterostructures it has

been suggested [16] that the valley current is determined by currents through
the X-point levels in the AlAs barriers. In the tunnel emitter bipolar transistor,
the process of injection of hot electrons through a thick AlAs emitter barrier is
central to operation of the device [17]. The importance of the X-point levels in
the emitter barrier of such structures has not been discussed, and could be very
significant to the injection process for electrons. There has also been experimen-
tal evidence of X-point related resonances in the current-voltage characteristics
of double-barrier (18, 19, 20] and single-barrier [21, 22] devices.

From the examples discussed above, it is clear that there are a wide variety
of devices in which the indirect X-point conduction band minima of AlAs are im-
portant, particularly in electron tunneling through AlAs barriers. Studies of the
escape of photoexcited carriers in GaAs/AlAs/GaAs/AlAs/GaAs double-barrier
heterostructures such as those described in Ref. [23] and Chapter 2 of this thesis,
have shown that photoluminescence is a powerful technique for studies of tun-
neling. In these previous studies, however, the confinement of the quantum well
states was not sufficient to enable interaction with the X-point levels in the AlAs
layers. In contrast, in the work described in this chapter, we have used photo-
luminescence to study structures in which the interaction of electrons escaping
from the quantum well with the X-point levels in the barriers is important. To il-
lustrate the structures studied, we show in Fig. 3.1 the conduction band diagrams
for two representative undoped GaAs/AlAs/GaAs/AlAs/GaAs heterostructures.
The ['-point and X-point conduction band edges are shown as a function of po-
sition as the solid, and light gray lines, respectively. The I'-point profile is the
familiar double barrier potential, whereas for the X-point the inversion of the rel-
ative band offset leads to the double well potential for the conduction band edge.
The energies of the lowest I’-point level, localized in the GaAs quantum well, and

the lowest X-point levels, localized in the two AlAs barriers, are schematically

(a)

(b)

Figure 3.1: Conduction band edges at the I'-point (dark line) and X-point (gray
line) versus position for two GaAs/AlAs/GaAs/AlAs/GaAs double-barrier het-
erostructures with differing quantum well widths. The position in energy of the
lowest I’-point and X-point states are schematically shown with dashed lines. (a)
Wide quantum well, where the ['-point state in the quantum well lies below the
energy of the X-point levels in the barriers. (b) Narrow quantum well, where

T-point and X-point states are at comparable energies.

shown as dashed lines. In Fig. 3.1(a) we show the band diagram for a struc-
ture with a fairly wide quantum well. In this structure, the confinement of the
[-point levels in the GaAs is insufficient to allow interaction with the X-point
levels in the barriers. However, if the quantum well width is decreased, as shown
in Fig. 3.1(b), the confinement energy for the I’-point level in the GaAs quantum
well is increased. In the case illustrated in Fig. 3.1(b), the confinement raises
the [-point state in the quantum well to an energy nearly equal to that of the
X-point levels in the barriers.

The effect of the X-point levels on the escape process for electrons initially
created in the [-point states in the quantum well could be considerable, and
could lead to novel behavior during escape. To illustrate this, we show in Fig. 3.2
calculations using the one-band Wannier orbital model (OBWOM) [5], of the
escape of electrons initially localized in the the quantum well, for two different
GaAs/AlAs/GaAs/AlAs/GaAs double-barrier heterostructures. The one-band
Wannier orbital model describes the conduction band structure of both the GaAs
and AlAs materials with a single orbital per unit cell, considering overlap of or-
bitals over distances of several unit cells. This model allows a realistic while
computationally efficient calculation of the conduction band structure, including
the behavior at the X-point [5]. The calculations presented in Fig. 3.2 show two
examples of the evolution of the probability density integrated over the quantum
well region, for an electron wavefunction initially localized in the GaAs quantum
well. In Fig. 3.2(a) we show the behavior for a structure with a 15 monolayer
GaAs quantum well, and 10 monolayer AlAs barriers. This structure corresponds
to the situation illustrated in Fig. 3.1(a), where the effect of the X-point levels
is small. The decay of the initial wavefunction localized in the well can be de-
scribed by a simple exponential. The time constant for the decay corresponds

to the quasi-bound state lifetime, which can be calculated [24] from the energy

(a)

10 <0

0.5 | |

Integrated Well Probability Density
fo

0) 1 eC 3

Time (ps)

Figure 3.2: Calculated decay of the probability density, integrated over the quan-
tum well region, for an electron initially localized in the quantum well of two dif-
ferent GaAs/AlAs/GaAs/AlAs/GaAs heterostructures. (a) 15 monolayer quan-
tum well, 10 monolayer barriers. The evolution is described by a simple exponen-
tial, with a time constant corresponding to the quasi-bound state lifetime. (b)
12 monolayer quantum well, 10 monolayer barriers. In this case interaction with
the X-point levels causes oscillations in the probability density during decay of

the quasi-bound state.

width of the transmission resonance, AEpwym, using the uncertainty relation
+ = h/AEpwun, as described in Section 2.5. In Fig. 3.2(b) we show a simi-
lar calculation for a structure with a 12 monolayer GaAs quantum well, and 10
monolayer AlAs barriers. In this structure, the X-point and I-point levels are
close in energy, and the evolution is very different. The decay of the probability
density in the quantum well shows oscillations during the decay process, due to
coupling between the I’-point levels in the GaAs quantum well, and the X-point
levels in the AlAs barriers. This example shows that the interaction between the
X-point levels and the [-point levels in the double-barrier heterostructure can
lead to qualitatively different phenomena from the case where the X-point levels
are much higher in energy than the [-point levels.

In this chapter we describe an experimental study of the effect of the X-point
levels localized in the AlAs barriers upon the escape of electrons photoexcited in
the quantum well. In a series of GaAs/AlAs/GaAs/AlAs/GaAs double-barrier
heterostructures with varying well thicknesses, we have been able to study the
transition from the situation illustrated in Fig. 3.1(a), where the effect of the
X-point levels is small, to the case in Fig. 3.1(b), where the X-point levels are

important.

3.1.2 Summary of Results

We have used photoluminescence to study a series of GaAs/AlAs/GaAs/-
AlAs/GaAs double-barrier heterostructures. We report the first observation in
these structures of photoluminescence from the recombination of electrons at X-
point levels localized in the AlAs barriers, with heavy holes localized in the GaAs
quantum well. The integrated photoluminescence intensity from levels localized

in the GaAs quantum well decreases dramatically as the I-point confinement

energy is increased. This decrease is attributed to rapid escape of electrons from

the quantum well via X-point states in the AlAs barriers.

3.1.3 Outline of Chapter

In Section 3.2, we describe the sample parameters, details of the sample prepa-
ration, and the photoluminescence experimental techniques. In Section 3.3 we
present the experimental results, and discuss their interpretation. A summary of

our conclusions is given in Section 3.4.

3.2 Experimental Techniques

Samples were grown at 600°C by molecular beam epitaxy (MBE) in a Perkin
Elmer 430 system, on (100) GaAs substrates. After growth of a 0.5um GaAs
layer, the symmetrical GaAs/AlAs/GaAs/AlAs/GaAs double-barrier heterostruc-
ture was grown. The thickness of the final GaAs cap layer was 300 A. Nominal
layer thicknesses, based on bulk growth rate measurements, are shown in Ta-
ble 3.1 for the 9 samples studied. The GaAs growth rate was determined for each
sample by measurement of the total film thickness. The AlAs growth rate was
calibrated using reflection high energy electron diffraction (RHEED) oscillations.
The nominal quantum well thickness ranges from 9.4 to 20.6 monolayers, and
the barrier thicknesses were maintained constant at 13.0 monolayers for all of the
samples except for sample 9, in which the barriers were nominally 11.9 monolay-
ers thick. All layers were undoped, with an estimated residual carbon acceptor
concentration of 10'* cm~?.

During the course of this work, it was found that details of the MBE growth
techniques used were important to the photoluminescence characteristics of the

devices. Initial devices were grown with 1 minute growth interrupts at each

Sample Growth Well Barrier Peak FWHM Assignment

No. No. (ML) (ML) (meV) (meV)
1 Y-342 = 9.4 13.0 1776 8 X
1853 20 r
2 III-332 10.7 13.0 1757 6 Xx
1800 17 T
3 III-335 11.8 13.0 1751 6 Xx
1779 12 r
4 III-331 12.7 13.0 1774 12 r-X
5 II-339 =. 13.1 13.0 1724 8 r
6 ITI-341 14.0 13.0 1711 7 r
7 III-329 §=15.8 13.0 1690 6 r
8 III-336 16.8 13.0 1667 5) r
9 III-059 20.6 11.9 1625 5 r

Table 3.1: Sample parameters, observed photoluminescence peak energies at 5K,
and assignment of observed peaks. The nominal layer thicknesses shown for
the GaAs quantum well were determined from bulk growth rates determined
from measurements of the total film thickness for each sample. The AlAs layer
thicknesses were obtained from growth rates calibrated using RHEED oscillations.
The assignment of the peaks to transitions involving I’-point or X-point electron

levels is discussed in the text.

interface, in an As overpressure. Studies of these structures, showed photolumi-
nescence spectra with two peaks. The two peaks, separated by approximately
8 meV, were consistent with excitonic luminescence, and luminescence involving
impurities. The lower energy peak was found to saturate with increasing pump
intensity, appearing in some cases only as a weak shoulder. The saturation, spec-
tral dependence, and energy separation from the exciton peak are all consistent
with previous reports of recombination involving impurities in GaAs quantum
wells [26]. The origin of the impurity-related level was correlated to the use of
growth interrupts, which is consistent with the recent conclusions of Kohrbruck
et al. [25]. The nonradiative center has not been identified, but may be related
to carbon, as suggested in Ref. [26], or oxygen [27]. Accordingly, for all of the
samples described in the present work, growth interrupts were not used. The pro-
cedure used to outgas the Al source material after loading into the MBE was also
found to be very important to the photoluminescence efficiency of the samples.
When the Al source material is replaced, it is subsequently outgassed at 1130°C
for 6 hours (corresponding to growth of approximately 8 ym of AlAs). This pro-
cedure allows growth of devices with high photoluminescence efficiency. However,
it was found that the photoluminescence efficency was severely degraded when
using an Al source that had been outgassed, exposed to atmosphere, and subse-
quently outgassed as described above. Further outgassing for 4 hours at a higher
temperature of 1170°C was necessary, corresponding to growth of approximately
12 pm of AlAs, before double-barrier heterostructures with high photolumines-
cence efficiency could be grown. The increased requirement for outgassing in the
latter case is attributed to the increased surface area of the Al source material,
due to wetting of the effusion cell crucible.

CW photoluminescence experiments were performed at 5K, in a helium im-

mersion dewar with sapphire windows. The 5145A line from an argon laser

was used for photoexcitation, and luminescence was dispersed with a double-
pass spectrometer and detected with a GaAs photomultiplier tube and photon-

counting electronics.

3.3 Results and Discussion

In Fig. 3.3 we show typical photoluminescence spectra, taken at 5 K, for three
representative samples. Fig. 3.3(a) shows the spectrum for sample 7, which has a
nominal quantum well width of 15.8 monolayers. A single, narrow peak, centered
at 1690 meV, with a FWHM of 6 meV, is observed. Shown in Fig. 3.3(b) is the
spectrum for sample 5, which has a quantum well width of 13.1 monolayers. The
photoluminescence from this sample also shows a single peak, now centered at
1724 meV, with a width of 8 meV. The spectrum for sample 1, which has the
narrowest quantum well width of 9.4 monolayers, is shown in Fig. 3.3(c). This
spectrum shows two peaks of comparable intensity. The peak at 1776 meV has
a FWHM of 8 meV, whereas the peak at 1853 meV has a FWHM of 20 meV.
The intensities of the photoluminescence signals shown in Fig. 3.3 differ consid-
erably, decreasing rapidly with decreasing well width. The spectrum shown in
Fig. 3.3(c) is very weak, and extraneous signals from the sapphire dewar windows
at 1790 and 1786 meV obscure the photoluminescence from the double-barrier
sample. The gap in the spectrum shown in Fig. 3.3(c) is due to this interference.
The background seen in Fig. 3.3(c) is due to hot-carrier luminescence from the
undoped GaAs cap and buffer layers. Other samples show spectra similar to one
of the three cases shown in Fig. 3.3. A summary of the peak energies and widths
seen in photoluminescence is given in Table 3.1. For samples 1 to 3, two peaks
in the photoluminescence are observed, whereas for samples 4 through 9 only

single peaks are seen. It can be seen from Table 3.1 that the lower energy peaks

(a) L =15.8 ML

(b) L=13.1 ML

Intensity (a.u.)

1600 1700 1800 1900

Energy (meV)

Figure 3.3: Typical photoluminescence spectra at 5K. (a) Sample 7, with quan-
tum well thickness Lw=15.8 monolayer. (b) Sample 5, Lw=13.1 monolayer. (c)
Sample 1, Lw=9.4 monolayers. Interference from impurities in the sapphire de-
war windows prevents observation of the photoluminescence at approximately

1788 meV, and is responsible for the gap in the spectrum shown in (c).

observed in samples 1-3 are all a factor of approximately 2.5 narrower than the
higher energy peaks in the same samples.

In Fig. 3.4(a) we plot the energies of the peaks in the photoluminescence
spectra, as a function of the quantum well thickness. The appearance of a second
peak for quantum well widths less than approximately 12.7 monolayers suggests
the importance of another electron or hole state in the photoluminescence. To
allow comparison of the experimental results with theory, in Fig. 3.4(b) we show
the energies for conduction band to lowest heavy hole (hh; ) transitions, calculated
using the one-band Wannier orbital model (OBWOM). The I’-point conduction
band edge in the GaAs was adjusted to lie 190 meV below the X-point band
edge in AlAs for these calculations, to obtain agreement with the experimentally
observed crossover point seen in Fig. 3.4(a). This value of 190 meV agrees well
with the value of 160 meV found in Ref. [28]. Energies of the lowest I-point
(Ti hh,), lowest X-point (X;hh,), and first excited X-point (Xghh;) transitions
to the lowest heavy hole state are labelled. Transitions involving electron states
with significant (greater than 5% of the total) probability density in the quantum
well are indicated in Fig. 3.4(b) by “x” symbols, and those involving significant
density in the barriers by “+” symbols. Mixed states with significant probability
density in both the well and the barriers are denoted by both symbols.

The origin of the observed peaks can be understood by comparing the ex-
perimental data of Fig. 3.4(a) with the calculated energies shown in Fig. 3.4(b).
For samples 5 through 9, which have quantum wells wider than 12.7 monolayers,
the luminescence is consistent with the [', hh, recombination, involving electrons
and holes both localized in the quantum well. The linewidths of the peaks in
these samples, given in Table 3.1, are consistent with monolayer fluctuations in
the quantum well width. The higher energy peaks in samples 1 to 3, which have

quantum wells narrower than 12.7 monolayers, are also consistent with hh, re-

1900 + (a) Expt J
5 )
1800} . o , J
ome) o
[e)
1700 - ° re) 7
fe]
> 1600 °
£ 8 12 16 20 24
Py
ap
L . T 7 T r T r T
x 1900; , (b) Theory 7
a x
1800 + . " ; . i ee X,hh, |
1700 | ST Xyhhy |
1600 | * Pybhy |
8 12 16 20 24

Well Width (ML)

Figure 3.4: (a) Photoluminescence peak energies at 5 K. The lower energy peaks
observed for Lw<12.7 monolayers are due to recombination of electrons localized
at X-point levels in the AlAs with heavy holes localized in I-point states in the
GaAs quantum well. (b) Calculated energies of the lowest I-point state I’; , lowest
X-point state X,, and first excited X-point state Xz to lowest heavy hole (hh,)
transitions. Transitions involving electron states with significant (greater than
5%) probability density in the quantum well are shown by “x” symbols, and

states with significant density in the barriers by “+” symbols.

combination, with a linewidth consistent with monolayer fluctuations in quantum
well width. The lower energy peaks seen in Fig. 3.4(a) for Lw<12.7 monolay-
ers are consistent with the X,hh, transitions, which involve electrons at X-point
levels in the AlAs barriers and heavy holes in the GaAs quantum well. The ris-
ing energy of the X-point peaks with decreasing well width is due to increasing
confinement of the heavy holes. The identification of the lower energy peaks
for narrow well widths with X-point-related luminescence is supported by the
widths of the photoluminescence peaks shown in Table 3.1. The photolumines-
cence peaks observed for the X-point levels are narrower than those involving
T-point levels. This is due to the reduced impact of monolayer fluctuations in
the AlAs barrier thickness on the confinement energy of the X-point levels, which
is much smaller than the confinement energy of the ['-point levels. The X-point-
related luminescence is the first observation, in GaAs/AlAs/GaAs/AlAs/GaAs
double-barrier heterostructures, of recombination that is indirect in real space and
momentum. The X-point levels involved in this recombination are quasi-bound
states, in contrast with the X-point levels observed in indirect recombination in
GaAs/AlAs short period superlattices [8]-[14]. The X-point levels in the super-
lattices are the lowest energy electron states, and the observation of luminescence
from these levels is indicative of the long lifetime for electrons localized in X-point
states. In contrast, the X-point levels in our structures correspond to quasi-bound
states in the AlAs barriers, and would not be expected to have a lifetime long
enough to enable significant recombination with ['-point heavy hole levels in the
GaAs quantum well. Observation of the weak luminescence from these levels
suggests that electrons localized at the X-point levels in the AlAs barriers have
some [-point character, although a radiative recombination involving emission
of a phonon is an alternative explanation. Sample 4, which is situated at the

crossover of the [ and X-point electron levels may show mixed I’-X character.

100

The peak assignments for all of the samples are summarized in Table 3.1.

In Fig. 3.5 we show the integrated photoluminescence intensity at 5K for
all of the samples, observed under identical conditions with a pump intensity
of 800 W/cm’. The intensity of the I-point peaks are shown in Fig. 3.5 by
“x” symbols, and the X-point-related peaks by “+” symbols. The integrated
intensity of the ['-point peaks shows little variation as the quantum well thickness
is decreased from 20.5 monolayers to approximately 16 monolayers, and then
drops rapidly with further decrease in well width. A change in the rate of decrease
of intensity with well width can be seen for the samples with Lw<12.7 monolayers.
The drop in integrated intensity for narrower quantum wells is quite dramatic,
with a total drop of more than 5 orders of magnitude over the entire range of well
thicknesses. The intensity of the X-point peaks is less than that of the I’-point
peaks in all of the samples, but from Fig. 3.5 it can be seen that the X-point
peaks become relatively more intense as the quantum well width is reduced.

The integrated photoluminescence intensity shown in Fig. 3.5 depends upon
the electron and heavy hole tunneling escape times, the optical absorption, and
the radiative recombination rate. In principle, all of these parameters are de-
pendent upon the quantum well width, and could contribute to the variation of
photoluminescence intensity with well width seen in Fig. 3.5; we will examine the
importance of the various parameters to show why variation in the electron es-
cape time is the most important contribution. First, we consider the absorption.
With the 2.4 eV excitation energy used, several transitions between confined elec-
tron and hole states contribute to absorption. Decreasing quantum well width
will result in a decrease in absorption at the exciting laser energy, because of
the increasing energy of the absorption threshold. This will tend to decrease the
photoluminescence intensity with decreasing quantum well width. Calculations

of the direct allowed absorption processes for the range of quantum well widths

101

5 t x
n x ;
q 41 1
x 10 x E
co 3 f 1
se,
o 10°) x ’
DL .
© 10F . :
E F xX

1 1

8 12 16 20
Well Width (ML)

Figure 3.5: Integrated photoluminescence intensity under identical conditions, at
5K. The intensities of the [’-point luminescence are shown with “x” symbols, and
the X-point intensities as “+” symbols. The drop in intensity with decreasing well
width is attributed to rapid escape of photoexcited electrons from the quantum

well, via the X-point levels in the AlAs barriers.

102

covered in Fig. 3.5 show that the [,hh, and I',lh, transitions are energetically
allowed over the entire range of well widths. The ['jhh2 transition is allowed for
Lw > 12 ML, and the I'alh2 transition is allowed for Lw > 16 ML. Measurements
of the absorption in wide GaAs quantum wells have shown that the band-to-band
absorption is approximately independent of well width [29], and that the absorp-
tion contribution for a given subband does not depend strongly upon the excess
energy of the incoming photon. Therefore, the dependence of absorption upon
well width is due mostly to the number of allowed subbands participating in the
absorption. This is not expected to affect the absorption by more than a factor of
2-4 over the range of quantum well widths considered here, and therefore is not
a major effect. Next we consider the radiative transition rate. Masselink et al.
[29] measured the exciton oscillator strengths in wide GaAs quantum wells, and
found that the oscillator strength depends upon well width Lw approximately
as 1/(Lw)’. Over the range of well widths considered in Fig. 3.5 this results in
variation by a factor of approximately 5, which is fairly small, and would lead
to increased photoluminescence intensity for narrower quantum wells. Since the
observed intensity shows the opposite behavior, i.e., it decreases for narrow wells,
we can conclude that the radiative recombination rate is not the dominant ef-
fect responsible for the drop in photoluminescence intensity for narrow quantum
wells seen in Fig. 3.5. Therefore, the drop in photoluminescence intensity seen
in Fig. 3.5 is due to the rapid escape of either electrons or heavy holes. As de-
scribed in Chapter 2, the escape of heavy holes from double-barrier structures is
affected by valence band mixing, and depends upon several parameters, includ-
ing the barrier thickness, population, and carrier temperature. The light- and
heavy-hole escape times are expected, based on a calculation of the transmission

resonance width AE and the expression r = h/AE,,,,,,, (described in de-

FWHM

tail in Section 2.5) to smoothly decrease with decreasing quantum well width.

103

Similarly, no abrupt changes in the population, which is dependent upon the
absorption, or the carrier temperature are expected with varying well width. In
contrast, the behavior shown in Fig. 3.5 is not smoothly dependent upon the well
width, and shows a pronounced change at a quantum well width of approximately
14 monolayers. Having estimated that the absorption, radiative recombination
tate, and heavy hole tunneling escape time cannot explain the dependence of the
photoluminescence intensity upon the quantum well width, we conclude that the
most important contribution is the rapid escape of electrons in structures with
narrow quantum wells. Comparing the crossover of I’-point and X-point energy
levels shown Fig. 3.4(a) to the photoluminescence intensity shown in Fig. 3.5,
we see that the drop in photoluminescence intensity occurs at a well width of
approximately 14 monolayers, which is slightly greater than the well width for
crossover of I-point and X-point levels, which is 13 monolayers. This indicates
that even before the [-point state lies higher in energy than the X-point state,
the X-point levels influence escape from the quantum well. This may be due to
thermal effects, in which carriers with excess kinetic energy escape through the

X-point levels, or mixing between the [-point and X-point levels.

3.4 Conclusions

We have studied a series of GaAs/AlAs/GaAs/AlAs/GaAs double-barrier het-
erostructures with varying quantum well widths, using photoluminescence. We
report the first observation in these structures, of recombination that is indi-
rect in both momentum and real space, involving electrons localized at X-point
levels in the AlAs barriers with heavy holes localized at I’-point levels in the
GaAs quantum well. This luminescence involves X-point quasi-bound states, in

contrast to previous observations of indirect luminescence in GaAs/AlAs short

104

period superlattices. Studies of the photoluminesence intensity show a dramatic
drop as the quantum well width is decreased. This drop is attributed to the
rapid escape of electrons from the quantum well, involving the X-point levels in

the AlAs barriers.

105

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[24] N. Harada and S. Kuroda, Jpn. J. Appl. Phys., Pt. 2, 25, L871 (1986).

(25) R. Kohrbrick, S. Munnix, D. Bimberg, D.E. Mars, and J.N. Miller, presented
at the Seventeenth Annual Conference on the Physics and Chemistry of

Semiconductor Interfaces, January 31-February 2, 1990, Clearwater, Florida.

[26] R.C. Miller, A.C. Gossard, W.T. Tsang, and O. Munteau, Phys. Rev. B 25,
3871 (1982).

(27] T.F. Keuch, private communication; K. Akimoto, M. Kamada, K. Taira, M.
Arai, and N. Watanabe, J. Appl. Phys. 59, 2833 (1986).

[28] Landolt-Bérnstein: Numerical Data and Functional Relationships in Science
and Technology, edited by O. Madelung, Vol. III/22(a), (Springer-Verlag,
Berlin, 1987), pgs. 63, 82.

[29] W.T. Masselink, P.J. Pearah, J. Klem, C.K. Peng, H. Morkog, G.D. Sanders,
and Y.-C. Chang, Phys. Rev. B 32, 8027 (1985).

108

Chapter 4

Studies of Electrically Biased

Double-Barrier Heterostructures

4.1 Introduction

4.1.1 Motivation and Background

As described in Chapter 1, the tunneling response times of double-barrier
heterostructures are of interest because of the application of these structures in
high-frequency circuits. While investigations such as those described in Chap-
ter 2 yield information regarding tunneling escape times in undoped structures,
the structures studied are not functional as electrical devices. Since the appli-
cation of the double-barrier heterostructure is in electrical circuits where it is
normally operated under significant bias, it is of interest to measure the speed of
the device under electrical bias. This chapter describes studies of time-resolved
photoluminescence and photocurrents in electrically biased double-barrier het-
erostructures.

The transient response of operational double-barrier heterostructures was

109

first studied with electrooptic sampling [1, 2]. This approach, described in Sec-
tion 1.3.1, requires the double-barrier device to be mounted in a stripline environ-
ment compatible with the propagation of high-frequency transient signals. The
experimental difficulties associated with the device mounting and electrooptic
sampling are compounded by the effects of parasitic capacitances and inductances
associated with contacting and packaging of the device. One of the motivations
for the work described in this chapter was to develop techniques that would be
complementary to studies in stripline environments, and perhaps enable a fuller
understanding of the effects of such parasitics on device response times.

Time-resolved photoluminescence techniques have previously been used to
study tunneling times in certain electrically biased heterostructures, but the
structures studied to date have been insulating structures, in which no signif-
icant current flow is involved. Norris et al. [3] have used photoluminescence
decay to study the effect of electric fields on tunneling escape from GaAs quan-
tum wells. The electrons and holes were confined to the quantum well by an
infinite Al,Ga,_,As barrier on one side, and a relatively thin Al,Ga,_,As barrier
on the other side, and the quantum well was embedded in a p-i-n diode, operated
in reverse bias. Oberli and coworkers [4] and Liu et al. [5] have used time-resolved
photoluminescence to study tunneling in electrically biased double quantum well
structures. Since the devices used in both of the above studies were essentially
insulating, the main effect of the electric field was to change the energies of elec-
tron and hole levels through the Stark effect, and to change the shape and height
of the barriers through which electrons and holes were tunneling.

In contrast to previous studies of time-resolved photoluminescence in biased
structures, the GaAs/AlAs/GaAs/AlAs/GaAs double-barrier heterostructures
studied in the present work all show negative differential resistance, and sub-

stantial current flow. The use of photoluminescence in these structures differs

110

from studies of undoped structures such as those described in Chapter 2, because
the photogenerated electrons and holes created in the electrode regions can move
through the device, and can flow into the quantum well. As will be shown in Sec-
tion 4.2, the photoexcited carriers from the electrodes can dominate the observed
quantum well photoluminescence. This observation motivated a study of pho-
tocurrents in the double-barrier heterostructures. In conventional time-resolved
photocurrent studies, the current response to photoexcitation by an optical pulse
is directly time resolved with high-frequency electronics. However, in the devices
studied in the present work, the tunneling times were expected to be on the order
of 200 to 1000 ps, which would be difficult to resolve with conventional electron-
ics. A different approach to the photocurrent measurements was used, which
was similar to that briefly considered by Sasaki et al. [6]. This new technique
is analogous to the correlation photoluminescence technique used in Chapter 2,

modified for a study of photocurrents.

4.1.2 Summary of Results

We have fabricated electrically operational double-barrier heterostructures,
showing negative differential resistance while simultaneously allowing optical in-
jection of electrons and holes in the double-barrier region. Studies of time-
resolved photoluminescence in these structures show that at zero bias, results
very similar to those for the undoped structures studied in Chapter 2 are recov-
ered. However, for electrical biases sufficient to cause significant current flow in
the absence of photoexcitation, the decay of the quantum well photoluminescence
with delay is much less pronounced. These results can be explained by flow of
photoexcited electrons or holes into the quantum well of the double-barrier device

during the course of the measurement. These photocurrents, which result from

111

the flow of photoexcited carriers, were studied using an extension of the two-
beam photoluminescence excitation correlation spectroscopy (PECS) technique
described in Chapter 2. In this novel experiment, photocurrents were observed at
the sum chopping frequency, indicating an effect of the photogenerated electrons
and holes from one optical pulse on the photocurrent due to a delayed pulse. The
sum-frequency photocurrent was found to vary with the delay and with the elec-
trical bias voltage. At certain bias voltages, the dependence of the sum-frequency
photocurrent upon delay shows exponential components with time constants very
similar to the tunneling times in undoped structures determined by time-resolved
photoluminescence. One explanation for the observed signals suggests that this
technique could be used to study the transient response of other electrical devices

that are not amenable to study with time-resolved photoluminescence.

4.1.3 Outline of Chapter

Studies of time-resolved photoluminescence are described in Section 4.2, which
also includes details of the device preparation. The correlation photocurrent
studies are described in Section 4.3, with a description of device preparation and
electrical characteristics in Section 4.3.1. The experimental setup used to make
the correlation photocurrent measurements is described in Section 4.3.2; results
are presented in Section 4.3.3 and discussed in Section 4.3.4. Conclusions are

summarized in Section 4.4.

112

4.2 Time-Resolved Photoluminescence

4.2.1 Device Preparation

The device (growth number III-082) used for studies of photoluminescence
decay was grown by molecular beam epitaxy at 600°C on an n* GaAs (100)
substrate. After growth of 0.5um of n+ GaAs (n ~ 5 x 10'8cm~), 500A of
GaAs lightly n-doped (n ~ 2 x 10'cm~3), and a 25A undoped GaAs spacer
layer were grown. This was followed by 34A AlAs barrier, 58A GaAs well,
and 34A AlAs barrier layers. Finally another 25 A undoped GaAs spacer layer,
275A of GaAs lightly n-doped (n ~ 2 x 10%cm73), and 300A of n+ GaAs
(n ~ 5 x 1018cm~?) were grown. Si was used for n-type doping. Relatively
thick barriers were used so that current densities would be low, allowing use of a
relatively thin n* top contact layer without suffering detrimental effects due to
series resistance of this layer. A thin top contact layer places the double-barrier
region of the device closer to the surface, which reduces attenuation of laser light
into, and photoluminescence collected from, the quantum well region. A 60A
layer of Au/Ge was deposited using an electron-beam evaporator to form the top
contact. No annealing of the contacts was performed, because of the proximity
of the double-barrier device to the surface. Because of the low current densities
in this device, contact resistance did not pose a problem. Mesas were defined
and etched using standard photolithographic techniques, and the bottom of the
substrate was used as the back contact. Devices were mounted in a TO-5 header
using silver paint, and wire bonds were made to the tops of the mesas.

The current-voltage characteristic at 77K of a 250m diameter device is
shown in Fig. 4.1 for reverse bias (negative bias of the top contact with respect

to the back contact). The peak currents in devices of various sizes were found to

113

Voltage (V)

—-1.2 -—0.8 —0.4 0
T . T T T 9 O

ae)

* — —4 =
: 7 -5
—6

Figure 4.1: Current-voltage characteristic in reverse bias for a 250m diameter
device, at 77K. Negative bias corresponds to the flow of electrons into the top
of the mesa. The circles mark the biases at which the photoluminescence decay

scans shown in Fig. 4.3 were taken.

114

scale reasonably well with the mesa area, indicating that current is flowing over
the whole mesa device, and not just under the wire bond. However, the wire
bonding process was found to affect the series resistance of the contact, resulting
in variations in the peak voltage due to differing series voltage drops across the
metal-semiconductor top contact. The peak current was not affected, indicating
that the differences between devices were confined to the contact regions of the

devices.

4.2.2 Experimental Arrangement

To measure the photoluminescence under electrical bias, the double-barrier
device mounted on a TO-5 header was placed in a helium immersion dewar, mod-
ified to allow electrical contacts to the device. The temperature was maintained
at 80K. The laser spot was focused on an area of the mesa not obscured by the
wire bond, requiring the use of mesas at least 150m in diameter. The photo-
luminescence excitation correlation spectroscopy (PECS) technique described in
Section 2.2 was used for time-resolved photoluminescence measurements, with
the photoluminescence being collected from the top of the mesa and imaged into
a spectrometer. Electrical bias was provided by either a constant-current source,

a constant voltage source, or a Tektronix Model 577 curve tracer.

4.2.3 Results

Time-resolved photoluminescence data were obtained using the photolumi-
nescence excitation correlation spectroscopy (PECS) technique described in Sec-
tion 2.2. The photoluminescence spectrum at the sum chopping frequency in the
region of the peak of the quantum well luminescence is shown in Fig. 4.2, for

a bias current of -l1mA. The linewidth of the quantum well peak in Fig. 4.2 is

115

60 1 T T r q T U

Amplitude (a.u.)

r@) 1 1 L 1 L it i
7600 7620 7640 7660 7680 7700 7720 7740

Wavelength (A)

Figure 4.2: Photoluminescence spectrum from the quantum well at the sum chop-
ping frequency, for a current of -1mA, and at 80K. The rising background at

longer wavelengths is due to recombination from the n* GaAs electrode regions.

116

consistent with monolayer fluctuations in the quantum well thickness, and the
rising background at longer wavelengths is due to recombination in the n+ GaAs
electrode regions. As expected, a Stark shift of the quantum well photolumines-
cence peak to longer wavelengths (i.e., a red shift) is observed as the bias across
the sample is increased. The fact that a Stark shift is observed in luminescence
from an area of the mesa that is not directly underneath the wire bond indicates
that significant electric fields are developed across the quantum well due to the
applied bias. This conclusion is consistent with the current-voltage data, which
indicated that current flow is fairly uniform across the mesa area.

In Fig. 4.3 we show the dependence upon delay of the sum-frequency ampli-
tude at an energy corresponding to the peak of the quantum well photolumines-
cence. A variety of bias currents were used, with Figs. 4.3(a), (b), (c), and (d)
corresponding to the bias currents of 0, -1, -3, and -5mA, respectively, which
were indicated in Fig. 4.1 by circles. Sum-frequency photoluminescence delay
scans were studied with varying optical powers and bias schemes. It was found
that for nonzero bias and average optical powers on the order of 1 mW per beam
after chopping, the variation of the sum frequency photoluminescence with delay
was different depending upon whether a current source, voltage source, or curve
tracer was used to provide electrical bias. This effect was found to be less severe
with lower optical power; at a power of 135W per beam, the variation with
delay was independent of the source of electrical bias. Accordingly, we present
data only for low optical powers.

From Fig. 4.3(a) it can be seen that at zero bias significant decay of the
photoluminescence signal is observed within the +500 ps delay accessible experi-
mentally. This correponds well to the expected lifetime of approximately 800 ps
observed for the two undoped samples with 34 A AlAs barriers and 58 A quantum

wells studied in Chapter 2. The decay of the photoluminescence signal at higher

117

Amplitude (a.u.)

Delay (ps)

Figure 4.3: Sum-frequency photoluminescence delay scans for sample III-082, at
the peak of the quantum well luminescence, at 80K, for the various bias levels
indicated in Fig. 4.1: (a) zero bias, (b) -1 mA, (c) -3mA, (d) -5 mA. The solid line
connects the experimental points to aid the eye. The decay in (a) is comparable
to that observed in similar undoped structures. The decays in (b), (c), and (d)
are much less over the same range, due to the influx of photoexcited carriers from
the electrodes. The coherence peak at zero delay does not reflect decay of the

carrier densities.

118

bias, shown in Figs. 4.3(b)-(d), is very different. The coherence peak at exactly
zero delay, an artifact due to optical interference of the two pump pulses which
was discussed in Chapter 2, is still seen in all scans. However, the behavior for
nonzero delay times is quite different as seen in Figs. 4.3(b)-(d). The decay of the
sum frequency signal is negligible over the +500 ps range of delay times. This in-
dicates that decay of the electron and hole densities in the quantum well occurs on
a time scale much longer than 500 ps, in contrast to the tunneling escape lifetime
of approximately 800 ps expected from measurements in the undoped structures,
and seen in Fig. 4.3(a). This difference in the decay can be explained in terms
of the effects of electrons and/or holes photoexcited in the electrode regions, as

will be discussed in the following section.

4.2.4 Discussion

In order to understand the delay scans shown in Fig. 4.3, it is helpful to re-
examine the analysis of the PECS measurement technique given in Section 2.2
for the undoped structures. In structures at zero bias, it is reasonable to assume
that the flow of photoexcited carriers from the electrode region into the quan-
tum well is insignificant, because carriers relax very quickly to the band edges,
where they are energetically forbidden from tunneling into the quantum well.
However, significant current flow can be obtained in the biased structure (as is
the case for Figs. 4.3(b)-(d)). It is reasonable, then, to expect that photoexcited
electrons and/or holes can flow from the electrodes into the quantum well. In
this case, the decay of the quantum well photoluminescence would be much less
rapid, as escaping carriers initially photoexcited in the quantum well are replaced
by photoexcited carriers in the electrodes tunneling into the quantum well. We

attribute the decreased decay of the photoluminescence from the quantum well

119

at nonzero bias seen in Figs. 4.3(b)-(d) to the flow of photoexcited carriers from
the electrodes into the quantum well. This explanation of the decreased rate
of decay of the photoluminescence at nonzero bias is supported by the recent
work of Vodjdani et al. [7], who studied continuous wave (CW) photolumines-
cence from structures very similar to the ones studied in the present work. By
utilizing photoexcitation energies below and above the quantum well photolu-
minescence energy, they were able to photoexcite only in the electrodes, or in
both the electrodes and the quantum well. For biases near the peak voltage,
they observed that the intensity of the quantum well photoluminescence was the
same for both excitation energies. This result suggests that the majority of the
carriers contributing to the photoluminescence signal originate in the electrodes,
consistent with our conclusion that carriers photoexcited in the electrodes are
important in the time-resolved data for nonzero bias shown in Fig. 4.3. The idea
that significant flow of photoexcited carriers occurs during the photoluminescence
measurement motivated the study of photocurrents in these devices, described in

the following section.

4.3 Photocurrent Measurements

4.3.1 Device Preparation and Current-Voltage Charac-

teristics

Time-resolved photocurrents were studied in three devices with varying bar-
rier thicknesses. The growth of the devices was identical to those described in
Section 4.2.1, except that the top n* layer thicknesses in the present devices
were all 600A. The n+ layer thickness was increased to aid in distribution of

current over the whole mesa area. Three devices, differing only in the thickness

120

of the AlAs barriers, were grown: III-083 with 34A barriers, IIJ-222 with 31A
barriers, and III-221 with 28 A barriers. The processing of the MBE wafers into
devices was somewhat different from the procedure described in Section 4.2.1. In
the present devices, 350 zm mesas with annular AuGe contacts were defined us-
ing liftoff photolithographic techniques. The AuGe thickness was approximately
1000 A, and the inner and outer diameters of the annular contacts were 125 and
275m, respectively. As with the previous device studied by photoluminescence,
no annealing of the contacts was performed, because of the proximity of the
double-barrier device to the surface. Contact resistance did not pose a problem,
resulting only in a series resistance which shifted the peak in the current-voltage
characteristic to higher voltage. The bottom of the substrate was used as the
back contact, and devices were mounted in a TO-5 header using silver paint.
The large area of the annular contact allowed individual mesas to be contacted
by up to three wire bonds, which was important because of the increased current
density in the 28 A-barrier sample.

The current-voltage characteristics at 77 K of the three devices are shown in
Fig. 4.4 for reverse bias (negative bias of the top contact with respect to the back
contact). All three devices shown in Fig. 4.4 show reasonable negative differential
resistance (NDR) characteristics, and the peak current densities increase with
decreasing barrier thickness. The increase in current density with decreasing
barrier thickness is quantitatively in good agreement with the tunneling times
measured in Chapter 2. The current densities and inverse tunneling times are
expected to follow the same trend with barrier thickness because they both reflect
the energy width of the quasi-bound state in the quantum well. This agreement
confirms that the barrier thicknesses in the three samples vary as expected from
the nominal growth parameters. It can be seen in Fig. 4.4 that the peak current

shifts to higher voltages as the barriers become thinner. This trend is due to

121

Voltage (V)

-3.0 -25 -2.0 -15 -10 -05 0

-3.0 -25 -20 -15 -10 -05 0

(b)

. . i . 1 1 7)
(c)
/ r - 150

- - 300

(_w9/y) Ajisuag juading

Figure 4.4: Current-voltage characteristics in reverse bias for the three devices
studied, at 77K. (a) III-083 (34 A barriers), (b) III-222 (31 A barriers), (c) III-221
(28 A barriers). The peak current density increases with decreasing barrier thick-
ness, quantitatively as expected. The effect of series resistance of the top contact
can be seen, as the peak voltage shifts to progressively higher voltages. Negative

bias corresponds to the flow of electrons into the top of the mesa.

122

series resistance in the nonannealed top contacts, which becomes increasingly
important with higher current densities. To check that the current in the mesa
samples with annular top contacts was flowing over the whole mesa area, variable
size mesas with thick AuGe top contacts were fabricated. The peak currents in
the variable size mesas scaled well with area, and the current densities in the
devices with annular contacts were in good agreement with the current densities

observed with variable size mesas.

4.3.2. Experimental Apparatus

The photocurrent measurements were made at 80 K, with the devices mounted
in a helium immersion dewar, modified to allow electrical contacts to the device
while mounted in the dewar. As in the photoluminescence excitation correlation
spectroscopy (PECS) technique described in Section 2.2, the output from the col-
liding pulse mode-locked (CPM) dye laser was split into two pulse trains of equal
amplitude. Each pulse train was mechanically chopped at a different frequency,
and the beams were recombined with a variable delay time 7 between them. The
recombined beam was focused to a 40 zm diameter spot in the center of the mesa.

The arrangement used for the electrical biasing and photocurrent detection
is shown schematically in Fig. 4.5. Electrical bias across the device was provided
by a Hewlett Packard model 6115A precision constant voltage source labelled
VS. The current flow to the device was measured with an Ithaco 1211 current-to-
voltage preamplifier labelled PA, in series with the voltage source. Because the
current-to-voltage preamplifier was limited to a current of 10mA, and the total
currents through the 350m mesas were as large as 400mA, it was necessary
to use a constant current source IS to bypass most of the DC current around

the current-to-voltage amplifier. A Keithley 220 current source was used for

123

aw Optical Dewar

Input from laser
and interferometer

= vs
IS

“Oy

+} j= foum= f,+
\PA _t
AWA ,

ref
™ mm 6ULLA

Figure 4.5: Experimental arrangement for photocurrent experiment. Constant
voltage bias is provided to the double-barrier device, which is mounted in an
optical dewar, by the precision constant voltage source VS. The photocurrent
is monitored using the current-to-voltage preamplifier PA, and the output is
detected by the lock-in amplifier LA. DC current bypass around the preamplifier

is provided by the constant current source IS.

124

some measurements, but measurements on the higher current devices required the
construction of a high-current constant current source using standard high power
bipolar transistors. For a given bias voltage, the current source was adjusted
so that the current preamplifier operated in its linear range. The output of the
preamplifier was detected by the lock-in amplifier labelled LA. The reference
signal for the lock-in amplifier was obtained by combining the reference signals
from the two choppers using a simple TTL “AND” gate, and recovering the
sum-frequency component with a frequency-selective amplifier.

The simplicity of the experimental apparatus in Fig. 4.5 is to be contrasted
with the setup required for the all-optical measurements described in Chapter 2,
or for electrooptic sampling measurements. All electronics used are low frequency,
and it is not necessary to collect luminescence from the sample or to use a spec-

trometer.

4.3.3 Results

The dependence of the sum-frequency photocurrent upon delay for sample
III-221 (28A barriers) at -2.4V is shown in Fig. 4.6. The real and imaginary
parts of the photocurrent signal are shown in Fig. 4.6 as solid and dashed lines,
respectively, defined with respect to an arbitrary absolute phase. The sum fre-
quency photocurrent signal is on the order of a few microamperes in this scan,
which was taken with an optical power of 0.75mW per beam after chopping.
The DC photocurrent is much larger, and is on the order of 800A (with both
chopped beams on the sample) at a bias of -2.4 V.

As seen in Fig. 4.6 both the real and imaginary parts show significant varia-
tion over the +500 ps delay accessible experimentally. This is in contrast to the

only previous study of photocurrents using this technique, in which no change

125

Sum Photocurrent (A)

-500 -—250 0 250 500
Delay (ps)

Figure 4.6: Typical sum-frequency photocurrent delay scan, for sample III-221
(28 A barriers) at a bias of -2.4V. The real and imaginary parts of the photocur-
rent, defined with respect to an arbitrary absolute phase, are shown as solid and
dashed lines, respectively, where the lines connect the experimental points to aid
the eye. The slight asymmetry with respect to zero delay seen in the imaginary

component is attributed to noise in the phase of the detected photocurrent.

126

of the sum-frequency signal with delay was reported [6]. A coherence peak is
seen in both scans at zero delay, due to optical interference of the pump laser
pulses. The real part of the signal shown in Fig. 4.6 can be described as a sum
of a constant and an exponential with a time constant on the order of 200 ps.
Optical measurements, presented in Chapter 2, of a similar undoped sample with
28 A barriers showed a tunneling escape time of 236 + 20 ps, and suggest that
the observed decay of the photocurrent signal may coincide with the time for a
tunneling process in the sample.

It can be seen in Fig. 4.6 that the signal is mostly real at long delay, and
mostly imaginary for zero delay. The only quantity which was varied during the
measurement was the position of the moveable arm of the interferometer used to
delay the pulses with respect to each other. Similar changes in phase with delay
were observed in the same sample at other bias voltages, and in other samples with
differing barrier thicknesses. The change from predominantly real to imaginary
was not always as pronounced as in Fig. 4.6, but was a reproducible effect. The
fact that the time-varying component of the real part of the photocurrent seen
in Fig. 4.6 decays to a nonzero background suggests that the photocurrent signal
at the sum frequency consists of signals with two different origins. The variation
of the phase with delay suggests that the two signals are out of phase with each
other by approximately 90 degrees, which may reflect the difference between
resistive and reactive responses. The phase of the total signal then depends upon
the relative amplitudes of the two components, which varies with delay. As the
two chopping frequencies used in this experiment are 1600 and 2000 Hz, the sum
frequency of 3600 Hz has a period of 280 ys. A phase shift of 90 degrees at this
frequency corresponds to a time delay between the two processes of one quarter
of a period, or 70 ws. The origin of such a long delay in this structure is not clear.

However, in photocurrent studies of doped GalnAs/InP superlattices, Ripamonti

127

et al. [13] observed transient photocurrents with a time constant of 200 ps at 80 K,
which they attributed to the presence of traps in the n regions of their devices
(including InP and the superlattice layers). He and coworkers [14] have also
considered the effects of capture of photoelectrons in Si-doped GaAs/Al,Ga,_,As
heterostructures, upon persistent photocurrent decay, in which very long time
constants were observed. These mechanisms involving traps may be responsible
for the component of the photocurrent that has a very long time delay.

The dependence upon bias of the real part of the sum-frequency photocurrent
for sample II]-221 is shown in Fig. 4.7, defined with respect to the same absolute
phase as in Fig. 4.6. The scans are all shown on the same scale, but are offset
vertically for clarity. The coherence peak is seen in all scans, although for -2.4 V
it is opposite in sign to the peak seen in the other scans. It can be seen that
at some biases, there is very little change of the photocurrent signal with delay,
and in other cases, there is significant decay over the +500 ps of delay shown.
The greatest decay occurs for a bias voltage of approximately -0.3 V, and then
decreases with increasing reverse bias. The bias of -0.3 V can be seen, from the
current-voltage characteristic shown in Fig. 4.4(c), to correspond to a bias voltage
near the threshold for the tunneling current. For biases past the peak voltage
of -2.0 V, the variation of the signal with delay is inverted, as seen in the scan
at -2.4V shown in Fig. 4.7. No further qualitative changes were observed with
increasing bias.

The qualitative behavior seen in Fig. 4.7 is reproduced in all three of the
samples: there is little decay at low bias, a pronounced decay near the turn-on
in tunneling current, little decay between the turn-on and the peak, and pro-
nounced decay again with bias greater than the peak voltage. To compare delay
scans from the three samples, we show in Fig. 4.8 photocurrent delay scans for

the three samples studied, at bias voltages greater (i.e., more negative) than the

128

Photocurrent Amplitude (a.u.)

—0.3V
~_ -0.1V
-500 -250 0 250 500

Delay (ps)

Figure 4.7: The real part of the sum-frequency photocurrent as a function of
delay, for sample IIJ-221 (28A barriers), as a function of bias. All scans are
shown with the same vertical scale, but have been offset vertically for clarity.
The solid lines connect the experimental points to guide the eye. The amount
of decay varies with bias, showing pronounced decay at -0.3V and -2.4V. The
photocurrent for -2.4. V, which corresponds to bias greater than the peak voltage,

shows inverted behavior with respect to that seen at lower biases.

129

peak voltage. The decay behaviors seen in the three scans are quite different.
While the scans shown in Figs. 4.8(b) and (c), (for samples with 31 and 28A
barriers, respectively) show a signal which can be described by a constant plus
an exponential with a time constant on the order of 200 ps, the scan shown in
Fig. 4.8(a) can only be fitted by a constant and an exponential with a time con-
stant long compared to 500 ps. The differing decay behavior may be indicative
of the differing tunneling times in the three samples. From the time-resolved
photoluminescence measurements of undoped structures presented in Chapter 2,
the tunneling times for samples with 34, 31, and 28A barriers are expected to
be approximately 800, 440, and 240 ps, respectively. Fits of an exponential plus
a constant to the data shown in Fig. 4.8 give good agreement between the pho-
tocurrent decay times, and the photoluminescence decay times, for the samples
with 34 and 28 A barriers, shown in Figs. 4.8(a) and (c), respectively. However,
the time required to fit to the photocurrent decay for the sample with 31 A barri-
ers is on the order of 200 ps, which differs considerably from the tunneling escape

time of 440 ps expected from photoluminescence decay.

4.3.4 Discussion

The photocurrent data clearly show that a photocurrent signal is observed
at the sum chopping frequency, and that this photocurrent depends upon bias
and sample parameters. The observation of a sum-frequency photocurrent sig-
nal indicates that the photocurrent responses to the photoexcitation at the two
chopping frequencies, f,; and f2, are not independent.* Thus, the magnitude of

the sum-frequency photocurrent is a measure of the influence of the presence of

“If the responses were independent, then the only frequency components in the detected

photocurrent would be at the two chopping frequencies f, and fo.

130

oO a
—G 4
(a)
$ -12{ . \ :
" —500 —250 re) 250 500
ue}
a. 8
7 6
Soa
Sy 4 l I L
ba
9 -500 —250 0) 250 500
pe)
el 4 q EJ * i

—500 —250 0 250 500

Delay (ps)

Figure 4.8: Comparative sum-frequency photocurrent delay scans at biases
greater than the peak voltage. (a) III-083 (34 A barriers), (b) III-222 (31 A bar-
riers), (c) III-221 (28 A barriers). The differing decay behavior may be indicative
of the differing tunneling times in the three samples, which are expected, from
the measurements of undoped structures presented in Chapter 2, to be approx-
imately 800, 440, and 240 ps for (a), (b), and (c), respectively. The agreement
between the photoluminescence time constants and the decay behavior is quite

good for (a) and (c), but not for (b).

131

photocarriers excited by one pulse train, at frequency f,, for example, upon the
current due to photocarriers excited by the other pulse train at frequency fo.
The observation of a sum-frequency photocurrent means that we can mea-
sure the interaction between the two sets of photocarriers. We now consider the
dependence of the sum-frequency photocurrent upon delay, to see why the exper-
imental data might be expected to change with increasing delay between the two
pulse trains. With an excitation photon energy of 2eV, carriers are photoexcited
throughout the GaAs electrodes, and in the quantum well of the double-barrier
device. Taking the absorption length to be approximately 0.25m for GaAs at
this energy [8], we note that significant carrier densities will be photoexcited to
a depth from the surface of a few times the absorption length, which is on the
order of 0.5 to 1 zm in this case. In principle, the interaction of the photocarriers
from the two pulse trains occurs over the entire photoexcited volume. It is likely,
however, that the interaction is strongest in regions in the device where accumu-
lations of carriers, or large electric fields which separate photoexcited electrons
and holes, are present. If we assume that the interaction region is confined to
a single location, then we can form a simple picture of why the sum-frequency
photocurrent might vary with delay between the two pulses. If the lifetime of
photoexcited electrons and/or holes in this localized interaction region is rT, then
the effect of photocarriers from the first pulse train will be negligible if the sec-
ond pulse train is delayed by significantly more than 7. This is exactly what
happens in the PECS photoluminescence experiment used in Chapter 2. In the
photoluminescence experiment, the carriers photoexcited by the two pulse trains
interact via the two-particle nature of the photoluminescence process. When the
delay between the two pulse trains is greater than both the electron and the hole
escape times, then there is no interaction of the photocarriers excited by the two

pulse trains, and no sum-frequency photoluminescence signal is detected. Simply

132

stated, the photoexcited carriers from the two pulse trains never coexist in the
region of interaction, which is the quantum well in this case. A similar effect
could be responsible for the variation of the sum-frequency photocurrent with
delay presented above. The time for decay of the sum-frequency photocurrent
would be the time required for photocarriers to escape from the region in which
they influence the photocurrent from the delayed pulse train. Possible mecha-
nisms for the interaction of the two pulse trains, and their relation to tunneling
times, will be considered further in the following paragraphs.

To consider one of several possible mechanisms for the interaction of the
carriers that would lead to a sum-frequency photocurrent, we show in Fig. 4.9(a)
the conduction band profile, for sample III-083. The profile was calculated using
the Thomas-Fermi approximation and solving the Poisson equation at a bias of
-0.25 V. The quasi- Fermi levels in the left and right electrodes are assumed to be
constant, up to the undoped double-barrier region, and are indicated in Fig. 4.9(a)
by dot-dashed lines. The surface of the device is located at -900 A in Fig. 4.9(a),
and we have neglected the effect of surface depletion in this calculation. The
depicted bias level of -0.25 V corresponds to the threshold in the current-voltage
curves of Fig. 4.4. At this bias, current flow in the absence of photoexcitation is
low, and is due to the few electrons in the injecting electrode with sufficiently high
kinetic energy to allow tunneling through the quasi-bound state in the quantum
well. In Fig. 4.9(b), we show a magnified view of the electron accumulation
region and the quantum well. The approximate energy of the confined state in
the quantum well is indicated in Fig. 4.9(b) by a dotted line in the quantum
well, and the dot-dashed line again shows the position of the Fermi level with no
photoexcitation. The electron density will be increased by absorption of photons,
and the quasi-Fermi level that would reflect such an increase in electron density

is shown in Fig. 4.9(b) for excitation by one or two optical pulses, as shown

133

‘el
oo
[2]
—400 oO 400 800
oo (b)
9 iit rait ES J
oo
be
a)
it)
—0.08 a
Legend(Fermi Levels):
Trrtteee 2 beams ;
wees meee 1 beam
one — 0 beams
~0.12 i 1

-—100 (¢) 100
Position (3)

Figure 4.9: (a) Conduction band profile calculated for sample III-221 (28 A bar-
riers) at a bias of -0.25 V, neglecting depletion at the surface which is at -900 A.
The dot-dashed line indicates the positions of the quasi-Fermi levels in the two
electrodes. (b) Magnified view of the accumulation region. The dotted line shows
the energy level of the quasi-bound state in the quantum well. The quasi-Fermi
levels are shown, as indicated in the legend, for the cases of no photoexcitation,
and immediately after photoexcitation by one or two pulses. The photoexcited
carriers from the first pulse increase the average energy of the carriers photoex-

cited by the second pulse.

134

in the legend to the figure. The increased quasi-Fermi level affects the portion
of the injecting electron distribution with large kinetic energy, increasing the
density of electrons at an energy sufficient to allow tunneling through the quasi-
bound state in the quantum well, and resulting in a photocurrent. In the case of
photoexcitation by two optical pulses, the presence of the electrons photoexcited
by the first pulse results in a higher average kinetic energy for the electrons
excited by the second pulse. This effectively increases the fraction of carriers
from the second pulse that have sufficiently high kinetic energy to tunnel through
the quasi-bound state, and results in a greater photocurrent. This mechanism
would result in an interaction between the two pulse trains, and could explain the
observation of a sum-frequency photocurrent. This explanation is supported by
the fact that the photocurrent scans shown in Fig. 4.7 show pronounced variation
with delay at a bias of -0.3 V, which is very close to the —0.25 V bias illustrated
in Fig. 4.9. We suggest that the mechanism described above could be responsible
for the interaction between the carriers photoexcited by the two pulse trains,
and give rise to the sum-frequency photocurrent data presented in Section 4.3 for
biases near threshold. The additional effects of photoexcitation in the quantum
well region, which were not considered in the above description, could also prove
to be significant.

If, as suggested above, the interaction of the carriers in the tail of the inject-
ing electron distribution is responsible for the observed photocurrent decay, then
the appropriate decay time for the interaction, and therefore the sum-frequency
photocurrent, would be the time required for electrons to tunnel from the inject-
ing electrode through the double-barrier. This would mean that measurements
of the photocurrent decay would reflect the tunneling times in the structures,
and explain the similarity between the photocurrent decay times and photolu-

minescence decay times. It is also possible that the same approach would be

135

successful in many other tunneling structures, such as single barrier [9, 10] or
interband tunnel structures [11, 12], which are difficult or impossible to study us-
ing time-resolved photoluminescence. The possibility of using the photocurrent
technique presented above to study the dynamics of tunneling in these structures
suggests that further study of this photocurrent technique could be very fruit-
ful. There are several remaining questions that must be answered regarding the
interpretation of data from this type of experiment. For instance, we have only
considered one possible mechanism for interaction between the two pulse trains.
Others that could be important are interaction in the quantum well, interaction
in the surface depletion region, and effects analogous to those described above for
the holes photoexcited on the substrate side of the double-barrier. The possible
importance of trapping processes, which could be responsible for a component of
the photocurrent that is delayed with respect to excitation by long times, and
give rise to the varying phase with delay seen in the photocurrent data shown in
Fig. 4.6, must also be considered.

As with many correlation techniques, this time-resolved photocurrent exper-
iment is fairly simple. A thorough understanding of the interaction process is
necessary, however, in order to interpret the sum-frequency data obtained, and
this will require a more detailed study of the processes important to the pho-

tocurrents in the double-barrier devices studied.

4.4 Conclusions

We have presented a study of time-resolved photoluminescence and pho-
tocurrent in electrically biased GaAs/AlAs/GaAs/AlAs/GaAs double-barrier
heterostructures. As expected, the time-resolved photoluminescence from the

quantum well region shows a decay time at zero bias that is comparable to sim-

136

ilar measurements in undoped structures. However, the behavior with nonzero
bias is quite different. Little decay of the quantum well photoluminescence with
delay is observed, due to the flow of photoexcited electrons and/or holes from
the electrodes into the quantum well. The photocurrents due to the flow of the
photoexcited carriers were studied using a time-resolved photocurrent technique,
analogous to the PECS photoluminescence technique described in Chapter 2. Us-
ing this technique, photocurrents were measured during photoexcitation by two
mechanically chopped optical pulse trains, delayed with respect to each other by
a variable time y. Small photocurrent signals were observed at the sum chopping
frequency, and were seen to vary with time delay 7, bias voltage, and sample
parameters. The time constants extracted from the decay of the sum-frequency
photocurrents are similar to the tunneling times measured in undoped structures,
although detailed agreement is obtained only for two of the three samples stud-
ied. A possible explanation for the observation in the photocurrent of a decay
time related to the tunneling time was presented, suggesting that the technique
could be used to study other tunneling devices that cannot be studied by photo-

luminescence.

137

References

[1]

[2]

[3]

[5]

[6]
[7]

J.F. Whitaker, G.A. Mourou, T.C.L.G. Sollner, and W.D. Goodhue, Appl.
Phys. Lett. 53, 385 (1988).

S.K. Diamond, E. Ozbay, M.J.W. Rodwell, D.M. Bloom, Y.C. Pao, E.
Wolak, and J.S. Harris, in OSA Proceedings on Picosecond Electronics and
Optoelectronics, Vol. 4 of the OSA Proceeding Series, T.C.L.G. Sollner and
D.M. Bloom, eds. (Optical Society of America, Washington, D.C., 1989),
p. 101.

T.B. Norris, X.J. Song, W.J. Schaff, L.F. Eastman, G. Wicks, and G.A.
Mourou, Appl. Phys. Lett. 54, 60 (1989).

D.Y. Oberli, J. Shah, B. Deveaud, and T.C. Damen, in OSA Proceedings on
Picosecond Electronics and Optoelectronics, Vol. 4 of the OSA Proceeding
Series, T.C.L.G. Sollner and D.M. Bloom, eds. (Optical Society of America,
Washington, D.C., 1989), p. 94.

H.W. Liv, R. Ferreira, G. Bastard, C. Delalande, J.F. Palmier, and B. Eti-
enne, Appl. Phys. Lett. 54, 2082 (1989).

F. Sasaki and Y. Masumoto, Phys. Rev. B 40, 3996 (1989).

N. Vodjdani, D. Cote, D. Thomas, B. Sermage, P. Bois, E. Costard, and J.
Nagle, Appl. Phys. Lett. 56, 33 (1990).

138

(8] M. Cardona and G. Harbeke, J. Appl. Phys. 34, 813 (1963).

[9] D.H. Chow, T.C. McGill, I.K. Sou, J.P. Faurie, and C.W. Nieh, Appl. Phys.
Lett. 52, 54 (1987).

[10] J.R. Séderstr6m, D.H. Chow, and T.C. McGill, Appl. Phys. Lett. 55, 1348
(1989).

[11] M. Sweeny and J. Xu, Appl. Phys. Lett. 54, 546 (1989).

[12] J.R. Séderstrom, D.H. Chow, and T.C. McGill, Appl. Phys. Lett. 55, 1094
(1989).

[13] G. Ripamonti, F. Capasso, and W.T. Tsang, J. Appl. Phys. 67, 583 (1989).

[14] L.X. He, K.P. Martin, and R.J. Higgins, Phys. Rev. B 36, 6508 (1987).

139

Chapter 5

Raman Scattering

Determination of Strain in

CdTe/ZnTe Superlattices

5.1 Introduction

5.1.1 Background

As discussed in Chapter 1, wide bandgap II-VI semiconductors are of interest
because of their potential use as visible light emitters, with application to short
wavelength optical storage and printing. The difficulties involved in doping these
materials both p- and n-type to useful densities have hindered the development
of homojunction devices. This has stimulated interest in heterojunction devices,
such as superlattices [1]. CdTe/ZnTe is one system that has attracted atten-
tion as the two materials can be usefully doped opposite types and are readily
grown by molecular beam epitaxy (MBE) [2] or organometallic vapour phase ex-

pitaxy (OMVPE) [3]. Previous work has shown that CdTe/ZnTe superlattices

140

display intense, visible photoluminescence which is orders of magnitude brighter
than that from corresponding Cd,Zn,_,Te alloys [4], while Cdo.25Zno,75Te/ZnTe
superlattices have recently demonstrated optically pumped, visible-wavelength,
lasing at room temperature [5].

An important issue in the fabrication of CdTe/ZnTe heterostructures is the
accommodation by elastic strain of the large 6% lattice mismatch between the
two bulk materials, without formation of significant densities of defects. Methods
which have been used to determine the strain configuration include photolumi-
nescence (PL) [4], x-ray diffraction [6], in-sztu reflection high energy electron
diffraction (RHEED) [6, 7], transmission electron microscopy (TEM) [8], and
resonance Raman scattering [9]. In this chapter we present a study of strain in

four CdTe/ZnTe superlattices by Raman scattering.

5.1.2 Summary of Results

The strain configuration in CdTe/ZnTe strained-layer superlattices has been
measured by Raman scattering near resonance. The ZnTe-like longitudinal opti-
cal phonon energy in the superlattice is significantly shifted from the bulk value to
lower energies, and the shift increases with increasing superlattice CdTe fraction.
Unlike previous photoluminescence studies of the same samples(4] in which it was
not possible to distinguish between unstrained and free-standing strain configura-
tions, the Raman scattering data indicate that the superlattices are significantly
strained. The observed shifts agree with calculations of strain shifts based on a
free-standing strain distribution, and are consistent with previous studies using
X-ray diffraction. In the free-standing strain distribution, the superlattices adopt
an in-plane lattice constant that minimizes the strain energy of the superlattice,

and is independent of the buffer layer upon which they are grown.

141

5.1.3 Outline of Chapter

In Section 5.2 we describe the superlattice samples. Section 5.3 describes
the experimental setup, and Section 5.4 presents the results of measurements of
phonon energies. Section 5.5 presents a discussion of the peak assignments, and

discussion of the phonon energies. Finally, conclusions are summarized in Section

5.6.

5.2 Samples

The samples studied were grown on (100) GaAs substrates by MBE in a Riber
2300. Four samples were studied, with layer thicknesses from 23 to 56 A, grown
on a series of buffer layers that has been described previously [4]. The final buffer
layer was CdTe for three of the samples, and Cdo.4g¢Zno.54Te for the fourth. The
superlattices each consist of 150 to 200 periods, or a total superlattice thickness
between 1.1 and 1.6um. Sample layer thicknesses obtained by x-ray diffraction
and energy dispersive spectroscopy (EDS) in Ref. [6] are listed in Table 5.1, along

with the photoluminescence bandgaps observed at 5 K.

5.3 Experimental Setup

The experimental arrangement used is illustrated schematically in Fig. 5.1.
An argon ion laser pumps a Coherent model 590 continuous (CW) dye laser, which
is operated with the dye 4-dicyanomethylene-2-methyl-6-p-dimethylaminostyryl-
4H-pyran, more commonly referred to as DCM. The dye concentration was 0.38 g/l,
in a solvent consisting of 4.9 parts ethylene glycol and 1 part benzyl alcohol. A
pump power of 5 W was used, with the Argon laser operating on all visible lines,

and an output power of approximately 1W was obtained. The laser energy was

142

Double-pass
Argon spectrometer
Laser
Photomultiplier
Dye _——_————
Laser ———

“uv

Optical Dewar

Figure 5.1: Experimental setup for Raman scattering. The output from the tune-
able, continuous wave (CW) dye laser, is passed through a grating-slit filter, to
remove the fluorescence background, and then focused on the sample. Scattered
light is collected with aberration-corrected lenses, and then dispersed by a dou-
ble-pass spectrometer, which is followed by detection with a GaAs photomultiplier

tube and photon-counting electronics.

143

Sample Superlattice Buffer Layer PL Bandgap LZ, Phonon Energy

(CdTe/ZnTe)
(A) (eV) (cm~*)
1 26/32 CdTe 1.87 202.4 + 0.8
2 35/32 Cdo.seZno.54Te 1.74 199.0 +0.5
3 56/50 CdTe 1.69 199.5 + 1.2
4 31/23 CdTe 1.81 197.4411

Table 5.1: CdTe/ZnTe superlattice sample parameters, observed photolumines-
cence bandgaps and LZ, phonon energies, at 5 K. Samples are ordered by increas-

ing average CdTe content.

tuned with a three plate birefringent tuning element, yielding a linewidth less
than 1.5cm~? for all scans. To remove the fluorescence background, which inter-
feres with the Raman scattering signal, the laser output was passed through a
Spex Lasermate grating-slit filter. This filter, which has a bandpass of 12 A, was
readjusted for maximum throughput every time the dye laser energy was changed.
Experiments were performed in a quasi-backscattering arrangement, with scat-
tered light collected along the [100] growth direction. The incident beam was
polarized along the [010] direction, at an angle outside the crystal of approxi-
mately 15° towards the [010] direction. No polarization analyzers were used on
the collected light. Scattered light was dispersed with a Spex 1404 double pass
spectrometer, and detected by a GaAs photomultiplier tube and photon counting
electronics. In order to attain sufficient resolution to resolve the phonon energies

to within a fraction of a millivolt, narrow spectrometer slit settings are necessary.

144

Because the intensity of the scattered light is very low in Raman scattering, it is
important to couple as much of the scattered light as possible into the spectrom-
eter. The use of precision doublet lenses, which are corrected for aberrations,
and collection optics matched to the fnumber of the spectrometer, were found to
help the signal-to-noise ratio considerably. The incident laser energy for differ-
ent scans was varied from just above the photoluminescence bandgap to higher
energies at which the scattered light became too weak to be detected. All data

were taken at 5K in an atmosphere of helium.

5.4 Results

Typical Raman spectra for the four samples are shown in Fig. 5.2. The
scattered intensity is shown as a function of the energy loss from the incident
laser energy, and is plotted in the range corresponding to single optical-phonon
scattering. The 0.8A resolution of the spectrometer is shown on the plots. All
scans shown in Fig. 5.2 were taken with incident energies near resonance with the
photoluminescence bandgap. It can be seen that the peak occurring at the highest
energy loss shifts to lower energy as the CdTe content progressively increases
from samples 1 to 4. The spectra show up to four peaks or shoulders, with
the maxima in the scattered intensity occurring at the peak with the greatest
energy loss in the scans shown. Peaks occurring at lower energy loss are more
prominent in the spectra for samples 2 and 3. A linear dependence of the scattered
intensity upon pump power was observed over a range of pump powers, confirming
the expected behavior for Raman scattering, and distinguishing the observed
peaks from photoluminescence, which showed a nonlinear dependence upon pump
intensity.

Between five and eleven Raman scans were collected for each sample, with

145

Sample 1, 26/32A
(45% CdTe) H

Sample 2, 35 /32A
(52% CdTe)

Sample 3, 56/50A
(53% CdTe) 7

Sample 4, 31/23A
(57% CdTe) H

Scattered Intensity (a. u.)

130 150 170 190 210

Energy Loss (cm7‘)

Figure 5.2: Representative near-resonance Raman scattering intensity at 5 K ver-
sus energy loss, in the range of single optical-phonon scattering. The peak oc-
curring at the highest energy loss shifts to lower energies as the average CdTe
content increases progressively from samples | to 4, due to the increasing strain
in the ZnTe layers, and shifts the ZnTe-like phonon energy from its bulk value
of 208cm7!. The laser energies for samples 1-4 were 1.965, 1.833, 1.818, and
1.849eV, respectively. The spectrometer resolution, sample layer thicknesses,

and CdTe volume fraction are shown on each plot for reference.

146

varying laser energies. The values of the energy loss at the highest energy-loss
peak in the scattered intensity were averaged for all scans taken on a given sample.
The results are summarized in Table I and plotted in Fig. 5.3 for the four samples.
The positioning of the points along the horizontal axis in Fig. 5.3 is simply to
group the experimental and theoretical results according to the sample, which are
ordered by increasing CdTe fraction. The position of the highest energy-loss peak
clearly varies with the average CdTe content of the superlattice. The observed
energy loss at this peak is the highest in sample 1, which has the lowest average
content of CdTe, and is the lowest in sample 4, which has the highest fraction of
CdTe. Results for samples 2 and 3 fall between those for samples 1 and 4, but
the two are quite close in average composition, and are difficult to distinguish

from each other within the uncertainties in the measured values.

5.5 Discussion

To compare the experimentally observed phonon energies with theory, we
have estimated the expected energies in the superlattice of the lowest confined
longitudinal optical (LO) and transverse optical (TO) phonons propagating in the
growth direction. The energies of phonons in a strained superlattice are affected
by both strain and confinement, but for our structures the main contribution
to the shift from the bulk phonon energies is due to strain, as will be shown
in the following. The energy range of the highest-energy peaks observed is from
approximately 196 to 203 cm~?, which is quite close to the bulk value of 208 cm7!
for the LO phonon in ZnTe [11], and much greater than the value of 170 cm7!
for the LO phonon in CdTe [11]. We have therefore confined our attention to the
ZnTe-like phonons, i.e., phonons confined in the ZnTe layers. Estimates of the

effects of confinement on the LZ, mode (the highest-energy confined ZnTe-like

147

-| TJ Expt. GOUnstr.TO s«Str.TO |

=~ 210 7 fe) fo) fe) fe) |

& i I ]

2 200; ° ex el ,

> 5 a
ap
hy

4 190 fF 7

fx — a = a

180+ oO oO o o

a en A, Oy A, Se 4

#1 #2 #3 #4
26/32A 35/32A 56/50A 31/23A
(45%) (52%) (53%) (57%)

Sample Number

Figure 5.3: Comparison of theoretical with experimental results for the 4 samples,
which are ordered by increasing CdTe volume fraction. Data points are the
experimentally observed LZ, energies. The circles and squares are the bulk ZnTe
LO and TO energies, respectively. The open symbols are the unstrained energies,
and the filled symbols are calculated for strained bulk with strain appropriate to
the free-standing superlattice. The points are positioned along the horizontal
axis simply to group the experimental and theoretical results according to the

sample.

148

optical phonon) using a simple spring-mass model of the longitudinal phonons
propagating in the growth direction give energy shifts less than 1cm™! for the
samples studied. Confinement effects on the TO-phonon energies are of a similar
magnitude. This small contribution due to confinement has been neglected, which
means that the lowest confined LO and TO phonon energies in the superlattice
will occur approximately at the strained bulk LO and TO energies. The energies
of the LO and TO phonons in strained bulk ZnTe are calculated using the method
of Ref. [10]. From Ref. [9], the phonon deformation constants p and q are related
to the mode Gruneisen parameter y by y = —(p + 2q)/(6w?.) and the shear
deformation parameter a, by a, = (p — q)/(2w7.). We take y = 1.2 and a, = 0.6
[9]. Bulk LO and TO energies are taken from Ref. {11] to be: ZnTe LO, 208 cm7};
ZnTe TO, 180cm~!; CdTe LO, 170cm~!; CdTe TO, 145cm7!.

The phonon energies for strained bulk ZnTe have been calculated for the four
samples. The strain used in the calculation is that appropriate to a free-standing
superlattice, i.e., the in-plane lattice constant is calculated to minimize the
elastic energy of the whole superlattice, independent of the composition of the
buffer layer on which the superlattice is grown. Values of the elastic constants for
CdTe were taken from Ref. [12], and those for ZnTe from Ref. [13]. In Fig. 5.3, we
plot the LO (circles) and TO (squares) ZnTe phonon energies for the four samples.
The open symbols are the bulk unstrained phonon energies from Ref. [11], and
the filled symbols are the bulk strained energies calculated as described above for
a free-standing superlattice.

We assign the highest energy loss peak observed to the first confined ZnTe-like
LO mode, LZ,. As the LZ, mode is expected to have the highest energy of all the
superlattice phonons, assignment of the highest energy loss peak observed to LZ;
is unambiguous. However, assignment of the lower energy loss peaks observed is

much less certain, as they occur at energies which could be assigned to various

149

superlattice phonon modes. The significant shift of the LZ, energy from the
unstrained value of 208 cm~! indicates that there is significant strain of the ZnTe
layers in the superlattices. Comparing the theoretical estimates of the ZnTe
phonon energies shown in Fig. 5.3 with the observed values, we see that there
is good agreement with the strained LO-phonon energy calculated for the free-
standing strain configuration. This is consistent with previous conclusions(4, 6]
based on photoluminescence and x-ray measurements. If the ZnTe superlattice
layers in our samples were strained to the buffer layer lattice constant, then the
energy of the LZ; phonon would be the same for samples 1, 3, and 4, and would
be much lower than the position observed. The calculated position of the LZ,
phonon for sample 2, if it is assumed to be lattice matched to the Cdo.4gZno.54Te
buffer layer would be 195 cm™', which does not agree with the observed position.

Although interface modes in unstrained superlattices have been studied [14,
15, 16], little work has been done in heavily strained superlattices. In unstrained
superlattices, interface modes are located between the bulk LO and TO energies.
As the highest energy loss peaks observed in our samples occur in the range
between the bulk ZnTe LO and TO energies, where interface modes are expected
to occur, there is a possibility that they are in fact due to an interface mode,
and not to a confined LO mode. If the interface modes in strained superlattices
occur at energies determined solely by the bulk LO and TO phonon energies,
and are independent of the strain, then no shift with increasing average CdTe
content should be observed, which does not agree with the observations. On the
other hand, if the interface modes occur at energies determined by the strained
LO and TO energies, then some dependence on the average CdTe content might
be observed. However, by considering the strained ZnTe LO and TO energies
shown in Fig. 5.3, we see that an interface mode occurring at some position

midway between the two energies would be at an energy consistently lower than

150

the observed peak positions. Hence, we think it unlikely that the highest energy
loss mode observed is an interface mode.

It should be noted that the free-standing strain configuration demonstrated
in this chapter is at variance with results reported in a previous CdTe/ZnTe reso-
nant Raman scattering study [9]. Although direct comparison of the two studies
is complicated by differences in sample thicknesses and growth conditions, previ-
ous structural studies[6] draw into question the conclusions of Ref. [9]. Implicit
in the derivation of strains from Raman peak shifts is the assumption of ho-
mogeneous strains within like superlattice layers. Structural studies [6] of the
superlattices examined here reveal that strain relaxation is not confined to the
superlattice/buffer-layer interface, as growth is highly dislocated and nonuniform
within approximately one-half micron of this interface. However, a substantial
improvement in crystal structure appears beyond this region, as evidenced by
TEM [8], in-situ RHEED [6, 7], and x-ray diffraction measurements [6]. As the
samples used in this study consist of 1.1 to 1.6m thick superlattices, and the
above bandgap light used is sensitive mainly to the surface region, the assumption
of strain homogeneity in this work appears sound. The basis of this assumption
of uniformity is less clear in the work of Ref. [9], however, as the samples studied
were much thinner (less than 0.25ym). Thus, while it is possible that the par-
ticular superlattice layer thicknesses chosen in Ref. [9] yielded one superlattice
that was coherent with the buffer layer, it is unlikely that another superlattice
which was shown to relax had a well-defined strain configuration so close to
the superlattice/buffer-layer interface. The relaxation of a thin superlattice to a
single free-standing lattice constant for all the superlattice layers would require
the nucleation of a large number of defects only at the superlattice/buffer-layer

interface, immediately followed by growth at a single in-plane lattice constant.

151
5.6 Conclusions

In conclusion, we have used near-resonance Raman scattering to measure the
confined ZnTe-like phonon energy in four CdTe/ZnTe superlattices. Observed
phonon energies are shifted from the bulk energies by amounts that increase
with increasing superlattice CdTe content, and indicate that the superlattices
are highly strained. Observed energies are in agreement with calculations of the
expected phonon energies that account for strain, and indicate that the superlat-

tices relax to a free-standing configuration.

152

References

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(1987).

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[3] D. W. Kisker, P. H. Fuoss, J. J. Krajewski, P. M. Amirtharaj, S. Nakahara,
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[4] R. H. Miles, G. Y. Wu, M. B. Johnson, T. C. McGill, J. P. Faurie, and S.
Sivananthan, Appl. Phys. Lett. 48, 1383 (1986).

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[6] R. H. Miles, T. C. McGill, S. Sivananthan, X. Chu, and J. P. Faurie, J. Vac.
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[7] G. Monfroy, X. Chu, M. Lange, and J. P. Faurie (unpublished).
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[9] J. Menéndez, A. Pinczuk, J. P. Valladares, R. D. Feldman, and R. F. Austin,
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154

Appendices

155

Appendix A

Colliding Pulse Mode-Locked

Laser

A.1 Introduction

A.1.1 Background

In this appendix we will discuss the colliding pulse mode-locked (CPM) dye
laser, which is the source of ultrafast pulses used in the work described in this
thesis. Before discussing the CPM, however, we will briefly review sources of
short optical pulses that are currently available. Since the first demonstration in
1960 of lasing action in ruby [1], the laser has proved to be an invaluable tool in
scientific studies, because it provides a unique source of coherent optical radiation.
In 1964 and 1965 it was realized that the longitudinal modes of the laser, could be
locked together (mode-locked) to create short pulses [2]-[4]. By forcing a number
of cavity modes to oscillate with a fixed phase relationship, periodic pulse trains
can be formed with pulse widths inversely proportional to the frequency width

of the laser spectrum. Since 1965 there has been great progress in mode-locking

156

of lasers, and at the present there are a wide variety of techniques used [5]-(7],
which we will examine in the following paragraphs.

Active mode-locking uses external radio-frequency modulation of cavity loss
or phase, with a period corresponding to the round-trip delay for light travelling
around the optical resonator. This type of mode-locking is commonly used in
argon ion, krypton ion, Nd:YAG (trivalent neodymium ions in a host yttrium
aluminum garnet, Y3Al;O2 crystal) or Nd:YLF (neodymium in yttrium lithium
fluoride, LiYF,) lasers, which can produce relatively high average output pow-
ers (1-20 W) with pulse widths on the order of fifty to several hundred picosec-
onds. These lasers operate at a finite number of frequencies, characteristic of the
line spectrum of the gain medium, that cover the range from 1.06 um (Nd:YAG,
Nd:YLF) to the blue region of the spectrum (argon and krypton). Active mode-
locking of semiconductor injection lasers is also possible, and can be achieved
by high-frequency modulation of the drive current, to produce pulses as short as
20 ps [8, 9].

Synchronous pumping is another form of mode-locking, based on periodic op-
tical modulation of the laser gain by another mode-locked laser. The typical
pump laser in such systems is an actively mode-locked ion, or frequency-doubled
Nd:YAG (or Nd: YLF) laser, and the synchronously pumped laser is most often a
dye laser. Mode-locking in these lasers is due to the periodic modulation of the
dye laser gain by the absorption of pump photons, requiring close matching of
the period of the pump laser to that of the dye laser. This stringent matching
requirement is a major practical difficulty with synchronously pumped lasers, and
has prompted some companies to incorporate active cavity length stabilization
schemes in commercial products [10]. The large organic dye molecules used in
such systems have a very wide gain spectrum (extending for example from ap-

proximately 5400 to 6600 A in Rhodamine 6G [11], a typical commercially avail-

157

able dye) which allows formation of very short pulses. In addition to the wide
tunability of any given dye, a great variety of dyes are available spanning the
entire visible spectrum, and extending into the near infrared [12]. Synchronously
pumped dye lasers are tunable over a wide range, produce up to 500 mW average
output power (when pumped by approximately 2 W), and produce pulses as short
as 220 fs [10].

Another approach to mode-locking, which is used to generate the shortest op-
tical pulses, is known as passive mode-locking. Passive mode-locking, which does
not involve any externally modulated elements in the optical cavity, arises from
the presence of a saturable absorber” in the laser cavity. When the cavity starts
lasing, but before mode-locking is established, many longitudinal modes oscillate
with random phase. The randomly oscillating modes will occasionally have a
phase relationship that results in an increased intensity, due to constructive inter-
ference, at the saturable absorber. When this occurs, saturation of the absorber
results in decreased cavity loss, and subsequent increase of the intensity of the
modes that have the phase relationship required to saturate the absorber. This
process continues to preferentially amplify the modes that are phase-locked, and
finally results in stable mode-locking and pulse formation [13]. The advantages of
the passively mode-locked laser include formation of the shortest optical pulses,
tolerance of fluctuations of the total cavity length (in contrast to synchronously
pumped systems), and compatability with CW pumping schemes using lasers, or
flashlamps. Passive mode-locking is used in high-power solid-state lasers such as
ruby [14] and Nd:glass [15], where the output pulse energies can be as large as
10 mJ per pulse with pulse widths of 2 to 20 ps. Passive mode-locking is also used

in dye lasers [16], and has produced pulses as short as 27 fs in the CPM dye laser

“An absorbing dye whose opacity decreases with increasing incident optical power

158

[17]. The main difficulty with passive mode-locking is the required matching of
the nonlinear properties of the saturable absorber to a particular gain medium.
This has limited the spectral range that can be accessed by passively mode-locked
dye lasers to less than that which can be achieved with synchronously pumped
dye lasers. French et al. {18] have developed several dye-absorber combinations
producing pulses shorter than 1 ps and spanning the range from 4900 to 8000 A,
although not all intermediate wavelengths are accessible. In the red to near in-
frared portion of the spectrum, recent developments of the Ti:Al,O3 laser show
great promise. The extremely broad gain spectrum in Ti:Al,O3 covers the entire
range from 6800 A to 1.05ym [19]. Passively mode-locked Ti:Al,03 lasers have
generated 1.4ps pulses using nonlinear optical effects in a fiber-optic external
cavity [20], or 4ps using a saturable dye jet [21]. Finally, passive mode-locking
has been used to produce trains of mode-locked pulses as short as 0.65 ps from
semiconductor diode lasers [22]-|24]. The origin of the saturable nonlinearity used
to cause mode-locking in semiconductor lasers has varied, and has included dark
line defects in the laser caused by aging [22], defects created by intentional proton
bombardment of the laser [23], and multiple quantum wells placed in an external
cavity [24].

In addition to the ability of mode-locked lasers to provide short pulses, the
output from such a laser may subsequently be amplified [25], or modified to
shorten the pulses, or change the wavelength and bandwidth pulses. This al-
lows the production of ultrafast laser pulses with wavelengths, pulse lengths,
and energies unavailable directly from mode-locked lasers. Pulse shortening us-
ing nonlinear properties of optical fibers, in conjunction with diffraction gratings
[26], or diffraction gratings and prisms [27], can significantly reduce optical pulse
widths. The shortest optical pulse ever generated, with a width of 6 fs, was pro-

duced by compressing the output of a CPM dye laser [27]. In addition to the

159

use of nonlinear processes for pulse compression, there are a wide variety of non-
linear optical processes that can be used to shift the wavelength of mode-locked
lasers. For example, second harmonic generation using a mode-locked Nd:YAG
laser operating at 1.06m produces pulses at 5320A, and tripling the output
frequency is also practical. The high peak powers available with mode-locked
lasers make such nonlinear processes quite efficient, and conversion efficiencies
greater than 10% are possible. Similar mixing processes can be used to combine
the output more than one laser (typically a synchronously mode-locked dye laser
and its pump laser), to produce tunable pulses in spectral regions inaccessible
by other means. Parametric oscillators, also based on nonlinear processes, have
been used to generate tunable subpicosecond pulses, and show potential tunabil-
ity over the range from 0.72 to 4.5m [28, 29]. The technique of continuum
generation, based on self-phase modulation in ethylene glycol or water jets, is
a very powerful technique for generation of ultrafast pulses. The pulses created
with this technique are spectrally broadened, possessing components extending
over the entire visible spectrum, while maintaining pulsewidths as short as 80 fs
[30]. These provide a unique source of ultrafast pulses that can be used to make
time-resolved absorption measurements.

In summary, there are many ways of producing short optical pulses by direct
generation using a mode-locked laser. Subsequent modification of a mode-locked
laser output can consist of amplification, pulse compression, or nonlinear conver-
sion to other spectral regions. This field has advanced extremely rapidly in the
last 10 years, and reliable sources of short optical pulses are becoming increasingly

available.

160

A.1.2 Outline of Appendix

The appendix begins with Section A.2, a brief description of the operating
principles of a CPM laser. Section A.3 describes some design considerations for
a CPM laser. Section A.5 presents a detailed procedure for aligning the laser.
Section A.6 describes routine maintenance procedures necessary in day to day

use of the laser, and finally, Section A.7 describes the performance of the laser.

A.2 Operating Principles

The CPM dye laser used in the present work, and described in this appendix,
is a passively mode-locked dye laser. An excellent description of the CPM laser
is presented in Ref. [31], and a more theoretical analysis is given in Refs. [32]
and [33]. The content of these papers will not be reproduced here, but a brief
summary will be presented.

The CPM laser, illustrated in Fig. A.1, uses a ring cavity, a gain dye jet, a
saturable absorber dye jet, and dispersion compensation. Based on the original
demonstration of passive mode-locking of dye lasers by Ippen et al. [16] the CPM
ring resonator was the first to produce pulses shorter than 100 fs [34]. Theoretical
work by Martinez et al. [32, 33] suggested that the proper balancing of self-phase
modulation (SPM), which occurs due to nonlinearities in the dye jets, and group
velocity dispersion (GVD) in the cavity could lead to soliton-like pulse shaping
[36]. Valdmanis et al. demonstrated this behavior, producing pulses as short as
27 fs [17, 31]. One of the important advances was to use a four-prism sequence
[35] to add a continuously adjustable negative group velocity compensation to
the cavity. At the time of writing, the 27 fs pulses produced by the dispersion-

compensated CPM laser are the shortest directly produced by any mode-locked

161

Output Beams
bo.
22cm

54cm
32cm

P2 M2
~ M6

9cm t

{—-————-._ Gain Dye Jet

P3 '

) i

Argon Laser In &

32cm 43cm

—_—————_ Absorber Dye Jet

37cm M3

32cm

Figure A.1: Plan view diagram of the 6-mirror CPM laser (to scale). Mirrors
M1 and M2 (the gain cavity), and mirrors M3 and M4 (the absorber cavity), are
separated by approximately 10 and 5cm, respectively. Prism sequence P1-P4 is
used for group velocity dispersion compensation. The angles formed by the beam
travelling along M2-M1-OC, and M1-M2-M3, are 5°, and angles M2-M3-M4 and
M3-M4-M65 are 7°.

162

laser.

The experiments described in this thesis were performed with two similar
variants of the CPM, one with seven mirrors, and one with six; dispersion com-
pensation was used in some experiments, and not in others. The most satisfactory
operation of the laser was obtained with the dispersion compensated 6-mirror cav-
ity shown in plan view in Fig. A.1. The entire CPM laser is mounted on a 2x4 ft
optical breadboard. The two dye jets flow from stainless steel nozzles, and fall
vertically through holes in the optical breadboard where they are collected and
recirculated continuously. The output at 5145 A of a CW argon ion laser is di-
rected by flat mirror M7, and focused onto the gain dye jet by mirror M6 (radius
R=10cm). The pump laser is polarized parallel to the optical breadboard, and
the dye and absorber jets are both oriented at Brewster’s angle with respect to
the intracavity beam. Both M6 and M7 are coated for peak reflectivity at 5145 A
and normal incidence. The cavity formed around the gain jet by mirrors M1 and
M2 (R=10 cm each) serves to focus the intracavity beam to a waist at the gain jet
that is coincident with the pump beam. Mirrors M4 and M5 (R=5cm) similarly
focus the intracavity beam to a waist at the absorber jet, with the shorter focal
length of the pair resulting in a smaller beam waist at the absorber than the gain
jet. Mirror M5 is a high reflector (HR) and the partially transmissive output
coupler OC couples a small fraction of the intracavity beam out of the laser. Sev-
eral values of the output coupler transmission were used, but the most reliable
operation was obtained with 2% transmission. With higher output coupler trans-
mission, the output power for a given intracavity intensity is higher; however, the
additional loss makes it increasingly difficult to achieve high enough intracavity
intensities to cause the nonlinearities necessary for mode-locking. Although mul-
tistack dielectric mirror coatings are normally used to give high reflectivity over

a wide bandwidth, the dispersion caused by these mirrors result in pulse broad-

163

ening in the CPM [31]. Accordingly, single stack dielectric coatings were used
for all intracavity mirrors, optimized for peak reflectivity at 6328 A and normal
incidence. Prism sequence P1-P4 is used to provide adjustable group velocity
dispersion. The four-prism sequence provides a net negative group velocity dis-
persion (GVD), because of the geometrical arrangement of the prisms [35]. In
addition, the material dispersion of the prisms (which are made from Schlieren
grade fused silica) results in positive GVD proportional to the distance the in-
tracavity beam travels through the prism material. Since both prism faces are
oriented at Brewster’s angle to the intracavity beam, the prism may be translated
perpendicular to their base without producing deviation of the intracavity beam.
This allows a variable amount of prism material to be added to the cavity, by
translating one of the prisms perpendicular to its base, while lasing is sustained.
This enables continuous adjustment of the total cavity GVD for formation of the
shortest pulses, or the greatest stability.

During mode-locked operation, the intracavity beam in the laser consists of
two counterpropagating pulses, which collide at the absorber jet, once per round-
trip. The pulse formation process that leads to stable mode-locking in the CPM is
quite complex, and is similar to soliton propagation in optical fibers [36]. The self-
phase modulation (SPM) in the dye jets, combined with the appropriate GVD,
leads to stable formation of short pulses. As with solitons in optical fibers, stable
pulse shortening (and mode-locking) is only possible for negative GVD, and the
correct adjustment of the intracavity prism material is crucial to stable operation
of the laser. A highly asymmetric dependence of pulse formation upon the sign of
the GVD is observed in such lasers, and no stable formation of pulses is possible
if the net GVD is positive [31]. This characteristic behavior is easily observed
in the laser spectrum, which becomes progressively wider (indicating narrowing

of the pulses) as the GVD is made more positive, until the shortest pulses are

164

formed. Further positive GVD results in an abrupt shift of the laser spectrum,
and disappearance of the laser autocorrelation trace, which are indicative of loss

of mode-locking.

A.3 Design Considerations

In this section we will discuss some aspects of the implementation of a CPM
laser. The 6-mirror CPM laser was constructed by modifying a 7-mirror CPM
constructed by M.B. Johnson [37]. Many of the aspects of the design were well
described in Ref. [37], and will not be reproduced here. We will concentrate upon
the modifications made to the laser, and the rationale behind them.

One of the main reasons for choosing the 6-mirror cavity was because of dif-
ficulties in obtaining a symmetrical and stable Gaussian spatial mode with the
7-mirror cavity. Stable transverse mode formation, which is essential for the
PECS measurements described in Chapter 2, is easier in the 6-mirror CPM be-
cause of decreased astigmatism (31, 38]. The astigmatism in the CPM originates
in the use of spherical lenses for off-axis focusing in the dye and absorber cavities
formed by M1 and M2, and M3 and M4, respectively. This off-axis placement
leads to astigmatism because rays in the saggital and tangential planes are fo-
cused at different points [39]. In CW dye laser cavities, this astigmatism can be
corrected by the presence of the dye jet, which is also asymmetrical with respect
to interchange of the tangential and saggital planes [40]. Such compensation is
not possible in the CPM, because of thin dye and absorber jets necessary for
mode-locked operation and formation of short pulses. Therefore, in a CPM it is
important to use the spherical mirrors as close to normal incidence as possible,
by reducing the fold angles around the dye and absorber cavities as much as

possible. Because the radius of curvature is smaller in the absorber cavity (M3

165

and M4), the astigmatism is more severe than at the gain jet. The minimum fold
angles are determined by the requirement for clearance of the collimated beams
(between M2 and M3, and between M4 and M5) around the absorber jet. The
coma-compensated absorber cavity in the 6-mirror CPM allows the absorber jet
to be placed asymmetrically, using a portion of the jet closer to the edge, and
thus allows smaller fold angles than the “Z” absorber cavity used in the 7-mirror
CPM.

In addition to the reduced astigmatism possible with the 6-mirror CPM, there
are other cavity parameters that affect the spatial mode of the laser. In order to
achieve efficient coupling of the pump laser to the intracavity mode, it is necessary
to focus the pump to a small spot on the gain jet. This results in heating of the
ethylene glycol solvent, and thermal lensing (also known as thermal blooming
because of the increased size of the transmitted pump spot at the onset of thermal
effects). This thermal lensing that occurs in the gain jet can affect the alignment
of the optical resonator. It is necessary, then, to align the resonator using low
pump powers (1-2 W), where thermal lensing is less important. Finally, when
mode-locking is desired, the pump power is increased to 4-5 W, and the absorber
dye is added. At high pump power, and in the absence of the absorber dye, the
spatial mode of the laser will be asymmetrical and poor, because of the thermal
blooming. However, addition of the absorber improves the mode dramatically,
and the same spatial mode obtained at low powers in the alignment procedure
can be recovered when pumping at high powers. This is because the Gaussian
intracavity beam profile saturates the absorber dye more at the center of the
beam than at the edges, resulting in a “soft aperture” around the beam at the
absorber jet, which controls the spatial mode very nicely.

In addition to problems with the spatial mode, fluctuations in the output

power, and loss of mode-locking were problems with the laser. In a properly

166

constructed CPM, the main sources of noise are the pump laser fluctuations, and
mechanical instabilities of the dye jets [41]. In order to reduce instabilities in the
dye jets, it is important to pay attention to the pumping mechanism, and the
manner in which the flowing dye is collected after the dye nozzle. The pumping
scheme used, described in detail in Ref. [37], involves pulsation dampening, and
dye accumulation. This was modified somewhat in the present work by mechan-
ically isolating the pulsation dampener and accumulator from the vibrations of
the pump motor. It has been suggested [38, 41, 42] that the correct design of the
dye catching tube is important. This is necessary in order both to avoid foaming
of the dye upon contact with the catcher tube, and also to create a stable flow
pattern that does not suffer from instabilities. To accomplish this, custom-made
glass catching tubes were fabricated, paying particular attention to the smooth
flow of dye from the point where it strikes the surface of the glass. The nozzles
used to create the dye jet have an opening approximately 0.3x2 mm (gain jet)
and 0.12x2mm (absorber jet). This produces a thin flat jet that flares out in
width after exiting the nozzle. Further from the nozzle, a series of nodes and
antinodes are formed, where the jet changes both in width and the orientation of
the flat surface. To minimize instabilities, the glass catching tube was positioned
so that the dye jet struck the tube at a glancing angle, and at a node in the jet
flow pattern.

The use of a 6-mirror CPM required some design changes in the optics and
the optical mounts. In order to reduce the “Z” fold angles in the gain cavity (M1
and M2), and keep the pump and intracavity beams as close to collinear as pos-
sible, mirror M2 was cut in half, yielding a D-shaped mirror approximately 7mm
across. Because mirrors M1 through M4 are only adjusted infrequently, and to
prevent accidental misalignment, these mirrors were mounted in Newport OEM

mounts, which are adjusted by set screws. Although this complicates the align-

167

ment procedure somewhat compared to precision micrometer mounts, it reduces
any subsequent temptation to readjust these mirrors once they are correctly set.
These mounts are also much more compact, and cheaper than precision mounts.
Mirrors M1-M4 were all mounted on translation stages, that allowed the motion
of the mirrors towards the dye jet, which is essential in alignment of the laser.
In particular, it was found to be helpful to have M2 mounted on such a stage, to
allow adjustment of the resonator mirrors while leaving the focusing of the pump
laser (by M6) and the position of the gain jet unperturbed.

A recurring problem with the CPM was the accumulation of dust on the optics,
due to the fairly high levels of dust in the laboratory. This caused problems when
dust particles landed on the optics, which occasionally resulted in diffraction of
the intracavity beam, and affected operation of the laser. Because this problem
was fairly common, and nearly impossible to diagnose, the entire 2x4 ft optical
breadboard was mounted under a Dexon filtered blower. The blower and filter
were mounted to the laboratory roof using unistrut beams, and plastic curtains
were hung from the blower to the breadboard. This approach solved the problem
with dust, which greatly reduced the required amount of cleaning of optics (along
with the associated misalignment and wear). However, the high air flow was
found to affect the jets, and resulted in a fluctuations in the jet positions. This
effect was minimized by reducing the airflow to the absolute minimum required
to exclude dust, which was easily determined during operation due to scattering

of the intracavity beam by the dust.

A.4 Diagnostic Equipment

Several pieces of equipment are useful in diagnosis of the CPM. In order to ob-

serve the spatial mode, one or more lenses are used to magnify the output of the

168

laser, and project the magnified image upon a screen or wall. It is most helpful
if the magnified mode is quite large (20-40 cm in diameter) and easily accessible
for close inspection and measurement. As will be described in Section A.5, the
adjustment of the gain and absorber cavity mirror separation affects the size of
the mode, and detailed observations of the size, shape, and stability of the mode
during alignment are essential. Perhaps the most powerful diagnostic tool, and
also one of the simplest, is a diffraction grating, arranged to project the laser
spectrum onto a screen or wall. The wavelength scale of diffracted pattern can
be calibrated, and serves both as an indication of whether mode-locking is occur-
ring, and of the length of the pulse. A photodiode with sufficiently fast response
to resolve pulses separated by the cavity round trip time of 10ns is useful, and is
routinely monitored during laser operation. This allows the detection of “double-
pulsing,” where mode-locking is incomplete and pulses are formed in the cavity
at twice the round trip frequency, as well as loss of mode-locking. The photo-
diode also allows observation of rapid (1-50 Hz) fluctuations in the laser output
power. Finally, an autocorrelator is useful for absolute calibration of the laser
pulsewidth, and as a check of proper mode-locking. The autocorrelator used in
the present work was constructed using a stepper motor to adjust the length of
the moveable arm of the interferometer, and the autocorrelation was obtained by
recombining the beams in KDP, a crystal used for second-harmonic generation
(SHG). The SHG signal was detected by a photomultiplier tube (after filtering
to remove the red components of the beam), and displayed on an oscilloscope.
The stepper motor was rapidly scanned under control of an IBM PS/2 Model 80
microcomputer, which supplied pulses to the stepper, and also output a voltage
proportional to the stepper position, for the oscilloscope display. The stepper
motor arrangement was sufficiently stable to generate an interferometric auto-

correlation trace [43, 44], while scanning the autocorrelation trace faster than

169

once per second. Metal-coated retroreflectors were used (Newport “BBR”), be-
cause they preserve the polarization of the beam. This is important because the
reflectivity of the beam splitter used is a function of the polarization of the in-
coming light, and rotation of the polarization by solid retroreflector cubes based
on total internal reflection results in differences between the intensities of the
two recombined beams. The degree of mode-locking can be ascertained from the
peak-to-background ratio of the autocorrelation trace [5], and the pulsewidth can
be obtained from the autocorrelation full width at half maximum (assuming a

sech? pulse shape [32, 33]) by dividing by 1.55.

A.5 Alignment Procedure

This alignment procedure is intended to be used only when the laser is aligned
from the very beginning. It is not intended to be performed on a regular basis,
and in fact, a major portion of the development work on this laser was to develop
operating procedures which avoided this tedious alignment procedure. It is pos-
sible to align a CPM laser once, and then routinely replace the dyes and adjust
only the positions of the saturable absorber jet, and the dispersion compensat-
ing prisms, in order to return to standard operating conditions. The routine
maintenance procedures are described in Section A.6.

The final 6-mirror, coma-compensated cavity shown in Fig A.1 is a compli-
cated optical resonator. It contains two dye jets, eight mirrors (six in the cavity,
and two for the pump beam), and four prisms. With z, y, and z translational,
and either two or three rotational degrees of freedom, there are more than fifty
degrees of freedom in the optical alignment alone. In addition, there are dye
concentrations, jet pressures, and the optical pump power. In order to make this

problem manageable, it is necessary to build the final mode-locked laser up from

170

the simplest possible CW laser, in a series of stages. At each stage, it is impor-
tant to focus one’s attention on the correct alignment of a small, manageable
subset of the degrees of freedom, with clear objectives and ways of determining
their achievement. Once a subset of the cavity parameters/positions has been
determined, it is possible to move on to add more components, and for the most

part, to leave settings already determined alone.

A.5.1 Linear Cavity, Gain Only

Alignment commences with the simple linear cavity shown in Fig. A.2(a). At
first, only ethylene glycol (EG) is circulated through the gain jet, at a pressure of
approximately 60 psi. The argon pump (run at a power of 2 W) beam is aligned
from M7 to M6 to be parallel to the optical table. Although it is expected that
best operation be obtained when the pump beam strikes M6 as close to the edge
near M2 as possible, higher output power from the linear cavity was obtained
when the beam struck M6 approximately 1cm from the edge of M2. The same
height from the table used for the pump beam will be used for all beams in the
cavity, and it is helpful to have a metal ruler with a small hole drilled in it at the
height desired. Mirror M6 is adjusted so that the beam is focused slightly before
the jet, and is centered on a flat portion of the jet, avoiding the edges, where the
jet is thicker and more unstable. The dye used was Rhodamine tetrafluoroborate,
a variant of the R6G laser dye (which is based on a chloride version of the same
dye molecule). A sufficient quantity (4g) of Rhodamine dye is dissolved in 200 ml
of methanol, and heated slightly to aid the dissolving of the dye. Once dissolved,
200 ml of EG is added to the mixture, and it is left on a hotplate (at low heat)
for several hours, to evaporate the methanol. This supersaturated stock solution

is then slowly added to the pure EG circulating in the gain jet, until the pump

171

(b)

Figure A.2: CPM configuration during alignment. (a) Linear cavity, (b) Linear
cavity with gain and absorber jets, (c) Ring cavity with gain and absorber. The

figure is drawn approximately to scale.

172

laser transmission is 5%. It is important to check the shape of the transmitted
pump beam to ensure that no evidence of thermal lensing is evident at this stage.
Also, the jet should be oriented at nearly Brewter’s angle to the pump; this can
be determined by monitoring the pump reflection from the jet surface. It is also
necessary that the flat region of the jet be oriented perpendicular to the table
surface, which can be determined by measuring the height of the beam reflected
from the surface. It was found that a concentration of 1.48 g/l] yielded the required
5% transmission. Once the required dye concentration is attained, pump beam
should be focused slightly before the jet, and slightly before the onset of thermal
lensing. It is necessary, however, to be very close to the onset of thermal lensing
in order to get sufficient coupling to allow proper mode-locking at later stages.
With the pump beam striking the gain jet, bright fluorescence will be emitted
from the pumped volume. This fluorescence will be imaged by M1 (towards OC)
and M2 (towards M5), and is used to align M1 and M2. To align M1, an iris
approximately 2mm in diameter is placed near M2, at the height and position
desired for the final intracavity beam. The fluorescence imaged through this
iris is viewed on a card placed near OC, and aligned to the desired intracavity
beam height. Then M1 is translated towards the jet until the fluorescence spot
is focused at a distance on the order of approximately 2m (place a flat mirror
between M1 and OC to determine this, without having to remove OC). M2 is
aligned using the same procedure, placing an iris as close to M7 as possible, and
translating M2 until the fluorescence spot is focused at the same distance used in
aligning M1 (approximately 2m). Now M5 and OC are adjusted to obtain lasing
by retroreflecting the fluorescence spots through the irises and back into the jet.
When aligning OC, it is helpful to view the fluorescence spot imaged on M5;
when OC is correctly aligned, a brighter spot will be seen. Similarly, align M5

while viewing the fluorescence spot on OC. When the irises are opened, lasing

173

should be observed, and M5 and OC shouldbe adjusted to obtain maximum
power. The dye jet should be rotated until it is at exactly Brewster’s angle to
the intracavity beam, which can be determined by observing the reflection of the
intracavity beam from the jet. The optimized intracavity beam should be at the
desired height throughout the cavity; if it is not, it is indicative of a problem with
the previous alignment, which should be repeated more precisely. In particular,
the precise orientation of the jet perpendicular to the optical table is essential.

The final requirement in the alignment is to precisely set the separation of
M1 and M2, which controls the cavity spatial mode. As discussed by Valdmanis
[31], variation of the spacing results in a series of stable and unstable cavity
modes, whose size (at the output) increases with decreasing separation. For small
separations, a large mode is obtained, which becomes crescent shaped, and finally
cannot be sustained for sufficiently small separation. Best operation is obtained
for slightly larger separation, at the next stable mode that can be obtained. This
behavior is observed by adjusting the translation of M1 and M2 symmetrically
with respect to the jet (using the translation stage micrometers for reference),
and viewing the spatial mode as described in Section A.4. After each adjustment
of the translation, M5 and OC should be readjusted for maximum power. It was
found that the stable mode desired was obtained over a range of 0.5mm in the
separation; a separation close to the center of this range was chosen.

The final outcome of this stage of the alignment should be a stable, Gaussian
mode, and an intracavity beam that is parallel to the optical table at all points.
The output power, for an input power of 2 W, and a 2% output coupler, should

be approximately 400 mW.

174

A.5.2 Linear Cavity, Gain and Absorber

Once the alignment described above is complete, the cavity shown in Fig. A.2(b)
is aligned. This is performed by placing M3 in the cavity, and ensuring that the
fluorescence spot is imaged at the correct height in the direction of M4. Then M4
is placed to image the spot towards M5, at the correct height. M4 is placed at
a distance from M3 that preserves the diameter of the fluorescence spot defined
by the iris placed between M3 and M2. M5 is then repositioned as shown in
Fig. A.2(b), and adjusted to retroreflect the beam, obtain lasing, and optimize
the output power. The separation between M3 and M4 should be adjusted, by
translating M4 and reoptimizing the output power with M5, until the same cav-
ity mode obtained in alignment described in the previous subsection is recovered.
The intracavity beam should be parallel to the optical table, and any deviation
is likely due to slight misalignment of M3 and M4; this should be corrected by
viewing the fluorescence spots, and repeating the above procedure. An output
power of approximately 270 mW should be obtained. Now the absorber jet, which
should only be circulating pure EG at this point (at a pressure of 16 psi), is moved
into the beam between M3 and M4, near the focus, and at Brewster’s angle with
respect to the intracavity beam. It may be necessary to slightly adjust M5 to
regain lasing; once this is accomplished, the absorber jet should be rotated to
minimize the surface reflection of the intracavity beam, indicative of correct po-
sitioning at Brewster’s angle. M4 may need to be translated slightly to regain the
correct Gaussian spatial mode, and the output power should be approximately

260 mW.

175
A.5.3 Ring Cavity

Now the cavity shown in Fig. A.2(c) can be aligned, simply by adjusting M5
and OC to reflect the beam around the ring cavity. Because the total cavity
length in the ring cavity is greater than the linear cavity shown in Fig. A.2, it
may be necessary to adjust the separation between M3 and M4 slightly to recover
the desired cavity mode. An output power of approximately 100 mW per beam
should be obtained. The final step in the alignment of the CW laser before mode-
locking is obtained is the addition of the prism sequence P1-P4, shown in Fig. A.1.
The prisms should be added without adjusting any of the rest of the cavity, and
it is useful to view the fluorescence spots transmitted through the prisms as P1
through P4 are aligned. The fluorescence spots should pass through the prisms
near the apices, and correct orientation of the prism at Brewster’s angle can be
obtained by noting that the deviation of the fluorescence spots is at an extremum
when the prism is oriented at Brewster’s angle. Once the fluorescence spot has
been aligned correctly from P1 to P4, the final prism P4 should be translated
until the fluorescence spot from P4 on M5 overlaps with the spot from M4 on M5.
When this is achieved, lasing can be regained. The prisms are then all adjusted
to yield maximum output power, by rotation, tilt, and translation, keeping the
beam as close as possible to the prism apices. The correct adjustment of the tilt
of the prisms can be determined by monitoring the weak reflections from the two
prism surfaces. Both reflections from any given prism should be collinear, and
can be observed far from the laser. The output power should be approximately

100mW per beam at this stage.

176

A.5.4 Achieving Mode-Locking

The final stage in the alignment, which is to achieve mode-locking, should
be performed with a pump power of 4-5W. A stock solution of 2g of DODCI
in 200 ml of EG is slowly added to the EG circulating in the absorber jet. As
the DODCI is added, the output power of the laser will decrease. The absorber
jet can be positioned at the focus of the absorber cavity by maximizing the
output power of the CPM at low DODCI concentrations. The jet should be
moved slightly away from the focus for best operation. At a concentration of
approximately 0.24 g/l signs of structure with a period of the round trip time
of the cavity are observed in the photodiode trace. More DODCI is added, and
eventually mode-locking is achieved. This requires adjustment of the position
of the absorber jet, and may require adjustment of the pump pointing mirror
M7. To obtain the shortest pulses, prism P1 should be translated parallel to
its base, to increase the length the intracavity beam travels through the prism
material. For a pump power of 4 W, stable mode-locking was routinely achieved
at a concentration of approximately 0.75g/l, and an average output power of

25 mW per beam.

A.6 Routine Maintenance of Laser

Immediately after replacement of the dyes, the only adjustments to the CPM
normally required are to M7, which compensates for drift of the pump laser
pointing, and to the position of the absorber jet, which affects mode-locking.
Cleaning of the optics is not necessary, because of the clean air environment in
which the laser is operated.

After a period of approximately two weeks, a noticeable degradation in the

177

laser performance becomes apparent, due to degradation of the laser dyes. This
is evidenced by poor mode-locking, and accompanying fluctuations and insta-
bilities in the laser output. It is possible to add a small amount of DODCI to
the absorber solution, but eventually it becomes necessary to replace the dyes
completely. Dye replacement is a fairly simple procedure that does not require
repetition of the entire alignment procedure described in Section A.2. The old
dye filters and solutions are removed, and replaced with clean filters and new
EG (occasionally methanol is circulated throughout the system for cleaning).
The stock Rhodamine tetrafluoroborate solution is prepared as described in Sec-
tion A.2, and the standardized quantity determined by absorption measurement
is added. It is not necessary to measure the absorption every time the dyes are
replaced. Then, with the pump laser at 2W, CW lasing is recovered. This will
usually require adjustment of the pump pointing, and the absorber jet position.
Occasionally, it is necessary to slightly adjust M5 and OC to optimize the output
power, which should be the same obtained in the original alignment of the cavity.
Then the same procedure described in Section A.2 for addition of DODCI to
achieve mode-locking is repeated. It was found that this simple dye replacement
procedure was very reliable, and was capable of restoring the CPM to a consis-
tent state. The advantages associated with avoiding the complete realignment

are tremendous, and make the laser a much more useful tool for experiments.

A.7? Performance of Laser

At a pump power of 4W, stable mode-locking was obtained with average
output powers of 20-35mW per beam. The pulse width could be varied from
a minimum of approximately 80 fs to a maximum on the order of 300fs. The

spectrum of the laser extended from approximately 6200 to 6300A with 300fs

178

pulses, and from 6100 to almost 6400A with 80fs pulses. The average output
power was stable to a few percent, and mode-locking could be maintained during

significant variations in pump power.

179

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