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Structural and Optical Properties of Strained-Layer Superlattices
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Miles, Richard Henry
(1989)
Structural and Optical Properties of Strained-Layer Superlattices.
Dissertation (Ph.D.), California Institute of Technology.
doi:10.7907/042y-d234.
Abstract
This thesis describes investigations into the optical and structural properties of strained-layer superlattices. The purpose of the work was twofold: to establish the merits of strained-layer structures in applications, particularly to optoelectronics; and to examine structural characteristics of superlattices in which the lattice-mismatch between adjacent layers is large. Optical properties of CdTe/ZnTe superlattices have been examined through photoluminescence experiments. Observed band gaps have been compared with those expected from calculations of electronic band structure, including effects that are due to strain. Band gaps of a variety of II-VI superlattices have been calculated based on the agreement between theory and experiment in the CdTe/ZnTe system. The accommodation of lattice mismatch has been investigated for CdTe/ZnTe and Ge
0.5
Si
0.5
/Si superlattices. The assumptions behind traditional single-film critical thicknesses and their extensions to multilayer structures were of particular interest in these studies.
In Chapter 2 we use photoluminescence experiments to examine the optical properties of CdTe/ZnTe superlattices grown on a variety of Cd
Zn
1-x
Te buffer layers. The work was motivated by interest in wide-band-gap II-VI's as possible visible light emitters and detectors and, more generally, by interest in the effects of strain and dislocations on the optical properties of strained-layer superlattices. Photoluminescence from the superlattices is observed to be several orders of magnitude more intense than from a Cd
0.37
Zn
0.63
Te alloy. Spectra are dominated by Gaussian distributions of excitonic lines. The 20-30meV widths of these distributions show that superlattice layer thicknesses were controlled to approximately one monolayer. Identifying the superlattice band gaps as the high-energy edges of the observed excitonic luminescence yields sample energy gaps substantially lower than expected for alloys. Observed gaps are in excellent agreement with those calculated from a
k •
p model, assuming strain appropriate to a free-standing structure. This configuration is one in which dislocations at the superlattice/buffer-layer interface have redistributed strain within an otherwise dislocation-free superlattice in manner that minimizes the elastic strain energy within the structure. The free-standing configuration is argued to be plausible in view of calculated critical thicknesses and strain relaxation rates. Calculations of the effects of a free-standing strain on the electronic band structure of CdTe/ZnTe superlattices show that strain can substantially reduce band gaps (on the order of 100meV for a 6% mismatch), and causes transitions from type-I to type-II band alignments. Attempts to observe laser oscillation in these CdTe/ZnTe superlattice structures have proven unsuccessful to date, although Cd
0.25
Zn
0.75
Te/ZnTe structures have recently been reported to lase.
Chapter 3 describes a structural study of the CdTe/ZnTe superlattices examined in Chapter 2. Strain fields and dislocation densities are inferred from x-ray diffraction,
in situ
reflection high-energy electron diffraction (RHEED), and transmission electron microscopy (TEM). All of our samples are observed to exceed the critical thickness for the nucleation of misfit-accommodating dislocations. Although each of the structures appears to be highly defective, the free-standing limit appears to be plausible, as defect densities drop substantially within a micron of the superlattice/buffer-layer interface, regardless of the buffer layer used. Although several samples substantially exceed predicted critical thicknesses, the sample that shows the smallest degree of residual strain lies below limits derived from a previous empirical study. This result demonstrates that dislocation formation in superlattices is not appropriately characterized by applying traditional critical thickness models to an alloy of equivalent total thickness and average composition. Variations in strain fields appear to be correlated with sample growth conditions. As growth parameters are neglected in traditional energy-balancing models of critical thickness, it is argued that activation barriers associated with the nucleation or glide of dislocations can substantially inhibit the relaxation of strain beyond the equilibrium limits.
In Chapter 4 we demonstrate that the accommodation of lattice mismatch in Ge
0.5
Si
0.5
/Si superlattices is highly dependent on the conditions under which a sample is grown. Dislocation densities of 1.5 x 10
cm
-1
drop to levels undetectable by TEM (< 10
cm
-2
) as the growth temperature of compositionally identical superlattices is lowered from 530°C to 365°C. Thus, by lowering growth temperatures, it is possible to freeze a structure in a highly strained metastable state well beyond the critical thickness limits calculated by equilibrium theories. There appears to be a large kinetic barrier blocking dislocation nucleation or glide; the effect we observe cannot be explained by mismatched thermal expansion coefficients alone. These results are contrary to initial studies of Ge
Si
1-x
alloys, which appear to display critical thicknesses relatively independent of temperature over the ranges described here. Recognizing that defect creation can be inhibited in severely mismatched superlattices should be important in growing heavily strained films of high quality.
Finally, the Appendix contains maps of band gap as a function of layer thicknesses for a variety of II-VI superlattice systems, calculated using the Bastard model described in Chapter 2. Agreement with experiment is good for the CdTe/ZnTe superlattices examined here. As mentioned in Chapter 1, comparison of these calculated gaps with those measured experimentally leads to a prediction of ΔE
= 1.0 ± 0.1eV for the ZnSe/ZnTe valence band offset.
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. (advisor)
Bellan, Paul Murray (co-advisor)
Thesis Committee:
McGill, Thomas C. (chair)
Chan, Sunney I.
Tombrello, Thomas A.
Fultz, Brent T.
Cross, Michael Clifford
Johnson, William Lewis
Vahala, Kerry J.
Bellan, Paul Murray
Defense Date:
18 August 1988
Funders:
Funding Agency
Grant Number
Caltech
UNSPECIFIED
International Business Machines Corporation
UNSPECIFIED
General Telephone
UNSPECIFIED
Army Research Office (ARO)
UNSPECIFIED
Office of Naval Research (ONR)
UNSPECIFIED
Record Number:
CaltechETD:etd-02082007-093744
Persistent URL:
DOI:
10.7907/042y-d234
Related URLs:
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Description
DOI
Article adapted for Chapter 1.
DOI
Article adapted for Chapter 1.
DOI
Article adapted for Chapter 2.
DOI
Article adapted for Chapter 3.
DOI
Book chapter adapted for Chapter 3.
DOI
Article adapted for Chapter 3.
DOI
Article adapted for Chapter 4.
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STRUCTURAL AND OPTICAL
PROPERTIES OF
STRAINED-LAYER SUPERLATTICES

Thesis by
Richard Henry Miles

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

California Institute of Technology
Pasadena, California
1989

(Submitted August 18, 1988)

Acknowledgments
It is a pleasure to acknowledge my advisor, Dr. T. C. McGill, whose guidance

and support have contributed tremendously to this work and to my own personal
and scientific development.
I am fortunate to have benefited from interactions with a great number of people
at Caltech. I especially wish to thank Dr. T. A. Tombrello, whose enthusiasm has
been passed to many students, this one included. I would also like to thank Dr. S.

I. Chan, who has always given freely and gladly of his time to discuss numerous
matters, both personal and professional.
Many students, past and present, have contributed greatly to my years as a
graduate student. Little of the optical work could have been done without the
experience patiently passed along by Dr. Steve Hetzler. I have also profited from
useful discussions with Drs. G. Y. Wu and T. E. Schlesinger. I especially wish to
acknowledge the people with whom I have interacted extensively: Dr. Bob Hauenstein, who was always happy to share his keen curiosity and deep understanding
of physics; Matthew Johnson, to whom I owe the better half of my experimental technique, and who is every bit as foolhardy as myself on a mountain; and
Mike Jackson, whose insight, good nature, and good sense are a pleasure to encounter. It has been a delight interacting on numerous occasions with Dave Chow,
to whom I am particularly grateful for a critical reading of Chapter 1, and with
Yasantha Rajakarunanayake, who has so often taken the time to explain theory to
an experimentalist. It is also a pleasure to acknowledge many discussions with my
classmates, Wesley Bondville and Ted Woodward, as well as with Dr. Dave Ting,
Ed Croke, Ed Yu, and Pete Zampardi.
Many thanks are due Marcia Hudson and Carol McCollum, without whose help
on many matters, administrative and otherwise, the group would rapidly grind to
a halt. I have greatly enjoyed conversing with Brian Cole in the brief moments

111

free to an engineer working with a multichamber MBE machine. I also wish to
recognize the excellent secretarial help of Vere Snell, who is greatly missed.
I have profited from many valuable discussions with Dr. J. 0. McCaldin, Dr. D.
L. Smith of Los Alamos National Laboratories, and Mr. 0. J. Marsh and Dr. A. T.
Hunter of Hughes Research Laboratories. I also wish to thank Dr. M. D. Strathman
of Charles Evans and Associates, for performing the RBS measurements; Dr. C.
W. Nieh, who provided the TEM work on the Gea:Sii-z samples; Dr. P. P. Chow
of Perkin-Elmer, who provided the Gea:Sii-a: samples; and Dr. J.-P. Faurie of the
University of Illinois, who provided the Cda:Zn1 _a: Te samples.
I would like to acknowledge the financial support of the California Institute of
Technology, International Business Machines corporation, General Telephone, the
Army Research Office, and the Office of Naval Research.
Finally, I wish to acknowledge my parents, without whom none of this would
have been possible, and my wife Mayumi, who put up with all of this.

Abstract
This thesis describes investigations into the optical and structural properties
of strained-layer superlattices. The purpose of the work was twofold: to establish
the merits of strained-layer structures in applications, particularly to optoelectronics; and to examine structural characteristics of superlattices in which the latticemismatch between adjacent layers is large. Optical properties of CdTe/ZnTe superlattices have been examined through photoluminescence experiments. Observed
band gaps have been compared with those expected from calculations of electronic
band structure, including effects that are due to strain. Band gaps of a variety of
II-VI superlattices have been calculated based on the agreement between theory
and experiment in the CdTe/ZnTe system. The accommodation of lattice mismatch has been investigated for CdTe/ZnTe and Ge0 . 5 Si 0 . 5 /Si superlattices. The
assumptions behind traditional single-film critical thicknesses and their extensions
to multilayer structures were of particular interest in these studies.

In Chapter 2 we use photoluminescence experiments to examine the optical
properties of CdTe/ZnTe superlattices grown on a variety of Cda,Zn1 _a, Te buffer
layers. The work was motivated by interest in wide-band-gap II-VI's as possible
visible light emitters and detectors and, more generally, by interest in the effects
of strain and dislocations on the optical properties of strained-layer superlattices.
Photoluminescence from the superlattices is observed to be several orders of magnitude more intense than from a Cd0 •3 1Zn0 .63 Te alloy. Spectra are dominated by
Gaussian distributions of excitonic lines. The 20-30meV widths of these distributions show that superlattice layer thicknesses were controlled to approximately one
monolayer. Identifying the superlattice band gaps as the high-energy edges of the
observed excitonic luminescence yields sample energy gaps substantially lower than
expected for alloys. Observed gaps are in excellent agreement with those calculated
from a k · p model, assuming strain appropriate to a free-standing structure. This

configuration is one in which dislocations at the superlattice/buffer-layer interface
have redistributed strain within an otherwise dislocation-free superlattice in a manner that minimizes the elastic strain energy within the structure. The free-standing
configuration is argued to be plausible in view of calculated critical thicknesses and
strain relaxation rates. Calculations of the effects of a free-standing strain on the
electronic band structure of CdTe/ZnTe superlattices show that strain can substantially reduce band gaps (on the order of l00meV for a 6% mismatch), and
causes transitions from type-I to type-II band alignments. Attempts to observe
laser oscillation in these Cd Te/Zn Te superlattice stmctures have proven unsuccessful to date, although Cd0 . 25 Zn0 . 75 Te/ZnTe structures have recently been reported
to lase.
Chapter 3 describes a structural study of the CdTe/ZnTe superlattices examined in Chapter 2. Strain :fields and dislocation densities are inferred from x-ray
diffraction, in situ reflection high-energy electron diffraction (RHEED), and transmission electron microscopy (TEM). All of our samples are observed to exceed
the critical thickness for the nucleation of misfit-accommodating dislocations. Although each of the structures appears to be highly defective, the free-standing
limit appears to be plausible, as defect densities drop substantially within a micron of the superlattice/buffer-layer interface, regardless of the buffer layer used.
Although several samples substantially exceed predicted critical thicknesses, the
sample that shows the smallest degree of residual strain lies below limits derived
from a previous empirical study. This result demonstrates that dislocation formation in superlattices is not appropriately characterized by applying traditional
critical thickness models to an alloy of equivalent total thickness and average composition. Variations in strain fields appear to be correlated with sample growth
conditions. As growth parameters are neglected in traditional energy-balancing
models of critical thickness, it is argued that activation barriers associated with

the nucleation or glide of dislocations can substantially inhibit the relaxation of
strain beyond the equilibrium limits.
In Chapter 4 we demonstrate that the accommodation of lattice mismatch in
Ge0 . 5 Si 0 . 5 /Si superlattices is highly dependent on the conditions under which a sample is grown. Dislocation densities of 1.5 x 10 5 cm- 1 drop to levels undetectable by
TEM ( < 10 5 cm- 2 ) as the growth temperature of compositionally identical superlattices is lowered from 530°C to 365°C. Thus, by lowering growth temperatures,
it is possible to freeze a structure in a highly strained metastable state well beyond
the critical thickness limits calculated by equilibrium theories. There appears to
be a large kinetic barrier blocking dislocation nucleation or glide; the effect we
observe cannot be explained by mismatched thermal expansion coefficients alone.
These results are contrary to initial studies of Gea:Sii-a: alloys, which appear to
display critical thicknesses relatively independent of temperature over the ranges
described here. Recognizing that defect creation can be inhibited in severely mismatched superlattices should be important in growing heavily strained films of
high quality.
Finally, the Appendix contains maps of band gap as a function of layer thicknesses for a variety of II-VI superlattice systems, calculated using the Bastard
model described in Chapter 2. Agreement with experiment is good for the CdTe/ZnTe
superlattices examined here. As mentioned in Chapter 1, comparison of these calculated gaps with those measured experimentally leads to a prediction of flE,, =
1.0 ± O.leV for the ZnSe/ZnTe valence band offset.

Vll

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

Chapter 1:
Variation in the Properties of Superlattices with Band Offsets,

T. C. McGill, R. H. Miles, and G. Y. Wu, Mater. Res. Soc. Symp. Proc.
90, 143 (1987).

Band Structure of ZnSe-ZnTe Superlatiices,

Y. Rajakarunanayake, R.H. Miles, G. Y. Wu, and T. C. McGill, Phys. Rev.
B 37, 10215 (1988).
Band Offset of the ZnSe-ZnTe Superlattices: A fit to photoluminescence data by k • p theory,

Y. Rajakarunanayake, R. H. Miles, G. Y. Wu, and T. C. McGill, J. Vac.
Sci. Technol. B, to be published.
Energy-band Structure of ZnSe-ZnTe Superlattices Calculated by
k • p Theory,

Y. Rajakarunanayake, R.H. Miles, G. Y. Wu, and T. C. McGill, submitted
to Optical Engineering.

Chapter 2:
Photoluminescence Spectra from CdTe-ZnTe Superlattices,
R. H. Miles, G. Y. Wu, M. B. Johnson, T. C. McGill, J. P. Faurie, and S.
Sivananthan, Bull. Am. Phys. Soc. 31, 654 (1986).

Vlll

Photoluminescence Studies of ZnTe/CdTe Strained-layer Superlattices,

R. H. Miles, G. Y. Wu, M. B. Johnson, T. C. McGill, J. P. Faurie, and S.
Sivananthan, Appl. Phys. Lett. 48, 1383 (1986).
Chapter 3:
Structure of CdTe/ZnTe Superlattices,

R.H. Miles, T. C. McGill, S. Sivananthan, X. Chu, and J.P. Faurie, J. Vac.
Sci. Technol. B 5, 1263 (1987).
Perspectives on Formation and Properties of Semiconductor Interfaces,

R. S. Bauer, R. H. Miles, and T. C. McGill, in Semiconductor Interfaces:
Formation and Properties, edited by G. Le Lay, J. Derrien, and N. Boccara

(Springer, Berlin, 1987), p. 372.
Superlattices of II-VI Semiconductors,

R.H. Miles, J. 0. McCaldin, and T. C. McGill, J. Cryst. Growth 85, 188
(1987).

Chapter 4:
Opportunities in Devices and Physics,

T. C. McGill, R.H. Miles, R. J. Hauenstein, and 0. J. Marsh, in Proceedings
of the 2nd International Symposium on Si MBE (Electrochemical Society,

Pennington, USA, 1988), p. 1.
Photoluminescence Studies of Ge/Si Superlattices,

R.H. Miles, T. C. McGill, P. P. Chow, 0. J. Marsh, and R. J. Hauenstein,
Bull. Am. Phys. Soc. 33, 1349 (1988).

Dependence of Critical Thickness on Growth Temperature in Gea:Si 1 _,,/Si
Superlattices,

R. H. Miles, T. C. McGill, P. P. Chow, D. C. Johnson, R. J. Hauenstein,
C. W. Nieh, and M. D. Strathman, Appl. Phys. Lett. 52, 916 (1988).
Accommodation of Lattice Mismatch in Gea:Sh-a:/Si Superlattices,

R.H. Miles, P. P. Chow, D. C. Johnson, R. J. Hauenstein, 0. J. Marsh, C.
W. Nieh, M. D. Strathman, and T. C. McGill, J. Vac. Sci. Technol. B, to
be published.
Raman Study of Temperature-Dependent Strain Relaxation m
SiGe/Si Strained-Layer Superlattices,

R. J. Hauenstein, A. T. Hunter, R.H. Miles, T. C. McGill, and P. P. Chow,
in preparation.

Contents

Acknowledgments

Abstract

List of Publications

List of Figures

xiii

List of Tables

1 Introduction

1.1

Introduction to thesis .

1.2

Background . . .

1.3

Small structures .

1.3.1

Superlattices

1.3.2

Strained-layer structures

Effects arising from strain . . .

1.4.1

Electronic band structure

1.4.2

Defect formation

1.4

1.5

Summary of thesis

. . .

1.5.1

Luminescence from CdTe/ZnTe superlattices .

1.5.2

Structural properties of CdTe/ZnTe superlattices

1.5.3

Dislocation formation in Ge0 •5 Sio.s/Si superlattices .

References

2 Luminescence from CdTe/ZnTe Supe:rlattices
2.1

Introduction . . . .

2.1.1

Background

2.1.2

Results of this work .

2.1.3

Outline of chapter

2.2

Samples . . . . . .

2.3

Photoluminescence

2.3.1

Theory . . .

2.3.2

Experimental setup

2.3.3

Results . . . . . . .

2.4

Calculations of electronic band structure

2.4.1

Bastard and k •p models

2.4.2

Results . . . .

2.5

Stimulated Emission

2.6

Conclusions

References . . . .

Structural Properties of CdTe/ZnTe Superlattices

3.1

Introduction . . . .

3.1.1

Background

3.1.2

Results of this work .

3.1.3

Outline of chapter

3.2

X-ray diffraction

3.2.1

Theory .

3.2.2

Results .

Xll

3.3

In-situ RHEED and TEM

3.4

Conclusions

References . . . .

Dislocation Formation in Ge 0 . 5 Si 0 . 5 /Si Superlattices

4.1

Introduction . . . .

4.1.1

Background

4.1.2

Results of this work .

100

4.1.3

Outline of chapter

101

4.2

Samples

...

101

4.3

Experimental

103

4.3.1

X-ray Diffraction

105

4.3.2

Channeled RBS

107

4.3.3

TEM.

112

4.4

Discussion .

115

4.5

Conclusions

118

References .

119

A Appendix

123

References . ................................. . 131

Xlll

List of Figures
1.1

Superlattice structure . . . . . . . . . .

1.2

HgTe/CdTe superlattice characteristics

1.3

Semiconductor band gaps and lattice constants

1.4

Energy bands . . . . . . . . . . . . .

1.5

Band edges in a strained superlattice

1.6

Electronic band structure of bulk ZnSe and ZnTe

1. 7

Coherently strained commensurate superlattice

1.8

Unstrained superlattice .

1.9

Critical thickness . . . .

1.10 Free-standing superlattice

2.1

Photoluminescence process

2.2

Photoluminescence apparatus

2.3

Photoluminescence from a CdTe/ZnTe superlattice and alloy

2.4

CdTe/ZnTe photoluminescence line shape

2.5

Temperature dependence of photoluminescence from CdTe/ZnTe
superlattice sample 8 . . . . . . .

2.6

Critical thickness of Cd:i:Zn1 _:i: Te

2.7

Relaxation of strain beyond the critical thickness

2.8

Unstrained CdTe/ZnTe superlattice band gaps ..

XIV

Free-standing CdTe/ZnTe superlattice band gaps

2.10 Band edges in CdTe/ZnTe superlattices . . . . . .

2.9

2.11 Transition between type-I and type-II CdTe/ZnTe superlattice band
alignments . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.12 CdTe/ZnTe photoluminescence under pulsed pump conditions

3.1

Unstrained CdTe/ZnTe superlattice

3.2

Strained CdTe/ZnTe superlattices .

3.3

Calculated superlattice x-ray diffraction .

3.4

Dependence of superlattice diffraction on strain

3.5

X-ray diffraction from sample 8

3.6

X-ray diffraction from sample 3

3. 7

X-ray diffraction from sample 7

4.1

Geo.sSio.s/Si superlattice x-ray diffraction .

106

4.2

Rutherford Backscattering Spectroscopy

107

4.3

Channeled RBS . . . . . . . . . . . . . .

108

4.4

Channeled RBS from Geo. 5 Si 0 . 5 /Si superlattices

110

4.5

Plan-view TEM image of Ge0 . 5 Si 0 . 5 /Si superlattice grown at 530 °c 113

4.6

Cross-sectional TEM image of Geo.sSi 0 . 5 /Si superlattice grown at

330°c .................................. 114
A.l Free-standing CdSe/ZnSe superlattice band gaps .

125

A.2 Free-standing CdS /ZnS superlattice band gaps .

126

A.3 Free-standing ZnS /ZnSe superlattice band gaps

127

A.4 Free-standing ZnSe/ZnTe superlattice band gaps .

128

A.5 Free-standing CdS/CdSe superlattice band gaps .

129

A.6 Free-standing CdSe/CdTe superlattice band gaps

130

List of Tables
1.1

Deformation potentials of some zinc blende II-VI semiconductors .

2.1

CdTe/ZnTe superlattice samples . . . . . . .

2.2

CdTe/ZnTe superlattice and alloy band gaps

2.3

CdTe/ZnTe experimental and calculated superlattice band gaps

4.1

Geo. 5 Sio.s/Si superlattice samples

103

4.2

Geo.sSio.s/Si superlattice Xm.in's

111

A.1 Properties of II-VI semiconductors

124

Chapter 1
Introduction

1. 1

Introduction to thesis

This thesis describes investigations into the optical and structural properties
of strained-layer superlattices. The experimental work is divided between studies
of CdTe/ZnTe and Gea:Sii_.,/Si structures. Although the results presented are
derived exclusively from these systems, many of the conclusions can be extended
to other heteroepitaxial structures in which the lattice match between constituent
materials is poor. The excellent optical properties of the CdTe/ZnTe superlattices
have recently been matched by other wide-band-gap II-VI superlattices, and the
nature of the dislocation network observed in these structures is similar to that
of extended defects in strained III-V and group-IV semiconductor systems. To
date, the Gea:Si 1 _.,/Si structural results have not been confirmed in other materials
systems, but it is believed that the nature of stress relaxation should be similar in
other lattice-mismatched heterostructures.
The purpose of Chapter 1 is to summarize the results obtained in the thesis
and to place the work in context. Section 1.2 briefly outlines the motivation for
investigations into small structures. Section 1.3 describes strained-layer superlat-

tices with an emphasis on the advantages of these structures over alloys or closely
lattice-matched superlattices. Effects that are due to strain are the subject of
Section 1.4. Perturbations of the electronic band structure arising from strain are
discussed (Section 1.4.1), as well as defect formation and the attempts to model
it in a strained heterostructure (Section 1.4.2). The thesis is summarized in Section 1.5. A photoluminescence study of CdTe/ZnTe superlattices is outlined in
Section 1.5.1. The section that follows this describes investigations of the structural characteristics of these samples, addressing in particular the degree to which
lattice mismatch is accommodated by elastic strain for growth on a variety of templates. Lastly, Section 1.5.3 summarizes a study of the effects of growth conditions
on defect formation in Ge 0 . 5 Si0 .5 /Si superlattices.

1. 2

Background

The drive to create electronic devices that are both faster and more compact is
leading to enormous improvements in device fabrication and processing techniques.
Foremost amongst the improvements in crystal growth has been development of
the techniques of molecular beam epitaxy (MBE) and chemical vapor deposition
(CVD), which has made possible the fabrication of epitaxial films with deposition
controlled to the submonolayer coverage level. While promising to greatly improve
the speed and packing density of conventional solid-state electronic devices, these
technologies have also forced changes in descriptions of the physics behind old
devices and introduced a host of new structures demonstrating a wealth of new
characteristics.
When device dimensions approach the de Broglie wavelength of an electron
in a crystal,* device characteristics are rarely described adequately by extensions
*Within the effective mass approximation, >..

= .l!...
~ 2.4 ~A~ 35A in GaAs.
me

of bulk material properties through semiclassical theories. Several factors contribute to this breakdown. Effects associated with confinement radically alter the
electronic states within a structure, making quantum mechanical descriptions necessary. Crystal band gaps are shifted substantially from those of the constituent
materials, yielding very different radiative recombination energies. Phenomena
such as electron or hole tunneling can make large, if not dominant, contributions
to the behavior of a given device. Transport properties are further removed from
classical theory by scattering lengths that are comparable to device dimensions.
While greatly changing the descriptions necessary to predict the characteristics
of a particular structure, reducing device size also presents the possibility of growth
of a large number of lattice-mismatched heterostructures with a minimum of structural defects. The desirability of commensurate* growth has long been recognized;
extended dislocations often act as sources of electrically and optically active point
defects or are themselves active, to the detriment of device performance. Until
recently, this had limited attention to a few closely-lattice-matched pairs ( e.g.,
GaAs/ AlAs and HgTe/CdTe) in applications in which device performance was at
a premium. This situation has changed in the last few years, however, as it has
become possible to reproducibly deposit films that are sufficiently thin to inhibit
dislocation formation for lattice mismatches as large as 7%. Relaxing the constraint of lattice match to this degree has opened to investigation a great number
of new commensurate heterostructures.
The subject of this thesis is the strained-layer superlattice, a structure that was
first suggested in 1983 by Osbourn 1 and that springs directly from the capability to
grow ultrathin epitaxial films with a high degree of reproducibility. The potential
*While the term commensurate is defined variously in the literature, we will restrict its use
to heterostructures in which the interfaces between adjacent layers are dislocation-free. The
"coherently strained" structure that results is one in which stress arising from lattice mismatch
is accommodated purely by elastic strain.

of these structures is great; relaxing the constraint of lattice match allows a large
number of new heterostructures to be grown, while the strain that results from a
substantial lattice mismatch can have enormous effects on the optical and electrical
properties of a structure. However, the obstacles to introducing strained-layer
structures within devices are considerable; extended structural defects are readily
introduced during growth and processing, and the stability of strained devices
under prolonged use remains uncertain.
The work presented here is aimed at three goals. It was primarily the hope
of new light-emitters and detectors that initially stimulated the optical experiments described in Chapter 2. The effects on electronic band structure of strain
arising from a substantial lattice mismatch are still uncertain, and this provided
additional direction and motivation for the work in this chapter. The structural
experiments presented in Chapters 3 and 4 investigated the limits on commensurate strained epitaxy and the nature of stress relaxation in strained superlattices.
Resolution of these issues will be essential to the successful application of strained
heterostruct ures.

1. 3

Small structures

1.3.1

Superlattices

Semiconductor superlattices have attracted much attention since being proposed by Esaki and Tsu 2 in 1970. Fig. 1.1 is a schematic representation of such a
structure. Growth takes place on a clean, heated substrate, starting typically with
the deposition of one or more buffer layers of thickness on the order of a micron.
While buffer layers are rarely essential to the superlattice itself, they serve several
functions. An appropriate choice of buffer material and growth conditions can
improve subsequent growth by providing a surface that is both cleaner and more

Moteriol 8~
Moteriot A~
Buffer ~

Figure 1.1: Schematic of a semiconductor superlattice, consisting of two distinct
layers deposited consecutively and repeatedly to form a periodic structure. The
superlattice is typically grown atop a comparatively thick substrate after deposition
of one or more buffer layers. (From Ref. 3.)

abrupt than can be achieved by standard substrate preparation procedures. In addition, buffer layers can improve crystal quality by bending dislocations threading
through the substrate, forcing them to the edge of a wafer rather than allowing
them to propagate through subsequent overlayers. Lastly, the topmost buffer may
act as a template for future growth, with the result that strain within a superlattice
can sometimes be modulated by the choice of this top layer.

The superlattice itself is grown on top of the buffers and consists of thin layers
of one semiconductor interleaved between thin layers of another. This alternating
structure is typically repeated for many periods, with layer thicknesses and compositions controlled for optimal uniformity and regularity. While adjacent layers
are compositionally distinct in the superlattices studied in this thesis, it is also
possible to grow a superlattice by periodically grading the introduction of impurities during deposition of a single material. 4 Such modulation-doped superlattices

display many of the electrical characteristics of compositionally graded structures.
Superlattices have several advantages over alloys. Although it is often possible
to reproduce the band gap of a superlattice by growing an alloy composed of the
same materials,* superlattices provide the parameter of layer thickness in addition
to overall composition.

The importance of this extra parameter is illustrated in

Fig. 1.2, which depicts energy gaps and effective masses for transport normal to
the layers in HgTe/CdTe superlattices. The abscissa and ordinate correspond to
numbers of monolayers of CdTe and HgTe, respectively, per superlattice period.
Whereas growth of an alloy with a given energy gap constrains the effective mass
to one or two values, it is clear from Fig. 1.2 that by changing HgTe and CdTe
layer thicknesses it is possible to adjust the effective mass over a comparatively
wide range while maintaining a single value of the band gap.
Practical considerations sometimes provide additional motivation for growing
superlattices rather than alloys. Although precise alloy composition can be difficult
to reproduce with techniques such as MBE, layer thicknesses are easily monitored
during growth. Although the situation is complicated by issues such as interdiffusion between adjacent superlattice layers and by the precision to which composition
and layer thickness must be defined for a particular application, there are many
circumstances in which superlattice characteristics are more readily reproduced
than those of alloys. Alloy decomposition is another problem that can be circumvented by growing superlattices composed of alternating layers of pure material
(this is one of the motivations for growing CdTe/ZnTe instead of Cda:Zn1 _a,Te).
Another practical consideration is the difficulty associated with growing a thick
highly strained film. While it is possible to grow a thick commensurate superlattice consisting of layers strained alternately in tension and compression, growth of a
*This is usually the case, but not always; e.g., strained Ga.,In 1 _.,Sb/Gayln 1 _ySb superlattices
can be grown with band gaps smaller than obtainable in Gazln 1 _,.Sb alloy films of comparable
thickness. 5

HgTe/CdTe SUPERLATIICE ENERGY GAP

30 .............,..............,..,...,,...,.............,.....,..,..,..,...,,.........,..,.'T'T"I

(a)

...

1l 10

:::i

20
10
Number of CdTe Layers

HgTe/CdTe SUPERLATIICE EFFECTIVE MASS
30.......,..................................................................................,....,....

(b)
f?

~ 20

..J

O>
::r:

...

1l 10
:::i

Number of CdTe layers

Figure 1.2: Properties of the HgTe/CdTe superlattice, calculated from a Bastard
model 6 assuming zero valence band offset.

The axes correspond to the num-

ber of HgTe and CdTe layers per superlattice period. (a) Energy band gaps of
HgTe/CdTe superlattices at 4.2K. Energies are expressed in meV. (b) Effective
masses for transport normal to the superlattice layers, expressed in fractions of
the free-electron mass. Contours have been omitted for masses greater than me.
( Adapted from Ref. 7.)

thick highly strained single film results in dislocation formation. This phenomenon
is described in greater detail in Section 1.4.2.
Lastly, radiative efficiencies of superlattices have often been observed to be
superior to those of alloys, 8,9 for reasons not entirely understood. Improvements
have been attributed variously to carrier confinement in quantum wells, 10 defect
and impurity gettering at interfaces, 11 and reductions in surface recombination
velocities.12 Differences in oscillator strengths do not appear to be sufficient to
explain the radiative enhancements. 13 It is probable that each of these effects
improves the radiative efficiencies of superlattices.

1.3.2

Strained-layer structures

It has been known for some time that overlayers deposited on a substrate to
which they are poorly lattice matched often relieve mismatch stresses by developing
dense networks of interfacial dislocations. 14.1 5,16 .1 7 Although limiting the amount
of material deposited on a substrate to a so-called "critical thickness" was long
ago observed to inhibit the appearance of these structural defects, these limiting
thicknesses were sufficiently thin to preclude defect-free epitaxial growth for all
but a few closely lattice matched systems. The development of techniques such
as MBE has made possible the growth of ultrathin epitaxial films, which has in
turn opened to investigation a large number of commensurate heterostructures
composed of poorly lattice-matched materials.
As illustrated in Fig. 1.3, very few semiconductors are lattice-matched well to
others. The number of materials that can be usefully codeposited within a single
growth chamber is further reduced by constraining pairs to be in the same group
in the periodic table. This limitation springs from doping considerations; elements
from one column of the periodic table act as electron donors or acceptors in a
semiconductor composed of elements from other columns. Growing, for example,

e ZnS

BAND GAP vs. LATTICE CONSTANT

GROUP IV
D GROUP m-v
0 GROUP II-VI
FILLED - DIRECT
UNFILLED - INDIRECT

...
• ZnSe

e CdS

OAIP

• ZnTe

0 GaP
□ AIAs

>c., 2 -

e CdSe

a:::

OAISb
Ill GaAs

e CdTe

Ill lnP

6 Si

IIGaSb

6 Ge

111 lnAs
111 lnSb

5.4

5.6

5.8

6.2

6.4

LATTICE CONSTANT (Angstroms)

Figure 1.3: Energy band gaps and lattice constants of assorted semiconductors
at 4.2K. Group-IV, III-V, and II-VI semiconductors are labeled differently, as
indicated in the inset. Direct band gap materials are indicated with solid symbols,
indirect with unfilled.18,19,20

10
type II-VI semiconductors in a III-V growth chamber can be expected to have
long-term effects on the electrical and optical characteristics of future structures
grown in that chamber. While some such pairs have been grown ( e.g., ZnSe with
GaAs2 1 ), research on mixed-system heterostructures has been slow.

It is clear from Fig. 1.3 that relaxing the constraint of lattice match to allow
growth of materials with lattice constants differing by as much as 7% greatly increases the number of material combinations possible within heterostructures. The
elastic strain which arises from commensurate lattice-mismatched growth acts as a
considerable perturbation on electronic band structure. 22 This effect is described
in greater detail in Section 1.4.1. While strain cannot always be viewed as a free
parameter to be adjusted at will, 9 it can be used to advantage. The interest in
heterojunction bipolar transistors (HBT's) fabricated from Gea:Sii_., is fueled in
large part by the effect of strain-induced conduction band splitting on transport in
the growth direction. Strain-induced band-gap shrinkages have brought attention
to Ga.,In1-a:Sb /Gayin1_ySb superlattices as possible alternatives to Hg.,Cd 1_., Te
for application as infrared detectors in the 8 - 12 µm range. 5 There are many other
examples of structures in which strain can act as a beneficial perturbation.
Recently, strained films have been used to improve the structural quality of subsequent epitaxial growth. Thin strained-layer superlattices incorporated in buffer
layers have been shown to greatly reduce the number of dislocations threading from
a substrate to an overlayer .16 ,23 At present it is not clear that lattice mismatch is
intrinsic to this effect; it is possible that layered structures composed of materials
differing only in elastic properties would bend dislocations along interfaces and out
of a crystal. Lastly, it is sometimes possible to isolate mismatch-accommodating
dislocations to a buffer-layer/substrate interface, greatly improving the structural
perfection of an overlayer poorly lattice-matched to its substrate. This technique
has been applied successfully in the Ga.,In 1_.,Sb system, 5 where a Ga.,In 1_.,Sb

4N STATES
0 ELECTRONS

0::

1--

6N STATES (ZPI

ZN ELECTRONS

"-0

ZN STATES (ZS)
ZN ELECTRONS

0::

COHESIVE

ENERGY

CTUAL LATTICE CONSTANT OF CRYSTAL
ATOMIC SEPARATION

Figure 1.4: Banding of energy levels in diamond as atoms are drawn together.
(From Ref. 24.)

buffer layer grossly mismatched to an InSb substrate eliminates microcracks and
dislocations in a subsequent structure.

1.4

Effects arising from strain

1.4.1

Electronic band structure

The complex nature of the electronic band structure of solids arises directly
from the interactions of electrons in close proximity to each other. As depicted
in Fig. 1.4, distantly separated atoms display electronic levels at essentially identical energies. As atoms are drawn together, these levels interact to satisfy the
Pauli Exclusion Principle, splitting and shifting according to the proximity and
geometry of surrounding atoms. As can be inferred from Fig. 1.4, this interaction

12
substantially alters the relative and absolute positions of electronic bands; changes
in interatomic distances associated with strain will clearly have a substantial effect
on the band structure.
The regular arrangement of atoms on a lattice greatly simplifies the electronic
band structure of a crystal. Knowledge of the space group to which a particular
crystal belongs allows predictions of the interactions and energetic degeneracies of
the electronic states within that crystal. Strains are readily divided into two classes
according to their effects on the crystal space group: hydrostatic strains, which
(barring a phase transition) preserve the space group and consequently the highsymmetry degeneracies; and uniaxial, which in general lower the crystal symmetry
and split these degeneracies. In the following discussion we will limit ourselves to
considerations of the shifts of the conduction and valence bands under hydrostatic
and < 100 > uniaxial strains in zinc blende crystals. This is a case of real interest
in strained-layer superlattices, as the majority of structures grown to date are
either diamond or zinc blende in structure and are biaxially strained to fit a twodimensional < 100 >- or < 111 >-oriented template.*
As is apparent from Fig. 1.4, hydrostatic strains change the absolute positions
of the conduction and valence band edges, as well as the energy gap separating them. These shifts are approximately linear with atomic separation for small
strains. Following the notation of Ref. 25, the change in absolute position of the
valence band edge under hydrostatic dilation or contraction, c, can be expressed
in terms of a deformation potential a as b,.Ev = a€. We define a parameter c that
satisfies an analogous relationship for the conduction band. While the change in
energy gap under hydrostatic strain is readily measured and yields ( c - a) with
high accuracy, the relative shifts of band edges in different materials ( i.e., the absolute values of a and c) are difficult to determine experimentally. Relative band
*Note that these biaxial strains are equivalent to sums of hydrostatic and uniaxial strains.

13
offsets across heterojunctions are typically determined for structures in which lattice mismatches are small or in which stresses have been relieved by the formation
of misfit defects. The role of strain in determining the band offsets has not yet
been measured. We have chosen to use values of a and c calculated by chemical
bonding considerations. 26 Strained band offsets have been obtained by adding the
shifts from these deformation potentials to the measured values of the unstrained
band offsets. Recently, there have been calculations that suggest that hydrostatic
strain has very little effect on the band offsets. 27 This issue remains to be resolved.
The effects of uniaxial strains on states at the Brillouin zone center are described
by parameters b and d, which characterize band splittings under the influence of
[100]- and [111 ]-oriented strains, respectively. Exciton splittings determined from
reflection spectroscopy provide accurate estimates of these deformation potentials
for stresses up to approximately lkbar (equivalent to a strain of about 0.1% in these
systems). Observed exciton splittings are approximately linear with applied stress
at these pressures 28 ,29 but are assumed to deviate substantially from linearity for
strains of the magnitude typically encountered in strained-layer superlattices. For
[001]-oriented, zinc blende, strained-layer superlattices, the r-point band edges
become
b2

ELH

a€+ b( Czz - C:z:a:) + 2 Li. ( Czz - C:z:a:) 2

(1.1)

EHH

ac - b(czz - ca:a:)

(1.2)

Eco

Egap

+ Cc

(1.3)

(to first order in spin-orbit splitting, Li.). Deformation potentials are typically on
the order of electron-Volts. Values for zinc blende II-VI semiconductors are listed
in Table 1.1.
The effects of strain on the band edges of a ZnSe/ZnTe superlattice are illustrated in Fig. 1.5. For the strained case we have calculated for a configuration in

Table 1.1: Deformation potentials of some zinc blende II-VI semiconductors. Energies are in eV.

Material

ZnTe

1.35

-2.7

-1. 78b

-4.58b

ZnSe

1.35

-2.82

-l.2c

-3.81 C

ZnS

1.58

-3.6

0.53d

-3.7ld

CdTe

1.23

-2.2

-l.18e

-4.83e

CdSe

1.24

-2.47

CdS

1.31

-2.68

a. From Ref. 26.

b. From Ref. 28.

c. From Ref. 30.
d. From Ref. 31.
e. From Ref. 29.

which the elastic energy of a [100]-oriented, 50% ZnSe, 50% ZnTe structure has
been minimized with respect to a single in-plane lattice constant. In this "freestanding" case the lattice constant is an average of the bulk lattice constants of the
constituent materials, weighted by layer thicknesses and relative rigidities of the
bulk materials (see Section 2.4.1). ZnSe, with a bulk lattice constant of 5.669A, is
under biaxial tension when combined with ZnTe, which has an unstrained lattice
constant of 6.104A. This biaxial tension is equivalent to a hydrostatic dilation and

15
UNSTRAINED

COHERENTLY STRAINED

ZnTe ZnSe ZnTe

LH, HH

LH
HH

Figure 1.5: Effect of strain on the band edges in a ZnSe/ZnTe superlattice. A
valence band offset of le V was assumed before the application of strain. 32

a uniaxial compression. In this case the hydrostatic component shifts the ZnSe valence and conduction bands to lower the band gap by several tens of me V's, while
the uniaxial component shifts the light hole band above the heavy hole by 218meV.
Conversely, biaxial compression moves the ZnTe heavy-hole band above the lighthole by 253meV and further separates the conduction band edge from the energy
of the unsplit valence bands. Note that the strained ZnTe band gap is actually
smaller than that of unstrained ZnTe; uniaxial splitting more than compensates
for the increase in band gap coming from hydrostatic compression.

While there are several methods for calculating electronic band structure that
incorporate effects arising from strain, 25 ,33 our calculations are based on a k •p
perturbation theory. The fact that the strain tensor Cij transforms like kikj under
the symmetry operations of a given space group makes this technique particularly

16
well suited to the incorporation of strain. In addition, this is the method of choice
for calculations of optical properties since < '1/Ji IPl'!fj > matrix elements are dealt
with explicitly. These are readily related to oscillator strengths, from which it is
possible to calculate optical properties of interest.
The k •p method is a perturbation technique that allows complex band structure to be calculated around a point for which the eigenvalues of the system are
known. Details of the technique are described in Section 2.4.1. This method can,
in principle, yield complex band structure to arbitrarily great accuracy as more
bands are included and higher-order corrections are added to the Hamiltonian.
As with any perturbation method, the approximations are best near the point at
which the eigenvalues are known (in our case, the zone center). Uncertainties associated with deformation potentials are much larger than those associated with
the k · p method for the superlattices we have considered.*
Results of the k · p calculations for the ZnSe/ZnTe system are shown in Fig. 1.6.
The figure shows bulk band structures calculated for k11 = 0 for the cases in which
material is either unstrained or biaxially strained along < 100 > directions. As
in Fig. 1.5, the strained band structures were calculated under the assumption
that the two in-plane < 100 > lattice constants had adopted a value appropriate
to a free-standing structure composed of equal amounts of ZnSe and ZnTe. It is
apparent from the figure that the higher valence band is light-hole-like in ZnSe
and heavy-hole-like in Zn Te. This could be expected to have a significant effect on
transport of holes in this direction.

*The envelope function approximation starts to break down in the limit of very thin superlattice
layers. 34 The thinnest layers we have considered are 20 A, for which the approximation should
still be good.

ZnSe

ZnTe

UNSTRAINED
UNSTRAINED

0.25

STRAINED

0.25

k (1r/a)

0.25

Figure 1.6: Electronic band structure of bulk ZnSe and ZnTe for k11 = 0 showing
the effects of strain. A ZnSe/ZnTe valence band offset of leV was assumed in
aligning the band structures of the two materials in the unstrained case. 32 The
strained band structure was calculated assuming a biaxial < 100 > strain chosen
to minimize the elastic energy of a coherent structure composed of equal quantities
of ZnSe and ZnTe. Spacing between tick marks on the ordinate is leV. (Adapted
from Ref. 32.)

1.4.2

Defect formation

Overlayers poorly lattice-matched to a substrate have long been known to generate mismatch-accommodating structural defects under certain circumstances. 14.1 5,16 .1 7
The appearance of these misfit dislocations is typically observed when the film is
grown beyond a "critical thickness," below which growth is relatively defect-free.
Determining these critical thicknesses and understanding the nature of dislocation
formation, nucleation, and interaction have become increasingly important with
the development of techniques for fabricating heteroepitaxial structures composed
of highly dissimilar materials. Dislocations create electrically active deep levels 24
that act as alternate carrier decay channels and also provide mechanisms for the
generation of point defects and defect complexes. 35 Degradation of light-emitting
diodes (LED's) has been associated with dark line defects created during nonradiative recombinations at dislocation-related deep levels, 35 and misfit dislocations
appear to limit the gain of Ge:i:Sii-:i: HBT's. 36 Growing dislocation-free structures
is clearly desirable for a wide variety of device applications.
There are two limiting cases for lattice-mismatched growth, depicted in Figs. 1. 7
and 1.8. In the dislocation-free case the overlayer is in perfect registry with the
underlying lattice, with the result that the strained layer distorts tetragonally
according to a biaxial analogue of Poisson's ratio (ezz = -2(C12 /C11 )e:i::z:), Alternatively, the mismatch can be accommodated purely by misfit defects. In this
case, dislocations are regularly spaced at an interval of (b sin /3 cos 1 ) / f, where b is
the Burger's vector associated with the particular type of dislocation, f is the mismatch jao - a 1 j/ai, /3 is the angle between the Burger's vector and the dislocation
line, and I is that between the interface and glide plane. 15
Early attempts by Van der Merwe 14.1 5 to model critical thickness relied on
estimating the thickness at which the limiting case of the completely unstrained
lattice becomes energetically favored over the dislocation-free strained lattice. Ac-

COHERENTLY STRAINED COMMENSURATE SUPERLATTICE

_j_
a 5;

5. 431 A)

_j_

Si
substrate

Figure 1.7: Schematic indicating the arrangement of unit cells in a coherently
strained, commensurate superlattice.

Atoms in the superlattice are in perfect

registry with those in the substrate.

In the case shown here all of the strain

lies in the Gea,Sii-m layers, resulting in tetragonal distortion of these layers. The
magnitude of the distortion has been exaggerated for clarity ( the numerical lattice
parameters are correct, however).

UNSTRAINED SUPERLATTICE

_1_
OSi

(5.431.i)

_1_
Oolloy

5.545.A)

Si
substrate

Figure 1.8: Schematic of the arrangement of unit cells in an unstrained superlattice. Lattice mismatch is accommodated by regularly spaced networks of misfit
dislocations lying at the interfaces. The difference in bulk cubic lattice constants
is exaggerated in the diagram, although the numerical values are correct.

21
cording to continuum elasticity theory, the areal strain energy Es of an overlayer
constrained to grow on a lattice-mismatched template increases linearly with film
thickness,

whereµ indicates shear modulus and l indicates film thickness. 37 The areal energy
density associated with a network of dislocations sufficiently dense to totally relieve
strain is

(1.5)
where Ed is the energy per unit length of a single misfit dislocation. For a single
misfit-accommodating dislocation this energy is

Ed=:~ c-t~:•~)log(~}

(1.6)

where v 1s Poisson's ratio and p determines the radius within the core of the
dislocation at which the integration of energy begins (p is typically chosen to be
4). 37 Equating the strain-field and misfit-dislocation energy densities yields an
implicit equation for critical thickness le:

b(l - v cos /3)
- 47rlc(l + v) sin/3 cos 1' og

f _

(Plc)

T ·

(1.7)

A critical thickness relation based on an early energy-balancing argument1 4 is
plotted in Fig. 1.9 for Burger's vectors appropriate to Si. Misfit-accommodating
dislocations typically found in diamond or zinc blende structures are characterized
by {111} slip planes, Burger's vectors of (a/2) < 110 >, and dislocation lines
along < 110 > directions in an < 001 > interface. 16 In this case, 1' = 35.3 ° and

/3 = 60 ° for < 100 >-oriented growth. While some data are in agreement with
the predictions of this early model, 38 .1 4 many films have been observed to remain
coherently strained well beyond this limit. 39

Attempts to explain the discrepancies between observed and predicted critical
thicknesses led to a force balancing argument by Matthews and Blakeslee. 16 .1 7 The
stress exerted on a dislocation line at a lattice-mismatched interface is proportional
to the thickness of the overlayer,
(1.8)
where A is the angle between the direction of slip and the line in the interface that
is perpendicular to the intersection of the slip plane and the interface. As there is
a maximum tension beyond which a dislocation undergoes further slip, a thickness
can be derived at which a grown-in threading dislocation will jump discontinuously
at a strained interface. For a single thin film this thickness is described by

[i (le) ]

b(l
---vcos
- -a)
- og - +1,
f -_ 81rcos.:\(l + v)lc

(1.9)

where a is the angle between the Burger's vector and the dislocation line. This
relation has been plotted for Gea:Sii-a: in Fig. 1.9. While this theory has seen some
agreement with experiment, grown-in threading dislocations are rarely present in
sufficient densities to provide significant relaxation of mismatch stresses. Forcebalancing arguments have been applied to the nucleation of half loops, but the
importance of these dislocations in relieving mismatch stresses remains unclear_ 17
Good agreement with experiment has been achieved with a recent adaptation
of the old energy balancing arguments. 39 By terminating the strain field associated
with a single dislocation at a radius w /2 (independent of misfit, f) and inserting
the energy expression for a screw dislocation into the energy-balance equation, one
obtains the relationship
(1.10)
Choosing w = 5b yields the plot in Fig. 1.9, which is in excellent agreement with
experiment in the Gea:Sii-a: system. Unfortunately, the physical basis of this model

105
SINGLE FILM CRITICAL THICKNESS

•\

'\
'\
•\
'\

104

(Si parameters)

Van der Merwe, 1963

,,.-...
<(

......,,
en
en

103

Blakeslee, 1974

Matthews &

----

Bean, 1986

People &

' \.

' '\

' ' ,,,

., .

, . , ...,

I-

...

.............

.....

.............

............

...... _

.... ......

.............

-- -- ---

MISFIT

(%)

Figure 1.9: Theoretical predictions of critical thickness at which a thin film poorly
lattice-matched to a substrate breaks away from that substrate with the formation of misfit dislocations. Calculations assumed dislocations appropriate to

< 100 >-oriented growth of Si. The predictions can be extended to many zinc
blende semiconductors by scaling thickness with the lattice constant of the material in question. The curve labeled Van der Merwe comes from an energy-balancing
relation 14 similar to Eqn. 1.7; Matthews and Blakeslee is from Eqn. 1.9, Ref. 16;
and People and Bean is from Eqn. 1.10, Ref. 39.

is doubtful. The validity of terminating the strain field is unclear, as is the assumption that w is independent of misfit. In addition, a screw dislocation corresponds
to a lateral displacement of atoms across a half-plane cut, which does not involve
the addition or removal of atoms. Thus, unlike an edge-type dislocation, a screw
dislocation does not relieve lattice mismatch. TEM studies 35 have confirmed that
mismatch-relieving dislocations nucleated at the critical thickness are not screwtype. It is probable that the agreement between this theory and experiment comes
primarily from the addition of a free parameter, w, in the problem. Note that
neither the original force- nor energy-balancing arguments included such a parameter.
Although each of these theories is concerned with the critical thickness of a
single film, there are simple prescriptions for extending the predictions to strainedlayer superlattices. The energy-balancing arguments are readily seen to form two
criteria: one for the stability of the individual layers, and one for the stability of
the superlattice as a whole. The individual layer and overall superlattice strain
energies can be thought of as AC and DC components of the strain field in the
superlattice; 40 stability of the structure requires that neither component grow too
large. The prediction of coherence of the individual layers is identical to that
for the single film case. The superlattice as a whole has an elastic strain energy
that is approximately equal to that of an alloy of the same overall composition
and thickness.

Thus, if the equivalent alloy lies beyond the predicted critical

thickness, the superlattice should also lie beyond this thickness. It has recently
been shown that this can give rise to the configuration depicted in Fig. 1.10,9,40 in
which the superlattice has broken away from the substrate. In this "free-standing"
configuration lattice mismatch within the superlattice is accommodated purely by
elastic strain, with a large biaxial compression of the Ge.,Sii_., layers converted
into lesser expansions and contractions of adjacent Si and Ge.,Sii_., layers.

FREE-STANDING STRAINED SUPERLATTICE

_1_
as;

( "'5.39A)

_1_
a alloy

("'

5 . 5 9 A)

Si
substrate

Figure 1.10: Arrangement of unit cells in a free-standing superlattice. A network
of dislocations at the superlattice/buffer-layer interface relieves the overall strain
between the superlattice and buffer. Lattice-mismatch is accommodated elastically
within the superlattice, with strain divided between the layers to minimize the
elastic energy of the structure. Tetragonal distortions within the superlattice are
exaggerated for clarity, but the numerical lattice constants are correct.

26
While it should be possible to extend force-balancing arguments similarly for
multilayer structures, to date this has been done for only a few cases. 16 It is worth
noting that in the case of a multilayer structure the lattice mismatch associated
with a given critical thickness is claimed to be twice that of the single film case,
owing to the creation of two misfit dislocation lines (one each at the top and bottom
of a single layer).
Recent experiments have suggested that certain strained-layer structures are
metastable and hence are not appropriately described by the classical criticalthickness theories. 41 ,42 ,43 It has become clear that the critical thickness displayed
by a particular sample is dependent on more than bulk material parameters.
Rather than satisfy zero-temperature energy minimization requirements, strained
structures have been shown to display activation barriers against the nucleation
and glide of dislocations. These barriers enable highly strained layers to be grown
far beyond the energy-balancing critical thicknesses. 42 This is the subject of Chapter 4.

1 .. 5

Summary of thesis

1.5.1

Luminescence from CdTe/ZnTe superlattices

Chapter 2 presents a photoluminescence study of CdTe/ZnTe superlattices and
a Cda:Zn 1 _a: Te alloy and a comparison of experimentally observed superlattice band
gaps with those calculated using k · p theory. Attempts to observe stimulated
emission by optically pumping small cleaved cavities were also made. The work was
motivated by several factors. The II-VI semiconductors having large direct band
gaps are of technological interest as visible light emitters and detectors. Doping
considerations make the CdTe/ZnTe system particularly attractive; high-mobility
p-type ZnTe is easily grown, and, unlike many of the II-VI semiconductors, CdTe

is readily doped p- and n-type. The enormous lattice mismatch between CdTe and
ZnTe (/ = 6%) raised questions as to the effects of strain on the optical properties
of the superlattice as well as the ability of such a structure to accommodate large
stresses.
The results can be summarized as follows. Each of the superlattices emitted
visible photoluminescence several orders of magnitude more intense than that from
a Cd:l!Zn1 _m Te alloy. Spectra were dominated by a single Gaussian line probably
due to an exciton.

The choice of topmost buffer layer was not systematically

related to photoluminescent intensity or peak position, in contrast to results obtained from systems of smaller lattice mismatch. Energy band gaps calculated
using a k •p model incorporating effects arising from strain were in disagreement
with experiment when strain was assumed to be derived from a CdTe buffer layer.
Excellent agreement was obtained when it was assumed that the superlattices had
broken away from this buffer to adopt a strained configuration that minimized the
elastic energy of the superlattice. In view of calculated critical thicknesses, this
was proposed as a viable configuration for such a structure. However, these experiments alone were insufficient to establish the free-standing configuration as that
of our samples; band gaps calculated under the assumption of entirely unstrained
superlattices (i.e., with dislocation networks at every interface in the superlattice)
were also in agreement with experiment. Based on the band structure calculations,
predictions of transitions between type-I and type-II band alignments were made
for coherently strained superlattices. Attempts to obtain stimulated emission from
an optically pumped sample have been unsuccessful to date; this is the subject of
on-going work.

1.5.2

Structural properties of CdTe/ZnTe superlattices

X-ray diffraction, in situ reflection high-energy electron diffraction (RHEED),
and TEM studies of CdTe/ZnTe superlattices are the subject of Chapter 3. The
purpose of the work was to examine the distribution of elastic strain in a highly
lattice-mismatched superlattice. In addition, these samples provided a test of predictions for single-layer critical thicknesses and their extrapolation to superlattices.

It was concluded that each of the samples had been grown beyond the critical
thickness for creation of misfit defects. Defect densities were seen to drop dramatically away from the superlattice/buffer-layer interface, however, with structures
approaching a free-standing configuration. Substantial free-standing superlattice
strains were observed in all but one of the samples. The most highly defective
superlattice was below the critical thicknesses predicted for the individual layers
and for the superlattice as a whole, unlike a number of more highly strained samples. This result was attributed to slight variations in sample-to-sample growth
conditions. The work suggested that the critical thickness of a particular sample is
dependent on the thermal history of the sample, in addition to the material system
and lattice mismatch.

1.5.3

Dislocation formation in Ge 0.5 Si0.5 /Si superlattices

Chapter 4 presents a study of dislocation formation in Ge0 •5 Si 0 . 5 /Si superlattices
by channeled Rutherford Backscattering Spectroscopy (RBS), x-ray diffraction, in

situ RHEED, and cross-sectional and plan-view TEM. The dependence of dislocation formation on growth temperature was examined to investigate the equilibrium
assumptions behind the critical thickness theories and to try to account for discrepancies in critical thicknesses reported in the literature. Ge/Si structures are
particularly well suited to this study as they are readily grown over a wide range of
temperatures ( approximately 300 °C to 850 °C for single-crystal growth). Aecom-

29
modation of lattice mismatch in this system is of particular interest as the success
of proposed Ge 00 Sii_., HBT's and light emitters and modulators will in part be
dependent upon maintaining high levels of coherent strain.
The density of misfit-accommodating dislocations was found to be strongly dependent on growth temperature. Dislocation densities dropped from 1.5 x 10 5 cm- 1
at a growth temperature of 530°C to < 10 5 cm- 2 at 365°C. Dislocation networks were most dense near the superlattice/buffer-layer interface; several structures adopted an almost defect-free configuration near the free-standing limit. The
results have been taken as evidence of an activation barrier against the nucleation
or glide of dislocations. While the equilibrium critical thickness of a sample may
still be regarded as dependent only on bulk material properties, the appearance of
misfit defects in a particular sample is dearly dependent on thermodynamic factors which may effectively freeze a sample in a highly strained, metastable state.
Our data are in support of a plastic-flow model of defect formation currently being
developed. 44

References
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2. L. Esaki and R. Tsu, IR/\,f J. Res. Develop. 14, 61 (1970).
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4. G. H. Dohler, Physica Scripta 24, 430 (1981).
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6. G. Bastard, Phys. Rev. B 24, 5693 (1981).
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Phys. Lett. 48, 1383 (1986).

9. R. H. Miles, T. C. McGill, S. Sivananthan, X. Chu, and J. P. Faurie, J. Vac.
Sci. Technol. B 5, 1263 (1987).

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31
12. R. N. Bicknell, N. C. Giles-Taylor, D. K. Blanks, R. W. Yanka, E. L. Buckland,
and J. F. Schetzina, J. Vac. Sci. Technol. B 3, 709 (1985).
13. D. L. Smith, private communication.
14. J. H. Van der Merwe, J. Appl. Phys. 34, 123 (1963).
15. C. A. B. Ball and J. H. Van der Merwe, in Dislocations in Solids, Volume 6,
edited by F. R. N. Nabarro (North Holland, Amsterdam, 1983), p. 122.
16. J. W. Matthews and A. E. Blakeslee, J. Cryst. Growth 27 118 (1974); 29 273
(1975); 32 265 (1976).
17. J. W. Matthews, in Epitaxial Growth, Part B, edited by J. W. Matthews
(Academic, New York, 1968).
18. S. M. Sze, Physics of Semiconductor Devices (Wiley, New Yo:rk, 1981).
19. W. L. Roth, in Physics and Chemistry of II- VI Compounds, edited by M. A ven
and J. S. Prener (Wiley, New York, 1967), p. 119.
20. S. S. Devlin, in Physics and Chemistry of II-VI Compounds, edited by M.
Aven and J. S. Prener (Wiley, New York, 1967), p. 551.
21. G. D. Studtmann, R. L. Gunshor, L. A. Kolodziejski, M. R. Melloch, J. A.
Cooper, Jr., R. F. Pierret, D. P. Munich, C. Choi, and N. Otsuka, Appl. Phys.

Lett. 52, 1249 (1988).
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24. J. I. Pankove, Optical Processes in Semiconductors (Dover, New York, 1975).

32
25. G. L. Bir and G. E. Pikus, Symmetry and Strain-Induced Effects in Semiconductors (Keter, Jerusalem, 1974).
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(1971).
27. C. G. Van de Walle and R. M. Martin, Phys. Rev. B 35, 8154 (1987).
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29. D. G. Thomas, J. Appl. Phys. Suppl. 32, 2298 (1961).
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(1970).
31. A. Gavini and M. Cardona, Phys. Rev. B 1, 627 (1970).
32. Y. Rajakarunanayake, R. H. Miles, G. Y. Wu, and T. C. McGill, Phys. Rev.
B, to be published.
33. S. Froyen, D. M. Wood, and A. Zunger, Proc. Mater. Res. Soc., to be published.
34. J. N. Schulman and Y.-C. Chang, Phys. Rev. B 24, 4445 (1981).
35. P. M. Petroff, in Semiconductors and Semimetals, Vol. 22, Part A, edited by
W. T. Tsang (Academic, Orlando, 1985).
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37. F. R. N. Nabarro, Theory of Crystal Dislocations (Dover, New York, 1987).
38. G. J. Whaley and P. I. Cohen, J. Vac. Sci. Technol. B, to be published.
39. R. People and J.C. Bean, Appl. Phys. Lett. 47, 322 (1985); 49, 229(E) (1986).

33
40. R. Hull, J. C. Bean, F. Cerdeira, A. T. Fiory, and J. M. Gibson, Appl. Phys.

Lett. 48, 56 (1986).
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42. R.H. Miles, P. P. Chow, D. C. Johnson, R. J. Hauenstein, C. W. Nieh, M. D.
Strathman, and T. C. McGill, Appl. Phys. Lett. 52, 916 (1988).
43. B. W. Dodson, J. Y. Tsao, and P. A. Taylor, Proceedings of the Third Inter-

national Conference on Superlattices, Microstructures, and Microdevices, to
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44. B. W. Dodson and J. Y. Tsao, Appl. Phys. Lett. 51, 1325 (1987).

Chapter 2
Luminescence from CdTe/ZnTe
Super lattices
2. 1

Introduction

2.1.1

Background

The wide band gap II-VI semiconductors have attracted attention for some time
as possible visible light emitters or detectors. 1 With direct band gaps ranging from
3300A to 7800A, the II-Vi's span the visible region of the spectrum. However,
the introduction of these materials within devices has been hindered by difficulties
associated with doping, primarily because of autocompensation during growth and
processing. In addition, the band-gap tunability offered by ternary alloys has been
difficult to realize experimentally, as the material is often of poor uniformity and
structural quality. 2 Each of these problems may now be surmountable with recent
developments in II-VI molecular-beam epitaxy (MBE) and metalorganic chemical
vapor deposition (MOCVD).
While the problem of doping II-VI thin films is beginning to be reassessed,*
*Results such as the recent demonstration of 9 x 10 17 p-type ZnSe are particularly noteworthy. 3

35
doping was not a major concern in this study. The ease with which CdTe is doped
p- or n-type has brought attention to Cd.,Zn1 _., Te for application in p-n structures
for some time. The near-band-gap emission of such a device would be in the green
to deep-red portion of the spectrum; CdTe has a band gap of 1.60eV (7750A) at
4K, and ZnTe has a gap of 2.38eV (5210A) at this temperature.
The structural quality and uniformity of ternary II-VI alloys have been demonstrated to be serious problems in both CVD- and MBE-grown films. Cda:Zn1 _,, Te
in particular has been shown to phase-separate for many alloy compositions. 4 Although avoiding the problems intrinsic to alloys, superlattices consisting of layers
of CdTe alternating with layers of ZnTe present additional problems associated
with the large lattice mismatch between the two materials. CdTe has a bulk lattice constant of 6.481 A, while that of Zn Te is 6.104A, resulting in a 6% mismatch.
The manner in which this mismatch is accommodated was of interest in this study,
as was the effect on the optical properties of the strain field and/or dislocations
arising from this mismatch.
The Cd Te/ZnTe superlattices examined here were the first wide band gap II-VI
superlattices studied. More recent work has demonstrated the successful growth
and excellent optical properties of ZnS/ZnSe 5 and ZnSe/ZnTe 6 superlattices. Our
study was also one of the first in a system with a large lattice mismatch. Although
several highly strained III-V structures had been examined prior to this CdTe/ZnTe
work (notably in the In.,Ga1 _,,As system 7 ), it was unclear that the effects of strain
and dislocations on the optical properties would be similar.

2.1.2

Results of this work

Photoluminescence from CdTe/ZnTe superlattices has been observed for the
first time. Superlattices with individual CdTe and ZnTe layer thicknesses between
approximately 20.A and 50.A have been compared with a Cdo.3'rZn0 •63 Te alloy. Each

36
of the superlattices displays intense, visible luminescence at substantially lower
energies than expected from corresponding Cda,Zn1-m Te alloys. Temperature and
pump-power dependences suggest that the dominant luminescent peaks are due
to excitonic recombinations. Experimental gaps based on this identification have
been compared with gaps calculated by a second-order k · p model including effects
that are due to strain. These calculations show that superlattices grown on CdTe
buffer layers are not strained according to the template set by this topmost buffer.
Calculated band gaps are in excellent agreement with experiment when the strain
distribution is assumed to conform to a minimum elastic-strain-energy condition
within the superlattice ( i.e., a free-standing configuration). This configuration is
argued to be stable for these superlattices, based on classical critical-thickness calculations, and is shown to be plausible based on the slow relaxation of stresses
once the critical thickness for nucleation of misfit defects is exceeded. Conversely,
strains set by topmost CdTe or ZnTe buffer layers are shown to lie far beyond
the accepted limits to defect-free growth for superlattice thicknesses comparable
to ours. Calculated gaps are also shown to be in good agreement with experiment
when strain effects are neglected. The unstrained configuration is unlikely, however, since the densities of dislocations necessary to reduce strains substantially
should open strong non-radiative decay channels, a result that is inconsistent with
the intense luminescence observed. Although the nearly free-standing nature of
the strain field in these superlattices has subsequently been verified by the structural characterizations described in Chapter 3, the two cases of free-standing and
unstrained growth could not be distinguished solely on the basis of band gaps.
Based on the agreement between theory and experiment, band gaps have been
calculated for a grid of Cd Te/Zn Te superlattices for the two cases of free-standing
strained growth and unstrained growth. Strain that is due to lattice mismatch is
shown to have a dramatic effect on the band-edge positions and on the energies

37
of the superlattice ground states. Transitions between type-I and type-II band
alignments are predicted based on these calculations.
Attempts to observe laser oscillation in a cleaved CdTe/ZnTe superlattice cavity
have proven unsuccessful to date. However, Cdo.2sZno.1sTe/ZnTe superlattices have
been recently reported to lase. 8

2.1.3

Outline of chapter

The samples examined in this study are described in Section 2.2. A study of the
photoluminescence spectra from these samples is presented in Section 2.3. Luminescent intensities and peak positions of the superlattices and alloy are compared,
and the primary peaks are identified to establish approximate values of the sample
band gaps. Section 2.4 describes calculations of the electronic band structure of
CdTe/ZnTe superlattices. Two- and eight-band k •ff models are briefly outlined, as
is the incorporation of strain within these models. Experimental gaps are compared
with those calculated assuming a variety of strains. Critical thickness arguments
are used to argue for the free-standing configuration, which is found to give the best
agreement between theory and experiment. Results of band-gap calculations for a
grid of superlattices are also presented. Section 2.5 describes attempts to observe
lasing in a CdTe/ZnTe structure. The conclusions are summarized in Section 2.6.

2. 2

Samples

The Cda:Zn1-a: Te samples used in this study were grown in a Riber 2300 MBE
machine. Each superlattice was grown on buffer layers deposited upon a (100)oriented GaAs substrate. Although Cda:Zn1_a:Te sometimes adopts a (111) orientation on (100) GaAs, 9 the initial buffer layers used in this study were chosen to
establish (100) epitaxy. Topmost buffers were either Cd Te, ZnTe or a Cda:Zn 1 _a: Te

38
alloy. The superlattices were grown at approximately 180 °C. Individual Cd Te
and ZnTe layers within the superlattices ranged in thickness between approximately 20 A and 50 A, as indicated in Table 2.1. Superlattices consisted of several
hundred repeats; total superlattice thicknesses were roughly a micron. The buffer
layers for samples 4 and 8 were grown directly on GaAs substrates. Samples 1,
2, and 3 were each grown on step-graded Cda:Zn1 _a: Te buffer layers, starting with
ZnTe on a (100) GaAs substrate and increasing Cd content in discrete increments
as growth proceeded. The Cda:Zni-a: Te buffer layer of sample 6 was grown on a
30A/30A CdTe/ZnTe superlattice, whereas that of sample 7 was grown on three
superlattices of increasing Cd content.
Superlattice compositions and layer thicknesses were determined by a variety
of means. In situ growth-monitoring techniques were of limited use in determining
sample characteristics as these were amongst the first such films grown. The average thickness of individual superlattice periods was determined by x-ray diffraction
(see Section 3.2.1). Relative ratios of Cd to Zn were determined for each sample
through energy dispersive spectroscopy (EDS). This was a source of potential error, however, as the volume sampled by this technique is comparable in depth
to the thickness of the superlattices. Signal from the substrate was minimized
by reducing the energy of the impinging electron beam and by tilting the sample with respect to this beam. The accuracy of the compositions determined by
EDS was checked by analyzing x-ray diffraction spectra from intentionally alloyed
pieces of samples 2, 3, and 4. Compositions determined by applying Vegard's Law

( i.e., linear change of alloy lattice constant with composition) to these data are in
reasonable agreement with results derived from EDS.
CdTe and ZnTe layer thicknesses quoted in Table 2.1 were calculated from the
measured superlattice compositions and periodicities based on the assumption of
negligible interdiffusion. Layer thicknesses determined by TEM for sample 8 are

Table 2.1: CdTe/ZnTe superlattice samples.

Superlattice
Sample

Cd Te/Zn Te ( A)

Periods

Top buffer

(Reference No.)

26/32

200

CdTe

(199 35)

31/23

200

CdTe

(197 33)

56/50

150

CdTe

(194 32)

27/30

200

ZnTe

(198 34)

24/30

200

Cdo.sZno.sTe

(201 36)

27/30

200

Cdo.sZno.sTe

(206 40)

35/32

200

Cdo.sZno.sTe

(207 41)

21/20

400

Cdo.sZno.sTe

(120 17)

29/35

250

Cdo.sZno.sTe

(122 18)

in agreement with the calculated values. The assumption of minimal interdiffusion
is borne out by photoluminescence and TEM data from these samples, but this
is not true of all CdTe/ZnTe superlattices; interdiffusion has been shown to be
significant in this system at higher growth temperatures. 10
A Cdo,31Zno.63Te sample was grown for comparison with the superlattices.
Composition of the film was determined by EDS and has been confirmed by photoluminescence. The alloy was grown to a thickness of 4.lµm on a (100)-oriented
GaAs substrate.

2. 3

Photoluminescence

2.3.1

Theory

Light resulting from the radiative decay of an electron-hole pair subsequent
to optical excitation is referred to as photoluminescence. Analysis of this luminescence can yield a variety of information pertaining to the static and dynamic
electronic properties of a material. Photoluminescence is usually a nondestructive
experiment, and as a consequence it has become popular to parlay spectra into a
variety of diagnostic information (pertaining to alloy compositions, impurity concentrations, or strain distributions, for example).
A typical photoluminescence process is depicted schematically in Fig. 2.1. An
incoming photon with an energy exceeding the band gap of the material is absorbed
to create an excited electron-hole pair. In an indirect-gap material this process can
require the emission or absorption of a phonon, but in direct-gap semiconductors
such as Cd Te and Zn Te the dominant process is absorption without the involvement
of phonons. For the purposes of the experiments described here, the electrons
and holes can be described as dropping rapidly to the band extrema through the
emission of phonons. This process usually takes place on a subnanosecond time
scale. 11 In reality, the dynamics of this process can be quite complicated, with
electron-electron interactions bringing the carriers into a quasi-thermal distribution
on a lOOpsec time scale. This distribution may couple only weakly to the lattice,
with the phonon temperature reaching equilibrium with that of the carriers on a
somewhat longer time scale. Carriers relaxing to the conduction and valence band
extrema may recombine radiatively, giving up a photon of energy approximately
equal to the band gap E 9 of the material, or may form bound electron-hole pairs
( excitons) with ground-state binding energies on the order of several me V ( Eex =
m;e 4 /2h 2 E2 , where 1/m; = 1/m: + 1/mii, for electron and hole effective masses

PHOTOLUMINESCENCE
CB

hvilW\/\t+

'V\J\l\t+hvout

VB
Figure 2.1: A typical photoluminescence process, with absorption of a photon
with energy fiwin and emission of a photon with energy close to the band gap of
the semiconductor fiwout ~ E 9 • The case illustrated is for a direct-gap semiconductor, in which the valence and conduction band extrema lie at the same point
in k-space. Momentum conservation requires emission or absorption of a phonon
for recombination near an indirect band gap.

and mh, respectively ). 12 Subsequent radiative decay of these excitons occurs at an
energy Eout ~ E 9

Eex•

The ratio of band-to-band versus excitonic luminescence

is strongly dependent upon the binding energy of the exciton and the temperature
of the sample.
Effects such as nonradiative recombinations and radiative decays associated
with impurities or defects greatly complicate the nature of the luminescence from
many samples. Impurities introduce electronic levels at well-defined energies within
a material, with the result that the energy of band-to-impurity recombinations can
yield information pertaining to the doping of a particular sample. Nonradiative
decays are by nature less difficult to isolate, but are known to result from surfaces
or structural defects in addition to higher-order scattering (Auger or multiphonon)
events.
Luminescence features can often be identified by observing the temperature and
pump-power dependences of the lines or by time-resolved techniques. The decay of
a particular line with increasing temperature gives an approximate measure of the
binding energy of that feature. Extrinsic lines can often be distinguished from intrinsic by the power levels at which the features saturate. In addition, excitonic or
band-to-band features display different power dependences from impurity-to-band
lines, which in turn differ from lines associated with impurity-to-impurity transitions. In practice, the impurity associated with a particular line is usually identified
by intentionally changing the concentration of various impurities from sample to
sample. 13 There are, however, methods such as selective excitation luminescence
which can yield excited state information unique to a particular impurity. 14
Numerous schemes have been employed to spatially resolve photoluminescence
across the surface of a wafer and as a function of depth. The absorption of light
within a semiconductor is governed by the joint density of states separated by
the energy of the incoming photon hw, weighted by an occupation factor and a

43
probability associated with the transition. For the case of a direct-gap semiconductor in which the probability of valence-to-conduction-band transitions is largely
independent of k, the absorption coefficient is

e - ( 2 m*m*
A*~ - h e

nch 2 m*e

m*h

+ m*e

)½

(2.1)

where E 9 is the energy gap of the semiconductor and n is the index of refraction.
This dependence on the energy of the incoming light means that by changing the
wavelength of the exciting beam it is possible to probe different regions in a sample.
This technique is particularly useful in direct-gap semiconductors, as MBE-grown
film thicknesses are of approximately the same magnitude as typical absorption
lengths (roughly lµm). Networks of structural defects have been isolated using
this technique. 15

2.3.2

Experimental setup

The photoluminescence setup used in these experiments is depicted in Fig. 2.2.
Optical excitation of the samples was provided by a Coherent CR-3000K krypton
laser and a Coherent Innova 20 argon ion laser. Kr violet lines at 4131 A and 4154 A
and an Ar green line at 5145 A were chosen to pump the samples at energies greater
than the band gaps. The lasers were operated in a continuous wave (cw) mode
with typical power levels of lmW, obtained by lowering the current through the
laser tube and by attenuating the output beam with neutral density :filters. A Spex
Lasermate was sometimes used between the laser and sample to monochromate the
beam. Notch filters reduced background noise that was due to plasma lines when
the Lasermate was not in place. The beam was focused to a spot roughly lmm 2
in area at the sample. Samples were cooled to temperatures between 2 - 77K in a
Janis Model DT-8 liquid He immersion dewar.
Luminescence from the samples was focused by collection optics onto the front

double grating
spectrometer

[[

filter

luminescence

sample
dewar

S-1 PMT

Kr+
amplifier

laser

disc.

Computer

MCS

Figure 2.2: Schematic of the apparatus used in the photoluminescence experiments.
Adapted from Ref. 16.

45
slit of a Spex 1404 double-grating spectrometer. Gratings blazed at 1.6 µm were
used in second order to maximize spectrometer throughput around 8000 A. Cutoff
filters were placed in front of the spectrometer to attenuate light out of the spectral
range of interest (if allowed to pass through a grating spectrometer, this light
can diffract in a different order and appear superimposed upon the spectra under
study). Luminescence passing through the spectrometer was detected by an S-1
photomultiplier tube (PMT) cooled to 77K. Signal from the PMT was amplified,
passed through a discriminator, and triggered a time-to-pulse-height converter,
which outputs uniform pulses. The length of these pulses (5µsec) inserted a dead
time into the system, which limited useful count rates to less than lOOkHz. (The
PMT recovery time of ~ 30nsec was not a limiting factor.) Pulses were binned by
a multichannel scaler (MCS). Data were subsequently transferred to computers for
analysis.

2.3.3

Results

Typical CdTe/ZnTe superlattice luminescence is compared with that from a
Cdo,31Zno.63Te alloy sample in Fig. 2.3. The alloy luminescence is characterized
by a weak, broad feature with a high-energy cutoff of 2.02eV at 5K. The observed
luminescence is in excellent agreement with that obtained in previous Cd.,Zn 1 _., Te
alloy studies, 17 and is approximately two orders of magnitude less intense than
that from the superlattices under the pump conditions described here. Photoluminescence from the superlattices is dominated by intense lines at the high-energy
end of the spectrum. Sample 3 displays two such peaks and sample 8 displays four.
All other superlattices display a single peak. The full width at half maximum of
these intense peaks varies between 20 - 30meV from sample to sample. Additional
luminescence is observed in each sample at lower energies and substantially lower
intensities than the primary lines. Luminescence at the primary peaks increases

CdTe/ZnTe PHOTOLUMINESCENCE

....._30 meV

.....,

SUPERLATTICE

·..0

T -

.......,,,,.

zw
......
ALLOY

1.6

1.7

1.8

1 .9

2.0

ENERGY (eV)

Figure 2.3: Photoluminescence spectra for CdTe/ZnTe superlattice sample 2 and a
Cdo.31Zn0 •6 3Te alloy at 5K. Luminescent intensity is plotted against emitted photon
energy. Spectra are plotted on different vertical scales.

47
superlinearly with pump power at a rate greater than that of the lower energy
lines.
The intense luminescence features observed from the superlattices appear to be
associated with excitonic recombinations. The absence of any appreciable luminescence at energies greater than the cutoff suggests that the observed line is very near
the sample band gap. Both the superlinear power dependences of the lines and the
absence of noticeable saturation at the pump powers used here suggest that the
lines are not associated with impurities. The lines decay rapidly with increasing
temperature; typical luminescent intensities at 30K are down by a factor of 2-3
from the 5K intensity, and at 65K the features have almost disappeared. This
temperature dependence is consistent with a weakly bound feature, and would not
usually be expected for band-to-band luminescence, which typically becomes more
prominent as previously bound carriers are thermally excited into the bands. As
shown in Fig. 2.4, the lines are fit by Gaussians. This line shape is suggestive of
a random variation within the samples, in this case in layer thickness. Note that
the line shape cannot be used to argue for excitonic versus band-to-band luminescence, as self-absorption should not play a major role in determining the line
shape near the band edges over energies of a few tens of meV. The inset of Fig. 2.4
compares the Gaussian fit to the luminescence line to that expected from band-toband recombinations across the same Gaussian distribution of band gaps, assuming
self-absorption calculated from Eqn. 2.1. The inset shows almost identical spectra
with and without self-absorption from the band edges; line shape cannot be used
to distinguish above- and below-band-gap luminescence in this case.
Two of the superlattices display several intense lines. Luminescence from sample 8 is characterized by four such lines, and sample 3 by two. The temperature
dependence of the photoluminescence from sample 8 is shown in Fig. 2.5. The scans
shown in this figure were taken under identical pump conditions. Spectra taken at

CdTe/ZnTe PHOTOLUMINESCENCE

(./)

zw
.....

PL
FIT

1.7

1.8

1.9

ENERGY (eV)

Figure 2.4: Intense photoluminescence line from CdTe/ZnTe superlattice sample
5. The line shape is nearly Gaussian, probably resulting from a random variation within the sample (in layer thickness, in this case). The inset compares the fit
with that calculated from a Gaussian distribution of band-to-band recombinations,
including effects that are due to self-absorption. The line shapes are almost identical; the luminescence cannot be positively identified as band-to-band or excitonic
simply on the basis of line shape.

20K, 35K, and 50K come from the same part of the sample; the 5K luminescence
comes from an area just to the side of that probed in the other scans. Luminescence below 1.7eV is seen to be almost independent of temperature. These
features can be related to an underlying Cd0 . 5 Zn0 . 5 Te buffer layer. Features at
higher energies show strong temperature dependences and appear to be coming
from the superlattice. The intensities of these lines show nearly identical superlinear dependences on incident pump power. The similarity of the temperature and

TEMPERATURE-DEPENDENT PHOTOLUMINESCENCE

_...
(I)

::J

102

....
·.a
L.
L.

...._,.

....·->.
....
( I)

(1)

SAMPLE 8

1.6

1.7

1.8

Energy (eV)
Figure 2.5: Photoluminescence spectra for CdTe/ZnTe superlattice sample 8 at
5K, 20K, 35K, and SOK under constant pump conditions. Luminescent intensity
is plotted against emitted photon energy. Each of the four distinct luminescence
peaks from the superlattice (above 1.7eV) shows a strong temperature dependence,
whereas luminescence from the Cd0 _5 Zn0 . 5 buffer (below 1.7eV) shows almost none.
The regular 30meV spacing and the similarity of the temperature and pump-power
dependences of the superlattice peaks suggest that they originate from the same
basic recombination process but are associated with quantum wells that differ in
width by a single monolayer of CdTe. Narrow spikes on the spectra are due to
plasma lines from the pump laser.

pump-power dependences strongly suggest that the lines are associated with the
same basic recombination process. The four discernible peaks are regularly spaced
at an interval of approximately 30meV. This is the shift in band gap expected
from a fluctuation in Cd Te layer thickness of one monolayer ( ~ 3 A) around a
mean thickness of 20 A. Thus, the features are probably due to a single recombination process taking place in layers that fluctuate in thickness over a range of
2a 0 • The presence of distinct peaks, rather than a single broad feature, is evidence

of islanding with a characteristic dimension at least as large as the exciton within
this sample. The Bohr radius of an exciton in bulk Cd Te is ~ 60 A. 18 Confinement
in one dimension can be expected to increase this radius slightly.
Sample 8 is unique in displaying similar distinct peaks and in showing superlattice luminescence over such a broad range of energies. While it is not certain
why sample 8 alone displays these peaks, growth kinetics presents a plausible explanation. Small changes in growth conditions are known to play a large role in
determining growth modes; mobilities of atoms deposited upon a surface must be
high enough to establish epitaxy but not so great as to tip the balance between
two-dimensional and three-dimensional (island) growth. 19 While the growth conditions were nominally identical for all of the superlattices, a small change (in growth
temperature, for example) could clearly affect the mobilities of surface atoms sufficiently to stimulate two-dimensional clustering. While the evidence that sample
8 was grown at a higher temperature than the other superlattices is not conclusive, this is a plausible explanation for the islanding that results in the regularly
spaced photoluminescence peaks observed from this sample. Regardless of the exact reason for the change in growth mode, it is clear that this sample alone displays
two-dimensional clustering on a scale of ~ 100 A.
The origin of the two intense lines observed in the luminescence from sample 3 is
less clear. Each of the two peaks displays a strong temperature dependence, but the

51
binding energies of the two features appear to be substantially different. Based on
this observation, it is unlikely that the two lines arise from the same recombination
process. As shown in Section 2.4, band structure calculations have suggested that
the lines could be due to recombinations related to the heavy-hole and light-hole
ground states ( confined in the CdTe and ZnTe layers, respectively). These levels are
predicted to differ in energy by only 16meV in this sample, in excellent agreement
with the observed 28meV separation between the lines. Attributing the lines to
light- and heavy-hole excitonic recombinations is also consistent with the differing
temperature dependences we observe, as excitons associated with the two hole
states would not be expected to have the same binding energies.
Each of the superlattices displays luminescence of low intensity at energies lower
than those of the intense peaks. The observed lines can be systematically related
to the Cda:Zn 1 _a: Te buffer layers and GaAs substrates. Although luminescence at
energies substantially less than the band gap is to be expected from each of the
superlattices, the background signal from underlying layers makes this difficult to
isolate. As the strain-shifted band gaps of the superlattices were of primary interest
in this study and could be inferred from the intense peaks, the luminescence at
lower energies was not examined in detail.
We have chosen to associate the sample band gaps with the high-energy cutoffs
of the intense luminescence peaks, typically approximately 40meV higher in energy
than the peak. This may have introduced a systematic error into our experimental
band gaps, but the magnitude of this error is unlikely to be more than 30meV.
Luminescence that is due to a free exciton would appear at an energy E = E 9 -Eex,
where the binding energy Eex is lOmeV in bulk CdTe or ZnTe 20 and would be less
than 40meV after 2-dimensional confi.nement. 21 There is some evidence that the
observed excitons drop into slightly lower energy states resulting from fluctuations
within individual layers. 18 This would have the effect of further removing the

Table 2.2: CdTe/ZnTe superlattice and alloy band gaps. Energies are in eV.

Sample

Observed Gap

Alloy Gap

1.87

1.99

1.81

1.89

1.67

1.93

1.81

1.97

1.83

1.99

1.82

1.97

1.74

1.99

1.78

1.98

Cdo.31Zno.63 Te

2.02

2.04

observed luminescence line from the sample band gap, by an energy in the range
of 20meV . 18 In view of the uncertainties involved, the assignment of sample band
gaps to the high-energy luminescence edges seems a good one, within a systematic
error of less than 30me V.
The band gap of Cd(l-y) Zny Te at 12K has been measured to be 17

Eo(eV) = (1.598 ± 0.005) + (0.614 ± 0.0lO)y + (0.166 ± 0.010)y 2

(2.2)

for Zn fraction y. As shown in Table 2.2, observed superlattice band gaps are
substantially smaller than those calculated for equivalent alloys. This shift to
lower energy is in general agreement with theory; superlattices typically display
band gaps that are lower in energy than those of alloys with the same composition.

2. 4

Calculations of electronic band structure

The electronic band structure of strained II-VI superlattices has been calculated using Bastard 22 and k •p23 ,24 ,25 ,26 models which incorporate effects that
are due to strain. The calculations were performed to infer strain distributions
in CdTe/ZnTe superlattices from observed band gaps. Independent experiments
reveal the strain distributions to be in excellent agreement with those predicted
by this method (see Chapter 3). The success of the two-band model in describing
CdTe/ZnTe band gaps and the ease of computation have stimulated predictions
of band gaps for a wide range of strained II-VI superlattices (included in the Appendix). These calculations demonstrate the sensitivity of superlattice band gaps
to valence band offsets and suggest that photoluminescence experiments may be
able to resolve long-standing uncertainties over II-VI band offsets .

2.4.1

....
Bastard and k • p models

The k •p model used to calculate CdTe/ZnTe superlattice band gaps has been
described extensively elsewhere. 23 ,24 ,25 ,26 The method is a perturbation technique
that allows bulk band structure to be calculated around a point for which the
eigenvalues of the system are known. Superlattice band structure is derived by
imposing the conditions of wave-function continuity and conservation of current
at the interfaces, as well as invariance of the Bloch functions under lattice vector
translations. Ours is a second-order perturbation calculation with spin-orbit and
strain effects included. The basis set consists of the two bottom ( s-like) conduction
bands and six highest (p-like) valence bands. Effects that are due to bands not
included in the basis set are added through Luttinger valence-band parameters.27
Our basis set is described by the band gap at the I'-point E 0 ; the spin-orbit
splitting Llo at this point; and Ep, which is related to the square of the momentum

54
matrix element between s and p states. These and the Luttinger parameters q,
12 , and 13 were taken from Lawaetz.

28 We set q to zero and ,2 and

1 3 equal

to the average of 12 and 13 . This approximation simplifies computations and is
consistent with characteristics of isotropic bulk bands. We assume a zero valence
band offset between ZnTe and CdTe. Although the value of the valence band offset
is uncertain, it is thought to be small; Due and Faurie 29 report an experimental
CdTe/ZnTe offset of lOOmeV, whereas Katnani and Margaritondo 30 find an offset
of -lOOmeV. Calculations suggest that the offset is approximately zero. 31 We use
4K band gaps of 1.606eV for CdTe and 2.38eV for ZnTe. 28
Strain effects are included through a four-parameter deformation potential.
We follow Bir and Pikus 32 in defining the three independent strain parameters
a, b, and d. Hydrostatic shifts in energy bands originating from p-like orbitals
are described by a, whereas parameters b and d characterize shifts arising from
(100)- and (111)-oriented uniaxial strains, respectively. In addition, a parameter
c is introduced to describe hydrostatic shifts in s-like energy bands. For ZnTe

we take b = -1.78eV and d = -4.58eV, from Kaplyanskii and Suslina. 33 For
CdTe, b = -1.18eV and d = -4.83eV, in accordance with Thomas. 34 Pressure
coefficients yield a= 1.35eV, c = -2.70eV for ZnTe and a= 1.23eV, c = -2.20eV
for CdTe. 35 Elastic constants were taken from McSkimin and Thomas 36 for CdTe
and from Berlincourt et al. 37 for ZnTe.
A first-order k · p theory has been used to calculate band gaps of a variety of
II-VI superlattices. The method is essentially one that is due to Bastard, 22 with
the addition of strain effects. Although this method. does not include the higherorder corrections to the Hamiltonian incorporated in the second-order theory, it
yields a simple analytical expression for the zone-center band gaps.
The Bastard model gives solutions for the slowly varying envelope functions

55
that modulate the Bloch functions to form the superlattice wave function,

'lp:t = ( aA,B(z)eik•r + ,aA,B(z)e-ik•r)unk·

(2.3)

The superlattice wave function is constrained to be continuous and to conserve
current at the interfaces (i.e., 'If;,..,!.(~~) continuous). Inserting this wave function
into the Schrodinger equation yields an implicit equation for the dispersion q( E)
of the electronic valence and conduction bands: 22

where
(2.5)
in the light particle case and
mAkB
:v=-mBkA

for the heavy-hole bands.

(2.6)

In these equations, q denotes the superlattice wave

vector, li is the thickness of layers of material i within the superlattice, ki describes
electronic motion along the superlattice axis in layer i, and flEAB is the energy
offset between the bulk bands ( i.e., the height of the quantum well).
Strain effects are easily incorporated within this model for calculations of zone
center band gaps. The shifts are readily calculated according to Eqn. 1.3 and are
incorporated as modifications to the input band-edge positions. Correct treatment
of the coupling between light- and heavy-hole states requires additional terms in
the Hamiltonian for k ::j:. 0, but the approach used here is correct for the zone
center. 38 The strains e:(i) within material i are determined by the in-plane lattice
constants af() within the superlattice. For the case of (100)-oriented growth these
are given by

(2.7)

(2.8)
where the C's are bulk elastic constants. All other ei/s are zero in this case.
One case of particular interest is that of the free-standing superlattice, in which
the elastic energy of the structure has been minimized with respect to a single inplane lattice constant.* The elastic energy density of a cubic crystal reduces to

(2.9)
for (100)-oriented growth. Minimizing lAU(A) + lBU(B) with respect to all yields
(2.10)
where
(i)2

+ c_ .,~ C12(i) .
Gi -_ c11
12
Cu

(2.11)

Inserting strains derived from these expressions into Eqn. 1.3 gives the shifts in
bulk band edges within a free-standing superlattice.

2.4.2

Results

Measured CdTe/ZnTe superlattice band gaps are compared with those calculated from second-order k •p theory in Table 2.3. Band gaps have been calculated
for the three cases of growth strained according to the template set by the topmost
buffer layer, free-standing strained growth, and unstrained growth. As is apparent from the table, agreement between k •p calculations and experiment is good
when the in-plane lattice constants are assumed to be those of the free-standing
superlattices. Calculations based on these lattice constants are in all cases within
*Physically, this is achieved by a network of misfit dislocations lying at the superlattice/buffer
layer interface. However, the superlattice itself is dislocation-free in this configuration.

Table 2.3: CdTe/ZnTe experimental and calculated superlattice band gaps. Energies are in eV.

k · p with strain

k·p

Sample

Experiment

( a~ee-standing)

( a ubstrate)

(unstrained)

1.87

1.81

1.55

1.83

1.81

1.76

1.56

1.78

1.67

1.66

1.38

1.69

1.81

1.80

1.78

1.82

1.83

1.79

1.85

1.82

1.80

1.78

1.82

1.74

1.72

1.76

1.78

1.74

1.80

60 meV of the observed band gaps. By contrast, calculations that assume superlattice lattice constants equal to that of pure CdTe top buffer layers yield band
gaps that are 250 to 320meV lower than observed. Calculations based on a strain
distribution derived from the topmost buffer layer are in better agreement with
experiment when the layer is Zn Te or Cda:Zn1 _a: Te, but the agreement is best when
the superlattice is assumed to be free-standing.

Agreement between the free-standing calculations and experiment is as good
as could be hoped, given the uncertainties in deformation potentials, experimental
band gaps, and precise sample compositions. It is probable that samples 1-3, grown
on Cd Te buffer layers, are actually less Cd Te-rich than suggested by EDS, owing to
the volume probed by this technique (which extends slightly into the buffer layer).

This error is unlikely to be more than ::c::'. 5%, which would raise the calculated
gaps by a few tens of meV, bringing them into closer agreement with experiment.
However, the magnitude of this and other errors is not sufficient to explain the
discrepancies between experiment and theory when the superlattice is assumed to
be commensurate with the CdTe buffer; strain in these samples is clearly not set
by this layer. The same can probably be said of the strain field in sample 4, grown
on a pure ZnTe buffer, but by chance the calculated gaps are too close to allow
such a conclusion from consideration of band gaps alone.
Consideration of strain energies and critical thicknesses m the CdTe/ZnTe
system suggests that the free-standing configuration is plausible. As shown in
Eqn. 2.9, the elastic energy is quadratic in strain e. Dividing a 6% strain in
one set of layers into two 3% strains alternating between tension and compression clearly lowers the elastic energy considerably. For the superlattices considered
here, this energy difference more than offsets the energy necessary to create a network of mismatch-relieving dislocations at the superlattice/buffer-layer interface
(see Eqns. 1.4 and 1.5); the free-standing case is truly a lower energy state than
the case of a structure strained to a pure CdTe or ZnTe buffer for the superlattices
considered here.
Predictions of the critical thickness for the nucleation of misfit defects in Cd.,Zn 1 _., Te
films are plotted in Fig. 2.6.

Also included are the thicknesses and net mis-

matches of the superlattices examined here. Note that each sample contributes
several points, connected by lines for purposes of identification, corresponding to
the thicknesses and misfits of the individual Cd Te and Zn Te layers and of the alloy
equivalent in composition and thickness to the superlattice as a whole. Sample 8,
for example, gives a point at (0.07%, 1.64µm), since this superlattice is 1.64µm
thick with a 51% CdTe, 49% ZnTe volume-averaged composition, grown on a
Cd.soZn.soTe buffer layer (acdo.61 zno. 49 Te/acdo.sZno.6 Te = 0.07% misfit). This point

1 o5

'•

SINGLE FILM CRITICAL THICKNESS

(CdTe parameters)

104

,...,_
<(
...._
C.I)
C.I)

::!IC:'.

1 o3

I-

102

...

' ' ...

... ...

....

.....................

MISFIT (%)

Figure 2.6:

Figure 2.6: Theoretical predictions of critical thickness at which a thin Cda:Zn1_., Te
film poorly lattice-matched to a substrate breaks away from that substrate with
the formation of misfit dislocations. Calculations assumed dislocations appropriate
to (100)-oriented growth of CdTe. The solid curve comes from an energy-balancing
argument 39 similar to that of Eqn. 1.7; the dashed curve below it is from Eqn. 1.9,
Ref. 40; and the last is from Eqn. 1.10, Ref. 41. Also included are points corresponding to sample thicknesses and misfits. Each sample contributed several
points, connected by lines for purposes of identification, appropriate to the thicknesses and misfits of the individual layers in the superlattice (filled circles) and
of the alloy of identical composition and thickness to the overall superlattice (unfilled circles). Sample 2, for example, gives a point at {2.47%, l.0Sµm) since this
is a 1.08 µm-thick superlattice with a composition equivalent to a Cdo. 5 1Zn0 •43 Te
alloy, grown on a CdTe buffer layer (2.47% mismatch). This point is connected
to one at (5.8%,23A) appropriate to the 23A ZnTe layers grown on the CdTe
buffer. The point derived from the individual Cd Te layers, (0%, 31 A), has not
been plotted since the zero mismatch places no constraints on CdTe layer thickness. Theory clearly predicts that this particular superlattice should exceed the
critical thickness. This agrees with experiment.

61
is connected to others at (3.0%,21A) and (3.0%,20A) appropriate to the thicknesses and misfits of the individual CdTe and Zn Te layers, respectively. (Note that
samples grown on pure CdTe or ZnTe contribute only two points as there is no
critical thickness requirement for the individual CdTe or ZnTe layers, respectively,
in these structures.) The superlattices grown on pure CdTe or ZnTe buffer layers
exceed both of the critical thickness requirements outlined in Section 1.4.2. As
shown in the figure, the individual ZnTe or CdTe layers within these superlattices
lie well beyond the limits for defect-free growth. In addition, the superlattices are
of sufficient overall thickness to substantially exceed the critical thickness for the
creation of mismatch-accommodating dislocations at the superlattice/buffer-layer
interface.
While several of the superlattices appear to exceed the limits of dislocationfree growth, allowing the superlattices to break away from the topmost buffer layer
to assume a free-standing configuration puts them below the critical thicknesses
predicted by the empirical model of People and Bean. 41 . Their calculations suggest
that individual CdTe and ZnTe layers with a 3% strain can be grown beyond a
thickness of 50 A. Note that the overall superlattice thickness does not impose a
critical thickness constraint as the DC component of the strain field is zero in this
configuration.
As shown in Fig. 2. 7, the relaxation of mismatch stresses can be sufficiently
gradual beyond the critical thickness to allow a large strain to be divided into
lesser expansions and contractions. In the limit of very thick individual superlattice
layers, dislocation networks could form at every interface in sufficient densities to
totally relieve the strain within the structure. This does not appear to be the case in
our samples. Such dislocation-filled structures would not be expected to luminesce
efficiently, in contrast to our observations from these CdTe/ZnTe superlattices.
Although the electronic band structure of an unstrained superlattice should be

4o/.---------------------,
.4--[LASTICITY

THEORY

ALLOY
THICKNESS

\100A/

"I- 2%

(L)

.....

...._' ,

' ;'-,500A
'-

I--

ff)

'\
"\.

' 0,-

'- '-.JOOOA

'--....

..J
..J

...............

'''
....... ......
-.
--.
--2500A -.........._
---- -'-

0 I

0.3

0.5

.......

0.9

GERMANIUM FRACTION (Xl

Figure 2. 7: Strain relaxation beyond the critical thickness in the Gea:Si1-a: system.
From Ref. 42.

very different from that of a free-standing structure, we were unable to distinguish
the two cases simply on the basis of observed band gaps.

For these samples,

valence band shifts arising from uniaxial strains approximately cancel the band
gap dilations expected from hydrostatic strain. This coincidence arises solely from
our choice of superlattice compositions; there should be a sizable difference in
band gaps of free-standing and unstrained superlattices in structures substantially
CdTe- or ZnTe-rich.

To summarize, comparison of observed and calculated band gaps shows that superlattices grown on CdTe buffer layers are not strained to fit this template. Based
on calculations of strain effects, it is proposed that the superlattices may be in a
nearly free-standing configuration, with a dislocation network at the superlattice/bufferlayer interface dividing the strain between adjacent layers to minimize the elastic

63
energy of the structure. This is a plausible configuration for our samples, as the
gradual relaxation of strain observed in the Ge.,Sh_., system beyond the critical
thickness demonstrates that initial CdTe or ZnTe superlattice layers might experience only partial relaxation. Consideration of critical thicknesses shows that our
superlattices could be grown defect-free if the strain were distributed in a manner
close to the free-standing limit. Although the free-standing configuration cannot
be distinguished from the case of an unstrained lattice simply on the basis of observed band gaps, the unstrained limit is highly improbable in view of the high
luminescent efficiencies observed from these structures.
Theoretical superlattice band gaps for samples with 1 to 30 CdTe or ZnTe
layers per superlattice period are shown in Figs. 2.8 and 2.9. Fig. 2.8 shows the
superlattice band gap at 5K as calculated from a Bastard model, 22 neglecting
effects that are due to strain. Fig. 2.9 displays results of the same calculation when
strain effects appropriate to a free-standing superlattice are included. Second-order
corrections described by Luttinger valence band parameters have been neglected in
our Bastard model calculations, resulting in band gaps consistently 10 to 20 meV
lower than predicted by the eight-band k •p calculations. The Bastard model was
chosen for these plots as it reduced computation time and differed from the k · p
calculations only by this uniform 10 to 20meV shift.
The unstrained band structure in Fig. 2.8 shows band gaps which vary between the bulk CdTe and ZnTe gaps of 1.6 and 2.38eV. Given the assumption
of zero valence band offset between the constituent materials, the layer thickness
dependences apparent in the figure are determined solely by the conduction band
states. The path of the contours agrees with that expected from the basic periodic
quantum-well problem ( i.e., Kronig-Penney modeI 43 ). Increasing the ZnTe barrier
thickness beyond ~ 10 monolayers has almost no effect on the band gap, as the
quantum wells are virtually uncoupled in this limit.* Increasing the width of the
*Structures in which the coupling between adjacent wells is negligible are commonly referred to

ZnTe-CdTe SUPERLATTICE BAND GAP (eV)
(no strain)

30 . . . . . .

........,....,...,..,_...,....,........-,--,,-,--,--,-,-,---,-,--,--r-r--,-r-TT""--r--T---.--r-.-""T"""""T~

(/)

(I)

>,.

(I)

....0

lf)

I'.

10
20
Number of CdTe Layers

Figure 2.8: Theoretical CdTe/ZnTe superlattice band gaps at 5 K as a function of
number of monatomic layers per superlattice period. Contour interval is 50meV.
Calculations are based on a Bastard model, neglecting effects that are due to strain.

ZnTe-CdTe SUPERLATTICE BAND GAP (eV)
(lattice constant of free-standing superlattice)
30M""ffl"'1M'TT~T""1""r-""'l'"""T-n--r-r--,--,---,-r,--,--,---,-.,-"'-,-.,--,-,-,

I...

(I)

>-.

.,_
(I)

'-I-

I...

(I)

..Q

::,

l()

r--,...

....-I

10
20
Number of CdTe Layers

Figure 2.9: Calculated CdTe/ZnTe superlattice hand gaps with strain effects included. Contour interval is 50meV. Calculations assume in-plane lattice constants
appropriate to free-standing superlattices.

66
CdTe wells draws the superlattice band gap asymptotically closer to that of CdTe,
regardless of the ZnTe layer thickness.
Fig. 2.9 illustrates the role of strain in changing the superlattice band gap as
CdTe or ZnTe layer thickness is modulated. For thick CdTe layers (more than
about 15 monolayers), increasing the width of the ZnTe layers lowers the band
gap over certain ranges of ZnTe thicknesses. This arises from the type-II character
of the superlattices (in which carriers associated with conduction and valence band
extrema are localized in different layers), depicted in Fig. 2.10.

In both CdTe

and ZnTe the light-hole band is pushed above the heavy hole for uniaxial compressional strain and below for uniaxial dilational strain. Hence, in our system the
CdTe valence-band maximum is defined by the heavy-hole band edge, whereas the
light-hole band maximum determines the ZnTe energy gap. Near the CdTe axis
the ZnTe layers are heavily strained, pushing the ZnTe light-hole band above the
CdTe bands and resulting in a light-hole to conduction-band energy gap for the
superlattice. As the width of the Zn Te layer is increased, the superlattice valenceband edge approaches the ZnTe light-hole edge. This causes the band gap to
decrease. However, as ZnTe concentration increases, the strain in the ZnTe layers
is lowered, pulling the ZnTe light-hole band down. This effect starts to dominate
at higher ZnTe concentrations, where the band gap starts to increase with greater
ZnTe layer thicknesses. For high ZnTe-to-CdTe ratios, the ZnTe light-hole band
drops sufficiently that the band gap is defined by the heavy-hole band. The transition between type-I and type-II band alignments is indicated in Fig. 2.11. Points
in this figure correspond to the superlattices examined in this study. Note that of
the samples we examined, only sample 3 should display a type-II band alignment,
in agreement with photoluminescence.

It is worth noting that the accuracy of calculated superlattice band gaps 1s
as multiquantum well structures, rather than superlattices.

67
(a)

CdTe

ZnTe

·-·

( b)

----.

CdTe

-----.

CdTe

ZnTe

. - - - CB

CdTe
VB

ZnTe

CdTe

=ti-------------------- -- -----LJ ·-------------- ------------ti= VB
Figure 2.10: Calculated alignments of CdTe and ZnTe band edges with strain
effects included. Three cases are shown: (a) Zn Te-rich superlattice, (b) equal
CdTe and ZnTe layer thicknesses, and (c) CdTe-rich superlattice. Calculations
assume strains appropriate to free-standing superlattices. Strain splits the valence
band; heavy-hole valence-band edges are indicated by solid lines and light-hole
edges by broken lines.

68
ZnTe-CdTe SUPERLATTICE BAND ALIGNMENT
30~~~-....,.....,,-,-,-,-..-,-..--r-,-,-..,.,.....-,-.-,-r-,--,-,--r-,

(/)
,._

(I)

lYPE I

I-

.. .

....(I)
..0

:::,

lYPE II

10
20
Number of CdTe Layers

Figure 2.11: Band alignments for CdTe/ZnTe superlattices. In a type-I band
alignment, carriers associated with valence- and conduction-band extrema lie in
the same layers. Type-II alignments localize electrons and holes in different layers
within the superlattice. Superlattices examined here are labeled by points. Only
sample 3 is predicted to be type-II.

dependent upon the estimate of the valence band offset between the constituent
materials. This dependence means that it is sometimes possible to infer a band offset by comparing experimental band gaps with those calculated from theory. While
cumulative errors in theoretical and experimental band gaps translate into larger
errors in valence band offset, uncertainties in offsets are sometimes large enough
that this method can still be used to advantage. In the case of CdTe/ZnTe, our
assumption of a zero valence band offset between CdTe and ZnTe yields gaps that
are in good agreement with experiment. However, errors in deformation potentials, superlattice characteristics, and experimental band gaps could also place the

69
offset at ±lOOmeV, as suggested by other work. 29 ,30 ZnSe/ZnTe is an example of
a system in which the offsets are less well known. Predictions 44 ,45 place this offset
anywhere from 0.28eV to 1.20eV. Comparison of experimental and theoretical gaps
suggests that b..Ev = 1.0 ± O.leV in this system. 46

2.5

Stimulated Emission

Attempts have been made to observe laser oscillation in a Cd Te/Zn Te superlattice. As much of the interest in CdTe/ZnTe structures arises from the possibility of
fabricating efficient light-emitting diodes with emission in the visible region of the
spectrum, the demonstration of lasing in these superlattices is of practical interest. The intensity of the luminescence observed from our samples at 5K suggests
that nonradiative or deep-level loss mechanisms may not preclude lasing. However, the stability of heavily strained structures under high pump power conditions
is uncertain, as is the effect dislocations would have on the luminescence. 47 Although previous experiments on Ina:Ga1 _a:As 1 _yP y structures with strains ::; 1.25%
have demonstrated a catastrophic loss of luminescence after short periods of intense stimulated emission,48 it is unclear that these results can be translated to
Cda:Zn1 _a: Te structures. The elastic properties of II-VI semiconductors are substantially different from those of III-V's, as are the effects of dislocations on luminescent
efficiency.
Stimulated emission refers to the creation of a photon of energy 1iw as a consequence of the decay of an excited electron-hole pair through interactions with
another photon of energy 1iw. When gain that is due to stimulated emission equals
or exceeds losses arising from absorption in a given medium, light passing through
the medium experiences a net amplification. Placing this amplifying medium inside a resonant cavity establishes laser oscillation when, for a single round-trip

70
through the cavity, the gains equal or exceed the losses ( arising, for example, from
absorption and cavity reflection coefficients). For a cavity of length l, absorption
coefficient a, and mirror reflectivities r 1 and r 2 , the threshold gain condition is 49
(2.12)
Equating this threshold gain with that from stimulated emission in an excited twolevel system yields an expression for the electron population inversion necessary to
establish lasing in a particular structure. Above the excitation threshold necessary
to establish lasing, the output power in a laser mode increases linearly with input

power at a rate substantially in excess of that below threshold. This "knee" in
output efficiency makes the threshold easy to identify experimentally.
In our experiment, inversion of the electron population was attempted by aboveband-gap optical excitation, provided by the 5145A line of an Ar+ ion laser. The
laser was operated in a cavity-dumped mode with 12nsec pulses at repetition rates
of 2. 7kHz to 1.1MHz ( chosen to keep the power at the sample low to reduce heating
and possible damage effects). Peak pump powers were varied below 3W, providing
incident powers on the order of kW /cm 2 after focussing. This is in the range
expected for semiconductor lasing thresholds. 50
With the exception of the pump laser, the experimental setup is identical to that
described in Section 2.3.2 for the cw photoluminescence experiments. Spectra were
accumulated at temperatures of 5 - 8K. Only sample 4 has been examined to date.
This sample was chosen because of the ZnTe buffer layer on which it was grown,
which helps to confine the superlattice luminescence within the active region. Two
cavities were cleaved, approximately 120 µm x 450 µmin size. Luminescence from
the edge and front surface of these samples was compared with that from a large
piece of sample 4 accumulated under identical conditions.
As shown in Fig. 2.12, the cleaved cavities exhibit a catastrophic loss ofluminescence after intense pumping(~ lkW /cm 2 ), while the undeaved sample continues

PULSED-PUMP PHOTOLUMINESCENCE

(/)

uncleaved

cleaved

1.6

1.7

1.8

1.9

2.0

ENERGY (eV)
Figure 2.12: Photoluminescence at SK from cleaved and uncleaved pieces of sample 4 under a pulsed Ar+ pump with a peak power of ~ lk W / cm 2 • The intense
excitonic peak has disappeared from the spectrum coming from the cleaved cavity,
leaving only a weak, broad feature. The spectra are plotted on different vertical scales; luminescence from the uncleaved sample was more than two orders of
magnitude more intense than that from the cleaved cavity.

to display a strong excitonic line. This loss occurred prior to the observation of
Fabry Perot modes on the spectrum, although it should be noted that the samples
were illuminated for several minutes before a complete photoluminescence spectrum was accumulated. Whether this loss of luminescence is intrinsic to heavily
strained CdTe/ZnTe superlattices is unclear at this time. The recent observation of lasing in an InAs/GaAs multiquantum well structure 51 with a 7.4% lattice
mismatch demonstrates that large strain fields can be accommodated during stimulated emission. By tailoring CdTe/ZnTe superlattices during growth, it may be

72
possible to inhibit the mechanisms responsible for the degradation of luminescence
under intense pump conditions. This is the subject of ongoing work.
Despite the failure to obtain laser oscillation in superlattices with layers composed of pure CdTe and ZnTe, it should be noted that Cdo.2sZno.1sTe/ZnTe superlattices have recently been shown to lase. 8 These structures appear to be less
susceptible to structural damage owing to the smaller lattice mismatch between
adjacent layers. In addition, the Zn-rich composition results in higher-energy primary emission, in the yellow-orange region of the spectrum. These superlattices
have been observed to lase without noticable degradation at room temperature,*
providing optimism for future device applications.

2.6

Conclusions

We have examined optical properties of CdTe/ZnTe superlattices grown on a
variety of Cda:Zn1 _m Te buffer layers. Photoluminescence from the superlattices is
several orders of magnitude more intense than from a Cd0 •3 1Zn0 •63 Te alloy under
the conditions examined here. Spectra are dominated by broad lines probably
associated with excitons. The 30meV width of these lines suggests that superlattice layer thicknesses were controlled to approximately one monolayer. Identifying
the superlattice band gaps as the high-energy edges of the observed excitonic luminescence yields sample band gaps substantially lower than expected for alloys.
Observed gaps are in excellent agreement with those calculated from a k •p model,
assuming strain appropriate to a free-standing structure. This configuration is one
in which dislocations at the superlattice/buffer-layer interface have redistributed
strain within an otherwise dislocation-free superlattice in a manner which minimizes the elastic strain energy within the structure. The free-standing confi.gu*These are believed to be the first II-VI superlattices to lase at room temperature.

ration is plausible in view of calculated critical thicknesses and strain relaxation
rates. We have made calculations of the effects of a free-standing strain on the superlattice valence and conduction band edges. Strain is shown to reduce band gaps
by up to lOOmeV over the range studied, and to result in transitions from type-I
to type-II band alignments. Attempts to observe laser oscillation in CdTe/ZnTe
superlattice structures have proven unsuccessful to date, but this is the subject of
further work; the intensity of the luminescence observed from these superlattices
suggests that they may ultimately find application as visible light emitters.

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47, 1172 (1985).
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Phys. Rev. B 34, 4423 (1986).
19. R. Ludeke, J. Vac. Sci. Technol. B 2, 400 (1984).
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edited by M. Aven and J. S. Prener (Wiley, New York, 1967), p. 319.
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and A. C. Beer (Academic, New York, 1966), Vol. 1, p. 75.
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25. G. Y. Wu, Ph.D. Thesis, California Institute of Technology, 1988.
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ductors (Keter, Jerusalem, 1974).
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77
42. R. People, IEEE J. Quant. Elect. QE-22, 1696 (1986).
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Lett. 50, 1266 (1987).

Chapter 3
Structural Properties of
CdTe/ZnTe Superlattices
3.1

Introduction

3.1.1

Background

The structural studies described here represent an extension of the Cd Te/Zn Te
work described in Chapter 2. Although the photoluminescence study in the previous chapter revealed that CdTe/ZnTe superlattices grown on CdTe buffers do not
maintain the in-plane lattice constant of CdTe, it was not possible to distinguish
the case of free-standing growth from that in which lattice mismatch is wholly
accommodated by dislocations.
As dislocations are known to affect the durability and performance of a latticemismatched device, 1•2 determining the levels of elastic strain in these superlattices
is of practical interest. However, in addition to the particular interest of accommodating lattice mismatch in a material system of technological interest, these
samples provide a test of the traditional single-film critical thickness theories and
their extrapolation to superlattices. Although the x-ray diffraction experiment

presented here reproduced data obtained in a previous study, 3 our interpretation
of the data yields conclusions substantially at variance with those drawn from
application of Vegard's Law in the previous study.

3.1.2

Results of this work

X-ray diffraction shows that each of the CdTe/ZnTe superlattices examined
here lies beyond the critical thickness for creation of misfit defects.

However,

TEM and in-situ RHEED results show that defect densities drop dramatically away
from the superlattice/bu:ffer-layer interface. Substantial free-standing superlattice
strains are observed in all but one of the samples. The most highly defective
superlattice is below the critical thicknesses predicted for the individual layers and
for the superlattice as a whole, unlike a number of more highly strained samples.
Photoluminescence data suggest that this relaxation may be attributable to a slight
variation in sample-to-sample growth conditions. Our results demonstrate that the
critical thickness of a particular sample may be dependent upon the thermal history
of the sample, in addition to the material system and lattice mismatch.

3.1.3

Outline of chapter

Section 3.2.1 describes the application of x-ray diffraction to the determination
of strain in a superlattice. A kinematical model of x-ray diffraction is also presented
in this section. Section 3.2.2 summarizes results of x-ray diffraction experiments
on the CdTe/ZnTe superlattices described in Chapter 2. Observed diffraction is
compared with that calculated for the three limiting cases of unstrained, freestanding strained, and commensurate structures. Results from x-ray diffraction
are compared with conclusions drawn from the photoluminescence experiments and
critical thickness calculations described in Chapter 2. TEM and in-situ RHEED
results are outlined in Section 3.3. The conclusions are summarized in Section 3.4.

_J_
aZnTe

(6.104.A.)

ZnTe

_J_
aCdT• ( 6.481 A)

CdTe

ZnTe
substrate

Figure 3.1: Arrangement of cubic unit cells in an unstrained CdTe/ZnTe superlattice.

3 .. 2

X-ray diffraction

3.2.1

Theory

By revealing the structure and lattice constants of a crystal, x-ray diffraction
provides a means of identifying the three limiting cases of unstrained, commensurate strained, and free-standing strained growth (depicted in Figs. 3.1 and 3.2).
Assuming (100)-oriented epitaxy and applicability of linear elasticity theory, the
degree to which lattice mismatch has been accommodated by elastic strain can
be determined by a single measurement of the growth-direction lattice constants
within a superlattice. As shown in Section 2.4.1, growth-direction strains Czz are

_j_
QZnTe

ZnTe

~5.95.A)

...
_j_
QCdTe

CdTe

~6.82.A)

Ii'

ZnTe
substrate

_j_
oZnTe

(6.1 04A)

ZnTe

_j_
OCdTe

~7. Q 1 A)

CdTe

ZnTe

substrate

Figure 3.2:

Tetragonal distortion in strained CdTe/ZnTe superlattices.

(a)

Free-standing coherently strained superlattice. (b) Commensurate superlattice,
strained to fit a ZnTe buffer layer.

82
related to in-plane strains €mm by

(3.1)
for (100)-oriented superlattices. The growth-direction and in-plane lattice constants (aj_ and a11, respectively) can then be related to the bulk lattice constants
through these strains by
A,B _

A,B(l + cA,B)

(3.2)

= aoA,B(l + czz
c-A,B) •
a A,B
J_

(3.3)

all

- ao

cmm

Thus, measurement of the growth-direction lattice constants yields the in-plane
lattice constants.
If the in-plane lattice constants are identical in the two sets of layers comprising

the superlattice, the structure is coherently strained. If a coherently strained
superlattice has an in-plane lattice constant equal to that of the topmost buffer
layer, the structure is described as commensurate. This is the case illustrated in
Fig. 3.2(b ). However, this is clearly not the only possible strained configuration.
Another case of interest is that in which a superlattice assumes a single in-plane
lattice constant that minimizes the elastic energy of the structure, depicted in
Fig. 3.2( a). As shown in Section 2.4.1, the in-plane lattice constant that minimizes
the elastic free energy of the structure is related to the thicknesses lA,B of the
individual layers within the superlattice by

lAGAa:Zat lBQBat a:
au =
l A QA aoB2 + l B QB aoA2 '

for bulk lattice constants

(3.4)

ai and a:, where
0A,B2

+ cA,B
- 2-12_
11
12
CA,B ·

QA,B = cA,B

(3.5)

By revealing the in-plane lattice constants within a superlattice, x-ray diffraction
allows the unstrained, free-standing, and commensurate strained cases to be distinguished.

We have chosen to simulate the x-ray diffraction from a superlattice through a
kinematical model. This is a good approximation when x-ray penetration depths
are long compared to the size of the crystal being analyzed, as is the case in
our experiment. Our model neglects effects that are due to superlattice periods
consisting of non-integral numbers of monolayers* and variations in superlattice
periodicity, as well as effects such as extinction usually incorporated in dynamical
models. While these effects have not been modeled simply to date, the dominant effect associated with discrete fluctuations is typically a slight increase in the
width and decrease in intensity of observed superlattice x-ray lines. Intuitively,
the diffraction expected from a typical imperfect superlattice can be viewed as an
incoherent sum of diffraction from layered structures that are subsets of the total
superlattice (this incoherent diffraction is characterized by sums in intensity from
scattering crystallites, rather than sums in amplitude). This problem has been
modeled in detail elsewhere. 4
In the kinematical approximation, the structure of an x-ray diffraction pattern
is calculated by summing contributions from a single unit cell across the extent
of the crystal. For the case of growth-direction diffraction from a superlattice,
in which each unit cell is composed of several layers of one material followed by
several layers of another, the intensity of diffracted x-rays I can be expressed as

(3.6)

I(fy••L) [~e

(3.7)
In this equation, /; are the atomic form factors,

rt are the growth-direction co-

*Superlattice periods not corresponding to integral numbers of monolayers are achieved by fractional layer coverages. Except in the growth technique of atomic-layer epitaxy, interfaces are
always associated with partial layer coverages.

ordinates of the atoms in a single unit cell, aA,B are the growth-direction lattice
constants of the constituent materials, and L is the length of the superlattice unit
cell. The first sum extends over the number of superlattice unit cells N, the second
describes a single superlattice cell as a sum over M constituent material unit cells,
and the third describes atomic contributions to a standard bulk-like unit cell.
Equation 3. 7 can be rewritten as

sin (NkL/ 2) JsuM OVER LAYER A
sin 2 (kL/2)
+ SUM OVER LAYER

nJ2.
(3.8)

From this construction it is apparent that the structure will be dominated by
sharp, closely spaced peaks described by sin 2 (NkL/2)/ sin 2 (kL/2), which result
from the requirement that scattered waves maintain coherence between superlattice unit cells. For superlattices in which the period is short, the diffraction
condition arising from a single superlattice unit cell is not a stringent one. In particular, this condition appears as a slow modulation in amplitude of these narrow
peaks. The envelope modulating the closely spaced superlattice peaks is illustrated in Fig. 3.3, which compares calculated superlattice diffraction from a single
superlattice period with that from a 200-period structure. It should be noted that
the slow modulation coming from a single superlattice period ( described by the
!LAYER A+ LAYER Bl 2 term) provides the only information relating to the lattice constants within each layer. While the spacing between narrow peaks yields
the period of the superlattice L, the size of the superlattice unit cell is typically
unrelated to the lattice constants of the constituent materials. Thus, the positions
of the narrow peaks defined by this periodicity carry no information pertaining to
these parameters.
Growth-direction lattice constants in the two materials forming the superlattice
are only readily deduced if the envelopes associated with diffraction from adjacent
layers are separated sufficiently to be distinguished from each other. The widths

CALCULATED SUPERLATTICE DIFFRACTION

,,,,
.,,,,,

:I\

1 period
200 periods

zw
1-z

'II

I•

,,,;
: I

T'NO THETA { degrees)
Figure 3.3: fJ /28 x-ray diffraction calculated from a single superlattice period and
from a 200-period superlattice. The calculation assumed parameters appropriate
to a free-standing 56 A Cd Te / 50 A Zn Te superlattice ( i.e., sample 3). Increasing
the number of periods yields narrow peaks with amplitudes determined by the
single-period diffraction envelope and positions determined by the periodicity of
the superlattice.

86
of these envelopes can be approximated by Scherrer's formula, 5
OFWHM ~ 0.9 L

cos

(3.9)

where the thickness of each layer of material within a superlattice period is given
by LA,B = MA,BaA,B· Since positions of the two envelopes can be determined by
Bragg's law, we find that constituent lattice constants can be separated only if
(3.10)
For the bulk ZnTe and CdTe lattice constants of 6.104A and 6.481.A, (1/ LA +
1/ L 8

t must exceed approximately 20 A for the (400]-like diffraction peaks to be

distinguished. This condition is satisfied only for sample 3; in the remainder of our
samples the envelopes can be resolved only if the growth-direction lattice constants
deviate substantially from bulk values. As illustrated in Fig. 3.2, such deviations
are to be expected in heavily strained lattices.
Figure 3.4 shows calculated x-ray diffraction from a single period of sample 3
for the three cases of free-standing strained growth, growth strained to a CdTe
buffer layer, and unstrained growth. Form factors used in these calculations have
been taken from Ref. 6. Although the superlattice layers are sufficiently thick to
allow two (400]-like envelopes to be distinguished in each case, the spacing of the
envelopes increases greatly with the tetragonal distortions resulting from strain.
A large offset in the absolute angle at which diffraction occurs distinguishes the
free-standing superlattice from one strained to match the CdTe buffer layer.

3.2.2

Results

Diffraction of Cu Ka X rays was measured in a 0/20 arrangement. Since the
geometry chosen was symmetric about each sample's growth axis, we were probing
lattice constants only in the growth direction. Spectra were accumulated on a

CALCULATED X-RAY DIFFRACTION

FREE-STANDING STRAIN

Cl)
zw
1z

BUFFER STRAIN

UNSTRAINED

TWO THETA {degrees)

Figure 3.4: X-ray diffraction calculated for a single period of sample 3 under different strain conditions. The degree to which lattice mismatch is accommodated
elastically within the superlattice can be inferred from the separation of [400]-like
peaks, which increases with tetragonal distortion. Shifts in the absolute angles
associated with diffraction distinguish the free-standing structure from the superlattice commensurate with the CdTe buffer layer.

88
Phillips diffractometer with a Cu source. A Ni foil placed between the sample
and source reduced K/3 X rays while passing the Ka lines. Additional scans were
gathered on a Siemens D500 Kristallofl.ex Diffractometer. Contributions from Cu

K/3 were not filtered in this setup but were subsequently removed by applying a
Rachinger correction5 to the data.

0/20 scans revealed [200]-like and [400]-like superlattice peaks (referred to the
cubic Cd Te or Zn Te unit cells), as well as single peaks attributable to Cda:Zn1 _a: Te
buffer layers and to GaAs substrates. Experimental results have been compared
with diffraction calculated from the kinematical model outlined in the previous
section. Observed diffraction from CdTe/ZnTe superlattice sample 8, shown in
Fig. 3.5, appears to be in excellent agreement with theory when the structure
is assumed to be unstrained.

The most intense [400]-like superlattice peak is

enhanced by the superposition of diffraction from the buffer layer at this angle,
but agreement with the unstrained limit is good nevertheless. Figures 3.6 and
3.7 show diffraction representative of the remaining samples. These samples show
high levels of residual strain, as evidenced by the appearance of two [400]-like
envelopes, but are not in perfect agreement with calculated diffraction appropriate
to a coherently strained structure. The envelopes are not separated as much as
would be expected for a perfectly strained structure; lattice mismatch appears to
accommodated by a combination of misfit defects and elastic strain. However,
diffraction envelopes are symmetrically placed about the average lattice constant
expected in a free-standing structure; samples grown on CdTe or ZnTe show no
evidence of being strained to fit this template, in agreement with the results from
photoluminescence described in Chapter 2.
No attempt has been made to perform a quantitative fit to these experimental
data by taking the growth direction lattice parameters as free variables. Such
fits are of questionable significance once the existence of large defect densities has

X-RAY DIFFRACTION
SAMPLE 8

GaAs

EXPERIMENT

I-

UNSTRAINED

BUFFER STRAIN

FREE-STANDING

T'NO THETA (degrees)
Figure 3.5: () /W x-ray diffraction from Cd Te/ZnTe superlattice sample 8 showing
[200]-like and [400]-like diffraction peaks. The sample was irradiated with Cu
Ka X rays. Also shown are diffraction patterns calculated in the kinematical ap-

proximation for the cases of unstrained growth, free-standing strained growth, and
strained growth commensurate with the Cd0 . 5 Zn0 . 5 Te buffer layer. The truncated
peak at 66.1 ° is due to the GaAs substrate.

X-RAY DIFFRACTION
SAMPLE 3

GoAs

CdTe

EXPERIMENT

zw
1-z
FREE-STANDING

BUFFER STRAIN

UNSTRAINED

TWO THETA (degrees)

Figure 3.6:

() /20 x-ray diffraction from Cd Te/Zn Te superlattice sample 3.

[400]-like diffraction peaks are split into two envelopes around () = 58 °. Although
the splitting is not as great as expected for a coherently strained structure, it
indicates high levels of residual strain.

X-RAY DIFFRACTION CdZnTe
SAMPLE 7

GaAs

EXPERIMENT

zw
......
FREE-STANDING

I I

BUFFER STRAIN

UNSTRAINED

TWO THETA (degrees)

Figure 3. 7: f) /20 x-ray diffraction from Cd Te/Zn Te superlattice sample 7. Truncated peaks at 66.1 ° and 58. 7 ° are associated with the GaAs substrate and
Cd0 .5 Zn0 . 5 Te buffer, respectively.

92
been inferred; x-ray penetration depths are on the order of microns, resulting in
diffraction that averages over the extent of the superlattice and over a variety of
inhomogeneous strain fields. Although diffraction from defective structures can be
modeled with contributions from differently strained crystallites, such a fit to the
data is far from unique for a single x-ray diffraction scan.
The x-ray diffraction results can be summarized as follows. None of the samples shows x-ray diffraction expected from a commensurate, coherently strained
structure. Diffraction from sample 8 is in good agreement with calculation for
an unstrained structure, although contributions from a Cd0 . 5 Zn 0 . 5 Te buffer cannot
be distinguished from the diffraction from this superlattice and thus improve the
apparent fit. The remaining superlattices show evidence of large strain fields. Envelopes associated with diffraction from a single unit cell are placed symmetrically
around the average lattice constant expected in a free-standing superlattice; structures grown on pure CdTe or ZnTe show no tendency to maintain the in-plane
lattice constant of the buffer layer.
These results are not entirely consistent with expectations from the classical
critical thickness theories, 7,8,9,lO,ll plotted in Fig. 2.6. Although samples grown
on pure CdTe or ZnTe buffer layers are defective, as predicted by the classical
limits, superlattices grown on Cd0 . 5 Zn0 . 5 Te buffer layers lie in a more uncertain
regime. Sample 8, in particular, appears to satisfy both the individual layer and
overall superlattice critical thickness requirements, 12.1 3.1 4 but is highly defective.
Although the role of fluctuations ( e.g., in layer thicknesses) cannot be discounted
in samples lying so dose to the predicted limits, the discrepancy may be attributed
to growth conditions. As shown in Chapter 2, sample 8 appears to have grown in a
mode unique amongst the samples studied here. Photoluminescence data described
in Section 2.3.3 show evidence of islanding at interfaces within the superlattice,
characteristic of growth at slightly increased temperatures.* Regardless of the
*In support of this argument, it should be noted that samples 8 and 9 were among the first

93
exact origin of this change, it is clear that factors influencing the growth mode of a
supe:rlattice are capable of greatly changing the density and type of defects observed
in a particular structure. This observation provided some of the motivation for the
Ge0 . 5 Si 0 . 5 /Si growth-temperature studies described in Chapter 4.

3. 3

In-situ RHEED and TEM

Despite the agreement between conclusions drawn from photoluminescence and
x-ray diffraction, it was not possible to fully characterize the strains in the superlattices from these experiments alone. Although the structures are clearly highly
defective, x-ray diffraction probes large areas of the crystal and consequently is
not readily applied to characterizing dislocation networks. TEM 15 and in-situ
RHEED 16 experiments have been used to further examine the structural quality
of CdTe/ZnTe superlattices.
Superlattice epitaxy has been studied during growth through in-situ reflection
high-energy electron diffraction (RHEED) measurements performed on a single
sample. Data were accumulated for a superlattice consisting of 200 repeats of 25 A
CdTe and 25A. ZnTe grown on a CdTe buffer layer. Spotty RHEED patterns during
the first half-micron of growth show that the first 100 superlattice periods grown
were highly defective. At this point, however, the RHEED patterns rapidly assume
the well-defined streaks characteristic of high-quality two-dimensional epitaxial
growth. 16 This change is presumed to be associated with a substantial drop in
dislocation density, as expected when strain set by a CdTe buffer is divided into
lesser contractions and dilations of adjacent superlattice layers.
RHEED results are consistent with the substantial reduction of defect densities
away from the superlattice/buffer-layer interface observed through transmission
samples grown, before standard growth conditions were established.

electron microscopy (TEM) of sample 8. 15 Misfit-accommodating 60 ° dislocations
have been observed to drop in density from 1010 -10 11 cm- 2 near the first interfaces
to'.::::'. 108 cm- 2 near the top surface of the sample. Although these densities are very
high, it should be noted that this particular sample appears to be the least strained
of the superlattices examined, as shown previously.

3 .. 4

Conclusions

All of our samples have been observed to exceed the critical thickness for the
nucleation of misfit-accommodating dislocations. Sample 8, which satisfies the
critical thickness criteria imposed by a number of traditional models, appears to
show the smallest degree of residual strain. Although layer thickness fluctuations
could account for this discrepancy, it is probable that growth conditions played a
role in distributing strain in these superlattices. In particular, sample 8 appears to
have grown in a mode unique among the samples studied. A mechanism affecting
a sample's growth mode could be expected to alter substantially the density and
distribution of dislocations in the sampie.
Previous experiments confirm the role of temperature in nucleating dislocations.
Annealing studies of Ge.,Sii_., superlattices have demonstrated the metastable nature of these structures. 17 In particular, annealing at temperatures higher than
those typically used during MBE growth results in the formation of substantial
numbers of defects in these structures. It should not be surprising that such a
system might be sensitive even to small changes in growth conditions. Consideration of growth parameters should be important in predicting the critical thickness
associated with a particular sample. While Van der Merwe's model 8 presents a
plausible lowest-energy state for greatly strained structures, the degree to which a
sample displays a critical thickness in agreement with this prediction depends on

its ability to acquire the activation energy necessary to reach this state.
The structure of a number of CdTe-ZnTe superlattices has been examined.
Each of the samples studied has been grown beyond the critical thickness for generation of misfit defects, in disagreement with predictions based on extrapolations
from empirical single-film critical thicknesses to those of superlattices. Our data
suggest that growth conditions play a role in determining the onset of defect formation, in contrast to the assumptions behind current critical-thickness models.
Defect densities drop dramatically within a micron of the superlattice/buffer-layer
interface, regardless of the buffer layer used. While the resulting epitaxy is far from
defect-free, identifying the mechanisms responsible for inhibiting defect formation
should be valuable for future device applications.

References
1. M. D. Camras, J.M. Brown, N. Holonyak, Jr., M. D. Nixon, R. W. Kaliski, M.

J. Ludowise, W. T. Dietze, and C.R. Lewis, J. Appl. Phys. 54, 6183 (1983).
2. H. Jung, A. Fischer, and K. Ploog, Appl. Phys. A 33, 97 (1984).
3. G. Monfroy, S. Sivananthan, X. Chu, J. P. Faurie, R. D. Knox, and J. L.
Staudenmann, Appl. Phys. Lett. 49, 152 (1986).
4. B. M. Clemens and J. G. Gay, Phys. Rev. B 35, 9337 (1987).
5. H. P. Klug and L. E. Alexander, X-Ray Diffraction Procedures For Polycrystal.line and Amorphous Materials (Wiley, New York, 1974).
6. International Tables for X-ray Crystallography, edited by C. H. MacGillavry
and G. D. Rieck (Kynoch, Birmingham, 1963).
7. R. People and J.C. Bean, Appl. Phys. Lett. 47, 322 (1985); 49, 229(E) (1986).
8. J. H. Van der Merwe, J. Appl. Phys. 34, 123 (1963).
9. C. A. B. Ball and J. H. Van der Merwe, in Dislocations in Solids, Volume 6,
edited by F. R. N. Nabarro (North Holland, Amsterdam, 1983), p. 122.
10. J. W. Matthews and A. E. Blakeslee, J. Cryst. Growth 27, 118 (1974); 29,
273 (1975); 32, 265 (1976).

11. J. W. Matthews, in Epitaxial Growth, Part B, edited by J. W. Matthews
(Academic, New York, 1968).
12. J.C. Bean, in Silicon Molecular Beam Epitaxy, edited by E. Kasper and J.C.
Bean (Chemical Rubber, Boca Raton, FL, 1987).
13. M. Y. Yen, A. Madhukar, B. F. Lewis, R. Fernandez, L. Eng, and F. J. Grunthaner, Surf. Sci. 174, 606 (1986).
14. T. C. Lee, M. Y. Yen, P. Chen, and A. Madhukar, Surf. Sci. 174, 55 (1986).
15. P. M. Petroff, unpublished.
16. G. Monfroy, X. Chu, M. Lange, and J. P. Faurie, unpublished.
17. A. T. Fiory, J. C. Bean, R. Hull, and S. Nakahara, Phys. Rev. B 31, 4063
(1985).

Chapter 4
Dislocation Formation in
Ge 0 _5 Si 0 _5 /Si Superlattices
4.1

Introduction

4.1.1

Background

This chapter describes studies of the effect of growth temperature on stress
relaxation in lattice-mismatched superlattices. As discussed in Section 1.4.2, much
work has been devoted to the prediction and measurement of the critical thickness
beyond which a thin film breaks away from a substrate to which it is poorly
lattice-matched. The importance of this limit has been recognized for some time;
while coherent strain can be an effective parameter in tailoring the properties of a
lattice-mismatched device, 1 structural defects associated with stress relaxation can
seriously degrade device performance. 2 Traditional critical thickness theories are
in poor agreement with each other, however, as illustrated in Fig. 1.9 for the case
of Gea:Sii-a:and in Fig. 2.6 for Cd"'Zn1 _"' Te. In addition, there is little agreement
between experimentally determined critical thicknesses, although the traditional
theories span a sufficiently large range that agreement with one of the models is

99
usually claimed.
While some of the variation in reported critical thicknesses can be ascribed
to the different sensitivities of various techniques to misfit dislocations, identical
methods sometimes give substantially different results. 3 Discrepancies between observed critical thicknesses have been attributed to a number of factors. It has been
suggested that different structures ( i.e., single films, quantum wells, superlattices,
etc.) display different critical thicknesses. Structures composed of different materials with dissimilar elastic properties clearly display different limits. Recently, there
have been suggestions that variations in the reported critical thicknesses might be
a consequence of differences in growth conditions. 4,5,6 ,7 In this study we examine
the role of growth conditions in relieving stresses that are due to lattice mismatch.
We have chosen to examine growth-temperature variations in Ge0 . 5 Si 0 . 5 /Si superlattices. Structures composed of Ge.,Sii_., have recently attracted attention
for use in a variety of applications. Heterojunction bipolar transistors (HBT's)
fabricated from coherently strained layers have been shown to display current
gains superior to those of traditional HBT's. 8,9.lO Improvements in speed and
gain are reiated to strain-induced splitting of the conduction band, which reduces
the effective mass for transport in the growth direction while also inhibiting intervalley scattering associated with phonons. Modulation-doped field-effect transistors (MODFET's) have also been shown to benefit from a high-mobility Gea:Si 1 _.,
channel. 11 In addition to the interest generated by Gea:Sh_., HBT's and MODFET's, optical effects have recently brought attention to Ge.,Sii_., superlattices.
The electronic band structure of superlattices is such that band extrema located
away from the zone center for bulk material can, in certain cases, be folded into
the I'-point, yielding a "quasi-direct" band gap. Although the symmetries of
the conduction- and valence-band states may still limit the oscillator strengths
obtainable in such a superlattice, such a band structure allows radiative decays

100
across the band gap without the involvement of phonons. The possibility of integrating Gea:Sii-a: light emitters or modulators on a chip has stimulated a variety
of experimental 12.1 3 and theoretical 14.1 5,16 studies into the optical properties of
these structures. While no efficient light emission has been demonstrated to date,
high photoconductive gains have brought attention to Gea:Sii-a:/Si superlattices as
long-wavelength photodetectors. 17

In addition to being of technological interest, the Gea:Sii-a: system is particularly well suited to a growth temperature study of strain. Unlike many compound
semiconductors, Ge and Si can be grown epitaxially over a wide range of temperatures ( single-crystal MBE growth temperatures range from approximately 300 ° C
to 1000 ° C ). Strain effects are large in this system; bulk Ge has a lattice constant
of 5.658 A, whereas that of Si is 5.431 A, yielding a net mismatch of 4.2%. Much
experimental work has been devoted to measuring the critical thicknesses imposed
by this mismatch. 6,18 ,19

4.1.2

Results of this work

We demonstrate the dependence of stress relaxation on growth temperature in
a lattice-mismatched epitaxial system. Strains have been measured for Ge 0 _5 Si 0 •5 /Si
superlattices grown by MBE on ( 100 )-Si substrates at temperatures between 330 ° C
and 530°C. The accommodation of lattice mismatch by elastic strain has been
determined through x-ray diffraction, channeled RBS, and TEM. Lattice mismatch
is found to be accommodated elastically in a structure grown at 365 °c, with a
dislocation density too low to be resolved by TEM ( < 10 5 cm- 2 ). Samples grown at
higher temperatures display greater numbers of misfit-accommodating dislocations,
with the density of dislocations reaching 1.5 x 10 5 cm- 1 at a growth temperature
of 530 °C. This growth-temperature dependence may account for inconsistencies
in critical thickness data reported in the literature. Although equilibrium critical

101
thicknesses may be adequately described by bulk material properties, these limits
do not adequately describe films frozen in metastable states. Our results clearly
demonstrate the need to account adequately for the kinetics of defect formation in
the prediction of critical thicknesses.

4.1.3

Outline of chapter

The Ge0 . 5 Si 0 . 5 /Si superlattice samples used in this study are described in Section 4.2. Details pertaining to the growth of the samples are presented, as precise
conditions appear to play a major role in the process of defect formation. Section 4.3 details the results of x-ray diffraction, TEM, and channeled RBS studies
of the strain distributions within the superlattices. Attention is paid to the sensitivities of the various techniques to different densities of defects, as this has
become a controversial issue in the measurement of critical thicknesses. Observed
growth-temperature dependences are discussed in the context of models describing
the onset of dislocation formation in Section 4.4. The results are summarized in
Section 4.5.

4.2

Samples

Compositionally identical Ge0 . 5 Sio. 5 /Si samples were grown in a modified III-V
Perkin-Elmer MBE machine at temperatures between 330°C and 530°C. Growth
temperatures were inferred from optical pyrometer and thermocouple readings,
calibrated with the aid of eutectic reactions observed in situ. We estimate our
growth temperatures to be accurate to within 20 °C. (100)-oriented Si substrates
were cleaned following a modified Shiraki procedure 20, 2 l consisting of repeated

ea; situ oxide growths and etches. This was followed by a final oxide desorption
at 800°C in the growth chamber under ultrahigh vacuum (UHV) conditions. The

102
cleaning procedure was followed by growth of an epitaxial Si buffer layer ( ~ 1000 A
in thickness), during which the growth temperature was lowered continuously from
700°C. Superlattices fabricated at higher temperatures (530°C) were grown without interruption on the Si buffer layers. Growth at temperatures lower than this
required an interruption of less than 30 minutes after deposition of the buffer
layer to allow the substrate to cool further. The superlattice layers were grown
by codeposition of Si and Ge at feedback-stabilized deposition rates of 1 A/sec,
independent of the growth temperature.

In situ reflection high-energy electron diffraction (RHEED) patterns show that
the growth becomes single-crystal at a tern perature of 300 ° C. TEM confirms the
single-crystal nature of our superlattices. We did not observe any polycrystalline
growth. Previous work had suggested "amorphous or disordered growth" 22 at
400°C under certain circumstances and poor channeling yields under others. We
saw no evidence of either of these in our films.* The reason for this discrepancy
is not clear at this point, although it should be noted that the substrate cleaning
procedure used here is substantially different from the sputter and anneal technique
used in the previous study. 22
Superlattice characteristics are listed in Table 4.1. Four samples were grown
with identical layer thicknesses, compositions, and numbers of superlattice periods.
Growth temperature alone was varied between these samples. Two other superlattices (SL 29 and SL 37) were grown, at temperatures of 330°C and 530°C.
Although the defect densities observed in these samples are consistent with results
obtained from the other four samples, the different number of periods makes it
impossible to isolate growth temperature conclusively as the cause of observed differences. X-ray diffraction measurements have confirmed the superlattice periods
*Discrepancies such as these highlight the difficulties associated with comparisons of data taken
from different sources. Although data exist for Ge.,Sii_., critical thicknesses at growth temperatures of 550 °C 18 and 750 °C, 23 it is not clear that these data are comparable.

103

Table 4.1: Geo. 5 Sio.5/Si superlattice samples.

Sample

Layer Thicknesses

Periods

Geo.5Sio.5/Si ( A)

Growth

(Reference No.)

Temp. (°C)

SL 78

65/65

365

(SL 87.078)

SL 71

65/65

390

(SL 87.071)

SL 77

65/65

450

(SL 87.077)

SL 72

65/65

530

(SL 87.072)

SL 29

70/70

330

(SL 87.029)

SL 37

70/70

530

(SL 87.037)

to be within ±5 A of the quoted values. Rutherford backscattering spectroscopy
(RBS) shows a random variation in Ge content of< 5% from intended fractions.

4. 3

Experimental

Numerous experimental methods are available for the measurement of strain or
dislocation densities in a thin film. Sensitivity of the various methods to different
levels of coherent strain has recently led to substantial debate over the accuracy of
measured critical thicknesses. 24 The following is a short summary of some common
techniques.
Methods commonly employed to measure dislocation densities are TEM, cathodoluminescence, photoluminescence, and etch-pit density measurements. TEM is
the only one of these techniques capable of resolving densely packed grids of dislocations. However, the technique is of limited use at low dislocation densities

104

(below approximately 10 5 cm- 2 ), and sample preparation procedures are capable
of introducing damage into the specimen under study. 25 The remaining methods
have been applied exclusively at low dislocation densities ( < 10 5 cm- 2 ). The luminescence methods are preferable to the etch-pit density measurements in being
relatively nondestructive, but rely on optically active dislocations.
Lattice distortions are commonly examined directly by high-resolution TEM,
x-ray diffraction, and channeled RBS. Each of these methods is insensitive to low
levels of dislocations but provides a measurement of the compressions and dilations
associated with stresses that are due to lattice mismatch. Channeled RBS is particularly useful for identifying depths at which the lattice distortions change, whereas
x-ray diffraction yields lattice parameters averaged over a substantial penetration
depth (typically c:::'. lOµm). Recently, RHEED oscillations have been shown to drop
dramatically during growth of a strained film. 6•7 While the precise interpretation
of this drop is not certain at this point, this method appears to promise an excellent

in situ determination of changes in growth mode.
Miscellaneous methods that measure effects arising from strain include Raman
scattering, spatially resolved absorption spectroscopy, and luminescence. Techniques relating to optical absorption and photoluminescence can be used to track
changes in electronic band structure with strain (see Chapter 2). These shifts are
then translated into strains through deformation potentials. Although typically
suffering from low signal levels, the technique of Raman scattering benefits from
displaying large relative shifts in phonon frequencies with changing strain.
We have chosen to measure strain distributions and dislocation densities within
the superlattices by x-ray diffraction, channeled RBS, and TEM. The "low-resolution"
techniques of x-ray diffraction and channeled RBS are particularly useful for tracking the relaxation of strains, whereas TEM has been used to identify densities and
types of defects present in the superlattices. The results have been recently cor-

105

roborated by Raman experiments, which have provided independent confirmation
of sample compositions and strains. 26

4.3.1

X-ray Diffraction

Growth-direction lattice constants a1i and a7eo.5 Sio.5 of the Si and Geo.sSio.s
layers within the superlattices have been inferred from x-ray diffraction. Since
elasticity theory relates a 1. to the biaxial strain within a layer,27 measurements of
the growth-direction lattice constants reveal the degree to which lattice mismatch
has been accommodated elastically within the superlattices.
X-ray diffraction scans were taken in a fJ /2() geometry symmetric about the
growth direction. Data were accumulated on a Siemens DS00 Kristallo:flex Diffractometer using a Cu source. A Rachinger correction 28 was used to isolate contributions from the Cu Ka lines by removing those that were due to K/3. X-ray
diffraction from samples SL 29 and SL 37 are compared in Fig. 4.1. With the exception of the single intense peak associated with the Si substrate, structure in the
experimental curves is due to [400]-like diffraction from the superlattices (the [400]
designation is referred to the standard Si or Ge cubic unit cells). The experimental
diffraction consists of narrow peaks modulated by broad envelopes. In our scans,
the widths of the narrow peaks are determined by instrumental resolution.
As shown in Chapter 3, the positions of the narrow peaks yield the period of the
superlattice, while the growth-direction lattice constants within the structure are
inferred from the broad envelopes modulating these peaks. The kinematical model
described in Section 3.2.1 has been used to calculate the diffraction expected from a
single period of a coherently strained superlattice. This calculated pattern is shown
in Fig. 4.1 (indicated by dashed lines). Form factors used in the model were taken
from Ref. 29. As can be seen from the figure, the observed diffraction is in excellent
agreement with the envelope calculated under the assumption of coherent strain

106

Geo.sSio.s/Si SUPERLATTICE X-RAY DIFFRACTION
EXPERIMENT
---- THEORY (STRAINED)

Si substrate

en
zw

SL29

t--

Si substrate

SL37

TWO THETA {degrees)

Figure 4.1: (400]-like x-ray diffraction from Ge0 . 5 Si 0 . 5 /Si superlattice samples SL
29 and SL 35. Experimental (solid) curves are compared with theoretical (dashed)
envelopes calculated under the assumption of coherent strain set by the Si substrate. Sample SL 35, grown at 530 °C, has clearly undergone substantial relaxation, whereas SL 29, grown at 330°C, appears to be coherently strained (within
the resolution limit of x-ray diffraction).

107

M1, Z1

----

------

O M 2 , Z2
ID

M3,Z3

...J

ENERGY

Figure 4.2: Basic Rutherford Backscattering process, in which ions from an incident
beam are backscattered with energies characterizing the type and depth of atoms
within a solid. From Ref. 30.

when the growth temperature is 330 C. However, raising the growth temperature

to 530 C results in diffraction in poor agreement with these calculations. Whereas
the sample grown at the higher temperature displays substantial strain relaxation,
the superlattice grown at 330 °C appears to be coherently strained, to within the
resolution of x-ray diffraction.

4.3.2

Channeled RBS

Rutherford Backscattering Spectroscopy 1s commonly applied in studies of
depth-resolved composition and strain profiles of thin films. 30 ,31 The basic processes involved in the method are depicted in Figs. 4.2 and 4.3. Energetic (Me V)

108

..J

ENERGY

Figure 4.3: Comparison of a channeled RBS spectrum, accumulated for a beam
incident along a high-symmetry crystallographic direction, and a spectrum accumulated along an arbitrary (random) direction. From Ref. 30.

ions incident upon a crystal occasionally scatter elastically off atomic nuclei ( O"n ~
10- 24 cm- 2 ), transferring an amount of energy that is determined by the scattering
geometry, masses of the incoming and scattering particles, and energy of the incident beam. Since the amount of energy transferred is dependent upon the mass of
the scattering nucleus, it is possible to identify the elements present in a film by
monitoring the energies of ions backscattered at a particular angle from a monoenergetic incident beam. Depth profiling of the composition is also possible, since
incident and scattered ions lose energy to high-cross-section (ue ~ 10- 16 cm- 2 )

109
electronic excitations as they pass through a sample. Structural information can
be obtained by aligning the incident beam with a crystallographic "channel." Although some of the beam is scattered at the surface of the crystal, ions entering
along high-symmetry crystallographic directions are effectively channeled, experiencing nuclear scattering events only occasionally if the crystal is of high quality.
Previous studies have made extensive use of channeled RBS for determining the
crystalline quality and critical thicknesses of Gea:Sii-a: films. 22 ,32 By independently monitoring Ge and Si backscattering rates while rocking a sample away
from the growth direction, it is possible to identify differences in channeling directions within adjacent layers. These directions are determined by the alternating
growth-direction compression and dilation within a strained film; identifying offgrowth-axis minima associated with the elements in each set of layers reveals the
degree of tetragonal distortion, and hence coherent strain, within the layers. The
perfection of a particular sample can also be inferred by examining scattering
from an incident beam aligned with the growth axis. In particular, the presence
of misfit-accommodating dislocations can be expected to increase backscattering
substantially.
Channeled RBS spectra have been obtained for each of our superlattices with
an incident 2.275 MeV 4 He 2 + beam aligned with the [100] growth direction. These
have been compared with "random" spectra taken with the beam impinging upon
samples rotating about the growth axis and tilted off the high-symmetry crystallographic directions. As illustrated in Fig. 4.4, the backscattered yield drops sharply
as the growth temperature is lowered to 365 °c. The rapid rise in counts behind
the Si surface peak (at ~1.25 MeV) for the samples grown at 450°C and 530°C is
indicative of a large number of structural defects. Sample SL 71, grown at 390 °c,
shows no great increase in backscattering yield until the interface with the Si buffer
layer(~ 1.05 MeV). The counts rise dramatically at this point, however, indicating

110

RUTHERFORD BACKSCATTERING

"''-•4tv','""'I',

, .. ,>,,/,\..\

RANDOM

,,.,,,4

''('/,*'IJ,,,...

1'\

SL72

~(530°C)

en
zw
.__

SL77

(450°C)

SL71

(390°C)
SL78

(365°C)

1.2

1.4

1.6

1.8

ENERGY (MeV)

Figure 4.4: Channeled Rutherford Backscattering spectra ( solid curves) for superlattice samples grown at temperatures between 330°C and 530°C. Spectra were
accumulated at 168 ° with respect to the incident 2.275 MeV 4 He 2 + beam, which
was aligned with the [100] growth axis. Backscattered yield below the Si surface
peak ( around 1.25 Me V) rises substantially as the growth temperature is increased,
indicating an increase in the density of structural defects. An unchanneled RBS
spectrum for sample SL 72 (dashed curve) is shown for comparison. Spectra are
plotted on the same scale but are displaced vertically for clarity.

111

Table 4.2: Ge0 . 5 Si0 •5 /Si superlattice Xmin's. Total scattering from the films is also
shown, indicated as a percentage of backscattered yield from the rotating random
scans over the same range of energies.

Sample

Growth Temperature

Xmin (%)

Film Scattering (%)

SL 29

330

13.8

29.4

SL 78

365

6.5

10.2

SL 71

390

4.9

14.5

SL 77

450

6.8

19.4

SL 72

530

8.8

25.4

SL 37

530

14.5

39.8

a great number of defects near this first superlattice interface. Superlattice SL 78,
grown at 365 ° C, is unique in showing a low backscattering yield throughout the
film. The structure grown at 330 °C, although observed through x-ray diffraction
to be highly strained, shows very poor channeling, indicative of a high number of
defects incapable of relieving stresses arising from lattice mismatch.

Values of Xmin have been calculated for each of our superlattices by determining the ratio of counts in the channeled spectrum to counts in the unchanneled
spectrum at an energy just behind the surface peak. Experimental values are
listed in Table 4.2. For comparison, Xmin is expected to be approximately 3.5%
in high-quality Si or Ge, with scattering resulting primarily from thermal motion
of atoms. 32 With the exception of samples SL 29 and SL 78, our Xmin 's increase
monotonically with growth temperature and sample thickness, as expected. The
structure grown at 330°C, although observed through x-ray diffraction to be highly

112
strained, shows very poor channeling. These results are consistent with the observation from TEM of numerous dislocations threading through this film. The origin
of the comparatively poor Xmin obtained for SL 78 is not apparent at this point,
although total backscattered yield from this film is the lowest. Whether high levels
of coherent strain can increase densities oflocalized defects (such as point defects)
sufficiently to account for this high value of Xmin is unclear.

4.3.3

TEM

Several of our samples have been examined through cross-sectional and planview TEM to identify the types and densities of dislocations present in the superlattices. Figure 4.5 shows a dark-field plan-view image taken from SL 37, grown
at 530 ° C. A network of misfit-accommodating dislocations is clearly visible, at a
density of approximately 1.5 x 10 5 cm- 1 • Etching away the top half of the superlattice has no significant effect on the dislocation density, which is consistent with the
suggestion from channeling and from previous studies 4 that misfit defects are often
confined to the first superlattice interfaces. Plan-view studies of SL 78, grown at
365 °C, reveals no such network of misfit dislocations, nor any appreciable number
of threading dislocations. Considering the area examined, the misfit dislocation
density in this sample is < 10 5 cm- 2 • Plan-view TEM of sample SL 29, grown
at 330 °C, also reveals no network of misfit dislocations but shows poor surface
morphology. A cross-sectional micrograph taken from this superlattice is shown
in Fig. 4.6. Although the sample appears to be single-crystal, a large number of
dislocations thread from the superlattice/buffer-layer interface to the surface of the
sample. In addition, while the first superlattice layers appear to be quite planar,
the morphology degrades higher in the superlattice, resulting in a poor top surface.
This sample is unique in showing a high density of threading dislocations.

113

Figure 4.5: Bright-field plan-view TEM image of sample SL 37, grown at 530 °C,
showing a network of misfit dislocations lying near the Si buffer-layer/superlattice
interface. The dislocation density is approximately 1.5 x 10 5 cm- 1 •

114

100nm

Figure 4.6: Cross-sectional TEM micrograph of sample SL 29, grown at 330 °C.
Although superla.ttice layers near the Si buffer layer a.re quite planar, the morphology degrades considerably near the top surface. Note also the high density of
threading dislocations.

115

4.4

Discussion

The experimental results can be summarized as follows. We observe singlecrystal growth above 300°C. Superlattice SL 29, grown at 330°C, accommodates
lattice mismatch primarily through elastic strain. This sample displays a high
number of threading dislocations, however. The structure grown at 365 °C (SL 78)
shows excellent surface morphology and a defect density too low to be detected
by TEM ( < 10 5 cm- 2 ). As the growth temperature is increased to 530 °C, the
superlattices display monotonically increasing densities of structural defects, with
misfit dislocation densities reaching 1.5 x 10 5 cm- 1 for SL 37, grown at 530 °C.
Our results clearly demonstrate that the appea~ance of misfit dislocations is
strongly dependent on growth conditions. The nature of this temperature-driven
process is not clear at present. Examination of the mismatch between the thermal
expansion coefficients of Ge and Si shows that the changes we observe cannot
be attributed solely to bulk thermal contractions and expansions. Differences in
thermal expansion coefficients33 strain samples at 530 °C by an additional 0.03%
compared to those at 330°C. As the lattice mismatch for Ge grown on Si is 4.2%,
this temperature effect is equivalent to a change in Ge fraction of less than 1%

( i.e., consideration of thermal expansion coefficients suggests that a superlattice
at 530 ° C will be under less stress than a superlattice with a 1 % greater Ge fraction
at 330 °C). Thus, the effect of thermal expansion coefficients is very small, and is
more than compensated by the spread in composition of our samples, which exceeds
1 %. Ge-rich structures grown at low temperatures display lower defect densities
than less-stressed samples grown at higher temperatures. Thus, the temperature
activation we observe is more likely associated with dislocation nucleation, glide,
or interaction. The precise nature of the process is currently under study.
Comparison with theoretical critical thicknesses suggests that our samples
should be highly defective. Calculated limits are plotted in Fig. 1.9 for the Gea:Sii-a:

116

system. The individual 65 A Ge 0 . 5 Si 0 . 5 layers within the superlattices are sufficiently thin to lie below the critical thickness predicted by the People and Bean
model, 34 but exceed the limits calculated by Ball and Van der Merwe35 ,36 and
Matthews and Blakeslee. 37 However, treating the superlattices as alloys of equivalent total thickness and average composition 38 shows that the overall structures
lie beyond all of the predicted limits. 34,35 ,36 ,37 Nevertheless, although samples
grown at high temperatures display misfit dislocations in keeping with the predictions of the traditional critical thickness models, we find lattice mismatch to be
elastically accommodated in a compositionally identical sample grown at 365 ° C.
It is important to note that past critical thickness calculations have been

based on equilibrium theories that neglect parameters such as temperature. Lowtemperature growth techniques such as MBE clearly produce metastable structures 39
in which kinetics plays a dominant role. Thus, it should not be surprising that
the appearance of misfit dislocations is rarely seen to be in agreement with theory.
Our results suggest that critical thicknesses are not uniquely specified by lattice
mismatch and material system. Recent attempts to model the relaxation of misfit
stresses in a metastable system have met with some success. 40 Whether models
such as these can be used to predict the onset of dislocation formation in a variety
of structures remains to be determined.
It should be noted in passing that the precise definition of critical thickness

is currently a matter of debate. In the past, critical thickness has typically been
identified as the point at which average strain fields begin to deviate substantially
from coherently strained values. With the development of cathodoluminescence
techniques, 41 it has become possible to identify the thickness at which the first
dislocation is nucleated in a thin film poorly lattice-matched to its substrate. The
point at which this occurs is of questionable significance, however. Even under
circumstances in which each of the appropriate growth parameters is precisely

117
reproduced, the process of dislocation nucleation would appear to be better characterized by the activation conditions under which statistically significant densities
of dislocations are observed, rather than by identification of the first fluctuation
sufficient to nucleate a misfit dislocation on a 3" wafer. From a practical standpoint, the tolerance of a particular application to the presence of dislocations will
determine a requirement of crystalline perfection that may be best described by
activation energies characterizing the introduction of defects during the various
stages of device growth and processing. Such activation energies are beginning to
be examined in the Gea:Sii-a: system. 42 Initial results suggest the presence of different activation energy domains, defined by the increased importance of dislocation
interactions at high defect densities.
Regardless of the choice of definition of critical thickness, it is clear that the
appearance of dislocations is not uniquely specified by a particular lattice mismatch and material system. We have demonstrated that growth conditions play
a major role in inhibiting the introduction of dislocations within a film.* It is
reasonable to expect that critical thicknesses should also be dependent on factors
such as growth direction. Strain relaxation rates are known to vary substantially
for films grown along different orientations; 43 ,44 identical critical thicknesses are
exceedingly unlikely when either the component of the Burger's vector in the plane
of the interfaces or the extent of the glide necessary for dislocation motion changes
because of a change in growth direction.

*Note that dislocation formation is appropriately described as inhibited, rather than stimulated,
by these growth conditions, as the calculations of Ball and Van der Merwe35,36 show that the
free-standing or unstrained cases represent substantially lower-energy states than the commensurate limit for the samples examined here.

118

4. 5

Conclusions

The accommodation of lattice mismatch in Gea:Sii-a)Si superlattices has been
demonstrated to be highly dependent on the conditions under which a sample is
grown. Dislocation densities of 1.5 x 10 5 cm- 1 and < 10 5 cm- 2 have been measured
in compositionally identical superlattices grown at 530 °C and 365 °C, respectively.
It is clear that by lowering growth temperatures it is possible to freeze a struc-

ture in a highly strained metastable state well beyond the critical thickness limits
calculated by equilibrium theories. There appears to be a large kinetic barrier
blocking dislocation nucleation or glide; the effect we observe cannot be explained
by mismatched thermal expansion coefficients alone.
The film thickness at which dislocations appear is clearly dependent on growth
conditions. While past theories provide equilibrium limits to defect-free growth,
predicting the appearance of defects in samples grown at low temperatures will

require consideration of the kinetics of defect formation. It should not be surprising that experimentally observed critical thicknesses vary substantially, given the
importance of variations in growth conditions in fundamentally metastable structures. Recognizing that defect creation can be inhibited in severely mismatched
systems should be important in growing heavily strained films of high quality.
While the durability of these structures under prolonged use remains uncertain,
by tailoring growth conditions it is possible to obtain defect-free structures well
beyond the equilibrium critical thicknesses.

119

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120
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587

123

Appendix A
Appendix
Electronic band gaps have been calculated for a variety of superlattices composed of II-VI semiconductors. Calculations are based on the Bastard model 1
described in Section 2.4, with strain effects included through a four-parameter
deformation potential. 2 The superlattices are assumed to be strained in a freestanding configuration. As explained in Section 2.4, this configuration minimizes
the elastic energy of the coherently-strained superlattice. A (100)-oriented zincblende crystal structure is assumed.
Parameters used in the calculations are listed in Table A.1.

124

Table A.1: Properties of II-VI semiconductors.

Egap,

CdTe

CdSe

CdS

ZnTe

ZnSe

ZnS

E4K
gap

1.606

1.84

2.56

2.38

2.82

3.80

E,,,

-0.88

-1.33

-1.73

-0.98

-1.41

-1.87

b.o

0.91

0.42

0.07

0.92

0.43

0.07

m*h

1.38

1.6

1.27

1.44

1.76

20.7

23.

21.

19.1

24.2

20.4

6.481

6.05

5.820

6.104

5.669

5.409

1.23

1.24

1.31

1.35

1.58

" n
-£,.£,

-2.47

-2.68

-2.7

-2.82

-3.60

-1.18

-1.

0.4

-1.78

-1.2

0.53

-4.83

-3.

-4.58

-3.81

-3.71

5.351

7.4

8.581

7.13

8.10

10.46

C12

3.681

4.52

5.334

4.07

4.88

6.53

C44

1.994

1.317

1.487

3.12

4.41

4.613

E,,,, b.o, Ep, a, c, b, and dare in eV; mii is expressed as a fraction of a free-

electron mass, a 0 is in A, and elastic constants C are in units of 1011 dyne/ cm 2 •
Band gaps, spin-orbit splittings, heavy-hole masses, and p-matrix elements are
from Ref. 3. Absolute energies of valence band edges were taken from Refs. 4
and 5. Deformation potentials are from Refs. 6, 7,8. Lattice constants and elastic
constants are from Ref. 9.

125

CdSe-ZnSe SUPERLATTICE BAND GAP (eV)
(lattice constant of free-standing superlattice)
30--~.......---.---.-.---.-...--.-.-..-,-.---r-,~---r-r---rr-r---r-r--.--,

(/)
Q)

>,.

(/)

'+--

I'"\.
.....,

..0

lf)
(\J

10
20
Number of CdSe Layers

Figure A.1: Calculated CdSe/ZnSe superlattice band gaps with strain effects included. Contour interval is 50meV. Calculations assume in-plane lattice constants
appropriate to free-standing superlattices.

126

CdS-ZnS SUPERLATTICE BAND GAP (eV)
(lattice constant of free-standing superlattice)

30,.,.._,.,...,....,,......,,....,.....,...___.........,..._-,-,-r-r-,.......,.......---r-,-.......-r--r--n--.-.--r-,

(/J

(l)

(I)

(l)

..0

E 10
:::J

10
20
Number of CdS Layers

Figure A.2: Calculated free-standing CdS/ZnS superlattice band gaps.

127

ZnSe-ZnS SUPERLATTICE BAND GAP (eV)
(lattice constant of free-standing superlattice)

30 . . . . . . . . . . . . . . . ,.....,..,..........,.............,.....,....-,-,-...........-,........,-,.....,..-,-.-.---.-.--,-,--.-..-....---,

(/)
!....

(I)

>-.

(/)

'-I--

!....

(I)

..0

E 10
::J

Number of ZnSe Layers

Figure A.3: Calculated free-standing ZnS/ZnSe superlattice band gaps.

128

ZnTe-ZnSe SUPERLATTICE BAND GAP (eV)
(lattice constant of free-standing superlattice)
30..,,,_...,..,.......,..,.......,r-.-......-.-.......-r-.-~..,..........--,-.-,-......-.-.......-.--,-,-,---,---r-,-,

Cl)

(1)

>..

2.250

(I)

(/)

'+-

(1)

..0

::::;

10
20
Number of ZnTe Layers

Figure A.4: Calculated free-standing ZnSe/ZnTe superlattice band gaps.

129

CdSe-CdS SUPERLATTICE BAND GAP (eV)
(lattice constant of free-standing superlattice)

30....------------.--.-............--.-.-........-,.....,........__,.___,..___.....-,-..,........

(l)

>,.

(/)

-0

4--

(l)

...0

::J

10
20
Number of CdSe Layers

Figure A.5: Calculated free-standing CdS/CdSe superlattice band gaps.

130

CdTe-CdSe SUPERLATTICE BAND GAP (eV)
(lattice constant of free-standing superlattice)
30..,,.,.,.....,~---.----.----r--r--,--,---,--r-~~r---,--r--r--,----..--r-~--i---r---r-1

"'=

>..

(/)

-0

'+-

..0

::)

1.. 500

Number of CdTe Layers

Figure A.6: Calculated free-standing CdSe/CdTe superlattice band gaps.

131

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