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The study of interdiffusion and defect mechanisms in Si1-x Gex single quantum well and superlattice materials

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The study of interdiffusion and defect mechanisms in Si1-x Gex single quantum well and superlattice materials
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Griglione, Michelle Denise
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Activation energy ( jstor )
Ambient temperature ( jstor )
Annealing ( jstor )
Artificial satellites ( jstor )
Conceptual lattices ( jstor )
Diffusion coefficient ( jstor )
Nitriding ( jstor )
Oxidation ( jstor )
Semiconductors ( jstor )
Superlattices ( jstor )
Chemical Engineering thesis, Ph. D ( lcsh )
Dissertations, Academic -- Chemical Engineering -- UF ( lcsh )
Germanium compounds ( lcsh )
Semiconductors ( lcsh )
Silicon compounds ( lcsh )
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Thesis:
Thesis (Ph. D.)--University of Florida, 1999.
Bibliography:
Includes bibliographical references (leaves 215-221).
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Typescript.
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Vita.
Statement of Responsibility:
by Michelle Denise Griglione.

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THE STUDY OF INTERDIFFUSION AND DEFECT MECHANISMS IN
SIi.xGEx SINGLE QUANTUM WELL AND SUPERLATTICE MATERIALS













By

MICHELLE DENISE GRIGLIONE


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


1999
























Copyright 1999

by

Michelle Denise Griglione




























For Rob, Dad and Mom












ACKNOWLEDGMENTS


The completion of this research work and my graduate career would

not have been possible without help from many people. The contributions of

my committee members Dr. Cammy Abernathy and Dr. Rich Dickinson are

greatly appreciated. I am indebted to Dr. Mark Law for his patience as I either

waltzed into or paced outside of his open door with my latest triumphs or

traumas. Dr. Kevin Jones has allowed generous access to his labs, TEM

equipment and post-docs. I am most indebted to Dr. Tim Anderson, my

project advisor, for his scientific guidance as well as personal support for my

unorthodox graduate career.

Dr. Yaser Haddara receives my greatest appreciation for the knowledge

that he imparted to me regarding solid state diffusion and process simulation.

Our weekly discussions were invaluable. I am also grateful to Dr. Wish

Krishnamoorthy for TEM analysis and for sharing his wisdom regarding

HRXRD and basic physical science. I owe unending gratitude to Erik Kuryliw

for his persistent partnership in discovering the surprising versatility of the

rapid thermal processor.

I thank Pete Axson for generously lending his technical expertise in

such tricky areas as welding gas lines and his patient troubleshooting. Many

thanks to Courtney Hazelton, Steve Schein and the rest of the cleanroom







crew for their friendly service with a smile, as well as Dennis Vince in the

ChemE shop. I am grateful to Dr. Margarida Puga-Lambers for her dedicated

and timely SIMS characterization. Doug Meyers of ASM Epitaxy, Alex Van de

Bogaard of Delft University, and Bruce Gnade of Texas Instruments are

credited with growth of the materials used in this study. Dr. Olga Kryliok is

appreciated for her support and interest. Lance Robertson of SWAMP Center

has contributed to the overall morale of this research project.

Acknowledgment is also due to my secondary school science teachers,

Ms. Betty Johnson and Dr. John Lieberman, who made my first brushes with

science fun and fascinating. My parents taught me the value of knowledge,

personal achievement and striving to make a contribution. They have

supported me wholeheartedly throughout this endeavor, as they have

through every other, and I thank them. Last, but certainly not least, I thank

Rob Baker for his help with the manuscript, and more significantly, the

personal encouragement and understanding that he provided on a daily basis

... especially on the days when more than the usual amount of understanding

and encouragement was needed.












TABLE OF CONTENTS



ACKNOWLEDGMENTS.................................. ...................................................

LIST OF TABLES ......................................................................................................ix

LIST OF FIGURES .................................................................................................... xi

ABSTRACT ..............................................................................................................xv

1 INTRODUCTION.................................................................................................. 1

1.1 Selected Material Properties and Device Applications........................... 3
1.1.1 Material Properties............................................................................. 3
1.1.2 Device Applications........................................................................... 8
1.2 Strain and Strain Relaxation in SiGe Heterostructures............... ... 11
1.3 Diffusion in Elemental Semiconductors................................................ 15
1.3.1 Continuum Theory ......................................................................... 16
1.3.2 Point Defects and Diffusion Mechanisms.......................................... 18
1.4 Non-equilibrium Point Defect Injection................................ ........... ... 24
1.4.1 Interstitial Injection (Oxide Growth) ................................................... 25
1.4.2 Vacancy Injection (Nitride Growth) ......................................... ... 27
1.5 Literature Review ............................................................................................. 28
1.5.1 Self-Diffusion and Intrinsic Interdiffusion........................................ 28
1.5.1.1 Self-diffusion............................................................................ 28
1.5.1.2 Tracer studies of Ge in Si......................................... ........... ... 29
1.5.1.3 Diffusion studies of Sil.-Gex/Si heterostructures................... 30
1.5.2 Oxidation and Nitridation Enhanced Diffusion............................. 32

2 SAMPLE PREPARATION AND CHARACTERIZATION................................ 34

2.1 Growth Parameters and Structure............................................................ 34
2.2 Transmission Electron Microscopy.......................................................... 37
2.2.1 Overview ............................................................................................. 37
2.2.2 TEM Sample Preparation ............................................................... 40
2.2.2.1 Plan view ................................................................................. 40
2.2.2.2 Cross-sectional........................................................................... 41
2.2.3 Images of Structures...................................... .................................. 42
2.2.3.1 XTEM .......................................................................................... 42
2.2.3.2 PTEM........................................................................................... 44







2.3 Secondary Ion Mass Spectroscopy ......................................................................45
2.3.1 Determination of the Ge Depth Profile in SiGe Structures............ 50
2.3.2 Determination of the Error in D................................. ................ 54
2.4 X-ray Diffraction ......................................................................................... 56
2.4.1 Overview ....................................................................... ......................... 56
2.4.2 Optimization Procedures............................... ........................... 61
2.4.3 Determination of Interdiffusivity of Superlattice Layers .............. 62
2.4.4 Determination of Strain Relaxation.................................................... 64

3 BEHAVIOR OF ANNEALED Sil.xGex SINGLE QUANTUM WELLS..........67

3.1 Growth Parameters and Structure......................... ............... ............ 68
3.2 Processing.................................................................................................... 69
3.2.1 Rapid Thermal Processing .......................................... ............ .... 69
3.2.2 Furnace Processing............................................................................ 72
3.3 Simulation of Diffusion ................................................ ........................ 73
3.4 Results......................................................................................................... 79
3.4.1 Diffusivities and Activation Energies from SIMS/FLOOPS........... 79
3.4.2 Diffusion Behavior of Partially Relaxed Structures....................... 84
3.4.3 Sil.-Ge, Single Quantum Well with Boron Marker Layer............. 85
3.4.4 Estimation of Fractional Interstitial Components of
Diffusion.................................................................................................... 89
3.4.5 TEM.............................................................................................................95
3.5 Discussion........................................................................................................ 98
3.5.1 Diffusivities of Fully-Strained Structures...................................... 98
3.5.2 Diffusivities of Partially-relaxed Structures .................................. 114
3.5.3 Misfit Dislocation Effects .................................................................... 116
3.5.4 Fractional Interstitial Components from Marker Layer
Experiments.................................................................................... 121
3.6 Conclusions................................................................................................... 123

4 BEHAVIOR OF ANNEALED ASYMMETRICALLY STRAINED Si/Si1.-Gex
SUPERLATTICES WITH Sil-xGex BUFFER................................................... 126

4.1 Growth Parameters and Structure............................................................... 127
4.2 Strain State................................................................................................. 129
4.3 Processing................................................................................................... 131
4.4 Simulation of Diffusion ........................................................................... 132
4.5 Results .................................. ...................................................................... 132
4.5.1 SIMS/FLOOPS...................................................................................... 132
4.5.2 High Resolution Xray Diffraction...................................................... 135
4.5.2.1 Diffusivities............................................................................... 135
4.5.2.2 Strain relaxation......................................................................... 139
4.5.3 TEM.................................................................................................... 141
4.6 Discussion .................................................................................................... 147
4.6.1 Diffusivities Determined from SIMS and FLOOPS...................... 147








4.6.2 Diffusivities Determined from HRXRD ........................................... 156
4.6.3 Strain Relaxation Determined from HRXRD.................................. 159
4.7 Conclusions ...................................................................................................... 161

5 BEHAVIOR OF ANNEALED ASYMMETRICALLY STRAINED Si/Sil-xGex
SUPERLATTICES W ITH Si BUFFER.......................................................... 164

5.1 Growth Parameters and Structure.......... ............................................ 165
5.2 Strain State.................................................................................................. 166
5.3 Processing.................................................................................................... 168
5.4 Simulation of Diffusion .............................................................................. 168
5.5 Results ......................................................................................................... 169
5.5.1 SIMS/FLOOPS................................................................................... 169
5.5.2 High Resolution Xray Diffraction...................................................... 171
5.5.2.1 Diffusivities.................................................................................... 172
5.5.2.2 Strain relaxation.......................................................................... 175
5.5.3 TEM ........................................................................................................ 176
5.6 Discussion............ .......................................................................................... 179
5.6.1 Diffusivities Determined from SIMS and FLOOPS........................ 179
5.6.2 Diffusivities Determined from HRXRD ........................................... 187
5.6.3 Strain Relaxation from HRXRD ....................................................... 189
5.6.4 Effect of Strain State on Diffusivity Values.................................... 191
5.7 Conclusions..................................................................................................... 194

6 CONCLUSIONS AND FUTURE W ORK......................................................... 197

6.1 Conclusions ...................................................................................................... 197
6.1.1 Single Quantum W ell Structures................................................ 197
6.1.2 Superlattice Structures........................................................................ 199
6.1.3 Strain Effects ........................................................................................ 201
6.2 Contributions .............................................................................................. 201
6.2.1 Modeling ................................................................................................ 201
6.2.2 Experimental......................................................................................... 202
6.3 Future W ork ............................................................................................... 203
6.3.1 Single Quantum W ell Investigations ............................................... 203
6.3.2 Superlattice Investigations.............................................................. 204
6.3.3 Simulations and M odeling................................................................ 205

APPENDIX A EXAMPLES OF FLOOPS PROGRAMS...................................... 206

APPENDIX B GLOSSARY ..................................................................................... 211

REFERENCES............................... .......................................................................... 215

BIOGRAPHICAL SKETCH...................................................................................... 222












LIST OF TABLES


Table page

1-1. Advantages and disadvantages of SiGe used in device applications.......... 8

3-1. Extracted diffusivity and enhancement values for SQW/MBE ................. 82

3-2. Extracted diffusivity and enhancement values for SQW/VPE ................ 82

3-3. Extracted diffusivities for initially partially relaxed SQW/MBE................ 85

3-4. Anneal times needed in FLOOPS to achieve actual B diffusion
pro files .................................................................................................................... 88

3-5. Fractional interstitial components and modified diffusivities and
point defect supersaturations determined for diffusion in inert
am bient............................................................................................................. 93

3-6. Fractional interstitial components and modified diffusivities and
point defect supersaturations determined for diffusion in oxidizing
am bient............................................................................................................. 94

3-7. Comparison of diffusivities of SQW/MBE and SQW/VPE in inert
and oxidizing ambients............................................................................... 107

4-1. Extracted diffusivity and enhancement values for SL/SiGe..................... 133

4-2. Extracted diffusivities for SL/SiGe using HRXRD..................................... 136

4-3. Parallel and perpendicular lattice constants of SL/SiGe........................... 142

4-4. Comparison of parameters of interdiffusion of SQW/MBE and
SL/SiG e........................................................................................................... 155

4-5. Diffusivities of SL/SiGe extracted from FLOOPS and HRXRD................. 159

5-1. Extracted diffusivity and enhancement values for SL/Si........................ 169

5-2. Extracted diffusivity values for SL/Si using HRXRD................................ 174

5-3. Parallel and perpendicular lattice constants of SL/Si............................... 177







5-4. Diffusivities of SL/Si extracted from FLOOPS and HRXRD.................... 189

5-5. Comparison of diffusivities of SL/SiGe and SL/Si in inert,
oxidizing and nitriding ambients.................................................................. 193

5-6. Comparison of activation energies of SL/SiGe and SL/Si in inert,
oxidizing and nitriding ambients............................................................... 194












LIST OF FIGURES


Figure page

1-1. Phase diagram of the Si-Ge system [Kas95]..................................................... 4

1-2. The diamond cubic structure of Sil-xGex alloy [Kas95]..................................... 4

1-3. Lattice constant of Sil-xGe, versus Ge composition..................................... 5

1-4. Critical thickness versus germanium fraction for Sil-xGex films on
a Si substrate ...................................................................................................... 6

1-5. Energy gap versus germanium fraction for unstrained and
coherently strained Sil.-Gex [Peo86]. ............................................ ............ ... 7

1-6. Cross-section of a Si1.xGex HBT [Tem88]............................................................. 9

1-7. Possible waveguide-photodetector structure using Si.,xGex alloy
[Pre95] ................................................................................................................ 10

1-8. Evolution of a misfit dislocation at the Si and Ge interface....................... 13

1-9. Termination of a misfit dislocation............................. ....................... 14

1-10. The direct interstitial mechanism.............................................................. 19

1-11. The vacancy mechanism................................................ ............................... 20

1-12. The Frank-Tumbull (dissociative) mechanism........................................... 21

1-13. The kick-out mechanism...................................................................... 22

2-1. Sil.-Gex sample structures used in these investigations............................. 35

2-2. Sample structure SQW/MBE, a single quantum well grown by
M B E ..........................................................................................................................36

2-3. Schematic of ray paths originating from the object which create a
TEM image [Wil96]. ........................................................................................ 38

2-4. Schematic of TEM views..................................................................................... 39







2-5. Front and rear views of the XTEM assembly after preparation
[W il96]...................................................................................................................... 41

2-6. Cross sectional view TEM (XTEM) micrographs of as-grown (a)
structure SL/SiGe and (b) structure SL/Si ......................................... 46

2-7. XTEM micrographs of as-grown (a) structure SQW/MBE and (b)
structure SQW /VPE ...................................................................................... 47

2-8. Plan view TEM micrographs of as-grown (a) structure SL/SiGe and
(b) structure SL/Si.2-9.................................................................................... 48

2-9. Figure 2-9. Plan view TEM micrographs of as-grown (a) structure
SQW/MBE and (b) structure SQW/VPE................................. ............ ... 49

2-10. Ge concentration profile determined from SIMS for sample
structure SL/SiGe........................................................................................... 52

2-11. Ge concentration profile determined from SIMS for sample
structure SL/Si ................................................................................................ 52

2-12. Ge concentration profile determined from SIMS for sample
structure SQW/VPE. ...................................................................................... 53

2-13. Ge concentration profile determined from SIMS for sample
structure SQW /M BE. .......................................................................... ....... .... 53

2-14. SIMS profile of structure SQW/MBE..................................... ............. 54

2-15. Schematic of symmetric x-ray Bragg reflection [Cul78]...............................56

2-16. Schematic of the monochromator/collimator................. ............... 57

2-17. Schematic of the x-ray path used in triple axis mode............................... 59

2-18. X-ray rocking curve of structure SL/SiGe before anneal....................... 60

2-19. X-ray rocking curve of structure SL/Si before anneal................................. 60

2-20. Miscut of substrate and mistilt of epilayer.............................................. 62

2-21. Example of positive and negative x-ray diffraction from an
asym m etric plane........................................................................................... 66

3-1. Schematic of sample structures SQW/MBE and SQW/VPE.................... 69

3-2. Effective Ge diffusivity of structure SQW/MBE as a function of
annealing temperature in inert, oxidizing, and nitriding ambients.........81







3-3. Effective Ge diffusivity of structure SQW/VPE as a function of
annealing temperature in inert, oxidizing, and nitriding ambients.........83

3-4. Schematic of test structure SQW/B. .......................................... ............... 86

3-5. Diffusion of as-grown B marker layer in all ambients...............................88

3-6. Cross sectional view TEM micrographs of structure SQW/MBE
after annealing in inert ambient at (a) 1000 C for 43 min and (b)
1200 C for 1 m in ............................................................................................ 99

3-7. Plan view TEM micrographs of structure SQW/MBE after
annealing in inert ambient at (a) 900 OC for 330 min and (b) 1200 C
for 1 m in......................................................................................................... 100

3-8. Plan view TEM micrographs of structure SQW/VPE after
annealing at (a) 900 OC for 330 min in oxidizing ambient and (b)
1200 *C for 1 min in inert ambient............................................................... 101

3-9. Comparison of experimentally determined SIMS profile and
FLOO PS profile................................................................................................. 103

3-10. Illustration of non-Gaussian shape of SQW diffused profiles................ 104

3-11. Comparison of diffusivities of structures SQW/MBE and
SQW/VPE in (a) inert ambient and (b) oxidizing ambient...................... 106

3-12. Diffusivities of Ge in Si/Sil.-Gex/Si SQWs from previous studies
and this w ork ................................................................... ................................. 108

3-13. Plot of diffusivities of all anneal times in inert ambient for each
temperature for SQW/MBE......................................................................... 111

3-14. Comparison of Ge SIMS profiles in inert, oxidizing and nitriding
ambients for SQW/MBE................................................................................. 112

3-15. Comparison of Ge diffusivities of partially relaxed structures in
inert am bient................................................................................................. 115

4-1. Schematic of sample structure SL/SiGe....................................................... 128

4-2. Effective Ge diffusivity of structure SL/SiGe as a function of
annealing temperature in inert, oxidizing, and nitriding ambients....... 134

4-3. X-ray diffractometer scans of the SL/SiGe superlattice peaks about
Si(004) with increasing anneal times in inert ambient............................. 137







4-4. Decay of the integrated intensity of the first order superlattice peak
about Si(004) as a function of annealing time, temperature and
am bient of SL/SiG e............................................................................... ........... 138

4-5. Cross sectional view TEM micrograph of structure SL/SiGe after
annealing in oxidizing ambient at 850 C for 8 min................................. 145

4-6. Plan view TEM micrographs of structure SL/SiGe after annealing
in inert ambient at (a) 850 C for 8 min and (b) 1000 C for 2 min............ 146

4-7. Comparison of experimentally determined SIMS profile and
FLOOPS profile using the Fermi model for samples annealed at 950
C and 3 min in (a) inert (b) oxidizing and (c) nitriding ambient............. 148

4-8. Diffusivities of Ge in Sil.-Ge,/Si SLs with a SilxGex buffer layer
from (+) Hollander et al. and (*) this work............................................... 150

4-9. Comparison of Ge SIMS profiles in inert, oxidizing, and nitriding
am bients for SL/SiGe ........................................................................................ 154

5-1. Schematic of sample structure SL/Si........................................................... 166

5-2. Effective Ge diffusivity of structure SL/Si as a function of
annealing temperature in inert, oxidizing, and nitriding ambient........ 170

5-3. X-ray diffractometer scans of the SL/SiGe superlattice peaks about
Si(004) with increasing anneal times in inert ambient............................. 173

5-4. Decay of the integrated intensity of the first order superlattice peak
about Si(004) as a function of annealing time, temperature and
am bient of SL/Si........................................................................................... 174

5-5. Plan view TEM micrograph of structure SL/Si after annealing in
inert ambient at 850 C for 8 min..................................................................... 178

5-6. Comparison of experimentally determined SIMS profile and
FLOOPS profile for 950 C and 3 min in (a) inert (b) oxidizing and
(c) nitriding am bient........................................................................................... 180

5-7. Diffusivities of Ge in Sil.xGe./Si SLs with a Si(100) buffer layer
from previous studies and this work ...................... ....................................... 184

5-8. Comparison of Ge SIMS profiles in inert, oxidizing and nitriding
am bients for SL/Si......................................................................................... 185












Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

THE STUDY OF INTERDIFFUSION AND DEFECT MECHANISMS IN
Sil.-Gex SINGLE QUANTUM WELL AND SUPERLATTICE MATERIALS

By

Michelle Denise Griglione

May 1999



Chairman: Dr. Tim Anderson
Major Department: Chemical Engineering

Dimensions of Si microelectronic devices continue to shrink in pursuit

of higher speed operation. Soon, these dimensions will reach a minimum

and an alternative material must be found. The alloy Si-Ge has been

suggested as a replacement due to its ability to be band-gap engineered, as well

as its compatibility with current Si-only processing, low cost, and

environmental friendliness. The fabrication of Si-Ge devices includes several

high temperature processing steps which can degrade device performance if

interdiffusion occurs within the material. This dissertation investigated the

interdiffusion of Si-Ge structures as a function of processing temperature (850

to 1200 C), layer structure, and anneal time. In particular, the roles of

vacancy and interstitial point defects in the diffusion process were







investigated and a model presented which simulated diffusion under a

variety of material and processing conditions.

Activation energies of diffusion in inert, oxidizing, and nitriding

ambients for single quantum well (SQW) material were found to be 5.8, 5.0,

and 3.0 eV, respectively. Diffusion in inert and oxidizing ambients was

similar, while significant retardation of diffusion was seen in nitriding

ambient.

Activation energies of diffusion in inert, oxidizing and nitriding

ambients for a superlattice (SL) with a Sil.xGex buffer layer were found to be

3.1, 2.4, and 4.0 eV, respectively. Activation energies of diffusion in inert,

oxidizing, and nitriding ambients for a SL with a Si buffer layer were found to

be 3.63, 2.81, and 4.1 eV, respectively. Slight enhancement of diffusion was

observed in oxidizing ambient at lower temperatures, while retardation of

diffusion was observed in nitriding ambient at all temperatures. No

difference in diffusion behavior was observed between the two SL structures.

Transmission electron microscopy confirmed that dislocations were

present and grew with increased anneal time and were believed to have a

significant effect on diffusivity values. Experiments using SQWs with buried

boron marker layers determined that a portion of interstitials injected in an

oxidizing ambient were captured by dislocations, however, enough remained

available to aid in the diffusion process.












CHAPTER 1
INTRODUCTION

Recently there has been increased interest in alloys of silicon and

germanium (Si1-xGe,) for applications in electronics and photonics. Devices

incorporating Si-Ge solid solutions show increased speeds as well as other

desirable features over the equivalent pure Si devices. The manufacture of

these devices includes several high-temperature and oxidation steps, and it is

necessary that Si.-xGe, heterostructures be able to withstand these processing

steps without device degradation such as interface broadening and

intermixing of the device layer structure. Therefore, it is important to

understand the diffusion processes that cause degradation.

Common Sil.,Ge, device designs include single quantum well (SQW),

monolayer superlattice, and multiple quantum well (MQW) structures. The

single quantum well material normally consists of a buffer layer grown on a

Si substrate, followed by a Sil.xGe, layer and a Si cap layer, Si/Si-,,Ge./Si. In

the monolayer superlattice material, m atomic layers of pure Si are deposited

followed by n atomic layers of pure Ge (m and n are usually <10), with this

pattern repeated p times, (Si.Ge),p. For the MQW material a layer of pure Si

is grown, followed by a layer of Si1.xGex alloy of particular composition, x, with

this pattern repeated for a determined number of periods, p, (Si/Si-.Gex)p.

Each structure has diffusion characteristics which are influenced by such







parameters as anneal time and temperature, alloy composition, strain state, as

well as quantum well (layer) thickness and periodicity.

A review of the literature reveals that work done thus far in thermally

activated interdiffusion of Si-Ge material can be divided into two categories:

(1) interdiffusion of SQW and SL materials in an inert environment [Van90,

Sun94, Hol92, Zau94] and (2) impurity diffusion in inert and reactive

environments [Kuo95, Pai95, Fan96, Kuz98]. There has been discussion about

identification of which atoms (Si, Ge, or both) are diffusing in the undoped

case as well as the fractional contribution of interstitials and vacancies

towards diffusion in both cases. A detailed model for either, however, has

not been proposed.

This work has investigated intrinsic interdiffusion of undoped SQW

and SL material in inert, oxidizing, and nitriding environments over the

temperature range 800 to 1200 C. Experiments were conducted to measure

the extent of interface intermixing and the corresponding diffusion

coefficient. The effects of surface oxidation and nitridation have been

examined to determine the extent of diffusion enhancement or retardation as

a result of processing under point defect supersaturation conditions.

Estimates of the fractional contributions of interstitials and vacancies to

Si/Sii.xGex diffusion have been ascertained. Finally, the effect of dislocations

on the concentration of injected point defects available to aid in

interdiffusion has been studied.







1.1 Selected Material Properties and Device Applications


1.1.1 Material Properties

In microelectronics, interest in a semiconductor material evolves if the

material has basic properties suitable for device applications. Device

fabrication and operation requirements then dictate what specific material

properties need to be investigated and adapted further. It is therefore

important to introduce the device applications and material properties of

Si1xGex that make it an increasingly appealing material in the semiconductor

industry. The crystal structure, lattice constant, critical thickness, phase

diagram, and band gap of Sij.xGex are all properties that determine

performance in several different device applications. These material

properties are also of particular importance in this investigation because they

either have a primary or secondary effect on interface diffusion, and they

must be known to effectively analyze the data obtained from the

characterization methods described in Chapter 2.

The Si-Ge system exhibits an isomorphous phase diagram with nearly

ideal-solution behavior in both the liquid and solid solutions [Kas95]. The

solid and liquid phases are separated by a region of coexistence, which gives

rise to segregation upon crystallization from the melt (Figure 1-1).







Weight Percent


1412


Si 0.1


Germanium


01 040 40 50 4<








Ills


Figure 1-1. Phase diagram of the Si-Ge system [Kas95]. The gray section
indicates the area of composition and temperature studied in this thesis.


The alloy silicon-germanium, Si-.xGe,, is a semiconductor which

crystallizes in a diamond cubic-type substitutional structure. This structure

can be considered as two face-centered cubic sublattices shifted by one quarter

of the body-diagonal, R=1/4<111>, as shown in Figure 1-2.


Figure 1-2. The diamond cubic structure of SilxGe, alloy [Kas95].


The lattice parameter, a, is a function of Ge composition, x, and has been

found to follow [Kas95]:


D70 80
-, 1500

---- 1400
L
S-- 1300

1200 T (C)

1100

S1000
940
0.4 0.5 0.6 0.7 0.8 0.9 Ge
Ge Fraction, x









a(x) = 0.002733x2 + 0.01992x + 0.5431(nm) (1-1)

showing a slight deviation from Vegard's rule, which predicts the lattice

constant of the alloy based on linearity between the endpoint lattice

parameters of pure Si and Ge:


a(x)= (ace-as)x+asi=0.0227x+0.5431 (nm) (Vegard's Rule) (1-2)

Figure 1-3 shows the composition dependence of the lattice constant predicted

using Vegard's rule, as well as the curve predicted by Equation 1-1.



0.57
a =0.5658 nm
0.565 G

0.56 -
a (nm) Vegards's Rule -
0.555 '
(experimental)
nv L Actual
0.55

0.545
a --0.5431 nm
0.54 1 a 1 1I 1 1 1 I 1 I 1 1 1 I 1
0 0.2 0.4 0.6 0.8 1
Ge Fraction, x

Figure 1-3. Lattice constant of Si,.xGex versus Ge composition. Curves
predicted by Vegard's rule and experimental [Kas95].



For epitaxially grown, pseudomorphic (the lattice planes of the epilayer

and substrate are in perfect registry) Sil.xGe, films, there is built-in strain

which is fixed by the lattice constant of the substrate on which the film is







grown. The lattice mismatch between Si and Ge is = 4.2% with Ge having the

larger lattice parameter. Strain energy plays a critical role in band alignment

and energy gap values. The critical thickness for pseudomorphic growth

decreases rapidly with increasing Ge content. For example, a capped layer

with Ge composition of x=0.1 has a critical thickness of -650 A, while at Ge

composition x=0.5 the critical layer thickness reduces to -30 A (Figure 1-4).


Ge Fraction, x-

Figure 1-4. Critical thickness versus germanium fraction for Silx-Ge, films on
a Si substrate. Curve 1 is for Si-capped material, while curve 2 is for uncapped
material [Jai94].




Sii.-Gex has an indirect band gap which spans the 0.85 to 1.35 lm range.

The energy gap is different for the unstrained bulk alloy and coherently

strained alloy. The energy gap is dependent upon both the Ge content and the








temperature. Figure 1-5 shows the composition dependence of the unstrained

bulk alloy. The alloy has a Si-like A-conduction-band minimum from x=0 to

x=0.85. At this composition there is a crossover to the Ge-like L-conduction-

band minimum[Lan85]. Compressive strain in the alloy produced by the

underlying Si substrate reduces the Sil.xGex bandgap energy. In Si/Sil-xGe,

superlattices the bandgap is strongly influenced by not only the strain state,

but also the layer thickness and period.


1.10



1.00



S0.90

CP

C 0.80



0.70


0.60


1.13



1.24


E
1.38
CO


1.55 0



1.77


2907


0 0.2 0.4 0.6 0.8 1.0
Germanium fraction, x

Figure 1-5. Energy gap versus germanium fraction for unstrained and
coherently strained Sil.,Ge, [Peo86].







1.1.2 Device Applications

The semiconductor industry has long been based on Si, yet Si

technology is fast approaching its physical limits. Compound semiconductors

made of elements in the Il and V columns in the periodic table have been

used in specific applications that require a tunable direct bandgap energy and

high carrier mobilities. These IUI-V semiconductors, however, are more

complex to process. Incorporating Ge into Si to create Sil.xGe, devices

provides a good compromise between Si and compound semiconductor

technology. Sil-.Gex technology allows bandgap engineering similar to that of

compound semiconductors while retaining the economical and advanced

aspects of Si technology. While Sil.xGe, technology is progressing rapidly,

there are still drawbacks in device manufacturing. Of major concern is the

lattice mismatch between Si and Ge (4.2%) which can cause growth and

performance challenges for certain device applications. Table 1 summarizes

the advantages and disadvantages of Si1.-Ge, for device applications.




Table 1-1. Advantages and disadvantages of SiGe used in device applications.

Advantages Disadvantages
* Able to bandgap tailor Large lattice mismatch Si-Ge
* Able to deposit atomically sharp Large dopant out-diffusion
SiGe interface
* Economical Indirect bandgap
* Can be incorporated into standard
Si processing
* Environmentally harmless







Because Si and Ge form a continuous solid solution with a wide range

of energy gaps, the alloy has a wide range of optical and electronal

applications. The most common applications are in Heterojunction Bipolar

Transistors (HBTs), Modulation Doped Field Effect Transistors (MODFETs)

and quantum well light emitters and detectors. The incorporation of a

narrow band-gap Six-Ge, strained superlattice structure [Tem88] or bulk alloy

in a Si bipolar junction transistor (BJT) has many advantages relative to a

standard Si homojunction bipolar transistor. It offers increased emitter

injection efficiency and current gain, lower base resistance, shorter base transit

times, and better low temperature operation. Cut off frequencies, f,, as high as

130 GHz for a Sil-xGe, HBT have been reported [Oda97], while f, for Si BJTs are

commonly -75 GHz.




n+ CONTACT


n-5 x 1017 cr3
0.5 Im, EMITTER
p-BASE
/ 50 A Geo.i S ios WELLS

250 A Si BARRIERS
n-,5 x 10'1 cmfr 20 PERIODS
1.0 pm, COLLECTOR
n+-Si BUFFER



Figure 1-6. Cross-section of a Sil..Ge, HBT [Tem88].







In optoelectronic applications, both light detectors and emitters

operating in the near (1.3gm) and mid-infrared (=10m) ranges can be

fabricated using the Si-Ge system, particularly the (SimGen)p superlattice

system. The best of these photodetector devices use a waveguide rib where

the light enters sideways through the rib and is absorbed in the active layer

(Figure 1-7), making the absorption region and overall absorption larger than

in vertical mesa-type structures, while having a geometry better suited for

optical communication links.



n*-Si Contact
(1020cm-3 Sb)
Contacts

Si Buffer

Si,.,Ge,/Si SL-MQW

PHOTODETECTOR


p-SiGe Waveguide
WAVEGUIDE *



p-Si Substrate


Figure 1-7. Possible waveguide-photodetector structure using Si,-.Ge. alloy
[Pre95].



Si1.xGex heterostructures can be grown on either a Si or Si,.xGex buffer

creating band alignments which lead to spatial separation of ionized dopant

atoms and mobile carriers which can be used in a MODFET. Electron







mobilities in these Sii.-Gex structures are almost five times higher than in the

corresponding Si structures.

1.2 Strain and Strain Relaxation in SiGe Heterostructures


Strain develops when an epitaxial layer of a certain lattice parameter,

a,, is grown on a substrate of a differing lattice parameter, a,. When ae
epitaxial layer is said to be under tensile strain. When ae>as the layer is under

compressive strain. Regardless of the Ge composition, x, Silx-Ge, epitaxial

layers grown on a Si buffer are always under compressive strain. As

schematically depicted in Figure 1-8b, the cubic Sil.xGex lattice theoretically is

compressed so that the parallel lattice parameter, a,, matches that of the cubic

Si lattice. Because the total volume of the Sil.-Ge, unit cell is considered

constant, the perpendicular lattice parameter, a., increases, rendering the Si,.

xGex unit cell no longer cubic but tetragonal (termed tetragonal distortion).

The Si-.xGe, monolayers are grown on top of each other this way and the

strain energy stored in the dislocation-free film, Es,, is described by:


Ei=MhE2 (1-3)

where M is the biaxial elastic modulus of the epilayer, e is the strain and h is

the thickness of the epilayer. The energy necessary to generate a dislocation,

Edjiafn, is described by:



Edslocatioon = Gb2 lh (1-4)
4x(1 a) X b







where G is the shear modulus, assumed to be the same in the film and

substrate, b is the Burger's vector of the dislocation, a is Poisson's ratio, and

2/X is the dislocation length per unit area of the epitaxial layer. When

ES>Ed.,i, the epitaxial layer is fully strained and dislocation free,

otherwise known as pseudomorphic. When Es=Edaoc ,o, the layer

thickness is at a critical thickness, termed h, (Section 1.1). Above this critical

thickness, Edisoca>Est and it is energetically favorable to relieve strain

through dislocation formation.

Epilayer strain is most often relieved through the growth and

propagation of misfit dislocations. Misfit dislocations can be nucleated

homogeneously, through dislocation loops or half loops present at the surface

or an interface, or heterogeneously, through impurities or inclusions

incorporated during the growth process. A misfit dislocation is commonly

viewed as the creation of extra planes of atoms in the lattice structure (Figure

1-8c).

Geometrically, a misfit dislocation cannot terminate within the bulk of

a crystal; it must either form a closed loop (terminate upon itself), join with

another line defect, or end at the nearest free surface. Misfit dislocations

rarely have sufficient propagation velocity to span across the entire lateral

dimension of the crystal, thus they generally terminate by intersecting with a

threading dislocation (Figure 1-9). Threading dislocations extend from the

surface of the epitaxial material to the substrate, traversing through any

intervening strained layers. They exist due to imperfections in the growth







process and can glide through a double/single kink motion. This movement

allows propagation of misfit dislocations [Kas95, Jain94].


Lttt-t


as

as


3e
*


aLSi

asi


K(f r(r(r6i


a/. r r _


Figure 1-8. Evolution of a misfit dislocation at the Si and Ge interface. (a) an
isolated Ge layer (gray), and an isolated Si layer (white) of smaller lattice
constant, asi; (b) the Ge layer is compressively strained in the parallel direction
to match the Si substrate lattice constant to produce tetragonal distortion; (c)
extra lattice planes are inserted as misfit dislocations as the Ge layer relaxes
towards its original lattice constant.



Heterostructures used in device applications mentioned in Section 1.1

contain Six-xGex layers that are generally metastable with regard to misfit

dislocation formation, due to either layer thickness or growth temperature.

These heterostructures tend to relax through the injection and propagation of

misfit dislocations at the Sil-xGex/Si interfaces when subjected to high


aG
aGe


-


/




14

temperature thermal treatment. Misfit dislocation propagation can lead to

the simultaneous propagation of threading dislocations that can penetrate





si B si B si

SiGe SiGe SiGe

A A A
Si Si A Si A


a. b. c.

Figure 1-9. Termination of a misfit dislocation. (a) Misfit dislocation along a
Si/ Sil.xGex interface meets a threading dislocation, AB; misfit terminates by
(b) forming new misfit terminating at lateral surface or (c) termination of
threading dislocation AB at free surface.



heterojunctions and increase current leakage. Heterostructures with

dislocation densities greater than -103 cm-2 are unsuitable for device

applications [Hou91]. Thus, the characterization and quantification of

dislocations in Silx-Gex/Si is vital in developing the material for device

applications. Parts of this dissertation address whether dislocations alter the

diffusion that occurs during high temperature thermal treatment (Sections

3.4.2 and 3.5.2) and whether dislocations capture the excess point defects

injected during oxidation and nitridation (Sections 3.4.3 and 3.5.3), thus

limiting or prohibiting their interaction in the diffusion process.







1.3 Diffusion in Elemental Semiconductors


Diffusion is the process in which random atomic motions result in the

transport of matter from one part of a system to another. When an

inhomogeneous single-phase alloy is annealed, matter will flow in a

direction which will decrease the chemical potential gradient. If annealed

sufficiently at constant temperature and pressure, the alloy will reach

equilibrium: there will be no net flow of matter and the alloy will be

homogeneous.

Diffusion in semiconductors can be examined through three different

modeling approaches: (1) empirical, in which the diffusion is studied and

described entirely through experimental analysis, (2) semi-empirical, in

which mathematical models and experimental data are used conjunctively to

indicate the diffusion process, and (3) atomistic, in which mathematical

modeling is used almost exclusively to indicate how individual atoms are

diffusing. The empirical approach has been used extensively to study self and

dopant diffusion in silicon, most notably by Fair et al.[Fai75a, Fai75b, Fai77].

Examples of the semi-empirical approach include the FLorida Object Oriented

Process Simulator (FLOOPS) [Law96] and the Stanford University Process and

Engineering Models (SUPREM) [Han93]. In the semi-empirical approach,

expressions for species diffusivities are developed from detailed atomistic

mechanisms and these expressions are incorporated into a continuum

description of the diffusion process. The parameters in the expressions for

the species diffusion coefficients are estimated by a comparison with







experimental results. Monte Carlo (MC) and Molecular Dynamics (MD)

simulations are examples of methods used in the atomistic approach. These

are not common in complete modeling of diffusion because the small time

scale limits their use to the study of unit steps of diffusion only.

1.3.1 Continuum Theory

Diffusivity values as well as fractional contributions to diffusion of

interstitials and vacancies have been estimated in this work using the semi-

empirical approach. Experimental results obtained through Secondary Ion

Mass Spectrometry (SIMS) (Section 2.3) have been used to estimate

parameters used in the continuum and atomistic mechanism models

incorporated in FLOOPS. It is therefore important to describe the

fundamentals of continuum theory in order to understand the models and

results presented throughout this work.

The semi-empirical approach to describing diffusive transport in a

diffusion couple is based on Fick's first law, which describes mathematically

the flux in one dimension as:


F =-D c(1-5)
Jx
where F is the flux of atoms, c is the concentration of the diffusing

component, x is the space coordinate measured normal to the section, and D

is the diffusion coefficient. The minus sign in Equation 1-5 indicates that the

diffusion occurs in the direction of decreasing concentration. Fick's first law







is most useful in experimental situations with steady state diffusion, where

dc/dt=0.

Fick's second law is normally used in systems with non-steady-state

concentration. Combining Fick's law with the continuity equation for the

diffusing species yields the diffusion equation:


ac a D ac (1-6)

The solution to Equation 1-6 will be the concentration as a function of

position and time, c(x,t), for specified initial and boundary conditions. When

the diffusion distance is short with respect to the dimensions of the structure,

c(x,t) is mostly expressed by error functions. For example, isothermal

diffusion of a constant concentration source into a thick (infinite) substrate

with a constant diffusion coefficient can be described by :

x
C= Coerfc /2 (1-7)
2(Dt)'
where x is the depth into the semiconductor, CO is the concentration of the

source at x=0, D is the diffusivity, and t is time. Solutions to the diffusion

equations for many different boundary conditions can be found in several

classic references [Cra75, Tuc74].

In the systems studied here, complexities in using Fick's law arise from

two different sources: (1) the dependence of D on the properties of the system

can be complex and (2) multiple equations must be written to describe

multiple species. The value of D can vary with time (e.g., imposed







temperature variation and transient phenomena) and composition. The

temperature dependence of the diffusion coefficient in solids is generally well

described by an Arrhenius relation:


D = Do exp(-Ea /kT) (1-8)

where Do is the weakly temperature-dependent pre-exponential factor, E, is

the activation energy of transitions of the solute between adjacent lattice sites,

k is the Boltzmann constant, and T is temperature. The magnitude of E, can

help to identify the diffusion mechanism. Both Do and E, can depend on the

strain state, composition, and gas ambient (e.g., inert, oxidizing, or nitriding).

1.3.2 Point Defects and Diffusion Mechanisms

Derivation of a form for D used in continuum equations necessitates

an understanding of the atomistic mechanism by which the diffusing species

migrates through the crystal lattice. Hence, the coupling of a continuum

approach to describe the spatial and temperal concentration dependency and

an atomistic approach to describe the functional form of the mass diffusivity

is the basis of the semi-empirical approach. There are several atomic

pathways available for diffusion, of which the ring, interstitial, and vacancy

mechanisms are the most elementary.

The ring mechanism is simply the exchange of two neighboring lattice

atoms, without the involvement of point defects. This mechanism has not

been seen experimentally, and would be theoretically improbable due the






large activation energy required for the exchange [Had95]. It will be ignored as

a possible diffusion pathway for the rest of this dissertation.

The direct interstitial mechanism is movement of either a self or

impurity atom from interstitial site to interstitial site through the lattice, as

schematically shown in Figure 1-10. This mechanism is energetically possible

for self interstitials or impurities which are small compared to the host lattice

atoms; it is energetically unfavorable for atoms which are large compared to

the lattice atoms, due to the lattice distortions involved [She89, Bor88].



0 0 00
OO~OO


0000
Figure 1-10. The direct interstitial mechanism.


Lattice sites that are unoccupied are known as vacancies. The vacancy

mechanism is movement of a self or impurity atom sitting on a lattice site

into a neighboring vacancy, occupying that site substitutionally (Figure 1-11).

There will be a net flux of vacancies equal and opposite to the flux of the

diffusing species. The amount of diffusion that occurs via the vacancy

mechanism depends on the probability that an atom rests next to a vacancy,

which in turn, depends on the total mole fraction of vacancies in the crystal

[She89, Bor88].







0000 0000
0o 0 o0 0o
0000 0000
Figure 1-11. The vacancy mechanism.



The simple mechanisms just discussed are generally insufficient

individually to predict the diffusion of self or impurity atoms in a

semiconductor crystal. Self and impurity diffusion in both Si and GaAs have

shown to be some combination of the vacancy and interstitial mechanisms

discussed above, involving both interstitial and vacancy point defects [Fra91,

Had95]. The approach used in this dissertation to model Si-Ge diffusion has

assumed a similar cooperative contribution of interstitials and vacancies,

therefore it is important to consider both substitutional and interstitial

mechanisms while examining Si-.xGe, interdiffusion. It is important,

however, to note that the mechanism of Ge diffusion in Si1-xGex is slightly

different than the usual impurity diffusion in either Si or GaAs, as the Ge

"impurity" is neutral within the Sil.xGex lattice. Due to the neutrality of the

Ge in Sil-xGe, this thesis ignores the possibility of pair model diffusion

[Had95], which normally occurs when the point defect and impurity are both

charged.

The substitutional-interstitial diffusion model (SID) offers two

plausible mechanisms which couple the impurity atoms and native point

defects. In each mechanism, the mobile species is the impurity interstitial.

The first mechanism, known as the Frank-Turnbull or dissociative







mechanism, describes the movement of an impurity atom from a

substitutional site to an interstitial site, leaving behind a vacancy (reverse

reaction in Figure 1-12). The mechanism is both interstitial- and vacancy-

dependent. The diffusion equation for the impurity, in this case Ge, is given

as [Had95]:


(S) = V DeGe(S) CVlnC n (1-9)


where Css) is the concentration of impurities occupying substitutional sites,

C, and Cv* are the actual and equilibrium concentrations of vacancies,

respectively, p is the hole density, and n, is the intrinsic carrier concentration.

D, is described by:



D~ Ge= fiD (1-10)

where f, is the fraction of diffusion that occurs via interstitials, and Di/ is the

diffusivity of the interstitial impurity in charge state j.




00000 00000



Figure 1-12. The Frank-Turnbull (dissociative) mechanism. The black atom
represents the impurity atom.






The second mechanism, known as the kick-out mechanism, describes
the movement of an impurity interstitial into a substitutional site, causing a
lattice atom to be bumped into an interstitial position (Figure 1-13).



00000 00 0 0 0
0 o0 0 0 0 0 0
0O0 O OO 00 0
Figure 1-13. The kick-out mechanism.


Unlike the Frank-Turnbull mechanism, the kick-out mechanism is
dependent on the interstitial concentration only, and the diffusion equation
for the impurity (Ge) can be described by [Had95]:

aCGe(s) _. C ln [C p (1-11)
t GeGe(S)CI I ni

where C and C,* are the non-equilibrium and equilibrium concentrations of
interstitials, respectively. The continuity equations for the interstitials and
vacancies in either the Frank-Turnbull or kick-out mechanism are:


I VDICV Ci ) + V(_Jmech) kr(CiCv *) + s(1-12)
^I= V Dyc C' +V(-J )-kr(CC -CICv)+


Cv= V DvCi V +V(-Jhi)-k,(CiCv -CIC)-p'v (1-13)


where D, and Dv are the interstitial and vacancy diffusivities, respectively, J,
is the flux of the impurity diffusing by the mechanism in consideration, k is







the interstitial-vacancy first-order recombination rate, and
independent sources or sinks for interstitials and vacancies, respectively. By

solving the continuity equations for all species involved for a specific

diffusion mechanism (e.g., Equations 1-11 through 1-13 for a kickout

mechanism), an expression for D can be reached.

At thermal equilibrium, the concentration of point defects is the single

most important influence on diffusion within the atomic lattice. The neutral

point defects can accept or donate an electron to become a charged defect,

which in turn can accept or donate another electron to become doubly

charged and so forth. The thermal equilibrium concentrations of charged

point defects depends on the Fermi level of the crystal as well as the electronic

level position in the bandgap corresponding to the defect. Hence, the total

concentration of point defects at thermal equilibrium are known functions of

the Fermi level and temperature. These quantities are denoted C,* and Cv*, as

mentioned above and are given by [Had95]:



Cx = niX j=O, 1, :2, ... n (1-14)


where X represents either I or V and is a constant which represents the

contribution from the bandgap position, and j is the charge state of the defect.







1.4 Non-equilibrium Point Defect Injection


The generation and annihilation of non-equilibrium point defects is a

topic which is crucial for the understanding of semiconductor diffusion

phenomena. It has been generally accepted that thermal oxidation of silicon

injects interstitials, while thermal nitridation injects vacancies [Fah89a,

Hu92]. The proportional dependence of a material's self-diffusion

mechanism or dopant's diffusion mechanism on these defects can be

determined by monitoring any enhancement or retardation of the diffusion

with the addition of these defects. The total diffusivity of the self or dopant

atom being studied can be described as the sum of the vacancy and interstitial

diffusivities:


D = D + D (1-15)

where, in the case of Ge diffusion in Si, D is equivalent to Dc in Equation 1-

11, and D, and Dv are equivalent to the variables by the same name in

Equations 1-12 and 1-13. The fractional interstitial component of diffusivity,

f,, is defined as:


D; D*
fI = = D(1-16)
D; + Dv D*

where D* denotes the value of the diffusivity when the actual interstitial and

vacancy concentrations are their equilibrium values, which occurs when

diffusing in a high temperature, inert ambient. The fractional vacancy

component, fy, is simply (1-f,). Under nonequilibrium conditions, as during







oxidation or nitridation, there will be an enhancement of the effective

diffusivity given by:


D C
enh =f + (1 f,) (1-17)
D' C* C*,

where C, and Cv are the actual concentrations and C,* and Cv* are the

equilibrium concentrations of vacancies and interstitials. Note that if enh
diffusion is retarded rather than enhanced. If D* is known, f, may be

estimated from measuring enh during oxidation or nitridation and

comparing with dopants for which f, is known (e.g., phosphorous, f,=1). This

is explained in detail in Section 3.3.

1.4.1 Interstitial Injection (Oxide Growth)

As stated in Section 1.4, oxidation of the silicon surface results in the

injection of interstitial point defects into the Si bulk. During oxidation,

oxygen gas reacts with the Si surface and the rate is controlled by the overall

chemical reaction:


Si(s) + 02(g) -- SiO,, (1-18)

The silicon dioxide layer continues to grow by the transport of oxygen species

through the oxide layer to the Si-SiO, interface where it reacts with the Si

[Dea65]. The formation of the oxide causes the Si to be consumed so that for

every angstrom of oxide grown, approximately a half angstrom of the Si

surface is consumed [May90].







The supersaturation of interstitials produced by oxidation in the range

of temperatures used in this dissertation is well documented [Pac91] and will

be used to model the dependence of interdiffusion on interstitials. For

example, Packan and Plummer [Pac90] estimated C,/C,*-13 resulting from dry

oxidation for 1 hour at 900 C. They also found that interstitial

supersaturation was dependent on oxide growth velocity.

While there are a substantial number of theories, there has yet to be a

proven mechanism for injection of interstitials through the formation of

SiO2 thin films. Several theories are briefly reviewed here: (1) Dunham and

Plummer [Dun86] proposed that interstitials created by the oxidation process

accumulate in the SiO2 layer near the interface. The difference between the

rate of interstitial creation and the flux of the interstitials into the oxide

causes the interstitials to diffuse into the bulk. (2) Tan and G6sele [Tan81]

proposed that the free volume difference between the Si and SiO2 at the

interface causes viscoelastic flow of the SiO2 resulting in a supersaturation of

interstitials. (3) Hu [Hu74] proposed that a fraction of silicon available is not

oxidized and Si atoms are displaced from their lattice sites by the advancing

SiO2/Si interface, becoming interstitials. Unfortunately, none of these

theories has been supported by experimental evidence and an accurate model

must still be established. It is sufficient for the purposes of these

investigations, however, to know that interstitials are indeed injected.







1.4.2 Vacancy Injection (Nitride Growth)

As described in Section 1.4, it has been well-established that the

nitridation of the Si surface results in the injection of vacancies into the bulk.

The overall nitridation reaction that occurs is:


3Si+4NH3 ----Si3N4 +6H2 (1-19)

In a variety of growth conditions, there is an initial fast-growth regime,

followed by a very slow growth regime in which the total thermal nitride

layer grows no thicker than approximately 4 nm [Hay82, Mos85a] regardless of

processing time. It is also important to note here that direct thermal

nitridation of a bare silicon surface results in nitride films with a substantial

amount of oxygen (the ratio of the concentration of nitrogen to the total

concentration of nitrogen and oxygen is approximately 50 %:

[N]/[N]+[O]=0.50) [Mog96, Mur79, Hay82]. Technically these films are

oxynitrides, yet in this dissertation they will be termed simply 'nitrides'.

Quantitatively, the supersaturation of vacancies produced by

nitridation of silicon in the range of temperatures used in this dissertation is

not as well documented as in the oxidation/interstitial injection case. Mogi

[Mog96] performed one of the most extensive investigations to date, and

found Cv/Cv*~4 resulting from thermal nitridation in NH3 for 1 hour at 910

C. His results will be used to model the dependence of interdiffusion on

vacancies.







Like the oxidation process, the process of vacancy injection is not well

understood. The injection of vacancies is thought to be the result of stress at

the nitride/silicon interface, causing interstitials at the interface to move into

the nitride layer and vacancies to move into the Si bulk [Hay82, Osa95]. No

mechanism has been substantiated and better studies are needed.

1.5 Literature Review


1.5.1 Self-Diffusion and Intrinsic Interdiffusion

1.5.1.1 Self-diffusion

Vacancies and self-interstitials in Si coexist under thermal equilibrium

at all temperatures above the athermal regime. Based on the results of early

studies, Si self-diffusion was thought to be due entirely to a vacancy

mechanism. Through Ge tracer studies, Seeger and Chik [See68] found a

break in the Arrhenius curve and subsequently proposed self-diffusion

dominated by vacancies at temperatures below -1000 C, and interstitials at

temperatures above. In 1974 Hu [Hu74] was the first to suggest a dual

mechanism which included both vacancies and interstitials at all

temperatures in the range 700 to 1200 C. This was the mechanism that most

researchers agreed upon until experiments involving oxidation enhanced

diffusion established that Si predominantly diffuses by an interstitial

mechanism at temperatures above 800 C. The reported activation energies

for Si self-diffusion range from 4 to 5 eV.







Si and Ge are very similar in their elemental properties, thus it is

surprising that they differ so significantly in their self-diffusion mechanisms

and the defects present in thermal equilibrium. Unlike Si, there is very little

debate over the mechanism of Ge self-diffusion. Effects of hydrostatic

pressure [Wer85], dopant studies [Sto85] and calculations of interstitial

migration energies [Kho90] all conclude that diffusion occurs exclusively via

monovacancies. The work of Mitha et al. [Mit96] is the only investigation to

disagree, claiming that the smaller-than-expected activation volume opens

the door for possible interstitialcy and direct exchange contributions. They

imply, however, that these contributions would be relatively small. The

activation energy for Ge self-diffusion is -3 eV, with a pre-exponential value

on the order of -10' m2/s [Wer85, Sto85]. The large difference of 1 to 2 eV

between the activation energies for Si self-diffusion and Ge self-diffusion as

well as the interstitial dominated as compared to the vacancy dominated

mechanism above 800 C suggest that there must be a strong concentration

dependence of Si-Ge interdiffusion in Silx-Ge, structures.

1.5.1.2 Tracer studies of Ge in Si

Thermally activated interdiffusion studies of Si-Ge systems have

shown that interdiffusion occurs most likely through Ge atoms which diffuse

into the Si lattice; therefore, it is imperative to discuss the diffusion of Ge in

Si. While the values of the tracer diffusivity and activation energy of

diffusion (5.39 eV over a temperature range of 850 to 1400 OC) of Ge in Si agree

well from study to study [Bou86, Dor84], the dispute that arises is the same as







for Si self-diffusion. Is there a break in the Arrhenius line where the

mechanism changes from interstitial to vacancy at lower temperature?

Seeger and Chik [See68] were the first to propose that the diffusion takes place

via a dual interstitial and vacancy mechanism. They claimed that diffusion is

dominated by interstitials at high temperatures and vacancies at low

temperatures with cross-over at -1050 C. Dorner et al. [Dor84] observed a

break in the curve at about 1050 C but Bouchetout et al. [Bou86], Hettich et al.

[Het79], and McVay and Ducharme [McV74] observed none. Fahey et al.

[Fah89b] were the only researchers to actually report the fraction of diffusion

proceeding via an interstitial or vacancy mechanism. Their study, however,

was only for the single temperature 1050 C, the temperature of the disputed

break. At this temperature they proposed a mechanism with 30 to 40%

interstitial assisted diffusion and 70 to 80% vacancy assisted diffusion. There

are several issues associated with this conclusion: (1) they assume a kickout

mechanism as opposed to a dissociative mechanism for interstitial

movement (2) they do not address the question of the Arrhenius break and

(3) the samples underwent oxidation anneal before having the oxynitride

layer deposited and then annealed. It is obvious that more studies are needed

to verify the relative contributions as well as exact mechanism of vacancy and

interstitial movement of Ge atoms in Si.

1.5.1.3 Diffusion studies of Sil.-GeSi heterostructures

There have been many studies of the interdiffusion in Si/Sil-xGex/Si

single quantum well (SQW) structures, (Si.Gen)p superlattices and Si/Sil.Ge,







superlattices. The interdiffusion is found to be dependent upon such primary

variables as Ge content, x, the amount and type of strain, e, and anneal

temperature, T, as well as secondary variables such as thickness of the layers,

d, and time of anneal, t. The wide range of parameters makes it difficult to

compile a comparison between the data. For example, small differences in

strain create large differences in diffusion coefficients. Compositionally, it has

been found that the interdiffusivity increases by an order of magnitude with

each approximately 0.10 step increase in x. From x=1 to x=0, the diffusivity

can change by as much as six orders of magnitude [Hol92, Van90].

Diffusion in strained Sil.xGex/Si single quantum wells has been found

to have an activation energy of -3 eV [Hol92, Van90, Sun94]. While the

extent of diffusion can be estimated using the tracer Ge diffusion coefficient in

bulk Si, all studies see an increasing deviation with decreasing anneal

temperature. Some studies contend that strain relaxation leads to a change in

diffusivity with temperature, while others believe that change in local Ge

concentration, not strain relaxation, is the reason for the difference in

diffusivity. None of the studies proposes a possible diffusion mechanism.

Interdiffusion of Sil.xGex/Si superlattice layers is different than in SQW

structures due to the ability to engineer the strain state of the material by the

layer structure. Si.-xGex/Si superlattices can be grown with two different types

of coherent strain, asymmetric or symmetric. In an asymmetrically-strained

superlattice (ASL), most commonly the Si layers are almost stress-free while

the Sil.-Ge. layers are under biaxial compressive stress and annealing causes







relaxation of the inherent strain. In a symmetrically-strained superlattice

(SSL), a Si_.GeY buffer layer is first grown on the substrate causing the Si and

Si1,xGex layers to be alternately under tensile and compressive strain (y
These alternating strains of equal magnitude lead to a structure which is

theoretically strain-free.

In the case of Sil-xGe,/Si SLs there is no agreement among the various

reported values of diffusivities and activation energies. Some investigations

have reported energies as high as 5.0 eV [Bea85] while others have reported

energies as low as 2.1 eV [Lui96]. The high activation energies support the

theory that diffusion is controlled by the migration of Ge, first through the Sil.

xGex layers and then into the Si layers since Ge diffusion in Si has an

activation energy of -5 eV. The studies reporting low activation energies do

not suggest any possible mechanism, nor do they reach a conclusion

regarding the discrepancy with the high activation energy studies. The only

explanation given is that the deviation may arise due to differences in sample

structures, annealing temperatures and times, or data analysis method.

1.5.2 Oxidation and Nitridation Enhanced Diffusion

A review of the literature reveals that there has been only one

investigation of Ge diffusion in strained Sij.xGe, under an oxidizing ambient.

Cowern et al. [Cow96] investigated Ge diffusion throughout a structure with a

coherent Si070Ge0.ao layer. For a single anneal temperature of 875 C, they

determined that diffusion is predominately vacancy-mediated, and estimated

a f, of 0.220.04. They also calculated an enhancement under oxidizing







ambient compared to inert ambient of D/D*=3.6. No diffusivity values were

reported and no activation energy was calculated. There are no known

investigations of Ge diffusion in SilxGe, under nitriding ambient.

There has been limited investigation of oxidation and nitridation

enhanced diffusion of impurities in Si/Si-.xGex/Si SQW structures. An

excellent summary of research to date can be found in Nylandsted Larsen et

al. [Nyl97]. Kuo et al. [Kuo95] measured the diffusivity of boron in Si/Si,.

xGex/Si SQWs and found that the oxidation enhanced diffusion (OED)

enhancement factor was comparable to that in Si, fn,=10. The diffusivity of B

in Sii.-Gex, however, was less than that in Si by almost half. While there is no

explanation for the difference in B diffusivity between the materials, the

similarity of enhancement indicates that the interstitial contribution of B

diffusion in Six-XGex is comparable to that in Si. Kuo et al.'s investigation was

limited to data for only one anneal temperature, 800 C. Fang [Fan96]

measured nitridation retarded diffusion (NRD) of B in Si-,.Gex SQWs at one

temperature, 850 *C. She found that the retardation factor in Si-.xGex was

comparable to that in Si, f,,-0.8, and she also found a smaller intrinsic B

diffusion in Si,-xGex than Si.












CHAPTER 2
SAMPLE PREPARATION AND CHARACTERIZATION


2.1 Growth Parameters and Structure


Four sample structures were used in this investigation to determine

the interdiffusion behavior of Si/Sil.xGex. Three structures were grown using

an ASM Epsilon 1 vapor phase epitaxial instrument. Figure 2-1(a) shows a

strained SL structure grown on a Si0o.sGeo.15 buffer layer, hereafter referred to

as sample structure SL/SiGe. This structure consists of a (100) Si substrate

followed by a 100 nm ungraded Sio.85Geo.15 buffer and 15 periods of 6 nm

SiossGeo.1 and 12 nm Si. Figure 2-1(b) shows another strained SL structure but

grown on a Si buffer layer, hereafter referred to as sample structure SL/Si.

This structure consists of a (100) Si substrate followed by a 100 nm Si buffer, 16

periods of 6 nm Sio.8Geo.15 and 12 nm Si, and capped with 50 nm of Si. Figure

2-1(c) shows the structure of a SQW, hereafter referred to as sample structure

SQW/VPE, which consists of a (100) Si substrate followed by a 100 nm Si

buffer layer, a 50 nm layer of Si0~.Ge0.15, and a 50 nm Si cap.

The final structure was grown by Molecular Beam Epitaxy (MBE).

Figure 2-2 shows a strained single quantum well (SQW) structure, hereafter

referred to as sample structure SQW/MBE, which consists of a Si (100)

substrate with a 100 nm Si buffer layer, a 50 nm Sio.G0o.15 with a 50 nm Si cap.












12nm SI
6nm SLG5,s
x15
12nm SI
6nm S____,,_


100nm SLGe,, Buffer


SI Substrate

(a)

50nm SI Cap
12nm SI

Sx16
12nm SI
6nm S____


100nm


50nm Si Cap
50nm SG,5,,


SI Buffer


100nm


SI Substrate


SI Buffer


SI Substrate


Figure 2-1. Si,.xGex sample structures used in these investigations. (a) Sample
structure SL/SiGe, a strained superlattice on a Si,.xGe, buffer (b) sample
structure SL/Si, a strained superlattice on a Si buffer (c) sample structure
SQW/VPE, a single quantum well.





36

50nm Si Cap
50nm SiGe.ls

100nm Si Buffer


SI Substrate

Figure 2-2. Sample structure SQW/MBE, a single quantum well grown by
MBE.



Secondary ion mass spectrometry (SIMS) and cross-sectional

transmission electron microscopy (XTEM) were performed on each sample

structure to verify the thickness of the layers as well as the number of periods.

Rutherford Backscattering Spectrometry (RBS) verified the Ge content using

He2" ions with a beam current of 10nA and a collector charge of 4 mC. Each

sample was rotated 100 and tilted 10 to prevent channeling. The Si-.xGe,

layers in all structures were shown to have the same Ge content (=0.15)

within experimental error (5%) [Sch90].

From Figure 1-3, the critical thicknesses of a capped Si.xGe, layer with a

Ge composition of 0.15 is hc~30nm. The 50 nm thicknesses of the Sil.,Gex

layers of both sample structure SQW/VPE and SQW/MBE exceeded this

critical thickness, therefore misfit dislocations were expected to be present in

the materials. The structures were consequently examined by plan view TEM

to determine qualitatively their dislocation densities (Section 22.3.2).

To determine the critical thickness for a multilayer structure, the

conventional method is to reduce the multilayer to an equivalent single







strained layer. Kasper [Kas95] cites a model in which the average Ge content,

x,v, is determined by:


-v xdSie (2-1)
d SiGe + ds,

where x is the Ge composition in the Sil,-Gex layer, dsic, is the thickness of the

Sil.-Gex layers and dsi is the thickness of the Si layers. Using this equation, the

Ge concentration averaged over all multilayers of SL structures SL/SiGe and

SL/Si was x=0.05. The critical thickness of a capped layer of Si,.xGex grown on

a Si buffer is h-c100nm (Figure 1-4). The total multilayer thickness of

structure SL/Si, 288 nm, greatly exceeded this value, therefore misfit

dislocations were expected to be present. For structure SL/SiGe an average Ge

composition of x=0.05 created a 'bulk' lattice constant of 0.5441 nm, leading to

a lattice mismatch with the Sio.sGeo0s buffer of 0.18%. The critical layer

thickness, he, of an uncapped Si-.xGe, layer with a lattice mismatch, f., of

0.0018, was approximately 80 nm [Jai93]. The total thickness of the 'pseudo-

epilayer' of structure SL/SiGe was 270 nm which was more than three times

the critical layer thickness; therefore, like the SL/Si structure, dislocations

were expected to exist in structure SL/SiGe.

2.2 Transmission Electron Microscopy


2.2.1 Overview

In transmission electron microscopy (TEM) electrons from an electron

gun are accelerated to high voltages (100 to 400 kV) and focused onto a sample







of interest using a condenser lens. The sample is sufficiently thin that the

majority of impinging electrons are transmitted or forward scattered through

the sample, rather than backscattered or absorbed. These transmitted and

forward scattered electrons pass through an objective lens to form a back focal

plane and an image plane (Figure 2-3). A diffraction pattern is formed on the

back focal plane and a magnified image is formed on the image plane. Both

the diffraction pattern and the magnified image can be projected onto a screen

for either viewing or photographic recording [Wil96, Run98, Sch90].

There are two basic views of the sample that can be achieved through

TEM, depending on the original sample preparation. Plan-view TEM (PTEM)

provides an image of the sample from a direction parallel to layer growth

object plane








lens



back focal plane



image plane

Figure 2-3. Schematic of ray paths originating from the object which create a
TEM image [Wil96].















Layered Semiconductor Sample
I '


Plan-view


Cross Section


Figure 2-4. Schematic of TEM views. Both cross-sectional and plan view of
the semiconductor sample can be obtained.







direction (Figure 2-4), essentially providing a view looking down at the top of

the sample. Cross-sectional TEM (XTEM) provides an image of the sample

(Figure 2-4) perpendicular to layer growth direction, as if one were looking at

a slice of the sample from a side direction.

PTEM was used specifically in this work to determine qualitatively the

density of misfit and threading dislocations and their lengths. PTEM was also

used to observe their evolution with increasing time and temperature, as

well as how they differed in inert, oxidizing and nitriding environments.

XTEM is used in this work to determine the quality of the layer interfaces

(sharpness, flatness), as well as the thickness of the layers. The grayscale

contrast of the Si and Si.xGe, layers allowed the observation of smearing of

the interface due to diffusion after annealing. XTEM was also used to observe

any threading dislocation evolution from the substrate/buffer interface to the

surface.

2.2.2 TEM Sample Preparation

Procedures for sample preparation for PTEM and XTEM applications

are quite different. Also, individual techniques used in both cases vary from

researcher to researcher. The following sections describe the preparation

methods used to create TEM images shown in this work.

2.2.2.1 Plan view

To provide a top surface view, preparation was begun by coring a

circular piece out of the sample and mechanically thinning the backside of

this core using a 15 pm powder. The top surface of the thinned piece was








then coated with wax to prevent etching, while the backside was etched using

a solution of 25% HF: 75% HNO3. The sample was etched until a small hole

with a slightly frayed edge developed at the center. This provided a region of

the sample that was sufficiently thin for the electrons to be transmitted in the

microscope and an image of the sample to be obtained.

2.2.2.2 Cross-sectional


Back View


Copper Ring






Silicon Supports


SIGo Sips


Copper Ring
14 /


Front View


* Silicon Support


I
SI Stips

Figure 2-5. Front and rear views of the XTEM assembly after preparation
[Wil96].







XTEM preparation was begun by slicing the sample into thin sections

approximately 25 milli-inches wide. Two of these sections were glued

together, surface to surface, with M600 Bond epoxy. This structure was

sandwiched between two thin sections of Si, which acted as structural support

(Figure 2-5).

The entire stack was mechanically thinned to ~ 15 gm and polished. A

3mm copper ring was attached via G Bond epoxy to one side of the sample.

This composite structure was thinned in a two stage Gatan 600 dual ion mill

using Ar* ions at a gun voltage of 5kV and a current of 0.5 mA. Ion milling is

a process in which low energy Ar' ions bombard both exposed sides of the

sample at low angles, slowly knocking off surface atoms, eventually thinning

the sample to a bowl-shaped cavity just breaking a hole into the back surface.

This minimum thickness allows electrons to be transmitted through the

sample and an image of the cross section to be formed in the microscope.

2.2.3 Images of Structures

As-grown and annealed samples were analyzed by cross-sectional and

plan-view TEM using a JEOL 4000FX for high resolution images and a JEOL

200CX for low resolution images.

2.23.1 XTEM

XTEM photos were taken of the as-grown structures to verify the layer

thicknesses, number of periods, as well as quality of the interfaces. The Si and

Sil.xGex layers were imaged by absorption contrast due to differences in atomic

number. Figure 2-6a shows the as-grown structure of SL/SiGe at a







magnification of xl00,000 (100k). There are clearly 15 periods with abrupt,

sharp interfaces at the top periods. The periods towards the Six-Ge, buffer are

increasingly smeared. This could be due to the focus of the TEM or could be

due to true lack of abruptness of the interfaces. Also, the thicknesses of the

dark colored Si layers decrease towards the buffer, while the thicknesses of the

light colored Sil.xGe, layers increase. The periodicity of the SL layers is lost.

There are no visible dislocations (see below). Figure 2-6b shows the as-grown

structure of SL/Si at a magnification of x50k. There are 16 periods with abrupt

interfaces and constant thicknesses. However, Figure 2-6b shows a threading

dislocation running from the beginning of the MQW to the surface, across the

layers. This is one visible dislocation which is indicative of other threading

dislocations throughout the entire structure. It is nearly impossible to get an

estimate of the dislocation density from XTEM images. XTEM investigates a

very small area'of the sample and is therefore statistically unmeaningful for

dislocation densities below 107 cm-2. Also, in cross-section only half the

dislocation is visible due to the direction of the view, so it is impossible to

know exactly how many dislocations are present within the thickness of the

sample [Iye89]. Therefore, even in cross-section images such as Figures 2-6

and 2-7, where there are no visible dislocations, there can indeed be

dislocations present in the structure.

Figure 2-7a shows the cross sectional TEM micrograph of SQW/MBE at

a magnification of xl00k. The surface is somewhat rough as is the interface







between the substrate and buffer layer. The layers are not particularly straight

but are fairly abrupt.

Figure 2-7b shows the micrograph of SQW/VPE at a magnification of

xl00k. The interfaces are extremely abrupt and uniform, with no apparent

roughness. The thicknesses of the Six-xGe, well layer and Si cap layer are equal

to the intended growth thickness, within resolution of TEM (-0.2 nm) [Sch90].

No dislocations are visible in this image (see above paragraph).

2.2.3.2 PTEM

The micrograph of SL/SiGe in plan-view is shown in Figure 2-8a. The

as-grown SL/SiGe exhibits strain relief through an array of misfit dislocations

spaced an average of approximately 0.5 pm apart. The micrograph of SL/Si in

plan-view is shown in Figure 2-8b. The as-grown SL/Si exhibits strain relief

through an array of misfit dislocations spaced an average of approximately

0.35 pm apart. In the micrograph shown, there are sample preparation

artifacts which represent back-etched dislocations that are wider and less

resolved than the unetched dislocations visible as well.

The micrograph of SQW/MBE in plan-view is shown in Figure 2-9a.

The as-grown SQW/MBE exhibits strain relief through an array of misfit

dislocations spaced an average of approximately 1 pm apart. The micrograph

of SQW/VPE in plan-view is shown in Figure 2-8b. The as-grown SQW/VPE

exhibits strain relief through an array of misfit dislocations spaced from 0.25

tol.50 pm apart. Sample preparation artifacts such as etch pits and back-

etched dislocations are present in both micrographs.







23 Secondary Ion Mass Spectroscopy


Secondary ion mass spectroscopy (SIMS) is a powerful technique for

characterization of concentration profiles in semiconductors. In this

technique, a primary ion beam is incident upon the sample and sputters

atoms from the surface. Incident ions lose energy through momentum

transfer during collisions with atoms in the crystal. The incident ions

eventually lose enough energy to come to rest several hundreds of angstroms

from the surface of the crystal. These collisions also cause the atoms in the

solid to be displaced, some of which escape from the crystal. Most of the

ejected atoms are neutral and cannot be detected by normal SIMS, however, a

small amount of atoms are ionized above the surface (secondary ions). A plot

of the secondary ion yield versus the sputtering time allows quantitative

depth profiling. The crater depth after completed analysis is measured and

divided by the total sputter time. This gives a sputter rate which can be used

to estimate the depth axis. Details of SIMS theory, instrumentation and

analysis can be found in several references [Ben87]. The conversion of the

secondary ion yield into an impurity concentration is more difficult than

depth conversion from sputter rates and is discussed further in section 2.3.1.

Unless otherwise noted all SIMS analysis in this study was done at the

University of Florida's Microfabritech Facility using a Perkin Elmer PHI 6600

quadrapole analyzer. Most profiles obtained in this study used O primary




























100,oOox -
10mM


1


50,o000x
20onm


Figure 2-6. Cross sectional view TEM (XTEM) micrographs of as-grown (a)
structure SL/SiGe and (b) structure SL/Si.











r


o100,o0x m












0oo0,oox 1
10Onm


Figure 2-7. XTEM micrographs of as-grown (a) structure SQW/MBE and (b)
structure SQW/VPE.


































20,000x n
500nm


20,000x
500nm



Figure 2-8. Plan view TEM micrograph of as-grown (a) structure SL/SiGe and
(b) structure SL/Si.














"We


20,000x
500nm


20,5000x0
500nm


Figure 2-9. Plan view TEM micrograph of as-grown (a) structure SQW/MBE
and (b) structure SQW/VPE.







ions supplied by a dual plasmatron gun. A few profiles used Cs' ions

generated by a separate cesium gun to detect oxygen and nitrogen content.

The crater depths were measured with a Tencor Alpha-Step 500 surface

profiler to determine the sputter rate.

2.3.1 Determination of the Ge Depth Profile in SiGe Structures

Determination of the Ge concentration from a count of secondary ions

is complex [Pru97a, New97, Kru97]. The overall concentration of Ge in the

alloy of the as-grown structures was too high for SIMS calibration with an

implanted standard, which is the usual method. The maximum

concentration allowable for this method is approximately one percent. A Si1.

xGex standard cannot be used at high concentrations because of the

contradiction of the matrix signals from the Ge in the Sil.xGex alloy and the

signals from the Ge atoms that have diffused in small quantities into the Si

layers. This is commonly known as a matrix effect, in which the secondary

ion yield of a particular element varies in different crystal lattices. A

linearization technique has been proposed which relates the secondary ion

signal of the Ge to the secondary ion signal of the Si [Pru97a, New97]. The

linearization is based on the counts from a sample of known Ge

concentration using Rutherford Backscattering Spectrometry (RBS). The

method applied to the samples used in this work involves the assumption

that the amount of Ge present each sample (as grown and annealed) remains

constant and then standardizing the Ge dose of the annealed samples to the

dose of the structure as grown. Specifically, the Ge concentrations of the







annealed profiles were standardized by (1) assuming a Ge concentration of

15% for the as-grown samples determined from RBS (2) assuming that Ge

concentration remains constant within the sample regardless of processing

history (3) integrating the area under the as-grown profile curve (4)

calculating the ratio of this area to the integrated area under the annealed

profile curve and (5) multiplying the concentration of the annealed profile by

this ratio. In all cases this proved to be a highly successful concentration

standardization technique.

SIMS concentration versus depth analysis of the as-grown structures

are shown in Figures 2-10 through 2-13. For the SQW materials it can be seen

that the layer thicknesses are close to the requested thicknesses. For structure

SQW/VPE (Figure 2-12), the Si cap/ Si.xGe, well interface was very abrupt,

while the Si1x-Ge, well/Si buffer interface was much less abrupt, almost

graded. For structure SQW/MBE (Figure 2-13) neither the cap/well nor the

well/buffer interface were abrupt. Both interfaces were graded over

approximately 0.03 gm. For the SLs, the SIMS profiles verify the layer

thicknesses as well as the total number of periods. For both SLs (Figures 2-10

and 2-11), the interfaces were very abrupt. All structures were also analyzed

for C and 0 content, since these impurities can act as traps and greatly alter

the diffusion properties of the material. Structures SL/SiGe, SL/Si and

SQW/VPE showed very low concentrations of C and O throughout the

materials. Structure SQW/MBE, however, showed a high C pileup at the

substrate/buffer interface (Figure 2-14).























1019 N *


10 e a a I I a a I A I I I A I t I I .
10'
0 0.1 0.2 0.3 0.4 0.5 0.6
Depth (gm)

Figure 2-10. Ge concentration profile determined from SIMS for sample
structure SL/SiGe.


101


102

C)

102
0

o--
I 10 o
0
10,
1019


1018


Depth (pum)


Figure 2-11. Ge concentration profile determined from SIMS for sample
structure SL/Si.








10"




10




O 10,
E



0
C
O
10
0

10



1018


0.05


Figure 2-12. Ge concentration
structure SQW/VPE.









102

E




0
0`


Ci


0.1 0.15 0.2 0.25
Depth (gm)

profile determined from SIMS for sample


1081 i a I a a a I 1 I I A a I 2
0 0.05 0.1 0.15 0.2
Depth (rm)


0.25


Figure 2-13. Ge concentration profile determined
structure SQW/MBE.


from SIMS for sample










60





w I
',










S,J1 "-Ge70
% I' i 1



0 1, I. .,.,,.,
0 5 10 15
Sputter Time (min)

Figure 2-14. SIMS profile of structure SQW/MBE. The concentrations of
oxygen and carbon impurities with depth are shown. Both O and C are piled
up at the buffer/substrate interface at sputter time -12 min.



2.3.2 Determination of the Error in D

Throughout this study, SIMS was the primary method used (in

conjunction with FLOOPS) to determine interdiffusivity values. It was

therefore important to quantify the error involved in SIMS analysis to

determine the error incorporated in the extracted D values. There were two

sources of error in SIMS profiles: statistical fluctuations from (1) the

determined concentrations and (2) the depth scale. The error bars on the

extracted diffusivity values were determined from analysis of these errors







using a Monte Carlo simulation approach. The error in the fluctuation of the

concentration was determined by examining the fluctuation of the signal in

the pure silicon regions of the sample. The error in depth scale was estimated

to be 5% [Gos93] and the method of error analysis was taken from H.-J.

Gossman et al. [Gos93] and is based upon the equations:


i = ci + G-ci (2-2a)

i = z(1+ GX) (2.2b)

where c, is the experimentally determined concentration, z is the

experimentally determined depth into the sample, G is a Gaussian distributed

random variable with mean E(G)=0 and variance E(G2)=1 and y is the

concentration corresponding to a count of 1 in the experimental instrument.

The numerically generated concentration and depth into the sample are

represented by ci and zi, respectively. X represents one standard deviation in

the relative depth scale error and, as stated above, was estimated as 5% for the

purposes of this analysis. A new Ci(i,t) set was generated using Equations 2-

2, creating a profile that was fitted using FLOOPS to determine a new D,. This

was done 11 times and the mean of these values as well as the experimentally

determined value was taken as the diffusivity, D, and the standard deviation,


o, as the error.







2.4 X-ray Diffraction


2.4.1 Overview

X-ray diffraction (XRD) is one of the most powerful and widely used

tools in semiconductor characterization [Bau96]. The applications vary from

crystal identification to measuring the quality of crystal growth. XRD is based

on Bragg's Law:

2dsine, = nX (2-3)

An x-ray beam of wavelength X is incident upon a crystal at an angle 68, the

Bragg angle. A diffracted beam composed of a large number of scattered rays

mutually reinforcing one another is reflected from the atom planes. By using

x-rays of known wavelength and measuring the Bragg angle one can

determine the spacing, d, of the planes of the crystal.





1 plane normal
1'
2
2'

3OR ,3'


Figure 2-15. Schematic of symmetric x-ray Bragg reflection [Cul78].







All scans were taken using a Phillips high resolution XRG 3100 five

crystal diffractometer. This instrument consists of four main parts: an x-ray

source, a monochromator, a goniometer and a detector. This system setup

has been previously described in detail by Krishnamoorthy [Kri95] and will be

summarized here.

A generator operating at 40kV and 40mA creates electrons at a cathode.

These electrons are accelerated through a field and bombard a Cu target anode

emitting CuK,, x-ray radiation with broad angular and wavelength ranges.

The x-ray beam is monochromatized and collimated prior to impingement

upon the sample using a four crystal Bartels monochromator/collimator

setup shown in Figure 2-16. The x-ray beam, upon leaving the

monochromator/collimator, impinges on the sample crystal which is

mounted on the stage of the goniometer. The goniometer controls the x, y, z,

tilt (\y) and rotation (<) positions of the sample.




Monochromator/collimator
--------------- ------
2 Detector


Source (I -- 1 4
Sample


Figure 2-16. Schematic of the monochromator/collimator. X-rays impinge
the first crystal and are subsequently collimated and monochromated by
crystals 2 through 4, after which they impinge on the sample.




58

The angle between the incident beam and the projected diffracted beam

which reaches the detector is defined as 20, and is controlled by the

goniometer. The angle between the incident beam and the sample surface is

defined as o, which is also controlled by the goniometer. Rocking curve scans

occur through the independent movement of both the 20 and o angles. The

two scans utilized in this work are the o scan and the 0/20 scan. In the o

scan, the detector (20) is stationary while the sample is rocked over a specified

c0 range. The 20 value is fixed to satisfy Bragg's law so that at a certain value

of o an x-ray peak is observed. In the 0/20 scan both a 20 range and an Co

range are designated. The detector is rotated through the 20 range twice as

fast (but in the same direction) as the sample is rotated through the o range;

the angle between the incident beam and the sample surface changes. This

scan is most useful when the sample crystal is composed of more than one

material (i.e. Si and Si,.xGex) and the Bragg conditions of only one material are

known (Si).

When the x-ray beam reflected from the sample crystal is directed

immediately into a detector, as shown in Figure 2-16, it is considered to be a

double axis spectrometer. This double axis mode was employed in both 0) and

0 /20 scans in this study. In a triple axis spectrometer (Figure 2-17), the x-ray

beam reflected from the sample is directed towards a two-crystal analyzer

before entering a detector. This offers improved angular resolution and







intensity, which allows observation of weak diffraction satellite peaks from

thin superlattice layers. Triple axis mode was employed in 20 scans in this

study to identify the Bragg angle in weak reflections from the Si/Si_-xGex

superlattice layers.



Detector
Monochromator/collimator />
r-- -- ----1
2 3 2

Crystal Analyzer
Source
Sample
--------------------J

Figure 2-17. Schematic of the x-ray path used in triple axis mode. The x-rays
are directed to a double crystal analyzer after impinging on the sample and
before heading to the detector.



X-ray rocking curves were taken of the superlattice structures SL/SiGe

and SL/Si as grown using the methods just described (Figure 2-18 and 2-19).

Distinct satellite peaks, of both positive and negative order, can be seen for

each structure, surrounding the high intensity Si substrate peak at o034.5.

The first satellite peak to the left of the substrate peak is considered the Oth

order peak and denotes the average composition of the Si,1-Gex/Si layers. The

1st order peak to the left of the Oth order peak is the first peak that represents

the periodicity of the Si/ Silx-Gex SL layers. This is the peak used in this work

to extract diffusivities from HRXRD scans (Section 2.4.3). In each scan,













104


4,-
1000
0
O


C 100

10

Cr
n 10
oc


32 33 34 35 36 37

Omega (0)

Figure 2-18. X-ray rocking curve of structure SL/SiGe before anneal.


10



3 1000
o


CD
8,

100
c


% 10
)a
oC


33 34 35 36 37
Omega (0)


Figure 2-19. X-ray rocking curve of structure SL/Si before anneal.


L







satellite peaks up to the +3rd order can be seen, while only the -1st order peak

can be observed to the left of the Si substrate peak.

The x-ray rocking curve of structure SL/SiGe shows broad satellite

peaks, indicating that the periodicity of the SL layers is imprecise. XTEM

images of the layers indeed show that the layer widths slightly decrease nearer

to the Sii.-Gex buffer layer. The x-ray rocking curve of structure SL/Si shows

very sharp satellite peaks confirming that the periodicity of the SL layers is

consistent throughout the structure.

2.4.2 Optimization Procedures

Typically, substrates used for growth are intentionally miscut; a silicon

(100) substrate can be miscut 1 to 50 off the (100) plane towards the nearest

(110) plane (Figure 2-20). This causes the characteristic substrate x-ray peak

position to differ from its real value (0o=). A epitaxial layer can also be

misoriented with respect to both the intended substrate growth direction as

well as the miscut substrate surface normal direction (Figure 2-20).

To obtain the true o values for both the substrate and epilayer,

optimization procedures involving o, the sample crystal rotation angle, ),

and crystal tilt, (p, were performed [Kri95]. These procedures are extremely

important when trying to identify and measure satellite peaks for thin

superlattice layers, as the satellite peaks tend to decay very rapidly with

increasing Ac (Figure 4-4 and 5-4). Even more intensity decay of the satellite

peaks is observed after annealing the sample crystal at high temperature.







Optimizing intensity of the silicon substrate Bragg signal allows the smaller

decayed satellite peaks to be more easily observed and measured.


Figure 2-20. Miscut of substrate and mistilt of epilayer. The lower unshaded
region shows the possible miscut of the substrate, y. The top shaded region
shows the additional possible mistilt of epilayer grown on substrate, Q.



X-ray diffraction peak positions discussed hereafter are assumed to

represent optimized values unless otherwise stated.

2.4.3 Determination of Interdiffusivity of Superlattice Layers

The periodicity of a superlattice structure causes a similar effect in XRD

as the periodicity of the planes of lattice atoms. The diffraction of the

superlattice is modulated and results in well-defined satellite peaks. The

superlattice period can be obtained from [Pel91]:


2sinO. -2sine n (24)
X A







where n is the order of the satellite peak of interest, 0, is Bragg angle of the

nth order satellite peak, 0SL is the Bragg angle of the satellite peak of interest, X

is the wavelength of x-ray used, and A is superlattice period.

Through HRXRD the value of D will be calculated from the measured

decay of the intensity of the first satellite peak about the substrate as a

function of annealing time and resulting interdiffusion. The substrate peak

from the (004) reflection remains the same regardless of processing history.

The Oth order satellite peak represents the spacing of the lattice of the average

composition of the total of the deposited layers. The 1st order satellite peak

represents the periodicity of the SL layers, which changes significantly and

quickly upon annealing, therefore it is the satellite peak of interest. The decay

in the intensity, I, of the first order satellite x-ray peak after a long time

anneal, is directly related to the interdiffusion coefficient by:


SIn- = D (2-5)
dt io 12

where X is the SL period (cm) and Io is the initial satellite x-ray peak intensity

before annealing [Bar90, Pro90]. By plotting ln(I/I) versus time, one can

determine D for different temperatures. Then, by plotting In(D) versus 1/T,

for multiple temperatures, an Arrhenius expression for diffusion can be

obtained.







2.4.4 Determination of Strain Relaxation

X-ray double crystal diffractometry allows the accurate determination of

the orientation, size and shape of the deformed unit cell of the layer

compared to the cubic unit cell of the Si or SilxGex substrate or buffer. The

amount of strain between layer and substrate can be determined through

analysis of their respective co peak positions. When the Si._xGe, layer of larger

lattice parameter, a,, is deposited on the Si substrate of smaller lattice

parameter, a, the cubic cell of the Sil.-Ge, lattice must be compressed in the

parallel direction so that the lattice parameter matches that of the Si lattice,

a//. The volume of the Si.-xGex cubic cell, however, is constant to a good

approximation, so the compression in the parallel direction is accommodated

by an increase in the perpendicular lattice parameter, a,. The Si.-xGex cell is

no longer cubic, but tetragonal and the strain introduced is known as

tetragonal strain (Section 1.2).

The angular separation between the substrate and epilayer peaks for the

symmetric reflection (the angle of incidence equals the angle of reflection, i.e.,

the sample surface is oriented in the same direction as the reflection plane)

can be used to determine the perpendicular lattice mismatch between the

epilayer and substrate [Kri95]:


(a, -as = -(, -0 )cotOe (2-6)
a.^ ), =







To completely define the epilayer strain state, however, both the

perpendicular and parallel lattice mismatch must be determined. This can be

done through HRXRD rocking curves from asymmetric lattice planes making

an angle with the surface (Figure 2-21). This method is described in detail in

[Bar78, Kri95] and has been used in this investigation to determine the strain

relaxation of sample structures SL/SiGe and SL/Si after thermal treatment

(Sections 4.5.3 and 5.5.3). Briefly, the Bragg condition for an asymmetric plane

is satisfied at two different oC angles:


)1 = 0 + (2-7a)

o2 = 0- (2-7b)

The values of ol and )2 for both the epilayer and substrate are obtained

through asymmetric rocking curve scans, and Equations 2-7 are solved

simultaneously for the values of 0 and 0 for both the epilayer and substrate.

These values are used in:


a-ass- =(,1 ps)tan ,s -(61 -e,s)cotes (2-8a)
as )


S--Is = -( s)cot)s -(, -es)cot (2-8b)
as //

to determine the perpendicular and parallel lattice mismatches.








detector source


source I detector
toor( plae I g +





asymmeric plane


Figure 2-21. Example of positive and negative x-ray diffraction from an
asymmetric plane. (, 8 and 0 are identified. For a symmetric reflection, the
diffraction plane would be parallel to the sample surface, o=0.












CHAPTER 3
BEHAVIOR OF ANNEALED Si,.xGex SINGLE QUANTUM WELLS

One of the fastest growing applications for Si,.xGe, material is

heterojunction bipolar transistor (HBT) technology (Section 1.1.2). HBTs use

doped Sil.-Gex as the base and surrounding Si layers as the emitter and

collector regions. A Sil.,Gex base region allows greater doping than Si without

reducing emitter injection efficiency [Gha95]. Out-diffusion, however, from

the base of both the Ge and dopant during growth and processing forms

parasitic barriers at the heterojunctions, which severely degrades device

performance. Also, base widths are currently slightly greater than the critical

layer thickness [Gru97, Heu96, deB97], which introduces possible SilxGe, layer

relaxation through formation of dislocations. It is therefore important to Sil.

xGex HBT technology to be able to predict the interdiffusion behavior and

dislocation effects of Si/Si1.-Ge,/Si single quantum well (SQW) structures.

Interdiffusion of Si/Sio.85Geo.5/Si SQW material in inert, oxidizing, and

nitriding ambients over a temperature range 900 to 1200 C has been

investigated. Thermal processing in all three ambients over the same

temperature range allowed estimation of the enhancement factor of

interdiffusion of Si/Sio.Ge0.15/Si material under interstitial and vacancy

supersaturation as well as under inert (equilibrium defect concentration)

conditions. An estimate of the fractional contribution of interstitial and







vacancy mechanisms to interdiffusion in Si0o85Geo,0./Si SQWs was been made

by comparing SIMS profiles of annealed samples to profiles calculated by

FLOOPS diffusion simulations. Investigation of a Si/Sil.xGe,/Si structure

with a buried boron (B) marker layer in the Si buffer region has addressed the

impact of dislocated Sil-xGe, layers on interdiffusion (Section 3.4.2).

3.1 Growth Parameters and Structure

A SQW test structure (SQW/MBE) was grown by Molecular Beam

Epitaxy (MBE) at a temperature of 520 C. As shown in Figure 3-1, the

structure consisted of a lightly p-doped (100) Si substrate with an undoped 100

nm Si buffer layer, followed by an undoped 50 nm Sio.sGeo.! layer and an

undoped 50 nm Si cap.

Another SQW test structure (SQW/VPE) was grown using an ASM

Epsilon 1 vapor phase epitaxy reactor at a temperature of 700 C. The

structure consisted of a lightly p-doped (100) Si substrate with an undoped 100

nm Si buffer, followed by an undoped 50 nm Si0.85Geo.5 layer and an undoped

50 nm Si cap. Structures SQW/MBE and SQW/VPE nominally differ only by

their growth method. The Sio.e5Geoi. layer in SQW/VPE was grown using

SiCl2H2 (dichlorosilane), GeH4 (germane), and hydrogen (H2) as the carrier gas.

The silicon layers were grown at a rate of 5.0 nm/min while the Sio.sGe0.15

layer was grown at a rate of 18.8 nm/min. The Ge concentrations of the Si1.

xGex layers for both structures were verified by Rutherford Backscattering

Spectroscopy (RBS) and the layer thicknesses were verified by cross-sectional

Transmission Electron Microscopy (XTEM).








50nm Si Cap
50nm SisGe.ls

100nm Si Buffer


Si Substrate

Figure 3-1. Schematic of sample structures SQW/MBE and SQW/VPE.


The Ge depth versus concentration profiles for as-grown and annealed

samples were determined by Secondary Ion Mass Spectroscopy (SIMS) using a

Perkin Elmer PHI 6600 quadrapole analyzer with a 6 kV oxygen beam. The

profile depth scales were determined from Tencor Alpha-Step 500 surface

profiler measurements of the SIMS sputtered craters. All concentrations and

depths profiles were standardized using the method described in Section 2.3.1.

3.2 Processing


3.2.1 Rapid Thermal Processing

Samples annealed at high temperatures and short times (less than

approximately five minutes) in Ar, 02 or NH3 were processed in a rapid

thermal processor (RTP). The traditional furnace anneal is inappropriate for

short time, high temperature anneals because of increased impurity

concentrations in the ambient as well as larger temperature nonuniformities

due to the nonequilibrium state of the sample. Also, the high diffusivities of

some species require short anneal times for controlled, measurable diffusion

lengths. During high temperature heating the radiative heat transfer







component exceeds those of convection and conduction. RTP uses this

energy transfer between the radiant heat source and an object to process

sample material [Sin88]. Because of the optical nature of the radiative energy

transfer, the reactor wall is not in thermal equilibrium with the sample

[Tim97].

An AG Associates Heatpulse 2101 was used for all RTP anneals. The

Heatpulse 2101 uses an array of line source tungsten-halogen lamps to

achieve isothermal heating, with banks of twelve lamps both above and

below the heating chamber. The chamber and wafer holder are both made of

quartz, which transmits the entire spectrum emitted by the lamps (middle

infrared, 3 to 6 gm). This causes the chamber and holder to remain at a

temperature far below the sample temperature. The chamber is considered to

be a warm wall chamber, surrounded by a reflective water- and air-cooled

metal housing, and can reach temperatures of ~400 C [Roo93].

The Heatpulse 2101 controls the temperature of the wafer through the

use of an IRCON optical pyrometer and closed loop feedback software. The

pyrometer measures the emissivity from the sample and converts the

emissivity value to a temperature value. Based on this temperature feedback,

the RTP then adjusts the lamp power to maintain the desired temperature.

Optical pyrometry is noninvasive and fast, yet is sensitive to emissivity

changes during processing (from wafer warping, film growth, backside

roughness, etc.). The pyrometer must be carefully calibrated. The most robust

method of calibration involves concurrent thermocouple use. At high







temperature (1000 to 1200 *C), however, the measurement of oxide thickness

is a very reliable approach to calibrating surface temperature. At lower

temperatures (600 to 1000 C) activation of dopant implants is often used

[Roo93].

The RTP temperature for these investigations was initially calibrated

through oxide measurements [Mos85, Gon94]. Temperature uniformity

across the wafer is a main concern during RTP. The edge temperature can

often be lower than the center temperature, with an overall wafer

temperature non-uniformity of as much as 20C [Pet91]. To determine the

extent of temperature uniformity across the silicon wafer, the wafer was

processed in the RTP in flowing dry 02 ambient at processing times and

temperatures similar to those used to process the Si-.xGex/Si structures. The

resulting oxide film was characterized using an ellipsometer to measure

thickness at five points across the wafer. Film thickness was found to be the

same across the wafer, within the error of ellipsometer measurement (1 n m

[Sch90]). This indicates that the uniformity across a four inch wafer is within

the error of temperature measurement, 10 C.

To more accurately determine the RTP calibration, a thermocouple

wafer was also used to calibrate the pyrometer. A W5%Re/W26%Re (Type C)

thermocouple was embedded in a Si wafer using e-beam welding [Hoy88]. The

reading of this thermocouple was compared to the pyrometer output at

temperatures from 800 to 1200 C at 50 degree intervals. At each temperature,







the emissivity dial was adjusted so that the pyrometer reading equaled the

thermocouple reading.

The Heatpulse 2101 has a quartz wafer tray inside the chamber which

holds 4" wafers only, therefore the small 1 x 1 cm samples had to be placed on

top of a 4" silicon "dummy" wafer. This raised questions regarding the heat

transfer between the wafer and the sample, as well as the heat transfer

between the sample and the lamps. To determine experimentally the impact

this had on the temperature of the sample compared to the underlying wafer,

a stack of three rectangular samples of decreasing area was oxidized on a

dummy wafer and the oxide thickness on the exposed area of each was

measured. Within the error of the ellipsometer ( 1 nm) [Sch90], there was

no difference in the oxide thickness on any of the three samples or the wafer

and therefore the heat transfer can be considered to be thorough (10 C

[Gon94]).

Before annealing, the test wafer was cut into 1 x 1 cm pieces which were

cleaned using a regimen of deionized water, H2SO4:H202 (1:2) and H20:HF

(10:1), and then dried with N2. Samples were rapid thermal processed with all

ambient gases (Ar, 02, NH3) flowing at 1.5 slm.

3.2.2 Furnace Processing

Samples annealed for longer than five minutes in either N2 or 02were

processed in a Thermco furnace. Furnace anneal at times longer than

approximately 5 minutes allows greater temperature control. During furnace

anneal the compartment is heated to anneal temperature before the sample is







placed in the oven. When the sample is placed in the oven, it heats rapidly to

be in thermal equilibrium with the entire furnace environment. The furnace

was not equipped with NH3 gas, therefore samples were not furnace annealed

in nitriding ambient.

SilXGex test pieces underwent preparations identical to those for RTP

(Section 3.2.1). Since Ar and N2 have similar thermal conductivities the

thermal profiles of samples processed in these gases are expected to be similar.

The diffusion profiles of the samples processed in the RTP using Ar and the

samples processed in the furnace using N2 can therefore be accurately

compared.

3.3 Simulation of Diffusion


The diffused Ge profiles were analyzed using the FLorida Object

Oriented Process Simulator (FLOOPS) [Law96]. This is a computer simulation

program which predicts the diffusion profile of a semiconductor material

after preprocessing and processing steps such as ion implantation, oxide

growth, annealing, and etching. A grid is defined for a region of interest and

modified versions of Fick's law are numerically solved within this grid. The

fineness of the grid determines the resolution of the profile as well as the

computation time of the simulation. After processing, the dopant, defect or

interface diffusion profiles can be plotted as concentration versus depth.

Three different diffusion models are available in FLOOPS: the Neutral,

Fermi, and Pair models. In the Neutral model, Fick's law is solved in the

form:







= VDVC+ YEfeld (3-1)
at

with the diffusivity of the dopant, D, given as:


DD=D= D exp(-a (3-2)

where C is the concentration of dopant atoms (cm'3), t is time (min), and Ef

is the electric field (V/cm). DN denotes the diffusivity of the neutral

(uncharged) dopant atom (cm2/s), Do is a pre-exponential constant (cm2/s), E,

is the activation energy (eV) and k is the Boltzmann constant (8.62x10'

eV/K).

In the Fermi model, Fick's law is solved in the same form as equation

3-1, but the diffusivity is given as:



D = D + D P+D n +D++(L +D.( n +... (3-3)
n, n, n, n,}

where Do is the diffusivity of the dopant in its neutral state, D. and D. are the

diffusivities of the dopant in its singly positively and negatively charged

states respectively, D+, and D. are the diffusivities of the dopant in its doubly

positively and negatively charged states, respectively, p and n are the hole and

electron densities, respectively, and n, is the intrinsic carrier concentration.

The ionized dopant diffusivities are expressed in an Arrhenius form after

equation 3-2.

The Pair model uses Fick's law in the form:







aC CxA Cx n
-= YVDAXCA. -XVlog(CA' Cx ni (3-4)

where X designates either interstitial or vacancy point defects, DAX denotes the

diffusivity of the dopant occurring through either vacancies or interstitials,

CA is the concentration of dopant in its ionized state, Cx is the actual point

defect concentration of either interstitials or vacancies, and Cx, is the

equilibrium point defect concentration. The log(n/n,) term accounts for the

contribution of the electric field to any concentration change. Equations 3-4

and 3-4 would be written for acceptors by inverting the n/ni term. The total

diffusivity of the dopant is defined as:


D = fCI +fv (3-5)
D* C, C

where f, and f, are the fraction of diffusion which occurs via interstitials and

vacancies, respectively, and D* is the diffusivity under inert ambient.

The Neutral model assumes that the dopant diffuses in its neutral

charge state only, and does not include contributions to the diffusivity from

point defects. The Fermi model accounts for all possible charge states of the

diffusing dopant atom, known as Fermi-level effects, but still does not

include contributions to the diffusivity from point defects. The only

difference between the Neutral and Fermi models is that the Neutral model

uses only the first term of Equation 3-3. The Pair model includes the

contributions to the diffusivity of any point defects present. The C,* and Cv*

expressions are a function of the Fermi level, which is the electron







electrochemical potential. The Fermi level therefore changes as the electron

concentration changes. Fermi level effects due to all charge states of the

dopant are still accounted for through the D* parameter which is described by

equation 3-3.

In this study the Fermi model was used to determine the diffusivity

under inert conditions as well as the diffusivity occurring during vacancy and

interstitial supersaturation. In the case of Ge atoms in a Si lattice, the Ge is

neutral (uncharged) within the Si lattice, so there are no dopant Fermi-level

effects and therefore the Fermi model and Neutral model are equivalent in

this case. Any electric field effects were ignored in the initial attempts to

model the system. There were two reasons for this: (1) Fermi level effects of

ionized defects were assumed to be orders of magnitude smaller than dopant

concentrations-too small to contribute to an electric field and (2) the

substitutional dopant atom (Ge) is neutral within the host lattice (Si).

The Pair model was used to determine the fractional interstitial and

vacancy components, f, and fv. The diffusivity under inert conditions,

previously determined from the Fermi model, was used as the value for D*.

The inert diffusivity was proportioned into interstitial and vacancy

components such that:


D* = D; + Dv (3-6)

so that the parameter f, could be defined such that:







f, = I with fv=1-f, (3-7)
D; + D,

At a given temperature f, remains the same under any ambient and is not

dependent upon point defect supersaturation.

Values of C,/C,* and Cv/Cv* for each temperature under either

oxidizing or nitriding ambients were extracted from diffusion data reported in

literature. By assuming phosphorous to have an fr=l, phosphorous diffusion

data was fit to extract C,/C,* and Cy/Cv* values under oxidizing conditions.

Similarly, by assuming antimony to have an f,=0, Sb diffusion data was fit to

extract C,/C,* and Cv/Cy* values under nitriding conditions. The previous

assumptions regarding f, are broadly accepted in the Si diffusion community

[Fah89a, Hu94]. Equation 3-4 was then solved for the concentration of the

dopant, using the value of D calculated from Equation 3-5. The resulting

profile was compared to the experimental profile, and the ratio of D,* and Dv*,

hence f,, was adjusted until the profiles matched as judged by a Gaussian fit.

At this point a good estimate of f, was made. It is important to note here, as in

Section 1.4, that f, values extracted for Ge diffusion employed the Cq/C,* and

Cv/Cv* values from fitting the phosphorous and antimony diffusion data.

The approach used in all FLOOPS simulations in this dissertation was

to model the Si1-xGex alloy regions as Ge dopant in the Si lattice. In this case,

there are five system species: a Si substitutional (Sis), a Ge substitutional (Ges),

a Si interstitial (Is), a Ge interstitial (Ia), and a lattice vacancy (V). Because

there are five species, five equations are needed to completely describe the







system. Ideally, these five equations can be obtained through a continuity

equation for each component, in the form of either equation 3-1 or 3-3. There

is also an equation for conservation of lattice sites which allows us to

eliminate one of the five continuity equations. Because Sis is the most

abundant species, computationally it will be the most difficult for which to

account, so Sis would most logically be chosen to be replaced by the

conservation of lattice site equation. Ultimately, the system could be

completely described by four continuity equations (Ges, I, Is,, and V) and one

equation for conservation of Si lattice sites.

The actual FLOOPS model employs several assumptions which

simplify the above model. It is first assumed that since Ge is treated as a

dopant in the Si lattice, Ge on substitutional sites may be ignored when added

to Si substitutionals; the Ges concentration is negligible when compared to

the Sis concentration. This assumption also allows the equation for

conservation of lattice sites to be ignored. It is further assumed that the

concentration of mobile Ge is much lower than the concentration of

substitutional (immobile) Ge. Mobile Ge may occur as Ge-V complexes or

uncomplexed Ge diffusing substitutionally through adjacent vacancies

(accounted for through Dv or Dv*), or as Ge-I complexes or uncomplexed

interstitial Ge atoms (accounted for through D, or D,*). This allows one

equation describing mobile and immobile Ge to be written, in which the

expression of interest is the ratio of the two. This ratio of mobile to immobile

Ge concentrations was calculated by assuming local equilibrium between the







two species. Ultimately, FLOOPS used expressions for interstitial and vacancy

concentrations as well as total Ge concentration to solve the diffusion

equations and provide a final depth versus concentration profile.

The as grown Ge profiles for each structure, determined from SIMS,

were used as the initial profile for the FLOOPS diffusion simulations. The

value of the diffusivity was taken to be a function of temperature only,

ignoring possible concentration and stress dependencies. Diffusion was

simulated for one dimension (1D) only, in the direction perpendicular to the

sample surface. As stated previously, electric field effects were ignored.

Appendix A gives examples of FLOOPS codes used to simulate 1D diffusion

with the Fermi model and Pair model.

3.4 Results

3.4.1 Diffusivities and Activation Energies from SIMS/FLOOPS

The SIMS profiles of the annealed samples were standardized using the

method described in Section 2.3.1. The Ge concentrations of the annealed

profiles were standardized with respect to the total Ge concentration of the as-

grown profile. The depth scale of the SQW/MBE was standardized by

aligning the segregation peak of the annealed and as-grown profiles. This

SIMS profile peak was unique to the SQW/MBE material. The depth scale of

the SQW/VPE profiles was standardized by aligning the bisectors of the full

width at half maximum sector of the Ge well. In each case, the depth scale of

annealed samples was shifted no more than 20 nm in one direction. This







lateral movement is well within one standard deviation, estimated at 0.05, in

relative depth scale error of SIMS [Gos93].

The extracted diffusivity values for structure SQW/MBE annealed in

inert, oxidizing, and nitriding ambients are given in Table 3-1. The value of

the diffusivity and enhancement in oxidizing ambient for anneal

temperature 900 C and time 2206 min could not be extracted because the

50nm Si cap had been consumed by the oxide and oxidation of the Silx-Ge,

layer had occurred. Diffusivity and enhancement values for diffusion in

nitriding ambient at 900 and 1000 C in a furnace were not investigated; only

the RTA was equipped with ammonia gas. It is important to note here that

all extracted diffusivities discussed in Chapters 3 through 5 are effective

diffusivities, DS, and are only referred to as diffusivities for textual

convenience.

The values of the diffusivities for structure SQW/MBE as a function of

temperature in inert, oxidizing, and nitriding ambients are shown in Figure

3-2. Error analysis of the diffusion coefficients was performed using the

method described in Section 2.3.2. Fitting this data to Arrhenius expressions

results in the following equations when the interdiffusion is carried out in

inert, oxidizing, and nitriding ambients:


D' (SQW / MBE) = 1.6 x 108 exp(-5.87eV 0.14 / kT) cm/s (3-8)

D (SQW / MBE) = 6.1 x 105 exp(-5.27eV 0.11/ kT) cm2/s (3-9)

DNi (SQW /MBE) = 1.1x 10 2 exp(-3.27eV 0.10 /kT) cm2/s (3-10)







This is the first time that activation energies for interdiffusion of Sil.Gex/Si

layers under interstitial injection and vacancy injection have been directly

determined from experiment. The activation energy in nitriding ambient is

provided for comparison purposes only, and is not statistically reliable

because it was extracted from only two data points. This statement also

applies to Equation 3-13 for SQW/VPE.








1200 C 11000C 1000 C 900 C
I I I I
--:--- Inert
10-12 -Oxidizing
.- Nitriding

1013


10"1





10-15

1017 1 I

6.5 7 7.5 8 8.5 9
1/T 104 (K-1)

Figure 3-2. Effective Ge diffusivity of structure SQW/MBE as a function of
annealing temperature in inert, oxidizing, and nitriding ambients.







Table 3-1. Extracted diffusivity and enhancement values for SQW/MBE.


s


DO '(cm2/s)


T (C) time
(min)
900 330
980
1532
2206
1000 43
55
87
125
1100 1
2
3
4
1200 1
1.5
2
3


D,"(cm2/s)


1.70x10-17
2.29x10-17
2.08x10-17
2.08x10-17
3.00x10-16
3.29x1 0-16
3.29x10-'6
3.00x10-'6
5.20x10-4
7.93x10-u4
6.69x10-4
8.60x10-'4
2.38x10-'2
6.00x10-'3
1.08x10-12
1.08x10-12


D Nit(cm2 / s)


2.32x10-17
1.27x10-17
6.34x10-18

3.28x10-16
4.56x10-6
3.94x10-16
2.74x10-'6
1.14x10"4
5.20x10-4
4.21x10-"
7.93x10-4
4.05x10-1
4.93x10-'
4.56x10-3
4.56x10-3


feox f Nit
-enk en


1.49
0.555
0.305

1.09
1.38
1.20
0.913
0.219
0.656
0.629
0.922
0.170
0.822
0.422
0.422


0.281
0.062
0.238
0.144
0.046
0.041
0.094
0.046


The extracted diffusivity values for structure SQW/VPE annealed in

inert, oxidizing, and nitriding ambients are given in Table 3-2.



Table 3-2. Extracted diffusivity and enhancement values for SQW/VPE.

T (C) time D,~'(cm2/s) Do"(cm2/s) DNti(cm2/s) f X fiN
(min)
900 330 2.18x10-17 2.53x10-17 1.16
1000 43 3.94x10-'6 3.29x10-16 0.835 -
1100 1 9.00x10-" 4.72x10-" 1.73x10-14 0.524 0.192
1200 1 1.54x1012 2.73x10-13 1.40x10-13 0.177 0.091


1.46x10-14
4.88x10-s1
1.59x10-'4
1.24x10- 4
1.10x10-'3
2.47x10-4
1.02x10-"3
5.02x10-4


.~ ~ -


-~~ -~ ~--


.... --v







The values of the diffusivities for structure SQW/VPE as a function of

temperature in inert, oxidizing, and nitriding ambients are shown in Figure

3-3. Fitting this data to an Arrhenius expression results in the following

equations when the interdiffusion is carried out in inert, oxidizing, and

nitriding ambients:

De (SQW / VPE)= 4.8 x 107 exp(-5.71eV 0.23 / kT) cm2/s (3-11)

D (SQW / VPE) = 1.0 x 104 exp(-4.81eV 0.22 / kT) cm/s (3-12)

Ds (SQW / VPE) = 22 x 10 -exp(-2.73eV 0.10 / kT) cm2/s (3-13)


c(
E
,


10-12


10-13


10-14


10-15


10-16


6.5 7 7.5 8 8.5 9
1/T* 10 (K1)

Figure 3-3. Effective Ge diffusivity of structure SQW/VPE as a function of
annealing temperature in inert, oxidizing, and nitriding ambients.







3.4.2 Diffusion Behavior of Partially Relaxed Structures

The SQW/MBE and SQW/VPE structures have Sil.-Gex layers which

are greater than critical thickness and TEM analysis confirms that these layers

are partially relaxed through the presence of dislocations prior to any high-

temperature processing. The initial stage of high-temperature treatment of

these structures could cause additional strain relaxation by formation and

propagation of misfit dislocations as well as strain-enhanced diffusion,

thereby affecting the diffusivity. To address this issue, diffusivities of

structures which were initially partially relaxed were compared to the

diffusivities reported in Table 3-1 for the as-grown structures (for this

analysis, assumed to be fully strained).

The annealed SQW/MBE samples (Table 3-1) were used to represent

the partially relaxed structures, and their SIMS profiles were used as the

initial profiles in the FLOOPS simulations. For example, the SIMS profile of

the SQW/MBE sample annealed at 900 OC for 330 min was used as the initial

'partially relaxed' profile and diffusion was simulated for 650 min. A

diffusivity was extracted by fitting the resulting simulated profile to the SIMS

profile of the SQW/MBE sample that had been annealed at 900 C for 980

min. This method was used to extract diffusivities for all SQW/MBE samples

annealed in inert, oxidizing, and nitriding ambients. The values extracted for

each temperature and time are given in Table 3-3. Values in italics represent

the diffusivities of the as-grown structures after their first anneal and are

included for purposes of comparison. A value for the sample annealed in




Full Text
184
compared to that obtained in this investigation through HRXRD (Section
5.6.2) to determine whether, in this instance, analysis method affects
calculated values.
1014
10-15
')
10'16
8
Q
10-17
io-18
1019
7 7.5 8 8.5 9 9.5 10
1/T*104 (1C1)
Figure 5-7. Diffusivities of Ge in Sij.xGex/Si SLs with a Si(100) buffer layer
from previous studies and this work.
Comparison of diffusion in inert, oxidizing, and nitriding ambients
yields questionable conclusions due to the apparent non-Arrhenius behavior
of the actual diffusivity values in each ambient. At the lower temperatures
studied, Ge profiles in oxidizing ambient show greater diffusion than profiles
in inert ambient (Figure 5-8a). Diffusivities extracted at 850 and 900 C in
oxidizing ambient are greater than those in inert ambient and are not within
error of each other. This indicates that at these lower temperatures a
supersaturation of interstitials results in enhancement of Ge diffusion;
1000 C 950 C 900 C 850 C
1 1 1 1
+
+ + *
+
+
X
o
JIIIIIIII I I I I I l I I I I I I I I ill'll


47
Figure 2-7. XTEM micrographs of as-grown (a) structure SQW/MBE and (b)
structure SQW/VPE.


194
Table 5-6. Comparison of activation energies of SL/SiGe and SL/Si in inert,
oxidizing and nitriding ambients.
Ea:SL/SiGe (eV) Ea:SL/Si (eV)
3.14+0.20 3.630.24
1.7110.19 2.8110.21
4.0710.29 4.1610.22
5.7 Conclusions
The experimental results discussed above have provided considerable
contributions to the knowledge of Ge diffusion behavior in Si,_xGex/Si
asymmetrically strained SLs with a Si buffer, as well as the effect of strain on
interdiffusion in such a material. The diffusion model used in FLOOPS
simulations, while employing several simplifying assumptions, proved to be
a satisfactory first effort at predicting Ge diffusion behavior. The diffusion
coefficient exhibited Gaussian, concentration-independent behavior.
Diffusivities extracted in inert ambient were consistently higher than
previously reported values [Pro90, Bou96, Hol92, Bea85] and showed non-
Arrhenius behavior. Irregularities in the RTA temperature control may be a
reason for this behavior. An activation energy of diffusion of 3.63 eVi0.24
was extracted, which was within the range of previously reported values.
For the first time, diffusivities extracted under interstitial injection
conditions were reported, with a resulting activation energy for diffusion of
2.81 eV0.21. Slight enhancement of Ge diffusion was seen in oxidizing
ambient when compared to inert ambient at the lower temperatures, 850 and
T(C)
....
Inert
Oxidizing
Nitriding


5
a(x) = 0.002733x2 + 0.01992x + 0.5431(nm) (1-1)
showing a slight deviation from Vegard's rule, which predicts the lattice
constant of the alloy based on linearity between the endpoint lattice
parameters of pure Si and Ge:
a(x)= (aGe-aSi)x+aSi=0.0227x+0.5431 (nm) (Vegard's Rule) (1-2)
Figure 1-3 shows the composition dependence of the lattice constant predicted
using Vegard's rule, as well as the curve predicted by Equation 1-1.
Figure 1-3. Lattice constant of Si^Ge* versus Ge composition. Curves
predicted by Vegard's rule and experimental [Kas95].
For epitaxially grown, pseudomorphic (the lattice planes of the epilayer
and substrate are in perfect registry) Si1.xGex films, there is built-in strain
which is fixed by the lattice constant of the substrate on which the film is


90
Two possible reasons for the discrepancy between the results of the
oxidation and nitridation experiments were (1) the D* values measured in
Section 3.4.1 were not the correct values and had been affected in some
manner not accounted for in the Fermi model and (2) the interstitial and
vacancy supersaturation values, C,/C,* and Cv/Cv*, that occurred during these
oxidation and nitridation experiments differed from the values reported in
previous studies that were employed in the Pair model to estimate the f,
values. If either of these conditions proved to be true, then the D* values
extracted using the Fermi model and the f, values calculated using the Pair
model could be considered unreliable. It was imperative, therefore, to
determine as accurately as possible the actual values of D* and C,/C,* and
Cv/Cv* during processing of SQW/MBE in all three ambients. The best
means available to this investigator to determine these values were through
the B marker layer results discussed previously in Section 3.4.3 and later in
Section 3.5.3. The comparison of the actual processing time and the time
predicted by FLOOPS was used indicate the actual C,/C* value compared to
the default value used in FLOOPS. This approach is discussed in greater
detail in Section 3.5.3.
The analytical method which was adopted was: (1) a C,/C,* value in
inert ambient was determined for each temperature by taking the ratio of the
boron diffusion time predicted by FLOOPS and the actual processing time,
t^/tActual' as presented in Table 3-4. (2) A corresponding Cv/Cv* range in inert
ambient was then estimated by designating its upper limit as case (i) in which


LD
1780
199J
-3*5?
UNIVERSITY
OF
FLORIDA


125
difference in diffusion behavior when compared to initially fully strained
structures. This result seems to indicate that strain state does not affect Ge
diffusivity. Further investigations involving pseudomorphic structures is
needed to confirm this conclusion. Finally, a portion of injected excess
interstitials proved to be captured by misfit dislocations, however
enhancement of boron marker layer diffusion under oxidizing ambient
compared to inert ambient established that a modest amount of excess
interstitials are available to participate in the diffusion process.


40
direction (Figure 2-4), essentially providing a view looking down at the top of
the sample. Cross-sectional TEM (XTEM) provides an image of the sample
(Figure 2-4) perpendicular to layer growth direction, as if one were looking at
a slice of the sample from a side direction.
PTEM was used specifically in this work to determine qualitatively the
density of misfit and threading dislocations and their lengths. PTEM was also
used to observe their evolution with increasing time and temperature, as
well as how they differed in inert, oxidizing and nitriding environments.
XTEM is used in this work to determine the quality of the layer interfaces
(sharpness, flatness), as well as the thickness of the layers. The grayscale
contrast of the Si and Si!_xGex layers allowed the observation of smearing of
the interface due to diffusion after annealing. XTEM was also used to observe
any threading dislocation evolution from the substrate/buffer interface to the
surface.
2.2.2 TEM Sample Preparation
Procedures for sample preparation for PTEM and XTEM applications
are quite different. Also, individual techniques used in both cases vary from
researcher to researcher. The following sections describe the preparation
methods used to create TEM images shown in this work.
2.2.2.1 Plan view
To provide a top surface view, preparation was begun by coring a
circular piece out of the sample and mechanically thinning the backside of
this core using a 15 pm powder. The top surface of the thinned piece was


2
parameters as anneal time and temperature, alloy composition, strain state, as
well as quantum well (layer) thickness and periodicity.
A review of the literature reveals that work done thus far in thermally
activated interdiffusion of Si-Ge material can be divided into two categories:
(1) interdiffusion of SQW and SL materials in an inert environment [Van90,
Sun94, Hol92, Zau94] and (2) impurity diffusion in inert and reactive
environments [Kuo95, Pai95, Fan96, Kuz98]. There has been discussion about
identification of which atoms (Si, Ge, or both) are diffusing in the undoped
case as well as the fractional contribution of interstitials and vacancies
towards diffusion in both cases. A detailed model for either, however, has
not been proposed.
This work has investigated intrinsic interdiffusion of undoped SQW
and SL material in inert, oxidizing, and nitriding environments over the
temperature range 800 to 1200 C. Experiments were conducted to measure
the extent of interface intermixing and the corresponding diffusion
coefficient. The effects of surface oxidation and nitridation have been
examined to determine the extent of diffusion enhancement or retardation as
a result of processing under point defect supersaturation conditions.
Estimates of the fractional contributions of interstitials and vacancies to
Si/Si^Ge,, diffusion have been ascertained. Finally, the effect of dislocations
on the concentration of injected point defects available to aid in
interdiffusion has been studied.


205
6.3.3 Simulations and Modeling
The model employed in Si1.xGex/Si FLOOPS diffusion simulations in
this dissertation should be revised to include some means of accounting for
the high concentrations of Ge in the alloy, instead of approximating the
concentration by dopant levels. C,* and Cv* values for Si,.xGex are thought to
be different than those for Si. The increasing availability of data for dopant
diffusion in Sij.xGex might allow f, and fv values to be extracted based on Si,_
xGex values instead of Si values.


121
dislocated and dislocation-free structures and whether f, is, in fact, greater
than indicated by oxidation experiments.
3.5.4 Fractional Interstitial Components from Marker Layer Experiments
In Section 3.4.4 it was suggested that the measured D* values
represented diffusion which was severely altered by dislocations and this
might account for the inability to estimate an f, from nitride experiments
using the Pair model. The inert diffusivities, D*, calculated using the method
described in Section 3.4.4 were different from those measured in Section 3.4.1.
The higher bound of Cv/Cv* produced diffusivities which were lower than
the measured values while the lower bound of Cv/Cv* produced diffusivities
which were higher. In all cases, however, the calculated values were within
error of the measured values. It could be concluded that the dislocations had
a negligible effect on the Ge diffusivity in inert ambient and that Equation 3-8
should have been able to accurately estimate an f, using the measured D*
values.
It was alternately suggested in Section 3.4.4 that C,/C,* and Cv/Cv* could
be different in the dislocated SQW/MBE in all ambients from the established
values for silicon under normal intrinsic, interstitial supersaturation and
vacancy supersaturation conditions. The calculated C,/C,* values given in
Tables 3-5 and 3-6 were indeed different, and in most cases lower, than the
generally accepted values [Pac90, Pac91] for intrinsic and interstitial
supersaturation conditions. Both intrinsic and injected interstitials were
captured by the dislocations, altering both C,/C,* and Cv/Cv*. A general result


5-4. Diffusivities of SL/Si extracted from FLOOPS and HRXRD 189
5-5. Comparison of diffusivities of SL/SiGe and SL/Si in inert,
oxidizing and nitriding ambients 193
5-6. Comparison of activation energies of SL/SiGe and SL/Si in inert,
oxidizing and nitriding ambients 194
x


174
The decay of the intensity of the first order satellite peak with
increasing anneal time resulted in diffusion coefficients extracted using
Equation 5-1 for anneal temperatures of 900 and 1000 C in inert, oxidizing,
and nitriding ambient (Figure 5-4). These diffusivities are presented in Table
5-2. A diffusion coefficient for SL/Si annealed in oxidizing ambient at 900 C
could not be extracted because of the positive slope of the decay of the
intensity of the first order satellite peak.
Figure 5-4. Decay of the integrated intensity of the first order superlattice peak
about Si(004) as a function of annealing time, temperature and ambient of
SL/Si.
T(C)
"900
1000
Table 5-2. Extracted diffusivity values for SL/Si using HRXRD.
Dr.x(cm2/s)
Pj^CcmVs)
2.13xl016
5.17xl016
6.14xl017
Df'.Nitr(cm2/s)
5.24xl0'17
1.29x1 O'15


investigated and a model presented which simulated diffusion under a
variety of material and processing conditions.
Activation energies of diffusion in inert, oxidizing, and nitriding
ambients for single quantum well (SQW) material were found to be 5.8, 5.0,
and 3.0 eV, respectively. Diffusion in inert and oxidizing ambients was
similar, while signifigant retardation of diffusion was seen in nitriding
ambient.
Activation energies of diffusion in inert, oxidizing and nitriding
ambients for a superlattice (SL) with a Si1_xGex buffer layer were found to be
3.1, 2.4, and 4.0 eV, respectively. Activation energies of diffusion in inert,
oxidizing, and nitriding ambients for a SL with a Si buffer layer were found to
be 3.63, 2.81, and 4.1 eV, respectively. Slight enhancement of diffusion was
observed in oxidizing ambient at lower temperatures, while retardation of
diffusion was observed in nitriding ambient at all temperatures. No
difference in diffusion behavior was observed between the two SL structures.
Transmission electron microscopy confirmed that dislocations were
present and grew with increased anneal time and were believed to have a
significant effect on diffusivity values. Experiments using SQWs with buried
T
boron marker layers determined that a portion of interstitials injected in an
oxidizing ambient were captured by dislocations, however, enough remained
available to aid in the diffusion process.
xvi


195
900 C. At the higher temperatures, 950 and 1000 C, no enhancement was
seen. This leads to the conclusion that interstitials play a decreasing role in
diffusion with increasing temperature, due to either an actual decrease in
interstitial contribution to the diffusion mechanism or to the increase in the
recombination rate of interstitials and vacancies.
For the first time, diffusivities extracted under vacancy injection
conditions were reported, with a resulting activation energy for diffusion of
4.16 eV0.22. Significant retardation of Ge diffusion was seen in nitriding
ambient when compared to inert ambient at all temperatures, indicating that
diffusion is dominated by interstitials. This contradicted the results of the
oxidation experiments.
Plan-view TEM micrographs showed qualitatively that dislocation
density remained constant after anneal relative to the as-deposited value.
This suggests that a minimal amount of misfit dislocations, and therefore
relaxation, is created with thermal processing. This conclusion was supported
by HRXRD analysis of SL/Si strain relaxation. The lattice constants of the
SL/Si pseudo-epilayer were seen to remain constant upon anneal when
compared to the as-deposited values. Attempts to extract a diffusion
coefficient from the intensities of the first order satellite peaks from o-20
HRXRD scans provided values that were unreliable. While characterization
through HRXRD seems promising, future work must be done to perfect the
experimental technique and diffusion coefficient extraction method.


190
is expected that progressive relaxation would cause the parallel lattice
constant to increase towards its natural value, while the perpendicular lattice
constant would decrease towards its unstrained value. The values of ae// in
Table 5-3 were expected to increase with increasing anneal time, while the
values of a^ were expected to decrease. After calculations were performed
using Equations 2-7 and 2-8, the values of both ae// and ael were found to
remain constant with time in all ambients, with values almost identical to
those of the as deposited cubic unit cell.
Disregarding the possible errors in lattice constant measurement,
which are estimated at only 0.0002 nm, and assuming the evident trends are
correct, it is logical to conclude that the strain state of the structure must be
redefined to fit the experimental results. The reason for uniform ae// and ae
could be due to shear deformation in the epitaxial layer [Bar78] or distortion
in all three lattice directions. In a normal cubic unit cell, the lengths of the
sides of the cell, a, b, and c, are all equal. In tetragonal strain discussed
previously, a=b=*c, in which a and b have been denoted as ae// during this
work, and c has been denoted as ael. In orthogonal strain, a*b*c. The b
direction cannot be measured using the normal HRXRD method described, so
if a and b are not equal, then there might be relaxation in the b direction that
is immeasurable. Further studies are needed to determine the reason for this
behavior. There are two other possible reasons for the constant lattice
parameter values: (1) the as-deposited structure is fully relaxed, from


191
dislocations generated during the growth process or (2) the annealed
structures do not relax significantly. The first reason is highly improbable
due to PTEM results discussed in Section 5.5.3, in which a low density of
misfit dislocations were seen in micrographs of the as-deposited structure.
While the as grown structure is definitely slightly relaxed, due to threading
dislocations visible in XTEM micrographs, the lack of misfit dislocations in
the PTEM micrograph indicate that it is far from fully relaxed. The second
reason is more probable because qualitatively the same misfit dislocations are
visible in micrographs of annealed samples as the as grown sample. Further
studies must be done to determine the reasons for the uniform lattice
constants seen in Table 5-3.
5.6.4 Effect of Strain State on Diffusivity Values
As has been stated throughout this dissertation, diffusion of Ge in Sij.
xGex/Si materials is affected by both strain and compositional changes.
Chapter 4 presented results and discussion of the strain relaxation of SL/SiGe
after thermal treatment through TEM and HRXRD characterization. Results
of compositional changes were also presented for SL/SiGe through
characterization by SIMS and analysis using FLOOPS. Chapter 5 presented
results of these same influences on structure SL/Si. The utility of both sets of
information is the ability to directly compare the respective parameters of
SL/Si and SL/SiGe, whose only difference is the strain state of the Si and Si,.
xGex layers in the periodic material. This section attempts to provide an
organized, tabular comparison of the diffusion coefficients, fractional vacancy,


157
Confirmation of diffusion and relaxation of SL/SiGe through the
behavior of the zero order peak introduces the question of why the first order
satellite peak behaved anomalously. The irregularities can most likely be
attributed to instrumental issues that consistently arose during HRXRD
characterization. Specifically, the maximum intensity of the Si(004) substrate
peak was surprisingly low, compared to expected values, for all scans of
samples annealed in inert and oxidizing ambients. The low intensity of the
substrate peaks resulted in first order peaks that had very small intensities,
even when long scans with small angular steps sizes and longer times per
step were employed. Upon annealing, the first order peak decreased very
quickly with time to intensity levels that were either very small or else were
beyond detection. Detection of small changes in intensities of first order
peaks with time under these instrumental conditions was therefore
questionable. However, the scans of samples annealed in nitriding ambient
were performed at a later date, when much higher substrate intensities were
obtained, yet there were still anomalies in the resulting data, so this
explanation is not necessarily correct.
Figure 4-4 is a plot of the natural logarithm of the standardized
intensity of the first order satellite peak versus time. The slope of the decay of
the intensity is expected to be negative and is the value to be used in equation
4-5 to extract diffusion coefficients for each temperature. The slopes of the
curves for the decrease in intensity of the first order satellite peak for
increasing anneal times at 900 C in inert, oxidizing and nitriding ambients


62
Optimizing intensity of the silicon substrate Bragg signal allows the smaller
decayed satellite peaks to be more easily observed and measured.
Figure 2-20. Miscut of substrate and mistilt of epilayer. The lower unshaded
region shows the possible miscut of the substrate, vj/. The top shaded region
shows the additional possible mistilt of epilayer grown on substrate, Q.
X-ray diffraction peak positions discussed hereafter are assumed to
represent optimized values unless otherwise stated.
2.4.3 Determination of Interdiffusivity of Superlattice Layers
The periodicity of a superlattice structure causes a similar effect in XRD
as the periodicity of the planes of lattice atoms. The diffraction of the
superlattice is modulated and results in well-defined satellite peaks. The
superlattice period can be obtained from [Pel91]:
2sinen-2sin8sL ^n (2_4)
A


CHAPTER 4
BEHAVIOR OF ANNEALED ASYMMETRICALLY STRAINED Si/Si^Ge,
SUPERLATTICES WITH Sij.xGex BUFFER
A basic requirement for any optical application of a material is its
transparency in the near infrared (IR) region, at wavelengths of A.=1.3gm
and/or A,=1.55pm. This basic condition is met by silicon and can also be met
by Si^Ge, through material engineering. In properly designed quantum
wells (QWs), absorption results in photodetection and the QW absorption can
be used for IR detection. There has been growing interest in Si-Ge for
applications in optics such as photodetectors, waveguides and photodiodes
[Qas98, Eng97], Most of these devices use thin, periodic Si,_xGex and Si layers
in superlattice form. The bandgap for absorption in the 1.3 to 1.55 |im range
can be obtained with Ge fraction x>0.25 in a single strained alloy layer.
However, critical thickness for these large Ge fractions is small and
sufficiently thick strained layers without misfit dislocations are currently
impossible to grow. This difficulty is overcome by using a Si^Ge^Si
superlattice, as the thin Si^Ge,, layers are more stable even for large values of
Ge fraction because the average value of x is not large. In particular, when Si1_
xGex and Si layers are grown on a Sij.yGey substrate such that the Si layers are
under tensile strain, the conduction band offset is large and n type quantum
wells (electron confinement in the conduction band) can be formed which
126


103
Depth (pm)
Figure 3-9. Comparison of experimentally determined SIMS profile and
FLOOPS profile. Sample annealed at 1000 C for 43 min in (a) inert ambient
and (b) oxidizing ambient; (c) annealed at 1100 C for 3 min in nitriding
ambient.


7
temperature. Figure 1-5 shows the composition dependence of the unstrained
bulk alloy. The alloy has a Si-like A-conduction-band minimum from x=0 to
x=0.85. At this composition there is a crossover to the Ge-like L-conduction-
band minimum[Lan85]. Compressive strain in the alloy produced by the
underlying Si substrate reduces the Sij.xGex bandgap energy. In Si/Sij.xGex
superlattices the bandgap is strongly influenced by not only the strain state,
but also the layer thickness and period.
E
3
Q.
(C
0
>>
o>
l
C
LU
Figure 1-5. Energy gap versus germanium fraction for unstrained and
coherently strained S!.xGex [Peo86].


141
At both (O' and (D+, scans were taken at a rotational angle of -90 and 90. co-26
scans were taken over a Io range of (o, with a step size of 0.00025 and time per
step of 0.5s for a total of 4001 steps.
Scans of the as grown SL/SiGe structure were taken in order to
determine what were considered fully-strained values of the parallel and
perpendicular lattice constants. These values gave a good idea of the
dimensions of the original unit cell of the epilayer and allowed estimation of
the comparative amount of relaxation that occurred through processing. It
must be stated, though, that these values are probably not the actual fully-
strained values, as TEM micrographs of the as grown structure showed
evidence of relaxation through misfit dislocation formation (Section 4.5.3).
Scans were limited to two anneal temperatures, 900 and 1000 C, and two
anneal times 6 and 8 min and 1 and 3 min for 900 and 1000 C, respectively.
Scans were taken of samples annealed at these temperatures and times in
inert, oxidizing, and nitriding ambients. Table 4-3 presents the resulting ae//
and a^ values after analysis using the equations given in Section 2.4.4. The
error was determined through the minimum resolution in the omega angle,
(0.00025) which is the only parameter used to calculate ae// and aei. The error
in both ae// and ael was estimated at 0.0002nm.
4.5.3 TEM
The amount of initial relaxation of the structures immediately after
growth is determined by the growth temperature, layer thickness, number of


188
data points yields a negative slope for both inert and nitriding ambients, yet
the slope of the decay in oxidizing ambient is positive, such that a diffusion
coefficient cannot be extracted using Equation 4-5. Diffusivity values can be
calculated from all curves except that for 1000 C in oxidizing ambient, but
based purely on the intensity data, no extracted diffusivity can be considered
reliable. As stated in Chapter 4, HRXRD characterization in conjunction with
Equation 4-5 shows potential for providing dependable diffusion coefficient
data, however much more work needs to be done to refine the instrumental
method needed to obtain scans that are reliable.
It is still of interest to compare these values with those determined
from SIMS and FLOOPS presented in Section 5.5.1 (Table 5-4). The
diffusivities in inert and nitriding ambients at an anneal temperature of 900
C are not within error of each other. At an anneal temperature of 1000 C
only the diffusivities in nitriding ambient are within error of each other. In
inert and oxidizing ambients the diffusion coefficients of the two methods
disagree by orders of magnitude. Due to the reasons explained above, the
diffusivities extracted using SIMS/FLOOPS are considered to be much more
reliable. It is pointless to fit these diffusivities to an Arrhenius expression, as
there are only two temperatures investigated.
As a final analysis of the diffusivities extracted using HRXRD, it is
interesting to compare them with the values reported by Prokes and Wang
[Pro90] using the same method. Prokes and Wang studied diffusion in inert
ambient over a lower temperature range than that of this study, 700 to 880 C.


138
Figure 4-4. Decay of the integrated intensity of the first order superlattice peak
about Si(004) as a function of annealing time, temperature and ambient of
SL/SiGe.
The decay of the intensity of the first order satellite peak with
increasing anneal time resulted in diffusion coefficients extracted using
equation 4-5 for anneal temperatures of 900 and 1000 C in inert, oxidizing,
and nitriding ambient (Figure 4-4). These diffusivities are presented in Table
4-2. The absence of a diffusivity for processing in oxidizing ambient at 1000 C
is explained in Section 4.6.2.
The relative intensities of the substrate, zeroth order and satellite peaks
can vary from scan to scan, therefore scans must undergo a standardization
procedure to enable peak intensities to be compared and used accurately in
equation 4-5. The (004) substrate peak is expected to remain constant


55
using a Monte Carlo simulation approach. The error in the fluctuation of the
concentration was determined by examining the fluctuation of the signal in
the pure silicon regions of the sample. The error in depth scale was estimated
to be 5% [Gos93] and the method of error analysis was taken from H.-J.
Gossman et al. [Gos93] and is based upon the equations:
Cj=Ci+GVcj (2-2a)
z,=z(l + Gx) (2.2b)
where c¡ is the experimentally determined concentration, z is the
experimentally determined depth into the sample, G is a Gaussian distributed
random variable with mean E(G)=0 and variance E(G2)=1 and y is the
concentration corresponding to a count of 1 in the experimental instrument.
The numerically generated concentration and depth into the sample are
represented by c¡ and z,, respectively. % represents one standard deviation in
the relative depth scale error and, as stated above, was estimated as 5% for the
purposes of this analysis. A new ¡(z^t) set was generated using Equations 2-
2, creating a profile that was fitted using FLOOPS to determine a new D¡. This
was done 11 times and the mean of these values as well as the experimentally
determined value was taken as the diffusivity, D, and the standard deviation,
o, as the error.


44
between the substrate and buffer layer. The layers are not particularly straight
but are fairly abrupt.
Figure 2-7b shows the micrograph of SQW/VPE at a magnification of
xlOOk. The interfaces are extremely abrupt and uniform, with no apparent
roughness. The thicknesses of the Sij.xGex well layer and Si cap layer are equal
to the intended growth thickness, within resolution of TEM (~0.2 nm) [Sch90].
No dislocations are visible in this image (see above paragraph).
2.23.2 PTEM
The micrograph of SL/SiGe in plan-view is shown in Figure 2-8a. The
as-grown SL/SiGe exhibits strain relief through an array of misfit dislocations
spaced an average of approximately 0.5 pm apart. The micrograph of SL/Si in
plan-view is shown in Figure 2-8b. The as-grown SL/Si exhibits strain relief
through an array of misfit dislocations spaced an average of approximately
0.35 pm apart. In the micrograph shown, there are sample preparation
artifacts which represent back-etched dislocations that are wider and less
resolved than the unetched dislocations visible as well.
The micrograph of SQW/MBE in plan-view is shown in Figure 2-9a.
The as-grown SQW/MBE exhibits strain relief through an array of misfit
dislocations spaced an average of approximately 1 pm apart. The micrograph
of SQW/VPE in plan-view is shown in Figure 2-8b. The as-grown SQW/VPE
exhibits strain relief through an array of misfit dislocations spaced from 0.25
tol.50 pm apart. Sample preparation artifacts such as etch pits and back-
etched dislocations are present in both micrographs.


50
ions supplied by a dual plasmatron gun. A few profiles used Cs+ ions
generated by a separate cesium gun to detect oxygen and nitrogen content.
The crater depths were measured with a Tencor Alpha-Step 500 surface
profiler to determine the sputter rate.
2.3.1 Determination of the Ge Depth Profile in SiGe Structures
Determination of the Ge concentration from a count of secondary ions
is complex [Pru97a, New97, Kru97]. The overall concentration of Ge in the
alloy of the as-grown structures was too high for SIMS calibration with an
implanted standard, which is the usual method. The maximum
concentration allowable for this method is approximately one percent. A Si,.
xGex standard cannot be used at high concentrations because of the
contradiction of the matrix signals from the Ge in the Si,.xGex alloy and the
signals from the Ge atoms that have diffused in small quantities into the Si
layers. This is commonly known as a matrix effect, in which the secondary
ion yield of a particular element varies in different crystal lattices. A
linearization technique has been proposed which relates the secondary ion
signal of the Ge to the secondary ion signal of the Si [Pru97a, New97]. The
linearization is based on the counts from a sample of known Ge
concentration using Rutherford Backscattering Spectrometry (RBS). The
method applied to the samples used in this work involves the assumption
that the amount of Ge present each sample (as grown and annealed) remains
constant and then standardizing the Ge dose of the annealed samples to the
dose of the structure as grown. Specifically, the Ge concentrations of the


168
constant, a;/, increases. These values can be measured using high resolution
x-ray diffraction (Section 5.5.3), to completely determine the strain state after
anneal.
5.3 Processing
All samples were processed in an AG Associates Heatpulse 2101 rapid
thermal processor (RTP), the details of which can be found in section 3.2.1.
Anneal times and temperatures were identical to those of structure SL/SiGe
to enable comparison of results with regard to the effect of strain state. Before
annealing, the test wafer was cut into 1 x 1 cm pieces which were cleaned
using a regimen of deionized water, H2S04:H202 (1:2) and H20:HF (10:1) and
then dried with N2. Samples were rapid thermal processed with all ambient
gases (Ar, 02, NH3) flowing at 1.5 slm.
5.4 Simulation of Diffusion
The diffused Ge profiles were analyzed using the FLorida Object
Oriented Process Simulator (FLOOPS) [Law96]. Details regarding the FLOOPS
simulation program can be found in section 3.3. The model used to simulate
SQW and SL/SiGe diffusion was used to determine diffusivities for structure
SL/Si as well. Once again, details can be found in Section 3.3.


120
marker layer. Fang concludes that under interstitial supersaturation,
dislocations act as interstitial sinks, while under inert ambient they do not.
Kuo et al. [Kuo95] also examined the effects of oxidation upon diffusion
of boron marker layers in Si/Si^Ge^Si structures similar to those used in
Fang. Unlike the results of Fang, they found that a thin Si^Ge,, layer does not
interfere with the motion of interstitials. In particular they investigated a
highly unstable structure that had a Si070Ge030 layer that was 53nm thick, and
saw no difference in oxidation enhancements between the surface and buried
B marker layers. Fang discussed this study and offered no explanation for the
conflicting results.
It is concluded from this experiment, with consideration of the results
presented by Fang and Kuo et al, as well as those of the partially relaxed
structures (Section 3.5.2), that a portion of interstitials injected during surface
oxidation travel throughout the Sij.xGex layer and beyond. The remaining
excess interstitials are captured by dislocations. This merely means that the f,
estimated in this work is a lower bound for the fraction of Ge diffusion
occurring via interstitials. This also supports the possibility discussed in
Section 3.5.1 that dislocations alter C,/C* and Cv/Cv* ratios. In the next
section the boron marker layer results will be used to give a best estimate of
the C,/C* and Cv/Cv* ratios for the SQW structure investigated in this
chapter. It is recommended, however, that future work with pseudomorphic
structures be done to determine if there is any difference between of


LIST OF TABLES
Tablg page
1-1. Advantages and disadvantages of SiGe used in device applications 8
3-1. Extracted diffusivity and enhancement values for SQW/MBE 82
3-2. Extracted diffusivity and enhancement values for SQW/VPE 82
3-3. Extracted diffusivities for initially partially relaxed SQW/MBE 85
3-4. Anneal times needed in FLOOPS to achieve actual B diffusion
profiles 88
3-5. Fractional interstitial components and modified diffusivities and
point defect supersaturations determined for diffusion in inert
ambient 93
3-6. Fractional interstitial components and modified diffusivities and
point defect supersaturations determined for diffusion in oxidizing
ambient 94
3-7. Comparison of diffusivities of SQW/MBE and SQW/VPE in inert
and oxidizing ambients 107
4-1. Extracted diffusivity and enhancement values for SL/SiGe 133
4-2. Extracted diffusivities for SL/SiGe using HRXRD 136
4-3. Parallel and perpendicular lattice constants of SL/SiGe 142
4-4. Comparison of parameters of interdiffusion of SQW/MBE and
SL/SiGe 155
4-5. Diffusivities of SL/SiGe extracted from FLOOPS and HRXRD 159
5-1. Extracted diffusivity and enhancement values for SL/Si 169
5-2. Extracted diffusivity values for SL/Si using HRXRD 174
5-3. Parallel and perpendicular lattice constants of SL/Si 177
ix


218
Kas95 Kasper, E., Ed., Properties of Strained and Relaxed Silicon
Germanium. (INSPEC, London, 1995).
Kho90 Khoo, G.S. & Ong, C.K., I. Phvs. Chem. Solids 5L 1177 (1990).
Kri95 Krishanmoorthy, V., PhD Thesis, University of Florida, 1995.
Kru97 Kruger, D., Iltgen, K., Heinemann, B., Kurps, R., &
Benninghoven, A., Proc. of the 4th Inter. Workshop on
Measurement. Characterization and Modeling of Ultra-shallow
Doping Profiles in Semiconductors 4,9.1 (1997).
Kuo95 Kuo, P., Hoyt, J.L., Gibbons, J.F., Turner, J.E., & Lefforge, D., Appl.
Phvs. Lett. 67. 706 (1995).
Kuz98 Kuznetsov, A. Y., Cardenas, J., Svensson, B.G., Nylandsted
Larsen, A., & Lundsgaard Hansen, J., Materials Research Society
Proceedings. 1998.
Lan85 Lang, D.V., People, R., Bean, J.C., & Sergent, A.M., Appl. Phvs.
Lett 4Z, 1333 (1985).
Law96 Law, M.E., FLOOPS User's Manual. (University of Florida,
Gainesville, FL, 1996).
Lui96 Lui, X., Huang, D., Jiang, Z., & Wang, X., Phvs. Rev. B 53.4699
(1996).
May90 Mayer, J.W. & Lau, S.S., Electronic Materials Science: For
Integrated Circuits in Si and GaAs. (Macmillan, New York, 1990).
McV74 McVay, G.L. & DuCharme, A.R., Phvs. Rev. B % 627 (1974).
Mit96 Mitha, S., Aziz, M.J., Schiferl, D., & Poker, D.B., Appl. Phvs. Lett.
69,922 (1996).
Mog96 Mogi, Y., Ph.D. Thesis, Cornell University, 1996.
Mos85a Moslehi, M.M., & Saraswat, K.C., IEEE Trans. Electron Devices
ED-32.106 (1985).
Mos85b Moslehi, M.M., Shatas, S.C., & Saraswat, K.C., Appl. Phvs. Lett.
4Z, 1353 (1985).
Mur79 Murarka, S.P., Chang, C.C., & Adams, A.C., I. Electrochem. Soc.
126.996 (1979).


199
could not be estimated due to inert diffusivities that overestimated diffusion
in the FLOOPS Pair model.
Experiments conducted using buried boron marker layers verified that
excess interstitials injected as a result of surface oxidation during anneals in
oxidizing ambient did indeed travel to and through the Sij.xGex layer and
were available to participate in the diffusion process. These experiments also
indicated that a portion of the injected interstitials were captured by
dislocations. Experiments conducted using this same marker layer structure
verified that vacancies were injected as a result of surface nitridation and
were also partially trapped by the dislocations.
6.1.2 Superlattice Structures
In Chapters 4 and 5, the diffusion behavior of Sii.xGex/Si superlattices
over anneal temperatures 850 to 1000 C was investigated and results were
presented. Two structures were studied, a SL with a Sij.xGex buffer layer and a
SL with a Si buffer. It was determined from investigations of both structures
that rapid thermal annealing for the time and temperature profiles needed to
obtain the proper diffusion lengths was pushing the limits of the processor.
Accurate temperature control at these processing regimes was questionable.
The concentration versus depth profiles of the wells exhibited strictly
Gaussian decay, which indicated that the extracted diffusion coefficients were
concentration-independent. Calculated diffusivities for both structures were
higher at all temperatures than those previously reported in literature. These
diffusivities also exhibited non-Arrhenius behavior that was attributed to


108
literature over the temperature range 800 to 1010 C. The values at 1100 and
1200 C from this study are the only known diffusivities reported for this
temperature range. This work reports diffusivities that span over five orders
of magnitude (1017 cm2/s to 10'12 cm2/s) while previous studies report
diffusivities that extend over only two orders of magnitude at most.
Therefore, the diffusivity data and activation energies determined in this
study can be considered to be more reliable than any values reported
previously.
1200C 1100C
e r
E
o
* 10-15
10'16r
1 O'17 r
6.5
1000C 900 C
T

+ Van Ijzendoom et al.
10-12
r f
Sunamura et al.
O Hollander et al.
X Zaumseil et al.
10-13
r
this work
1014
*+ +-
O O o o +
!
8
7.5
8.5
9.5
1/T*104 (K'1)
Figure 3-12. Diffusivities of Ge in Si/Si^Ge^Si SQWs from previous studies
and this work.


36
50nm Si Cap
50nm '.Pe.is
100nm Si Buffer
llimuiiuotiiji -iiii'mi!'' min.i ii mili.'
Si Substrate
Figure 2-2. Sample structure SQW/MBE, a single quantum well grown by
MBE.
Secondary ion mass spectrometry (SIMS) and cross-sectional
transmission electron microscopy (XTEM) were performed on each sample
structure to verify the thickness of the layers as well as the number of periods.
Rutherford Backscattering Spectrometry (RBS) verified the Ge content using
He2+ ions with a beam current of lOnA and a collector charge of 4 mC. Each
sample was rotated 10 and tilted 10 to prevent channeling. The Si1_xGex
layers in all structures were shown to have the same Ge content (=0.15)
within experimental error (5%) [Sch90].
From Figure 1-3, the critical thicknesses of a capped Si1_xGex layer with a
Ge composition of 0.15 is hc~30nm. The 50 nm thicknesses of the Si^Ge,,
layers of both sample structure SQW/VPE and SQW/MBE exceeded this
critical thickness, therefore misfit dislocations were expected to be present in
the materials. The structures were consequently examined by plan view TEM
to determine qualitatively their dislocation densities (Section 2.2.3.2).
To determine the critical thickness for a multilayer structure, the
conventional method is to reduce the multilayer to an equivalent single


87
Boron diffuses in Si predominantly through an interstitial mechanism
[Fah89a]. If the B in the marker layer underneath the Si^Ge,, layer shows
enhanced diffusion after annealing in interstitial-injecting (Oz) ambient
compared to inert (N2/Ar) ambient, it can be concluded that the interstitials
are indeed traveling throughout the Sij.xGex layer without a significant
amount being captured by any dislocations formed. The interstitials are
therefore available to facilitate the diffusion process. Any differences in Ge
diffusion seen between inert and oxidizing ambients were indeed due to the
injection of point defects.
The SQW/B structure was furnace-annealed at 900 C for 330 min and
at 1000 C for 43 min in both N2 and 02. The SQW/B structure was also rapid
thermally processed at 1100 C for 2 min and at 1200 C for 1 min in Ar, Ozand
NH3. These are selected anneal conditions identical to four anneal conditions
used for structures SQW/MBE and SQW/VPE. The B profiles before and after
anneal were determined using SIMS (Figure 3-5). Qualitatively, B diffusion
was greater in 02 ambient than in Ar/N2 ambient for all temperatures. B
diffusion in NH3 was equivalent in NH3 ambient compared to Ar ambient.
FLOOPS was used to determine the quantitative transport of
interstitials through the Si1.xGex layer to the B marker layer. The SIMS profile
of the as grown boron marker layer was used as the initial B profile. The
diffusivity of B in Si under both inert [Bar84] and oxidizing [Pac90] conditions
is well-established, so the diffusion coefficient was maintained constant while
the time of anneal was changed in FLOOPS until the simulated profile fit the


46
200nm
Figure 2-6. Cross sectional view TEM (XTEM) micrographs of as-grown (a)
structure SL/SiGe and (b) structure SL/Si.


179
ambient at 850C for 8 min is shown in Figure 5-5. An isolated misfit is
present which qualitatively suggests that the annealed sample contained
approximately as many misfit dislocations as the as-deposited structure, and
the density was still significantly small. This is in direct contrast to the results
of structure SL/SiGe. Furthermore, no curved lines existed in micrographs of
SL/Si, as were seen for SL/SiGe (Figure 4-5). This indicates that the threading
dislocation density and lengths were minimal and far less than those in
SL/SiGe. In the micrograph shown in Figure 5-5 there are sample
preparation artifacts, light square areas, similar to those seen in SL/SiGe TEM
micrographs, which can be attributed to the etching process. These artifacts
did not, however, affect the ability to examine the dislocation density of the
structure. Clearly, the initial strain state of SL/Si is markedly different than
that of SL/SiGe and strain relaxation evolution through the generation of
dislocations is different as well. It would appear that SLs with Si^Ge* layers
in compressive strain generate less dislocations through relaxation than SLs
with Si layers in tensile strain.
5.6 Discussion
5.6.1 Diffusivities Determined from SIMS and FLOOPS
The diffusion profiles generated by the Fermi model provided very
good fits to the experimentally determined SIMS profiles in the case of
anneals performed in inert ambient, as demonstrated in Figure 5-6 for 950 C
and an anneal time of 3 min. This indicates that the assumptions made in


CHAPTER 2
SAMPLE PREPARATION AND CHARACTERIZATION
2.1 Growth Parameters and Structure
Four sample structures were used in this investigation to determine
the interdiffusion behavior of Si/Sij.xGex. Three structures were grown using
an ASM Epsilon 1 vapor phase epitaxial instrument. Figure 2-1 (a) shows a
strained SL structure grown on a Si0 85Ge015 buffer layer, hereafter referred to
as sample structure SL/SiGe. This structure consists of a (100) Si substrate
followed by a 100 nm ungraded Si0 85Ge015 buffer and 15 periods of 6 n m
Si085Ge015 and 12 nm Si. Figure 2-1 (b) shows another strained SL structure but
grown on a Si buffer layer, hereafter referred to as sample structure SL/Si.
This structure consists of a (100) Si substrate followed by a 100 nm Si buffer, 16
periods of 6 nm Si086Ge015 and 12 nm Si, and capped with 50 nm of Si. Figure
2-1 (c) shows the structure of a SQW, hereafter referred to as sample structure
SQW/VPE, which consists of a (100) Si substrate followed by a 100 nm Si
buffer layer, a 50 nm layer of Si085Ge0,5, and a 50 nm Si cap.
The final structure was grown by Molecular Beam Epitaxy (MBE).
Figure 2-2 shows a strained single quantum well (SQW) structure, hereafter
referred to as sample structure SQW/MBE, which consists of a Si (100)
substrate with a 100 nm Si buffer layer, a 50 nm Si0 85G015 with a 50 nm Si cap.
34


181
the FLOOPS model (Section 3.3), while not necessarily accurate, are good
enough to provide diffusivity values that are reasonable.
When analyzing the diffusion profiles for structure SQW/MBE and
SQW/VPE in Chapter 3, there was a question of whether the profiles were
flat, and if so, whether this indicated a concentration-dependent diffusivity
(Section 3.5.1). The diffusion profiles determined for SL/Si are Gaussian and
show no flatness in the wells whatsoever at any temperature. It can therefore
be concluded that diffusion in structure SL/Si is concentration-independent.
This corresponds with the concentration-independent diffusion found in
structure SL/SiGe discussed in Chapter 4.
There have been more studies and analysis of diffusion behavior in
inert ambient of Sij.xGex/Si SL structures with a Si buffer than for those with a
Sij_yGey buffer. Hollander et al. [Hol92] studied interdiffusion of a
Si080Ge020/Si SL with five periods of 10 nm Si and 10 nm Si080Ge0 20 layers. It
is also important to note that Hollander et al. investigated additional
structures with Ge compositions as high as x=0.70, but for purposes of direct
comparison to the results of this study, these structures will be ignored. The
diffusivities of Hollander et al. plotted in Figure 5-7 were extracted using a
Fourier algorithm to fit RBS spectra over anneal temperatures 1000 to 1125 C.
Prokes and Wang [Pro90] studied interdiffusion of a Si0 65Ge035/Si SL with
sixty periods of 12 nm Si and 4 nm Si0 65Ge0 35 layers. The diffusivities plotted
in Figure 5-7 were extracted using the decay of intensity of the first order
satellite peak from HRXRD scans, a method identical that described in Section


17
is most useful in experimental situations with steady state diffusion, where
dc/dt=0.
Fick's second law is normally used in systems with non-steady-state
concentration. Combining Fick's law with the continuity equation for the
diffusing species yields the diffusion equation:
3c _3_
3t 3x
D
3c
3x
d-6)
The solution to Equation 1-6 will be the concentration as a function of
position and time, c(x,t), for specified initial and boundary conditions. When
the diffusion distance is short with respect to the dimensions of the structure,
c(x,t) is mostly expressed by error functions. For example, isothermal
diffusion of a constant concentration source into a thick (infinite) substrate
with a constant diffusion coefficient can be described by :
C = Cerfc-
(1-7)
2(Dt)1/2
where x is the depth into the semiconductor, C0 is the concentration of the
source at x=0, D is the diffusivity, and t is time. Solutions to the diffusion
equations for many different boundary conditions can be found in several
classic references [Cra75, Tuc74].
In the systems studied here, complexities in using Fick's law arise from
two different sources: (1) the dependence of D on the properties of the system
can be complex and (2) multiple equations must be written to describe
multiple species. The value of D can vary with time (e.g., imposed


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9
Because Si and Ge form a continuous solid solution with a wide range
of energy gaps, the alloy has a wide range of optical and electronal
applications. The most common applications are in Heterojunction Bipolar
Transistors (HBTs), Modulation Doped Field Effect Transistors (MODFETs)
and quantum well light emitters and detectors. The incorporation of a
narrow band-gap Si,.xGex strained superlattice structure [Tem88] or bulk alloy
in a Si bipolar junction transistor (BJT) has many advantages relative to a
standard Si homojunction bipolar transistor. It offers increased emitter
injection efficiency and current gain, lower base resistance, shorter base transit
times, and better low temperature operation. Cut off frequencies, fT, as high as
130 GHz for a Si,.xGex HBT have been reported [Oda97], while fT for Si BJTs are
commonly ~75 GHz.
n+ CONTACT
n=5 x 1017 cm-3
0.5 pm, EMITTER
iizzzzzzzzzzzzzzzzz
ZZZZZZZZZZZZZZZZZZ
n=5 x 1016 crrr3
1.0 pm, COLLECTOR
n+-Si BUFFER
sssssss* n Sl Wsstfss
p-BASE
50 A Ge05Si0 5 WELLS
250 A Si BARRIERS
20 PERIODS
Figure 1-6. Cross-section of a Sij.xGex HBT [Tem88].


82
Table 3-1. Extracted diffusivity and enhancement values for SQW/MBE.
T(C)
time
(min)
D^icmVs)
DGex(cm2/s)
D^cmVs)
f Ox
*enh
f Nit
*enh
900
330
1.70xl0"17
2.32xl0"17
-
1.49
-
980
2.29xl0"17
1.27xl0'17
-
0.555
-
1532
2.08xl017
6.34xl0"18
-
0.305
-
2206
2.08xl0"17
-
-
-
-
1000
43
3.00xl016
3.28xl016
-
1.09
-
55
3.29xl016
4.56xl016
-
1.38
-
87
3.29xl016
3.94xl016
-
1.20
-
125
3.00xl016
2.74xl016
-
0.913
-
1100
1
5.20xl0"14
1.14xl014
1.46xl014
0.219
0.281
2
7.93xl0"14
5.20xl014
4.88x1015
0.656
0.062
3
6.69xl0"14
4.21xl0'14
1.59xl014
0.629
0.238
4
8.60xl014
7.93xl014
1.24x10"14
0.922
0.144
1200
1
2.38xl0"12
4.05xl013
l.lOxlO'13
0.170
0.046
1.5
6.00xl013
4.93xl0-13
2.47xl0"14
0.822
0.041
2
1.08xl0"12
4.56xl013
1.02X10"13
0.422
0.094
3
1.08xl012
4.56xl013
5.02X10"14
0.422
0.046
The extracted diffusivity values for structure SQW/VPE annealed in
inert, oxidizing, and nitriding ambients are given in Table 3-2.
Table 3-2. Extracted diffusivity and enhancement values for SQW/VPE.
T(C)
time
(min)
D^cmVs)
DGex(cm2/s)
DGeNlt(cm2/s)
f x
^enh
r Nit
*enh
900
330
2.18xl0"17
2.53xl0"17
-
1.16
-
1000
43
3.94X10"16
3.29xl0"16
-
0.835
-
1100
1
9.00x10"14
4.72xl0"14
1.73x10"14
0.524
0.192
1200
1
1.54xl0"12
2.73xl0"13
1.40xl0"13
0.177
0.091


132
Before annealing, the test wafer was cut into lxl cm pieces which were
cleaned using a regimen of deionized water, H2S04:H202 (1:2) and H20:HF
(10:1) and then dried with N2. Samples were rapid thermal processed with all
ambient gases (Ar, Oz, NH3) flowing at 1.5 slm.
4.4 Simulation of Diffusion
The diffused Ge profiles were analyzed using the FLorida Object
Oriented Process Simulator (FLOOPS) [Law96]. Details regarding the FLOOPS
simulation program can be found in section 3.3. The model used to simulate
SQW diffusion was used to determine diffusivities for structure SL/SiGe as
well. Once again, details can be found in Section 3.3.
4.5 Results
4.5.1 SIMS/FLOOPS
The Ge concentrations of the annealed SIMS profiles were standardized
with respect to the total Ge concentration of the as-grown profile using the
method described in Section 2.3.1. The depth scale of SL/SiGe was
standardized by aligning the Ge plateau (Figure 2-14) of the buffer layer of the
annealed and as-grown profiles. In each case, the depth scale of annealed
samples was shifted no more than 20 nm in one direction. This lateral
movement is well within one standard deviation, estimated at 0.05, in
relative depth scale error of SIMS [Gos93]. The error in the extracted
diffusivity values was determined from the method described in Section 2.3.2.


153
identical (Figure 4-9b). At these higher temperatures, diffusion is also
unaffected by interstitial superstaturation.
The activation energy of 2.43 eV0.19 calculated for interdiffusion in
oxidizing ambient is the first activation energy of interdiffusion under
interstitial injection reported for a Si/Si^Ge,, SL with a Si1_xGex buffer layer.
This activation energy is 0.7 eV less than that for diffusion in inert ambient.
The activation energy of 4.07 eV0.29 calculated for interdiffusion in
nitriding ambient is the first activation energy of interdiffusion under
vacancy injection reported for a Si/Sij.xGex SL with a S!.xGex buffer layer.
This activation energy is notably higher than that for diffusion in inert
ambient as well as in oxidizing ambient. From the activation energies alone,
one would expect that oxidation (interstitial injection) would enhance
diffusion, while nitridation (vacancy injection) would retard diffusion.
Significant retardation was indeed seen in profiles of samples annealed in
nitriding ambient, however, little, if any enhancement was observed for
samples annealed in oxidizing ambient. It is obvious that activation energies
in and of themselves do not provide an accurate picture of the diffusion
process.
It is natural to wish to compare the diffusion results of structure
SL/SiGe with those of SQW/MBE and SQW/VPE to determined the impact
of heterostructure on diffusion behavior. Table 4-4 gives a summary of the
major diffusion parameters of both structures for common temperatures


78
system. Ideally, these five equations can be obtained through a continuity
equation for each component, in the form of either equation 3-1 or 3-3. There
is also an equation for conservation of lattice sites which allows us to
eliminate one of the five continuity equations. Because Sis is the most
abundant species, computationally it will be the most difficult for which to
account, so Sis would most logically be chosen to be replaced by the
conservation of lattice site equation. Ultimately, the system could be
completely described by four continuity equations (Ges, 1^, Ig,, and V) and one
equation for conservation of Si lattice sites.
The actual FLOOPS model employs several assumptions which
simplify the above model. It is first assumed that since Ge is treated as a
dopant in the Si lattice, Ge on substitutional sites may be ignored when added
to Si substitutionals; the Ges concentration is negligible when compared to
the Sis concentration. This assumption also allows the equation for
conservation of lattice sites to be ignored. It is further assumed that the
concentration of mobile Ge is much lower than the concentration of
substitutional (immobile) Ge. Mobile Ge may occur as Ge-V complexes or
uncomplexed Ge diffusing substitutionally through adjacent vacancies
(accounted for through Dv or Dv*), or as Ge-I complexes or uncomplexed
interstitial Ge atoms (accounted for through D, or D,*). This allows one
equation describing mobile and immobile Ge to be written, in which the
expression of interest is the ratio of the two. This ratio of mobile to immobile
Ge concentrations was calculated by assuming local equilibrium between the


42
XTEM preparation was begun by slicing the sample into thin sections
approximately 25 milli-inches wide. Two of these sections were glued
together, surface to surface, with M600 Bond epoxy. This structure was
sandwiched between two thin sections of Si, which acted as structural support
(Figure 2-5).
The entire stack was mechanically thinned to ~ 15 pm and polished. A
3mm copper ring was attached via G Bond epoxy to one side of the sample.
This composite structure was thinned in a two stage Gatan 600 dual ion mill
using Ar+ ions at a gun voltage of 5kV and a current of 0.5 mA. Ion milling is
a process in which low energy Ar+ ions bombard both exposed sides of the
sample at low angles, slowly knocking off surface atoms, eventually thinning
the sample to a bowl-shaped cavity just breaking a hole into the back surface.
This minimum thickness allows electrons to be transmitted through the
sample and an image of the cross section to be formed in the microscope.
2.2.3 Images of Structures
As-grown and annealed samples were analyzed by cross-sectional and
plan-view TEM using a JEOL 4000FX for high resolution images and a JEOL
200CX for low resolution images.
2.2.3.1 XTEM
XTEM photos were taken of the as-grown structures to verify the layer
thicknesses, number of periods, as well as quality of the interfaces. The Si and
Si^Ge,, layers were imaged by absorption contrast due to differences in atomic
number. Figure 2-6a shows the as-grown structure of SL/SiGe at a


23
the interstitial-vacancy first-order recombination rate, and (p,s and (|\,s are any
independent sources or sinks for interstitials and vacancies, respectively. By
solving the continuity equations for all species involved for a specific
diffusion mechanism (e.g., Equations 1-11 through 1-13 for a kickout
mechanism), an expression for D can be reached.
At thermal equilibrium, the concentration of point defects is the single
most important influence on diffusion within the atomic lattice. The neutral
point defects can accept or donate an electron to become a charged defect,
which in turn can accept or donate another electron to become doubly
charged and so forth. The thermal equilibrium concentrations of charged
point defects depends on the Fermi level of the crystal as well as the electronic
level position in the bandgap corresponding to the defect. Hence, the total
concentration of point defects at thermal equilibrium are known functions of
the Fermi level and temperature. These quantities are denoted C,* and Cv*, as
mentioned above and are given by [Had95]:
Cx=X,
i
^PV'
j=0, 1, 2,... n
(1-14)
where X represents either I or V and 7 is a constant which represents the
contribution from the bandgap position, and j is the charge state of the defect.


35
12nm Si
6nm ~
fc
%
k
... k
12nm Si
6nm
x15
100nm SUG%1SBuffer
SI Substrate
(a)
50nm
12nm
6nm
12nm
6nm
100nm si Buffer
50nm Si Cap
50nm sUG lOOnm si Buffer
Si Substrate
Si Substrate
(b)
(c)
Figure 2-1. Sij.xGex sample structures used in these investigations, (a) Sample
structure SL/SiGe, a strained superlattice on a Si^Ge,, buffer (b) sample
structure SL/Si, a strained superlattice on a Si buffer (c) sample structure
SQW/VPE, a single quantum well.


135
either oxidation or nitridation experiments without some knowledge of
C,/C,* and Cv/Cv* for SL/SiGe under the investigated processing conditions.
4.5.2 High Resolution Xray Diffraction
As discussed in Section 4.2, diffusion in Si1.xGex/Si is thought by some
to be affected by both strain and composition. HRXRD is a versatile
characterization technique which can be used to determine the extent of both
diffusion and strain relaxation in heteroepitaxial structures. In Section 4.5.2.1,
the technique used in this work to extract diffusivity values for Si,.xGex/Si SLs
is described and results are presented. The analysis of the effect of high-
temperature processing on Sij.xGex/Si SLs is completed in Section 4.5.2.2 by
determining strain relaxation as a function of anneal time. The method of
using HRXRD to calculate strain is described and results are presented.
4.5.2.1 Diffusivities
In crystalline materials analyzed by XRD there will be Bragg reflections
from the lattice planes resulting in Bragg peaks. A composition modulation,
such as is created in a SL material, gives rise to satellites about these Bragg
peaks. The satellites about the zero-order reflection are the reflections that
can be attributed to the artificial Bragg planes created by the composition
modulation. For a sinusoidal composition modulation of wavelength X, the
intensity, I, of the corresponding Bragg reflection should decrease according
to:
d_
dt
V^o
D
(4-5)


161
begins at an amount that is the same as the fully relaxed cubic lattice constant.
While this departs from theory, it is still remarkably accurate for the
approximations made to obtain the theoretical values. The value decreases
only slightly from the as-deposited values, and, with one exception, remains
constant with anneal time, for both temperatures and in all ambients. This
could be due to shear deformation in the epitaxial layer [Bar78] or distortion
in all three lattice constants and further studies are needed. The only
exception is in nitriding ambient at 1000 C for an anneal time of 3 min,
where ael shrinks. This can probably be attributed to error in measurement.
4.7 Conclusions
The experimental results discussed above have provided considerable
contributions to the knowledge of Ge diffusion behavior in Sij.xGex/Si
asymmetrically strained SL with a Si,.xGex buffer. The diffusion model used
in FLOOPS simulations, while employing several simplifying assumptions,
proved to be a satisfactory first effort at predicting Ge diffusion behavior. The
diffusion coefficient exhibited Gaussian, concentration-independent
behavior. Diffusivities extracted from profiles obtained over a limited range
of anneal times and temperatures showed Ge diffusivity to have a possible
time-dependence. Further experiments must be performed to support this
conclusion.
A major contribution of this work was to extend the anneal
temperature regime below 1000 C for the first time, providing diffusivity


BIOGRAPHICAL SKETCH
Michelle D. Griglione received her Bachelor of Science degree from
Stanford University in 1991. She entered the Chemical Engineering doctoral
program at the University of Florida in 1992. She spent her first two years
working on the Robot Operated Materials Processing System (ROMPS) in
collaboration with NASA/Goddard Space Flight Center, culminating in a
shuttle flight experiment in September 1994. In 1996, she began her work in
SiGe.
222


180
Figure 5-6. Comparison of experimentally determined SIMS profile and
FLOOPS profile for 950 C and 3 min in (a) inert (b) oxidizing and (c) nitriding
ambient.


220
Ret98 Rettig, R., Marschner, T., Stolz, W., & Tapler, L., T. Applied Phys.
84/ 237 (1998).
Roo Roozeboom, F., Rapid Thermal Processing Science and
Technology 9, 349 (1993).
Run98 Runyan, W.R., & Shaffner, T.J., Semiconductor Measurements
and Instrumentation. (McGraw-Hill, New York, 1998).
Sch90 Schroder, D.K., Semiconductor Material and Device
Characterization. (John Wiley & Sons, New York, 1990).
See68 Seeger, A. & Chik, K.P., Phvs. Stat. Sol. 29.455 (1968).
She89 Shewmon, P., Diffusion in Solids. (Minerals, Metals and
Materials Society, Warrendale, PA, 1989).
Sin88 Singh. R.. I. Appl. Phys. 63. R59 (19881.
Sto85 Stolwijk, N.A., Frank, W., Holzl, J., Pearton, S.J., & Haller, E.E., L
Appl. Phys. 57,5211 (1985).
Sun94 Sunamura, H., Fukatsu, S., Usami, N., & Shiraki, Y.. Tpn. I. Appl.
Phys. 33.2344 (19941.
Tan81 Tan, T.Y. & Gosele, U., Appl. Phys. Lett. 39. 86 (1981).
Tem88 Temkin, H., Bean, J.C., Antreasyan, A., & Leibenguth, R., Appl.
Phys. Lett. 52.1089 (1988).
Tim97 Timans, P.J., Solid State Tech. 40. 63 (1997).
Tuc74 Tuck, B., Introduction to Diffusion in Semiconductors. (Peter
Peregrinus, Stevenage, England, 1974).
Van90 Van Ijzendoorn, L.J., Van De Walle, G.F.A., Van Gorkum, A.A.,
Theunissen, A.M.L., Van de Heuvel, R.A., & Barrett, J.H., Nucl.
Instr. and Meth. in Phys. Res. B 50.127 (1990).
Wer85 Werner, M., Mehrer, H., & Hochheimer, H.D., Phys. Rev. B 32.
3930 (1985).
Wil96 Williams, D.B. & Carter, C.B., Transmission Electron
Microscopy. (Plenum Press, New York, 1996).


ACKNOWLEDGMENTS
The completion of this research work and my graduate career would
not have been possible without help from many people. The contributions of
my committee members Dr. Cammy Abernathy and Dr. Rich Dickinson are
greatly appreciated. I am indebted to Dr. Mark Law for his patience as I either
waltzed into or paced outside of his open door with my latest triumphs or
traumas. Dr. Kevin Jones has allowed generous access to his labs, TEM
equipment and post-docs. I am most indebted to Dr. Tim Anderson, my
project advisor, for his scientific guidance as well as personal support for my
unorthodox graduate career.
Dr. Yaser Haddara receives my greatest appreciation for the knowledge
that he imparted to me regarding solid state diffusion and process simulation.
Our weekly discussions were invaluable. I am also grateful to Dr. Wish
Krishnamoorthy for TEM analysis and for sharing his wisdom regarding
HRXRD and basic physical science. I owe unending gratitude to Erik Kuryliw
for his persistent partnership in discovering the surprising versatility of the
rapid thermal processor.
I thank Pete Axson for generously lending his technical expertise in
such tricky areas as welding gas lines and his patient troubleshooting. Many
thanks to Courtney Hazelton, Steve Schein and the rest of the cleanroom
IV


a.
20,000x
500nm
b.
20,000x
500nm
Figure 2-9. Plan view TEM micrograph of as-grown (a) structure SQW/MBE
and (b) structure SQW/VPE.


I certify that I have read this study and that in my opinion it conforms
to acceptable standards of scholarly presentation and is fully adequate, in
scope and quality, as a dissertation for the degree of Doctor of Philosophy.
I certify that I have read this study and that in my opinion it conforms
to acceptable standards of scholarly presentation and is fully adequate, in
scope and quality, as a dissertation for the degree of Doctorof Philosophy.
Mark E. Law
Professor of Electrical and
Computer Engineering
I certify that I have read this study and that in my opinion it conforms
to acceptable standards of scholarly presentation and is fully adequate, in
scope and quality, as a dissertation for the degreejjf Doctor ^Philosophy.
Kevin S. Jom
Professor or Materials Science
and Engineering
I certify that I have read this study and that in my opinion it conforms
to acceptable standards of scholarly presentation and is fully adequate, in
scope and quality, as a dissertation for the degree of Doctor of Philosophy.
Cammy Abernathy
Professor of Materials Science
and Engineering
I certify that I have read this study and that in my opinion it conforms
to acceptable standards of scholarly presentation and is fully adequate, in
scope and quality, as a dissertation for the degree of Doctor of Philosophy.
Richard B. Dickinson
Assistant Professor of Chemical
Engineering


110
accepted error so will therefore be ignored. It can be concluded from this data
that diffusion in inert ambient is time-independent at all temperatures
within the studied range.
While the diffusivities for each temperature given in Table 3-1 for
oxidizing ambient seem to vary more than in the inert case, the calculated
error in measurement is greater. It can therefore be concluded that diffusion
in an oxidizing ambient is also time-independent at all temperatures within
900 to 1200 C. In nitriding ambient, at both anneal temperatures 1100 and
1200 C diffusivities at all anneal times are also within error of each other
and diffusion can be considered time-independent.
Comparison of diffusion in inert, oxidizing and nitriding ambients
yields interesting conclusions. At all temperatures, the diffusion profiles in
an oxidizing ambient are very similar to the diffusion profiles in an inert
ambient (Figure 3-14).
Diffusivities extracted are the same, within error, for temperatures 900
and 1000 C, as illustrated in Figures 3-2 and 3-3. This indicates that a
superstaturation of interstitials has very little effect on Ge diffusion at these
temperatures and that vacancies are the dominant diffusing species.
Diffusivities extracted for anneals at 1100 and 1200 C are also within error of
each other, as illustrated in Figures 3-2 and 3-3. The difference in diffusion
coefficients increases moderately with increasing temperature, with the
maximum divergence occurring at 1200 C. At these higher temperatures,
diffusivities are moderately smaller in oxidizing ambient than inert,


2.3 Secondary Ion Mass Spectroscopy 45
2.3.1 Determination of the Ge Depth Profile in SiGe Structures 50
2.3.2 Determination of the Error in D 54
2.4 X-ray Diffraction 56
2.4.1 Overview 56
2.4.2 Optimization Procedures 61
2.4.3 Determination of Interdiffusivity of Superlattice Layers 62
2.4.4 Determination of Strain Relaxation 64
3 BEHAVIOR OF ANNEALED Si,.xGex SINGLE QUANTUM WELLS 67
3.1 Growth Parameters and Structure 68
3.2 Processing 69
3.2.1 Rapid Thermal Processing 69
3.2.2 Furnace Processing 72
3.3 Simulation of Diffusion 73
3.4 Results 79
3.4.1 Diffusivities and Activation Energies from SIMS/FLOOPS 79
3.4.2 Diffusion Behavior of Partially Relaxed Structures 84
3.4.3 Si1.xGex Single Quantum Well with Boron Marker Layer 85
3.4.4 Estimation of Fractional Interstitial Components of
Diffusion 89
3.4.5 TEM 95
3.5 Discussion 98
3.5.1 Diffusivities of Fully-Strained Structures 98
3.5.2 Diffusivities of Partially-relaxed Structures 114
3.5.3 Misfit Dislocation Effects 116
3.5.4 Fractional Interstitial Components from Marker Layer
Experiments 121
3.6 Conclusions 123
4 BEHAVIOR OF ANNEALED ASYMMETRICALLY STRAINED Si/Sij.xGex
SUPERLATTICES WITH Si,.xGex BUFFER 126
4.1 Growth Parameters and Structure 127
4.2 Strain State 129
4.3 Processing 131
4.4 Simulation of Diffusion 132
4.5 Results 132
4.5.1 SIMS/FLOOPS 132
4.5.2 High Resolution Xray Diffraction 135
4.5.2.1 Diffusivities 135
4.5.2.2 Strain relaxation 139
4.5.3 TEM 141
4.6 Discussion 147
4.6.1 Diffusivities Determined from SIMS and FLOOPS 147
Vll


202
6.2.2 Experimental
Diffusion coefficients and an activation energy for diffusion of Si,.
xGex/Si SQWs were extracted for the temperature range 1000 to 1200 C in
inert ambient.
Diffusion coefficients spanning a larger temperature range than any
previous study and with values covering five orders of magnitude were
extracted for Si,.xGex/Si SQWs.
Diffusion coefficients and an activation energy for diffusion of Si,.
xGex/Si SQWs were extracted for temperatures 900 to 1200 C in oxidizing
ambient.
Diffusion coefficients and an activation energy for diffusion of Si,.
xGex/Si SQWs were extracted for temperatures 1100 and 1200 C in nitriding
ambient.
It was determined that the diffusion coefficients at constant
temperature for SQWs were independent of time in inert, oxidizing and
nitriding ambients.
A fractional interstitial component of diffusion, f,, for SQWs was
estimated for a temperature range 900 to 1200 C from oxidizing experiments.
Diffusivities of initially partially relaxed SQWs were extracted over a
temperature range 900 to 1200 C, for a wide variety of times in inert,
oxidizing, and nitriding ambients.


6
grown. The lattice mismatch between Si and Ge is = 4.2% with Ge having the
larger lattice parameter. Strain energy plays a critical role in band alignment
and energy gap values. The critical thickness for pseudomorphic growth
decreases rapidly with increasing Ge content. For example, a capped layer
O
with Ge composition of x=0.1 has a critical thickness of -650 A, while at Ge
o
composition x=0.5 the critical layer thickness reduces to -30 A (Figure 1-4).
Figure 1-4. Critical thickness versus germanium fraction for Sii_xGex films on
a Si substrate. Curve 1 is for Si-capped material, while curve 2 is for uncapped
material [Jai94].
S!.xGex has an indirect band gap which spans the 0.85 to 1.35 |im range.
The energy gap is different for the unstrained bulk alloy and coherently
strained alloy. The energy gap is dependent upon both the Ge content and the


52
1023 E~
cT
E
o
c 1021
o
|
c
£ 10*
o
o

a
10
10
19
I I
J I I I I I I I L l I I I I I I I I l
0.1 0.2 0.3 0.4 0.5 0.6
Depth (pm)
Figure 2-10. Ge concentration profile determined from SIMS for sample
structure SL/SiGe.
Figure 2-11. Ge concentration profile determined from SIMS for sample
structure SL/Si.


39
Layered Semiconductor Sample
Cross Section
Plan-view
Figure 2-4. Schematic of TEM views. Both cross-sectional and plan view of
the semiconductor sample can be obtained.


13
process and can glide through a double/single kink motion. This movement
allows propagation of misfit dislocations [Kas95, Jain94].
aSi (a) (b)
Figure 1-8. Evolution of a misfit dislocation at the Si and Ge interface, (a) an
isolated Ge layer (gray), and an isolated Si layer (white) of smaller lattice
constant, aSi; (b) the Ge layer is compressively strained in the parallel direction
to match the Si substrate lattice constant to produce tetragonal distortion; (c)
extra lattice planes are inserted as misfit dislocations as the Ge layer relaxes
towards its original lattice constant.
Heterostructures used in device applications mentioned in Section 1.1
contain Si^Ge* layers that are generally metastable with regard to misfit
dislocation formation, due to either layer thickness or growth temperature.
These heterostructures tend to relax through the injection and propagation of
misfit dislocations at the Sij.xGex/Si interfaces when subjected to high


LIST OF REFERENCES
Bar84
Bar90
Bar78
Bau96
Bea85
Ben87
Blo93
Bor88
Bou86
Bou96
Cra75
Cow96
Cul78
Barbuscia, D., Inter. Electron. Dev. Meeting 84, 757 (1984).
Baribeau, J.M., Pascual, R., & Saimoto, S., Appl. Phys. Lett. 5Z,
1502 (1990).
Bartels, W.J., & Nijman, W.. I. Crystal Growth 44,518 (1978).
Bauer, G., & Richter, W., eds., Optical Characterization of
Epitaxial Semiconductor Layers. (Springer-Verlag, Berlin, 1996).
Bean, J.C., Fiory, A.T., Hull, R. & Lynch, T.R., Proc. of the 1st
Inter. Svmp. on Si MBE 85-7.385 (1985).
Benninghoven, A., Rudenauer, F.G., & Werner H.W., Secondary
Ion Mass Spectrometry: Basic Concepts. Instrumental Aspects.
Applications, and Trends. (J. Wiley and Sons, New York, 1987).
Blchl, P.E., Smargiassi, E., Car, R., Laks, D.B., Andreoni, W., &
Pantelides, S.T., Phvs. Rev. Lett. 70.2435 (1993).
Borg, R.J., & Dienes, G.J., An Introduction to Solid State
Diffusion. (Academic Press, San Diego, 1988).
Bouchetout, A.L., Tabet, N., & Monty, C., Mat. Sci. Forum 10-12.
127 (1986).
Boucaud, P., Wu, L., Guedj, C., Julien, F.H., Sajnes, L,
Campidelli, Y., & Garchery, L., I. Appl. Phvs. 80.1414 (1996).
Crank, J., The Mathematics of Diffusion. (Oxford University
Press, Oxford, England, 1975).
Cowem, N.E.B., Kersten, W.J., de Kruif, R.C.M., van Berkum,
J.G.M., de Boer, W.B., Gravesteijn, D.J., & Bulle-Liewma, C.W.T.,
Proc. of the Electrochem. Soc. 96-4.195 (1996).
Cullity, B.D., Elements of X-ray Diffraction. (Addison-Wesley,
Reading, MA, 1978).
215


Relative Intensity (cps)
104 f
1000 -
100 -
10 -
33.6
33.8
34 34.2 34.4
Omega (degrees)
34.6
34.8
vi
CO
Figure 5-3. X-ray diffractometer scans of the SL/SiGe superlattice peaks about Si(004) with increasing anneal times in
inert ambient. The diffusion coefficients have been obtained from the decay of the SL peak marked '1st order'.


136
where I0 is the initial intensity of the satellite peak and D is a composition-
independent diffusion coefficient. By measuring the decay in the intensity of
the first order satellite with time, the diffusion coefficient can be extracted.
This was the procedure used to extract effective diffusion coefficients from
HRXRD scans taken of SL/SiGe.
For the purpose of measuring the intensity of the 1st order satellite
peak of SL/SiGe, symmetric scans only were needed. As described in Section
2.4.1, symmetric scans are those in which the reflection plane is identical to
the substrate/growth plane. The scans of SL/SiGe were performed using the
(004) reflection plane, the substrate/growth plane direction. Scans were taken
at (0=34.5 and 20=69.1, the values at which the Si(004) peak is at maximum
intensity, co-20 scans were taken over a 4 range of to, with a step size of
Table 4-2. Extracted diffusivities for SL/SiGe using HRXRD.
T (C) D^fcmVs) DGex(cm2/s) Dc,Nlt(cm2/s)
900 1.33xl017 1.23xl017 2.39xl017
1000 3.21xl016 1.32x1 O'16
0.00025 and time per step of 4s, resulting in 16001 steps. co-20 scans were
taken of the as-grown SL/SiGe structure as well as for samples annealed at 900
C for 4, 6 and 8 min and at 1000 C for 1, 2 and 3 min. Examples of resulting
scans are shown in Figure 4-3, taken at increasing anneal times for a constant
anneal temperature of 1000 C in inert ambient.


43
magnification of xl00,000 (100k). There are clearly 15 periods with abrupt,
sharp interfaces at the top periods. The periods towards the Si,.xGex buffer are
increasingly smeared. This could be due to the focus of the TEM or could be
due to true lack of abruptness of the interfaces. Also, the thicknesses of the
dark colored Si layers decrease towards the buffer, while the thicknesses of the
light colored Sij.xGex layers increase. The periodicity of the SL layers is lost.
There are no visible dislocations (see below). Figure 2-6b shows the as-grown
structure of SL/Si at a magnification of x50k. There are 16 periods with abrupt
interfaces and constant thicknesses. However, Figure 2-6b shows a threading
dislocation running from the beginning of the MQW to the surface, across the
layers. This is one visible dislocation which is indicative of other threading
dislocations throughout the entire structure. It is nearly impossible to get an
estimate of the dislocation density from XTEM images. XTEM investigates a
very small area of the sample and is therefore statistically unmeaningful for
dislocation densities below 10' cm'2. Also, in cross-section only half the
dislocation is visible due to the direction of the view, so it is impossible to
know exactly how many dislocations are present within the thickness of the
sample [Iye89]. Therefore, even in cross-section images such as Figures 2-6
and 2-7, where there are no visible dislocations, there can indeed be
dislocations present in the structure.
Figure 2-7a shows the cross sectional TEM micrograph of SQW/MBE at
a magnification of xlOOk. The surface is somewhat rough as is the interface


144
The cross sectional image of SL/SiGe annealed in oxidizing ambient at
850 C for 8 min exhibits threading and misfit dislocations at the
substrate/buffer interface that propagate into the substrate layer (Figure 4-5).
It is hard to conclude from the image whether the dislocations also propagate
into the buffer layer, but it seems that they do not. The minimal view of the
Si1.xGex/Si multilayers shows no threading or misfit dislocations. It can be
tentatively stated that most of the relaxation occurs in the Si substrate and not
in the Si1.xGex buffer or Sij_xGex/Si layers. This is probably due to differences
in Poisson's ratio and hardness of the two materials.
Plan view images were taken of samples annealed at the extremes of
the temperatures used in these experiments, 850 and 1000 C. The misfit
dislocation density increased dramatically for SL/SiGe annealed at 850 C for 8
minutes (Figure 4-6a). The misfit dislocations occurred an average of
approximately 2 pm apart. There was also an origination of curved segments
not seen in the as-grown materials. These are most likely expanded threading
dislocations seen from an overhead perspective. In the micrograph shown in
Figure 4-6a there were sample preparation artifacts, light square areas, which
can be attributed to the etching process. These artifacts did not, however,
affect the ability to examine the dislocation density of the structure. For the
sample annealed at 1000 C for 2 minutes, the dislocation density was very
similar to that at 850 C (Figure 4-6b), and once again, noticeably greater than


Table 3-7. Comparison of diffusivities of SQW/MBE and SQW/VPE in inert and oxidizing ambients.
T(C)
time
(min)
Inert
Oxidizing
Nitriding
D:SQW/MBE
(cm2/s)
D:SQW/VPE
(cm2/s)
D:SQW/MBE
(cm2/s)
D:SQW/VPE
(cm2/s)
D:SQW/MBE
(cm2/s)
D:SQW/VPE
(cm2/s)
900
330
1.70xl0'17
2.18xl017
2.32x1017
2.53xl017
-
-
1000
43
3-OOxlO'16
3.94xl0"16
3.028x1016
3.29x1016
-
-
1100
1
5.20xl014
9.00x1014
1.14xlOu
4.72xlOM
1.46x10 14
1.73xl014
1200
1
2.38xl012
1.54xl012
2.47x1014
2.73x1013
1.10x1013
1.40x1013


113
therefore diffusion is temperately retarded under interstitial supersaturation.
This leads to the conclusion that interstitials play a minimal role in diffusion
at all temperatures and at high temperature, injected interstitials may even
combine with vacancies, reducing the vacancy concentration and retarding
vacancy-dependent diffusion.
The activation energy of 5.27 eV0.11 (SQW/MBE) calculated for
interdiffusion in oxidizing ambient is the first activation energy reported for
S!.xGex/Si interdiffusion under interstitial injection. This activation energy
is similar to that in inert ambient and reinforces the belief that interstitials do
not have a significant affect on the interdiffusion process.
The activation energy of 3.27 eV0.10 calculated for the interdiffusion
in nitriding ambient is the first activation energy of interdiffusion under
vacancy injection reported for a Si/Si^Ge,, SQW. This activation energy is
approximately 2eV lower than that for diffusion in inert ambient as well as
oxidizing ambient. At anneal temperatures 1100 and 1200 C, the diffusion
profiles in a nitriding ambient show significant retardation compared to
diffusion profiles in inert and oxidizing ambients (Figure 3-14b). Diffusivities
extracted are much lower and not within error of those for inert and
oxidizing ambients (Figures 3-2 and 3-3). This indicates that interstitials are
the dominant diffusing species and that injected vacancies recombine with
intrinsic interstitials to lower the interstitial concentration and retard
diffusion. These results are opposite to those found from oxidizing
experiments, which predicted that vacancies are the dominant diffusion


57
All scans were taken using a Phillips high resolution XRG 3100 five
crystal diffractometer. This instrument consists of four main parts: an x-ray
source, a monochromator, a goniometer and a detector. This system setup
has been previously described in detail by Krishnamoorthy [Kri95] and will be
summarized here.
A generator operating at 40kV and 40mA creates electrons at a cathode.
These electrons are accelerated through a field and bombard a Cu target anode
emitting CuKal x-ray radiation with broad angular and wavelength ranges.
The x-ray beam is monochromatized and collimated prior to impingement
upon the sample using a four crystal Bartels monochromator/collimator
setup shown in Figure 2-16. The x-ray beam, upon leaving the
monochromator/collimator, impinges on the sample crystal which is
mounted on the stage of the goniometer. The goniometer controls the x, y, z,
tilt (\f/) and rotation (<|>) positions of the sample.
Monochromator/collimator
1
Sample
Detector
J
Figure 2-16. Schematic of the monochromator/collimator. X-rays impinge
the first crystal and are subsequently collimated and monochromated by
crystals 2 through 4, after which they impinge on the sample.


Ill
1012
1013
1014
10-15
1016
10'17
1200 C 1100C 1000C 900 C
!
1 1 1

-
z

least
_
X
2nd least
Z
3
E
2nd most
j
A
-

most

1
f
"5
r
-!
_i till n i
5
r
E
-
I
_
, 1
_l l l 1 l l l i 1 l 1
1 1
£
J- 1
6.5 7 7.5 8 8.5 9
1/T*104(K1)
Figure 3-13. Plot of diffusivities of all anneal times in inert ambient for each
temperature for SQW/MBE. Error bars show that at each temperature all
diffusivities are within error of each other.


139
regardless of sample thermal processing history, therefore this peak was used
to standardize all scans. The ratio of the intensity of the (004) substrate peak
in the scans of the annealed samples to the intensity of the (004) substrate
peak of the as grown structure was used to standardized the zeroth order and
higher order satellite peaks in the scans of the annealed samples. This
standardization technique results in a error in intensity measurement that is
negligible.
4.5.2.2 Strain relaxation
X-ray double crystal diffractometry allows the accurate determination of
the orientation and size of the unit cell of an epilayer compared to the unit
cell of its substrate. When a heteroepitaxial layer is grown on a single crystal
substrate, two diffraction peaks may be recorded with the diffractometer, one
from the substrate and one from the epilayer. The angular separation of these
two peaks allows the calculation of the difference in lattice spacing of the two
layers and therefore, ultimately, the strain. The method of extraction of
lattice constant values is described in detail in Section 2.4.4. This method was
employed to extract the change in lattice constants with increasing anneal
time of SL/SiGe in inert, oxidizing, and nitriding ambients. The entire Sij.
xGex multilayer structure was considered in this analysis to be the 'epilayer', as
discussed above. The angular separation of this peak and the substrate peak
was the main parameter used in calculating the overall strain. In this
particular analysis, quantitative calculation of changing lattice constants with
anneal time was used as a qualitative indication of changing strain.


12
where G is the shear modulus, assumed to be the same in the film and
substrate, b is the Burger's vector of the dislocation, a is Poisson's ratio, and
2A is the dislocation length per unit area of the epitaxial layer. When
Estiam^csiocation/ epitaxial layer is fully strained and dislocation free,
otherwise known as pseudomorphic. When Estrain=Edlslocahon, the layer
thickness is at a critical thickness, termed hc (Section 1.1). Above this critical
thickness, Edlslo<;atlon>Estrain and it is energetically favorable to relieve strain
through dislocation formation.
Epilayer strain is most often relieved through the growth and
propagation of misfit dislocations. Misfit dislocations can be nucleated
homogeneously, through dislocation loops or half loops present at the surface
or an interface, or heterogeneously, through impurities or inclusions
incorporated during the growth process. A misfit dislocation is commonly
viewed as the creation of extra planes of atoms in the lattice structure (Figure
l-8c).
Geometrically, a misfit dislocation cannot terminate within the bulk of
a crystal; it must either form a closed loop (terminate upon itself), join with
another line defect, or end at the nearest free surface. Misfit dislocations
rarely have sufficient propagation velocity to span across the entire lateral
dimension of the crystal, thus they generally terminate by intersecting with a
threading dislocation (Figure 1-9). Threading dislocations extend from the
surface of the epitaxial material to the substrate, traversing through any
intervening strained layers. They exist due to imperfections in the growth


30
for Si self-diffusion. Is there a break in the Arrhenius line where the
mechanism changes from interstitial to vacancy at lower temperature?
Seeger and Chik [See68] were the first to propose that the diffusion takes place
via a dual interstitial and vacancy mechanism. They claimed that diffusion is
dominated by interstitials at high temperatures and vacancies at low
temperatures with cross-over at -1050 C. Dorner et al. [Dor84] observed a
break in the curve at about 1050 C but Bouchetout et al. [Bou86], Hettich et al.
[Het79], and McVay and Ducharme [McV74] observed none. Fahey et al.
[Fah89b] were the only researchers to actually report the fraction of diffusion
proceeding via an interstitial or vacancy mechanism. Their study, however,
was only for the single temperature 1050 C, the temperature of the disputed
break. At this temperature they proposed a mechanism with 30 to 40%
interstitial assisted diffusion and 70 to 80% vacancy assisted diffusion. There
are several issues associated with this conclusion: (1) they assume a kickout
mechanism as opposed to a dissociative mechanism for interstitial
movement (2) they do not address the question of the Arrhenius break and
(3) the samples underwent oxidation anneal before having the oxynitride
layer deposited and then annealed. It is obvious that more studies are needed
to verify the relative contributions as well as exact mechanism of vacancy and
interstitial movement of Ge atoms in Si.
1.5.1.3 Diffusion studies of Si^GeySi heterostructures
There have been many studies of the interdiffusion in Si/Si1.xGex/Si
single quantum well (SQW) structures, (SimGen)p superlattices and Si/Si1.xGex


112
Figure 3-14. Comparison of Ge SIMS profiles in inert, oxidizing and nitriding
ambients for SQW/MBE. Sample annealed at (a) 900 C for 330 min in inert
and oxidizing ambient and (b) 1200 C for 2 min in all three ambients.


201
6.1.3 Strain Effects
Diffusion coefficients of initially fully strained samples were
equivalent to those simulated for initially partially relaxed samples after
anneal in both inert and oxidizing ambients. Strain relaxation and increased
dislocation densities seemed to have an insignificant effect on Ge diffusion in
Si/Si^GeySi SQWs. Diffusivities calculated for SLs with a Sij.xGex buffer and
for SLs with a Si buffer were equivalent. Both of these results led to the
conclusion that strain has a very minimal effect on diffusion.
Cross sectional and plan view TEM micrographs showed that in the
SQWs and the SL with the Si1.xGex buffer, dislocation densities increased
noticeably after anneal compared to as-deposited values. The SL with the
Sij.xGex buffer showed dislocation formation and propagation into the Si
substrate and cap layers only, with the Sij.xGex/Si multilayers relatively
dislocation-free. The SL with the Si buffer showed a very small increase in
dislocation density after anneal compared to its as-grown value.
6.2 Contributions
6.2.1 Modeling
A successful, simple model was developed within the Florida Object
Oriented Process Simulation software which effectively simulated the
diffusion behavior of both SQW and SL material in inert, oxidizing, and
nitriding ambients.


21
mechanism, describes the movement of an impurity atom from a
substitutional site to an interstitial site, leaving behind a vacancy (reverse
reaction in Figure 1-12). The mechanism is both interstitial- and vacancy-
dependent. The diffusion equation for the impurity, in this case Ge, is given
as [Had95]:
(1-9)
where Cq^ is the concentration of impurities occupying substitutional sites,
Cv and Cv* are the actual and equilibrium concentrations of vacancies,
respectively, p is the hole density, and r\ is the intrinsic carrier concentration,
is described by:
(MO)
where f, is the fraction of diffusion that occurs via interstitials, and D/ is the
diffusivity of the interstitial impurity in charge state j.
o o o o o
gmo^r o o
ero o o o
o o o o o
o o o o
o o o o o
Figure 1-12. The Frank-Tumbull (dissociative) mechanism. The black atom
represents the impurity atom.


84
3.4.2 Diffusion Behavior of Partially Relaxed Structures
The SQW/MBE and SQW/VPE structures have Sij.xGex layers which
are greater than critical thickness and TEM analysis confirms that these layers
are partially relaxed through the presence of dislocations prior to any high-
temperature processing. The initial stage of high-temperature treatment of
these structures could cause additional strain relaxation by formation and
propagation of misfit dislocations as well as strain-enhanced diffusion,
thereby affecting the diffusivity. To address this issue, diffusivities of
structures which were initially partially relaxed were compared to the
diffusivities reported in Table 3-1 for the as-grown structures (for this
analysis, assumed to be fully strained).
The annealed SQW/MBE samples (Table 3-1) were used to represent
the partially relaxed structures, and their SIMS profiles were used as the
initial profiles in the FLOOPS simulations. For example, the SIMS profile of
the SQW/MBE sample annealed at 900 C for 330 min was used as the initial
'partially relaxed' profile and diffusion was simulated for 650 min. A
diffusivity was extracted by fitting the resulting simulated profile to the SIMS
profile of the SQW/MBE sample that had been annealed at 900 C for 980
min. This method was used to extract diffusivities for all SQW/MBE samples
annealed in inert, oxidizing, and nitriding ambients. The values extracted for
each temperature and time are given in Table 3-3. Values in italics represent
the diffusivities of the as-grown structures after their first anneal and are
included for purposes of comparison. A value for the sample annealed in


219
New97
Nyl97
Osa95
Oda97
Pac90
Pac91
Pai95
Pel91
Peo86
Pet91
Pre95
Pro90
Pru97a
Pru97b
Qas98
Newey, J.P., Robbins, D.J., & Wallis, D., Proc. of the 11th Inter.
Conf. on Secondary Ion Mass Spectrometry (SIMS XD 11.979
(1997).
Nylandsted Larsen, A., & Kringhoj, P., Physica Scripta T69.92
(1997).
Osada, K., Zaitsu, Y., Matsumoto, S., Yoshida, M., Arai, E. & Abe,
T., T. Electrochem. Soc. 142.202 (1995).
Oda, K., Ohue, E., Tanabe, M., Shimamoto, H., Onae, T., &
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Meeting 14. 791 (1997).
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Paine, A.D.N., Marooka, M., Willoughby, A.F.W., Bonar, J.M.,
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196-201. 345 (1995).
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Tech. Lett. 10,807 (1998).


140
A Ge content of x=0.15 for the Si^Ge,, superlattice layers was estimated
originally using RBS. However, the peak in HRXRD which was used to
calculate strain relaxation represented the average epilayer composition of the
combined SL multilayers, which, from Section 4.2, was determined to be
x=0.05. Using Equation 1-1 in section 1.1.1, the fully-relaxed lattice constant of
the Si095Ge005 cubic unit cell is a1=al,=aJ=0.5441 nm, with a total cell volume of
0.1611 nm3. When the Si095Ge005 'epilayer' is grown on a Si0g5Ge015 buffer
layer, the Si095Ge005 'epilayer' is under tensile strain in the parallel direction
so that the fully strained value of aM is 0.5461 nm, identical to the lattice
constant of the Si085Ge015 buffer. At the same time, the unit cell becomes
tetragonally distorted such that a*ax. The total volume of the Si095Ge005 unit
cell must remain the same, however, so that the fully strained value of ax is
0.5402 nm. These theoretical values of a/; and ax for the epilayer will be
compared to those calculated through HRXRD scans of the as grown SL/SiGe
structure.
All scans mentioned in this study underwent optimization procedures
detailed in Section 2.4.2. Asymmetric scans are adequate to calculate the
parallel and perpendicular lattice constants, and, ultimately, the strain.
Symmetrical scans can be performed to obtain a perpendicular lattice constant
that can be used as a check against the symmetrical scan value. Asymmetric
scans were performed in this investigation using the (115) reflection plane.
Scans were taken at an go of -31.5 and an to+ of -63.2 and a 20 value of -95.0.


117
Qualitatively, at all anneal temperatures the boron marker layer diffused
farther in oxidizing ambient than in inert ambient (Figure 3-5). This result
indicates that interstitials are transported through the dislocated Si and Sij.
xGex layers, and reach the buried B layer to enhance its diffusion. It can
therefore be concluded that interstitials injected through the surface oxidation
process also are available to aid in the Ge diffusion across Si and Si1.xGex
layers.
Quantitatively, this conclusion requires further investigation. Using
FLOOPS, the simulated profiles and experimental SIMS profiles should fit
perfectly if and only if (1) the FLOOPS model of B diffusion in Si is perfect and
(2) the dislocations capture no interstitials. The first assumption is incorrect:
while the FLOOPS model for B diffusion in Si is the most accurate of
published models, it is restricted by the experimental data reported in the
literature to date. Differences in FLOOPS predicted profiles and experimental
profiles would therefore be expected even in the case of inert diffusion with
no point defect capture by dislocations. This deviation can be expressed as
[Dmertiactualj/D^iFLOOPS)]. Additionally, the diffusivity of boron, Dp, only
enters into the diffusion equations through the product Dt, so that the
deviation can be expressed with respect to the results listed in Table 6 as the
ratio [t^CFLOOPSJ/t^rtfactual)] when simulations are run with the default DB
value, which was done in this experiment. This time ratio represents a
'calibration' of the D*, indicating the accuracy of the experimental set-up and
the simulation model.


CHAPTER 6
CONCLUSIONS AND FUTURE WORK
This dissertation has focused on diffusion behavior of Sij.xGex/Si as a
function of layer structure, processing temperature and processing time. In
particular, the roles of vacancy and interstitial point defects in the diffusion
process have been investigated. Section 6.1 will summarize the conclusions
reached from this research, Section 6.2 will state the original contributions of
this work to the fast-growing interest in diffusion in Si^Ge,,, and Section 6.3
will offer suggestions for areas of continued research.
6.1 Conclusions
6.1.1 Single Quantum Well Structures
In Chapter 3, the diffusion behavior of single quantum wells of Si,.
xGex/Si over anneal temperatures 900 to 1200 C was investigated and results
were presented. The extraction of diffusion coefficients using SIMS and
FLOOPS yielded activation energies of ~5.8 eV, 5.0 eV, and 3.0 eV for diffusion
in inert, oxidizing, and nitriding ambients, respectively. No difference in
diffusion behavior was seen between SQW structures grown by molecular
beam epitaxy and vapor phase epitaxy.
The diffusivities extracted for diffusion in inert ambient agreed well
with values previously reported in literature. The calculated activation
197


77
f D-
1 d;+Dv
with fv=l-fi
(3-7)
At a given temperature f, remains the same under any ambient and is not
dependent upon point defect supersaturation.
Values of C,/C* and Cv/Cv* for each temperature under either
oxidizing or nitriding ambients were extracted from diffusion data reported in
literature. By assuming phosphorous to have an f,=l, phosphorous diffusion
data was fit to extract C,/C* and Cv/Cv* values under oxidizing conditions.
Similarly, by assuming antimony to have an fj=0, Sb diffusion data was fit to
extract C,/C,* and Cv/Cv* values under nitriding conditions. The previous
assumptions regarding fj are broadly accepted in the Si diffusion community
[Fah89a, Hu94]. Equation 3-4 was then solved for the concentration of the
dopant, using the value of D calculated from Equation 3-5. The resulting
profile was compared to the experimental profile, and the ratio of D,* and Dv*,
hence fv was adjusted until the profiles matched as judged by a Gaussian fit.
At this point a good estimate of f, was made. It is important to note here, as in
Section 1.4, that f, values extracted for Ge diffusion employed the C,/C* and
Cv/Cv* values from fitting the phosphorous and antimony diffusion data.
The approach used in all FLOOPS simulations in this dissertation was
to model the Si,.xGex alloy regions as Ge dopant in the Si lattice. In this case,
there are five system species: a Si substitutional (Sig), a Ge substitutional (Ges),
a Si interstitial (1$), a Ge interstitial (1^), and a lattice vacancy (V). Because
there are five species, five equations are needed to completely describe the


99
200nm
Figure 3-6. Cross sectional view TEM micrographs of structure SQW/MBE
after annealing in inert ambient at (a) 1000C for 43 min and (b) 1200C for 1
min.


216
Dea65 Deal, B.E., & Grove, A.S., I. Appl. Phys. 26/ 3770 (1965).
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11
mobilities in these Si^Ge,, structures are almost five times higher than in the
corresponding Si structures.
1.2 Strain and Strain Relaxation in SiGe Heterostructures
Strain develops when an epitaxial layer of a certain lattice parameter,
ae, is grown on a substrate of a differing lattice parameter, as. When ae epitaxial layer is said to be under tensile strain. When ae>as the layer is under
compressive strain. Regardless of the Ge composition, x, Sij.xGex epitaxial
layers grown on a Si buffer are always under compressive strain. As
schematically depicted in Figure l-8b, the cubic Si1_xGex lattice theoretically is
compressed so that the parallel lattice parameter, a, matches that of the cubic
Si lattice. Because the total volume of the Si^Ge,, unit cell is considered
constant, the perpendicular lattice parameter, a, increases, rendering the Si,_
xGex unit cell no longer cubic but tetragonal (termed tetragonal distortion).
The Sij.xGex monolayers are grown on top of each other this way and the
strain energy stored in the dislocation-free film, Estrain, is described by:
Estrain=Mhe2 (1-3)
where M is the biaxial elastic modulus of the epilayer, e is the strain and h is
the thickness of the epilayer. The energy necessary to generate a dislocation,
^dislocation' is described by:
E
dislocation
Gb2
47t(l-a)X lb,
d-4)


96
Both plan view and cross section can only provide qualitative defect
density data instead of quantitative results in the case of multiple deposited
epilayers. In plan view, the image is taken from the top of the sample surface,
so the interfaces of every multilayer are not visible. There may be
dislocations at interfaces that are buried from view using the plan view
perspective that make it impossible to precisely state the number of
dislocations present in an entire unit volume. Similarly, it is nearly
impossible to get a meaningful estimate of the number of dislocations from
cross-sectional view. XTEM only investigates a very small area of the entire
sample and is therefore not statistically significant. More importantly, the
direction of view used in these and most cross sections is the (110) direction,
so that half the dislocation is hidden while the other half lies parallel to the
interface, making it impossible to observe whether one or more dislocations
are contained within the thickness of the sample.
As discussed in Section 2.2.3, the as-grown SQW/MBE and SQW/VPE
exhibited strain relief through an array of misfit dislocations spaced an
average of approximately 1 pm apart, however, no threading dislocations
were present in cross sectional images of the as-deposited structures (Figure 2-
7). As stated above, this does not necessarily mean that there were no
threading dislocations, there was just no conclusive evidence of them. The
precise source of the misfit dislocations is unclear at present but could most
likely be due to the high growth temperature of 700 C.


129
4.2 Strain State
The diffusion coefficient for Si^GeySi has been thought by some
investigators to be a sum of strain and composition contributions [Cow96]. If
this theory is indeed true, it is important to completely determine the strain
state of a system under investigation in order to correctly interpret its
diffusion behavior. Initial characterization using SIMS, TEM and RBS
enables the general structure and composition of a system to be defined. High
Resolution Xray Diffraction (HRXRD) and FLOOPS together provide more
specific quantitative data which can correlate change in strain and diffusivity.
This progression of characterization techniques was used in this study to first
define the initial structure, composition and strain state of both SL/SiGe and
SL/Si (to be discussed in Chapter 5) and second to define the final strain state
and diffusion profile after thermal processing of these materials. Ultimately,
the diffusion and strain relaxation results determined for the ASL grown on a
Si1.xGex buffer will be compared to those of the ASL grown on a Si buffer to
establish independently the influence of strain distribution on the
interdiffusion. The general structure and composition of SL/SiGe as grown
have already been discussed, therefore it is important to now consider the
particulars of the initial strain state of the structure.
The structure SL/SiGe was originally intended to be a symmetrically
strained superlattice (SSL), in which the relaxed Sij.yGey buffer layer has an
intermediate lattice parameter between those of Si and the Sij.xGex SL layers.
This results in Si and Si^Ge,, layers which are altematingly under tensile and


93
Table 3-5. Fractional interstitial components and modified diffusivities and
point defect supersaturations determined for diffusion in inert ambient.
T(C)
900
1000
1100
1200
time
(min)
D(cm2/s)
D*(cm2/s)
C,/Q*
cv/cv*
f.
330
1.70X1017
1.28xl0"17
3.33
1.00
0.140
1.70xl0"17
2.38X10"17
3.33
0.330
0.127
980
2.29xl017
1.28xl0"17
6.64
1.00
0.140
2.29xl017
2.38X10"17
6.52
0.115
0.127
1532
2.08xl017
1.28xl0"17
5.46
1.00
0.140
2.08xl017
2.38xl0"17
5.67
0.176
0.127
2206
2.08xl017
1.28X10"17
5.46
1.00
0.140
2.08X1017
2.38xl0"17
5.67
0.176
0.127
43
3.00X1016
2.82X10"16
2.09
1.00
0.059
3.00X1016
4.19X10"'6
2.09
0.480
0.148
55
3.29xl016
2.82xl0"16
3.55
1.00
0.059
3.29xl016
4.19X10"16
3.78
0.265
0.148
87
3.29xl016
2.82X10"16
3.55
1.00
0.059
3.29xl016
4.19xl0"16
3.78
0.265
0.148
125
3.00X1016
2.82X10"16
2.09
1.00
0.059
3-OOxlO16
4.19X10"16
2.09
0.480
0.148
1
5.20x10
7.77x10
-
1.00
0.010
5.20x10
2.19X10"13
5.69
0.176
0.011
2
7.93x10
7.77x10
3.00
1.00
0.010
7.93x10
2.19X10"13
3.00
0.330
0.011
3
6.69x10
7.77x10
-
1.00
0.010
6.69x10
2.19xl0"13
3.72
0.269
0.011
4
8.60x10
7.77x10
11.8
1.00
0.010
8.60x10
2.19X10"13
2.74
0.365
0.011
1
2.38xl012
-
0.700
1.00
-
2.38xl012
1.70X10"12
0.700
1.43
0.045
1.5
6.00x10"13
-
-
-
-
6.00xl0"13
1.70X10"12
4.80
0.208
0.033
2
1.08xl0"12
-
-
-
-
1.08xl0'12
1.70X10"12
1.71
0.585
0.045
3
1.08xl0"12
-
-
-
-
1.08xl0",J
1.70xl0"12
1.71
0.585
0.045


175
5.5.2.2 Strain relaxation
The method of extraction of strain values is described in detail in
Sections 2.4.4 and 4.5.2.2. This method was employed to extract the change in
strain with increasing anneal time of SL/Si in inert, oxidizing, and nitriding
ambients.
A Ge content of x=0.15 for Si^Ge* superlattice layers was estimated
originally using RBS. As described in Section 4.5.2.2, the peak in HRXRD
which was used to calculate strain relaxation represents the average epilayer
composition of the combined SL multilayers, which was determined to be
0.05. Using Equation 1-1 from Section 1.1.1, the fully relaxed lattice constant
of the Si0 95Ge005 cubic unit cell is a1=a=a1=0.5441 nm, with a total volume of
0.1611 nm3. When the Si095Ge005 'layer' is grown on a Si buffer layer, the
Si0 95Ge005 is compressed in the parallel direction so that the fully strained
value of a is 0.5431 nm. At the same time, the unit cell becomes tetragonally
distorted such that a*ax. The total volume of the Si095Ge005 unit cell must
remain the same, however, so that the fully strained value of ax is 0.5461 nm.
These theoretical values of a/; and ax for the epilayer will be compared to
those calculated through HRXRD scans of the as grown SL/Si structure.
All scans mentioned in this study underwent optimization procedures
detailed in Section 2.4.2. Asymmetric scans are adequate to calculate the
parallel and perpendicular lattice constants, and, ultimately, the strain.
Symmetrical scans can be performed to obtain a perpendicular lattice constant


102
The enhancement of diffusion at high concentrations of dopant atoms
has been shown to manifest itself in a shape of the depth profile that is flatter
at its peak and has steeper shoulders than the Gaussian that is expected for a
concentration-independent diffusion coefficient, assuming that the initial
profile is Gaussian [Gos93]. In this study, selected SIMS profiles of Ge
obtained from anneals performed at 900 C and 1000 C show a flatter peak
and slightly more rectangular shape than the Gaussian FLOOPS profile
generated by a concentration-independent diffusivity (Figure 3-10). The flat
peak profiles could indicate a concentration-dependent diffusion coefficient at
these temperatures. There is a stronger possibility, however, that the flat
profiles at the lower temperatures are just manifestations of the maximum
allowable depth and concentration errors in SIMS measurement. This
conclusion is supported for two reasons: (1) There is no identifiable trend in
the flatness of the profiles with time and (2) profiles of samples with the same
thermal processing history obtained during SIMS operation on a different day
showed no peak flatness and were perfectly Gaussian. SIMS profiles obtained
from anneals performed at 1100 C and 1200 C do not show flat-peak,
concentration-dependent diffusion behavior at any anneal time. This may
only mean that at the longer Ge diffusion lengths resulting from these high
temperatures, the Sii.xGex well is no longer identifiable, so any concentration
dependency is unidentifiable. Cowem et al. [Cow96] have previously reported
enhanced diffusion at Ge concentrations of 30% and an anneal temperature of


155
studied. Diffusivities at anneal temperatures of 900 and 1000 C are
approximately one order of magnitude higher for SL/SiGe than for
SQW/MBE in both inert and oxidizing ambients. Diffusivities in nitriding
ambient cannot be compared since SQW/MBE was not annealed in NH3
ambient at 900 C and 1000 C. The activation energy for diffusion in inert
and oxidizing ambients is ~2.5 eV lower for SL/SiGe than for SQW/MBE. In
nitriding ambient, however, the activation energy of diffusion for SL/SiGe is
~1 eV higher than for SQW/MBE.
Table 4-4. Comparison of parameters of interdiffusion of SQW/MBE and
SL/SiGe.
SQW
SL/SiGe
EA:Inert
5.8 eV
3.14 eV
EA:Oxidizing
5.0 eV
2.43 eV
EA:Nitriding
3.0 eV
4.07 eV
DGenert :900C
2-OOxlO17 cm2/s
l.lxlO'16 cm2/s
Dj* :900C
l.OOxlO'17 cm2/s
3.46xl017 cm2/s
DGenert :1000C
3.00xl016 cm2/s
2.01xl015 cm2/s
Dj* :1000C
3.00xl016 cm2/s
2.13xl015 cm2/s
Disregarding possible equilibrium point defect concentration effects,
what other influences could be the cause of the different diffusion behaviors
of SQWs and SLs? One possible reason could be that the average Ge
composition of the superlattice layers, x=0.05, is substantially lower than the
Si085Ge015 layer of the SQW. This reason is unlikely, however, because
previous studies have reported diffusivities that have increased and


97
Cross sectional images, shown in Figure 3-6, were taken of SQW/MBE
samples annealed at 1000 C for 43 min and 1200 C for 1 min in inert ambient
and are shown at a magnification of x50k. In Figure 3-6a the substrate is
highly dislocated after processing at 1000 C for 43 min. Nearer to the surface,
where the Sij.xGex well lies, there are unusual artifacts which do not resemble
normal threading or misfit dislocations. They might be a result of sample
preparation. These obscure the layers so that no information on diffusion can
be obtained. In Figure 3-6b there are misfit dislocations along the interface as
well as threading dislocations from the substrate/buffer interface to the
surface, evidence that relaxation has occurred after processing at 1200 C for 1
min. Also, the S!_xGex layer is no longer clearly visible, so significant
diffusion has occurred.
Plan view images were taken of SQW/MBE samples annealed at the
extremes of the temperatures used in these experiments, 900 and 1200 C, and
are shown at a magnification of x20k. The misfit dislocation density
increased only slightly for SQW/MBE annealed at 900 C for 330 minutes
(Figure 3-7a). The distance between dislocations decreased to 0.5 pm from the
as-grown value of 1 pm. For the SQW/MBE sample annealed at 1200 C for 1
min (Figure 3-7b), the misfit dislocation density was very similar to that at 900
C, and once again, noticeably greater than that of the as-grown structure.
There was also an origination of curved segments not seen in the sample
annealed at 900 C or as-grown material. These were most likely expanded
threading dislocations seen from an overhead perspective. Oddly, plan view


27
1.4.2 Vacancy Injection (Nitride Growth)
As described in Section 1.4, it has been well-established that the
nitridation of the Si surface results in the injection of vacancies into the bulk.
The overall nitridation reaction that occurs is:
3Si + 4NH3 >Si3N4+6H2 (1-19)
In a variety of growth conditions, there is an initial fast-growth regime,
followed by a very slow growth regime in which the total thermal nitride
layer grows no thicker than approximately 4 nm [Hay82, Mos85a] regardless of
processing time. It is also important to note here that direct thermal
nitridation of a bare silicon surface results in nitride films with a substantial
amount of oxygen (the ratio of the concentration of nitrogen to the total
concentration of nitrogen and oxygen is approximately 50 %:
[N]/[N]+[O]=0.50) [Mog96, Mur79, Hay82]. Technically these films are
oxynitrides, yet in this dissertation they will be termed simply 'nitrides'.
Quantitatively, the supersaturation of vacancies produced by
nitridation of silicon in the range of temperatures used in this dissertation is
not as well documented as in the oxidation/interstitial injection case. Mogi
[Mog96] performed one of the most extensive investigations to date, and
found Cv/Cv*~4 resulting from thermal nitridation in NH3 for 1 hour at 910
C. His results will be used to model the dependence of interdiffusion on
vacancies.


29
Si and Ge are very similar in their elemental properties, thus it is
surprising that they differ so significantly in their self-diffusion mechanisms
and the defects present in thermal equilibrium. Unlike Si, there is very little
debate over the mechanism of Ge self-diffusion. Effects of hydrostatic
pressure [Wer85], dopant studies [Sto85] and calculations of interstitial
migration energies [Kho90] all conclude that diffusion occurs exclusively via
monovacancies. The work of Mitha et al. [Mit96] is the only investigation to
disagree, claiming that the smaller-than-expected activation volume opens
the door for possible interstitialcy and direct exchange contributions. They
imply, however, that these contributions would be relatively small. The
activation energy for Ge self-diffusion is ~3 eV, with a pre-exponential value
on the order of ~10'3 m2/s [Wer85, Sto85]. The large difference of 1 to 2 eV
between the activation energies for Si self-diffusion and Ge self-diffusion as
well as the interstitial dominated as compared to the vacancy dominated
mechanism above 800 C suggest that there must be a strong concentration
dependence of Si-Ge interdiffusion in Si^Ge* structures.
1.5.1.2 Tracer studies of Ge in Si
Thermally activated interdiffusion studies of Si-Ge systems have
shown that interdiffusion occurs most likely through Ge atoms which diffuse
into the Si lattice; therefore, it is imperative to discuss the diffusion of Ge in
Si. While the values of the tracer diffusivity and activation energy of
diffusion (5.39 eV over a temperature range of 850 to 1400 C) of Ge in Si agree
well from study to study [Bou86, Dor84], the dispute that arises is the same as


198
energy of diffusion in inert ambient, 5.8 eV, was higher than values
previously reported in literature. This was attributed to the much larger
temperature span used in this work. This factor, as well as resulting
diffusivities that cover over five orders of magnitude compared to just two
orders of magnitude of other studies, led to the conclusion that the value of
Ea calculated in this dissertation was more reliable than those of previous
investigations. The extracted diffusion coefficients, at constant temperature,
were found to be time-independent in all three ambients.
Neither enhancement nor retardation was observed for diffusion at the
lower temperatures of 900 and 1000 C in oxidizing ambient compared to inert
ambient. At the higher temperatures of 1100 and 1200 C, however, diffusion
retardation under oxidizing ambient (interstitial supersaturation) compared
to inert ambient was seen. This led to the conclusion that interstitial
participation is negligible and vacancy point defects dominate the diffusion
process. This conclusion was further supported by the estimated value of
fj=0.10 at the low temperatures and f¡=0.02 at the higher temperatures from
oxidation and B marker layer experiments. The large value of the vacancy
component of diffusion agreed well with that reported by Cowem et al.
[Cow96] for 875 C.
Significant retardation of diffusion occurred at all temperatures in
nitriding ambient compared to inert ambient. This contradicted the results
from oxidation experiments. Fractional interstitial and vacancy components


58
The angle between the incident beam and the projected diffracted beam
which reaches the detector is defined as 20, and is controlled by the
goniometer. The angle between the incident beam and the sample surface is
defined as 0), which is also controlled by the goniometer. Rocking curve scans
occur through the independent movement of both the 20 and (0 angles. The
two scans utilized in this work are the to scan and the co/20 scan. In the 0)
scan, the detector (20) is stationary while the sample is rocked over a specified
to range. The 20 value is fixed to satisfy Bragg's law so that at a certain value
of to an x-ray peak is observed. In the to/20 scan both a 20 range and an co
range are designated. The detector is rotated through the 20 range twice as
fast (but in the same direction) as the sample is rotated through the to range;
the angle between the incident beam and the sample surface changes. This
scan is most useful when the sample crystal is composed of more than one
material (i.e. Si and Sij.xGex) and the Bragg conditions of only one material are
known (Si).
When the x-ray beam reflected from the sample crystal is directed
immediately into a detector, as shown in Figure 2-16, it is considered to be a
double axis spectrometer. This double axis mode was employed in both co and
co /20 scans in this study. In a triple axis spectrometer (Figure 2-17), the x-ray
beam reflected from the sample is directed towards a two-crystal analyzer
before entering a detector. This offers improved angular resolution and


a.
20,000x
500nm
b.
20,000x
500nm
Figure 3-8. Plan-view TEM micrographs of SQW/VPE after annealing at (a)
900 C for 330 min in oxidizing ambient and (b) 1200 C for 1 min in inert
ambient.


32
relaxation of the inherent strain. In a symmetrically-strained superlattice
(SSL), a Si,.yGev buffer layer is first grown on the substrate causing the Si and
Si,.xGex layers to be alternately under tensile and compressive strain (y These alternating strains of equal magnitude lead to a structure which is
theoretically strain-free.
In the case of Si,.xGex/Si SLs there is no agreement among the various
reported values of diffusivities and activation energies. Some investigations
have reported energies as high as 5.0 eV [Bea85] while others have reported
energies as low as 2.1 eV [Lui96]. The high activation energies support the
theory that diffusion is controlled by the migration of Ge, first through the Si,.
xGex layers and then into the Si layers since Ge diffusion in Si has an
activation energy of ~5 eV. The studies reporting low activation energies do
not suggest any possible mechanism, nor do they reach a conclusion
regarding the discrepancy with the high activation energy studies. The only
explanation given is that the deviation may arise due to differences in sample
structures, annealing temperatures and times, or data analysis method.
1.5.2 Oxidation and Nitridation Enhanced Diffusion
A review of the literature reveals that there has been only one
investigation of Ge diffusion in strained Si,.xGex under an oxidizing ambient.
Cowem et al. [Cow96] investigated Ge diffusion throughout a structure with a
coherent Si0 70Ge0 ^ layer. For a single anneal temperature of 875 C, they
determined that diffusion is predominately vacancy-mediated, and estimated
a f, of 0.22+0.04. They also calculated an enhancement under oxidizing


TABLE OF CONTENTS
12age
ACKNOWLEDGMENTS i v
LIST OF TABLES ix
LIST OF FIGURES xi
ABSTRACT xv
1 INTRODUCTION 1
1.1 Selected Material Properties and Device Applications 3
1.1.1 Material Properties 3
1.1.2 Device Applications 8
1.2 Strain and Strain Relaxation in SiGe Heterostructures 11
1.3 Diffusion in Elemental Semiconductors 15
1.3.1 Continuum Theory 16
1.3.2 Point Defects and Diffusion Mechanisms 18
1.4 Non-equilibrium Point Defect Injection 24
1.4.1 Interstitial Injection (Oxide Growth) 25
1.4.2 Vacancy Injection (Nitride Growth) 27
1.5 Literature Review 28
1.5.1 Self-Diffusion and Intrinsic Interdiffusion 28
1.5.1.1 Self-diffusion 28
1.5.1.2 Tracer studies of Ge in Si 29
1.5.1.3 Diffusion studies of Sij.xGex/Si heterostructures 30
1.5.2 Oxidation and Nitridation Enhanced Diffusion 32
2 SAMPLE PREPARATION AND CHARACTERIZATION 34
2.1 Growth Parameters and Structure 34
2.2 Transmission Electron Microscopy 37
2.2.1 Overview 37
2.2.2 TEM Sample Preparation 40
2.2.2.1 Plan view 40
2.2.2.2 Cross-sectional 41
2.2.3 Images of Structures 42
2.2.3.1XTEM 42
2.2.32 PTEM 44
vi


51
annealed profiles were standardized by (1) assuming a Ge concentration of
15% for the as-grown samples determined from RBS (2) assuming that Ge
concentration remains constant within the sample regardless of processing
history (3) integrating the area under the as-grown profile curve (4)
calculating the ratio of this area to the integrated area under the annealed
profile curve and (5) multiplying the concentration of the annealed profile by
this ratio. In all cases this proved to be a highly successful concentration
standardization technique.
SIMS concentration versus depth analysis of the as-grown structures
are shown in Figures 2-10 through 2-13. For the SQW materials it can be seen
that the layer thicknesses are close to the requested thicknesses. For structure
SQW/VPE (Figure 2-12), the Si cap/ S!.xGex well interface was very abrupt,
while the Si^Ge,, well/Si buffer interface was much less abrupt, almost
graded. For structure SQW/MBE (Figure 2-13) neither the cap/well nor the
well/buffer interface were abrupt. Both interfaces were graded over
approximately 0.03 pm. For the SLs, the SIMS profiles verify the layer
thicknesses as well as the total number of periods. For both SLs (Figures 2-10
and 2-11), the interfaces were very abrupt. All structures were also analyzed
for C and O content, since these impurities can act as traps and greatly alter
the diffusion properties of the material. Structures SL/SiGe, SL/Si and
SQW/VPE showed very low concentrations of C and O throughout the
materials. Structure SQW/MBE, however, showed a high C pileup at the
substrate/buffer interface (Figure 2-14).


65
To completely define the epilayer strain state, however, both the
perpendicular and parallel lattice mismatch must be determined. This can be
done through HRXRD rocking curves from asymmetric lattice planes making
an angle p with the surface (Figure 2-21). This method is described in detail in
[Bar78, Kri95] and has been used in this investigation to determine the strain
relaxation of sample structures SL/SiGe and SL/Si after thermal treatment
(Sections 4.5.3 and 5.5.3). Briefly, the Bragg condition for an asymmetric plane
is satisfied at two different a> angles:
co, = 0 + p (2-7a)
co2 = 0 (2-7b)
The values of and to2 for both the epilayer and substrate are obtained
through asymmetric rocking curve scans, and Equations 2-7 are solved
simultaneously for the values of 0 and <() for both the epilayer and substrate.
These values are used in:
= (<)>i -4>s)tan<|>s -(0, -0s)cot0s (2-8a)
i
*-(01 -(!)s)cot //
to determine the perpendicular and parallel lattice mismatches.


85
oxidizing ambient from 1532 min to 2206 min could not be extracted because
after 2206 min the oxide had consumed the Si cap layer and had oxidized a
portion of the Si1.xGex layer.
Table 3-3. Extracted diffusivities for initially partially relaxed SQW/MBE.
T(C)
time (min)
D^XcmVs)
Dr*(cm2/s)
Dr/-(cm2/s)
900
0 to 330
lJOxlO'17
2.32x1037
-
330 to 980
2.53xl017
1.54xl017
-
980 to 1532
2.41xl0'17
1.15xl017
-
1532 to 2206
2.29xl0'17
-
-
1000
Oto 43
3.00x1016
3.28xl016
-
43 to 55
3.00xl016
6.22xl016
-
55 to 87
2.74xl016
2.50xl016
-
87 to 125
2.50xl0"16
2.74xl016
-
1100
0 to 1
5.20xl014
1.14x1 O'14
1.46x1014
1 to 2
5.90xl0'14
1.02xl013
1.37xl015
2 to 3
2.23xl014
5.20xl0"14
2.64xl0'14
3 to 4
7.29xl014
1.02xl013
4.88xl015
1200
0 to 1
2.38xlOu
2.47 xlO12
l.lOxlO13
1 to 1.5
4.21xl0'13
2.03xl012
2-llxlO14
1.5 to 2
4.21xl0'13
1.17xl012
2.24xl013
2 to3
7.91X1013
8.55xl013
1.42xl0'14
3.4.3 Sij.xGex Single Quantum Well with Boron Marker Layer
As stated in section 1.2 and 3.4.1, the thickness of the Si1.xGex layer in
both SQW sample structures was greater than the critical thickness.
Annealing caused strain relaxation through the generation of misfit and
threading dislocations. These dislocations (in either the Si or Si^Ge,, layer)
can possibly trap interstitials or vacancies injected during the oxidation or
nitridation process, thus severely limiting the role these excess point defects


149
There has been only one other known study of the diffusivity of Ge in
Si,.xGex/Si SL structures with a S!.xGex buffer, annealed in inert ambient.
Hollander et al. [Hol92] studied interdiffusion of a Si0g0Ge020/Si SL with five
periods of 10 nm Si and 10 nm Si0 80Ge0 20 layers. The Si082Ge0 lg buffer layer
was grown with a composition which created compressive strain in the
Si080Ge020 layers that was of equal magnitude to the tensile strain in the Si
layers. Thus, the SL investigated by Hollander et al. was symmetrically
strained. It is also important to note that Hollander et al. investigated
additional structures with Ge compositions as high as x=0.68, but for purposes
of direct comparison to the results of this study, these structures will be
ignored. The extracted diffusivities (using a Fourier algorithm to fit RBS
spectra) from Hollander et al. over anneal temperatures 1000 to 1125 C are
plotted in Figure 4-8. The study by Hollander et al. differs in temperature
range, structure composition, and strain state from that performed using
SL/SiGe. The symmetrically strained SL of their study had a different strain
state than asymmetrically strained SL/SiGe. The composition difference
between the two structures amounts to five percent and SL/SiGe has 10 more
periods than that used by Hollander et al. The only common anneal
temperature studied was 1000 C. Figure 4-8 illustrates that the diffusion
coefficient determined from SL/SiGe at this common temperature is greater
than, and not within error of, that reported by Hollander et al. The difference
in the diffusion coefficients is, however, well below an order of magnitude
and could be attributed to the minor differences in composition and layer


33
ambient compared to inert ambient of D/D*=3.6. No diffusivity values were
reported and no activation energy was calculated. There are no known
investigations of Ge diffusion in Sij^Ge* under nitriding ambient.
There has been limited investigation of oxidation and nitridation
enhanced diffusion of impurities in Si/Si^Ge^Si SQW structures. An
excellent summary of research to date can be found in Nylandsted Larsen et
al. [Nyl97]. Kuo et al. [Kuo95] measured the diffusivity of boron in Si/Si,.
xGex/Si SQWs and found that the oxidation enhanced diffusion (OED)
enhancement factor was comparable to that in Si, fenh=10. The diffusivity of B
in Sij.xGex, however, was less than that in Si by almost half. While there is no
explanation for the difference in B diffusivity between the materials, the
similarity of enhancement indicates that the interstitial contribution of B
diffusion in Si1_xGex is comparable to that in Si. Kuo et al.'s investigation was
limited to data for only one anneal temperature, 800 C. Fang [Fan96]
measured nitridation retarded diffusion (NRD) of B in Si1.xGex SQWs at one
temperature, 850 C. She found that the retardation factor in Sij.xGex was
comparable to that in Si, fre~0.8, and she also found a smaller intrinsic B
diffusion in Sij.xGex than Si.


Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
THE STUDY OF INTERDIFFUSION AND DEFECT MECHANISMS IN
Sij.xGex SINGLE QUANTUM WELL AND SUPERLATTICE MATERIALS
By
Michelle Denise Griglione
May 1999
Chairman: Dr. Tim Anderson
Major Department: Chemical Engineering
Dimensions of Si microelectronic devices continue to shrink in pursuit
of higher speed operation. Soon, these dimensions will reach a minimum
and an alternative material must be found. The alloy Si-Ge has been
suggested as a replacement due to its ability to be band-gap engineered, as well
as its compatibility with current Si-only processing, low cost, and
environmental friendliness. The fabrication of Si-Ge devices includes several
high temperature processing steps which can degrade device performance if
interdiffusion occurs within the material. This dissertation investigated the
interdiffusion of Si-Ge structures as a function of processing temperature (850
to 1200 C), layer structure, and anneal time. In particular, the roles of
vacancy and interstitial point defects in the diffusion process were
xv


208
PAIR MODEL-OXIDIZING AMBIENT
dopant add name=Germanium
pdbSetDouble Si Ge I DO $lvalue
pdbSetDouble Si Ge I Dp 0
pdbSetDouble Si Ge V DO $Vvalue
pdbSetDouble Si Ge V Dp 0
pdbSetSwitch Si Ge DiffModel Pair
line x loc = 0.0 tag = surf spac=0.003
line x loc = 0.05 tag = cap spac=0.003
line x loc = 0.10 tag = sige spac=0.005
line x loc = 0.20 tag = buffer spac=0.003
line x loc = 0.25 tag = back spac=1
region silicon xlo = surf xhi = back
init quiet
profile name=Germanium infile=1819AsGrown2.98
SetTemp 900
InitDefect 900
InitDopantPairs 900
sel z=log10(Germanium)
plot.ld label=lnitial
diffuse time=1532 temp=900 init=1 e-12 ladapt dry
sel z=log10(Germanium)
plot.ld label=Final lele
profile name=target infile=1819.900.1532f.Ox
sel z=log10(target)
plot.ld label=Experimental lele


89
3.4.4 Estimation of Fractional Interstitial Components of Diffusion
Initially, the Pair model was used in FLOOPS to provide simulated
concentration versus depth profiles which fit the SIMS profiles of the samples
processed in oxidizing ambient. The fractional interstitial components of
diffusion, fj, were estimated within the Pair model by solving Equation 3-5.
The values of the inert (intrinsic) diffusivity, D*, were simply the DGeInert
values listed in Table 3-1. The values of C,/C,* and Cv/Cv* under oxidizing
conditions for the temperatures studied were the default values used by
FLOOPS [Pac90]. The resultant f, values were -0.10, which corresponded well
with the minimal amount of diffusion enhancement seen during interstitial
supersaturation.
This method was repeated to estimate f, values for the samples
processed in nitriding ambient. Once again, the values of the inert (intrinsic)
diffusivity, D*, were the DGeInert values listed in Table 3-1. The values of C,/C,*
and Cv/Cv* under nitriding conditions for the temperatures studied were
those reported in an extensive study by Mogi [Mog96]. Quantitative f, values
could not be estimated because the D* values (DGeInert) for every processing
temperature and time were so large that they greatly overestimated the
diffusion. Qualitatively, the Pair model, when applied to the nitriding
experiments, indicated an extremely large interstitial component of diffusion.
While this result corresponded well with the significant retardation seen
during vacancy supersaturation, it contradicted the small interstitial
component predicted by the oxidation experiments.


176
that can be used as a check against the symmetrical scan value. Asymmetric
scans were performed in this investigation using the (115) reflection plane.
Scans were taken at an oo of -31.5 and an co+ of -63.2 and a 20 value of -95.0.
At both to' and (0+, scans were taken at a rotational angle of -90 and 90. o>-20
scans were taken over a Io range of go, with a step size of 0.00025 and time per
step of 0.5s for a total of 4001 steps.
Scans of the as grown SL/Si structure were taken in order to determine
what were considered fully-strained values of the parallel and perpendicular
lattice constants. These values gave a good idea of the dimensions of the
original unit cell of the epilayer and would allow estimation of the
comparative amount of relaxation that occurred through processing. Scans
were limited to two anneal temperatures, 900 and 1000 C, and two anneal
times 6 and 8 min and 1 and 3 min for 900 and 1000 C, respectively. Scans
were taken of samples annealed at these temperatures and times in inert,
oxidizing, and nitriding ambients. Table 5-3 presents the resulting ae// and ael
values after analysis using the equations given in Section 2.4.4. The
estimated error in the values of ae// and ael is 0.0002 nm and is derived from
the error in to angle measurement (0.00025).
5.5.3 TEM
Because SL/Si is strained and has been shown to have dislocations after
growth and before thermal processing, it is important to know at least
qualitatively the dislocation density after annealing compared to that of the as


For Rob, Dad and Mom


Copyright 1999
by
Michelle Denise Griglione


109
The activation energy of Ge diffusion in Si/Sij_xGex/Si in inert ambient
determined in this study, 5.87 eV0.14, is substantially higher than activation
energies previously reported [Van90, Sun94]. Van Ijzendoorn et al. and
Sunamura et al. both reported activation energies of approximately 2.5 eV for
SQWs with Ge compositions x=0.17 and 0.16, respectively. While the
thickness of the SQW studied in Sunamura et al. was below critical thickness,
the thickness of the SQW studied by Ijzendoorn et al. was above critical
thickness and the same as that of this study (50 nm). Because the SQWs of all
three studies are similar, the larger activation energy determined from this
study can most likely be attributed to the difference in temperature range
investigated. The studies of Van Ijzendoorn et al. and Sunamura et al. were
conducted in a relatively narrow temperature range from 800 to 1010 C. It
should also be noted that the activation energy calculated in this work (~5.8
eV) physically compares with the reported value for the Ge tracer diffusivity
in pure Si [Fah89]. There is a possibility that after the structure has relaxed
during the very first stage of processing, Ge diffusion in relaxed Si1.xGex is
similar to Ge diffusion in bulk (relaxed) Si.
The diffusivities given in Table 3-1 for inert ambient are constant with
increasing time within error for temperatures from 900 to 1200 C. At 1200 C,
the diffusivity of the shortest time anneal is not within error of the
diffusivities of the longer anneals (Figure 3-13). This slight deviation of D for
the shortest anneal time, however, is not seen at any other temperature. This
does not seem to indicate a trend and is within one standard deviation of the


105
875 C. Results from this study show clearly that, in conjunction with the
Cowem results, the possibility of a concentration dependent diffusion
coefficient needs to be investigated further. Flat peaks were not seen in
profiles of samples annealed in nitriding ambient.
Comparison of the diffusivities of the two structures SQW/MBE and
SQW/VPE (Table 3-7) shows that in inert, oxidizing, and nitriding ambients
the diffusivities are equivalent within error, as determined from the analysis
method in Section 2.3.2. Figure 3-11 shows this graphically for the inert and
oxidizing ambient cases.
Activation energies of diffusion for each ambient given in Equations 3-
8 through 3-10 are not all within one standard deviation of each other, but all
are well within two standard deviations of each other. Because the
diffusivities and activation energies of both SQW/MBE and SQW/VPE are
similar throughout the entire temperature range of this study, it can be
concluded that the different growth methods, in this case, have no effect on
diffusion behavior. For the remainder of the discussion on SQW results, the
two structures will be considered identical.
Previously reported values for the diffusivity of Ge in Si/Sij.xGex/Si
structures in inert ambient are shown in Figure 3-12 [Sun94, Hol89, Zau94,
Van90]. The diffusivities determined from this study at 900 and 1000 C are
slightly lower but still agree well with the diffusivities reported in the


182
5.5.2.1, over anneal temperature 700 to 880 C. Bean et al. [Bea85] studied
interdiffusion of a Si0 40Ge060/Si SL with three periods of 50 nm Si and 14 n m
Si040Ge060 layers. The diffusivities reported by Bean et al., plotted in Figure 5-
7, were extracted using an algorithm that fit the second moment of the peak
in the RBS spectra, over anneal temperatures 800 to 1050 C. Boucaud et al.
[Bou96] studied interdiffusion of a Si070Ge030/Si SL with fifty periods of 17 nm
Si and 2 nm Si070Ge030 layers. The diffusivities of Boucaud et al., covering
anneal temperatures 750 to 950 C plotted in Figure 5-10, were extracted using
the shifts of photoluminescence (PL) peaks.
Every study discussed above used Sij.xGex compositions, layer
structures, temperature ranges, and extraction methods which were different
from each other and different than those used in this work. Every previous
study used Sij.xGex layers with greater, and in some cases, much greater, Ge
composition than the x=0.15 for SL/Si. The temperature ranges of all studies
included at least one temperature common to those used for this
investigation. At all anneal temperatures used in this work, however,
diffusivities are higher than, and not within error of, those previously
reported (Figure 5-7). This may be due to differences in structure composition
or analysis methods used in each study compared to this investigation.
Interestingly, Prokes and Wang used the same HRXRD method to extract
diffusivities as was used to extract diffusivities presented in Section 5.5.2.I.
Comparison of these results (Section 5.6.2) will provide insight into the effect
of extraction method on diffusion coefficient values.


115
10'12
10'13
10'14
a
Q
1015
10'16
10'17
6.5 7 7.5 8 8.5 9
1/T*104(K'1)
Figure 3-15. Comparison of Ge diffusivities of partially relaxed structures in
inert ambient.
As explained in Section 3.4.2, the initial profile used in simulations
was the experimentally determined SIMS profile from samples annealed
from a time of 0 to t^,. The final profile used to extract the diffusivity was the
experimentally determined SIMS profile from samples annealed from a time
of 0 to tgn,,. The total time of anneal simulated in FLOOPS, tanneal, was t^-t^,.
It is ultimately desired that, in future work, the final profile used to extract
the diffusivity will be the experimentally determined SIMS profile from
samples previously annealed from 0 to t^,, which are subsequently annealed
from a time of 0 to tanneal. For example, the SIMS profile of a sample annealed
at 900 C from 0 to 330 min, known as Sample 1, was used as the initial
partially relaxed profile. In FLOOPS, this profile was annealed for 650 min


16
experimental results. Monte Carlo (MC) and Molecular Dynamics (MD)
simulations are examples of methods used in the atomistic approach. These
are not common in complete modeling of diffusion because the small time
scale limits their use to the study of unit steps of diffusion only.
1.3.1 Continuum Theory
Diffusivity values as well as fractional contributions to diffusion of
interstitials and vacancies have been estimated in this work using the semi-
empirical approach. Experimental results obtained through Secondary Ion
Mass Spectrometry (SIMS) (Section 2.3) have been used to estimate
parameters used in the continuum and atomistic mechanism models
incorporated in FLOOPS. It is therefore important to describe the
fundamentals of continuum theory in order to understand the models and
results presented throughout this work.
The semi-empirical approach to describing diffusive transport in a
diffusion couple is based on Fick's first law, which describes mathematically
the flux in one dimension as:
where F is the flux of atoms, c is the concentration of the diffusing
component, x is the space coordinate measured normal to the section, and D
is the diffusion coefficient. The minus sign in Equation 1-5 indicates that the
diffusion occurs in the direction of decreasing concentration. Fick's first law


14
temperature thermal treatment. Misfit dislocation propagation can lead to
the simultaneous propagation of threading dislocations that can penetrate
B
a. b. c.
Figure 1-9. Termination of a misfit dislocation, (a) Misfit dislocation along a
Si/ S!.xGex interface meets a threading dislocation, AB; misfit terminates by
(b) forming new misfit terminating at lateral surface or (c) termination of
threading dislocation AB at free surface.
heterojunctions and increase current leakage. Heterostructures with
dislocation densities greater than ~103 cm'2 are unsuitable for device
applications [Hou91]. Thus, the characterization and quantification of
dislocations in Sij.xGex/Si is vital in developing the material for device
applications. Parts of this dissertation address whether dislocations alter the
diffusion that occurs during high temperature thermal treatment (Sections
3.4.2 and 3.5.2) and whether dislocations capture the excess point defects
injected during oxidation and nitridation (Sections 3.4.3 and 3.5.3), thus
limiting or prohibiting their interaction in the diffusion process.


192
components of diffusion and activation energies of diffusion of SL/SiGe and
SL/Si extracted from SIMS/FLOOPS analysis. Comparison of HRXRD and
TEM results has already been modestly addressed in Sections 5.6.2, 5.6.3 and
5.5.3. HRXRD results, while interesting, were proven unreliable, and
therefore extensive comparison of the resulting values would be useless.
The diffusivities of SL/SiGe and SL/Si are compared in tabular form in
Table 5-5. In inert ambient values for 850, 950 and 1000 C are not within
error of each other, yet the separation is not large. The diffusion coefficients
for 900 C are the only values that are within error of each other. The values
for 850, 950 and 1000 C, while not within standard error, are within two
standard deviations of each other, which is not large. In oxidizing and
nitriding ambients, values at all temperatures are within error of each other.
Based on these results, it can be concluded that strain state of the Si and Sij.
xGex layers does not affect the overall diffusivity.
The activation energies of diffusion of SL/SiGe and SL/Si in inert,
oxidizing, and nitriding ambients are compared in Table 5-6. The activation
energies of SL/Si in inert and oxidizing ambient are higher than and not
within error of, those for SL/SiGe. This may indicate a possible effect of strain
state of the layers, however, it is unlikely. The activation energies in
nitriding ambient are within error of each other.
From the information presented above, it seems most likely that
diffusion is not significantly affected by the difference in tensile and
compressive strain in the periodic multilayers of the SLs studied.


Table 3-6. Fractional interstitial components and modified diffusivities and
point defect supersaturations determined for diffusion in oxidizing ambient.
T(C)
900
1000
1100
1200
time
(min)
D(cm2/s)
D*(cm2/s)
*
U
X
U
Cv/Cv
f,
330
2.32X1017
1.28X1017
6.67
1.00
0.140
2.32xl017
2.38xl017
6.67
0.150
0.127
980
1.27X1017
1.28xl017
0.940
1.00
0.140
1.27xl017
2.38xl017
3.40
0.290
0.077
1532
6.34X1018
1.28xl017
0.002
1.00
0.506
6.34xl018
2.38X1017
7.30
0.130
0.018
43
3.28X1016
2.82X1016
3.72
1.00
0.059
3.28X1016
4.19xl016
3.72
0.480
0.148
55
4.56X1016
2.82xl016
11.5
1.00
0.059
4.56xl0'16
4.19X1016
6.48
0.150
0.148
87
3.94xl016
2.82x1016
7.78
1.00
0.059
3.94xl016
4.19X1016
5.26
0.190
0.148
125
2.74xl016
2.82xl016
0.530
1.00
0.059
2.74X1016
4.19X1016
2.70
0.360
0.121
1
1.14xl0'14
7.77xl0'14
-
0.501
0.010
1.14X1014
2.19xl013
28.9
0.035
0.011
2
5.20xl0'14
7.77xl014
16.0
0.501
0.010
5.20xl014
2.19X1013
16.0
0.063
0.011
3
4.21X1014
7.77xl014
4.60
0.501
0.010
4.21X1014
2.19X1013
8.65
0.116
0.011
4
7.93xl0'14
7.77xl014
52.4
0.501
0.010
7.93xl0'14
2.19X1013
5.43
0.184
0.011
1
4.05xl013
-
0.600
1.00
-
4.05X1013
1.70X1012
0.600
1.67
0.045
1.5
4.93X1013
-
-
-
-
4.93X1013
1.70X1012
7.00
0.143
0.014
2
4.56X1013
-
-
-
-
4.56X1013
1.70xl012
5.90
0.169
0.021
3
4.56xl0'13
-
-
-
-
4.56xl013
1.70xl0'12
5.90
0.169
0.021
which diffuses through a predominantly vacancy mechanism, such as
antimony. Therefore, the upper bound of Cv/Cv* was unknown from the B
marker layer results and theoretically an infinite number of vacancies might
have been injected. For purposes of calculation, however, an upper bound of
Cv/Cv*=4 [Mog96] was used initially in step (2) to extract an f,. Unfortunately,
neither the lower bound of 1/(C,/C,*) nor the upper bound of 4 for Cv/Cv*


66
detector
source
Figure 2-21. Example of positive and negative x-ray diffraction from an
asymmetric plane, co, 0 and <)) are identified. For a symmetric reflection, the
diffraction plane would be parallel to the sample surface, (0=0.


APPENDIX B
GLOSSARY
acceptor- a negatively charged dopant that accepts an electron from the
semiconductor lattice when introduced.
ambient- atmospheric environment in which thermal processing occurs.
band gap- the difference in energy between the valence and conduction band
edges in a semiconductor.
base- part of a junction transistor.
base transit time- the time it takes a carrier to diffuse acrossthe base from the
emitter to the collector.
BJT- Bipolar Junction Transistor; a semiconductor transistor with two p-n
junctions in series made out of one semiconductor material.
buffer- a semiconductor layer situated between the substrate and the thin
epitaxial layers, intended to act as a barrier to diffusion and dislocation
formation.
cap- a final semiconductor layer grown on top of epitaxial layers intended to
prevent out-diffusion and other behaviors in a heterostructure.
carrier- mobile negatively or positively charged species in a semiconductor.
coherent- pseudomorphic, epitaxial layer thickness less than critical thickness.
conduction band- a band of allowed energies levels corresponding to
unbonded electrons free to travel throughout the crystal.
critical thickness- the thickness at which dislocations begin to form in an
epilayer lattice mismatched to its substrate.
current gain- a parameter used to judge HBT performance; the ratio of the
collector current to the base current.
cutoff frequencies- the frequency at which the magnitude of the current gain
is equal to 1.
dislocation- a deviation in the periodicity of a lattice arising from a line of
points.


170
The values of the diffusivities for structure SL/Si as a function of
temperature in inert, oxidizing, and nitriding ambients are shown in Figure
5-2. Fitting this data to Arrhenius expressions results in the following
equations when the processing was performed in inert, oxidizing, and
nitriding ambients:
D£frt (SL / Si) = 3.6 x 10_1 exp(-3.63eV 0.24 / kT)cm2/s (5-2)
D£ (SL/Si) = 2.3 x 10* exp(-2.81eV 0.21 /kT)cm2/s (5-3)
Dg (SL / Si) = 2.7 x 101 exp(-4.16eV 0.22 / kT)cm2/s (5-4)
1000 C 950 C 900 C 850 C
Figure 5-2. Effective Ge diffusivity of structure SL/Si as a function of
annealing temperature in inert, oxidizing, and nitriding ambient.


151
only at an intermediate temperature of 1000 C. If the Arrhenius expression
generated by the data points of Hollander et al. is extrapolated to the lower
temperatures studied for SL/SiGe, the values are still not within error of
those determined for SL/SiGe. The difference in temperature ranges studied
cannot, therefore, necessarily account for the disagreement in activation
energies. The discrepancy is most likely due to differences in layer thickness,
composition, or analysis method, as mentioned above, with neither study
considered more reliable than the other.
Time dependence of diffusion in structure SL/SiGe was not thoroughly
addressed compared to the investigation of structure SQW/MBE discussed in
Chapter 3. Only diffusion at 900 C was investigated for more than one
processing time. At this temperature, diffusivities for anneal times of 4 and 6
min were extracted. The diffusivities given in Table 4-1 for inert ambient are
not within error of each other, however they are well within two standard
deviations of each other. From this small amount of data, it cannot be stated
conclusively whether Si,_xGex/Si SL diffusion in inert ambient is independent
of time. Future studies must be done. The diffusivities given in Table 4-1 for
oxidizing ambient are not within error of each other and are in fact one entire
order of magnitude apart. There is therefore a strong possibility that diffusion
is time-dependent in oxidizing ambient. As in the inert ambient case, future
studies need to be performed to confirm this preliminary result. In both
ambients, this possible time dependence of diffusion is in contrast to the
definite time-independence of diffusion in the SQW structures discussed in


152
Chapter 3. The reason for this difference in behavior is presently not
understood and further studies are needed. One possible reason may be a
difference in the evolution of strain relaxation with time in the SQW
compared to the SL. The bulk Si1.xGex layer in the SQW may complete
relaxation in the initial phase of the thermal treatment, while the SL
relaxation may occur more gradually. The varying relaxation rates may affect
diffusion rates. The time dependence of SL/SiGe in nitriding ambient was
not investigated.
Comparison of diffusion in inert, oxidizing, and nitriding ambients
yields interesting conclusions. At the lower temperatures studied, Ge profiles
in oxidizing ambient show greater diffusion than profiles in inert ambient
(Figure 4-9a). The diffusivity extracted at 850 C in oxidizing ambient is
greater than that in inert ambient and the values are not within error of each
other. This indicates that at this low temperature a supersaturation of
interstitials results in enhancement of Ge diffusion; interstitial point defects
play a measurable role in the diffusion process. This logic, however, is not
supported by the diffusivities in inert and oxidizing ambients at 900 C, where
DGex is less than DGeInert and the values are not within error of each other. It is
most likely that, as indicated by the Arrhenius fit to the data, at these lower
temperatures, excess interstitial injection has very little effect on diffusion.
Diffusivities extracted for both ambients at higher temperatures 950 and 1000
C are similar and within error of each other, as illustrated in Figure 4-2. Ge
depth versus concentration profiles at these temperatures are virtually


64
2.4.4 Determination of Strain Relaxation
X-ray double crystal diffractometry allows the accurate determination of
the orientation, size and shape of the deformed unit cell of the layer
compared to the cubic unit cell of the Si or Si1.xGex substrate or buffer. The
amount of strain between layer and substrate can be determined through
analysis of their respective to peak positions. When the Si1.xGex layer of larger
lattice parameter, a is deposited on the Si substrate of smaller lattice
parameter, as, the cubic cell of the Si,.xGex lattice must be compressed in the
parallel direction so that the lattice parameter matches that of the Si lattice,
a/;. The volume of the Sij.xGex cubic cell, however, is constant to a good
approximation, so the compression in the parallel direction is accommodated
by an increase in the perpendicular lattice parameter, a. The Si1.xGex cell is
no longer cubic, but tetragonal and the strain introduced is known as
tetragonal strain (Section 1.2).
The angular separation between the substrate and epilayer peaks for the
symmetric reflection (the angle of incidence equals the angle of reflection, i.e.,
the sample surface is oriented in the same direction as the reflection plane)
can be used to determine the perpendicular lattice mismatch between the
epilayer and substrate [Kri95]:
= -(i es)cotes
v as )
(2-6)


83
The values of the diffusivities for structure SQW/VPE as a function of
temperature in inert, oxidizing, and nitriding ambients are shown in Figure
3-3. Fitting this data to an Arrhenius expression results in the following
equations when the interdiffusion is carried out in inert, oxidizing, and
nitriding ambients:
D£eert (SQW / VPE) = 4.8 x 107 exp(-5.71eV 0.23 / kT) cm2/s (3-11)
Dg(SQW/VPE) = 1.0 x 104 exp(-4.81eV 0.22/kT) cm2/s (3-12)
DS (SQW / VPE) = 2.2 x 10^ exp(-2.73eV 0.10 / kT) cm2/s (3-13)
1200C 1100C 1000 C 900 C
Figure 3-3. Effective Ge diffusivity of structure SQW/VPE as a function of
annealing temperature in inert, oxidizing, and nitriding ambients.


25
oxidation or nitridation, there will be an enhancement of the effective
diffusivity given by:
, D C] ( Cy
enh = = fj 7 + (1 fj)7-
D* C 1 C
(1-17)
where C, and Cv are the actual concentrations and C* and Cv* are the
equilibrium concentrations of vacancies and interstitials. Note that if enhcl
diffusion is retarded rather than enhanced. If D* is known, f, may be
estimated from measuring enh during oxidation or nitridation and
comparing with dopants for which f, is known (e.g., phosphorous, f,=l). This
is explained in detail in Section 3.3.
1.4.1 Interstitial Injection (Oxide Growth)
As stated in Section 1.4, oxidation of the silicon surface results in the
injection of interstitial point defects into the Si bulk. During oxidation,
oxygen gas reacts with the Si surface and the rate is controlled by the overall
chemical reaction:
Si(., + 2(g, SiOi(i) (1-18)
The silicon dioxide layer continues to grow by the transport of oxygen species
through the oxide layer to the Si-Si02 interface where it reacts with the Si
[Dea65]. The formation of the oxide causes the Si to be consumed so that for
every angstrom of oxide grown, approximately a half angstrom of the Si
surface is consumed [May90].


crew for their friendly service with a smile, as well as Dennis Vince in the
ChemE shop. I am grateful to Dr. Margarida Puga-Lambers for her dedicated
and timely SIMS characterization. Doug Meyers of ASM Epitaxy, Alex Van de
Bogaard of Delft University, and Bruce Gnade of Texas Instruments are
credited with growth of the materials used in this study. Dr. Olga Kryliok is
appreciated for her support and interest. Lance Robertson of SWAMP Center
has contributed to the overall morale of this research project.
Acknowledgment is also due to my secondary school science teachers,
Ms. Betty Johnson and Dr. John Lieberman, who made my first brushes with
science fun and fascinating. My parents taught me the value of knowledge,
personal achievement and striving to make a contribution. They have
supported me wholeheartedly throughout this endeavor, as they have
through every other, and I thank them. Last, but certainly not least, I thank
Rob Baker for his help with the manuscript, and more significantly, the
personal encouragement and understanding that he provided on a daily basis
... especially on the days when more than the usual amount of understanding
and encouragement was needed.
v


APPENDIX A
EXAMPLES OF FLOOPS PROGRAMS
Fermi Model: Inert Ambient
dopant add name=Germanium
pdbSetDouble Si Ge I DO { [Arrhenius 1.37e5 5.08]}
pdbSetDouble Si Ge I Dp 0
pdbSetDouble Si Ge V DO 0
pdbSetDouble Si Ge V Dp 0
pdbSetSwitch Si Ge DiffModel Fermi
line x loc = 0.0 tag = surf spac=0.003
line x loc = 0.05 tag = cap spac=0.003
line x loc = 0.10 tag = sige spac=0.005
line x loc = 0.20 tag = buffer spac=0.003
line x loc = 0.25 tag = back spac=1
region silicon xlo = surf xhi = back
i n it
profile name=Germanium infile=1819AsGrown2.98
sel z=log10(Germanium)
plot. 1 d label=lnitial
diffuse time=1532 temp=900
sel z=log10(Germanium)
plot. 1 d label=Final lele
profile name=target infile=1819.900.1532.f
sel z=log10(target)
plot.1 d label=Experimental lele
206


130
compressive strain respectively. These equal amounts of tensile and
compressive strain theoretically offset each other and result in a structure
which is essentially strain-free and therefore has a theoretically infinite
critical thickness. Structure SL/SiGe was also intended to have a 50 nm Si cap
layer as protection against oxide growth.
Structure SL/SiGe, however, was found through RBS characterization
to have a Sij.yGey buffer layer with the same Ge content as the Sij.xGex SL
layers, i.e. y=x (Figure 2-14). Structure SL/SiGe was then considered to be an
asymmetrically strained superlattice (ASL) because the Si layers were in
tensile strain and the Si085Ge015 layers were unstrained with respect to the
Si085Ge015 buffer layer. Also, it was determined from SIMS and XTEM
analysis that SL/SiGe lacked the intended 50 nm Si cap layer. However, for
the oxidation times and temperatures employed, the top 12 nm Si layer was
considered adequate protection against the possibility of oxide growth into the
topmost Si!_xGex layer.
There is a finite critical thickness which is approximated by the critical
layer thickness of a single alloy layer with the same volume-averaged Ge
composition as described in Section 2.1. The average Ge content, xav, is
determined by:
x X<^SiGe
aV dSiGe+dCi
Si
(4-1)
where x is the Ge composition in the Si1.xGex layer, dSiGe is the thickness of the
Si1.xGex layers and dSi is the thickness of the Si layers. Using this equation, the


48
500nm
500nm
Figure 2-8. Plan view TEM micrograph of as-grown (a) structure SL/SiGe and
(b) structure SL/Si.


22
The second mechanism, known as the kick-out mechanism, describes
the movement of an impurity interstitial into a substitutional site, causing a
lattice atom to be bumped into an interstitial position (Figure 1-13).
o o o o o o o ono o
p Overo O^OO 9 0 O
~cro 000 00000
Figure 1-13. The kick-out mechanism.
Unlike the Frank-Turnbull mechanism, the kick-out mechanism is
dependent on the interstitial concentration only, and the diffusion equation
for the impurity (Ge) can be described by [Had95]:
ac
Ge dt
^Ge^Ge(S)
'I
"Ge
£¡_p_
C, n¡
M
(Ml)
V '-I
where C, and C,* are the non-equilibrium and equilibrium concentrations of
interstitials, respectively. The continuity equations for the interstitials and
vacancies in either the Frank-Turnbull or kick-out mechanism are:
ac,
at
ac
= V
£
c
\
I >
D,c;v^f + v(-jmech)-kr(c,cv -c;c*v)+(Pi
at
^ = V
(
DvC*V%
v V (~< +
'-v y
+ V(-Jmech)-kr(CICv-CI*Cv)- (1-12)
(M3)
where D, and Dv are the interstitial and vacancy diffusivities, respectively, J
mech
is the flux of the impurity diffusing by the mechanism in consideration, kr is


28
Like the oxidation process, the process of vacancy injection is not well
understood. The injection of vacancies is thought to be the result of stress at
the nitride/silicon interface, causing interstitials at the interface to move into
the nitride layer and vacancies to move into the Si bulk [Hay82, Osa95]. No
mechanism has been substantiated and better studies are needed.
1.5 Literature Review
1.5.1 Self-Diffusion and Intrinsic Interdiffusion
1.5.1.1 Self-diffusion
Vacancies and self-interstitials in Si coexist under thermal equilibrium
at all temperatures above the athermal regime. Based on the results of early
studies, Si self-diffusion was thought to be due entirely to a vacancy
mechanism. Through Ge tracer studies, Seeger and Chik [See68] found a
break in the Arrhenius curve and subsequently proposed self-diffusion
dominated by vacancies at temperatures below -1000 C, and interstitials at
temperatures above. In 1974 Hu [Hu74] was the first to suggest a dual
mechanism which included both vacancies and interstitials at all
temperatures in the range 700 to 1200 C. This was the mechanism that most
researchers agreed upon until experiments involving oxidation enhanced
diffusion established that Si predominantly diffuses by an interstitial
mechanism at temperatures above 800 C. The reported activation energies
for Si self-diffusion range from 4 to 5 eV.


LIST OF FIGURES
Figure page
1-1. Phase diagram of the Si-Ge system [Kas95] 4
1-2. The diamond cubic structure of Sij.xGex alloy [Kas95] 4
1-3. Lattice constant of Sij.xGex versus Ge composition 5
1-4. Critical thickness versus germanium fraction for Si^Ge, films on
a Si substrate 6
1-5. Energy gap versus germanium fraction for unstrained and
coherently strained Sii_xGex [Peo86] 7
1-6. Cross-section of a Si,.xGex HBT [Tem88] 9
1-7. Possible waveguide-photodetector structure using Si^Ge,, alloy
[Pre95] 10
1-8. Evolution of a misfit dislocation at the Si and Ge interface 13
1-9. Termination of a misfit dislocation 14
1-10. The direct interstitial mechanism 19
1-11. The vacancy mechanism 20
1-12. The Frank-Tumbull (dissociative) mechanism 21
1-13. The kick-out mechanism 22
2-1. Si^Ge,, sample structures used in these investigations 35
2-2. Sample structure SQW/MBE, a single quantum well grown by
MBE 36
2-3. Schematic of ray paths originating from the object which create a
TEM image [Wil96] 38
2-4. Schematic of TEM views 39


183
The diffusivity values of this work show non-Arrhenius behavior
(Figure 5-7). The values at 850 and 900 C are practically the same, as are the
values at 950 and 1000 C. The diffusivity extracted for 950 C is the most
anomalous, with a value above that for 1000 C for this work and also much
greater than the general curve of previously reported values. Most of the
reported studies have larger temperature spans and provide diffusivities that
cover more orders of magnitude than those of this work. These factors
indicate that the extracted diffusivities of this work are more unreliable than
those reported in previous investigations. A possible reason for the
unreliability of the data of this work may be temperature measurement
problems with the RTA, especially within the smaller 50 degree increments.
The activation energy of Ge diffusion in Si,.xGex/Si SLs with a Si buffer
layer in inert ambient determined in this study, approximately 3.63 eV0.24,
is within the range of those previously reported. As stated above, the Ge
concentrations of the Si^Ge,, layers in previous studies were all significantly
higher than the Ge content of SL/Si. All SL structures and experimental
parameters of the respective studies have been described above. Hollander et
al. and Prokes and Wang reported intermediate activation energies of 4.0 eV
and 4.4 eV respectively. Boucaud et al. reported a low activation energy of
2.42 eV while Bean et al. reported the highest activation energy, 5.0 eV. This
wide range of activation energies may be due factors such as differences in
layer thicknesses, Ge content and analysis method used. Once again, the
activation energy reported by Prokes and Wang using HRXRD will be


131
Ge concentration, averaged over the entire thickness of the multilayers, of
SL/SiGe was x=0.05. This created a 'bulk' lattice constant of 0.5441 nm, leading
to a lattice mismatch with the Si085Ge015 buffer of 0.18%. The critical layer
thickness, hc, of an uncapped Si^Ge* layer with a lattice mismatch, fm, of
0.0018, is approximately 80 nm [Jai93]. The total thickness of the 'pseudo-
epilayer' of structure SL/SiGe was 270 nm which was more than three times
the critical layer thickness. High temperature thermal treatment was expected
to cause relaxation through significant misfit dislocation generation.
4.3 Processing
All samples were processed in an AG Associates Heatpulse 2101 rapid
thermal processor (RTP), the details of which can be found in section 3.2.1.
Initial experiments with structures SL/SiGe and SL/Si employed the
diffusivities determined from the single quantum well experiments in
Chapter 3. The resulting diffusion lengths after both furnace and rapid
thermal anneals were much too large; the structures had essentially annealed
to one average alloy composition, with no remaining wells in evidence. It
was concluded that, for the thickness of wells in structures SL/SiGe and
SL/Si, anneal temperatures and times must be lowered relative to the SQW
experiments. While anneal times were much too short to employ furnace
anneal, some anneal times were just beyond the reliability for RTP. The
longer SL anneals performed in the RTP were therefore pushing the limits of
the processing technique and future experiments should be done to confirm
the reliability at these times.


167
with respect to the Si buffer layer. This differs from SL/SiGe in which the Si
layers are in tensile strain while the Si085Ge015 layers are unstrained with
respect to the Si085Ge015 buffer layer. There is a finite critical thickness which
is approximated by the critical layer thickness of a single alloy layer with the
same volume-averaged Ge composition as described in Section 2.1. The
average Ge content, xav, is determined by [Kas95]:
xdc
x SiGe
aV dSiGe+dSl
(5-1)
where x is the Ge composition in the Sij.xGex layer, dSiGe is the thickness of the
S!.xGex layers and dSi is the thickness of the Si layers. Using this equation, the
Ge concentration, averaged over the entire thickness of the multilayers, of
SL/Si is x=0.05. The critical thickness of a capped layer of Si095Ge005 grown on
a Si buffer is hc~100nm [Jai94]. The total multilayer thickness of structure
SL/Si, 288 nm, greatly exceeds this value, therefore misfit dislocations are
expected to be present before and after thermal processing.
The cubic unit cell of the Sij.xGex can be isolated and used to describe
the strain state. A Ge composition of x=0.15 results in a lattice constant of
0.5461 nm and a volume of 0.1629 nm3 for the fully relaxed Si^Ge,, cubic unit
cell (Equation 1-1). Making an approximation which ignores any residual
strain in the Si layer, this lattice constant represents a lattice mismatch with
the underlying Si layer of 0.55% when fully strained. Assuming tetragonal
distortion, the perpendicular lattice constant, ax, is 0.5523 nm when fully
strained. As the structure relaxes, ax decreases while the parallel lattice


56
2.4 X-ray Diffraction
2.4.1 Overview
X-ray diffraction (XRD) is one of the most powerful and widely used
tools in semiconductor characterization [Bau96]. The applications vary from
crystal identification to measuring the quality of crystal growth. XRD is based
on Bragg's Law:
2dsin0B = nX (2-3)
An x-ray beam of wavelength X is incident upon a crystal at an angle 0B/ the
Bragg angle. A diffracted beam composed of a large number of scattered rays
mutually reinforcing one another is reflected from the atom planes. By using
x-rays of known wavelength and measuring the Bragg angle one can
determine the spacing, d, of the planes of the crystal.
Figure 2-15. Schematic of symmetric x-ray Bragg reflection [Cul78].


68
vacancy mechanisms to interdiffusion in Si0g5Ge015/Si SQWs was been made
by comparing SIMS profiles of annealed samples to profiles calculated by
FLOOPS diffusion simulations. Investigation of a Si/Si,.xGex/Si structure
with a buried boron (B) marker layer in the Si buffer region has addressed the
impact of dislocated Si,.xGex layers on interdiffusion (Section 3.4.2).
3.1 Growth Parameters and Structure
A SQW test structure (SQW/MBE) was grown by Molecular Beam
Epitaxy (MBE) at a temperature of 520 C. As shown in Figure 3-1, the
structure consisted of a lightly p-doped (100) Si substrate with an undoped 100
nm Si buffer layer, followed by an undoped 50 nm Si085Ge015 layer and an
undoped 50 nm Si cap.
Another SQW test structure (SQW/VPE) was grown using an ASM
Epsilon 1 vapor phase epitaxy reactor at a temperature of 700 C. The
structure consisted of a lightly p-doped (100) Si substrate with an undoped 100
nm Si buffer, followed by an undoped 50 nm Si085Ge015 layer and an undoped
50 nm Si cap. Structures SQW/MBE and SQW/VPE nominally differ only by
their growth method. The Si085Ge015 layer in SQW/VPE was grown using
SiCl2H2 (dichlorosilane), GeH4 (germane), and hydrogen (H2) as the carrier gas.
The silicon layers were grown at a rate of 5.0 nm/min while the Si0 85Ge015
layer was grown at a rate of 18.8 nm/min. The Ge concentrations of the Si,.
xGex layers for both structures were verified by Rutherford Backscattering
Spectroscopy (RBS) and the layer thicknesses were verified by cross-sectional
Transmission Electron Microscopy (XTEM).



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CHAPTER 5
BEHAVIOR OF ANNEALED ASYMMETRICALLY STRAINED Si/Si^Ge,
SUPERLATTICES WITH Si BUFFER
The limitless variations of Sij.xGex/Si superlattice structures enables
the synthesis of materials with custom-tailored electronic band structures
which can be utilized in a variety of optical applications. The Si,.xGex/Si SL
with a S!.xGex buffer discussed in Chapter 4, which produces n-type wells, is
one example of wavefunction engineering. Si1.xGex/Si superlattice layers
grown on a Si buffer result in p-type quantum wells which have most of the
band offset, and therefore hole confinement, in the valence band. This p-type
quantum well structure is easier and less costly to fabricate than the n-type
structure, due to its simple Si buffer. It is, therefore, more commonly used in
device applications and its interdiffusion behavior has been investigated
more thoroughly.
Even in superlattice material, with the Ge composition averaged over
many layers to create a more stable structure, strain relaxation through
dislocation formation and smearing of interfaces through interdiffusion
remain dominant issues in Sij.xGex/Si high temperature processing. The
effects of strain and composition are normally coupled, as Ge composition
determines overall strain between Si^Ge,, and Si layers. Comparing diffusion
behavior of Si1.xGex/Si SLs that are identical in every respect but their buffer
164


63
where n is the order of the satellite peak of interest, 0n is Bragg angle of the
nth order satellite peak, 0SL is the Bragg angle of the satellite peak of interest, X
is the wavelength of x-ray used, and A is superlattice period.
Through HRXRD the value of D will be calculated from the measured
decay of the intensity of the first satellite peak about the substrate as a
function of annealing time and resulting interdiffusion. The substrate peak
from the (004) reflection remains the same regardless of processing history.
The 0th order satellite peak represents the spacing of the lattice of the average
composition of the total of the deposited layers. The 1st order satellite peak
represents the periodicity of the SL layers, which changes significantly and
quickly upon annealing, therefore it is the satellite peak of interest. The decay
in the intensity, I, of the first order satellite x-ray peak after a long time
anneal, is directly related to the interdiffusion coefficient by:
T A
V^o J
(2-5)
where X is the SL period (cm) and IQ is the initial satellite x-ray peak intensity
before annealing [Bar90, Pro90]. By plotting ln(I/Ic) versus time, one can
determine D for different temperatures. Then, by plotting ln(D) versus 1/T,
for multiple temperatures, an Arrhenius expression for diffusion can be
obtained.


123
dominated by vacancies, as predicted by the oxidation experiments, would be
expected to show large enhancements under vacancy supersaturation. The
boron marker layer experiments indicated that vacancies were being injected
under nitriding ambient and should have enhanced the diffusion of the Ge.
A possible explanation for this contradictory behavior is that stress effects at
the nitride/silicon interface near the Si,.xGex layer, which are not present at
the depths of the B marker layer, contribute to this anomalous behavior of
the diffusion Ge. This possibility needs to be investigated further in future
work.
3.6 Conclusions
The experimental results discussed above have provided considerable
contributions to the knowledge of Ge diffusion behavior in Si1.xGex/Si single
quantum well structures. The diffusion model used in FLOOPS simulations,
while employing several simplifying assumptions, proved to be a satisfactory
first effort at predicting Ge diffusion behavior. The diffusion coefficient
appeared to be concentration-independent, however, further studies need to
be done to verify this conclusion. Diffusivities extracted from profiles
obtained over a wide range of anneal times and temperatures showed the Ge
diffusivity to be time-independent. Interdiffusivity also seemed to be
independent of growth method, as structures grown by both vapor phase
epitaxy or molecular beam epitaxy exhibited almost identical diffusion
behavior.


169
5.5 Results
5.5.1 SIMS/FLOOPS
The Ge concentrations of the annealed profiles were standardized with
respect to the total Ge concentration of the as-grown profile using the method
described in Section 2.3.1. The depth scale of SL/Si was difficult to standardize
because there was no Ge plateau or segregation peak with which to align the
as-grown and annealed profiles. The profiles were depth-aligned by matching
the depths of the first quantum well peak. In each case, the depth scale of
annealed samples was shifted no more than 20 nm in one direction. This
lateral movement was well within one standard deviation, estimated at 0.05,
in relative depth scale error of SIMS [Gos93]. Even so, minimal variations in
sputter rate from sample to sample caused a small amount of increasing
misalignment with depth. This misalignment did not hinder the fitting
process. The error in the extracted diffusivity values was determined from
the method described in Section 2.3.2.
The extracted diffusivity values for structure SL/Si annealed in inert,
oxidizing, and nitriding ambients are given in Table 5-1.
Table 5-1. Extracted diffusivity and enhancement values for SL/Si.
T (C)
time
(min)
DGeIner,(cm2/s)
DGex(cm2/s)
D^cmVs)
f *
Aenh
f Nit
*enh
850
8
4.00X10'17
1.12xl016
1.42x1 O'17
1.80
0.355
900
4
4.58xl017
4.58xl017
1.70xl017
1.00
0.371
950
3
1.73xl015
1.31xl0'15
3.46xl0'16
0.76
0.106
1000
2
1.18xl015
1.70xl015
1.07xl0'15
1.40
0.907


41
then coated with wax to prevent etching, while the backside was etched using
a solution of 25% HF: 75% HN03. The sample was etched until a small hole
with a slightly frayed edge developed at the center. This provided a region of
the sample that was sufficiently thin for the electrons to be transmitted in the
microscope and an image of the sample to be obtained.
2.2.2.2 Cross-sectional
Figure 2-5. Front and rear views of the XTEM assembly after preparation
[WU96].


54
Figure 2-14. SIMS profile of structure SQW/MBE. The concentrations of
oxygen and carbon impurities with depth are shown. Both O and C are piled
up at the buffer/substrate interface at sputter time ~12 min.
2.3.2 Determination of the Error in D
Throughout this study, SIMS was the primary method used (in
conjunction with FLOOPS) to determine interdiffusivity values. It was
therefore important to quantify the error involved in SIMS analysis to
determine the error incorporated in the extracted D values. There were two
sources of error in SIMS profiles: statistical fluctuations from (1) the
determined concentrations and (2) the depth scale. The error bars on the
extracted diffusivity values were determined from analysis of these errors


185
Depth (pm)
Depth (pm)
Figure 5-8. Comparison of Ge SIMS profiles in inert, oxidizing and nitriding
ambients for SL/Si. Sample annealed at (a) 900 C for 6 min and (b) 1000 C
for 2 min.


116
and fit to the SIMS profile determined from a sample annealed at 900 C from
0 to 980 min, known as Sample 2. In future work, a simulated anneal will be
performed on the initial profile (Sample 1) for 650 min and fitted to a SIMS
profile of Sample 1 further experimentally annealed at 900 C for 650 minutes.
While it is currently unknown whether there will be any difference in
diffusivity values between the two approaches, this second method will more
accurately reflect the simulations being performed.
It is also important to note here that Fang [Fan96] concluded that the
degree of Si^Ge, relaxation is relatively independent of the number of
absorbed interstitials and that the interstitials do not accelerate or hinder the
relaxation process.
3.5.3 Misfit Dislocation Effects
It is has been shown through XTEM and PTEM results (Section 3.4.3)
that, at such high processing temperatures, strain from the sample structure is
relieved through misfit and threading dislocation formation. There is then a
possibility that during processing in an oxidizing ambient or a nitriding
ambient, the injected interstitials or vacancies may be captured by the
dislocations. The injected interstitials or vacancies, once captured, can play
no role in altering the C, or Cv value under interstitial or vacancy injection
and therefore Q remains equal to Q* or Cv remains equal to Cv*. The
experiment described in Section 3.4.3 was employed to determine whether
excess interstitials injected through surface oxidation are captured by
dislocations or travel through the dislocated layers unimpeded.


203
Diffusion coefficients and an activation energy for diffusion of an Sij.
xGex/Si SL with a Si1.xGex buffer layer were extracted for the temperature range
850 to 1000 C in inert, oxidizing, and nitriding ambients.
Diffusion coefficients and an activation energy for diffusion of an Sij.
xGex/Si SL with a Si buffer layer were extracted for the temperature range 850
to 1000 C in inert, oxidizing and nitriding ambients.
Unit cell lattice parameter values for annealed SLs with both Sij.xGex
and Si buffer layers were calculated using HRXRD (inert, oxidizing, and
nitriding ambients).
6.3 Future Work
6.3.1 Single Quantum Well Investigations
It is recommended that attempts be made to replicate some of the less
conclusive experiments presented for SQW diffusion. Particularly, it should
be conclusively determined whether the fractional vacancy component is
constant with temperature, as interpreted in Chapter 3, and in relation,
whether the retarded diffusion observed in oxidizing ambient at high
temperatures can be attributed to an increasing fractional interstitial
component or to a higher recombination rate. It is also recommended that
experiments be performed to confirm whether diffusivities of fully strained
SQWs are different from those of partially relaxed for an anneal temperature
of 1200 C, as reported in Chapter 3. Further studies should also be performed


76
electrochemical potential. The Fermi level therefore changes as the electron
concentration changes. Fermi level effects due to all charge states of the
dopant are still accounted for through the D* parameter which is described by
equation 3-3.
In this study the Fermi model was used to determine the diffusivity
under inert conditions as well as the diffusivity occurring during vacancy and
interstitial supersaturation. In the case of Ge atoms in a Si lattice, the Ge is
neutral (uncharged) within the Si lattice, so there are no dopant Fermi-level
effects and therefore the Fermi model and Neutral model are equivalent in
this case. Any electric field effects were ignored in the initial attempts to
model the system. There were two reasons for this: (1) Fermi level effects of
ionized defects were assumed to be orders of magnitude smaller than dopant
concentrations-too small to contribute to an electric field and (2) the
substitutional dopant atom (Ge) is neutral within the host lattice (Si).
The Pair model was used to determine the fractional interstitial and
vacancy components, f, and fv. The diffusivity under inert conditions,
previously determined from the Fermi model, was used as the value for D*.
The inert diffusivity was proportioned into interstitial and vacancy
components such that:
D* =Df+Dv
(3-6)
so that the parameter f, could be defined such that:


CHAPTER 1
INTRODUCTION
Recently there has been increased interest in alloys of silicon and
germanium (Sij.xGex) for applications in electronics and photonics. Devices
incorporating Si-Ge solid solutions show increased speeds as well as other
desirable features over the equivalent pure Si devices. The manufacture of
these devices includes several high-temperature and oxidation steps, and it is
necessary that S!.xGex heterostructures be able to withstand these processing
steps without device degradation such as interface broadening and
intermixing of the device layer structure. Therefore, it is important to
understand the diffusion processes that cause degradation.
Common Si^Ge,, device designs include single quantum well (SQW),
monolayer superlattice, and multiple quantum well (MQW) structures. The
single quantum well material normally consists of a buffer layer grown on a
Si substrate, followed by a Si,.xGex layer and a Si cap layer, Si/Si1.xGex/Si. In
the monolayer superlattice material, m atomic layers of pure Si are deposited
followed by n atomic layers of pure Ge (m and n are usually <10), with this
pattern repeated p times, (SimGen)p. For the MQW material a layer of pure Si
is grown, followed by a layer of Sij.xGex alloy of particular composition, x, with
this pattern repeated for a determined number of periods, p, (Si/Si1.xGex)p.
Each structure has diffusion characteristics which are influenced by such
1


53
Figure 2-12. Ge concentration profile determined from SIMS for sample
structure SQW/VPE.
Figure 2-13. Ge concentration profile determined from SIMS for sample
structure SQW/MBE.


Relative intensity (counts) P Relative intensity (counts)
60
32 33 34 35 36 37
Omega ()
X-ray rocking curve of structure SL/SiGe before anneal.
104 F
1000 ^
100 r-
34 35
Omega ()
Figure 2-19. X-ray rocking curve of structure SL/Si before anneal.


59
intensity, which allows observation of weak diffraction satellite peaks from
thin superlattice layers. Triple axis mode was employed in 20 scans in this
study to identify the Bragg angle in weak reflections from the Si/Sij.xGex
superlattice layers.
Sample
J
Figure 2-17. Schematic of the x-ray path used in triple axis mode. The x-rays
are directed to a double crystal analyzer after impinging on the sample and
before heading to the detector.
X-ray rocking curves were taken of the superlattice structures SL/SiGe
and SL/Si as grown using the methods just described (Figure 2-18 and 2-19).
Distinct satellite peaks, of both positive and negative order, can be seen for
each structure, surrounding the high intensity Si substrate peak at (0=34.5.
The first satellite peak to the left of the substrate peak is considered the Oth
order peak and denotes the average composition of the Si1.xGex/Si layers. The
1st order peak to the left of the Oth order peak is the first peak that represents
the periodicity of the Si/ Si^Ge,, SL layers. This is the peak used in this work
to extract diffusivities from HRXRD scans (Section 2.4.3). In each scan,


119
to be written. Interstitials are captured but not completely, thus there is an
upper bound on the interstitial capture.
Movement of the B marker layer cannot determine the vacancy
supersaturation as a result of surface nitridation because it is primarily an
interstitial diffuser. Any evidence of retardation of B diffusion can, however,
qualitatively show that vacancies are being injected to the extent that they are
depleting the interstitial concentration. From the values of tNi(/tActua] given in
Table 3-4 for 1100 C, it is apparent that there is slight retardation of the
diffusion of the B marker layer, which indicates that vacancies are indeed
being injected into the bulk and are traveling to some extent through the Si,.
xGex layer. Future work with Sb marker layers (Sb is known to diffuse almost
entirely via a vacancy mechanism) would allow an quantitative estimate of
the vacancy supersaturation under nitriding ambient through similar a
method similar to that described above.
Fang [Fan96] also used the presence of misfit dislocations nucleated by
an unstably strained Si1_xGex layer to determine whether the dislocations act as
an interstitial barrier. Boron marker layers were grown in and on either side
of a Si0g0Ge020 layer of varying thickness and the resulting samples were
annealed at 850 C in either an inert or dry Oz ambient, much like the
experiment performed above. For the thin layers, including the 50 nm layer
similar to that used in this thesis, boron diffusivity was equivalent for the
surface and buried B marker layers in inert ambient. Under oxidizing
ambient, the surface marker layer diffused much more than the buried


71
temperature (1000 to 1200 C), however, the measurement of oxide thickness
is a very reliable approach to calibrating surface temperature. At lower
temperatures (600 to 1000 C) activation of dopant implants is often used
[Roo93].
The RTP temperature for these investigations was initially calibrated
through oxide measurements [Mos85, Gon94]. Temperature uniformity
across the wafer is a main concern during RTP. The edge temperature can
often be lower than the center temperature, with an overall wafer
temperature non-uniformity of as much as 20C [Pet91]. To determine the
extent of temperature uniformity across the silicon wafer, the wafer was
processed in the RTP in flowing dry 02 ambient at processing times and
temperatures similar to those used to process the Si1.xGex/Si structures. The
resulting oxide film was characterized using an ellipsometer to measure
thickness at five points across the wafer. Film thickness was found to be the
same across the wafer, within the error of ellipsometer measurement (1 n m
[Sch90]). This indicates that the uniformity across a four inch wafer is within
the error of temperature measurement, 10 C.
To more accurately determine the RTP calibration, a thermocouple
wafer was also used to calibrate the pyrometer. A W5%Re/W26%Re (Type C)
thermocouple was embedded in a Si wafer using e-beam welding [Hoy88]. The
reading of this thermocouple was compared to the pyrometer output at
temperatures from 800 to 1200 C at 50 degree intervals. At each temperature,


171
This is the first time that activation energies for interdiffusion under
interstitial injection and vacancy injection for Si,.xGex/Si superlattice layers
with a Si buffer have been directly determined from experiment.
As stated in Chapter 4 for SL/SiGe, the method used in Chapter 3 to
estimate fractional interstitial components of diffusion for SQW/MBE could
not be applied to SL/Si. No SL structure was available with a buried boron
marker layer underneath the multiple Sij.xGex/Si layers to estimate point
defect concentrations. Therefore, the non-equilibrium values of C, and Cv
specific to dislocated SL/Si which occured as a result of surface oxidation and
nitridation could not be estimated. It was considered scientifically pointless to
estimate an f, for diffusion from either oxidation or nitridation experiments
without some knowledge of C,/C,* and Cv/Cv* for SL/Si under the
investigated processing conditions.
5.5.2 High Resolution Xray Diffraction
As described in Section 4.5.2, HRXRD characterization provides
information about the lattice constants of a crystal structure both before and
after thermal treatment. The strain relaxation process resulting from anneal
can, therefore, be completely defined. Through alternate analysis, HRXRD
can also provide values of the diffusivities of the annealed crystal (Section
4.5.2). The knowledge of the process by which the crystal relaxes enables a
more thorough interpretation of the diffusivity data obtained. Lattice
constants and diffusivities of SL/SiGe have already been calculated and
reported in Chapter 4. Structures SL/SiGe and SL/Si are similar in every


163
dislocation densities of the annealed samples were approximately constant
regardless of anneal time or temperature. This suggests that misfit
dislocations are created in the initial stages of relaxation and remain constant
with further annealing. Cross-sectional TEM micrographs showed that, due
to differences in hardness between Si and Si^Ge,,, most of these misfit and
threading dislocations propagated into the Si substrate and Si cap, and not
into the Sij.xGex multilayer region. This conclusion regarding misfit
dislocation generation was supported by HRXRD analysis of SL/SiGe strain
relaxation. The lattice constants of the SL/SiGe pseudo-epilayer were seen to
change upon anneal when compared to the as-deposited values, but
remained relatively constant when compared to other annealed samples.
Attempts to extract a diffusion coefficient from the intensities of the first
order satellite peaks from g>-20 HRXRD scans provided values that were
unreliable. While characterization through HRXRD seems promising, future
work must be done to perfect the experimental technique and diffusion
coefficient extraction method.


Omega (degrees)
Figure 4-3. X-ray diffractometer scans of the SL/SiGe superlattice peaks about Si(004) with increasing anneal times
inert ambient. The diffusion coefficients have been obtained from the decay of the SL peak marked 1st order'.


18
temperature variation and transient phenomena) and composition. The
temperature dependence of the diffusion coefficient in solids is generally well
described by an Arrhenius relation:
D = D0exp(-Ea/kT) (1-8)
where D0 is the weakly temperature-dependent pre-exponential factor, Ea is
the activation energy of transitions of the solute between adjacent lattice sites,
k is the Boltzmann constant, and T is temperature. The magnitude of Ea can
help to identify the diffusion mechanism. Both D0 and Ea can depend on the
strain state, composition, and gas ambient (e.g., inert, oxidizing, or nitriding).
1.3.2 Point Defects and Diffusion Mechanisms
Derivation of a form for D used in continuum equations necessitates
an understanding of the atomistic mechanism by which the diffusing species
migrates through the crystal lattice. Hence, the coupling of a continuum
approach to describe the spatial and temperal concentration dependency and
an atomistic approach to describe the functional form of the mass diffusivity
is the basis of the semi-empirical approach. There are several atomic
pathways available for diffusion, of which the ring, interstitial, and vacancy
mechanisms are the most elementary.
The ring mechanism is simply the exchange of two neighboring lattice
atoms, without the involvement of point defects. This mechanism has not
been seen experimentally, and would be theoretically improbable due the


92
vacancies vary with processing time [Fah89]. (7) The D* and f, values from
step (6) were used in Equation 3-5 for each additional processing time, along
with the limiting values of Cv/Cv* from step (2), to determine upper and
lower bounds for C,/C,*. For some processing temperatures and times the
upper limit of Cv/Cv*=l was too high to give sensible values of either f, or
C,/C*, so the limit was lowered until sensible values could be obtained.
These values of D*, C,/C,*, Cv/Cv* and f, determined from steps (1) through (7)
for inert and oxidizing experiments for each temperature and processing time
are given in Tables 3-5 and Table 3-6 respectively. The first row for each
processing time represents the results using the lower bound for Cv/Cv*,
while the second row represents the results using the upper bound. The cells
with no data represent conditions in which the particular bound did not
provide reasonable results for either f, or C,/C,*.
The above method was applied to the nitriding ambient experiments
conducted at 1100 and 1200 C to determine f, and Cv/Cv* values during
vacancy supersaturation. The C,/C* ratio of SQW/MBE was estimated using
the tNit/tActual ratio from the values listed Table 3-4, but in this case Cv/Cv* had
a lower bound of l/( C,/C,*)and an upper bound of infinity. This was because
the B marker layer only measured the enhancement/retardation from the
interstitial concentration not the amount of vacancies being injected, thus
C,/C,* could be calculated but not Cv/Cv*. The supersaturation of vacancies
can only be reliably estimated by quantifying the movement of a dopant


189
If their Arrhenius expression derived for the diffusivity over this
temperature range is slightly extended to 900 C, a diffusion coefficient of
approximately 9.4xl0'17 cm2/s can be extracted, which is three orders of
magnitude lower that of this study, but almost the same as that determined
from SIMS/FLOOPS. This is additional verification that the values
determined through SIMS/FLOOPS are more reliable than those through
HRXRD and that, while HRXRD shows potential for providing dependable
diffusion coefficient data, much more work needs to be done to refine the
instrumental method needed to obtain scans that are reliable.
5.6.3 Strain Relaxation from HRXRD
Table 5-4. Diffusivities of SL/Si extracted from FLOOPS and HRXRD.
D(>lnert (cm2/s) DGex (cm2/s) D^* (cm2/s)
T CC) FLOOPS HRXRD FLOOPS HRXRD FLOOPS HRXRD
900 4.58xl017 2.13xl016 4.58xl017 1.70xl017 5.24xl017
1000 1.18xl0*15 5.17xl016 1.70xl015 6.14xl017 1.07xl015 1.29xl015
Section 5.5.2.2 briefly described the HRXRD method used to determine
the perpendicular and parallel lattice constants of the epilayer which are used
estimate the strain relaxation which occurs in periodic SLs with thermal
processing. All results using this method are listed for SL/Si in Table 5-3.
The change in the angular separation of the zero order epilayer peak
and the Si(004) substrate peak with time did not show the expected trend.
Because the epilayer is in compressive strain when grown on the Si buffer, it


186
interstitial point defects play a measurable role in the diffusion process in this
temperature range. Diffusivities extracted for both ambients at
highertemperatures 950 and 1000 C are similar and within error of each
other, as illustrated in Figure 5-2. Ge depth versus concentration profiles at
these temperatures are virtually identical (Figure 5-8b). At these higher
temperatures, diffusion is unaffected by interstitial superstaturation. This
leads to the conclusion that interstitials play a decreasing role in diffusion
with increasing temperature. Once again, because of the non-Arrhenius
behavior of the diffusivity values, these conclusions must be confirmed with
continued studies.
The activation energy of 2.81 eV0.21 calculated for interdiffusion in
oxidizing ambient is the first reported for Si/Si1.xGex SL with a Si buffer layer.
This activation energy is notably less than that for diffusion in inert ambient
and may indicate that the interstitial component of Si/Sij.xGex SL
interdiffusion is significant. This result is similar to that found for SL/SiGe.
The activation energy of 4.16 eV0.22 calculated for the interdiffusion
in nitriding ambient is the first activation energy of interdiffusion under
vacancy injection reported for a Si/Si1.xGex SL with a Si buffer layer. This
activation energy is 0.5 and 1.5 eV higher than that for diffusion in inert
ambient and oxidizing ambient, respectively, and very similar to the results
found for SL/SiGe. Like the behavior found for SL/SiGe, from the activation
energies alone, one would expect that oxidation (interstitial injection) of
SL/Si would enhance diffusion, while nitridation (vacancy injection) would


74
= VDVC + XEfield
(3-1)
with the diffusivity of the dopant, D, given as:
(3-2)
where C is the concentration of dopant atoms (cm'3), t is time (min), and E^
is the electric field (V/cm). DN denotes the diffusivity of the neutral
(uncharged) dopant atom (cm2/s), D0 is a pre-exponential constant (cm2/s), Ea
is the activation energy (eV) and k is the Boltzmann constant (8.62xl0'5
eV/K).
In the Fermi model, Fick's law is solved in the same form as equation
3-1, but the diffusivity is given as:
(3-3)
where D0 is the diffusivity of the dopant in its neutral state, D+ and D are the
diffusivities of the dopant in its singly positively and negatively charged
states respectively, D++ and D= are the diffusivities of the dopant in its doubly
positively and negatively charged states, respectively, p and n are the hole and
electron densities, respectively, and n¡ is the intrinsic carrier concentration.
The ionized dopant diffusivities are expressed in an Arrhenius form after
equation 3-2.
The Pair model uses Fick's law in the form:


172
respect except for their original strain state. Applying identical HRXRD
experimental method and analysis for structure SL/Si to that performed for
SL/SiGe will allow the impact of strain state to be determined directly.
The technique used to extract diffusivity values for SL/Si is identical to
that described in Section 4.5.2.I. In Section 5.5.2.1, results for SL/Si are
presented. The analysis of the effect of high-temperature processing on SL/Si
is completed in Section 5.5.2.2 by determining strain relaxation as a function
of anneal time.
5.5.2.1 Diffusivities
For the purpose of measuring the intensity of the 1st order satellite
peak of SL/Si, symmetric scans only were needed. The scans of SL/Si were
performed using the (004) reflection plane, the substrate/growth plane
direction. Scans were taken at co=34.5 and 20=69.1, the values at which the
Si(004) peak is at maximum intensity, to-20 scans were taken over a 4 range
of co, with a step size of 0.00025 and time per step of 4s, resulting in 16001
steps, to-20 scans were taken of the as-grown SL/Si structure as well as for
samples annealed at 900 C for 4, 6 and 8 min and at 1000 C for 1, 2 and 3 min.
These anneal times and temperatures were identical to those used in Chapter
4 for SL/SiGe, in order facilitate direct comparison of diffusion behavior in
both structures. Examples of resulting scans of SL/Si are shown in Figure 5-3,
taken at increasing anneal times for a constant anneal temperature of 1000 C
in inert ambient.


210
plot. 1 d label=Final !cle
profile name=target infile=1.950.180A
sel z=log10(target)
plot. 1 d label=Experimental lele


127
cause absorption and lead to photodetection. In this chapter results and
discussion of diffusion studies performed using this n type quantum well
structure are presented.
Thermal stability of these lattice-mismatched SL heterostructures is a
critical issue because high-temperature processing steps are often unavoidable
during optical device fabrication. Thermal treatment can result in
interdiffusion as well as strain relaxation through the formation of
dislocations. Any smearing of interfaces due to Ge segregation during the
growth and processing of the SLs can lower the transition energy significantly
[Fuj92]. As a consequence, the electronic and optical properties of the device
structure, such as band alignment, may change, severely degrading the device
performance [Zhu97].
Interdiffusion of Sij.xGex/Si asymmetrically strained superlattice (ASL)
material in inert, oxidizing, and nitriding ambients over a temperature range
850 to 1000 C has been investigated. Thermal processing in all three
ambients over the same temperature range has allowed estimation of
diffusivity values for interdiffusion of Si0g5Ge015/Si superlattice material with
Sii_xGex buffer under interstitial and vacancy supersaturation as well as under
inert conditions.
4.1 Growth Parameters and Structure
Test structure SL/SiGe was grown using an ASM Epsilon 1 vapor phase
epitaxy reactor at a temperature of 700 C. As shown in Figure 4-1, the
structure consists of a lightly p-doped (100) Si substrate with an undoped 100


slightly with time in all ambients, while the values of ael were found to
decrease slightly.
Disregarding the possible errors in lattice constant measurement
(Section 4.5.2.2), and assuming the evident trends are correct, it is logical to
conclude that the strain state of the structure must be redefined to fit the
experimental results. One possible way to accomplish this is to consider that
the Si1.xGex buffer layer contributes to the epilayer peak. The average
composition of the 'epilayer' then changes and the Si(004) substrate, not the
Sij.xGex buffer, becomes the basis for defining the state of the epilayer strain.
If this approach is adopted then the average composition of the
'epilayer' is now x=0.08. This creates a 'bulk' lattice constant of 0.5447 nm,
leading to a lattice mismatch with the Si(100) substrate of 0.29%. The strained
layer grown on the Si(100) buffer would be in compressive strain therefore its
parallel lattice constant would increase with increasing relaxation, while the
perpendicular lattice constant would decrease.
While this approach yields theoretical values that correspond better
with experimentally determined values than those of the original approach,
there are still some anomalies. The ae// value does increase with time in inert
and oxidizing ambients towards the fully relaxed value, reaching a partially
relaxed value of approximately 0.5440 nm for both temperatures. In nitriding
ambient at 900 C, ae// decreases from its original value but remains the same,
~ 0.5433 nm, with increasing anneal time, while at 1000 C there is obvious
relaxation with increasing time. In all ambients the ael value, however,


106
a.
8
o
10-12
10-13
10'14
10-15
1016
10-17
6.5 7 7.5 8 8.5 9
1/T 104 (K'1)
1200 C 1100 C 1000 C
Â¥
, i
900 C
SQW/MBE
O SQW/VPE
_i I i i i i I i l.
. 1
J I I I
1200 C 1100 C 1000 C 900 C
Figure 3-11. Comparison of diffusivities of structures SQW/MBE and
SQW/VPE in (a) inert ambient and (b) oxidizing ambient. Diffusivities at all
temperatures are within error of each other.


128
nm Si0g5Ge015 buffer, followed by 15 periods of 6 nm Si0g5Ge015 and 12 nm Si.
The Si0g5Ge015 layers were grown using dichlorosilane, GeH4 (germane), and
H2 as the carrier gas. The silicon layers were grown at a rate of 5.0 nm/min
while the Si0g5Ge015 layers were grown at a rate of 18.8 nm/min. The Ge
concentrations of both the buffer and superlattice layers were verified by
Rutherford Backscattering Spectroscopy (RBS) and the layer thicknesses were
verified by cross-sectional Transmission Electron Microscopy (XTEM).
12nm
6nm
12nm
6nm
100nm Si^e,; Buffer
Si Substrate
Figure 4-1. Schematic of sample structure SL/SiGe.
The Ge depth versus concentration profiles for as-grown and annealed
samples were determined by Secondary Ion Mass Spectroscopy (SIMS) using a
Perkin Elmer PHI 6600 quadrapole analyzer with a 6 kV oxygen beam. The
profile depth scales were determined from Tencor Alpha-Step 500 surface
profiler measurements of the SIMS sputtered craters.


98
images of sample SQW/VPE annealed at the same temperatures and times
show opposite results to those of SQW/MBE. The sample annealed at 900 C
for 330 min shows a very large increase in misfit dislocations, as well as large
numbers of threading dislocations (Figure 3-8a). After anneal at 1200 C for 1
min, there was a much lower misfit dislocation density and no evidence of
curved segments indicating threading dislocations (Figure 3-8b). The reason
for the contradictory behavior of SQW/MBE and SQW/VPE is unknown.
From the experiments done in this study, it is difficult to determine
exactly what impact this increase in dislocation density had on interdiffusion.
These TEM results suggest that future work needs to be done with structures
which are pseudomorphic.
3.5 Discussion
3.5.1 Diffusivities of Fully-Strained Structures
The FLOOPS diffusion models used in this study were the Fermi and
Pair models. The diffusion profiles generated by the Fermi model provided
very good fits to the experimentally determined SIMS profiles in the case of
anneals performed in inert ambient, as demonstrated in Figure 3-9a for 1000
C and an anneal time of 43 min. This indicates that the assumptions made
in the FLOOPS model (Section 3.3), while not necessarily accurate, are good
enough to provide diffusivity values that are reasonable.


150
thicknesses of the two structures, or to the more significant differences in
strain state and diffusivity extraction method. The temperature and
diffusivity spans of Hollander et al. and this study are almost identical,
therefore it is impossible to conclude that one study is more reliable than the
other. Furthermore, the diffusivities are similar enough to consider both
studies dependable contributions.
10'14
'w
eg
E
o, 10'15
8
a
10'16
nr17
7 7.5 8 8.5 9
1/T*104(K1)
Figure 4-8. Diffusivities of Ge in Si,.xGex/Si SLs with a Si,.xGex buffer layer
from (+) Hollander et al. and () this work.
The activation energy of Ge diffusion in Si1.xGex/Si SLs with a S!.xGex
buffer layer in inert ambient determined in this study, approximately 3.14
eV0.20, is lower than, and not within error of, that reported by Hollander et
al, 4.5 eV0.20. Once again, the temperature range of both studies overlaps at
1000 C 950 C 900 C
i 1 r


4.6.2 Diffusivities Determined from HRXRD 156
4.6.3 Strain Relaxation Determined from HRXRD 159
4.7 Conclusions 161
5 BEHAVIOR OF ANNEALED ASYMMETRICALLY STRAINED Si/Si, xGex
SUPERLATTICES WITH Si BUFFER 164
5.1 Growth Parameters and Structure 165
5.2 Strain State 166
5.3 Processing 168
5.4 Simulation of Diffusion 168
5.5 Results 169
5.5.1 SIMS/FLOOPS 169
5.5.2 High Resolution Xray Diffraction 171
5.5.2.1 Diffusivities 172
5.5.2.2 Strain relaxation 175
5.5.3 TEM 176
5.6 Discussion 179
5.6.1 Diffusivities Determined from SIMS and FLOOPS 179
5.6.2 Diffusivities Determined from HRXRD 187
5.6.3 Strain Relaxation from HRXRD 189
5.6.4 Effect of Strain State on Diffusivity Values 191
5.7 Conclusions 194
6 CONCLUSIONS AND FUTURE WORK 197
6.1 Conclusions 197
6.1.1 Single Quantum Well Structures 197
6.1.2 Super lattice Structures 199
6.1.3 Strain Effects 201
6.2 Contributions 201
6.2.1 Modeling 201
6.2.2 Experimental 202
6.3 Future Work 203
6.3.1 Single Quantum Well Investigations 203
6.3.2 Superlattice Investigations 204
6.3.3 Simulations and Modeling 205
APPENDIX A EXAMPLES OF FLOOPS PROGRAMS 206
APPENDIX B GLOSSARY 211
REFERENCES 215
BIOGRAPHICAL SKETCH 222
vm


166
grown at a rate of 5.0 run/min while the Si085Ge015 layers were grown at a rate
of 18.8 nm/min. The Ge concentrations of both the buffer and superlattice
layers were verified by Rutherford Backscattering Spectroscopy (RBS) and the
layer thicknesses were verified by cross-sectional Transmission Electron
Microscopy (XTEM).
50nm
12nm
6nm
12nm
6nm
100nm si Buffer
Si Substrate
Figure 5-1. Schematic of sample structure SL/Si.
The Ge depth versus concentration profiles for as-grown and annealed
samples were determined by Secondary Ion Mass Spectroscopy (SIMS) using a
Perkin Elmer PHI 6600 quadrapole analyzer with a 6 kV oxygen beam. The
profile depth scales were determined from Tencor Alpha-Step 500 surface
profiler measurements of the SIMS sputtered craters.
5.2 Strain State
Structure SL/Si is considered asymmetrically strained because the
Si0 85Ge015 layers are in compressive strain while the Si layers are unstrained
Si Cap
Si
Si
x16


88
SIMS profile after anneal. For diffusion in nitriding ambient, the vacancy
supersaturation at the surface was set at the established ratio [Mog96], which
then set the non-equilibrium interstitial concentration. Once again, the time
of anneal was changed in FLOOPS until the simulated profile fit the SIMS
profile after anneal. Table 3-4 gives a summary of the anneal times calculated
by FLOOPS compared to the actual anneal times in inert, oxidizing and
nitriding ambients. Actual anneal times are given in column 2.
CD
1020
1019
1018
1017
1 p16
1015
0 0.5 1 1.5 2 2.5
Depth (pm)
Figure 3-5. Diffusion of as-grown B marker layer in all ambients. Sample was
annealed at 1100 C for 2 minutes. Diffusion of B in oxidizing ambient is
noticeably greater than in inert and nitriding ambients.
Table 3-4. Anneal times needed in FLOOPS to achieve actual B diffusion
profiles.
T (C) actual anneal time
(min)
tAr (min)
tGx (min)
tNi, (min)
900
330
1100
2200
1000
43
90
160
1100
2
6
32
2.6
1200
1
0.7
0.6
0.5


37
strained layer. Kasper [Kas95] cites a model in which the average Ge content,
xav, is determined by:
_ X(^SiGe
aV dSiGe+dSl
(2-1)
where x is the Ge composition in the Sij.xGex layer, dSiGe is the thickness of the
Sij.xGex layers and dSi is the thickness of the Si layers. Using this equation, the
Ge concentration averaged over all multilayers of SL structures SL/SiGe and
SL/Si was x=0.05. The critical thickness of a capped layer of Si^Ge,, grown on
a Si buffer is hc~100nm (Figure 1-4). The total multilayer thickness of
structure SL/Si, 288 nm, greatly exceeded this value, therefore misfit
dislocations were expected to be present. For structure SL/SiGe an average Ge
composition of x=0.05 created a 'bulk' lattice constant of 0.5441 nm, leading to
a lattice mismatch with the Si085Ge015 buffer of 0.18%. The critical layer
thickness, hc, of an uncapped Si^Ge,^ layer with a lattice mismatch, fm, of
0.0018, was approximately 80 nm [Jai93]. The total thickness of the 'pseudo-
epilayer' of structure SL/SiGe was 270 nm which was more than three times
the critical layer thickness; therefore, like the SL/Si structure, dislocations
were expected to exist in structure SL/SiGe.
2.2 Transmission Electron Microscopy
2.2.1 Overview
In transmission electron microscopy (TEM) electrons from an electron
gun are accelerated to high voltages (100 to 400 kV) and focused onto a sample


81
This is the first time that activation energies for interdiffusion of Si,.xGex/Si
layers under interstitial injection and vacancy injection have been directly
determined from experiment. The activation energy in nitriding ambient is
provided for comparison purposes only, and is not statistically reliable
because it was extracted from only two data points. This statement also
applies to Equation 3-13 for SQW/VPE.
1200 C 1100C 1000 C 900 C
Figure 3-2. Effective Ge diffusivity of structure SQW/MBE as a function of
annealing temperature in inert, oxidizing, and nitriding ambients.


Ge concentration (cm'3) Ge concentration (cm'3)
154
Depth (pm)
Figure 4-9. Comparison of Ge SIMS profiles in inert, oxidizing, and nitriding
ambients for SL/SiGe. Samples annealed at (a) 850 C for 8 min and (b) 1000
C for 2 min.


86
play in Ge diffusion in the Si1.xGex layer. Before interpreting the diffusivity
results given above, it had to be determined whether the injected interstitials
were indeed trapped by the dislocations or whether they traveled to and
throughout the Sij.xGex layer to participate in the diffusion process.
A test structure, hereafter referred to as SQW/B, was grown which
consisted of a lightly doped p-type Si (100) substrate with a 50nm Si buffer,
followed by a 200nm boron-doped Si layer, with a B concentration of 5xl018
cm'3. A layer structure identical to that of the original SQW/MBE and
SQW/VPE test structures was grown on top of these layers: a 1 pm Si "buffer"
layer, followed by a 50 nm undoped Si^Ge,,^ layer and an undoped 50 nm Si
cap layer (Figure 3-4).
50nm Si Cap
50nm SijBe,,
1|xm
Si
200nm Si:B (Sxia^nv3)
50nm Si
p-Si(100) Substrate
Figure 3-4. Schematic of test structure SQW/B. A buried boron marker layer
is positioned below Si/Si1.xGex/Si layers similar to the SQW/MBE and
SQW/VPE test structures.


207
FERMI MODEL: OXIDIZING AMBIENT
dopant add name=Germanium
pdbSetDouble Si Ge I DO { [Arrhenius 1.37e5 5.2] }
pdbSetDouble Si Ge I Dp 0
pdbSetDouble Si Ge V DO 0
pdbSetDouble Si Ge V Dp 0
pdbSetSwitch Si Ge DiffModel Fermi
line x loc = 0.0 tag = surf spac=0.003
line x loc = 0.05 tag = cap spac=0.003
line x loc = 0.10 tag = sige spac=0.005
line x loc = 0.20 tag = buffer spac=0.003
line x loc = 0.25 tag = back spac=1
region silicon xlo = surf xhi = back
init
profile name=Germanium infile=1819AsGrown2.98
sel z=log10(Germanium)
plot. 1 d label=lnitial
diffuse time=1532 temp=900 dry
sel z=log10(Germanium)
plot. 1 d label=Final lele
profile name=target infile=1819.900.1532f.Ox
sel z=log10(target)
plot.ld label=Experimental lele


i i
178
20,000x
500nm
Figure 5-5. Plan view TEM micrographs of structure SL/Si after annealing in
inert ambient at 850C for 8 min.


165
layer allows the effects of composition and strain to be decoupled. Si^Ge^Si

multilayers grown on a Si^Ge,, buffer produces tensile strain in the Si layers
and only residual strain in the Si,.xGex layers. On the other hand, Sij_xGex/Si
multilayers grown on a Si buffer produces only residual strain in the Si layers
and compressive strain in the Si1.xGex layers. By comparing structures with
identical Ge composition, layer thickness and number of periods, the effect of
strain state on inter diffusion can be independently determined.
Interdiffusion of a Si1.xGex/Si asymmetrically strained superlattice
(ASL) with a Si(100) buffer over a temperature range 850 to 1000 C in inert,
oxidizing, and nitriding ambients has been investigated. Thermal processing
in all three ambients over the same temperature range has allowed
estimation of the diffusion coefficient of interdiffusion of Si085Ge015/Si
superlattice material with Si(100) buffer under interstitial and vacancy
supersaturation as well as under inert conditions. These results have been
compared to those reported in Chapter 4 for Si0 85Ge015/Si ASLs with a Si1_xGex
buffer to determine the effect of strain state on interdiffusion.
5.1 Growth Parameters and Structure
Test structure SL/Si was grown using an ASM Epsilon 1 vapor phase
epitaxy reactor at a temperature of 700 C. As shown in Figure 5-1, the
structure consists of a lightly p-doped (100) Si substrate with an undoped 100
nm Si buffer, followed by 16 periods of 6 nm Si0 85Ge015 and 12 nm Si and an
undoped 50 nm Si cap. The Si085Ge015 layers were grown using dichlorosilane
(DCS), GeH4 (germane), and H2 as the carrier gas. The silicon layers were


217
Gos93 Gossman, H.-J., Vredenberg, A.M., Rafferty, C.S., Luftman, H.S.,
Unterwald, F.C., Jacobson, D.C., Boone, T., & Poate, J.M., T. Appl.
Phvs. 74. 3150 (1993).
Gru97 Gruhle, A., & Schuppen, A., Thin Solid Films 294,246 (1997).
Had95 Haddara, Y.M., Lee, C.C., Hu, J.C., Deal, M.D., & Bravman, J.C.,
Materials Research Soc. Bulletin 20,41 (1995).
Han93 Hansen, S.E., & Deal, M.D., SUPREM IV.GS User's Manual,
(Stanford University, Stanford, CA, 1993).
Hay82 Hayafuji, Y., & Kajiwara, K., T. Electrochem Soc. 129,2102 (1982).
Het79 Hettich, G., Mehrer, H., & Maier, K., Defects and Radiation
Effects in Semiconductors 1978 46. 500 (1979).
Heu96 Heuting, R., Slotboom, J., Pruijmboom, A., de Boer, W.,
Timmering, C., & Cowem, N.E.B.. IEEE Trans, on Electron Dev.
43,1518 (1996).
Hol89 Hollander, B., Mantl, S., Stritzker, B., Jorke, H., & Kasper, E., J.
Mater. Res. 4,163 (1989).
Hol92 Hollander, B., Butz, R., & Mantl, S..Phvs. Rev. B 46.6975 (1992).
Hou91 Houghton, D. J. Appl. Phys. 70.2140 (1991).
Hoy88 Hoyt, J. L., Williams, K.E., & Gibbons, J.F., U.S. Patent No. 4 787
551 (1988).
Hu74 Hu, S.M., I. Appl. Phvs. 45,1567 (1974).
Hu92 Hu, S.M., T. Electrochem. Soc. 139.2066 (1992).
Hu94 Hu, S.M., Mater. Sci. and Eng. R R13.105 (1994).
Iye89 Iyer, S.S. & LeGoues, F.K., T. Appl, Phvs. 65,4693 (1989).
Jai94 Jain, S.C., Germanium-Silicon Strained Layers and
Heterostructures, (Academic Press, New York, 1994).
Jai93 Jain, U., Jain, S.C., Nijs, J., Willis, J.R., Bullough, R., Mertens, R.,
& Van Overstraeten, R., Solid-State Electron. 36.331 (1993).


79
two species. Ultimately, FLOOPS used expressions for interstitial and vacancy
concentrations as well as total Ge concentration to solve the diffusion
equations and provide a final depth versus concentration profile.
The as grown Ge profiles for each structure, determined from SIMS,
were used as the initial profile for the FLOOPS diffusion simulations. The
value of the diffusivity was taken to be a function of temperature only,
ignoring possible concentration and stress dependencies. Diffusion was
simulated for one dimension (ID) only, in the direction perpendicular to the
sample surface. As stated previously, electric field effects were ignored.
Appendix A gives examples of FLOOPS codes used to simulate ID diffusion
with the Fermi model and Pair model.
3.4 Results
3.4.1 Diffusivities and Activation Energies from SIMS/FLOOPS
The SIMS profiles of the annealed samples were standardized using the
method described in Section 2.3.1. The Ge concentrations of the annealed
profiles were standardized with respect to the total Ge concentration of the as-
grown profile. The depth scale of the SQW/MBE was standardized by
aligning the segregation peak of the annealed and as-grown profiles. This
SIMS profile peak was unique to the SQW/MBE material. The depth scale of
the SQW/VPE profiles was standardized by aligning the bisectors of the full
width at half maximum sector of the Ge well. In each case, the depth scale of
annealed samples was shifted no more than 20 nm in one direction. This


221
Zau94 Zaumseil, P., Jagdhold, U., & Kruger, D., T. Appl. Phvs. 76.2191
(1994).
Zhu95 Zhu, J., Yang, L.H., Mailhiot, C, Diaz de la Rubia, T., & Gilmer,
G.H., Nucl. Instr. and Meth. B 102. 29 (1995).
Zhu, Y., Yang, Q., & Wang, Q., IEEE I. Quantum Electronics 33.
761 (1997).
Zhu97


73
placed in the oven. When the sample is placed in the oven, it heats rapidly to
be in thermal equilibrium with the entire furnace environment. The furnace
was not equipped with NH-, gas, therefore samples were not furnace annealed
in nitriding ambient.
Si1.xGex test pieces underwent preparations identical to those for RTP
(Section 3.2.1). Since Ar and N2 have similar thermal conductivities the
thermal profiles of samples processed in these gases are expected to be similar.
The diffusion profiles of the samples processed in the RTP using Ar and the
samples processed in the furnace using N2 can therefore be accurately
compared.
3.3 Simulation of Diffusion
The diffused Ge profiles were analyzed using the FLorida Object
Oriented Process Simulator (FLOOPS) [Law96]. This is a computer simulation
program which predicts the diffusion profile of a semiconductor material
after preprocessing and processing steps such as ion implantation, oxide
growth, annealing, and etching. A grid is defined for a region of interest and
modified versions of Fick's law are numerically solved within this grid. The
fineness of the grid determines the resolution of the profile as well as the
computation time of the simulation. After processing, the dopant, defect or
interface diffusion profiles can be plotted as concentration versus depth.
Three different diffusion models are available in FLOOPS: the Neutral,
Fermi, and Pair models. In the Neutral model, Fick's law is solved in the
form:


26
The supersaturation of interstitials produced by oxidation in the range
of temperatures used in this dissertation is well documented [Pac91] and will
be used to model the dependence of interdiffusion on interstitials. For
example, Packan and Plummer [Pac90] estimated C,/C,*~13 resulting from dry
oxidation for 1 hour at 900 C. They also found that interstitial
supersaturation was dependent on oxide growth velocity.
While there are a substantial number of theories, there has yet to be a
proven mechanism for injection of interstitials through the formation of
Si02 thin films. Several theories are briefly reviewed here: (1) Dunham and
Plummer [Dun86] proposed that interstitials created by the oxidation process
accumulate in the Si02 layer near the interface. The difference between the
rate of interstitial creation and the flux of the interstitials into the oxide
causes the interstitials to diffuse into the bulk. (2) Tan and Gsele [Tan81]
proposed that the free volume difference between the Si and Si02 at the
interface causes viscoelastic flow of the Si02 resulting in a supersaturation of
interstitials. (3) Hu [Hu74] proposed that a fraction of silicon available is not
oxidized and Si atoms are displaced from their lattice sites by the advancing
Si02/Si interface, becoming interstitials. Unfortunately, none of these
theories has been supported by experimental evidence and an accurate model
must still be established. It is sufficient for the purposes of these
investigations, however, to know that interstitials are indeed injected.


61
satellite peaks up to the +3rd order can be seen, while only the -1st order peak
can be observed to the left of the Si substrate peak.
The x-ray rocking curve of structure SL/SiGe shows broad satellite
peaks, indicating that the periodicity of the SL layers is imprecise. XTEM
images of the layers indeed show that the layer widths slightly decrease nearer
to the Si1.xGex buffer layer. The x-ray rocking curve of structure SL/Si shows
very sharp satellite peaks confirming that the periodicity of the SL layers is
consistent throughout the structure.
2.4.2 Optimization Procedures
Typically, substrates used for growth are intentionally miscut; a silicon
(100) substrate can be miscut 1 to 5 off the (100) plane towards the nearest
(110) plane (Figure 2-20). This causes the characteristic substrate x-ray peak
position to differ from its real value (co=0). A epitaxial layer can also be
misoriented with respect to both the intended substrate growth direction as
well as the miscut substrate surface normal direction (Figure 2-20).
To obtain the true to values for both the substrate and epilayer,
optimization procedures involving to, the sample crystal rotation angle, <|),
and crystal tilt, (p, were performed [Kri95]. These procedures are extremely
important when trying to identify and measure satellite peaks for thin
superlattice layers, as the satellite peaks tend to decay very rapidly with
increasing Ad (Figure 4-4 and 5-4). Even more intensity decay of the satellite
peaks is observed after annealing the sample crystal at high temperature.


69
50nm Si Cap
50nm SissGe1s
100nm Si Buffer
7
Si Substrate
Figure 3-1. Schematic of sample structures SQW/MBE and SQW/VPE.
The Ge depth versus concentration profiles for as-grown and annealed
samples were determined by Secondary Ion Mass Spectroscopy (SIMS) using a
Perkin Elmer PHI 6600 quadrapole analyzer with a 6 kV oxygen beam. The
profile depth scales were determined from Tencor Alpha-Step 500 surface
profiler measurements of the SIMS sputtered craters. All concentrations and
depths profiles were standardized using the method described in Section 2.3.1.
3.2 Processing
3.2.1 Rapid Thermal Processing
Samples annealed at high temperatures and short times (less than
approximately five minutes) in Ar, 02 or NH3 were processed in a rapid
thermal processor (RTP). The traditional furnace anneal is inappropriate for
short time, high temperature anneals because of increased impurity
concentrations in the ambient as well as larger temperature nonuniformities
due to the nonequilibrium state of the sample. Also, the high diffusivities of
some species require short anneal times for controlled, measurable diffusion
lengths. During high temperature heating the radiative heat transfer


142
periods, Ge content and the initial condition of the substrate [Iye89]. Upon
annealing, the structure will relax to reduce the strain energy. The minimum
energy can be attained by compositional modulation of the superlattice or by
the generation of misfit dislocations. Both of these mechanisms compete and
their respective contributions are dictated by kinetic conditions. Because
SL/SiGe is strained and has been shown to have dislocations after growth and
before thermal processing, it is important to know at least qualitatively the
dislocation density after annealing compared to that of the as grown structure.
This will give a qualitative idea of the possible contribution of relaxation
through dislocation formation to the diffusivity values calculated in the
preceding section.
Table 4-3. Parallel and perpendicular lattice constants of SL/SiGe.
Inert
Oxidizing
Nitriding
T(C)
time
(min)
ae//(nm)
ael(nm)
ae//(nm)
ael(nm)
ae//(nm)
aei(nm)
As
Grown
-
0.5430
0.5446
0.5430
0.5446
0.5430
0.5446
900
6
0.5436
0.5443
0.5438
0.5442
0.5433
0.5444
900
8
0.5437
0.5443
0.5441
0.5442
0.5433
0.5444
1000
1
0.5434
0.5441
0.5438
0.5441
0.5434
0.5445
1000
3
0.5440
0.5441
0.5440
0.5442
0.5443
0.5440
All plan views were taken with the zone axis of (100) so that the
sample is exactly perpendicular to the electron beam, and the (220) reflection
was used.


158
are negative, making the calculated values D negative, even though for all
ambients actual ln(I/ID) values do not decay consistently with increasing
anneal time. The actual values of ln(I/ID) of the first order satellite peak for
increasing anneal times at 1000 C are even more erratic. A linear fit to the
data points yields a negative slope for both inert and nitriding ambients, yet
the slope of the decay in oxidizing ambient is positive, such that a diffusion
coefficient cannot be extracted using Equation 4-5. Diffusivity values can be
calculated from all curves except that for 1000 C in oxidizing ambient, but
based purely on the intensity data, no extracted diffusivity can be considered
reliable. HRXRD characterization in conjunction with Equation 4-5 shows
potential for providing dependable diffusion coefficient data, however much
more work needs to be done to refine the instrumental method needed to
obtain scans that are reliable.
Having questioned the dependability of the diffusivities obtained
through HRXRD, it is still of interest to compare these values with those
determined from SIMS and FLOOPS presented in Section 4.5.1. These values
are compared in Table 4-5. The diffusivities in all ambients at an anneal
temperature of 900 C are not within error of each other, yet show reasonable
agreement. The diffusivities in all ambients at an anneal temperature of 1000
C are also not within error of each other, and disagree by approximately an
order of magnitude. The slope of the decay in intensity of the first order
satellite peak with anneal time for SL/SiGe in oxidizing ambient at 1000 C
was found to be positive and therefore could not physically apply to Equation


15
1.3 Diffusion in Elemental Semiconductors
Diffusion is the process in which random atomic motions result in the
transport of matter from one part of a system to another. When an
inhomogeneous single-phase alloy is annealed, matter will flow in a
direction which will decrease the chemical potential gradient. If annealed
sufficiently at constant temperature and pressure, the alloy will reach
equilibrium: there will be no net flow of matter and the alloy will be
homogeneous.
Diffusion in semiconductors can be examined through three different
modeling approaches: (1) empirical, in which the diffusion is studied and
described entirely through experimental analysis, (2) semi-empirical, in
which mathematical models and experimental data are used conjunctively to
indicate the diffusion process, and (3) atomistic, in which mathematical
modeling is used almost exclusively to indicate how individual atoms are
diffusing. The empirical approach has been used extensively to study self and
dopant diffusion in silicon, most notably by Fair et a/.[Fai75a, Fai75b, Fai77].
Examples of the semi-empirical approach include the FLorida Object Oriented
Process Simulator (FLOOPS) [Law96] and the Stanford University Process and
Engineering Models (SUPREM) [Han93]. In the semi-empirical approach,
expressions for species diffusivities are developed from detailed atomistic
mechanisms and these expressions are incorporated into a continuum
description of the diffusion process. The parameters in the expressions for
the species diffusion coefficients are estimated by a comparison with


19
large activation energy required for the exchange [Had95]. It will be ignored as
a possible diffusion pathway for the rest of this dissertation.
The direct interstitial mechanism is movement of either a self or
impurity atom from interstitial site to interstitial site through the lattice, as
schematically shown in Figure 1-10. This mechanism is energetically possible
for self interstitials or impurities which are small compared to the host lattice
atoms; it is energetically unfavorable for atoms which are large compared to
the lattice atoms, due to the lattice distortions involved [She89, Bor88].
o o o o
O O OJO
ojoto o
O <0 o o
Figure 1-10. The direct interstitial mechanism.
Lattice sites that are unoccupied are known as vacancies. The vacancy
mechanism is movement of a self or impurity atom sitting on a lattice site
into a neighboring vacancy, occupying that site substitutionally (Figure 1-11).
There will be a net flux of vacancies equal and opposite to the flux of the
diffusing species. The amount of diffusion that occurs via the vacancy
mechanism depends on the probability that an atom rests next to a vacancy,
which in turn, depends on the total mole fraction of vacancies in the crystal
[She89, Bor88].


133
The extracted diffusivity and enhancement values for structure
SL/SiGe annealed in inert, oxidizing, and nitriding ambients are given in
Table 4-1. Diffusion occurring in nitriding ambient at 900 C for 6 min was
not investigated and data for these conditions is therefore absent in Table 4-1.
It is once again imperative to state here that the diffusivities measured and
discussed throughout this chapter represent effective diffusivities, and have
not been labeled DGeeff for purposes of textual convenience only.
Table 4-1. Extracted diffusivity and enhancement values for SL/SiGe.
T(C)
time
(min)
DGelnert(cm2/s)
DGex(cm2/s)
DGeNit(cm2/s)
r Ox
*enh
f Nil
*enh
850
8
6.70xl017
2.32x10-
8.49x10
3.46
0.13
900
4
6.80xl0'17
4.58xl017
1.70xl017
0.67
0.25
900
6
1.23x10-
4.04xl016
-
3.28.
-
950
3
1.73x10-
1.31x10
2.86x10
0.76
0.17
1000
2
1.77x10-
2.23X10'15
8.96x10
1.26
0.51
The values of the diffusivities for structure SL/SiGe as a function of
temperature in inert, oxidizing, and nitriding ambients are shown in Figure
4-2. Fitting this data to Arrhenius expressions results in the following
equations when the interdiffusion is carried out in inert, oxidizing and
nitriding ambients:
Dg?rt (SL / SiGe) = 6.7 x 10"3 exp(-3.14eV 0.20 / kT) cm2/s (4-2)
Dg (SL / SiGe) = 7.22 x 10-6 exp(-2.43eV 0.19 / kT) cm2/s (4-3)
Dg (SL / SiGe) = 10.8 exp(-4.07eV 0.29 / kT) cm2/s (4-4)


50,000x
200nm
Figure 4-5. Cross sectional view TEM micrograph of structure SL/SiGe after
annealing in oxidizing ambient at 850C for 8 min.


70
component exceeds those of convection and conduction. RTP uses this
energy transfer between the radiant heat source and an object to process
sample material [Sin88]. Because of the optical nature of the radiative energy
transfer, the reactor wall is not in thermal equilibrium with the sample
[Tim97].
An AG Associates Heatpulse 2101 was used for all RTP anneals. The
Heatpulse 2101 uses an array of line source tungsten-halogen lamps to
achieve isothermal heating, with banks of twelve lamps both above and
below the heating chamber. The chamber and wafer holder are both made of
quartz, which transmits the entire spectrum emitted by the lamps (middle
infrared, 3 to 6 |im). This causes the chamber and holder to remain at a
temperature far below the sample temperature. The chamber is considered to
be a warm wall chamber, surrounded by a reflective water- and air-cooled
metal housing, and can reach temperatures of -400 C [Roo93].
The Heatpulse 2101 controls the temperature of the wafer through the
use of an IRCON optical pyrometer and closed loop feedback software. The
pyrometer measures the emissivity from the sample and converts the
emissivity value to a temperature value. Based on this temperature feedback,
the RTP then adjusts the lamp power to maintain the desired temperature.
Optical pyrometry is noninvasive and fast, yet is sensitive to emissivity
changes during processing (from wafer warping, film growth, backside
roughness, etc.). The pyrometer must be carefully calibrated. The most robust
method of calibration involves concurrent thermocouple use. At high


196
Comparisons of SL/SiGe results from Chapter 4 with SL/Si results
presented in this chapter reveal that, whether the Si and Si1.xGex layers are in
tensile, compressive or strain-free states, diffusivities and activation energies
are similar. This could imply very sweeping statements regarding the lack of
contribution of the strain component to diffusion, however, throughout
Chapter 3, 4 and 5, there has been evidence that strain does have some sort of
impact on interdiffusion. Intense future work must be done to clarify the role
of strain energy in Sij.xGex/Si diffusion.


204
to study more closely the relationship between relaxation and interstitial
absorption.
The most important work that should be accomplished is to repeat all
diffusion experiments described in this dissertation using pseudomorphic
structures. This is the most definitive method of determining the impact of
dislocations and relaxation on Si^Ge^Si diffusion parameters and obtaining
fv and f, values from both oxidation and nitridation experiments that more
closely reflect the true values. Experimental anneal of partially relaxed
structures should also be done to address this issue, as well as to confirm the
simulated results of Section 3.4.2.
6.3.2 Superlattice Investigations
The non-Arrhenius behavior of both SL structures should be further
investigated. Two possible reasons for this behavior must be addressed: (1)
the reliability and effectiveness of rapid thermal processing at thermal
budgets needed for the correct diffusion lengths and (2) possible time
dependency of diffusion in SLs at constant temperature. If a time-dependent
diffusivity for SLs is confirmed, then it would be interesting to investigate the
reason they differ from the time-independent diffusivity of the SQWs.
The experimental and analytic method of determining diffusivities
and lattice constants from HRXRD data must be refined. More experiments
should be performed to conclude if strain state of the layers indeed has no
effect on diffusivity values. Better structure correspondence between SLs is
needed, and work with a symmetrically strained SL would be interesting.


45
2.3 Secondary Ion Mass Spectroscopy
Secondary ion mass spectroscopy (SIMS) is a powerful technique for
characterization of concentration profiles in semiconductors. In this
technique, a primary ion beam is incident upon the sample and sputters
atoms from the surface. Incident ions lose energy through momentum
transfer during collisions with atoms in the crystal. The incident ions
eventually lose enough energy to come to rest several hundreds of angstroms
from the surface of the crystal. These collisions also cause the atoms in the
solid to be displaced, some of which escape from the crystal. Most of the
ejected atoms are neutral and cannot be detected by normal SIMS, however, a
small amount of atoms are ionized above the surface (secondary ions). A plot
of the secondary ion yield versus the sputtering time allows quantitative
depth profiling. The crater depth after completed analysis is measured and
divided by the total sputter time. This gives a sputter rate which can be used
to estimate the depth axis. Details of SIMS theory, instrumentation and
analysis can be found in several references [Ben87], The conversion of the
secondary ion yield into an impurity concentration is more difficult than
depth conversion from sputter rates and is discussed further in section 2.3.1.
Unless otherwise noted all SIMS analysis in this study was done at the
University of Florida's Microfabritech Facility using a Perkin Elmer PHI 6600
quadrapole analyzer. Most profiles obtained in this study used 0+ primary


118
In an oxidizing ambient, if no injected interstitials are being captured
by dislocations, the ratio [toxi [tinertiFLOOPSVt^aCtUal)] SUch that:
toxidizing (FLOOPS) tmert(FLOOPS)
^oxidizing (actual)
which can be written as:
t inert (3Ctual)
(3-14)
^oxidizing (FLOOPS) toxidizing (actual)
(3-15)
t inert (FLOOPS) t inert (actual)
which means simply that the enhancement to boron diffusion seen in
FLOOPS must equal the actual boron diffusion enhancement. If there is
interstitial capture then:
enh(FLOOPS) > enh(actual)
If all interstitials are being captured then:
(3-16)
enh (actual) = 1 (3-17)
The time of anneals listed in Table 3-4 result in FLOOPS enhancements
which are greater than actual enhancements for each anneal temperature.
The enhancements predicted by FLOOPS vary from 1.78 to 5.33. This result,
along with the fact that enhancement of B diffusion is indeed seen in the
SIMS profiles (Figure 3-5), allows the expression:
1< enh(actual) < enh (FLOOPS)
(3-18)


114
species and injected interstitials recombine with the vacancies to retard
diffusion. Which experiment gives the correct results or how can the two
experiments be examined together to form an accurate theory of the actual
diffusion process? These questions are addressed in Section 3.5.4.
3.5.2 Diffusivities of Partially-relaxed Structures
Comparison of the Ge diffusivity in initially fully strained SQW
structures and initially partially relaxed structures shows that the value is the
same in both strain states, in inert, oxidizing, and nitriding ambients, within
error. The diffusivities in inert ambient, given in Table 3-3, are plotted
versus temperature in Figure 3-15. Diffusivities in oxidizing ambient and
nitriding ambient show much the same result. Dislocation formation and
strain relaxation seem to have an insignificant effect on Ge diffusion in Si/Sij.
xGex/Si SQWs in this case. This is supported, in some respects, by an
investigation by Kuo et al. [Kuo95], who found that there is no relation
between boron diffusion and strain in Si,.xGex. This led them to surmise that
the equilibrium interstitial concentration is independent of strain.
There are some issues, however, which need to be addressed in future
work. At 1200 C, the initially fully strained structure has a diffusivity in
inert ambient that is not within error of the values determined for the
partially relaxed structures. This divergence between fully strained and
partially relaxed values does not occur at any other temperature. This may
just be a one-time anomaly in the data, but further studies should be done at
this high temperature to confirm this result.


213
isomorphous- a crystalline compound phase that is capable of forming a
complete series of solid solutions across the entire composition range.
lattice constant/parameter- the length of a crystallographic axis of a unit cell.
lattice mismatch- a heterostructure with semiconductor materials which
have different lattice parameters.
metastable- semiconductor crystal condition between equilibrium theory and
experimental measurement which depends on growth conditions and
material parameters.
misfit dislocation- an extra plane of atoms inserted between existing lattice
planes.
mobility- ease of movement of the carrier by the applied electric field.
MODFET- Modulation Doped Field Effect Transistor; a semiconductor
transistor composed of source, channel and drain regions.
monochromator- an instrument which selects and transmits a narrow band
of wavelengths from a source of radiation.
monolayer- one atomic layer.
monovacancy- an vacancy unassociated with another vacancy or dopant
atom.
periodicity- the repeat distance of the alternating layers in a superlattice.
photodetector- a semiconductor device that absorbs photons to generate
electronic carriers.
photonics- a division of semiconductor device physics in which energies
from photons and electrons are exchanged.
point defect- a deviation in the periodicity of a lattice arising from a single
point. Examples are an interstitial, vacancy and substitutional.
pseudomorphic- when the thickness of a lattice-mismatched epitaxial layer
which is below critical thickness.
pyrometer- instrument which deduces a wafer's temperature from the
intensity of the thermal radiation it emits.


This dissertation was submitted to the Graduate Faculty of the College
of Engineering and to the Graduate School and was accepted as partial
fulfillment of the requirements for the degree of Doctor of Philosophy. ^
May 1999 ^
Winfred M. Phillips
Dean, College of Engineering
M.J. Ohanian
Dean, Graduate School


>
146
500nm
Figure 4-6. Plan view TEM micrographs of structure SL/SiGe after annealing
in inert ambient at (a) 850 C for 8 min and (b) 1000 C for 2 min.


3
1.1 Selected Material Properties and Device Applications
1.1.1 Material Properties
In microelectronics, interest in a semiconductor material evolves if the
material has basic properties suitable for device applications. Device
fabrication and operation requirements then dictate what specific material
properties need to be investigated and adapted further. It is therefore
important to introduce the device applications and material properties of
Si^Ge, that make it an increasingly appealing material in the semiconductor
industry. The crystal structure, lattice constant, critical thickness, phase
diagram, and band gap of Si1.xGex are all properties that determine
performance in several different device applications. These material
properties are also of particular importance in this investigation because they
either have a primary or secondary effect on interface diffusion, and they
must be known to effectively analyze the data obtained from the
characterization methods described in Chapter 2.
The Si-Ge system exhibits an isomorphous phase diagram with nearly
ideal-solution behavior in both the liquid and solid solutions [Kas95]. The
solid and liquid phases are separated by a region of coexistence, which gives
rise to segregation upon crystallization from the melt (Figure 1-1).


200
temperature control issues. For both structures, minimal diffusion
enhancement occurred in oxidizing ambient compared to inert ambient at all
temperatures. For both structures, diffusion retardation occured in nitriding
ambient compared to inert ambient at all temperatures. High resolution x-ray
diffraction was used as an alternate method to extract diffusion coefficients.
The resulting values were found to be unreliable and the experimental and
analysis method must be refined. Finally, the diffusivities, activation
energies and fractional vacancy components of the two structures were found
to be within error of each other.
The extraction of diffusion coefficients using SIMS and FLOOPS yielded
activation energies for the SL with a Si,.xGex buffer of 3.14, 2.43 and 4.07 eV for
diffusion in inert, oxidizing and nitriding ambients, respectively. HRXRD
analysis of the cubic unit cell revealed that, when the Sij.xGex buffer layer was
viewed as part of the pseudo-epilayer, the perpendicular lattice constant, aei,
was constant with increased annealing time, while the parallel lattice
constant, ae//, increased slightly.
The extraction of diffusion coefficients using SIMS and FLOOPS yielded
activation energies for the SL with a Si buffer of 3.63, 2.81 and 4.16 eV for
diffusion in inert, oxidizing, and nitriding ambients, respectively. HRXRD
analysis of the cubic unit cell of the Si1.xGex/Si pseudo-epilayer revealed that
both the perpendicular lattice constant, a^, and the parallel lattice constant,
ae/// remained constant with increasing anneal time.


72
the emissivity dial was adjusted so that the pyrometer reading equaled the
thermocouple reading.
The Heatpulse 2101 has a quartz wafer tray inside the chamber which
holds 4" wafers only, therefore the small 1 x 1 cm samples had to be placed on
top of a 4" silicon "dummy" wafer. This raised questions regarding the heat
transfer between the wafer and the sample, as well as the heat transfer
between the sample and the lamps. To determine experimentally the impact
this had on the temperature of the sample compared to the underlying wafer,
a stack of three rectangular samples of decreasing area was oxidized on a
dummy wafer and the oxide thickness on the exposed area of each was
measured. Within the error of the ellipsometer ( 1 nm) [Sch90], there was
no difference in the oxide thickness on any of the three samples or the wafer
and therefore the heat transfer can be considered to be thorough (10 C
[Gon94]).
Before annealing, the test wafer was cut into lxl cm pieces which were
cleaned using a regimen of deionized water, H2S04:H202 (1:2) and H20:HF
(10:1), and then dried with N2. Samples were rapid thermal processed with all
ambient gases (Ar, 02, NH3) flowing at 1.5 slm.
3.2.2 Furnace Processing
Samples annealed for longer than five minutes in either N2 or 02 were
processed in a Thermco furnace. Furnace anneal at times longer than
approximately 5 minutes allows greater temperature control. During furnace
anneal the compartment is heated to anneal temperature before the sample is


4-4. Decay of the integrated intensity of the first order superlattice peak
about Si(004) as a function of annealing time, temperature and
ambient of SL/SiGe 138
4-5. Cross sectional view TEM micrograph of structure SL/SiGe after
annealing in oxidizing ambient at 850 C for 8 min 145
4-6. Plan view TEM micrographs of structure SL/SiGe after annealing
in inert ambient at (a) 850 C for 8 min and (b) 1000 C for 2 min 146
4-7. Comparison of experimentally determined SIMS profile and
FLOOPS profile using the Fermi model for samples annealed at 950
C and 3 min in (a) inert (b) oxidizing and (c) nitriding ambient 148
4-8. Diffusivities of Ge in Sij.xGex/Si SLs with a Si,.xGex buffer layer
from (+) Hollander et al. and () this work 150
4-9. Comparison of Ge SIMS profiles in inert, oxidizing, and nitriding
ambients for SL/SiGe 154
5-1. Schematic of sample structure SL/Si 166
5-2. Effective Ge diffusivity of structure SL/Si as a function of
annealing temperature in inert, oxidizing, and nitriding ambient 170
5-3. X-ray diffractometer scans of the SL/SiGe superlattice peaks about
Si(004) with increasing anneal times in inert ambient 173
5-4. Decay of the integrated intensity of the first order superlattice peak
about Si(004) as a function of annealing time, temperature and
ambient of SL/Si 174
5-5. Plan view TEM micrograph of structure SL/Si after annealing in
inert ambient at 850 C for 8 min 178
5-6. Comparison of experimentally determined SIMS profile and
FLOOPS profile for 950 C and 3 min in (a) inert (b) oxidizing and
(c) nitriding ambient 180
5-7. Diffusivities of Ge in Sii.xGex/Si SLs with a Si(100) buffer layer
from previous studies and this work 184
5-8. Comparison of Ge SIMS profiles in inert, oxidizing and nitriding
ambients for SL/Si 185


100
500nm
Figure 3-7. Plan-view TEM micrographs of structure SQW/MBE after anneal
ing in inert ambient at (a) 900 C for 330 min and (b) 1200 C for 1 min.


31
superlattices. The interdiffusion is found to be dependent upon such primary
variables as Ge content, x, the amount and type of strain, e, and anneal
temperature, T, as well as secondary variables such as thickness of the layers,
d, and time of anneal, t. The wide range of parameters makes it difficult to
compile a comparison between the data. For example, small differences in
strain create large differences in diffusion coefficients. Compositionally, it has
been found that the interdiffusivity increases by an order of magnitude with
each approximately 0.10 step increase in x. From x=l to x=0, the diffusivity
can change by as much as six orders of magnitude [Ho 192, Van90].
Diffusion in strained Si^Ge^Si single quantum wells has been found
to have an activation energy of ~3 eV [Hol92, Van90, Sun94]. While the
extent of diffusion can be estimated using the tracer Ge diffusion coefficient in
bulk Si, all studies see an increasing deviation with decreasing anneal
temperature. Some studies contend that strain relaxation leads to a change in
diffusivity with temperature, while others believe that change in local Ge
concentration, not strain relaxation, is the reason for the difference in
diffusivity. None of the studies proposes a possible diffusion mechanism.
Interdiffusion of Sij.xGex/Si superlattice layers is different than in SQW
structures due to the ability to engineer the strain state of the material by the
layer structure. Si1.xGex/Si superlattices can be grown with two different types
of coherent strain, asymmetric or symmetric. In an asymmetrically-strained
superlattice (ASL), most commonly the Si layers are almost stress-free while
the Sij.xGex layers are under biaxial compressive stress and annealing causes


122
of the B marker layer analysis was that the lower bound for Cv/Cv* seemed to
result in C,/C* values that were more physically reasonable than those
resulting from the higher bound. This is most apparent at 1200 C where the
limit of Cv/Cv*=l could provide no reasonable results. It could be said that
the point defect balance is governed by the relation C,CV=C,*CV*.
This conclusion was then be used to estimate f, values for diffusion in
SQW/MBE. The lower bound of Cv/Cv* and the corresponding C,/C* values
resulted in similar f, values of 0.127 and 0.148 for 900 and 1000 C, respectively.
The values dropped significantly at 1100 C and 1200 C to approximately 0.01
and 0.03, respectively. It would seem that there is a significant change in the
respective contributions of interstitial and vacancy point defects between 1000
and 1100 C.
The only other estimate of f, determined from oxidation studies was
made by Cowem et al. [Cow96], who reported an f, value of 0.220 at 875 C.
While the value of Cowem et al. is greater than values estimated at 900 C
from this work, it is reasonably similar and corroborates a diffusion
mechanism dominated by vacancies.
The method employed with success to the oxidation experiments to
determine f, did not result in equal success when applied to the nitridation
experiments. As stated in Section 3.4.4, the D^'/D* ratios used in Equation
3-8 were consistently too small to extract f, values that were less than one,
regardless of the bounds used for Cv/Cv*. The problem of significant
retardation seen in all nitriding profiles remains unresolved. Diffusion


212
donor- a positively charged dopant that donates an electron to the
semiconductor lattice when introduced.
dopant- an electrically active element selectively introduced into a
semiconductor lattice.
effective diffusivity- measured diffusivity of an imperfect crystal (i.e.
including effects from impurities, dislocations, point defects).
ellipsometry- optical analysis technique which uses polarized light to
measure the thickness of thin dielectric films.
emissivity- the measure of the amount of thermal radiation emitted from a
body (semiconductor wafer) .
epitaxy- a technique to grow a thin crystalline layer on a crystalline substrate
so that the layer bears a certain crystallographic relationship to the underlying
substrate.
epitaxial layer- a thin crystalline layer on a crystalline substrate that bears a
certain crystallographic relationship to the underlying substrate.
Fermi level- a refemce energy for the probability of occupation of a set of
energylevels in a crystal.
FLOOPS- FLorida Object Oriented Process Simulator; a software program
based on continuum and atomic diffusion theory which predicts the diffusion
behavior of dopant in semiconductors.
graded- a gradual compositional transition within a semiconductor layer.
HBT- Heterojuction Bipolar Transistor; a semiconductor transistor consisting
of two p-n junctions in series where the emitter and base are made of two
semiconductors with different energy gaps.
heterojunction- the boundary between two layers of distinct semiconductor
materials.
heterostructures- semiconductor structures consisting of more than one type
of semiconductor material.
incoherent- epitaxial layer thickness greater than critical thickness,
interface- the boundary between two semiconductor layers,
intrinsic- undoped.


214
quantum well- a potential energy well created by junctions in conduction and
valence bands in which carriers are confined.
RBS- Rutherford Backscattering Spectrometry; an analytical technique based
on backscattering of ions or projectiles incident on a semiconductor sample.
satellite peaks- peaks which occur in x-ray diffraction as a result of the
periodicity of superlattice layers.
SIMS- Secondary Ion Mass Spectrometry; an analytical technique which uses
accelerated ions to produce depth versus concentration profiles of
semiconductor elements.
substrate- the original semiconductor material on which epitaxial layers are
grown or deposited.
superlattice- a series of alternating epitaxial layers of two mismatched
materials, each layer having a thickness below the critical thickness.
TEM- Transmission Electron Microscopy; an analytical technique in which
electrons are accelerated and focused througho a lens onto a sample such that
transmitted electrons form either a diffraction pattern or a magnified image.
threading dislocation- a line dislocation which traverses from the substrate
thorugh the epitaxial layers to the surface.
trap- an energy level introduced through imperfections in a lattice which
impede normal motion of carriers.
valence band- a band of allowed energy levels corresponding to unbonded
holes free to travel throughout the crystal.


10
In optoelectronic applications, both light detectors and emitters
operating in the near (1.3gm) and mid-infrared (=10gm) ranges can be
fabricated using the Si-Ge system, particularly the (SimGen)p superlattice
system. The best of these photodetector devices use a waveguide rib where
the light enters sideways through the rib and is absorbed in the active layer
(Figure 1-7), making the absorption region and overall absorption larger than
in vertical mesa-type structures, while having a geometry better suited for
optical communication links.
n+-Si Contact
Figure 1-7. Possible waveguide-photodetector structure using Sij.xGex alloy
[Pre95].
Si1.xGex heterostructures can be grown on either a Si or Si^Ge,, buffer
creating band alignments which lead to spatial separation of ionized dopant
atoms and mobile carriers which can be used in a MODFET. Electron


24
1.4 Non-equilibrium Point Defect Injection
The generation and annihilation of non-equilibrium point defects is a
topic which is crucial for the understanding of semiconductor diffusion
phenomena. It has been generally accepted that thermal oxidation of silicon
injects interstitials, while thermal nitridation injects vacancies [Fah89a,
Hu92]. The proportional dependence of a material's self-diffusion
mechanism or dopant's diffusion mechanism on these defects can be
determined by monitoring any enhancement or retardation of the diffusion
with the addition of these defects. The total diffusivity of the self or dopant
atom being studied can be described as the sum of the vacancy and interstitial
diffusivities:
D = D, + Dv (1-15)
where, in the case of Ge diffusion in Si, D is equivalent to in Equation 1-
11, and D, and Dv are equivalent to the variables by the same name in
Equations 1-12 and 1-13. The fractional interstitial component of diffusivity,
f,, is defined as:
f = i
1 d;+Dv d*
(1-16)
where D* denotes the value of the diffusivity when the actual interstitial and
vacancy concentrations are their equilibrium values, which occurs when
diffusing in a high temperature, inert ambient. The fractional vacancy
component, fv, is simply (l-f¡). Under nonequilibrium conditions, as during


CHAPTER 3
BEHAVIOR OF ANNEALED Si,.xGex SINGLE QUANTUM WELLS
One of the fastest growing applications for Sij.xGex material is
heterojunction bipolar transistor (HBT) technology (Section 1.1.2). HBTs use
doped Si,.xGex as the base and surrounding Si layers as the emitter and
collector regions. A Si,.xGex base region allows greater doping than Si without
reducing emitter injection efficiency [Gha95]. Out-diffusion, however, from
the base of both the Ge and dopant during growth and processing forms
parasitic barriers at the heterojunctions, which severely degrades device
performance. Also, base widths are currently slightly greater than the critical
layer thickness [Gru97, Heu96, deB97], which introduces possible Sij.xGex layer
relaxation through formation of dislocations. It is therefore important to Sij.
xGex HBT technology to be able to predict the interdiffusion behavior and
dislocation effects of Si/Sij.xGex/Si single quantum well (SQW) structures.
Interdiffusion of Si/Si085Ge015/Si SQW material in inert, oxidizing, and
nitriding ambients over a temperature range 900 to 1200 C has been
investigated. Thermal processing in all three ambients over the same
temperature range allowed estimation of the enhancement factor of
interdiffusion of Si/Si0g5Ge015/Si material under interstitial and vacancy
supersaturation as well as under inert (equilibrium defect concentration)
conditions. An estimate of the fractional contribution of interstitial and
67


8
1.1.2 Device Applications
The semiconductor industry has long been based on Si, yet Si
technology is fast approaching its physical limits. Compound semiconductors
made of elements in the III and V columns in the periodic table have been
used in specific applications that require a tunable direct bandgap energy and
high carrier mobilities. These III-V semiconductors, however, are more
complex to process. Incorporating Ge into Si to create Si1.xGex devices
provides a good compromise between Si and compound semiconductor
technology. Sij.xGex technology allows bandgap engineering similar to that of
compound semiconductors while retaining the economical and advanced
aspects of Si technology. While Si^Ge,, technology is progressing rapidly,
there are still drawbacks in device manufacturing. Of major concern is the
lattice mismatch between Si and Ge (4.2%) which can cause growth and
performance challenges for certain device applications. Table 1 summarizes
the advantages and disadvantages of S!.xGex for device applications.
Table 1-1. Advantages and disadvantages of SiGe used in device applications.
Advantages Disadvantages
Able to bandgap tailor Large lattice mismatch Si-Ge
Able to deposit atomically sharp Large dopant out-diffusion
SiGe interface
Economical Indirect bandgap
Can be incorporated into standard
Si processing
Environmentally harmless


209
PAIR MODEL-NITRIDING AMBIENT
pdbSetDouble Nitride_Silicon V injection 3.25e14
pdbSetBoolean Nitride_Silicon V time.inj 1
pdbSetBoolean Nitride_Si!icon V recomb 1
pdbSetDouble Nitride_Silicon V Ksurf 100
pdbSetDouble Nitride_Silicon V Ksurf2 0.0
dopant add name=Germanium
pdbSetDouble Si Germanium I DO $lvalue
pdbSetDouble Si Germanium I Dp 0
pdbSetDouble Si Germanium V DO $Vvalue
pdbSetDouble Si Germanium V Dp 0
pdbSetSwitch Si Germanium DiffModel Pair
pdbSetSwitch Si I DiffModel Numeric
pdbSetSwitch Si V DiffModel Numeric
line x loc = -0.1 tag = nit
line x loc = 0.0 tag = surf spac=0.003
line x loc = 0.05 tag = cap spac=0.003
line x loc = 0.10 tag = sige spac=0.005
line x loc = 0.20 tag = buffer spac=0.003
line x loc = 0.25 tag = back spac=1
region silicon xlo = surf xhi = back
region nitride xlo = nit xhi = surf
init quiet
profile name=Germanium infile=1 AsGrown
SetTemp 950
InitDefect 950
InitDopantPairs 950
sel z=log10(Germanium)
plot. 1 d iabel=lnitial
diffuse time=3 temp=950 init=1 e-12 ¡adapt
sel z=log10(Germanium)


104
l t .1.1 I I I I I I t i i i I I I J
0 0.05 0.1 0.15 0.2 0.25 0.3
Depth (pm)
Figure 3-10. Illustration of non-Gaussian shape of SQW diffused profiles, of
The as-grown, SIMS, and FLOOPS profiles of anneals at (a) 900 C for 1532
min and (b) 1000 C for 55 min. Each SIMS profile shows a flatter peak and
steeper slopes than the corresponding FLOOPS profile.


20
oooo oooo
O 0^0 o
oooo oooo
Figure 1-11. The vacancy mechanism.
The simple mechanisms just discussed are generally insufficient
individually to predict the diffusion of self or impurity atoms in a
semiconductor crystal. Self and impurity diffusion in both Si and GaAs have
shown to be some combination of the vacancy and interstitial mechanisms
discussed above, involving both interstitial and vacancy point defects [Fra91,
Had95]. The approach used in this dissertation to model Si-Ge diffusion has
assumed a similar cooperative contribution of interstitials and vacancies,
therefore it is important to consider both substitutional and interstitial
mechanisms while examining S!.xGex interdiffusion. It is important,
however, to note that the mechanism of Ge diffusion in Sij.xGex is slightly
different than the usual impurity diffusion in either Si or GaAs, as the Ge
"impurity" is neutral within the Si^Ge,, lattice. Due to the neutrality of the
Ge in Si^Ge,, this thesis ignores the possibility of pair model diffusion
[Had95], which normally occurs when the point defect and impurity are both
charged.
The substitutional-interstitial diffusion model (SID) offers two
plausible mechanisms which couple the impurity atoms and native point
defects. In each mechanism, the mobile species is the impurity interstitial.
The first mechanism, known as the Frank-Tumbull or dissociative


2-5. Front and rear views of the XTEM assembly after preparation
[Wil96] 41
2-6. Cross sectional view TEM (XTEM) micrographs of as-grown (a)
structure SL/SiGe and (b) structure SL/Si 46
2-7. XTEM micrographs of as-grown (a) structure SQW/MBE and (b)
structure SQW/VPE 47
2-8. Plan view TEM micrographs of as-grown (a) structure SL/SiGe and
(b) structure SL/Si.2-9 48
2-9. Figure 2-9. Plan view TEM micrographs of as-grown (a) structure
SQW/MBE and (b) structure SQW/VPE 49
2-10. Ge concentration profile determined from SIMS for sample
structure SL/SiGe 52
2-11. Ge concentration profile determined from SIMS for sample
structure SL/Si 52
2-12. Ge concentration profile determined from SIMS for sample
structure SQW/VPE 53
2-13. Ge concentration profile determined from SIMS for sample
structure SQW/MBE 53
2-14. SIMS profile of structure SQW/MBE 54
2-15. Schematic of symmetric x-ray Bragg reflection [Cul78] 56
2-16. Schematic of the monochromator/collimator 57
2-17. Schematic of the x-ray path used in triple axis mode 59
2-18. X-ray rocking curve of structure SL/SiGe before anneal 60
2-19. X-ray rocking curve of structure SL/Si before anneal 60
2-20. Miscut of substrate and mistilt of epilayer 62
2-21. Example of positive and negative x-ray diffraction from an
asymmetric plane 66
3-1. Schematic of sample structures SQW/MBE and SQW/VPE 69
3-2. Effective Ge diffusivity of structure SQW/MBE as a function of
annealing temperature in inert, oxidizing, and nitriding ambients 81
xu


4
Weight Percent Germanium
1500
1400
1300
1200 j(oq
1100
1000
940
900
Figure 1-1. Phase diagram of the Si-Ge system [Kas95]. The gray section
indicates the area of composition and temperature studied in this thesis.
The alloy silicon-germanium, Sij_xGex/ is a semiconductor which
crystallizes in a diamond cubic-type substitutional structure. This structure
can be considered as two face-centered cubic sublattices shifted by one quarter
of the body-diagonal, R=l/4<111>, as shown in Figure 1-2.
Figure 1-2. The diamond cubic structure of S!.xGex alloy [Kas95].
The lattice parameter, a, is a function of Ge composition, x, and has been
found to follow [Kas95]:


THE STUDY OF INTERDIFFUSION AND DEFECT MECHANISMS IN
SI10(GEX SINGLE QUANTUM WELL AND SUPERLATTICE MATERIALS
By
MICHELLE DENISE GRIGLIONE
A DISSERTAHON PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1999


124
Diffusivities extracted in an inert ambient at low temperature agreed
well with previously reported values. A major contribution of this work was
to extend the anneal temperature regime beyond 1000 C for the first time,
providing diffusivity values for temperatures up to 1200 C. An activation
energy of diffusion of 5.87 eV0.14 was extracted, which is much higher than
previously reported values. This investigation, however, covered a larger
temperature range and provided diffusivities spanning five orders of
magnitude, therefore, the extracted activation energy could be considered
more comprehensive than any previously reported.
For the first time, diffusivities extracted under interstitial injection
conditions were reported, with a resulting activation energy for diffusion of
5.27 eV0.11. No significant enhancement or retardation of Ge diffusion was
seen in oxidizing ambient when compared to inert ambient. Also for the first
time, diffusivities extracted under vacancy injection conditions were
reported, with a resulting activation energy for diffusion of 3.27 eV0.10.
Values of fj of approximately 0.10 at the lower temperatures and 0.02 at the
higher temperatures were estimated from oxidizing experiments, however, f,
could not be estimated from nitriding experiments, possibly due to stress
effects originating at the nitride/silicon interface. It was concluded that C,/C,*
and Cv/Cv* ratios were affected by material properties.
Two experiments were performed to investigate the effect of strain and
strain relief on Ge diffusivity as well as excess point defect concentrations in
Si1.xGex/Si structures. Initially partially relaxed structures showed no


156
activation energies that have decreased with increasing Ge composition,
which are both opposite trends to those seen in Table 4-4. Once again, it
seems as if the difference in strain states of the two materials might account
for the discrepancies. Interrelated factors such as layer thickness, dislocation
formation energy and Si versus Si1.xGex buffers may all contribute to the
general strain state of each material such that their diffusion behaviors differ
drastically.
4.6.2 Diffusivities Determined from HRXRD
Section 4.5.2.1 described the method used to determine diffusivities of
periodic SLs from co-20 scans using HRXRD and listed results for SL/SiGe.
The relative intensities of the first order satellite peaks did not show the
expected trends and therefore the desired diffusion coefficients were difficult
to extract. The co-20 scans resulted in standardized first order satellite peaks
that did not necessarily decrease progressively in intensity with increasing
anneal time (Figure 4-4) as they were expected to do. The zero order peak,
which represents the entire sum of epilayers deposited on the substrate,
broadened and increased in intensity, which indicated that the periodicity of
the SL layers was indeed degrading and the multilayers were stabilizing
towards one homogenized layer with an average composition. This zero
order epilayer peak shifted towards the angular value of the Si(004) substrate
peak, which indicated that the lattice constant of the 'epilayer' was slowly
approaching that of bulk Si, and therefore relaxation was occurring.


80
lateral movement is well within one standard deviation, estimated at 0.05, in
relative depth scale error of SIMS [Gos93].
The extracted diffusivity values for structure SQW/MBE annealed in
inert, oxidizing, and nitriding ambients are given in Table 3-1. The value of
the diffusivity and enhancement in oxidizing ambient for anneal
temperature 900 C and time 2206 min could not be extracted because the
50nm Si cap had been consumed by the oxide and oxidation of the Si^Ge*
layer had occurred. Diffusivity and enhancement values for diffusion in
nitriding ambient at 900 and 1000 C in a furnace were not investigated; only
the RTA was equipped with ammonia gas. It is important to note here that
all extracted diffusivities discussed in Chapters 3 through 5 are effective
diffusivities, Dq.6, and are only referred to as diffusivities for textual
convenience.
The values of the diffusivities for structure SQW/MBE as a function of
temperature in inert, oxidizing, and nitriding ambients are shown in Figure
3-2. Error analysis of the diffusion coefficients was performed using the
method described in Section 2.3.2. Fitting this data to Arrhenius expressions
results in the following equations when the interdiffusion is carried out in
inert, oxidizing, and nitriding ambients:
(3-8)
(3-9)
Dgert (SQW / MBE) = 1.6 x 108 exp(-5.87eV 0.14 / kT) cm2/s
Dg (SQW / MBE) = 6.1 x 105 exp(-5.27eV 0.11/ kT) cm2/s
Dg(SQW /MBE) = 1.1 x 102 exp(-3.27eV 0.10/kT) cm2/s
(3-10)


147
that of the as-deposited SL/SiGe. From the experiments done in this study, it
is difficult to determine exactly what impact this increase in dislocation
density had on interdiffusion. These TEM results do suggest that future work
needs to be done with structures which are pseudomorphic.
4.6 Discussion
4.6.1 Diffusivities Determined from SIMS and FLOOPS
The FLOOPS diffusion models used in this study were the Fermi and
Pair models. The diffusion profiles generated by the Fermi model provided
very good fits to the experimentally determined SIMS profiles in the case of
anneals performed in inert ambient, as demonstrated in Figure 4-7 for an
anneal temperature of 950 C and an anneal time of 3 min. This indicates
that the assumptions made in the Fermi model (Section 3.3), while not
completely accurate, provide diffusivity values that reflect the actual
diffusion process.
When analyzing the diffusion profiles for structure SQW/MBE and
SQW/VPE in Chapter 3, there was a question of whether the profiles were flat
in the high Ge concentration region and if so, whether this indicated a
concentration-dependent diffusivity (Section 3.5.1). The diffusion profiles
determined for SL/SiGe are Gaussian in all ambients and show no flatness in
high Ge concentration region of the wells whatsoever at any temperature. It
can therefore be concluded that diffusion in structure SL/SiGe is most likely
concentration-independent.


38
of interest using a condenser lens. The sample is sufficiently thin that the
majority of impinging electrons are transmitted or forward scattered through
the sample, rather than backscattered or absorbed. These transmitted and
forward scattered electrons pass through an objective lens to form a back focal
plane and an image plane (Figure 2-3). A diffraction pattern is formed on the
back focal plane and a magnified image is formed on the image plane. Both
the diffraction pattern and the magnified image can be projected onto a screen
for either viewing or photographic recording [Wil96, Run98, Sch90].
There are two basic views of the sample that can be achieved through
TEM, depending on the original sample preparation. Plan-view TEM (PTEM)
provides an image of the sample from a direction parallel to layer growth
Figure 2-3. Schematic of ray paths originating from the object which create a
TEM image [Wil96].


162
values for temperatures down to 850 C. Diffusivities extracted in inert
ambient at low temperatures agreed well with previously reported values.
An activation energy of diffusion of 3.14 eV0.20 was extracted, which is
considerably lower than the one available reported value of 4.5 eV [Hol92].
Both investigations spanned a similar temperature gradient and therefore
both can be considered as reliable in that respect as the other. The difference
in the diffusion coefficients is, however, well below an order of magnitude
and could be attributed to the minor differences in composition and layer
thicknesses of the two structures, or to the more significant differences in
strain state and diffusivity extraction method.
For the first time, diffusivities extracted under interstitial injection
conditions were reported, with a resulting activation energy for diffusion of
2.43 eV0.19. No significant enhancement of Ge diffusion was seen in
oxidizing ambient when compared to inert ambient at any temperature. This
leads to the conclusion that interstitials play a minimal role in diffusion.
For the first time, diffusivities extracted under vacancy injection
conditions were reported, with a resulting activation energy for diffusion of
4.07 eV0.29. Significant retardation of Ge diffusion was seen in nitriding
ambient when compared to inert ambient at all temperatures, indicating that
diffusion is dominated by interstitials. This contradicted the results of the
oxidation experiments.
Plan-view TEM micrographs showed qualitatively that dislocation
density increased from the as-deposited value after anneal. However, the


3-3. Effective Ge diffusivity of structure SQW/VPE as a function of
annealing temperature in inert, oxidizing, and nitriding ambients 83
3-4. Schematic of test structure SQW/B 86
3-5. Diffusion of as-grown B marker layer in all ambients 88
3-6. Cross sectional view TEM micrographs of structure SQW/MBE
after annealing in inert ambient at (a) 1000 C for 43 min and (b)
1200 C for 1 min 99
3-7. Plan view TEM micrographs of structure SQW/MBE after
annealing in inert ambient at (a) 900 C for 330 min and (b) 1200 C
for 1 min 100
3-8. Plan view TEM micrographs of structure SQW/VPE after
annealing at (a) 900 C for 330 min in oxidizing ambient and (b)
1200 C for 1 min in inert ambient 101
3-9. Comparison of experimentally determined SIMS profile and
FLOOPS profile 103
3-10. Illustration of non-Gaussian shape of SQW diffused profiles 104
3-11. Comparison of diffusivities of structures SQW/MBE and
SQW/VPE in (a) inert ambient and (b) oxidizing ambient 106
3-12. Diffusivities of Ge in Si/Si^Ge^Si SQWs from previous studies
and this work 108
3-13. Plot of diffusivities of all anneal times in inert ambient for each
temperature for SQW/MBE Ill
3-14. Comparison of Ge SIMS profiles in inert, oxidizing and nitriding
ambients for SQW/MBE 112
3-15. Comparison of Ge diffusivities of partially relaxed structures in
inert ambient 115
4-1. Schematic of sample structure SL/SiGe 128
4-2. Effective Ge diffusivity of structure SL/SiGe as a function of
annealing temperature in inert, oxidizing, and nitriding ambients 134
4-3. X-ray diffractometer scans of the SL/SiGe superlattice peaks about
Si(004) with increasing anneal times in inert ambient 137
xrn


143
Both plan view and cross section can only provide qualitative defect
density data instead of quantitative results in the case of multiple deposited
epilayers. In plan view, the image is taken from the top of the sample surface,
so the interfaces of every multilayer are not visible. There may be
dislocations at interfaces that are buried from view using the plan view
perspective that make it impossible to precisely state the number of
dislocations present in an entire unit volume. Similarly, it is nearly
impossible to get a meaningful estimate of the number of dislocations from
cross-sectional view. XTEM only investigates a very small area of the entire
sample and is therefore not statistically significant. More importantly, the
direction of view used in these and most cross sections is the (110) direction,
so that half the dislocation is hidden while the other half lies parallel to the
interface, making it impossible to observe whether one or more dislocations
are contained within the thickness of the sample.
As discussed in Section 2.2.3, the as-grown SL/SiGe exhibited strain
relief through an array of misfit dislocations spaced an average of
approximately 0.5 |im apart, however, no threading dislocations were present
in cross-section images of the as-deposited structure. As stated above, this
does not necessarily mean that there were no threading dislocations, there
was just no conclusive evidence of them. The precise source of the misfit
dislocations is unclear at present but could most likely be due to the high
growth temperature of 700 C.


4-5, and a diffusion coefficient could not be determined. Due to the reasons
explained above, the diffusivities extracted using SIMS/FLOOPS are
considered to be much more reliable.
Table 4-5. Diffusivities of SL/SiGe extracted from FLOOPS and HRXRD.
PGelnert (cm2/s) DGe* (cmVs) Dc"" (cm2/s)
T CQ FLOOPS HRXRD FLOOPS HRXRD FLOOPS HRXRD
900 6.80xl017 1.33x1 O'17 4.58xl017 1.23xl017 1.70xl017 2.39xl017
1000 1.77xl015 3.21xl016 2.23xl015 8.96xl016 1.32xl016
4.6.3 Strain Relaxation Determined from HRXRD
Section 4.5.2.2 described the HRXRD method used to determine the
perpendicular and parallel lattice constants of the epilayer which are used to
estimate the strain relaxation which occurs in periodic SLs with thermal
processing. All results using this method are listed for SL/SiGe in Table 4-3.
The change in the angular separation of the zero order epilayer peak
and the Si(004) substrate peak with time did not initially show the expected
trend. Because the epilayer is in tensile strain when grown on the Si,.xGex
buffer, it is expected that progressive relaxation would cause the parallel
lattice constant to shrink towards its natural value, while the perpendicular
lattice constant would increase towards its unstrained value. The values of
ae// were expected to decrease with increasing anneal time, while the values of
ael were expected to increase. After calculations were performed using the
equations given in Section 2.4.4, the values of ae// were found to increase


148
c Depth (pm)
Figure 4-7. Comparison of experimentally determined SIMS profile and
FLOOPS profile using the Fermi model for samples annealed at 950 C and 3
min in (a) inert (b) oxidizing and (c) nitriding ambient.


Table 5-5. Comparison of diffusivities of SL/SiGe and SL/Si in inert, oxidizing and nitriding ambients.
T(C)
Inert
Oxidizing
Nitriding
time
(min)
D:SL/SiGe
(cm2/s)
D:SL/Si
(cm2/s)
D:SL/SiGe
(cm2/s)
D:SL/Si (cm2/s)
D:SL/SiGe
(cm2/s)
D:SL/Si
(cm2/s)
850
8
6.70xl017
4.00xl017
2.32x1016
4.00xl017
8.49xl018
1.42xl0'17
900
4
6.80xl017
4.58x1017
4.58xl017
4.58xl017
1.70xl0'17
1.70xl017
950
3
1.73X1015
3.26xl015
1.31x1015
1.31xl015
2.86x1016
3.46xl016
1000
2
1.77X1015
1.18xl015
2.23xl015
1.77xl0'15
8.96xl016
1.07xl015


187
retard diffusion. Very slight retardation was seen in profiles of samples
annealed in nitriding ambient (Figure 5-8), however, little enhancement, and
in some cases retardation, was observed for samples annealed in oxidizing
ambient.
5.6.2 Diffusivities Determined from HRXRD
Section 5.5.2.1 described briefly the method used to determine
diffusivities of periodic SLs from to-20 scans using HRXRD and listed results
for SL/Si. As discussed in Section 4.6.2 for SL/SiGe, the relative intensities of
the first order satellite peaks showed the expected trends and diffusion
coefficients were extracted. The (0-20 scans resulted in standardized first order
satellite peaks that did not always decrease progressively in intensity with
time (Figure 5-4). As in Chapter 4, this can most likely be attributed to
instrumental error in the measurement of intensity.
Figure 5-4 is a plot of the natural logarithm of the standardized
intensity of the first order satellite peak versus time. The slope of the decay of
the intensity is expected to be negative and is the value to be used in Equation
4-5 to extract diffusion coefficients for each temperature. The slopes of the
fitted curves for the decrease in intensity of the first order satellite peak for
increasing anneal times at 1000 C in inert, oxidizing and nitriding ambients
are negative, making the calculated D values negative, even though for all
ambients actual ln(I/ID) values do not decay consistently with increasing
anneal time. The values of ln(I/I0) of the first order satellite peak for
increasing anneal times at 900 C are even more erratic. A linear fit to the


134
This is the first time that activation energies for interdiffusion under
interstitial injection and vacancy injection for Sij.xGex/Si superlattice layers
with a Si,.xGex buffer have been directly determined from experiment.
1000C 950 C 900 C 850 "C
Figure 4-2. Effective Ge diffusivity of structure SL/SiGe as a function of
annealing temperature in inert, oxidizing, and nitriding ambients.
The method used in Chapter 3 to estimate fractional interstitial
components of diffusion for SQW/MBE could not be applied to SL/SiGe. No
SL structure was available with a buried boron marker layer underneath the
multiple SiGe/Si layers to estimate point defect concentrations. Therefore,
the non-equilibrium values of C, and Cv specific to dislocated SL/SiGe which
occured as a result of surface oxidation and nitridation could not be estimated.
It was considered scientifically pointless to estimate an f, for diffusion from


91
the vacancies are supplied as fast as they are depleted and thus always remain
at their equilibrium concentration, such that Cv/Cv*=l, and its lower limit as
case (ii) in which the product of the interstitial and vacancy concentrations
remains constant and C,CV=C*CV* such that Cv/Cv*=l /(C,/C,*). (3) A C,/C*
value in oxidizing ambient was determined for each temperature by the ratio
of t^/tA^ from the values presented in Table 3-4. (4) A constant f, was
assumed for a constant temperature regardless of processing ambient. (5)
Equation 3-5 was solved simultaneously for both inert and oxidizing
ambients, using the and D^0* values given in Table 3-1 for D, the C,/C,*
values from steps (1) and (3), and the Cv/Cv* values from step (2) for both the
upper and lower limit cases. This fifth step creates two equations with two
unknowns, D* and f such that these two parameters can be computed for the
specific processing temperatures and times used for the B marker layer
experiments. The upper (i) and lower (ii) bound cases for Cv/Cv* create upper
and lower bounds for the resultant D* and f, values.
It is important to note here that these D* and f, values apply most
rigorously to only the processing temperatures and times at which they were
extracted from the B marker layer experiments. The analysis was adapted and
extended as follows to address the additional processing times for SQW/MBE
in Table 3-1. (6) The D* and f, values determined for a constant temperature
from step (5) were considered constant with increasing processing time, while
the C,/Q* and Cv/Cv* values were allowed to change with time. It has been
widely accepted that non-equilibrium concentrations of interstitials and


95
resulted in sensible values for f, using the B marker layer results. Even when
the lower bound was decreased below 1/(C,/C,*) and the upper bound for
Cv/Cv* was raised above 4, f,s could not be estimated because the DGeNl,/D*
ratio from the values in Tables 3-1 and 3-5 were consistently too small.
Discussion of this phenomena is presented in Section 3.5.4.
3.4.5 TEM
The amount of initial relaxation of the structures immediately after
growth is determined by the growth temperature, layer thickness, Ge content
and the initial condition of the substrate [Iye89]. Upon annealing, the
structure will relax to reduce the strain energy. The minimum energy can be
attained by diffusion of Ge towards a compositional average or by the
generation of misfit dislocations. Both of these mechanisms compete and
their respective contributions are dictated by kinetic conditions. Because
SQW/MBE and SQW/VPE are strained and have been shown to have
dislocations after growth and before thermal processing, it is important to
know at least qualitatively the dislocation densities after annealing compared
to that of the as grown structures. This will give a qualitative idea of the
possible contribution of relaxation through dislocation formation to the
diffusivity values calculated in the preceding section.
All plan views were taken with the zone axis of (100) so that the
sample is exactly perpendicular to the electron beam, and the (220) reflection
was used.


75
f = IVDAXCA.^fVlogcA^^
dt Cx l Cx n¡
(3-4)
where X designates either interstitial or vacancy point defects, DAX denotes the
diffusivity of the dopant occurring through either vacancies or interstitials,
CA+ is the concentration of dopant in its ionized state, Cx is the actual point
defect concentration of either interstitials or vacancies, and Cx* is the
equilibrium point defect concentration. The login/n^ term accounts for the
contribution of the electric field to any concentration change. Equations 3-4
and 3-4 would be written for acceptors by inverting the n/n, term. The total
diffusivity of the dopant is defined as:
= f ^T + f
D* 1C* V Cv
(3-5)
where f, and fv are the fraction of diffusion which occurs via interstitials and
vacancies, respectively, and D* is the diffusivity under inert ambient.
The Neutral model assumes that the dopant diffuses in its neutral
charge state only, and does not include contributions to the diffusivity from
point defects. The Fermi model accounts for all possible charge states of the
diffusing dopant atom, known as Fermi-level effects, but still does not
include contributions to the diffusivity from point defects. The only
difference between the Neutral and Fermi models is that the Neutral model
uses only the first term of Equation 3-3. The Pair model includes the
contributions to the diffusivity of any point defects present. The C,* and Cv*
expressions are a function of the Fermi level, which is the electron


177
grown structure. This will give a qualitative idea of the possible contribution
of relaxation through dislocation formation to the diffusivity values
calculated in the preceding section. All plan-views were taken with the zone
axis of (100) so that the sample is exactly perpendicular to the electron beam,
using the (220) reflection.
Table 5-3. Parallel and perpendicular lattice constants of SL/Si.
Inert Oxidizing Nitriding
T(C)
time
(min)
3e//
ae//
ae
ae//
ae
As Grown
-
0.5431
0.5448
0.5431
0.5448
0.5431
0.5448
900
6
0.5432
0.5447
0.5431
0.5447
0.5431
0.5447
900
8
0.5431
0.5447
0.5431
0.5447
0.5431
0.5447
1000
1
0.5431
0.5447
0.5432
0.5447
0.5431
0.5447
1000
3
0.5432
0.5447
0.5432
0.5447
0.5431
0.5447
As discussed in Section 2.2.3, the as-grown SL/Si exhibited no misfit
dislocations in the areas viewed by plan-view micrograph, however,
threading dislocations were present in cross-section images of the as-
deposited structure. One threading dislocation existed in the area of view,
spanning from the substrate/buffer interface to the surface. This was most
likely indicative of additional threading dislocations present throughout the
further regions of the structure. As stated above, due to the nature of XTEM,
it was impossible to determine precisely what this dislocation volume might
have been. The source of both the misfit and threading dislocations is
unclear at present but could most likely be due to the high growth
temperature of 700 C. The plan view image of SL/Si annealed in inert