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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Thesis:
Thesis (Ph. D.)--University of Florida, 1999.
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Includes bibliographical references (leaves 215-221).
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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




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