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Loop nucleation and stress effects in ion-implanted silicon

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Title:
Loop nucleation and stress effects in ion-implanted silicon
Creator:
Avci, Ibrahim, 1969-
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English
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xvi, 144 leaves : ill. ; 29 cm.

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Subjects / Keywords:
Annealing ( jstor )
Boron ( jstor )
Dosage ( jstor )
Modeling ( jstor )
Nitrides ( jstor )
Nucleation ( jstor )
Point defects ( jstor )
Silicon ( jstor )
Simulations ( jstor )
Stripes ( jstor )
Dissertations, Academic -- Electrical and Computer Engineering -- UF ( lcsh )
Electrical and Computer Engineering thesis, Ph.D ( lcsh )
Ion implantation ( lcsh )
Semiconductor doping ( lcsh )
Semiconductors -- Defects ( lcsh )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

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Thesis:
Thesis (Ph.D.)--University of Florida, 2002.
Bibliography:
Includes bibliographical references (leaves 137-143).
General Note:
Printout.
General Note:
Vita.
Statement of Responsibility:
by Ibrahim Avci.

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University of Florida
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University of Florida
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Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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LOOP NUCLEATION AND STRESS EFFECTS IN ION-IMPLANTED SILICON




















By

IBRAHIM AVCI


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

2002


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Copyright 2002

by

Ibrahim Avci

























To my parents, Mustafa and Fatma.













ACKNOWLEDGMENTS

I thank my advisor, Dr. Mark E. Law, for his guidance, support and

encouragement. He always shared his invaluable knowledge and wisdom and he provided

valuable advice and direction throughout my doctorate study. I also thank to Drs. Kevin

S. Jones, Robert M. Fox, Gijs Bosman and Tim Davis for their help and guidance as

members of my doctoral supervisory committee.

I am grateful to Drs. Martin Giles, Paul Packan and Steve Cea for providing

materials for my experiments and for their valuable advice. I acknowledge Drs. Rainer

Thoma, Craig Jasper and Hernan Rueda for their support, understanding and help. They

inspired me during my doctorate study. I also thank to Semiconductor Research

Corporation for its support of my doctorate study.

I have met so many beautiful, helpful, and understanding people in my research

group that I call them my SWAMP family. My heartfelt thanks go to each one of them. I

would especially like to thank Tony Saavedra, Erik Kuryliw and Mark Clark for helping

with my experiments and TEM analysis. I also thank Ljubo Radic, Dr. Susan Earles and

Dr. Lahir Adam for their support, discussion and friendship. I will always remember the

experiences we shared. Although Chad Lindfors, Drs. Aaron Lilak, Sushil Bharatan,

Patrick Keys and Rich Brindos pulled my leg and accused me of"iboing," I will

remember all the good times we had. I also thank my friends, Serdar Ozen, Rifat

Hacioglu, Ferda Soyer, Banu Ozarslan, Evren Ozarslan, Alper Ungor, Ugur Kalay, and







Elgay Kalay for their friendship, support and encouragement. They will always have a

special place in my heart.

I would like to express my love to my parents, Mustafa and Fatma, for their

never-ending love, support and encouragement throughout my life. I am grateful to have

them. I would also like to express my love to my brother Ergun; my sister-in-law;

Munevver and my nieces, Irem and Ceren for their love and support.














TABLE OF CONTENTS

page

ACKNOWLEDGMENTS ...........................................................................................iv

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

LIST OF FIGURES................................................................................................... x

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

CHAPTERS

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

1.1 Ion-Implantation Damage and Defects..................................... ................. 4
1.1. 1 Point Defects ........................................................................................... 5
1.1.2 Extended Defects................................................................................... .....5
1.1.2.1 Category I damage .................................................................................. 6
1.1.2.2 Category II damage................................................................................ 7
1.1.2.3 Category III damage......................................................................... ....... 7
1.1.2.4 Category IV damage ..................................................................... 7
1.1.2.5 Category V damage............................................................................ 8
1.2 Dislocation Loops................................................................................................. 8
1.2.1 Interaction between {311 }'s and Dislocation Loops.................. ........... .. 10
1.2.2 Effects of Dislocation Loops on Device Characteristics ............................... 11
1.3 Stress and Strain ............................................................................................ 13
1.3.1 Stress and Strain Sources in Silicon IC Processing ....................................... 16
1.3.1.1 Film Stress and Film Edge-Induced Stress............................. ........... 16
1.3.1.2 Stress from Oxidation and Device-Isolation Processes....................... 18
1.3.1.3 Dopant-Induced Stress ....................................................................... 19
1.4 Stress-Induced Dislocation Loops............................................................. 20
1.5 G oals ............................................................................................................... 22
1.6 Organization .......................... ......................................................................... 23

2 MODELING THE EVOLUTION OF DISLOCATION LOOPS FOR VARIOUS
PROCESS CONDITIONS ............................................................. ....................... 24

2.1 Modeling Dislocation Loop Evolution .............................................................. 25
2.1.1 Log Normal Distribution Function.............................................................. 26
2.1.2 Density of Dislocation Loops........................................................ ...... ....... 27







2.1.4 Coarsening and Dissolution of the Dislocation Loops ............................... 29
2.2 Experimental and Simulation Results to Calibrate the Model............................. 34
2.2.1 Simulation of the Evolution of Loops during Oxidation .............................35
2.2.2 Simulation of Loop Evolution during Annealing in Inert Ambient ..............40
2.3 Experimental and Simulation Results to Verify the Model...................................42
2.3.1 Simulation of Loop Dissolution as a Function of Loop Depth................... 42
2.3.2 Effects of Dislocation Loops on Boron Diffusion....................... ................ 44
2.4 Sum m ary .............................. .........................................................................47

3 MODELLING THE NUCLEATION AND EVOLUTION OF THREADING
D ISLO CA TIO N LO O PS......................................................................................... 48

3.1 Modeling Dislocation Loop Nucleation ............................................................50
3.2 Modeling Threading Dislocation Loop Nucleation...................................... 54
3.2.1 Simulation of the Nucleation and Evolution of Threading Dislocation Loops
........... ............................................................ .. ............................ ....... 56
3.3 Sum m ary ...................................................................................................... 62

4 NUCLEATION AND EVOLUTION OF END OF RANGE DISLOCATION
LO O PS ................................................................................................................... 63

4.1 Experim ental D details ..........................................................................................64
4.2 Experim ental Results..................................................... ............................. 65
4.3 Sim ulation Results........................................................ .............................. 72
4.4 Sum m ary ...................................................................................................... 81

5 VERIFICATION OF THE LOOP MODEL USING DIFFERENT IMPLANT
S P E C IE S ....................................................................................................................... 83

5.1 Defects in Boron Implanted Silicon ............................................. ............ 84
5.1.1 Sim ulation Results .................................................... ............................ 86
5.2 Defects in Germanium Implanted Silicon....................................... .......... 90
5.3 Defects in Arsenic Implanted Silicon...............................................................97
5.4 Sum m ary .......... .............................................................................................. 99

6 PROCESS INDUCED STRESS EFFECTS ON DISLOCATION LOOPS................ 100

6.1 Dislocation Loop Nucleation and Evolution under Tensile Stress.................... 102
6.1.1 Experim ental D etails................................................................................... 102
6.1.2 Stress-Assisted Loop Nucleation and Evolution Model............................ 108
6.1.3 Experimental and Simulation Results.......................................................10
6.2 Effects of Patterned Nitride Stripes on Dislocation Loops............................... 116
6.2.1 Experim ental D etails.................................................. ............................ 116
6.2.2 Experimental and Simulation Results........................................................ 117
6.3 Sum m ary .......................................................................................................... 122

7 SUMMARY AND FUTURE WORK....................................................................... 124







7.1 Sum m ary ........................................................................................................... 124
7.2 Future W ork ...................................................................................................... 129

EXTRACTED PARAM ETERS .................................................................................. 132

LIST OF REFERENCES ............................................................................................ 137

BIOG RAPHICAL SKETCH ..................................................................................... 144


V111













LIST OF TABLES


Table page

Table 5-1. Types of extended defects formed in B' implanted silicon............................... 85

Table 5-2. Simulation results for the types of extended defects formed in B' implanted
silicon after an anneal at 7500C for 5 min ..................................................... 87

Table 5-3 Simulation results for the types of extended defects formed in B' implanted
silicon after an anneal at 9000C for 15 min..................................................... 88













LIST OF FIGURES


Figure page

Figure 1-1 The range of ion implant energies and doses used in semiconductor
processes ................................................................................... ............. 3

Figure 1-2 Criteria of Extended Defect Generation......................................................... 6

Figure 1-3 Weak beam dark field images of dislocation loops and {311 ......................... 10

Figure 1-4 An arbitrary body subject to external forces ............................................ 13

Figure 1-5 Components of stress in a stress element ..................................... ........... 14

Figure 1-6 Shear strain ............................................................................................... 15

Figure 1-7 Two dimensional lattice deformation due to a dopant atom ......................... 19

Figure 1-8 Cross section of a modem day n type MOS transistor...................................... 21

Figure 2-1 Log normal density distribution function applied to the statistical distribution
of loop radius extracted from the TEM measurements under 900 oC dry
oxidation condition. ......................................................................................... 26

Figure 2-2 Pressure in silicon due to the dislocation loops............................................. 30

Figure 2-3 Density of the interstitials bounded by dislocation loops as a function of
oxidation time and simulation in the two different cases of Si implant dose,
2x10'5 and 5xl01 cm -2..................................................................................... 35

Figure 2-4 Variation of total density of dislocation loops with time and simulation results
for two different implant conditions ............................................ .......... ... 36

Figure 2-5 The average radius change with time during oxidation and corresponding
sim ulation results.. ....... ............ ..... ..................................................................37

Figure 2-6 Variation in total number of interstitials bounded by the loops as a function of
anneal time at different temperatures.............................................................38

Figure 2-7 Variation in total loop density as a function of anneal time at different
tem peratures. ...................................................................................... ....... 39







Figure 2-8 Experimental and simulated average loop radius as a function of annealing
tim e at different tem peratures.................................................... .................... 41

Figure 2-9 Simulation and experimental results for the loss of interstitials with time at
900 C ................................. ............. .... ................................................... 42

Figure 2-10 Simulation and experimental results for the loss of interstitials with time at
1000 C ................................... ........... ................................................... 4 3

Figure 2-11 SIMS profiles of DSL after Si' implantation at different dose rates and
annealing at 800 C for 3 m minutes. ................................................................ 45

Figure 2-12 Boron profiles with two different loop density and no loop layer, annealed at
800 OC for 3 m minutes. ....................................... ..................................... 46

Figure 3-1 Schematic representation of dislocation loop nucleation.......................................50

Figure 3-2 Nucleation rate N 'au change with time................................. ............. 52

Figure 3-3 TEM picture of dislocation loops and threading dislocation loops .................53

Figure 3-4 Schematic representation of TDLs in a distribution function..........................55

Figure 3-5 Initial excess interstitial concentration after an implantation of boron with a
dose of lxl014 cm-2 and an energy of 1.5 MeV.......................................... 57

Figure 3-6 Changes in defect densities with time after implantation of boron with a dose
of IxlO 4 cm-2 and an energy of 1.5 M eV.......................................................58

Figure 3-7 Density of all dislocation loops and threading dislocation loops vs. boron
dose with implant energy of 1.5 MeV. ..................................... ............ .. 60

Figure 3-8 Total number of interstitials bounded by loops for various boron implant dose
with im plant energy of 1.5 M eV ..................................................................... 61

Figure 4-1 Schematic representation of designed experiment....................................... 65

Figure 4-2 Weak beam dark field XTEM images of(a) 40 keV and (b) 80 keV Si+
implanted Si to a dose of 2xl015 cm-2 before furnace anneals......................... 66

Figure 4-3 Weak beam dark field plan view TEM images of 40 keV Si+ implanted Si to a
dose of 2x1015 cm-2, after an anneal at 700 C for (a) 30 min (b) 60 min (c) 90
min (d) 120 min (e) 240 min in N2. ................................................................ 68

Figure 4-4 Weak beam dark field plan view TEM images of 40 keV Si+ implanted Si to a
dose of 2x1015 cm-2, after an anneal at 750 OC for (a) 15 min (b) 30 min (c) 60
min (d) 90 min (e) 120 min in N2 ............................................................... .... 69







Figure 4-5 Weak beam dark field plan view TEM images of 80 keV Si+ implanted Si to a
dose of 2x10'5 cm-2, after an anneal at 700 C for (a) 30 min (b) 60 min (c) 90
min (d) 120 min (e) 240 min in N2. ........................................................ 70

Figure 4-6 Weak beam dark field plan view TEM images of 80 keV Sit implanted Si to a
dose of 2xl05 cm-2, after an anneal at 750 C for (a) 15 min (b) 30 min (c) 60
m in (d) 90 min (e) 120 min in N2................................................................... 71

Figure 4-7 Initial truncated excess interstitial concentration after an implantation of Si
with a dose of 2xl015cm2 and energy of 80 keV............................................ 73

Figure 4-8 Changes in defect densities with time at 700 C after implantation of Si' with
a dose of 2x 015 cm-2 and energy of 40 keV. The symbols are experimental
results and the lines are simulation results.................................... ............. 74

Figure 4-9 Changes in defect densities with time at 700 OC after implantation of Si+ with
a dose of 2x 015 cm-2 and energy of 40 keV. The symbols are experimental
results and the lines are simulation results. .........................................................75


Figure 4-10




Figure 4-11



Figure 4-12



Figure 4-13



Figure 4-14


Changes in defect densities with time at 700 OC after implantation of Si+
with a dose of 2x1015 cm"2 and energy of 40 keV. The symbols are
experimental results and the lines are simulation results. Amorphous depth
is set to 950 A and 1000 A as initial condition for two different simulations.. 76

Changes in defect densities with time at 750 C after implantation of Sit
with a dose of 2x1015 cm-2 and energy of 40 keV. The symbols are
experimental results and the lines are simulation results.............................. 77

Changes in defect densities with time at 700 OC after implantation of Si'
with a dose of 2x10'5 cm"2 and energy of 80 keV. The symbols are
experimental results and the lines are simulation results.............................. 78

Changes in defect densities with time at 750 OC after implantation of Si+
with a dose of 2x1015 cm-2 and energy of 80 keV. The symbols are
experimental results and the lines are simulation results.............................. 79

Changes in defect densities with time at 750 oC after implantation of Si+
with a dose of 2x1015 cm2 and energy of 40 keV. The symbols are
experimental results and the lines are simulation results. Amorphous depth
is set to 950 A and 1000 A as initial condition for two different simulations.. 80


Figure 5-1 Experimental and simulation results for the defect evolution for a 30 keV,
xl 0'5cm-2 Ge+ implant on silicon, annealed at 750 OC.....................................91

Figure 5-2 Experimental and simulation results for the defect evolution for a 30 keV,
lxl05cm-2 Ge+ implant on silicon, annealed at 825 C.....................................92







Figure 5-3 Experimental and simulation results for the defect evolution for a 10 keV,
lxl105 cm'2 Ge' implant on silicon, annealed at 750 C..................................94

Figure 5-4 Experimental and simulation results for the defect evolution for a 5 keV,
5xl014cm-2 Get implant on silicon, annealed at 750 C...................................95

Figure 5-5 Experimental and simulation results for defect evolution from 5 keV,
3xl015cm-2 Ge' implant on silicon, annealed at 750 C...................................96

Figure 5-6 Simulation results for the defect evolution for 3 keV, 5xl014cm-2, lxlO15 cm-2
and 5xl015 cm-2 As implants on silicon, annealed at 800 OC for 60 minutes......98

Figure 6-1 SEM image of Intel wafer with various patterns. Some structures are as small
as 0.5 m ................................................................................................ 10 1

Figure 6-2 SEM image of three bars on the wafers. Each bar consists of repeating nitride
patterns. Nitride stripes run from top to bottom of the page............................ 102

Figure 6-3 Magnified SEM image of three bar structure shown in Figure 6.2. Nitride bars
are 10 m wide and the spacing between them is 3.5gm ................................. 103

Figure 6-4 PTEM image of three bar structure shown in Figure 6.2. Nitride bars are
10gm wide and the spacing between them is 3.5pm ......................................... 104

Figure 6-5 SEM image of the other structure used in the experiment. Nitride stripes run
from left to the right of the page..................................................................... 104

Figure 6-6 Magnified SEM image of structure shown in Figure 6.4. Nitride stripes run
from left to the right of the page..................................................................... 105

Figure 6-7 PTEM image of structure shown in Figure 6.4. The spacing between nitride
bars is 3.5 n m .................................................................................................. 105

Figure 6-8 XTEM image of one of the un-annealed samples. The amorphous depth is
clearly visible and found to be 900A.............................................................. 106

Figure 6-9 XTEM image of one of the un-annealed samples. The amorphous region and
nitride pattern are visible. The amorphous depth and nitride thickness were
found to be 900A and 1500A respectively..................................................... 107

Figure 6-10 XTEM image of the annealed sample showing the damage in the trench
area. Defects curve towards the surface around the nitride edges................. 108

Figure 6-11 Magnified XTEM image of the structure shown in Figure 6.10. The defects
in the trench area are visible........................................................................ 108


xiii







Figure 6-12



Figure 6-13



Figure 6-14



Figure 6-15



Figure 6-16


Figure 6-17


Figure 6.18



Figure 6-19


Weak beam dark field plan view TEM images of 40 keV Si+ implanted Si to
a dose of lxl015 cm"2, after an anneal at 700 C for (a) 60 min (b) 120 min
(c) 180 min (d) 60 min (e) 120 min (f) 180 min in N2 ..................................I 1

Weak beam dark field plan view TEM images of 40 keV Si+ implanted Si to
a dose of x1015 cm-2, after an anneal at 750 C for (a) 30 min (b) 60 min (c)
120 min (d) 30 min (e) 60 min (f) 120 min in N2........................................... 112

Changes in defect densities with time at 700 C after implantation of Si'
with a dose of lx1015cm-2 and energy of 40 keV. The symbols are
experimental results and the lines are simulation results.............................. 113

Changes in defect densities with time at 750 C after implantation of Si'
with a dose of lxl015 cm2 and energy of 40 keV. The symbols are
experimental results and the lines are simulation results............................ 114

Variation of the hydrostatic pressure in the silicon substrate for samples with
10 pm and 150 pm nitride stripes................................................................ 115

The structure used to study the effects of nitride stripes on the evolution of
dislocation loops in silicon ............................................................................ 117

Variation of the hydrostatic pressure in the silicon substrate in compressive
and tensile regions under the patterned nitrides. Dislocation loops are
formed around the a/c interface..................................................................... 118

Experimental and simulated values of the net change in the average radius of
the dislocation loops from the tensile to compressive regions as a function of
nitride stripe w idth. ................ ........................................................................ 119


Figure 6-20 Experimental and simulation results of the net change in the total density
of dislocation loops from the tensile to the compressive regions as a function
of nitride stripe w idth................................................................................ 120

Figure 6-21 Experimental and simulated results of the net change in the number of
interstitials trapped by dislocation loops from the tensile to the compressive
regions as a function of nitride stripe......................................................... 122













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

LOOP NUCLEATION AND STRESS EFFECTS IN

ION IMPLANTED SILICON

By

Ibrahim Avci

August 2002
Chairman: Dr. Mark E. Law
Major Department: Electrical and Computer Engineering

Because of its reproducibility, accurate dose control, and the ability to tailor

dopant profiles, ion implantation has been used for years by the semiconductor industry

to introduce dopant atoms into the silicon substrate. Damage to the silicon substrate from

ion implantation is unavoidable, and annealing is required to repair the damage. Upon

annealing, dislocation loop and {311} defects are formed in the vicinity of ion implanted

region. These defects may degrade or even cause complete failure of devices.

Meanwhile, the semiconductor industry continues to scale successive generations

of integrated circuits to increase packing density and reduce device dimensions.

Unfortunately, these trends lead to increased stress levels in the silicon substrate. When

combined with ion implantation damage, high stress influences defect formation and

evolution.







To design better devices through predictive simulations, the magnitude, depth,

temperature and time dependence of ion implantation-induced defects should be modeled

correctly.

We developed statistical-point defect-based model for the evolution and

nucleation of dislocation loops in silicon-implanted silicon. The model assumes that all of

the dislocation loops evolve from unfaulting {311} defects. The model correctly predicts

three distinctive stages of dislocation loop evolution (i.e. nucleation, growth, Ostwald

repining) during annealing and is in agreement with the TEM data. We also tested the

model for different implant species such as boron, germanium and arsenic. The model

worked well for most of the implant and annealing conditions. The discrepancies between

the model and the experimental results were highlighted where they occurred. We used

the statistical nature of the model to determine threading dislocation loop densities by

comparing average loop radius to loop depth.

Finally, we studied the mechanical stress effects on dislocation loops. Stress in the

silicon substrate is varied by changing the deposited nitride stripe widths. The loop model

was expanded to account for stress effects. We confirmed that dislocation loops are

smaller and sparser in regions of compression when compared to the ones in the regions

of tension.


xvi












CHAPTER 1
INTRODUCTION

Relentless scaling of Complementary Metal Oxide Semiconductor (CMOS)

device dimensions has been the driving force for the growth of microelectronics industry

for more than 20 years. The most important features of scaling down device dimensions

are high packing density of Integrated Circuits (IC), high circuit speed, and low power

dissipation [Tho98]. As the industry progresses toward smaller device dimensions (0.1

pm or smaller), fabrication of such devices become increasingly difficult because of

fundamental limits imposed by quantum mechanics and thermodynamics [Tau99]. Most

of the effects not dominant in long-channel devices are becoming an issue in today's

short-channel devices. Carrier velocities reach saturation because of high normal electric

fields and the threshold voltage depends on junction depth and effective channel length of

short-channel devices [Kan96]. Thus, understanding the formation of shallow junctions is

key to building smaller devices. To form shallow junctions, parameters that control

dopant diffusion in silicon need to be understood and modeled. Ghandi [Gha94] reviewed

the various generic process steps involved in the fabrication of IC devices.

Ion implantation has been the primary source of introducing impurity atoms into

silicon substrate. Unfortunately, the ion implantation process causes extensive crystal

damage and creates point defects. This damage is repaired during subsequent annealing.

The diffusion of dopants occurs through interaction with point defects. During the anneal,

the point-defect concentrations reach their equilibrium values. However, until the defect

concentrations reach their equilibrium values, the diffusion of dopants would be a







nonequilibrium phenomenon. One such nonequilibrium effect is transient enhanced

diffusion (TED) [Fah89, Eag94]. If the implant doses are high enough, extended defects

such as dislocation loops and {311 }'s [Jon88, Jon95] can form during the annealing step.

In the fabrication of microelectronic devices, various process steps cause stress to

the substrate. Silicon oxide deposition and/or growth is one such process. Shallow Trench

Isolation (STI) is the dominant isolation technology used today and the STI process may

result in stress-induced dislocation loops in the silicon active area [Fah92]. Dislocation

loops will increase the leakage current in devices when they are located at or near the

device junction-especially in the depletion layer of a junction. Increased leakage current

will cause device degradation [Ros93] and increased power consumption in logic and

memory circuits.

Because of the prohibitive costs of manufacturing IC devices, accurate simulation

of these complex phenomena is a critical and fundamental component for IC

technologists to develop new processes and devices. In order to have accurate simulation

results, accurate simulation models are needed. In order to develop models, some

experimental data are needed. Once the model agrees with existing experimental data, the

model can be used to predict the results at other process conditions, thereby avoiding

continued costly experiments. Empirical models can be used to predict within the range

in which it is calibrated and are therefore useful only under interpolation conditions.

Physics-based models are more reliable because they also can be used under

extrapolation conditions (as they rely on the inherent physics of the process phenomena).

If the physics behind a process step is understood well enough, the model will have a

wider range of application.







Because of the complexity of the processes involved, we do not completely

understand all the relevant physics. Therefore, process models typically use certain

assumptions and/or approximations. Hence, process modeling is a continuous effort to

develop new technologies as the shrinking device dimensions may invalidate assumptions

used in old models. Tools such as Florida Object Oriented Process Simulator (FLOOPS)

[Law98] with ALAGATOR script language offer a great advantage to the end user in

developing new models and technologies within a short time. Trade-offs must be made

with respect to the accuracy of the model, CPU time, and ease of use. Although

Molecular Dynamics (MD) codes offer more accuracy and physical insight, they are

computationally intensive and hence are not yet practical for developing new


107


leOP


A2l


10 1010 10" 1012 1013 104 101 1016 1017 1018 1019
Ion Dose (Atoms/cm2)


Figure 1-1. Range of ion implant energies and doses used in semiconductor processes


Deep (retrograde) well CMOS Applications

Mid-well
Channel Halo
(Vertical punch-thruteral punch-thru
(Lateral punch-thru
control) SIMOX

Channel doping


control) oly-Si gate

doping
Source/Drain contact

Source/Drain extension
.a.. ...a ....~....J.. ... I .t- .-J 1..


I







technologies. Insight obtained from MD codes can be used in kinetic Monte Carlo

simulations to verify fundamental mechanisms. Then, this information is used to develop

more accurate physical-based continuum process models.

Validity of the physical models depends on the parameters that are physically

meaningful. Although some parameters have an established set of values, others must be

derived from systematic experiments. Models with consistent parameters extracted from

experiments are fundamental to developing future experiments and technologies.



1.1 Ion-Implantation Damage and Defects

Ion implantation is one of the most important steps in manufacturing very large

scale integrated (VLSI) Si devices. The main advantages of ion implantation are

introducing a desired impurity into a target material, accurate dose control,

reproducibility of the impurity profiles, lower process temperatures and the ability to

tailor the doping profile [Cha97]. Because of these advantages, ion implantation is used

repeatedly at various process steps (threshold voltage control adjustment, channel stop

implantation, source drain formation, etc.). Figure 1-1 shows the range of ion implant

energies and doses used in semiconductor processing.

The detrimental effect of the ion implantation is the damage caused to the silicon

substrate by incident ions. Two main stopping mechanisms are involved during

implantation. They are nuclear stopping and electronic stopping. Nuclear stopping is the

process of gradually retarding the motion of an implanted ion by collision with the target

(Si) atoms. Electronic stopping is the process of retarding the motion of an implanted ion

by interaction with the electron cloud of the target and the implanted ion (i.e., Electronic

stopping is a dragging force). While electronic stopping causes no damage to the







substrate, nuclear stopping produces all the damage due to primary and secondary

collisions of the incident ions into the silicon substrate [Wol86]. Nuclear collision

generates a large amount of point defects such as vacancies and interstitials. To repair the

damage created by ion implantation, post-implant annealing is required. Upon annealing,

several types of extended defects may also be formed in addition to the point defects.

These extended defects are categorized into Types I, II, III, IV, and V [Jon88]. Further,

defects that are vacancy-type in nature are generally classified as intrinsic defects and

those that are interstitial-type in nature are usually classified as extrinsic defects.


1.1.1 Point Defects

Point defects like vacancies and interstitials are localized defects. Vacancies,

interstitials, interstitialcies and impurity atoms are incorporated during implantation.

Vacancies, interstitials and interstitialcies are native point defects that exist in a pure

crystal structure. A vacancy is an empty lattice site. An interstitial is an atom that resides

in one of the interstices of the crystal lattice. A self-interstitial is an interstitial Si atom.

An interstitialcy defect consists of two atoms configured about a single lattice site.


1.1.2 Extended Defects

As mentioned previously, during the implantation process, the crystalline lattice

of the semiconductor is damaged and many point defects are created. An annealing step

is necessary to repair the damage and to activate the dopant. Depending on the

implantation energy, dose and annealing conditions, various kinds of extended defects

evolve. These defects are categorized into five types as shown by Jones et al.

[Jon88].









10 -
Critical Dose
-for Amorpiz ation

A-7

A. .., g Category I defeat




1,1." Category I defects



threshold
da'e ie Category II defects

14 d dose
10 I Category I1
No Extended Defects threshold
dose

13
0 20 40 60 s0 100 120 140
Ion mass (amu)


Figure 1-2. Criteria of extended defect generation [Par93, Jon88]



1.1.2.1 Category I damage

This damage is called subthresholdd" damage and occurs when the implant

damage is not sufficient to produce an amorphous layer. Category I defects form

at the projected range of the implant. These defects are typically rod-like (311) defects

and extrinsic dislocation loops that are precipitates of Si interstitial atoms. Type I defects

are usually formed by light ions. Heavy ions can produce an amorphous layer if the

implant dose exceeds the critical dose needed to form an amorphous layer. Therefore

Type I defects are a strong function of the implant dose.







1.1.2.2 Category II damage

If the implant dose is sufficiently high, an amorphous layer is formed. Upon post-

implant anneal, the amorphous region regrows very quickly into a perfect crystalline

structure through solid phase epitaxy (SPE) and Category II defects are formed at the

original amorphous-crystalline interface. These defects are called End of Range (EOR)

defects and consist of both dislocation loops and {311 }s depending on the annealing

temperature. Once the critical dose for amorphization is exceeded, any increase in the

dose has a minimal effect on the defect evolution. Therefore, the density of these defects

is not a strong dependence of the implant dose. Dislocation loops in this category can be

categorized as faulted dislocation loops and perfect dislocation loops. The major criteria

that distinguish Category I damage and Category II damage are the implant dose and

implanted ion species mass (shown in Figure 1-2.) Details of these defects are discussed

later.


1.1.2.3 Category III damage

Imperfect regrowth of the amorphous layer is the main source of Category III

defects. They are formed as "hairpin" dislocations, microtwins, and segregation defects.

Hairpin dislocations nucleate when misoriented microcrystalline regions are encountered

at the amorphous-to-crystalline interface. These defects can be avoided.


1.1.2.4 Category IV damage

Depending on the implant energy and implant dose, buried amorphous layer can

be formed in the substrate. This buried amorphous layer results in a layer of defects

called Category IV defects that are also called "clam-shell" or "zipper" defects. These







defects can be avoided by changing implant energy and dose to produce a surface

amorphous layer instead of a buried amorphous layer.


1.1.2.5 Category V damage

Solid solubility of a species in the substrate by ion implantation can be exceeded.

During the solid phase epitaxial growth of the amorphous layer, all of the dopant within

the amorphous layer is incorporated into the lattice sites. Further annealing causes

precipitation and defects associated with precipitation form at the projected range of the

dopant. The defects include both dislocation loops and precipitates.



1.2 Dislocation Loops

As long as the implantation dose is below the critical dose (Figure 1-2),

dislocation loops are not formed. The most common defects seen in IC devices today are

Type II defects because of to the high doses required to form highly activated shallow

junctions. By controlling the energy of the implant, the junction depths can be varied.

Therefore, ion implantation is the primary way of forming shallow junctions. Light ions,

such as B, are susceptible to channeling during implantation process. Channeling

increases junction depth. Forming an amorphous layer in crystalline structure before

forming the channel doping is a well known technique to prevent the channeling. Heavy

ions do not channel as much as light ions. However, amorphization is unavoidable in this

case because of the heavy ion mass and high implant doses required. To repair the

damage, post-implant anneals are required. During the growth of the solid phase epitaxial

growth of the amorphous layer, extended defects form at the amorphous to crystalline

interface. They are also known as end-of-range defects ranging from small clusters of a







few atoms to {311 }s and dislocation loops. All these defects are extrinsic in character.

The defects have been studied in great details by various researchers [Ben97, CofO,

Mau94, Eag94, Pan96].

The EOR loops are of two distinctive types. One is the faulted Frank dislocation

loop and the other is the perfect dislocation loop [CriOO]. The faulted loops lie on {111

planes and have a Burgers vector of(a/3)< 1> perpendicular to the loop plane. The

perfect dislocation loops also lie on { 111 } planes and have a Burgers vector of

(a/2). They are elongated along that particular <110> direction on their habit plane.

Evolution of these defects at various annealing temperatures and ambients has

been widely studied [Gil99, Liu95]. The EOR defects grow in size and reduce their

density at annealing temperatures below 900 oC. This regime is referred to as the

"coarsening" regime. The loops remain in the coarsening regime and the densities of

interstitials bound by the loops remain fairly constant. The larger loops grow at the

expense of the smaller ones. This is called the Ostwald ripening process [Bon98]. If the

annealing temperatures are above 900 C, EOR loops become thermally unstable and

start dissolving [Liu95]. These loops can be seen as reservoirs able to maintain a high

supersaturation of free self-interstitials during their dissolution [Cla95]. This enhances

the dopant diffusion through the formation of Si interstitial-dopant pairs. It is also shown

that EOR dislocation loops act as a sink for interstitials during oxidization [Par94a,

Men93]. They can be used as point defect detectors or to reduce the oxidation-enhanced

diffusion of boron in a buried layer because of the efficient interstitial capturing action of

dislocation loops. The capture rate depends on the distance of the loop layer from the

surface [TsoOO].

























Figure 1-3. Weak beam dark field images of dislocation loops and {311}


1.2.1 Interaction between {311 's and Dislocation Loops

Weak beam dark field images of dislocation loops are shown in Figure 1-3 along

with {311 }s. The {311 }s are rodlike defects consisting ofinterstitials that grow along the

<110> direction in a {311 } habit plane. It is shown that {311 } rodlike defects have three

stages of microstructural evolution: accumulation of point defects to form circular

interstitial clusters, growth of these circular clusters along <110> direction and

dissolution into matrix [Pan97a, Pan97b]. The {311} defects dissolve very fast at high

annealing temperatures (>7000C). As a result of dissolution, interstitials are released and

these are believed to be the primary source of the TED [Eag94].

Interactions between {311} defects and Type I and II dislocation loops were

studied by Jones et al. [Jon95]. The formation of Type I loops does not result in complete

trapping of interstitials released by {311} defects. Growth of the Type II loops is greater

than can be explained by {311 dissolution.







It has been shown qualitatively that {311 } defects are the source of dislocation

loops [Li98]. They studied the effects of {311} unfaulting into loops at 8000C through in

situ annealing after a non-amorphizing implant. They also suggested that TED will

saturate with increasing implant dose in a system where {311 } defects are the primary

source of TED.


1.2.2 Effects of Dislocation Loops on Device Characteristics

Electrical characteristics of silicon devices are effected by dislocation loops

[Tam81]. Ross et al. [Ros93] measured the characteristics of SiGe/Si p-n junction diodes

by introducing dislocations into these devices by heating in situ in the electron

microscope. A simple generation-recombination process occurring at the dislocation

cores does not explain the large amount of measured leakage current. The device

degradation due to the introduction of dislocation loops is related to the creation of point

defects and/or the diffusion impurities such as metals during the formation of the

dislocation loops. Significant decreases in free carrier mobility in bipolar transistors was

also reported because of the dislocation loops with the assumption that, in n-type crystals,

the dislocation loops behave like a line of negative charge surrounded by a positive space

charge that repels incident electrons [Fin79]

Bull et al. [Bul78] reported that dislocation loops intersecting the emitter-base

junction lead to low gains and high emitter-base leakage current in bipolar transistors.

Collector-emitter leakage currents also correlate with dislocation loops that pass through

the transistor from the emitter to collector. If the dislocation loop is decorated with

metallic impurities, it can be conductive enough to permit significant current flow

between collector and emitter even when the base terminal is open [Wol86].







Similar leakage currents are observed in metal oxide semiconductor (MOS)

devices when dislocation loops lie across the device junction [Miy97]. Because device

dimensions are shrinking with every new technology, the probability of having

dislocation loops decorated with metallic impurities across the junction is increasing, and

so is the leakage current. Reduction in the minority carrier lifetime is another problem

imposed by dislocation loops. Carrier lifetimes are reduced by dislocation loops through

the introduction of localized intermediate energy levels within the silicon bandgap.

Reduced carrier lifetimes require MOS dynamic RAMs to be refreshed more often. At the

same time, reduced carrier life can be helpful to suppress latch-up by reducing the current

gain of the parasitic transistor which is located away from the active device [Wol86].

Another effect of dislocation loops on device characteristics comes from their

ability to interact with point defects. Dislocation loops grow by capturing interstitials

[Hua93] and dissolve by emitting interstitials [Liu95]. They are very efficient sinks for

interstitials [Men93]. They change the concentration of point defects around the loop

layer. Because most of the dopant atoms pair with point defects [Fah89] and diffuse,

changing point defect concentration through point-defect-loop-interaction will change the

final doping profile. This will affect the junction depth and final electrical characteristics

of the device.

Dislocation loops exist with a significant stress field surrounding them in Si and

the stress can alter diffusion kinetics of the dopants [Par95]. This might be significant

enough to change the doping profile and the device characteristics. Thus, dislocation

loops indirectly affect the device characteristic. Many sources of stress exist in Si and

they are discussed in the next section.









f R n





F F3 F3



1 F1



Figure 1-4. An arbitrary body subject to external forces



1.3 Stress and Strain

To understand stress sources in silicon IC processing, some basic concepts of the

mechanical stress and strain should be known. If a body is subject to external forces, a

system of internal forces is developed. (Figure 1-4 ) [Mov80]. These internal forces tend

to separate and. bring closer together the material particles that make up the body.

Assuming an imaginary plane cuts the body into two parts, internal forces are transmitted

from one part of the body to the other through this imaginary plane. The free body

diagram of the lower part of the body is also shown in Figure 1-4. The forces F, F2 and

F, are held in equilibrium by the action of an internal system of forces. This system of

internal forces can be represented by a single resulting force R which may be

decomposed into a component F,, perpendicular to the plane and known as the normal

force, and a component F, parallel to the plane known as the shear force. If the area of

the imaginary plane is A, then F / A is called normal stress and F, / A is called shear








stress. Because these stresses are nonuniformly distributed through the area, normal stress

and shear stress should be defined using a differential area of AA and the forces AFt, and

A!F. Then the normal stress a and the shear stress r are given by

AF
0= lim AF
AA-O A
= (1.1)
.li AF
= Jim -'
AA --0 AA

A three-dimensional stress element is shown in Figure 1-5. Normal stress vectors

have a single subscript and shear stress vectors have a double subscript. The first

subscript of the stress vector indicates the plane on which stress is acting and the second

subscript indicates its direction. There are three normal stress components and nine shear

stress components. If the stress element is in equilibrium, shear stress vectors become



y y


x plane






dy





z 'plane


Figure 1-5. Components of stress in a stress element







Try = Tyx, = T., and Tr~ = Ty. By convention, a normal stress is positive if it points in

the direction of the outward normal plane. A positive normal stress produces tension and

negative normal stress produces compression. The stress components shown in Figure I-

5 are all positive.

When a nonrigid body is subject to stress it goes through deformation and

distortion. Thus any line element in the body goes through deformation if its length

increases or decreases. Then, the normal strain, ,, is the change in length per unit length

of the element. The normal strain at a point in the body is represented as

a de.
E = lim-= (1.2)
L-0 L dL

where 8 and L are the initial length of the line element and its deformation respectively.

4 T Distorted
shape

l I

\ \ \
\ <,



Figure 1-6. Shear strain


If the distortion in a stress element due to shear stresses does not involve a change

in the length but a change in the shape as shown in Figure 1-6, then the shear strain is

defined as the change in angle between two originally mutually perpendicular edges.

Thus, the shear stress is y = p where 9 is in radians.







The relation between the normal strain and stress for a particular material is

described by Hooke's law as

a = EE (1.3)

where E represents a unique property for a given material and is known as Young's

modulus of elasticity. In a similar way, the relation between the shear stress and strain is

expressed mathematically as

T = G (1.4)

G represents a unique property for a given material and is called the modulus of rigidity

or the modulus of elasticity in shear.

The relations given between the normal stress and normal strain or the shear stress

and shear strain are more complex in nature. More complex nonlinear models are usually

used in process simulators to calculate the process induced mechanical stress (for

example FLOOPS treats SiO2 as a nonlinear viscoelastic material) [Cea96].


1.3.1 Stress and Strain Sources in Silicon IC Processing

The IC processing technology is a complex process requiring embedding, butting,

and overlaying of a large variety of materials of different elastic and thermal properties.

Because these materials are subject to various thermal cycles during the IC processing,

stress develops. Stress sources can be classified into three main categories.


1.3.1.1 Film Stress and Film Edge-Induced Stress

Surface films are widely used for masking, passivation, dielectric insulation, and

electrical conduction in IC processing. The materials commonly used for this purpose are

silicon nitride, poly crystalline silicon and silicon oxide. Stress is inherently present in

these films. While stress due to thermal expansion mismatch between the films and their







substrates is called extrinsic stress, stress caused by the film growth process is called

intrinsic stress [Hu91]. The extrinsic stress can be tensile or compressive, based on

thermal expansion coefficients. For example, SiO2 grown or deposited on silicon at high

temperatures will have a compressive component as a part of its total stress. There will

not be a shear stress component due to extrinsic stress.

Intrinsic stress in films is due to the growth mechanism of the material during the

process and depends on thickness, deposition rate, deposition temperature, ambient

pressure, method of film preparation and type of substrate used. A tensile stress in the

film bends the substrate that makes the substrate concave, while a compressive stress

makes the substrate convex. Measuring the amount of bending in the substrate is a

common way of finding intrinsic stress in films. Most of the films (poly Si, Si3N4) exhibit

tensile intrinsic stress. On the other hand silicides such as TiSi2, and CoSi2, sputtered

oxides, chemical vapor deposited oxides and ion implanted polycristalline silicon exhibit

compressive intrinsic stress.

Continuous films produce only very low level stresses in the substrate because the

substrate is thicker than the films. Problems occur when the surface films are not planar

or they contain discontinuities such as window edges for masking purposes. These

discontinuities are the source of the large localized stresses in silicon substrates. Stress

relaxation through the use of composite films can be quite profound (such as the SiO2-Si3

N4 pad). The pad oxide allows a greater relaxation of the Si3N4 stress because the oxide

pad itself is discontinuous and the oxide pad is less than half as rigid as the silicon

substrate. More importantly, the oxide is capable of undergoing viscoelastic deformation







[Hu91]. Film edge-induced stress effects on the generation of dislocation were reported

before [Iso85] and details of this subject are discussed later.


1.3.1.2 Stress from Oxidation and Device-Isolation Processes

Oxidation is one of the fundamental process steps of IC processing technology.

During the thermal oxidation of silicon, 1 volume of silicon is consumed to form 2.25

volumes of SiO2. In a planar oxidation, a newly formed oxide layer will push the old

oxide layer perpendicular to the interface and the normal stress component in the

direction perpendicular to the film plane becomes zero. The film stress becomes uniform

everywhere and does not cause a problem.

In the oxidation of nonplanar surface, the volume expansion resulting from

converting silicon to SiO2 cannot be accommodated by simple vertical thickness increase

as in planar oxidation. On a concave surface, the neighboring volume elements grow into

each other generating a compressive stress in the material. On a convex surface, the

lateral stress would become more tensile as the neighboring elements grow away from

each other.

Local oxidation of silicon (LOCOS) was the primary source of isolating devices

from each other for a long time. The LOCOS was one of the isolation techniques where

compressive and tensile stresses would build up during the oxidation. Trench isolation

techniques took the place of LOCOS in modem ICs to obtain high chip density. A major

problem with these trench structures is that they cause a significant amount of mechanical

stress in silicon substrate [Chi91]. The sources of trench-induced stress are that the

thermal oxidation of nonplanar surface of the trench can produce enormous stress, that a






mismatch of thermal expansion coefficients exists between the trench fill and silicon
substrate; and that intrinsic stress exists in the trench fill material [Hu90].

1.3.1.3 Dopant-Induced Stress
Different types of dopants are introduced into the silicon substrate during IC
processing. Every dopant species has a different size of atom. Lattice mismatch can occur
if the incorporation of highly concentrated solute dopant atoms differs in size from the
silicon atoms. While dopants such as Boron and Phosphorus cause lattice contraction,
Germanium in a substitutional site results in lattice expansion (i.e., the silicon substrate
lattice constant decrease or increase linearly with the size and concentration of dopant
atoms). This generates localized strain in the crystal because of each dopant atom and can
add up to significant strain values [Rue99]. Figure 1-7 represents the lattice deformation

2D Lattice
00000 0 0 0 00

00000 0 000 0
Ge
00000 0 0@ 00

00000 0 0 0 0 0

00000 00000


Figure 1-7. Two dimensional lattice deformation due to a dopant atom


in Si due to a substitutional germanium atom. Because germanium atom is larger than a
Si atom, germanium will induce a compressive strain in the substrate. It should be







obvious that dopants can be used to reduce the strain in the substrate but the idea of strain

compensation will work only if the compensating atomic species do not interact. It is

therefore not possible to use a donor and acceptor as a compensating species, because of

the probability of ionic bonding.

Dislocation loops are also a source of stress in silicon substrates because they

change the mechanical state of the substrate. Stress due to loops can be calculated using

the same techniques used to calculate dopant-induced stress. Details of this are discussed

in the next chapter.



1.4 Stress-Induced Dislocation Loops

As mentioned previously, stresses in silicon substrate build up at various stages of

IC processing. Many problems of defective devices can be traced to these stresses. If the

stress is high enough, such that it is beyond the yielding point of the substrate, the

substrate will yield by generating dislocation loops.

Dislocation loop generation at the nitride edge has been known for a while

[Tam81]. If a pad oxide is inserted between the nitride film and the substrate the density

of dislocation loops decreases due to stress reduction in the substrate (Section 1.3.1.1).

Although thicker pad oxide is more effective for edge stress reduction [Iso85], it makes

the nitride a less effective diffusion mask. The nitride edge also generates dislocations

indirectly. Excess self-interstitials generated by the oxidation or the ion implantation drift

to the nitride edge, and help nucleate dislocation loops there. Point defects interact with

the stress vectors [Hu91]. Hu's [Hu78] experiment showed the interaction between the

point defects and a nitride edge. Point defects generated by ion implantation formed







dislocation loops around the nitride edge. No dislocation loops were observed in the

regions masked out from the ion implantation.

Figure 1-8 shows a typical simplified cross-section of a modern n-channel MOS

transistor. First, Shallow Trench Isolation (STI) process is performed by growing a thin

oxide along the trench walls and by filling the trench with CVD oxide. Then, source and

drain regions are doped by high dose arsenic implant after the gate oxide is grown and the

polysilicon gate material is deposited. These steps are followed by an annealing cycle for

activating the source and drain region. During the annealing cycle, a layer of dislocation

loops is formed around the source/drain-to-substrate junctions. Stresses from the STI

process play an important role in the generation of dislocation loops [Fah92, Del96]. Hu

[Hu91] states that stresses from STI structures interacts with the point defects the same

way as the film-edge-induced stresses interact with them. Fahey, et al.. [Fah92] showed

that reducing the stress in the STI process would reduce the dislocation density and even

eliminate them. It is concluded that raising the temperature of the oxidation or changes in

Polvsilicon eate SiO2


Al


~Bse~D


loop layer


Antipunch implant

p-type substrate


Figure 1-8. Cross section of a modem day n type MOS transistor.


Al







the masking nitride thickness or using different fill materials with less intrinsic stresses

would reduce the amount of stress. Other researchers [Chi91, Sti93, Hu90] also provided

ways of calculating stresses from STI structure in the substrate and gave an insight to

how to reduce them, for example, corer rounding at the top and bottom of the trench

reduces stress.



1.5 Goals

As MOS devices are scaled down to the sub-micron regime, new reliability

problems surface in each generation. Many of these problems can be traced back to

stresses that develop at various stages of the IC processing. One of the most important

defects observed is the stress-induced-dislocation-loops. Dislocation loops have been

reported at various stages of IC processing. It has also been known that they degrade

device performance by increasing leakage current if they lie across the junction. Since

device dimensions are shrinking with every new technology, the probability of having

dislocation loops across the junction is increasing, and so is the leakage current. Stresses

from isolation trenches are also a major factor contributing to the dislocation loop

formation.

One of the goals of this research is to investigate and model the effects of process-

induced mechanical stresses on the dislocation loop formation. A model that can predict

the density and the location of dislocation as well as the mechanical stress effects on

them is a valuable asset for device and process engineers. Such a model would help them

to change and adjust their device structures and process conditions without having to

build costly test lots. Based on the understanding of point defects and extended defects

interaction, a physics-based loop evolution model is developed. Relevant physics and







assumptions behind the model are explained. Experimental verification of the model has

been performed. This model takes into account both the nucleation and the evolution of

the dislocation loops. These concepts and the model development will be explained in

detail in the subsequent chapters. Comparison between the experimental data and

simulation results shows that the model can correctly predict the experimental

observations. Although stress due to dislocation loops is accounted in the model, effects

of mechanical stress from the other sources are yet to be investigated.



1.6 Organization

The thesis organized as follows: Chapter 2 describes a model for the evolution of

dislocation loops during annealing in inert or oxidizing ambient. In Chapter 3, the model

is extended to account for the nucleation of dislocation loops. The model assumes that all

the dislocation loops come from {311 } unfaulting. The statistical nature of the model is

also used to predict threading dislocation loop density. Chapter 4 explains the

experimental procedure that was used to calibrate the loop nucleation and evolution.

Chapter 5 investigates the behavior of the model under different implant and annealing

conditions. Chapter 6 takes the model one more step ahead by incorporating stress effects

into the model. Finally, conclusions and suggestions for future work are discussed in

Chapter 7.












CHAPTER 2
MODELING THE EVOLUTION OF DISLOCATION LOOPS FOR VARIOUS
PROCESS CONDITIONS

High dose ion implantation is one of many steps used in process technologies

today. If the dose is high enough, it results in the formation of an amorphous layer of Si

and produces large amount of extended defects below the amorphous to crystalline (a/c)

interface. In order to activate dopants and repair the implantation damage, annealing is

required. Upon annealing, the amorphous region re-grows through solid phase epitaxy

(SPE) with end-of-range (EOR) dislocation loops formed at the (a/c) interface. The

effects of dislocation loops on device characteristics are explained in Chapter 1, Section

1.2.2.

During the last few years, a great deal of work has been carried out in order to

better describe the evolution of dislocation loops. The coarsening of EOR defects and the

effects of the surface on the EOR defects were investigated by Giles, et al. [Gil99]. The

growth and shrinkage of a single loop or a periodic array of loops due to the capture and

emission of point defects was modeled by Borucki [Bor92]. Analytic expressions were

derived by Dunham [Dun93] for the growth rate of the disk shaped extended defects that

maintain their thickness as they grow. In the models summarized above, it is not possible

to obtain the distribution of loops with respect to their radius. Park, et al. [Par94b]

developed a statistically based model for the growth of loops in oxidizing ambient where

the interstitials injected from the growing oxide contribute to the growth of the large

loops. Assuming an asymmetric triangular density distribution of periodically circular







dislocation loops, Park's model reflected the nonuniform morphology of the loops as

observed in transmission electron microscopy (TEM) experiments. The pressure field

from the dislocation loops is incorporated into the point defect equations. Chaudhry, et

al., [Cha'95] modified Park's model to represent loop-to-loop interactions. This loop to

loop interactions can be described by the Ostwald ripening process during annealing. In

the Ostwald ripening process, the total number of interstitials bounded to dislocation

loops remains fairly constant with time while density of dislocation loops decreases (i.e.

Bigger loops grow at the expense of smaller ones) They correctly simulated the variation

and size distribution of the loops as a function of anneal time and temperature. However,

both of these models made different assumptions to model the growth and coarsening of

dislocation loops under oxidizing and inert-ambient annealing conditions. In this chapter,

a new statistical point defect based loop evolution model will be shown. The model

quantitatively analyses the size and density of dislocation loops as a function of annealing

time, temperature and conditions. It uses the same set of parameters to capture the loop

behavior under oxidizing or inert annealing conditions.



2.1 Modeling Dislocation Loop Evolution

In order to model the evolution of dislocation loops accurately and efficiently,

some assumptions need to be made. It is assumed that dislocation loop density and

average radius of loops follow a log normal distribution function. Therefore, a single set

of differential equations with the same set of parameters has been used to model the

dislocation loop evolution under both oxidizing and inert ambients. It is also assumed that

pressure from loops can be calculated using dopant-induced-stress techniques described

earlier.








2.1.1 Log Normal Distribution Function

It is known through the transmission electron microscopy (TEM) analysis that

dislocation loops do not show a uniform radius and density distribution. Thus, a model

that encapsulates the distribution of the loop sizes via a statistical function is needed.

Park, et al. [Par94b], used an asymmetric triangular distribution in the differential

equations used in their model. However, the asymmetric triangular distribution function

is not a continuous function. Therefore, the discontinuities in the function


8 109

7109

6 109

5 109

4 109

3 109

2 109

1 109

0


M V %n 0 [1- Q Q t1
'O)OO N O nN
R N N Ni No N N en e en

R(A)


Figure 2-1. Log normal density distribution function applied to the statistical distribution
of loop radius extracted from the TEM measurements [Men93] under 900 C
dry oxidation condition.



would render the derivative impossible to calculate in numerical process simulators like

FLOOPS, unless some special care is taken to circumvent the singularity conditions. In

this work, a log normal distribution function will be used to quantify the distribution of







the loop size because it is a continuous function and matches the TEM data. The log

normal distribution function is a function in which the logarithm of variables has a

normal distribution. The log normal probability density function, f,(R), is given as

f,(R)= D e-(InR-M)'I(2S') (2.1)
SR\-ir

where D,,1 (cm-3) is the total density of dislocation loops, R (cm) is the loop radius. S

and M are the deviation and the mean of the log normal distribution. S and M can be

derived from the Gaussian parameters, mean (p) and standard deviation (o) as follows

u = eM+S2 1 a2 =eS2 +2M (e -1) (2.2)

Figure 2-1 shows the statistical distribution of loops radius extracted from the TEM

measurements [Men93] under 900 C dry oxidation condition along with the log normal

density distribution function. The Log normal distribution function follows the

experimental results quite closely.


2.1.2 Density of Dislocation Loops

Dislocation loops are two-dimensional precipitates inserted between two

consecutive {111 } planes. The loop distribution can be modeled in the form of log

normal distribution function. The model assumes that all the loops are circular and their

radius and density follow a log normal distribution function. It is also assumed that

dislocation loops go through two phases during the thermal annealing cycle. First,

{311) 's nucleate and unfault to dislocation loops by consuming a large part of the

interstitials. Subsequently, Ostwald ripening process dominates. As explained above, in

the Ostwald ripening process, the total number of interstitials bounded to dislocation

loops remains fairly constant with time while density of dislocation loops decreases (i.e.







Bigger loops grow at the expense of smaller ones). In this section, only the evolution of

the dislocation loops during the thermal annealing cycle will be considered. The

nucleation of dislocation loops phase will be discussed in the next chapter.

Since dislocation loops lie on { 111} plane and are circular with a radius of R, the

number of interstitials bounded to these dislocation loops can be easily calculated as

N11n(R) = Dau(R)n7rR2 (2.3)

where D0,,(R) is the density of dislocation loops with a radius of R and n. (1.5xl015

cm-2) is the atomic density of silicon atoms on the { 11 } plane. Na,,(R) represents the

total number of interstitials bounded by these dislocation loops. Time derivative of the

Equation (2.3) will give the change in the density of dislocation loops with time.

dDau(R) 1 dN,,(R) 2D,,(R) dR
(2.4)
dt trR2n, dt R dt

The first term represents the nucleation rate of dislocation loops ND1. R, is assumed to

be the initial radius of the nucleated loop. The second term represents the Ostwald

ripening process. Bonafos, et al. [Bon98], worked extensively on the Ostwald ripening of

end of range defects in silicon and calculated the growth rate (dRIdt) of dislocation

loops as follows

dR=K (2.5)
dt R

The constant, K,, is the coarsening rate of dislocation loops and used as a fitting

parameter in the simulations. If Equation (2.5) is substituted in Equation (2.4), the change

in the density of dislocation loops with time becomes

dD, (R) NZ 2D(R) (2.6)
dt R2







As it can be seen from Equation (2.6), the density of dislocation loops with smaller radii.

decreases faster than those with larger radii. Thus, smaller loops dissolve faster by

emitting interstitials. These interstitials are absorbed by the bigger loops. Hence, bigger

loops grow at the expense of smaller ones. Physically, this means that it is energetically

more favorable for a larger loop to increase in size and a smaller loop to dissolve.


2.1.4 Coarsening and Dissolution of the Dislocation Loops

Dislocation loops grow in size and reduce their density at annealing temperatures

below 900 C. This regime is referred to as the "coarsening" regime. If the annealing

temperature is over 900 oC, dislocation loops becomes thermally unstable and start

dissolving by releasing interstitials. The growth rate of dislocation loops is higher under

oxidizing conditions than under inert conditions, since oxidation injects interstitials to the

bulk.

The interaction between the loops and point defects is primarily reflected on the

equilibrium concentration of point defects around the dislocation loop layer and the

pressure dependent concentrations of interstitials and vacancies are calculated as [Bor92]

C;(P)= C;(0)exp(-P ) (2.7)
kT

Cv(P) = C(0)exp( ) (2.8)
kT

where P is the pressure, AV, and AVv are the elastic volume expansions susceptible to

the external pressure effect on interstitial and vacancy, k and T are the Boltzman's

constant and absolute temperature respectively. "0" denotes the equilibrium

concentration in the absence of external pressure. If the lattice is under compressive

pressure the equilibrium interstitial concentration will be less than its nominal value








C; (0). If the lattice is under tensile pressure, then, the equilibrium concentration of

interstitials will be greater than its nominal value.

The pressure in the substrate due to dislocation loops can be calculated using dopant-

induced stress-calculation techniques (Section 1.3.1.3). The silicon lattice constant will

vary as a function of interstitials bounded by dislocation loops.


r4
u

-o

U,
C)
I-
0l


1.4 10

1.2 109

1 109

8 108

6108

4108

2108

0

-2 108


0 0.1 0.2 0.3
Depth (p)

Figure 2-2. Pressure in silicon due to the dislocation loops.


0.4


-0.015A of lattice expansion per percentage of interstitials bounded by dislocation loops

in Si is obtained from simulation results. Using this figure, the strain is calculated as

follows [Rue99]


Aa -0.015 N,1,,
e = ea, = =E 100
S e asi as, Ns,


(2.9)







where Aa is the change in the silicon lattice constant (a, =5.4295A) and Ns, is the

density of Si atoms (5.02x1022cm-3). After using the stress-strain relations described in

Chapter 1, Section 1.3, the pressure is easily calculated.

1
P =- (, + + a,) (2.10)

Figure 2-2 shows the simulated pressure in the substrate due to a dislocation loop layer

located at a depth of 1500A. The pressure peaks at the dislocation loop layer and

decreases rapidly away from it. The pressure is compressive inside the dislocation loops.

The absence of tensile pressure at the edge of the dislocation loop layer is due to the

dopant-induced stress calculation technique. Since the pressure is a linear function of the

interstitial concentration inside the loops and the concentration never goes to a negative

value, the tensile pressure due to loops is not calculated. The magnitude of the tensile

pressure at the loop edge is always a few times less than the magnitude of the

compressive pressure inside the loop and can therefore be neglected.

Growth and shrinkage of dislocation loops are determined by their interaction

with point defects at the loop boundaries. The effective equilibrium concentration of

interstitials (Cl,) and vacancies ( C,) at the loop boundaries are given by Borucki

[Bor92] as

-AE
C, = gC (P)exp( ') (2.11)
kT

C = g.'Cv(P)exp(--) (2.12)
where g is a geometric factor (0.7). A is the change in the defect formation energy
where g,, is a geometric factor (a0.7). AE, is the change in the defect formation energy







due to the self-force of a dislocation loop during the emission and absorption process at

its edge and is given by Gavazza, et al. [Gav76], as

_-bG 8R 2v-1
AE__= I ) 8 -I (2.13)
4r(1 -v)RI r 4v-4

where p is the shear modulus, b is the magnitude of the Burgers vector of the loop, Q is

the atomic volume of silicon, r, is the core radius of the loop, v is the Poisson's ratio,

and R is the radius of the dislocation loop.

The model based on the log normal distribution represents the loop distribution

change in agreement with the experimental observations as seen in Figure 2-1. The

capture and emission rate of interstitials by the dislocation loops can be expressed in

terms of the rates of emission and absorption of point defects at the loop layer boundaries

modulated by a log normal distribution function. The rate also depends on the unfaulting

rate of {311} 's during the nucleation phase (NN') and can be expressed as




at = NNG + K, (C, C,,)f (R)dR- K,, (C, C,)fD(R)R (2.14)
dt 0. 0. at loop layer
boundaries



where KIL is the constant of a reaction between the interstitials and the dislocation loop

assemble, KVL is a similar constant for vacancies. KIL and KvL are the function of the

loop radius and the diffusivity of interstitials and vacancies respectively. They are used as

calibration parameters during the simulations. C, and C, are the concentration of

interstitials and vacancies. Details of the unfaulting term, Na, will be discussed in the

next chapter. It is apparent that if the concentration of interstitials at the loop boundaries







is greater than the effective equilibrium concentration of interstitials at the loop

boundaries, loops will absorb interstitials. If the reverse is true, then, the loops will emit

interstitials. Modulating the emission and absorption rate by a log normal distribution

function allows us to include the effects of all dislocation loops in the loop layer. Total

number of interstitials bounded by all the loops in the loop layer is given as


N,, = nrR2DhlffD(R)dR (2.15)
0.

N. = Da.,,.e 2S' +2H (2.16)

Since the experiments for the evolution of loops usually focuses on the average

radius of the loop distribution, the loop radius R in Equation (2.6) and (2.14) can be

substituted with an average loop radius R,. If the normal distribution mean (pg) is

assumed to be the average radius (R,) of the loop distribution, log-normal-deviation (S)

and log-normal-mean (M) can be written by combining Equations (2.2) and (2.16)

S= ln(l+(e )2)/2 (2.17)
RP


M=ln( Nal )12 S2 (2.18)


The relation between a and R can be extracted statistically from various TEM data

[Par93, Cha95, Ram98] as an analytic function of Rp (cm) as follows

r =0.33+5xl04RP (2.19)
RP

Since the concentrations of interstitials and vacancies around the loop layer are

affected (Equation (2.14)), the interstitial and vacancy continuity equation needs to be







modified by adding a new flux due to the local variation of the interaction energy as in

Borucki [Bor92].

S=V DIC,(P)v( C- ]-K (CC, C (P)C;(P))- KIL r lb)D(R)dR (2.20)

at loop layer boundaries

dC V VD,,C'C,(P)V( ,1 KR(CIC, -C;(P)C;(P))- K (C, Cb)D(R)dR (2.21)
1t C--P) 0. (2.21)
at loop layer boundaries

KR is the bulk combination rate. The reaction rate now includes the pressure term, as

well. The flux due to loop to interstitial/vacancy interaction is the same as the ones in

Equation (2.14).

Similarly, (311) equations must be modified by adding nucleation terms.

C311 D (C C31\IEq) ?iaUl
ca D=-c Nte (2.22)
dt T3 at

311 -D311C311Eq D311 (2.23)
= -D"I-- NDe (2.23)
dt 311 C311 rate

C3,IEq is the equilibrium concentrations of {311)'s. r3,, is the {311} time constant.



2.2 Experimental and Simulation Results to Calibrate the Model

The model for the evolution of dislocation loops is implemented in FLOOPS.

Equation (2.6) is slightly modified as follows:

dD 1 2D011
dD = N al -2DK (2.24)
dt rae (C, / Cb +10) R,

The term (1/(C, / Cb +10)) allows the Ostwald ripening term to be small during the

nucleation phase (i.e. (C, / Cb) >> 10) and is arbitrarily chosen. Its function will be clear

in the next chapter. Since we are only interested in the evolution of dislocation loops for








now, N,f and NNa are set to zero. Oxidation experiments followed by inert ambient

annealing experiments are used to calibrate the model.


2.2.1 Simulation of the Evolution of Loops during Oxidation

Meng, et al. [Men93], investigated the interaction between oxidation induced

point defects and dislocation loops. First, they implanted silicon wafers with Si' ions at


Oxidation 9000C


Data 2e 15cm
Data 5el 5cm2
Simulation 2e 5cm2
Simulation 5el5cm2


S I I
U


I I I I I I I


o


Z
'9
z


0
0
0



s
-c
a


c41

1-D

0

I-


Time (h)


Figure 2-3.


Density of the interstitials bounded by dislocation loops as a function of
oxidation time and simulation in the two different cases of Si implant dose,
2x1015 and 5x10I cm-2.


-e-
0


I I I


2 3 4


1.6 1015


1.4 1015



1.2 105


10'15
1 1015






61014



41014


, I I


I I I I








50 keV and varied the implant doses from 2x10'5 cm-2 to 5x1015 cm-2. Then, they

annealed their samples at 900 oC for times between 30 minutes and 4 hours in a dry

oxygen ambient in a furnace.The average loop radius, loop density and total number of

interstitials bounded by the loops were measured. These experimental values are used to

calibrate the loop evolution model developed in this work.

Figure 2-3 shows the simulation results and experimental data on the temporal


3.5 1010


3 1010


2.5 10'0


2 1010


1.5 1010


1 101


5 109


Oxidation 9000C


SData 2e15cm 2
SData 5e 15cm2
O Simulation 2e 15cm2
Simulation 5e 15cm2



-
-


1- 1 -

I I i I t l I i l ~ t i -


Time (h)


Figure 2-4. Variation of total density of dislocation loops with time and simulation
results for two different implant conditions.








change in the number of interstitials bounded by dislocation loops per unit area during the

oxidation at 900 C for two different cases of Si implant doses (2x l0 'cm2 and

5xl0'5cm-2). As can be inferred from the figure, both the simulations and experiment

suggest that the dislocation loops capture interstitials injected into the bulk during

oxidation.

The variation of the dislocation loop density with time for two different implant


Oxidation 9000C


* Data 2e 15cmr
-2
* Data 5e 15cm2
O Simulation 2e 15cm"
E3 Simulation 5el5cm2


I I I I I i i i i I


*


II I I I I I


Time (h)


Figure 2-5. The average radius change with time during oxidation and corresponding
simulation results


700



600


v
es_
0.

Oi

0
0
hl
U

e!L


500



400



300


200



100


""""""'~~"'''''"







doses is shown in Figure 2-4. It can be seen that the loop density decreases with time.

Although simulation results and experimental data is in good agreement at short

annealing times, there are some discrepancies at longer annealing times. Non-uniformity

of loop size and shape can be seen at longer annealing times due to the formation of loop

networks (i.e. noncircular loops). Statistical interpretation of TEM pictures becomes

more complex. Since the model is derived assuming that all the loops are circular, the

accuracy of the model will decrease with increasing density of the noncircular loops at





Annealing in Inert Ambient

a14 Data 7000C O Simulation 7000C
2 8 10 -
Z Data 800C E Simulation 8000C
o Data 900C Simulation 9000C
S 1014 Data 1000C Simulation 10000C
610 -
-


0 014



O 2 014'




S0 200 400 600 800 1000
Time (minutes)


Figure 2-6. Variation in total number of interstitials bounded by the loops as a function
of anneal time at different temperatures.








the longer annealing times. The data point not shown at 900 OC, 4 hours corresponds to

this case.

The average radius of dislocation loops during the oxidation increases with time

as shown in Figure 2-5 Since the data show very little difference in the initial value of

the average loop radius between the two silicon implant conditions, simulation and data

show that the loop size will increase at almost the same rate during oxidation. Some





Annealing in Inert Ambient


Data 700C
Data 8000C
Data 9000C
Data 10000C


0 Simulation 7000C
E3 Simulation 800C
< Simulation 9000C
- Simulation 10000C


0-
- -


I -


200


400 600

Time (minutes)


800


1000


Figure 2-7. Variation in total loop density as a function of anneal time at different
temperatures.


10"

10"

10"

10"


410"

3 10"


10"

10"


I I I I







discrepancy between data and the simulation results are evident at the larger annealing

times due to the non-circularity of the dislocation loops as explained above.



2.2.2 Simulation of Loop Evolution during Annealing in Inert Ambient

A plan view TEM study of the distribution, geometry and time dependent anneal

behavior of the dislocation loops induced by lxl015 cm-2, 50 keV Si implantation into

silicon was presented by [Liu95]. After implantation, they capped their samples with

6000 A SiO2 to limit the oxidation in inert ambient. Then, samples are annealed in

nitrogen at 700, 800, 900 and 1000 oC for times of 15 minutes, 30 minutes, 1 hours, 2

hours, 4 hours and 16 hours at each temperature. Their experimental results seen in the

figures are used to calibrate the loop evolution model under inert annealing conditions.

Figure 2-6 represents the change in total number of interstitials (N,,,) bounded by

dislocation loops. Simulation results are plotted along with the experimental values. It is

seen that N,, is fairly constant below the 900 C annealing temperature. If the annealing

temperatures increases above 900 C, loops start dissolving. Simulation results are within

20% error margins of the measured data.

Variation in total loop density with time at different annealing times and

temperatures is shown in Figure 2-7. The loop density decreases with time. If the time is

kept constant, it decreases as the temperature increases. This is the result of the loop

coarsening process, during which the large loops grow at the expense of smaller ones

(Ostwald ripening). At higher annealing temperatures loops enter the dissolution regime.

Figure 2-8 shows the simulations that agree with the experimental observation

that the average loop radius increases with time upon annealing in an inert ambient. As







seen from the experimental data and simulations, the growth rate of the loops is

proportional to the annealing temperature. The average loop radius increases with the

annealing time. The increase is very small at the low temperatures but it is higher for

higher annealing temperatures.





Annealing in Inert Ambient
500 i
Data 7000C Simulation 7000C
Data 8000C E Simulation 8000C
400 Data 9000C Simulation 9000C
SData 10000C Simulation 10000C


300

O
0
200
--



100



0
0 200 400 600 800 1000

Time (minutes)

Figure 2-8. Experimental and simulated average loop radius as a function of annealing
time at different temperatures.








2.3 Experimental and Simulation Results to Verify the Model

After calibrating the loop model with the same fitting parameters for oxidation

and inert anneal data, the model is verified by comparing simulation results with others

researchers data [Lan97, Ram98].


Inert Ambient Annealing at 9000C


5 1014



4.5 1014



41014



3.5 1014



3 1014


2.5 10'4



2 1014


>-i
z

0
o


o
o





-c
.o



a
(i
< .






[--
0

E:


40 60 80 100 120 140

Time (minutes)


Figure 2-9. Simulation and experimental results for the loss of interstitials with time at
900 oC.



2.3.1 Simulation of Loop Dissolution as a Function of Loop Depth

Raman [Ram99] investigated the effect of surface proximity on the dissolution of

end of range dislocation (EOR) loops in silicon. First, they implanted Si+ into silicon at


0 20





43


30 keV and 120 keV and a dose of xl105 cm-2 to produce EOR dislocation loops. The

initial loop depth was 2600 A following a 30 minutes furnace anneal at 850 C. Second,

chemical mechanical polishing (CMP) technique was used to vary to loop depth to 1800


Inert Ambient Annealing at 10000C


5 1014

4.5 104

41014

3.5 1014

3 1014

2.5 1014

210'4
1.5 104
1.5 1014


E

z
M.
0



0
Vc



m
a
O







0




I


30 35


Figure 2-10. Simulation and experimental results for the loss of interstitials with time at
1000 OC.



A and 1000 A. Third, samples are annealed in an inert ambient at 900 OC for 30 minutes

and 120 minutes and at 1000 C for 15 minutes and 30 minutes. Loops are expected to be

in coarsening/dissolution mode at 900 C and in dissolution mode at 1000 C. Their

experimental results are used to verify the accuracy of the model.


0 5 10 15 20

Time (minutes)







Figure 2-9 shows the loss of interstitials bounded by dislocation loops as a

function of annealing time for the three different loop depths. As the loop layer gets

closer to the surface the rate of loss of interstitials from the dislocation loops increases

due to surface recombination. The data shows that fewer interstitials are lost after the

initial 30 minute anneal. Although there are some discrepancies between the data and the

simulation results, simulations predicts the same trends seen in the data.

Similar behaviors can be observed for the 1000 OC anneal (Figure 2-10 ). In this

case, the rate of loss of interstitials decreases after the initial 15 minutes of anneal time.

Simulation agrees with these results.


2.3.2 Effects of Dislocation Loops on Boron Diffusion

This model is used to study the effects of dislocation loops on boron diffusion, as

well. Simulation results will also verify that dislocation loops are very effective at

capturing interstitials. Experimental details are explained in [Lan97] and can be

summarized as follows: Boron doping superlattices (DSLs) were grown in silicon. A

series of Sii implants of 30 and 112 keV at a dose of lxl105 cm"2 was carried out to place

the amorphous to crystalline interface between the first and second doping spikes. The

dose rates of implants are varied. Post implantation anneals were done in a rapid thermal

annealing furnace at 800 C for 5 seconds and 3 minutes. It is shown that the implantation

dose rate affects the interstitial release from EOR implant damage region in silicon (e.g.

loop density changes). Therefore, the diffusion enhancement of boron changes. Figure 2-

11 is from [Lan97] and shows the secondary ion mass spectrometry (SIMS) profiles of

boron spikes after Si+ implantation at different dose rates and annealing at 800 C for 3







minutes. As the dose rate increases (loop density changes), the amount of interstitial flux

into the regrown region increases, as well.

The simulation results of boron profiles, annealed at 800 C for 3 minutes, with

two different loop densities are shown in Figure 2-12 along with the as grown profile. It





19 Inert Ambient Annealing at 8000C Boron (0.13mA cm 2)
10 I ', '" '" ......... Boron(0.3mA cm 2)
Boron (As Grown)



E 10s8

o J

pI i
o 17 J \.
u 10





1016
0 1000 2000 3000 4000 5000 6000 7000 8000
Depth (A)


Figure 2-11. SIMS profiles of DSL after Si' implantation at different dose rates and
annealing at 800 C for 3 minutes.


is assumed that EOR point defect profile does not change. Since the implantation

generated {311 }'s as well as dislocation loops at the EOR region in this experiment,

{311 }'s were simply modeled by an exponential decay in this simulation. Simulations





46


correctly predict the diffusion enhancement in both below and above the amorphous-

crystalline interface. The change in the diffusion enhancement rate of the first peak due to

dose rate change is not as significant as the experimental data. This might be due to the

fact that {311 } model used is very simple and EOR damage profile is arbitrarily chosen.


Inert Ambient Annealing at 8000C
10 9 I I I1 1 Il l II I


E
.-.
u

U


U
C
r-
0

0
I-
U
WQ


l018
10'1






10"


1016


0 1000 2000 3000 4000 5000 6000 7000 8000

Depth (A)


Figure 2-12. Boron profiles with two different loop density and no loop layer, annealed
at 800 C for 3 minutes.



It is also assumed that there is no interaction between loops and {311 }'s in the model.

Figure 2-12 also shows a simulation profile with no loop layer. In this case {311} defects

and excess interstitials below amorphous to crystalline interface exist but there are no
i







loops. The diffusivity enhancement of all boron spikes increases dramatically. It is very

clear that dislocation loops are efficient sinks for interstitials.


2.4 Summary

A single statistical point defect based model for the evolution of dislocation loops

during oxidation and annealing under an inert ambient is developed. The model assumes

that the radius and the density of dislocation loops follow a log normal distribution. Each

set of data is characterized by its average radius (R,), its density (Da,,) and total number

of interstitials bounded by the dislocation loops (Na,,). The developed model correctly

predicts R,, Dou, and N.u. It also agrees with the depth dependence of the data. Its

effects on the dopant diffusion are very clear.

So far, a model that predicts the evolution of the dislocation loops has been

explained. However, the nucleation of these loops also has to be modeled and then

coupled to the loop evolution model in order to have a single complete dislocation loop

model. Such a nucleation model has been developed and will be explained in detail in

Chapter 3.












CHAPTER 3
MODELLING THE NUCLEATION AND EVOLUTION OF THREADING
DISLOCATION LOOPS

As the technology progresses towards the smaller junction depths (i.e. less than

100 nm) for smaller device sizes, predictive simulations of dopant diffusion after ion

implantation and thermal annealing are essential. This would only be possible if the

amplitude, the depth, the temperature and the time dependencies of the extended defects

({311 }'s, dislocation loops, etc.,) were known and implemented into the existing

software. The evolution of these defects in various implant and annealing conditions has

been investigated and summarized in Chapter 2. There have been some recent studies on

the nucleation, growth and dissolution of extended defects [Cla99]. Plekhanov, et al.

[Ple98], modeled the nucleation and growth of voids and vacancy-type dislocation loops

under Si vacancy supersaturation condition during the Si crystal growth. They suggested

that similar approaches could be used to model the nucleation of interstitial-type

dislocation loops. Lampin, et al. [Lam99a] modeled the nucleation and growth of end of

range (EOR) dislocation loops. Their model had three distinct stages, the nucleation, the

pure growth and the Ostwald ripening. During the nucleation stage, a large part of the

interstitials, which were located beneath the amorphous to crystalline (a/c) interface

following an amorphizing implant, is consumed while the others begin to diffuse

following their gradients. The nucleation stage is followed by a pure growth stage.

During this stage, the density of dislocation loops remains unchanged but their size

increases with time while the remaining free interstitials concentration decreases. For







longer annealing times, the Ostwald ripening stage is reached. The total number of

interstitials bounded by dislocation loops remains constant with time while density of

them decreases. Their model is also used to study anomalous diffusion of boron

[Lam99b, LamOO]. But, they used different set of differential equations at each stage and

it is not very clear when to switch from one set of differential equation to another one

during the simulation. Their initial concentration of interstitials after the implantation

below the a/c interface are derived from the Monte Carlo simulations of Hobler, et al.

[Hob88]. The model also does not take into account interstitial cluster formations and the

interaction between the {311 }'s and dislocation loops.

In this chapter, a new loop nucleation model will be introduced and the simulation

results and experimental data will be compared. The model takes into account the

interaction between {311 }'s and dislocation loops. It also uses a set of differential

equations to describe the loop behavior through the all stages of nucleation and evolution

of the dislocation loops. It is possible to obtain statistical distribution of dislocation from

the simulation results, as well.

There will be some major differences between the model developed in Chapter 2

and the model developed in this chapter in terms of the loop layer definition. In Chapter

2, it is assumed that dislocation loops are confined into a single layer and this single layer

represents all the dislocation loops in the silicon substrate for the simplicity. This

assumption showed that the corresponding differential equations correctly model the loop

evolution during various annealing conditions. In this chapter, loops will be spread over

the damage region (i.e. Loop layer will be a function of {311} defect concentration)

giving more physical meaning to the simulation results.







3.1 Modeling Dislocation Loop Nucleation

As a result of ion implantation, large amount of excess interstitials is created

around the projected range of the implant or below the a/c interface depending on the

implant species and implant dose. Upon annealing, defects such as {311 }'s or dislocation


I+I ~IC12

SMICS

V + V< V2


Dissolve


Unfault to Loop and
evolve


Figure 3-1. Schematic representation of dislocation loop nucleation


UT-MARLOWE
Damage Profile







loops form where the excess interstitial concentration is high. The developed loop

nucleation model assumes that these excess interstitials are the source of the defects.

Figure 3-1 schematically explains the loop nucleation model. First, UT-MARLOWE, a

Monte Carlo simulation program, is used to calculate the damage created in silicon

substrate due to ion implantation. The damage profile and the implanted ion distribution

are utilized to generate excess interstitial profiles. The excess vacancy profile is also

obtained from UT-MARLOWE damage profiles. Second, interstitial and vacancy clusters

such as di-interstitials (12) di-vacancies (V2) and sub microscopic interstitial clusters

(SMICS) are created upon annealing. Third, {311} defects are nucleated from SMICS

[LawOO]. During this nucleation, large amount of excess interstitials is consumed. Some

of these nucleated become thermally unstable and unfault to dislocation loops and

become the source of dislocation loops [Li98]. Then, while the remaining start

dissolving, dislocation loops start evolving. In the developed loop nucleation model,

unfaulting process is called the nucleation stage of the dislocation loops and the evolution

of the loops is called the Ostwald ripening stage.

In Chapter 2, Section 2.1, it is shown that total number of interstitials bounded by

loops can be expressed as

dNa = Na + K, (C, C)f(R)dR KV f(C, C)fo(R)dR (3.1)
dt at loop layer
boundaries

where NNf' is defined to be nucleation rate of dislocation loops. When a {311) defect

unfaults to a dislocation loop, the number of interstitials bounded by that {311} is

transferred to the unfaulted loop. This can be shown as

Nr = KWC,, (3.2)








where K3,, is the unfaulting rate of to loops and C31, is the concentration of interstitials

trapped by A similar expression can be derived for the density of dislocation loops. It is

previously shown that D,, is given by

dDaI NDa 2Dal K (3.3)
dt -"T' (C,/Cb + 10) Rp

and N,', term is


NrD = 1 dN.u
raRe Rn dt


(3.4)


Nucleation Rate vs time


1 108



8107


E
0

o
a

Z


6107



4107


210'


5 10 15


Time (minutes)


Figure 3-2. Nucleation rate NSj' change with time







Since, only the first term of the Equation (3.1) is related to the loop nucleation, Equation

(3.4) becomes


N rate = K31 C311
N" K3,,CrR
r rR,2n,


(3.5)


where


SC311


(3.6)


D3,, is the density of {311 defects. If the Equation (3.6) is substituted in Equation (3.5),


Figure 3-3. TEM picture of dislocation loops and threading dislocation loops



the nucleation rate of dislocation loops can simply be written as


NZu = K, D311


(3.7)







In the simulations, K3, parameter is used as a fitting parameter to calibrate the

simulations. Figure 3-2 shows the change in the nucleation rate (N, ,) with time. The

rate is very high at the short time when the excess interstitial concentration is high and

{311 }'s are still nucleating. The nucleation rate diminishes as the time progresses.

It is known that the excess interstitial concentration will be high during the

nucleation stage due to the damage introduced by ion implantation. Nucleation of loops

will be energetically favorable as long as there exists a large super saturation of

interstitials. Until interstitial supersaturation is decreased, the Ostwald ripening does not

1
occur. At this stage loops are fairly small. Since Equation (3.3) has a -2 dependency, the
Rp

Ostwald ripening term will be dominant at this stage. In order to suppress the Ostwald

ripening term in Equation (3.3), 1/(C, I C, +10) term is incorporated into the equation.

The term is arbitrarily chosen. C, / Cb will be much higher than 10 during the nucleation

stage and will reach nominal values once the nucleation of {311 }'s and dislocation loops

is complete, allowing the Ostwald ripening process to dominate.




3.2 Modeling Threading Dislocation Loop Nucleation

High energy (i.e. MeV) non-amorphizing implants are commonly used to form

retrograde wells for CMOS latch-up immunity improvement and buried layers for bipolar

transistor subcollectors [Bou99]. However, heavy lattice damage can be generated near

the projected range of the implanted dopant as discussed before. One type of defect

associated with the high energy ion implants is the threading dislocation loops (TDLs).

The threading dislocation loops are long dislocation dipoles generated in the region of the






ion projected range which grow up to the surface [Che96, Jas99]. Figure 3-3 shows a

TEM picture of dislocation loops and TDLs.

If the distribution of loops with respect to their radius is known, it is possible to

obtain TDL information from this distribution. Figure 3-4 shows how to obtain TDL


Surface


Node 1


Node 2


XI
X1


K


Node 3


R


Rc > x, TDL


Figure 3-4. Schematic representation of TDLs in a distribution function


density from a distribution function. In the process simulators, physical shape of the

device is modeled using meshes. Every mesh is composed of nodes that hold the physical

data as shown in Figure 3-3 The developed loop nucleation model assumes that loop

density and radius follow the log normal distribution function and each node represents a

different distribution function. Dislocation loops whose radii are greater than their depth


.* S
Rci





Rc2




PR3


X2


1 ,


X3


1 ,


f-L







from the surface are considered as TDLs. In Figure 3-4, Rc, RK2, and Rc3 represent the

critical radii to be considered as a TDL at each loop depth (i.e. if R > x, loop is a TDL).

The total density of threading dislocation loops can simply be calculated by integrating

each distribution function from the critical radius to infinity (shaded areas in Figure 3-3 )

and adding them. The integration is given by

D ln(R,)- M
D"DL = Al( -erf( )) (3.8)
2 -rS

where DDL is the threading dislocation loop density and Re is the critical radius. The

threading dislocation loops are long dipoles and simulations assume all loops are circular.

In order to compensate the difference in the simulations, Re is taken to be 0.3x where x

is the loop depth from the surface.


3.2.1 Simulation of the Nucleation and Evolution of Threading Dislocation Loops

The formation of TDLs as a function of implant condition is studied in boron

implanted silicon by Jasper, et al. [JonOO], for various implant doses (1xl013 to 5x10'4

cm-2). The implant energy is also varied from 180 keV up to 3 MeV in 500 keV steps.

The major post implant thermal treatments include an oxidation step at 800 C for 20

minutes and an inert ambient annealing at 800 C for 70 minutes. In the simulations,

1.5MeV boron implant data was used to calibrate the simulation since the data included

more information such as defect density and defect size than the data for other implant

energies.

In order to simulate loop nucleation, damage profiles are generated for each

implant dose using UT-MARLOWE. Figure 3-5 shows the excess interstitial








concentration in the silicon substrate for a 1.5 MeV boron implant at a dose of lx 10' cm

2. The profile represents that all the excess interstitials are generated near the projected


E
U




4-c




0
a)
0
U


U
(L


1018

10'8


1016


104


1013


1012


2 2.2 2.4 2.6 2.8 3

Depth (i)


Figure 3-5. Initial excess interstitial concentration after an implantation of boron with a
dose of lxl014 cm-2 and an energy of 1.5 MeV.



range (=2.3 pm). It is composed of the interstitial part of the damage profile obtained

from UT-MARLOWE. Excess vacancy profile is also obtained in a similar way.

The excess interstitial and vacancy profiles provide the basis for the nucleation of

interstitials clusters (12, SMICS) and vacancy clusters (V2), eventually leading to the

nucleation of {311 }'s and the dislocation loops. Figure 3-6 shows the simulation results








of the changes in the defect densities with time after a 1.5 MeV boron implantation with a

dose of lx1014 cm-2. First 20 minutes of the simulation is an 800 C oxidation run, the

remaining 70 minutes is an inert ambient annealing run at the same temperature. As seen

in the figure, density of {311} 's, D3,,, increases very rapidly at short times then it starts


1015


E





O
-s

0






0
U-
0


a




'U
I-



a

U


1013


1012


10"


1010


109


108


107


0 20 40 60 80

Time (min)


Figure 3-6. Changes in defect densities with time after implantation of boron with a dose
of lxl014 cm"2 and an energy of 1.5 MeV.



decreasing. Total number ofinterstitials trapped by {311 }'s, C311, follow the same trends.

The nucleation of dislocation loops is slower than the nucleation of {31 1}'s since the







loops nucleate from unfaulted {311 }'s Total number of interstitials bounded by

dislocation loops, N,,,, increases very rapidly at short times and continues to increase

while dissolve. This shows that dislocation loops capture some of the interstitials released

by {311 }'s. Once the excess interstitials are consumed by loops and some of these excess

interstitials diffuse away from the damage region, loops go into Ostwald ripening

process. No significant change can be seen in Nt, for longer annealing times. Ostwald

ripening process can be seen in the density of dislocation loops (D.,,) profile as well. D,,t

increases very fast at the short times when the nucleation rate is high. When the

nucleation rate slows down, Da,, stay almost constant due to the fact that excess

interstitial concentration is still high. Thus, dislocation loops follow a pure growth

process during this time period. As soon as the excess interstitial concentration drops,

Ostwald ripening term in Equation (3.3) becomes dominant and D,, starts decreasing.

Meanwhile, Ne,, stays constant. Thus, the bigger loops grow at the expense of small ones.

Figure 3-7 shows density of all dislocation loops (D0,,) and the threading

dislocation loops (DrDL) as a function of boron implant dose along with the simulation

results. As the implant dose increase, D., and DrDL increase with the increasing dose to a

maximum at a dose of lxl014 cm-2. This is often referred to as the critical dose for

threading dislocation loops. This rapid increase in dislocation loop growth is due to the

increased number of trapped interstitials in the dislocation loops. Increasing the dose of

the implant will increase the excess interstitial population in the silicon substrate. Thus,

this will increase the growth of the loops. At doses beyond Ix1014 cm"2, while D1 keeps

increasing, DTL decreases rapidly back to close to the minimum detection limit (5xl 0

cm'2). Same trends can be seen in the simulation results (Figure 3-7 ) including the








dramatic change in the threading dislocation loop density at the critical dose of 1x1014

cm-2 Simulation predicts higher density of dislocation loops at the high implant doses but

the results are in good agreement with the experimental results at the other implant dose

values.


10 II
S* Data-Dall
10 Data-TDL

109

108
107



106

10



104


1000 1 1 1 1 1 1 1 1 1 1 1 4
0 1101 210 3 101
Dose (cm )


41014 5 1014 61014


Figure 3-7. Density of all dislocation loops and threading dislocation loops vs. boron
dose with implant energy of 1.5 MeV.



Total number of interstitials bounded by dislocation loops (Na,,) increases with

increasing implant dose as shown in the simulation results in Figure 3-8 There is a big


E

0
0
o

0
,-
E:
0)
QI








discrepancy between the simulation results and the data. The data is derived from

experimental results (loop density, average loop radius) using simple relation given in

Equation (2.3).


1016



10'5



1014


1012


0 1 1014 21014 3 1014 41014 5 1014 61014

Dose (cm2)


Figure 3-8.


Total number of interstitials bounded by loops for various boron implant
dose with implant energy of 1.5 MeV.


Since some of defects seen in the TEM pictures (i.e. TDLs) are non-circular,

using Equation (2.3) generates such discrepancies. Therefore, due to the method of

extraction of the data points, it is possible that the data points in Fig 3-8 are more

erroneous than the simulation results.


'a,

C.'
C-
-c
u

-o
v


a)
-o


.0


o

i-i

I
z







3.3 Summary

The loop evolution model developed in Chapter 2 is expanded to include the

nucleation of the dislocation loops. A single set of differential equations is used to

characterize the loop behavior through the nucleation and Ostwald ripening stages. The

model assumes that all the loops come from {311} unfaulting. The excess interstitial and

vacancy populations due to ion implantation are obtained from UT-MARLOWE. They

are utilized to generate interstitial and vacancy clusters, eventually leading to the

nucleation of {311 }'s and dislocation loops. Since the model keeps track of dislocation

loop distribution through the substrate, the density of threading dislocation loops is easily

calculated using these profiles. Simulation results are verified with the experimental data.

The work represented so far shows that the model can successfully predict the

loop nucleation and evolution. In order to get more physical insight about the nucleation

process, we should study the nucleation stage through different experiments. In the next

chapter, these experiments will be explained in detail.












CHAPTER 4
NUCLEATION AND EVOLUTION OF END OF RANGE DISLOCATION LOOPS

Ion implantation is the primary source of the introducing impurity atoms into the

silicon substrate due to the inherent controllability of the implanted profile. However

crystal damage is unavoidable and consequently defects form. Type II defects are some

of the more commonly observed defects in high dose implants that are required to form

highly activated ultra-shallow junctions. In most cases, depending on the mass of the

implanted dopant species, implanting at high doses amorphizes the implanted region. In

some cases, pre-amorphization is needed prior to implantation of light dopants such as

boron in order to prevent channeling. In order to repair the crystal damage, post-implant

anneals are required. During solid phase epitaxial re-growth of the amorphous layer,

extended defects form at the amorphous-crystalline interface. They are also known as

end-of-range (EOR) defects ranging from small clusters of a few atoms to {311 }'s and

dislocation loops. In Chapter 2, we mainly focused on time evolution of end of range

dislocation loops in oxidizing and inert ambients. The discussion on the loop model in

Chapter 2 accounts only for the evolution part of the model. The nucleation part of the

model was not verified as the experiments described in Chapter 2 were not optimized to

study nucleation of dislocation loops. Therefore, the model required the initialization of

the density of the distribution of loops and the number of interstitials bounded by loops as

input parameters. These initial parameters indirectly depended on the implant dose and

energy. Although, a great amount of information resulted from these experimental results,

the nucleation of dislocation loops should be closely investigated to learn more about the







nucleation of Type II defects. This effort is also important to improve and calibrate the

model.

In this chapter, due to the aforementioned reasons, the nucleation part of the loop

model will be verified through indigenously designed experiments that are specifically

optimized for studying loop nucleation.


4.1 Experimental Details

Figure 4-1 shows a schematic representation of the experiment. Single crystal

Czochralski silicon wafers (<100> orientation) were used as the starting material. Si+ ions

were implanted at either 80 keV or 40 keV at a dose of 2x1015 cm-2. Under these implant

conditions, a continuous amorphous layer forms. After the implant, the entire wafer was

capped with thick SiO2 before the anneal process to limit any oxidation in the inert

ambient. Prior to annealing, cross sectional TEM (XTEM) measurements were performed

to determine the amorphous/crystalline interface. The wafers were cut into smaller pieces

and annealed in a nitrogen ambient at 700 C and 750 C. Annealing times were chosen

to be 30, 60, 90, 120, 240 minutes for 700 C anneals and 15, 30, 60, 90, 120 minutes for

750 oC anneals. The annealing times and temperatures are chosen so that the nucleation

and evolution of {311}'s and dislocation loops will be slow. [Sto97]. This allowed us to

simultaneously observe the changes in {311 } and EOR dislocation densities for longer

annealing times at these temperatures. After the anneal, the capped oxide for all the

samples were removed by HF dip before mechanical and jet etching. The total loop

density, total {311} density and total number of interstitials bounded by the loops and

(311)}'s were measured from the plan view TEM studies.














































Figure 4-1. Schematic representation of designed experiment




4.2 Experimental Results


The XTEM micrographs of 40 keV and 80 keV Si+ implants to a dose of 2x1015

cm-2 before furnace anneals are shown in Figure 4-2. There is a clear contrast difference


2x1015 cm-2, 80 keV or 40 keV Si'
Implant
(Amorphizing)


EOR Loops at 1600 A or 900 A
(Starting Material)


Anneal at 700 C
(N2 ambient)
for
30 min
60 min
90 min
120 min
240 min


Anneal at 750 C
(N2 ambient)
for
15 min
30 min
60 min
90 min
120 min


PTEM
Loop Density, {311} Density


A--
















































Figure 4-2. Weak beam dark field XTEM images of(a) 40 keV and (b) 80 keV Si+
implanted Si to a dose of 2xl0'5 cm'2 before furnace anneals







between the amorphous and crystalline silicon. The amorphous/crystalline interface is

located around 965 A and 1800 A for 40 keV and 80 keV samples respectively. The

XTEM pictures also shows that a continuous amorphous silicon region extending to the

surface. End of range defects form at around the depth of the original amorphous-

crystalline interface upon subsequent furnace annealing.

Figures 4-3-4-4 represent the plan view TEM (PTEM) pictures of the 40 keV

samples after furnace anneals at 700 C and 750 OC for various annealing times. The g220

reflection was used to acquire all the PTEMs under the weak beam dark field imaging

conditions. It is observed that when dislocation loops and {311} defects are present at the

same time, it is difficult to distinguish an elongated loop from a {311} defect. In order to

obtain an accurate count of defects, PTEM pictures were taken with plus (+) and minus

(-) g reflections. If a defect exhibited an outside contrast with +g and inside contrast with

-g then it was considered as an extrinsic loop. Those studies showed that all the

elongated defects at longer annealing times in all samples were dislocation loops. It is

observed from Figures 4-3 and 4-4 that {311} defects nucleate and dissolve very fast at

all anneal temperatures and times. The dissolution rate of {311 }defects is slower at 700

"C than at 750 OC. No {311} defects have been observed after annealing for 120 minutes

and 90 minutes at 700 C and 750 C, respectively. It is also observed that dislocation

loops nucleate at a slower rate than (311 defects. The density of dislocation loops

increases at short times at 700 C. Then, it starts decreasing. The density of dislocation

loops decreases at a faster rate at 750 C than it does at 700 C. While smaller loops

dissolve, bigger loops grow (Ostwald ripening). The loops are smaller in size at the low

annealing temperature. The same trends can be observed in the density of {311}'s



















(a) (b) (c)


00









(d) (e)

Figure 4-3. Weak beam dark field plan view TEM images of 40 keV Si+ implanted Si to a dose of2x1015 cm-2, after an anneal at 700
C for (a) 30 min (b) 60 min (c) 90 min (d) 120 min (e) 240 min in N2.


















(a) (b) (c)


(d) (e)

Figure 4-4. Weak beam dark field plan view TEM images of 40 keV Si+ implanted Si to a dose of 2xl05 cm-2, after an anneal at 750
C for (a) 15 min (b) 30 min (c) 60 min (d) 90 min (e) 120 min in N2.


















(a) (b) (c)


(d) (e)

Figure 4-5. Weak beam dark field plan view TEM images of 80 keV Si' implanted Si to a dose of 2x1015 cm2, after an anneal at 700
C for (a) 30 min (b) 60 min (c) 90 min (d) 120 min (e) 240 min in N2.


















(a) (b) (c)


(d) (e)

Figure 4-6. Weak beam dark field plan view TEM images of 80 keV Si+ implanted Si to a dose of 2x1015 cm2, after an anneal at 750
OC for (a) 15 min (b) 30 min (c) 60 min (d) 90 min (e) 120 min in N2.







and dislocation loops for the samples implanted with 80 keV Si' to a dose of 2x10'5 cm-2

in Figures 4-5 and 4-6. Although Figure 4-5 shows the 80 keV sample annealed for 30

minutes at 700 OC, the defects as observed in the TEM were too small to count with any

reasonable accuracy. Defect counts for each sample will be given in the next section

along with simulation results.



4.3 Simulation Results

In order to simulate loops nucleation, excess interstitial and vacancy profiles are

generated for each implant dose and energy using UT-MARLOWE with kinetic

accumulative damage model (KADM). Figure 4-7 shows the truncated excess interstitial

concentration in the silicon substrate for a 80 keV Si+ implant at a dose of 2x1015 cm2.

UT-MARLOWE output files estimate the amorphous depths to be around 1600 A and

950 A for 80 keV and 40 keV implants, respectively. These values correspond very

closely with those obtained from XTEM pictures. The excess interstitial concentration is

set to the equilibrium interstitial concentration in the amorphous region using a truncation

function. The tail of excess interstitial profile seen in Figure 4-7 has a lot of noise. It is

possible to reduce the noise by increasing the number of ions used in UT-MARLOWE

simulation. However, increasing the number of ions will dramatically increase the

computation time of the UT-MARLOWE simulation. Excess vacancy profiles are

obtained in a similar way for all simulations. These excess interstitials and vacancies

provide the basis for the nucleation of interstitial and vacancy cluster, eventually leading

to the nucleation of {311} 's and dislocation loops as explained in Chapter 3.


* '*





73







102211l l l l -






m 20
0210



t 10


0
-9





1017
I 10




0 1000 2000 3000 4000 5000 6000 7000 8000
Depth (A)


Figure 4-7. Initial truncated excess interstitial concentration after an implantation of Sit
with a dose of 2x10'1cm-2 and energy of 80 keV



Figure 4-8 represents the changes in defect densities with time at an anneal

temperature of 700 C after implantation of Si+ with a dose of 2x 1015 cm2 and energy of

40 keV. The symbols represent the experimental data and the lines represent the

simulation results. As seen from the data, density of {311 }'s, D311, and the number of

interstitials bounded by {311 's, C311, decrease with increasing anneal time. C311 and

D311 show an exponential decay. Meanwhile, density of dislocation loops, Dai, and the

number of interstitials bounded by loops, N.i, increase with increasing time. There is no













105
10i'5 I i I I i i II I I I I I -

14A
1O A -

WI 13
S10 -- .

12
o 10 1
o

0 10

n 10 /
.10 -_-_

S109 C311 ---- --- C311 Simulation
S A Nail Nail Simulation
10 D311 -----D311 Simulation
0- Dall DallSimulation
u 10 I i I i i i i i ii i i
0 50 100 150 200 250
Time (min)



Figure 4-8. Changes in defect densities with time at 700 C after implantation of Si+ with
a dose of 2xl0'5 em2 and energy of 40 keV. The symbols are experimental
results and the lines are simulation results.



significant change in the loop density after an initial 60 minutes anneal time while Nau

continues to increase. If the simulation results are considered, it is easy to see that D311

and C311 increase very rapidly in short times and then they start decreasing It is also

obvious that the nucleation of dislocation loops are slower than the nucleation of {311 }'s

since the loops nucleate from unfaulted {311 }'s. In Figure 4-8, it is possible to observe

two of the three distinct stages of loop nucleation and evolution. At short anneal times,













10 5
I I 11' 1' I l I -
10 -

13
I 10'
P4 12
o 10

C 10
: t rt, ,


S 109 -
10


0 C311 C311 Simulation
S A Nail Nail Simulation
S 10 311 D- -D 311 Simulation
S* Dall -Dall Simulation
U 107
0 50 100 150 200 250
Time (min)


Figure 4-9. Changes in defect densities with time at 700 C after implantation of Si+ with
a dose of 2x1015 cm2 and energy of 40 keV. The symbols are experimental results and
the lines are simulation results.


both Nan and Dan increases rapidly when the nucleation rate is high. This is usually

referred to as the nucleation stage. The nucleation stage is followed by the pure growth

stage. During this stage, Dan stays almost constant while NaI keep increasing since excess

interstitial concentration is still high. In the third stage, Ostwald ripening occurs (not very

clear in Figure 4-8, but can be seen in Figures 4-11-4-13) and the loops go into this stage







as soon as the excess interstitial concentration drops. Dan starts decreasing and Nan stays

constant during this stage. The bigger loops grow at the expense of smaller ones.

Simulation results are mostly in good agreement with the experimental data. The

biggest discrepancy between the data and simulation is seen at the shortest anneal time

due to the smaller defect sizes seen in TEM picture (Figure 4-3.a). If the defect sizes are

too small, it becomes harder to distinguish {311} defects from dislocations and the error

increases. Therefore, the defects for the shortest anneal time are recounted to obtain the



1 I

4 C311
S-- A Nail
10 .. D311
S. Dall
CL 12 1 ...._ C311 a=950A
S- Nail a=950A
1 --- D311 a=950A
S10 -- Dall a=950A
-C311 a1OOOA
S 10 Nail a=1000A
S--------D311 a=1000A
S- Dalla=1000A
10
o = -

S10

U 107
0 50 100 150 200 250
Time (min)


Figure 4-10. Changes in defect densities with time at 700 OC after implantation of Si"
with a dose of 2x10'5 cm' and energy of 40 keV. The symbols are
experimental results and the lines are simulation results. Amorphous depth
is set to 950 A and 1000 A as initial condition for two different simulations.




77







15

-' 14 AL A A
10
10

12
0 1013

4* ... _
O 10
0 10 -



co 10 C311 C3.11 Simulation
14 A Nail Nall Simulation
lS 10- D 1 D311 -D Simulk on
S* NDall Dall Simulation =
o
S 107I I
0 20 40 60 80 100 120 140
Time (min)


Figure 4-11. Changes in defect densities with time at 750 OC after implantation of Si'
with a dose of 2x1015 cm2 and energy of 40 keV. The symbols are
experimental results and the lines are simulation results.



error bars shown in Figure 4-9. The upper bound on the error is obtained by assuming

that all defects are either dislocation loops or {311 }'s. The recount was done aggressively

to include every small defect. The lower bound on the error bar is obtained by pursuing a

non-aggressive approach where only the defects that are clearly {311)}'s or loops are

recounted. The results are shown in Figure 4-9. Error bars show that simulation results lie

within range of experimental errors.













S1015

S14
S1014 .

13
10, .



3102 ,." ..
S10






SC311 C- 311 Simulation
b 108 A Nail Nail Simulation
10 -
S D311 -- -- D311 Simulation
S Da Dall DaSimulation
0 7 I I
U. 10
0 50 100 150 200 250
Time (min)



Figure 4-12. Changes in defect densities with time at 700 C after implantation of Si+
with a dose of 2x10'5 cm-2 and energy of 80 keV. The symbols are
experimental results and the lines are simulation results.



Initial conditions used in the simulations also play an important role. Figure 4-10

shows the changes in defect density with time for the case of 700 oC, 40 keV. It also

shows two different simulation results with two different initial conditions. The excess

interstitial and vacancy profiles are obtained by assuming two different amorphization

depths. In the first case, the amorphous depth is set to 950 A and the excess interstitial





79


and vacancy profiles are truncated using this amorphous depth. Then the simulation is

carried out. In the second case, amorphous depth is set to 1000 A and the same procedure


= .


U


r'i
E



o
rn

U,



0
0


a
L-
U,
U
0
-d
Cu




c
b
U
U
0
U


1015


1014

1013





10"

10'


109


108


107


80 100 120 140
n)


0 20 40 60
Time (miu


Figure 4-13.


Changes in defect densities with time at 750 C after implantation of Si+
with a dose of 2x105 cm"2 and energy of 80 keV. The symbols are
experimental results and the lines are simulation results.


is repeated. As seen in Figure 4-10, the difference between the two simulations could be

quite significant. Increasing amorphous depth by 50 A shifts all profiles in negative y

directions. This is due to the fact that increasing amorphous depth reduces the number of

excess interstitials available for the nucleation of {311 }'s and dislocation loops. If Figure


A A
A


C311
Nail
D311

Dall


.C3 i Simulation
Nail Simutiwon
- D311 Simulation -

S--pall Si lulatioI


3








3

j










I I


~$ _r







4-7 is closely examined, it can be seen that the slope of the excess interstitial profile is

quite steep around the amorphous depth. Even if the amorphous depth is changed by 50

A, the change in the number of excess interstitials will be very significant.

Figure 4-11 shows the changes in defect densities with time for the 750 oC, 40

keV sample. Experimental and simulation results have all the characteristics explained

above. The nucleation rate of dislocation loops and dissolution rates of {311 }'s at 750 C

are faster than that at 700 C



1015
E U C311
1014 A .- A -A Nail
D311
S Dall
10 ......... -C311 a=1650 A
-- Nall a=1650 A
0 1012 D311 a=1650A
S- Dall a=1650 A
1. C311 a=1600 A
S10 ---- Nalla=1600A
S--- -- D311a=1600A
10 /. Dall a=1600 A

10
108 .
C 10
0 1 0

0 20 40 60 80 100 120 140
Time (min)


Figure 4-14. Changes in defect densities with time at 750 OC after implantation of Si+
with a dose of 2x10'5 cm2 and energy of 40 keV. The symbols are
experimental results and the lines are simulation results. Amorphous depth
is set to 950 A and 1000 A as initial condition for two different simulations







The changes in defect densities with time at 700 OC and 750 OC for 80 keV

samples are shown in Figures 4-12 and 4-14, respectively. The same trends observed in

defect densities in 40 keV samples are observed for these samples as well. 80 keV

samples generate deeper loop layers than the 40 keV samples. The surface effects on

defects for two cases (700 OC and 750 oC) would be different. Simulation results are in

good agreement with the experimental data in both sample sets. This shows that surface

effects are also modeled correctly in the model.

The variations in defect densities with time at 750 oC for 80keV samples with two

different simulation results are represented in Figure 4-14. The amorphous depths are set

to 1600 A and 1650 A to generate excess interstitial and vacancy profiles as two different

initial conditions for simulations as explained before. The importance of initial conditions

used for the simulations is emphasized in this figure one more time since the shift in the

profiles can be significant.



4.4 Summary

Since amorphization commonly occurs during ion implantation, EOR defects are

hard to avoid upon annealing. Therefore, EOR defects are very common in today's

technologies. It is very important to be able to predict their size and density using

physical models to design better devices. In this chapter, two sets of experiments are

designed to investigate the nucleation and evolution of EOR defects. In the first set of

experiments, EOR defects are generated around 1600 A and samples are annealed at 700

C and 750 C for various times. Defect densities are obtained from TEM pictures.

Simulations are carried out using UT-MARLOWE damage profiles. It is seen that

experiments and simulations are in good agreement. Performing the experiment at two







different temperatures helped to calibrate the model and determine the temperature

dependence of the fitting parameters used in the model. In the second set of experiments,

EOR defects are generated at around 900 A. Samples are annealed, analyzed and

simulations are carried in the same way as for the first set of experiments. Simulations

showed the same trends seen in experimental data. Having loops at two different depths

helped us to investigate surface effects on the nucleation of dislocation loops. The

importance of the initial conditions on the simulations is also emphasized.

So far, we have investigated only defects formed by Si+ into silicon implantation.

It is important to know how well the model works with other implant species. In the next

chapter, we will carry out some simulations with different implant species and compare

the results with the published data.












CHAPTER 5
VERIFICATION OF THE LOOP MODEL USING DIFFERENT IMPLANT SPECIES

So far, our studies have mainly focused on the formation and evolution of end of

range (EOR) defects in Si implanted wafers. The developed loop model is validated for

various experiments by changing the implant dose, energy and the annealing temperature.

It was shown [Jon88] that implant species play an important role on the defect formation

and defect evolution. Light ions, such as boron, cannot produce enough damage to cause

amorphization. They usually form {311}'s and dislocation loops around the projected

range after annealing which are classified as type I defects (Section 1.1.2). Meanwhile,

arsenic and germanium are heavy ions and they can produce amorphous layers if the

implant dose exceeds the critical dose. EOR defects are the product of these heavy ions.

Since most of the defects are extrinsic in nature, the amount of the excess interstitials

generated by the implant species will affect the defect densities.

In contrast to silicon self implants, some of these implant species may interact

with the excess interstitials and vacancies generated during the implantation process.

They may pair with interstitials and vacancies and diffuse away from the damaged

region. Doing so, they reduce the super saturation of excess interstitials and vacancies in

the damaged region. Thus, they indirectly affect the defect densities.

In this chapter, the developed loop model will be tested using Liu's boron

[Liu96], Gutierrez's germanium [GutOl], and Brindos' arsenic [BriOO] implant studies.

The limits of the model, where it fails or does a good job in predicting the experimental

results, will be discussed.







5.1 Defects in Boron Implanted Silicon

Liu [Liu96] systematically studied the defect formation threshold in the low energy

implant regime in order to understand how the sub-amorphization defects influence

dopant diffusion. Liu implanted n-type wafers with boron ions at energies of 5 keV, 10

keV, 20 keV, 30 keV and 40 keV at doses of 5x1013 cm-2, 1xl014 cm-2, 2x1014 cm-2

5x1014 cm-2 and lxl105 cm-2. Liu performed furnace anneals at 750 oC for 5 minutes in a

nitrogen ambient to study the formation threshold of {311} defects. She also performed

furnace anneals at 9000C for 15 minutes to study sub-amorphization dislocation loops.

PTEM analyzes were performed to determine defect densities. Liu chose a defect density

of 1.2x107 cm-2 to distinguish between samples with and without extended defects. Table

5-1 lists the formation threshold for both {311 } defects and dislocation loops for the

whole implant matrix after anneals at 750 C for 5 minutes and at 900C for 15 minutes.

Liu observed that there were no {311} defects in the 5 keV samples at a dose of lxlO14

cm-2. When the dose was doubled to 2xl014 cm-2, there were still no {311 } defects in the

5 keV sample, but more defects were present in the other two implants. Increasing the

dose further to 5x 014 cm-2 resulted in {311 } defects and sub-threshold dislocation loops.

The results showed that the critical dose for forming {311} defects decreased with

increasing implant energy. The defect density also increased with increasing energy. It

was concluded that the interstitial supersaturation necessary to nucleate {311} defects

was far less than that for dislocation loops, as well. In addition, the threshold dose for

{311} defects in a 20 keV boron implant was found to be around 2x1014 cm-2 which was

much greater than the threshold dose of 7x1012 cm-2 for a 40 keV silicon implant at




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LOOP NUCLEATION AND STRESS EFFECTS IN ION-IMPLANT ED SILICON By IBRAHIM A VCI 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 2002

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Copyright 2002 by Ibrahim A vci

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To my parents, Mustafa and Fatma.

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ACKNOWLEDGMENTS I thank my advisor Dr. Mark E. Law for his guidance support and encouragement. He always shared his invaluable knowledge and wisdom and he provided valuable advice and direction throughout my doctorate study. I also thank to Drs. Kevin S Jones Robert M. Fox Gijs Bosman and Tim Davis for their help and guidance as members of my doctoral supervisory committee I am grateful to Drs. Martin Giles Paul Packan and Steve Cea for providing materials for my experiments and for their valuable advice. I acknowledge Drs Rainer Thoma Craig Jasper and Hernan Rueda for their support understanding and help. The y inspired me during my doctorate study I also thank to Semiconductor Research Corporation for its support of my doctorate study. I have met so many beautiful helpful and understanding people in my research group that I call them my SW AMP family. My heartfelt thanks go to each one of them I would especially like to thank Tony Saavedra Erik Kuryliw and Mark Clark for helping with my experiments and TEM analysis. I also thank Ljubo Radie Dr. Susan Earles and Dr. Lahir Adam for their support discussion and friendship. I will always remember the experiences we shared. Although Chad Lindfors Drs Aaron Lilak Sushil Bharatan Patrick Keys and Rich Brindos pulled my leg and accused me of iboing ," I will remember all the good times we had. I also thank my friends Serdar Ozen Rifat Hacioglu, Ferda Soyer Banu Ozarslan Evren Ozarslan Alper Ungor Ugur Kalay and IV

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Elgay Kalay for their friendship support and encouragement. The y w ill al w a ys h ave a special place in my heart I would like to express my love to my parents Mustafa and F atma for th e i r never-ending love support and encouragement throughout my life. I am grateful t o ha ve them I would also like to express my love to my brother Ergun ; my sister-in-la w; Munevver and my nieces Irem and Ceren for their love and support V

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TABLE OF CONTENTS ACKNOWLEDGMENTS .............................................................................................. iv LIST OF TABLES ......................................................................................................... ix LIST OF FIGURES ................................................................................................ ... .... .. X ABSTRACT ........................................................................................................... ..... xv CHAPTERS 1 INTRODUCTION ........................................................................................................ 1 1.1 Ion-Implantation Damage and Defects .................................................................. 4 1.1.1 Point Defects ................................................................................................. 5 1.1.2 Extended Defects .............. ............................................. .............................. 5 1.1.2.1 Category I damage .................................................................................. 6 1.1.2.2 Category II damage ................................................................................. 7 1.1.2.3 Category III damage ................................................................................ 7 1 1.2.4 Category IV damage ....................................................................... ... .... 7 1.1.2.5 Category V damage ................................................................................. 8 1.2 Dislocation Loops ................................................................................................. 8 1.2.1 Interaction between { 311} 's and Dislocation Loops .................................. .. 10 1.2.2 Effects of Dislocation Loops on Device Characteristics ..................... ......... 11 1.3 Stress and Strain ................................................................................................. 13 1.3 .1 Stress and Strain Sources in Silicon IC Processing ....................................... 16 1.3.1.1 Film Stress and Film Edge-Induced Stress ...... .. ..... .... ............ .. ............ 16 1.3 .1.2 Stress from Oxidation and Device-Isolation Processes ........................... 18 1. 3 .1 3 DopantInduced Stress .......................................................................... 19 1.4 Stress-Induced Dislocation Loops ................................................................. ...... 20 1.5 Goals .................................................................................................................. 22 1.6 Organization ....................................................................................................... 23 2 MODELING THE EVOLUTION OF DISLOCATION LOOPS FOR VARIOUS PROCESS CONDITIONS ............................................................................................ 24 2.1 Modeling Dislocation Loop Evolution ................................................................. 25 2.1.1 Log Normal Distribution Function ............................................................... 26 2.1.2 Density of Dislocation Loops ....................................................................... 27 VI

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2.1.4 Coarsening and Dissolution of the Dislocation Loops . . . .. ........... ..... . ... . 2 9 2.2 Experimental and Simulation Results to Calibrate the Model . ...... . . . ................. 34 2.2.1 Simulation of the Evolution of Loops during Oxidation ..... . . .... . ............... 3 5 2.2.2 Simulation of Loop Evolution during Annealing in Inert Ambient . ............ 40 2.3 Experimental and Simulation Results to Verify the Model.. .. .......... . .... .. .. ... .. 4 2 2.3.1 Simulation of Loop Dissolution as a Function of Loop Depth ... ...... .. . .. .... . 42 2.3 .2 Effects of Dislocation Loops on Boron Diffusion ............... ............. .. ......... 44 2.4 Summary ................................................................ ...................... ...... . ..... ...... 47 3 MODELLING THE NUCLEATION AND EVOLUTION OF THREADING DISLOCATION LOOPS .... ............................................ ....... . . ................... .. .. ..... .... 48 3.1 Modeling Dislocation Loop Nucleation . ........ .... .. . . .. . ... .... . . . .. . . . ....... ... .. 50 3.2 Modeling Threading Dislocation Loop Nucleation .... ..................... . . .......... ..... 54 3.2.1 Simulation of the Nucleation and Evolution of Threading Dislocation Loops ...................................................................................................................... .. .. .. 56 3.3 Summary ............................................................................................ ............... 62 4 NUCLEATION AND EVOLUTION OF END OF RANGE DISLOCATION LOOPS ..................................... .. .. .................... ..... .. .. . .. . . .. . ........ . ... . .. . .. ... . .. .. 63 4.1 Experimental Details ........................................................................... . ..... .. ... 64 4.2 Experimental Results ........................................................................... . .. .. .. .. .. 65 4.3 Simulation Results .................................................................... ..... ....... .. ..... .. 72 4.4 Summary ......................................................................................................... .. 81 5 VERIFICATION OF THE LOOP MODEL USING DIFFERENT IMPLANT SPECIES ............................................................................. ............. ... .... . .... .. .. . ... . 83 5 .1 Defects in Boron Implanted Silicon ......................................... . . .. . . . .. .. ..... .. 84 5 .1.1 Simulation Results .................................................................................... .. 86 5 .2 Defects in Germanium Implanted Silicon ............................................................ 90 5.3 Defects in Arsenic Implanted Silicon ..................... .... .. ... . .. ... ........ . .. .. .. ..... 97 5.4 Summary ................................................................. .. . .... . . .. ... . . .. . .. . ... .. .. 99 6 PROCESS INDUCED STRESS EFFECTS ON DISLOCATION LOOPS ... ... ........ 100 6.1 Dislocation Loop Nucleation and Evolution under Tensile Stress .............. ...... 102 6.1.1 Experimental Details ................................................................................... 102 6.1.2 Stress-Assisted Loop Nucleation and Evolution Model ........................ ..... 108 6.1.3 Experimental and Simulation Results ........................................ . .... .. ....... 110 6.2 Effects of Patterned Nitride Stripes on Dislocation Loops .... ...... . ................... 116 6.2.1 Experimental Details ............................................ ...... .... . ... .... . ..... .. . . . 116 6.2.2 Experimental and Simulation Results .................... .... . .... ........ .......... ..... 117 6.3 Summary ............................................................. ..... . .. . ........ ......... ... ... . ..... 12 2 7 SUMMARY AND FUTURE WORK ................................................................. .. ... 124 Vll

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7.1 Summary ........................................................................................................... 124 7.2 Future Work ............. ... ......................... .......... .............................. ...... .. ............ 129 EXTRACTED PARAMETERS .. ....................................................... ..... ..... . ............ 132 LIST OF REFERENCES ............................................................................................ 137 BIOGRAPHICAL SKETCH ....................................................................................... 144 vm

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LIST OF TABLES Table 5-1. Types of extended defects formed in B + implanted silicon ..... ... . .. ..... .. .. . ..... 8 5 Table 5-2 Simulation results for the types of extended defects formed in B + implanted silicon after an anneal at 750C for 5 min .. .. ... . ......... ... ... .. . . .. ......... ... .. .. .. 87 Table 5-3 Simulation results for the types of extended defects formed in B + implanted silicon after an anneal at 900C for 15 min ... .. ... .............. ... .. .. .... .. ... .. .. .. .. ... . 88 lX

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LIST OF FIGURES Figure Figure 1-1 The range of ion implant energies and doses used in semiconductor processes ............... ........................................... .................. ........ ....... .......... .. 3 Figure 1-2 Criteria of Extended Defect Generation ............ ..... .............................. .......... 6 Figure 1-3 Weak beam dark field images of dislocation loops and {311} .. .. .. .............. ... 10 Figure 1-4 An arbitrary body subject to external forces ..... ............. ..... ..... . .. ........ .... .. .... 13 Figure 1-5 Components of stress in a stress element. ........................................................ 14 Figure 1-6 Shear strain .............................................................................. .................... .. 15 Figure 17 Two dimensional lattice deformation due to a dopant atom ............................. 19 Figure 1-8 Cross section of a modern day n type MOS transistor. ........................... ... .. ..... 21 Figure 2-1 Log normal density distribution function applied to the statistical distribution of loop radius extracted from the TEM measurements under 900 C dry oxidation condition .......................................................................................... 26 Figure 2-2 Pressure in silicon due to the dislocation loops ................................................ 30 Figure 2-3 Density of the interstitials bounded by dislocation loops as a function of oxidation time and simulation in the two different cases of Si implant dose 2xl0 15 and 5xl0 15 cm2 .................................................................................. 35 Figure 2-4 Variation of total density of dislocation loops with time and simulation results for two different implant conditions .................................................... .... .... ... 36 Figure 2-5 The average radius change with time during oxidation and corresponding simulation results .................................................................................... .. ....... 3 7 Figure 2-6 Variation in total number of interstitials bounded by the loops as a function of anneal time at different temperatures ................................................................ 3 8 Figure 27 Variation in total loop density as a function of anneal time at different temperatures .................................................................................................... 39 X

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Figure 2-8 Experimental and simulated average loop radius as a function of annealing time at different temperatures .... .. ..... ........ .. .. .. . . .. . .... ............ .. . .. ......... .. 41 Figure 2-9 Simulation and experimental results for the loss of interstitials with time at 900 C ............................................................................... ......... ....... ...... .. ... 42 Figure 2-10 Simulation and experimental results for the loss of interstitials with time at 1000 C ............................. ... ........................... ............. . . ........ .... ... .. .. . .. . 43 Figure 2-11 SIMS profiles of DSL after st implantation at different dose rates and annealing at 800 C for 3 minutes .......... ............... ... ..... .. ... . . .. . ..... ..... .. .. 45 Figure 2-12 Boron profiles with two different loop density and no loop layer annealed at 800 C for 3 minutes ........................................ .... .......... . ........ .. .. .. .. .... 46 Figure 3-1 Schematic representation of dislocation loop nucleation .. . . .... . . .... .. .. ... . .. .. 50 Figure 3-2 Nucleation rate N~~: 1 change with time ....................................... ............... . . 52 Figure 3-3 TEM picture of dislocation loops and threading dislocation loops .. ....... .. .. .. 53 Figure 3-4 Schematic representation of TD Ls in a distribution function ......................... .. 55 Figure 3-5 Initial excess interstitial concentration after an implantation of boron with a dose of lxl0 14 cm2 and an energy of 1.5 MeV ......... ... .. ..... . . . .. . . ..... .. . ....... 57 Figure 3-6 Changes in defect densities with time after implantation of boron with a dose of lxl0 14 cm2 and an energy of 1.5 MeV ............... .. .. .......... . . .... ............... . 58 Figure 37 Density of all dislocation loops and threading dislocation loops vs. boron dose with implant energy of 1.5 MeV ..................................... ...... . ... .. .. ...... 60 Figure 3-8 Total number of interstitials bounded by loops for various boron implant dose with implant energy of 1.5 MeV ......................................... . . . .. ....... .. ...... .. 61 Figure 4-1 Schematic representation of designed experiment . ........................... .. .... ... ..... 65 Figure 4-2 Weak beam dark field XTEM images of (a) 40 keV and (b) 80 keV Si + implanted Si to a dose of 2xl0 15 cm2 before furnace anneals ........... .. ..... .. ... 66 Figure 4-3 Weak beam dark field plan view TEM images of 40 keV Si + implanted Si to a dose of 2xl0 15 cm-2, after an anneal at 700 C for (a) 30 min (b) 60 min ( c ) 90 min (d) 120 min (e) 240 min in N 2 ................ ....... . ... ...... .... .... . . .. ........... . 68 Figure 4-4 Weak beam dark field plan view TEM images of 40 ke V st implanted Si to a dose of 2xl0 15 cm2 after an anneal at 750 C for (a) 15 min (b) 30 min (c) 60 min (d) 90 min (e) 120 min in N 2 ................................ . . .. . . . .. .... ..... .. ... ... 69 Xl

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Figure 4-5 Weak beam dark field plan view TEM images of 80 keV st implanted Si to a dose of 2xl0 15 cm2 after an anneal at 700 C for (a) 30 min (b) 60 min (c) 90 min (d) 120 min (e) 240 min in N 2 ................................................................... 70 Figure 4-6 Weak beam dark field plan view TEM images of 80 keV st implanted Si to a dose of 2xl0 15 cm2 after an anneal at 750 C for (a) 15 min (b) 30 min (c) 60 min (d) 90 min (e) 120 min in N 2 ..................................................................... 71 Figure 47 Initial truricated excess interstitial concentration after an implantation of st with a dose of 2xl0 15 cm2 and energy of 80 keV .............................................. 73 Figure 4-8 Changes in defect densities with time at 700 C after implantation of st with a dose of 2xl0 15 cm2 and energy of 40 keV The symbols are experimental results and the lines are simulation results ...................................... ............ .. .. . 7 4 Figure 4-9 Changes in defect densities with time at 700 C after implantation of st with a dose of 2xl0 15 cm2 and energy of 40 keV. The symbols are experimental results and the lines are simulation results ........................................................ 75 Figure 4-10 Changes in defect densities with time at 700 C after implantation of st with a dose of 2xl0 15 cm2 and energy of 40 keV. The symbols are experimental results and the lines are simulation results. Amorphous depth is set to 950 A and 1000 A as initial condition for two different simulations .. 76 Figure 4-11 Changes in defect densities with time at 750 C after implantation of st with a dose of 2x10 15 cm2 and energy of 40 keV. The symbols are experimental results and the lines are simulation results ............... ........ .. ... ... 77 Figure 4-12 Changes in defect densities with time at 700 C after implantation of St with a dose of2xl0 15 cm2 and energy of80 keV. The symbols are experimental results and the lines are simulation results ................................ 78 Figure 4-13 Changes in defect densities with time at 750 C after implantation of St with a dose of 2x 10 15 cm2 and energy of 80 ke V. The symbols are experimental results and the lines are simulation results ................................ 79 Figure 4-14 Changes in defect densities with time at 750 C after implantation of St with a dose of 2xl0 15 cm2 and energy of 40 keV. The symbols are experimental results and the lines are simulation results. Amorphous depth is set to 950 A and 1000 A as initial condition for two different simulations .. 80 Figure 5-1 Experimental and simulation results for the defect evolution for a 30 ke V lxl0 15 cm2 Ge+ implant on silicon, annealed at 750 C ................................... .. 91 Figure 5-2 Experimental and simulation results for the defect evolution for a 30 keV lx10 15 cm2 Ge+ implant on silicon, annealed at 825 C ..................................... 92 Xll

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Figure 5-3 Experimental and simulation results for the defect evolution for a 10 ke V lxl 0 15 cm2 Ge+ implant on silicon annealed at 750 C ........ .. ... .......... .. .. .. ..... 94 Figure 5-4 Experimental and simulation results for the defect evolution for a 5 ke V 5x10 14 cm2 Ge+ implant on silicon, annealed at 750 C .................. .. .. ........ ..... 95 Figure 5-5 Experimental and simulation results for defect evolution from 5 keV 3x10 15 cm2 Ge+ implant on silicon, annealed at 750 C .................. ................... 96 Figure 5-6 Simulation results for the defect evolution for 3 keV 5x10 14 cm2 l x 10 1 5 cm 2 and 5x10 15 cm2 As implants on silicon, annealed at 800 C for 60 minutes ... .. 98 Figure 6-1 SEM image of Intel wafer with various patterns. Some structures are as small as 0.5 m ................................................................................ . .... . .. .. . .. .. .. ... 101 Figure 6-2 SEM image of three bars on the wafers. Each bar consists of repeating nitride patterns. Nitride stripes run from top to bottom of the page ............... .. .... .... .. .. 102 Figure 6-3 Magnified SEM image of three bar structure shown in Figure 6.2. Nitride bars are l0m wide and the spacing between them is 3.5m ................................... 103 Figure 6-4 PTEM image of three bar structure shown in Figure 6.2. Nitride bars are l0m wide and the spacing between them is 3.5m ....................................... .. 104 Figure 6-5 SEM image of the other structure used in the experiment. Nitride stripes run from left to the right of the page ....... .. .. .......... .... . . .. . . ...... .. .. . .. .. .. . .. .. .. . 104 Figure 6-6 Magnified SEM image of structure shown in Figure 6.4. Nitride stripes run from left to the right of the page ............................................................ .. ......... 105 Figure 67 PTEM image of structure shown in Figure 6.4. The spacing between nitride bars is 3.5m ........................................................ ..... .... . .... .. .. .... ..... ... .. .. 105 Figure 6-8 XTEM image of one of the un-annealed samples. The amorphous depth is clearly visible and found to be 900A ................................................. .. .... .. .. .... 106 Figure 6-9 XTEM image of one of the un-annealed samples. The amorphous region and nitride pattern are visible. The amorphous depth and nitride thickness were found to be 900A and 1500A respectively .................................................... .. .. 107 Figure 6-10 XTEM image of the annealed sample showing the damage in the trench area. Defects curve towards the surface around the nitride edges ... .. ....... . ... 108 Figure 6-11 Magnified XTEM image of the structure shown in Figure 6.10. The defects in the trench area are visible .......................................................... .. ............. 108 Xlll

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Figure 6-12 Weak beam dark field plan view TEM images of 40 keV st implanted Si to a dose of lxl0 15 cm2 after an anneal at 700 C for (a) 60 min (b) 120 min (c) 180 min (d) 60 min (e) 120 min (f) 180 min in N 2 ............................ ........ 111 Figure 6-13 Weak beam dark field plan view TEM images of 40 ke V Si+ implanted Si to a dose of lxl0 15 cm-2, after an anneal at 750 C for (a) 30 min (b) 60 min (c) 120 min (d) 30 min (e) 60 min (f) 120 min in N 2 .................................. 112 Figure 6-14 Changes in defect densities with time at 700 C after implantation of st with a dose of lxl0 15 cm2 and energy of 40 keV. The symbols are experimental results and the lines are simulation results ................................ 113 Figure 6-15 Changes in defect densities with time at 750 C after implantation of st with a dose of lxl0 15 cm2 and energy of 40 keV The symbols are experimental results and the lines are simulation results ................................ 114 Figure 6-16 Variation of the hydrostatic pressure in the silicon substrate for samples with 10 m and 150 m nitride stripes ................................... .. .. .. ..... .. .. ... .. ...... .. 115 Figure 6-17 The structure used to study the effects of nitride stripes on the evolution of dislocation loops in silicon ............................................................................ 11 7 Figure 6.18 Variation of the hydrostatic pressure in the silicon substrate in compressive and tensile regions under the patterned nitrides. Dislocation loops are formed around the ale interface ..................................................................... 118 Figure 6-19 Experimental and simulated values of the net change in the average radius of the dislocation loops from the tensile to compressive regions as a function of nitride stripe width ........................................................................................ 119 Figure 6-20 Experimental and simulation results of the net change in the total density of dislocation loops from the tensile to the compressive regions as a function of nitride stripe width .................................................................................... 120 Figure 6-21 Experimental and simulated results of the net change in the number of interstitials trapped by dislocation loops from the tensile to the compressive regions as a function of nitride stripe ............................................................. 122 XIV

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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 LOOP NUCLEATION AND STRESS EFFECTS IN ION IMPLANTED SILICON By Ibrahim A vci August 2002 Chairman: Dr. Mark E. Law Major Department: Electrical and Computer Engineering Because of its reproducibility accurate dose control and the ability to tailor dopant profiles ion implantation has been used for years by the semiconductor industr y to introduce dopant atoms into the silicon substrate Damage to the silicon substrate from ion implantation is unavoidable, and annealing is required to repair the damage. Upon annealing dislocation loop and { 311} defects are formed in the vicinity of ion implanted region These defects may degrade or even cause complete failure of devices Meanwhile the semiconductor industry continues to scale successi v e generation s of integrated circuits to increase packing density and reduce device dimensions. Unfortunately these trends lead to increased stress levels in the silicon substrate When combined with ion implantation damage high stress influences defect formation and evolution. xv

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To design better devices through predictive simulations the magnitude depth temperature and time dependence of ion implantation-induced defects should be modeled correctly. We developed statistical-point defect-based model for the evolution and nucleation of dislocation loops in silicon-implanted silicon. The model assumes that all of the dislocation loops evolve from unfaulting {311} defects. The model correctly predicts three distinctive stages of dislocation loop evolution (i.e. nucleation, growth, Ostwald repining) during annealing and is in agreement with the TEM data. We also tested the model for different implant species such as boron germanium and arsenic. The model worked well for most of the implant and annealing conditions. The discrepancies between the model and the experimental results were highlighted where they occurred. We used the statistical nature of the model to determine threading dislocation loop densities by comparing average loop radius to loop depth. Finally, we studied the mechanical stress effects on dislocation loops. Stress in the silicon substrate is varied by changing the deposited nitride stripe widths. The loop model was expanded to account for stress effects. We confirmed that dislocation loops are smaller and sparser in regions of compression when compared to the ones in the regions of tension. XVI

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CHAPTER 1 INTRODUCTION Relentless scaling of Complementary Metal Oxide Semiconductor ( CMOS ) device dimensions has been the driving force for the growth of microelectronics indu s tr y for more than 20 years. The most important features of scaling down device dimensions are high packing density of Integrated Circuits (IC) high circuit speed and low power dissipation [Tho98]. As the industry progresses toward smaller device dimensions ( 0 1 m or smaller) fabrication of such devices become increasingly difficult because of fundamental limits imposed by quantum mechanics and thermodynamics [Tau99]. Most of the effects not dominant in long-channel devices are becoming an issue in toda y s short-channel devices. Carrier velocities reach saturation because of high normal electric fields and the threshold voltage depends on junction depth and effective channel length o f short-channel devices [Kan96]. Thus understanding the formation of shallow junctions i s key to building smaller devices To form shallow junctions parameters that control dopant diffusion in silicon need to be understood and modeled. Ghandi [Gha94] re v ie we d the various generic process steps involved in the fabrication ofIC devices Ion implantation has been the primary source of introducing impurity atoms into silicon substrate. Unfortunately the ion implantation process causes extensive cr y stal damage and creates point defects. This damage is repaired during subsequent annealin g. The diffusion of dopants occurs through interaction with point defects. During the ann e al the point-defect concentrations reach their equilibrium values. However until the defect concentrations reach their equilibrium values the diffusion of dopants would b e a 1

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2 nonequilibrium phenomenon. One such nonequilibrium effect is transient enhanced diffusion (TED) [Fah89 Eag94]. If the implant doses are high enough extended defects such as dislocation loops and {311} s [Jon88 Jon95] can form during the annealing step In the fabrication of microelectronic devices various process steps cause stress to the substrate. Silicon oxide deposition and/or growth is one such process. Shallow Trench Isolation (STI) is the dominant isolation technology used today and the STI process may result in stress-induced dislocation loops in the silicon active area [Fah92]. Dislocation loops will increase the leakage current in devices when they are located at or near the device junction-especially in the depletion layer of a junction. Increased leakage current will cause device degradation [Ros93] and increased power consumption in logic and memory circuits Because of the prohibitive costs of manufacturing IC devices accurate simulation of these complex phenomena is a critical and fundamental component for IC technologists to develop new processes and devices. In order to have accurate simulation results accurate simulation models are needed In order to develop models some experimental data are needed. Once the model agrees with existing experimental data the model can be used to predict the results at other process conditions thereby avoiding continued costly experiments. Empirical models can be used to predict within the range in which it is calibrated and are therefore useful only under interpolation conditions. Physics-based models are more reliable because they also can be used under extrapolation conditions (as they rely on the inherent physics of the process phenomena ). If the physics behind a process step is understood well enough, the model will have a wider range of application.

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3 Because of the complexity of the processes involved we do not complet e l y understand all the relevant physics. Therefore process models typicall y use c e rtain assumptions and / or approximations Hence process modeling is a continuou s effort to develop new technologies as the shrinking device dimensions may in v alidate a ss umpti o n s used in old models. Tools such as Florida Object Oriented Process Simulator (FL OOP S) [Law98] with ALA GA TOR script language offer a great advantage to the end us e r in developing new models and technologies within a short time. Trade-offs must be mad e with respect to the accuracy of the model, CPU time and ease of use Although Molecular Dynamics (MD) codes offer more accuracy and physical insight they are computationally intensive and hence are not yet practical for developing new 10 1 ------------------------= Deep (retrograde) well 10 6 Mid-well 10 5 CMOS Applications Channel Halo (Lateral punch-thru 8 102L-L.U.WloL....IU..U.WL-.J.J.IJJ.IIIL....L.&.I.I.UIIL...L.U.U.IIIL-U.UWIL...U.Wlll-'-L.L&.M,1L-1-L.1.1,,WL..~.LW.W 10 9 1010 1011 1012 1013 1014 1015 1016 1017 10 1 8 10 19 Ion Dose (Atoms/cm 2 ) Figure 1-1. Range of ion implant energies and doses used in semiconductor processes

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4 technologies. Insight obtained from MD codes can be used in kinetic Monte Carlo simulations to verify fundamental mechanisms. Then this information is used to develop more accurate physical-based continuum process models. Validity of the physical models depends on the parameters that are physically meaningful. Although some parameters have an established set of values others must be derived from systematic experiments. Models with consistent parameters extracted from experiments are fundamental to developing future experiments and technologies 1.1 Ion-Implantation Damage and Defects Ion implantation is one of the most important steps in manufacturing very large scale integrated (VLSI) Si devices. The main advantages of ion implantation are introducing a desired impurity into a target material accurate dose control reproducibility of the impurity profiles, lower process temperatures and the ability to tailor the doping profile [Cha97]. Because of these advantages, ion implantation is used repeatedly at various process steps (threshold voltage control adjustment channel stop implantation source drain formation etc.). Figure 1-1 shows the range of ion implant energies and doses used in semiconductor processing. The detrimental effect of the ion implantation is the damage caused to the silicon substrate by incident ions. Two main stopping mechanisms are involved during implantation. They are nuclear stopping and electronic stopping. Nuclear stopping is the process of gradually retarding the motion of an implanted ion by collision with the target (Si) atoms. Electronic stopping is the process of retarding the motion of an implanted ion by interaction with the electron cloud of the target and the implanted ion (i.e., Electronic stopping is a dragging force). While electronic stopping causes no damage to the

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5 substrate nuclear stopping produces all the damage due to primary and secondary collisions of the incident ions into the silicon substrate [W 0186]. Nuclear colli s ion generates a large amount of point defects such as vacancies and interstitials To r e p a ir th e damage created by ion implantation post-implant annealing is required Upon annealin g, several types of extended defects may also be formed in addition to the point defect s. These extended defects are categorized into Types I II III IV and V [ J on8 8] F urther defects that are vacancy-type in nature are generally classified as intrinsic defects and those that are interstitial-type in nature are usually classified as extrinsic defects 1 1.1 Point Defects Point defects like vacancies and interstitials are localized defects. Vacanci e s interstitials interstitialcies and impurity atoms are incorporated during implantation Vacancies interstitials and interstitialcies are native point defects that exist in a pure crystal structure. A vacancy is an empty lattice site. An interstitial is an atom that r es id es in one of the interstices of the crystal lattice. A self-interstitial is an interstitial Si atom. An interstitialcy defect consists of two atoms configured about a single lattice site 1.1 2 Extended Defects As mentioned previously, during the implantation process the crystalline lattice of the semiconductor is damaged and many point defects are created. An annealing st e p is necessary to repair the damage and to activate the dopant. Depending on the implantation energy dose and annealing conditions various kinds of extended defects evolve These defects are categorized into five types as shown by Jones et al. [Jon88]

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.r ~ 1 8 '--" ,u "' 0 17 10 16 10 "t:l 15 10 14 10 13 10 0 6 No Extended Defects JO 40 60 Ion mass (amu) 80 Cnt1cal Dose for Amorpl11:z.at1 on D Categ01y I defects II Catego1y I I defects 100 lJO Figure 1-2. Criteria of extended defect generation [Par93, Jon88] 1.1.2.1 Category I damage 140 Catego1y I threshold dose Catego1y II threshold close This damage is called "subthreshold" damage and occurs when the implant damage is not sufficient to produce an amorphous layer. Category I defects form at the projected range of the implant. These defects are typically rod-like {311} defects and extrinsic dislocation loops that are precipitates of Si interstitial atoms. Type I defects are usually formed by light ions. Heavy ions can produce an amorphous layer if the implant dose exceeds the critical dose needed to form an amorphous layer. Therefore Type I defects are a strong function of the implant dose.

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7 1.1 2 2 Category II damage If the implant dose is sufficiently high an amorphous layer is formed. U pon po s implant anneal the amorphous region regrows very quickly into a perfect crystallin e structure through solid phase epitaxy (SPE) and Category II defects are formed at the original amorphous-crystalline interface. These defects are called End of Range (E OR ) defects and consist of both dislocation loops and { 311} s depending on the annealing temperature. Once the critical dose for amorphization is exceeded any increase in the dose has a minimal effect on the defect evolution. Therefore the density of these defects is not a strong dependence of the implant dose. Dislocation loops in this category can be categorized as faulted dislocation loops and perfect dislocation loops. The major criteria that distinguish Category I damage and Category II damage are the implant dose and implanted ion species mass (shown in Figure 1-2.) Details of these defects are discussed later. 1.1.2.3 Category III damage Imperfect regrowth of the amorphous layer is the main source of Category III defects. They are formed as "hairpin" dislocations microtwins and segregation defects Hairpin dislocations nucleate when misoriented microcrystalline regions are encountered at the amorphous-to-crystalline interface. These defects can be avoided. 1.1.2.4 Category IV damage Depending on the implant energy and implant dose buried amorphous la y er can be formed in the substrate. This buried amorphous layer results in a layer of defects called Category IV defects that are also called "clam-shell or "zipper defects These

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8 defects can be avoided by changing implant energy and dose to produce a surface amorphous layer instead of a buried amorphous layer. 1.1.2 5 Category V damage Solid solubility of a species in the substrate by ion implantation can be exceeded During the solid phase epitaxial growth of the amorphous layer all of the dopant within the amorphous layer is incorporated into the lattice sites. Further annealing causes precipitation and defects associated with precipitation form at the projected range of the dopant. The defects include both dislocation loops and precipitates 1.2 Dislocation Loops As long as the implantation dose is below the critical dose (Figure 1-2 ), dislocation loops are not formed. The most common defects seen in IC devices toda y are Type II defects because of to the high doses required to form highly activated shallow junctions. By controlling the energy of the implant the junction depths can be varied Therefore ion implantation is the primary way of forming shallow junctions. Light ions such as B are susceptible to channeling during implantation process. Channeling increases junction depth. Forming an amorphous layer in crystalline structure before forming the channel doping is a well known technique to prevent the channeling. Heavy ions do not channel as much as light ions. However amorphization is unavoidable in this case because of the heavy ion mass and high implant doses required. To repair the damage post-implant anneals are required. During the growth of the solid phase epitaxial growth of the amorphous layer extended defects form at the amorphous to crystalline interface. They are also known as end-of-range defects ranging from small clusters of a

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9 few atoms to { 311} s and dislocation loops. All these defects are e x trinsic in chara cte r. The defects have been studied in great details by various researchers [Ben97 CofO0 Mau94 Eag94 Pan96]. The EOR loops are of two distinctive types. One is the faulted Frank dislocation loop and the other is the perfect dislocation loop [Cri00]. The faulted loops lie on { 111 } planes and have a Burgers vector of (a/3)<111> perpendicular to the loop plane. The perfect dislocation loops also lie on { 111} planes and have a Burgers vector of (a/2)<110>. They are elongated along that particular <110> direction on their habit plan e. Evolution of these defects at various annealing temperatures and ambients has been widely studied [Gil99 Liu95]. The EOR defects grow in size and reduce their density at annealing temperatures below 900 C. This regime is referred to as the coarsening regime. The loops remain in the coarsening regime and the densities o f interstitials bound by the loops remain fairly constant. The larger loops grow at the expense of the smaller ones. This is called the Ostwald ripening process [Bon98]. If the annealing temperatures are above 900 C EOR loops become thermally unstable and start dissolving [Liu95]. These loops can be seen as reservoirs able to maintain a high supersaturation of free self-interstitials during their dissolution [Cla95]. This enhances the dopant diffusion through the formation of Si interstitial-dopant pairs. It is also shown that EOR dislocation loops act as a sink for interstitials during oxidization [Par94a Men93]. They can be used as point defect detectors or to reduce the oxidation-enhanced diffusion of boron in a buried layer because of the efficient interstitial capturing action of dislocation loops. The capture rate depends on the distance of the loop layer from the surface [Tso00].

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10 ~c ... .. .. I ,,,, ) 'II! .. I , Figure 1-3. Weak beam dark field images of dislocation loops and { 311} 1.2.1 Interaction between {311} 'sand Dislocation Loops Weak beam dark field images of dislocation loops are shown in Figure 1-3 along with { 311 } s. The { 311 } s are rodlike defects consisting of interstitials that grow along the < 11 O > direction in a { 311 } habit plane. It is shown that { 311 } rodlike defects have three stages of microstructural evolution: accumulation of point defects to form circular interstitial clusters growth of these circular clusters along <11 O> direction and dissolution into matrix [Pan97a, Pan97b]. The {311} defects dissolve very fast at high annealing temperatures (> 700C). As a result of dissolution interstitials are released and these are believed to be the primary source of the TED [Eag94] Interactions between { 311} defects and Type I and II dislocation loops were studied by Jones et al. [Jon95]. The formation of Type I loops does not result in complete trapping of interstitials released by { 311} defects. Growth of the Type II loops is greater than can be explained by { 311} dissolution.

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11 It has been shown qualitatively that {311} defects are the source of dislocation loops [Li98]. They studied the effects of {311} unfaulting into loops at 800 C throu g h in situ annealing after a non-amorphizing implant. They also suggested that TED w ill saturate with increasing implant dose in a system where {311 } defects are the primar y source of TED. 1 2 2 Effects of Dislocation Loops on Device Characteristics Electrical characteristics of silicon devices are effected by dislocation loops [Tam8 l]. Ross et al. [Ros93] measured the characteristics of Si Ge/Si p-n junction diodes b y introducing dislocations into these devices by heating in situ in the electron microscope. A simple generation-recombination process occurring at the dislocation cores does not explain the large amount of measured leakage current. The device degradation due to the introduction of dislocation loops is related to the creation of point defects and / or the diffusion impurities such as metals during the formation of the dislocation loops Significant decreases in free carrier mobility in bipolar transistors w as also reported because of the dislocation loops with the assumption that in n-type crystals the dislocation loops behave like a line of negative charge surrounded by a positi v e space charge that repels incident electrons [Fin79] Bull et al. [Bul78] reported that dislocation loops intersecting the emitter-base junction lead to low gains and high emitter-base leakage current in bipolar transistors. Collector-emitter leakage currents also correlate with dislocation loops that pass through the transistor from the emitter to collector. If the dislocation loop is decorated with metallic impurities it can be conductive enough to permit significant current flow between collector and emitter even when the base terminal is open [W 0186].

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12 Similar leakage currents are observed in metal oxide semiconductor (MOS) devices when dislocation loops lie across the device junction [Miy97]. Because device dimensions are shrinking with every new technology the probability of having dislocation loops decorated with metallic impurities across the junction is increasing and so is the leakage current. Reduction in the minority carrier lifetime is another problem imposed by dislocation loops. Carrier lifetimes are reduced by dislocation loops through the introduction of localized intermediate energy levels within the silicon bandgap. Reduced carrier lifetimes require MOS dynamic RAMs to be refreshed more often. At the same time reduced carrier life can be helpful to suppress latch-up by reducing the current gain of the parasitic transistor which is located away from the active device [Wol86]. Another effect of dislocation loops on device characteristics comes from their ability to interact with point defects. Dislocation loops grow by capturing interstitials [Hua93] and dissolve by emitting interstitials [Liu95]. They are very efficient sinks for interstitials [Men93] They change the concentration of point defects around the loop layer. Because most of the dopant atoms pair with point defects [Fah89] and diffuse changing point defect concentration through point-defect-loop-interaction will change the final doping profile. This will affect the junction depth and final electrical characteristics of the device. Dislocation loops exist with a significant stress field surrounding them in Si and the stress can alter diffusion kinetics of the dopants [Par95]. This might be significant enough to change the doping profile and the device characteristics. Thus dislocation loops indirectly affect the device characteristic Many sources of stress exist in Si and they are discussed in the next section.

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13 t F 1 1 / n R Fl I ' I I I !:i. A ~F 3 / Figure 1-4. An arbitrary body subject to external forces 1.3 Stress and Strain To understand stress sources in silicon IC processing some basic concepts of the mechanical stress and strain should be known. If a body is subject to external forces a system of internal forces is developed. (Figure 1-4 ) [Mov80]. These internal forces tend to separate and. bring closer together the material particles that make up the body Assuming an imaginary plane cuts the body into two parts, internal forces are transmitted from one part of the body to the other through this imaginary plane. The free body diagram of the lower part of the body is also shown in Figure 1-4. The forces F; F; and F; are held in equilibrium by the action of an internal system of forces This system of internal forces can be represented by a single resulting force R which may be decomposed into a component ~, perpendicular to the plane and known as the normal force, and a component F; parallel to the plane known as the shear force. If the area of the imaginary plane is A, then / A is called normal stress and F; I A is called shear

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14 stress. Because these stresses are nonuniformly distributed through the area, normal stress and shear stress should be defined using a differential area of M and the forces ~ and ~ Then the normal stress a and the shear stress -r are given by 1 Af' CJ= Im __ n -r = lim M', (1.1) A three-dimensional stress element is shown in Figure 1-5. Normal stress vectors have a single subscript and shear stress vectors have a double subscript. The first subscript of the stress vector indicates the plane on which stress is acting and the second subscript indicates its direction. There are three normal stress components and nine shear stress components. If the stress element is in equilibrium, shear stress vectors become dy r t. I !"t, : lxy x plane ). t~ t~)--. CT X O'z I ,;.---------------------- x / ____ ,' ,. , ,, ," Figure 1-5. Components of stress in a stress element

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15 'r xy = 'r yx 'r xz = -r zx and 'r yz = 'r zy By convention, a normal stress is positive if it points in the direction of the outward normal plane. A positive normal stress produces tension and negative normal stress produces compression The stress components shown in Figure 15 are all positive. When a nonrigid body is subject to stress it goes through deformation and distortion. Thus any line element in the body goes through deformation if its length increases or decreases. Then, the normal strain, 11 is the change in length per unit length of the element. The normal strain at a point in the body is represented as 1 8 d8 = 1m-=11 L dL (1.2) where 8 and L are the initial length of the line element and its deformation respectively. ,:c \ \ \ \ \ \ \ Figure 1-6. Shear strain t Di~orted shape \ 't ________ 't If the distortion in a stress element due to shear stresses does not involve a change in the length but a change in the shape as shown in Figure 1-6, then the shear strain is defined as the change in angle between two originally mutually perpendicular edges. Thus, the shear stress is y =


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16 The relation between the normal strain and stress for a particular material is described by Hooke s law as a=E (1 3) where E represents a unique property for a given material and is known as Young s modulus of elasticity. In a similar way the relation between the shear stress and strain is expressed mathematically as (1.4 ) G represents a unique property for a given material and is called the modulus of rigidity or the modulus of elasticity in shear. The relations given between the normal stress and normal strain or the shear stress and shear strain are more complex in nature. More complex nonlinear models are usually used in process simulators to calculate the process induced mechanical stress ( for example FLOOPS treats Si0 2 as a nonlinear viscoelastic material) [Cea96]. 1.3.1 Stress and Strain Sources in Silicon IC Processing The IC processing technology is a complex process requiring embedding butting and overlaying of a large variety of materials of different elastic and thermal properties. Because these materials are subject to various thermal cycles during the IC processing stress develops. Stress sources can be classified into three main categories. 1.3.1.1 Film Stress and Film Edge-Induced Stress Surface films are widely used for masking, passivation, dielectric insulation and electrical conduction in IC processing. The materials commonly used for this purpose are silicon nitride, poly crystalline silicon and silicon oxide. Stress is inherently present in these films. While stress due to thermal expansion mismatch between the films and their

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17 substrates is called extrinsic stress, stress caused by the film growth process is called intrinsic stress [Hu91]. The extrinsic stress can be tensile or compressive based on thermal expansion coefficients. For example, Si0 2 grown or deposited on silicon at high temperatures will have a compressive component as a part of its total stress. There will not be a shear stress component due to extrinsic stress. Intrinsic stress in films is due to the growth mechanism of the material during the process and depends on thickness, deposition rate, deposition temperature, ambient pressure, method of film preparation and type of substrate used. A tensile stress in the film bends the substrate that makes the substrate concave, while a compressive stress makes the substrate convex. Measuring the amount of bending in the substrate is a common way of finding intrinsic stress in films. Most of the films (poly Si, Si 3 N 4 ) exhibit tensile intrinsic stress. On the other hand silicides such as TiSh, and CoSh, sputtered oxides, chemical vapor deposited oxides and ion implanted polycristalline silicon exhibit compressive intrinsic stress. Continuous films produce only very low level stresses in the substrate because the substrate is thicker than the films. Problems occur when the surface films are not planar or they contain discontinuities such as window edges for masking purposes. These discontinuities are the source of the large localized stresses in silicon substrates. Stress relaxation through the use of composite films can be quite profound (such as the Si02-Si3 N4 pad). The pad oxide allows a greater relaxation of the SbN 4 stress because the oxide pad itself is discontinuous and the oxide pad is less than half as rigid as the silicon substrate. More importantly, the oxide is capable of undergoing viscoelastic deformation

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18 [Hu91]. Film edge-induced stress effects on the generation of dislocation were reported before [Iso85] and details of this subject are discussed later. 1 3 1.2 Stress from Oxidation and Device-Isolation Processes Oxidation is one of the fundamental process steps ofIC processing technology. During the thermal oxidation of silicon 1 volume of silicon is consumed to form 2 25 volumes of Si 02 In a planar oxidation a newly formed oxide layer will push the old oxide layer perpendicular to the interface and the normal stress component in the direction perpendicular to the film plane becomes zero The film stress becomes uniform everywhere and does not cause a problem In the oxidation of nonplanar surface the volume expansion resulting from converting silicon to Si0 2 cannot be accommodated by simple vertical thickness increase as in planar oxidation. On a concave surface the neighboring volume elements grow into each other generating a compressive stress in the material. On a convex surface the lateral stress would become more tensile as the neighboring elements grow away from each other. Local oxidation of silicon (LOCOS) was the primary source of isolating devices from each other for a long time. The LOCOS was one of the isolation techniques where compressive and tensile stresses would build up during the oxidation Trench isolation techniques took the place of LOCOS in modem ICs to obtain high chip density. A major problem with these trench structures is that they cause a significant amount of mechanical stress in silicon substrate [Chi91] The sources of trench-induced stress are that the thermal oxidation of nonplanar surface of the trench can produce enormous stress that a

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19 mismatch of thermal expansion coefficients exists between the trench fill and s ili c on substrate ; and that intrinsic stress exists in the trench fill material [Hu90]. 1.3.1.3 Dopant-Induced Stress Different types of dopants are introduced into the silicon substrate during IC processing. Every dopant species has a different size of atom. Lattice mismatch can occur if the incorporation of highly concentrated solute dopant atoms differs in size from the silicon atoms. While dopants such as Boron and Phosphorus cause lattice contraction Germanium in a substitutional site results in lattice expansion (i.e ., the silicon substrate lattice constant decrease or increase linearly with the size and concentration of dopant atoms). This generates localized strain in the crystal because of each dopant atom and can add up to significant strain values [Rue99]. Figure 1-7 represents the lattice deformation 2D Lattice 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Ge 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Figure 17. Two dimensional lattice deformation due to a dopant atom in Si due to a substitutional germanium atom. Because germanium atom is larger than a Si atom germanium will induce a compressive strain in the substrate It should be

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20 obvious that dopants can be used to reduce the strain in the substrate but the idea of strain compensation will work only if the compensating atomic species do not interact. It is therefore not possible to use a donor and acceptor as a compensating species because of the probability of ionic bonding. Dislocation loops are also a source of stress in silicon substrates because they change the mechanical state of the substrate. Stress due to loops can be calculated using the same techniques used to calculate dopant-induced stress. Details of this are discussed in the next chapter. 1.4 Stress-Induced Dislocation Loops As mentioned previously, stresses in silicon substrate build up at various stages of IC processing Many problems of defective devices can be traced to these stresses. If the stress is high enough, such that it is beyond the yielding point of the substrate the substrate will yield by generating dislocation loops. Dislocation loop generation at the nitride edge has been known for a while [Tam81]. If a pad oxide is inserted between the nitride film and the substrate the density of dislocation loops decreases due to stress reduction in the substrate (Section 1.3 .1.1 ). Although thicker pad oxide is more effective for edge stress reduction [Iso85], it makes the nitride a less effective diffusion mask. The nitride edge also generates dislocations indirectly. Excess self-interstitials generated by the oxidation or the ion implantation drift to the nitride edge, and help nucleate dislocation loops there. Point defects interact with the stress vectors [Hu91]. Hu's [Hu78] experiment showed the interaction between the point defects and a nitride edge. Point defects generated by ion implantation formed

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21 dislocation loops around the nitride edge. No dislocation loops were ob s erv e d in th e regions masked out from the ion implantation Figure 1-8 shows a typical simplified cross-section of a modem n-channel MO S transistor. First Shallow Trench Isolation (STI) process is performed by growin g a thin oxide along the trench walls and by filling the trench with CVD oxide. Then sourc e and drain regions are doped by high dose arsenic implant after the gate oxide is grown and th e polysilicon gate material is deposited. These steps are followed by an annealing c y cle for activating the source and drain region. During the annealing cycle a layer of dislocation loops is formed around the source/drain-to-substrate junctions. Stresses from the STI process play an important role in the generation of dislocation loops [Fah92 Del96]. Hu [Hu91] states that stresses from STI structures interacts with the point defects the same way as the film-edge-induced stresses interact with them. Fahey, et al.. [Fah92] showed that reducing the stress in the STI process would reduce the dislocation density and e v en eliminate them. It is concluded that raising the temperature of the oxidation or changes in Polysilicon gate Si02 Antipunch implant p-type substrate Figure 1-8. Cross section of a modem day n type MOS transistor.

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22 the masking nitride thickness or using different fill materials with less intrinsic stresses would reduce the amount of stress. Other researchers [Chi9 l Sti93, Hu90] also provided ways of calculating stresses from STI structure in the substrate and gave an insight to how to reduce them for example comer rounding at the top and bottom of the trench reduces stress. 1.5 Goals As MOS devices are scaled down to the sub-micron regime new reliability problems surface in each generation. Many of these problems can be traced back to stresses that develop at various stages of the IC processing. One of the most important defects observed is the stress-induced-dislocation-loops. Dislocation loops have been reported at various stages ofIC processing It has also been known that they degrade device performance by increasing leakage current if they lie across the junction Since device dimensions are shrinking with every new technology the probability of having dislocation loops across the junction is increasing and so is the leakage current. Stresses from isolation trenches are also a major factor contributing to the dislocation loop formation. One of the goals of this research is to investigate and model the effects of process induced mechanical stresses on the dislocation loop formation. A model that can predict the density and the location of dislocation as well as the mechanical stress effects on them is a valuable asset for device and process engineers. Such a model would help them to change and adjust their device structures and process conditions without having to build costly test lots. Based on the understanding of point defects and extended defects interaction, a physics-based loop evolution model is developed Relevant physics and

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23 assumptions behind the model are explained. Experimental verification of the model has been performed. This model takes into account both the nucleation and the evolution of the dislocation loops. These concepts and the model development will be explained in detail in the subsequent chapters. Comparison between the experimental data and simulation results shows that the model can correctly predict the experimental observations. Although stress due to dislocation loops is accounted in the model effects of mechanical stress from the other sources are yet to be investigated. 1.6 Organization The thesis organized as follows: Chapter 2 describes a model for the evolution of dislocation loops during annealing in inert or oxidizing ambient. In Chapter 3 the model is extended to account for the nucleation of dislocation loops. The model assumes that all the dislocation loops come from {311} unfaulting. The statistical nature of the model is also used to predict threading dislocation loop density. Chapter 4 explains the experimental procedure that was used to calibrate the loop nucleation and evolution. Chapter 5 investigates the behavior of the model under different implant and annealing conditions. Chapter 6 takes the model one more step ahead by incorporating stress effects into the model. Finally, conclusions and suggestions for future work are discussed in Chapter 7.

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CHAPTER2 MODELING THE EVOLUTION OF DISLOCATION LOOPS FOR VARIOUS PROCESS CONDITIONS High dose ion implantation is one of many steps used in process technologies today. If the dose is high enough, it results in the formation of an amorphous layer of Si and produces large amount of extended defects below the amorphous to crystalline (ale) interface. In order to activate dopants and repair the implantation damage annealing is required. Upon annealing, the amorphous region re-grows through solid phase epitaxy (SPE) with end-of-range (EOR) dislocation loops formed at the (ale) interface. The effects of dislocation loops on device characteristics are explained in Chapter 1 Section 1.2.2. During the last few years, a great deal of work has been carried out in order to better describe the evolution of dislocation loops. The coarsening of EOR defects and the effects of the surface on the EOR defects were investigated by Giles et al. [Gil99]. The growth and shrinkage of a single loop or a periodic array of loops due to the capture and emission of point defects was modeled by Borucki [Bor92]. Analytic expressions were derived by Dunham [Dun93] for the growth rate of the disk shaped extended defects that maintain their thickness as they grow. In the models summarized above, it is not possible to obtain the distribution of loops with respect to their radius. Park et al. [Par94b] developed a statistically based model for the growth of loops in oxidizing ambient where the interstitials injected from the growing oxide contribute to the growth of the large loops. Assuming an asymmetric triangular density distribution of periodically circular 24

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25 dislocation loops, Park's model reflected the nonuniform morphology of the loops a s observed in transmission electron microscopy (TEM) experiments. The pressure field from the dislocation loops is incorporated into the point defect equations. Chaudhry e t al. [Cha 95] modified Park s model to represent loop-to-loop interactions Thi s loop t o loop interactions can be described by the Ostwald ripening process during annealing In the Ostwald ripening process, the total number of interstitials bounded to dislocation loops remains fairly constant with time while density of dislocation loops decreases ( i.e Bigger loops grow at the expense of smaller ones) They correctly simulated the variation and size distribution of the loops as a function of anneal time and temperature However both of these models made different assumptions to model the growth and coarsening of dislocation loops under oxidizing and inert-ambient annealing conditions. In this chapter a new statistical point defect based loop evolution model will be shown. The model quantitatively analyses the size and density of dislocation loops as a function of annealing time, temperature and conditions. It uses the same set of parameters to capture the loop behavior under oxidizing or inert annealing conditions. 2.1 Modeling Dislocation Loop Evolution In order to model the evolution of dislocation loops accurately and efficiently some assumptions need to be made. It is assumed that dislocation loop density and average radius of loops follow a log normal distribution function. Therefore a single set of differential equations with the same set of parameters has been used to model the dislocation loop evolution under both oxidizing and inert ambients. It is also assumed that pressure from loops can be calculated using dopant-induced-stress techniques described earlier.

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26 2 1.1 Log Normal Distribution Function It is known through the transmission electron microscopy (TEM) analysis that dislocation loops do not show a uniform radius and density distribution. Thus a model that encapsulates the distribution of the loop sizes via a statistical function is needed. Park et al. [Par94b ] used an asymmetric triangular distribution in the differential equations used in their model. However the asymmetric triangular distribution function is not a continuous function. Therefore the discontinuities in the function 8 10 9 Data 7 10 9 LogNormal ,,....._ 6 10 9 ";' E u 5 10 9 "-' Cll C. 0 0 4 10 9 ..J ..... 0 >--. 3 10 9 "'= Cll = (I.) Cl 2 10 9 1 10 9 0 0 V) 0 V) 0 0 0 0 0 0 0 0 0 0 0 0 V) 0 l) 0 N V) \C) r--00 0 M '
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27 the loop size because it is a continuous function and matches the T E M data Th e lo g normal distribution function is a function in which the logarithm of variables ha s a normal distribution. The log normal probability density function f 0 ( R ), is given as (2 .1 ) where D a u ( cm3 ) is the total density of dislocation loops R ( cm) is the loop radius S and M are the deviation and the mean of the log normal distribution. S and M can be derived from the Gaussian parameters, mean ( and standard deviation (CJ) as follows ( 2 2 ) Figure 2-1 shows the statistical distribution of loops radius extracted from the TEM measurements [Men93] under 900 C dry oxidation condition along with the log normal density distribution function. The Log normal distribution function follows the experimental results quite closely. 2.1.2 Density of Dislocation Loops Dislocation loops are two-dimensional precipitates inserted between two consecutive { 111} planes The loop distribution can be modeled in the form of log normal distribution function The model assumes that all the loops are circular and th e ir radius and density follow a log normal distribution function It is also assumed that dislocation loops go through two phases during the thermal annealing cycle First { 311 } 's nucleate and unfault to dislocation loops by consuming a large part of the interstitials. Subsequently Ostwald ripening process dominates. As explained above m the Ostwald ripening process, the total number of interstitials bounded to dislocation loops remains fairly constant with time while density of dislocation loops decreases ( i .e.

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28 Bigger loops grow at the expense of smaller ones). In this section only the evolution of the dislocation loops during the thermal annealing cycle will be considered. The nucleation of dislocation loops phase will be discussed in the next chapter. Since dislocation loops lie on { 111} plane and are circular with a radius of R the number of interstitials bounded to these dislocation loops can be easily calculated as ( 2 3 ) where Dau(R) is the density of dislocation loops with a radius of R and n a (1.5x10 1 5 cm2 ) is the atomic density of silicon atoms on the { 111} plane. N a 11 (R) represents the total number of interstitials bounded by these dislocation loops Time derivative of the Equation (2.3) will give the change in the density of dislocation loops with time. dDau(R) _1 __ dN_a_u(_R_) dt nR ; n a dt 2D a u(R) dR R dt (2.4 ) The first term represents the nucleation rate of dislocation loops N~ ~ 1 R 0 is assumed to be the initial radius of the nucleated loop The second term represents the Ostwald ripening process. Bonafos et al. [Bon98], worked extensively on the Ostwald ripening of end of range defects in silicon and calculated the growth rate ( dR I dt) of dislocation loops as follows dR KR -=dt R (2.5) The constant KR is the coarsening rate of dislocation loops and used as a fitting parameter in the simulations. If Equation (2.5) is substituted in Equation (2.4) the change in the density of dislocation loops with time becomes (2.6)

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29 As it can be seen from Equation (2 6) the density of dislocation loops with small e r radii decreases faster than those with larger radii Thus smaller loops dissolve faster b y emitting interstitials. These interstitials are absorbed by the bigger loops Hence bi gge r loops grow at the expense of smaller ones. Physically this means that it is energeticall y more favorable for a larger loop to increase in size and a smaller loop to dissolve 2.1.4 Coarsening and Dissolution of the Dislocation Loops Dislocation loops grow in size and reduce their density at annealing temperatur es below 900 C. This regime is referred to as the coarsening regime. If the annealing temperature is over 900 dislocation loops becomes thermally unstable and start dissolving by releasing interstitials. The growth rate of dislocation loops is higher under oxidizing conditions than under inert conditions since oxidation injects interstitials to the bulk. The interaction between the loops and point defects is primarily reflected on the equilibrium concentration of point defects around the dislocation loop layer and the pressure dependent concentrations of interstitials and vacancies are calculated as [Bor92] c; (P) = c; (O)exp(-P/::,. kT c : (P) = c:(O)exp(P!::,.V v ) kT (2. 7 ) (2. 8 ) where P is the pressure I::,. and I::,. V v are the elastic volume expansions susceptible to the external pressure effect on interstitial and vacancy. k and Tare the Boltzman s constant and absolute temperature respectively ." 0" denotes the equilibrium concentration in the absence of external pressure. If the lattice is under compressi v e pressure the equilibrium interstitial concentration will be less than its nominal v alue

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30 c; (0). If the lattice is under tensile pressure, then, the equilibrium concentration of interstitials will be greater than its nominal value. The pressure in the substrate due to dislocation loops can be calculated using dopant induced stress-calculation techniques (Section 1.3 .1.3). The silicon lattice constant will vary as a function of interstitials bounded by dislocation loops. --N s c..> Cl) 0.) C ;;,,-. ""d "--' 0.) :::1 Cl) Cl) 0.) ;.... 1.4 10 9 1.2 10 9 1 10 9 8 10 8 6 10 8 410 8 2 10 8 0 -2 10 8 0 0.1 Dislocation Loop Core 0.2 Depth() 0.3 0.4 Figure 2-2. Pressure in silicon due to the dislocation loops 0.5 -0.015A oflattice expansion per percentage of interstitials bounded by dislocation loops in Si is obtained from simulation results. Using this figure, the strain is calculated as follows [Rue99] (2.9)

PAGE 47

31 where /)..a is the change in the silicon lattice constant ( a s; =5.4295A ) and N s; i s th e density of Si atoms (5.02xl0 22 cm-3). After using the stress-strain relations described in Chapter 1 Section 1.3 the pressure is easily calculated. (2 10 ) Figure 2-2 shows the simulated pressure in the substrate due to a dislocation loop la y er located at a depth of 1500A. The pressure peaks at the dislocation loop layer and decreases rapidly away from it. The pressure is compressive inside the dislocation loops The absence of tensile pressure at the edge of the dislocation loop layer is due to the dopant-induced stress calculation technique. Since the pressure is a linear function of the interstitial concentration inside the loops and the concentration never goes to a negative value, the tensile pressure due to loops is not calculated. The magnitude of the tensile pressure at the loop edge is always a few times less than the magnitude of the compressive pressure inside the loop and can therefore be neglected. Growth and shrinkage of dislocation loops are determined by their interaction with point defects at the loop boundaries. The effective equilibrium concentration of interstitials ( C 1 b) and vacancies ( Cvb) at the loop boundaries are given by Borucki [Bor92] as ( 2.11 ) (2 .1 2) where gb c is a geometric factor (=0.7). M 1 is the change in the defect formation en e r gy

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32 due to the self-force of a dislocation loop during the emission and absorption process at its edge and is given by Gavazza et al. [Gav76] as M = bfJ. [ln(8R)2v-1] 1 4n(l-v)R r e 4v-4 (2.13 ) where is the shear modulus b is the magnitude of the Burgers vector of the loop Q is the atomic volume of silicon r e is the core radius of the loop v is the Poisson s ratio and R is the radius of the dislocation loop. The model based on the log normal distribution represents the loop distribution change in agreement with the experimental observations as seen in Figure 2-1. The capture and emission rate of interstitials by the dislocation loops can be expressed in terms of the rates of emission and absorption of point defects at the loop layer boundaries modulated by a log normal distribution function. The rate also depends on the unfaulting rate of {311} 's during the nucleation phase ( N Z~; 1 ) and can be expressed as where K 1 i is the constant of a reaction between the interstitials and the dislocation loop assemble K v i is a similar constant for vacancies K 1 L and K v L are the function of the loop radius and the diffusivity of interstitials and vacancies respectively. They are used as calibration parameters during the simulations. C 1 and Cv are the concentration of interstitials and vacancies. Details of the unfaulting term, NZ~ ; 1 will be discussed in the next chapter. It is apparent that if the concentration of interstitials at the loop boundaries

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33 is greater than the effective equilibrium concentration of interstitials at the loop boundaries, loops will absorb interstitials. If the reverse is true then, the loops will emit interstitials. Modulating the emission and absorption rate by a log normal distribution function allows us to include the effects of all dislocation loops in the loop layer. Total number of interstitials bounded by all the loops in the loop layer is given as 00 Nall= f nanR 2 DaufD(R)dR (2.15) o + (2 16) Since the experiments for the evolution of loops usually focuses on the average radius of the loop distribution, the loop radius R in Equation (2.6) and (2.14) can be substituted with an average loop radius RP. If the normal distribution mean() is assumed to be the average radius ( RP) of the loop distribution, log-normal-deviation ( S) and log-normal-mean ( M) can be written by combining Equations (2.2) and (2.16) (2.17) (2.18) The relation between a and RP can be extracted statistically from various TEM data [Par93, Cha95, Ram98] as an analytic function of RP (cm) as follows (2.19) Since the concentrations of interstitials and vacancies around the loop layer are affected (Equation (2.14) ), the interstitial and vacancy continuity equation needs to be

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34 modified by adding a new flux due to the local variation of the interaction energy as in Borucki [Bor92]. (2.20) at loop layer boundaries (2.21) at loop layer boundaries KR is the bulk combination rate. The reaction rate now includes the pressure term as well. The flux due to loop to interstitial/vacancy interaction is the same as the ones in Equation (2.14). Similarly, {311} equations must be modified by adding nucleation terms. ac311 = D31/C1 C311Eq) d( 'r31 I NNall rate (2.22) (2.23) C 311 Eq is the equilibrium concentrations of {311} 's. r311 is the {311} time constant. 2.2 Experimental and Simulation Results to Calibrate the Model The model for the evolution of dislocation loops is implemented in FLOOPS. Equation (2.6) is slightly modified as follows: dDa/1 = NDall l 2Dall K dt rate ( C / C + 10) R 2 R I lb p (2.24) The term ( 1 /( C 1 I C 1 b + l 0)) allows the Ostwald ripening term to be small during the nucleation phase (i.e. (C 1 I C 1 b) >> 10) and is arbitrarily chosen. Its function will be clear in the next chapter. Since we are only interested in the evolution of dislocation loops for

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35 now, N~~: 1 and N:a~: 1 are set to zero. Oxidation experiments followed by inert ambient annealing experiments are used to calibrate the model. 2.2.1 Simulation of the Evolution of Loops during Oxidation Meng, et al. [Men93], investigated the interaction between oxidation induced point defects and dislocation loops. First, they implanted silicon wafers with st ions at z 1.4 10 15 Cl) 0.. 0 ..s 1.2 10 15 "'O Cl) "'O _g 1 10 15 Cl) ] ."t:: -+-' Cl) 1-, Cl) -+-' .5 0 8 10 14 Oxidation 900C -2 Data 2e15cm Data 5el 5cm2 8 Simulation 2el5cm2 Simulation Se l 5cm2 4 1 0 14 '----'----'--_,___'------'------'--_,___'---'------'-----'-----J-----'--'-----'-----J '--'--'------'-----J-----'---'------'-----J'----' 0 1 2 3 4 5 Time (h) Figure 2-3 Density of the interstitials bounded by dislocation loops as a function of oxidation time and simulation in the two different cases of Si implant dose 2xl0 15 and 5xl0 15 cm2

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36 50 keV and varied the implant doses from 2xl0 15 cm2 to 5xl0 15 cm2 Then they annealed their samples at 900 C for times between 30 minutes and 4 hours in a dry oxygen ambient in a furnace.The average loop radius loop density and total number of interstitials bounded by the loops were measured These experimental values are used to calibrate the loop evolution model developed in this work. Figure 2-3 shows the simulation results and experimental data on the temporal Oxidation 900C 3 5 10 10 Data 2el5cm -2 Data 5el5cm 2 3 10 10 0 Simulation 2e 15cm -2 Simulation Se 15cm -2 E 2.5 10 10 co 0 (/) 2 10 10 C. 0 0 _J 0 1.5 1010
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37 change in the number of interstitials bounded by dislocation loops per unit area during the oxidation at 900 C for two different cases of Si implant doses (2xl0 15 cm 2 and 5xl0 15 cm 2 ). As can be inferred from the figure, both the simulations and experiment suggest that the dislocation loops capture interstitials injected into the bulk during oxidation. The variation of the dislocation loop density with time for two different implant Oxidation 900C 700 D aia 2e 15cm Data 5el5cm -2 600 0 -2 Simulation 2e 15cm ,-.., -2 Simulation Se 15cm ..._.., 0. 500 en ;:j ro 400 0.. 0 0 V b.O 300 ro I-< V >
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38 doses is shown in Figure 2-4. It can be seen that the loop density decreases with time. Although simulation results and experimental data is in good agreement at short annealing times there are some discrepancies at longer annealing times. Non-uniformity of loop size and shape can be seen at longer annealing times due to the formation of loop networks (i.e. noncircular loops). Statistical interpretation of TEM pictures becomes more complex Since the model is derived assuming that all the loops are circular the accuracy of the model will decrease with increasing density of the noncircular loops at rn 0.. 0 ..s 61014 "'O 0 "'O 0 .CJ rn 4 1014 ] .<;::: rn 0 .s 2 10 14 0 .CJ 0 0 200 Annealing in Inert Ambient Data 700 C 0 Simulation 700 C Data 800C Simulation 800C Data 900C 0 Simulation 900 C .A. Data l000C -&-Simulation 1000 C 400 600 800 1000 Time (minutes) Figure 2-6. Variation in total number of interstitials bounded by the loops as a function of anneal time at different temperatures.

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39 the longer annealing times. The data point not shown at 900 c, 4 hours corresponds to this case. The average radius of dislocation loops during the oxidation increases with time as shown in Figure 2-5 Since the data show very little difference in the initial value of the average loop radius between the two silicon implant conditions simulation and data show that the loop size will increase at almost the same rate during oxidation. Some Annealing in Inert Ambient 81011 71011 0 0 Simulation 700 C Data 700 C Data 800C Simulation 800 C 6 1011 E Data 900C 0 Simulation 900C A 0 Data 1000 C Simulation 1000 C C\1 51011 0 (/) a. 0 0 4 10 11 _J 0 :!' 3 10 11 en C: Q) 0 C\1 2 10 11 0 I11011 0 0 200 400 600 800 1000 Time (minutes) Figure 27 Variation in total loop density as a function of anneal time at different temperatures.

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40 discrepancy between data and the simulation results are evident at the larger annealing times due to the non-circularity of the dislocation loops as explained above 2 2.2 Simulation of Loop Evolution during Annealing in Inert Ambient A plan view TEM study of the distribution, geometry and time dependent anneal behavior of the dislocation loops induced by lxl0 1 5 cm2 50 keV Si+ implantation into silicon was presented by [Liu95]. After implantation they capped their samples with 6000 A SiO2 to limit the oxidation in inert ambient. Then samples are annealed in nitrogen at 700 800 900 and 1000 C for times of 15 minutes 30 minutes 1 hours 2 hours 4 hours and 16 hours at each temperature Their experimental results seen in the figures are used to calibrate the loop evolution model under inert annealing conditions Figure 2-6 represents the change in total number of interstitials ( N a u) bounded by dislocation loops Simulation results are plotted along with the experimental values. It is seen that N a u is fairly constant below the 900 C annealing temperature. If the annealing temperatures increases above 900 C, loops start dissolving. Simulation results are within 20% error margins of the measured data. Variation in total loop density with time at different annealing times and temperatures is shown in Figure 27 The loop density decreases with time. If the time is kept constant it decreases as the temperature increases. This is the result of the loop coarsening process during which the large loops grow at the expense of smaller ones (Ostwald ripening) At higher annealing temperatures loops enter the dissolution regime. Figure 2-8 shows the simulations that agree with the experimental observation that the average loop radius increases with time upon annealing in an inert ambient. As

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41 seen from the experimental data and simulations the growth rate of the loop s is proportional to the annealing temperature The average loop radius increases with the annealing time The increase is very small at the low temperatures but it is higher for higher annealing temperatures. 500 400 300 200 100 0 0 200 Annealing in Inert Ambient Data 700C O Simulation 700 C Data 800 C D Simulation 800 C Data 900C O Simulation 900 C Data 1000C -{s----Simulation 1000 C 400 600 800 1000 Time (minutes) Figure 2-8. Experimental and simulated average loop radius as a function of annealing time at different temperatures.

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42 2.3 Experimental and Simulation Results to Verify the Model After calibrating the loop model with the same fitting parameters for oxidation and inert anneal data the model is verified by comparing simulation results with others researchers data [Lan97 Ram98]. Inert Ambient Annealing at 900C 5 1014 ,-r --, T",,---,--,-----T7------,----,---,--r---r7r-----------...,., z 4 5 10 14 en 0.. 0 ..s >.. ..0 "O "O 4 10 14 0 3.5 1014 ..0 2 10 1 4 0 20 40 Data l000A Data 1800 A Data 2600A ---0Simulation 1 000A D Simulation 1800A 6 Simulation 2600A 60 80 100 120 140 Time (minutes) Figure 2-9. Simulation and experimental results for the loss of interstitials with time at 900 C. 2.3.1 Simulation of Loop Dissolution as a Function of Loop Depth Raman [Ram99] investigated the effect of surface proximity on the dissolution of end of range dislocation (EOR) loops in silicon. First, they implanted st into silicon at

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43 30 keV and 120 keV and a dose of lxl0 15 cm2 to produce EOR dislocation loops. Th e initial loop depth was 2600 A following a 30 minutes furnace anneal at 850 C. econd chemical mechanical polishing (CMP) technique was used to vary to loop depth to 1800 ,--.,. 5 10 14 s u '-' ...... ...... 4.5 10 14 c,::j z r:n 0.. 0 41014 .Q Inert Ambient Annealing at 1000C D ata 1000A Data 1800A Data 2600A -0Simulation 1 OOOA D Simulation 1800A 6 Simulation 2600A ;>.. .D ""O 3.5 10 14 Q) ""O 0 .D 3 10 14 r:n ...... -~ .-<;::: .... r:n 2.5 10 14 1-o Q) .... s 4--1 0 2 10 14 1-o Q) .D 1.5 10 14 s:: .... 0 0 5 10 15 20 25 30 35 Time (minutes) Figure 2-10. Simulation and experimental results for the loss of interstitials with time at 1000 C. A and 1000 A. Third, samples are annealed in an inert ambient at 900 C for 30 minutes and 120 minutes and at 1000 C for 15 minutes and 30 minutes. Loops are expected to be in coarsening/dissolution mode at 900 C and in dissolution mode at 1000 C. Their experimental results are used to verify the accuracy of the model.

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44 Figure 2-9 shows the loss of interstitials bounded by dislocation loops as a function of annealing time for the three different loop depths. As the loop layer gets closer to the surface the rate of loss of interstitials from the dislocation loops increases due to surface recombination. The data shows that fewer interstitials are lost after the initial 30 minute anneal. Although there are some discrepancies between the data and the simulation results, simulations predicts the same trends seen in the data. Similar behaviors can be observed for the 1000 C anneal (Figure 2-10 ). In this case, the rate of loss of interstitials decreases after the initial 15 minutes of anneal time. Simulation agrees with these results. 2.3 .2 Effects of Dislocation Loops on Boron Diffusion This model is used to study the effects of dislocation loops on boron diffusion as well. Simulation results will also verify that dislocation loops are very effective at capturing interstitials. Experimental details are explained in [Lan97] and can be summarized as follows: Boron doping superlattices (DSLs) were grown in silicon. A series ofS/ implants of 30 and 112 keV at a dose of lx10 15 cm2 was carried out to place the amorphous to crystalline interface between the first and second doping spikes. The dose rates of implants are varied. Post implantation anneals were done in a rapid thermal annealing furnace at 800 C for 5 seconds and 3 minutes. It is shown that the implantation dose rate affects the interstitial release from EOR implant damage region in silicon ( e.g. loop density changes). Therefore, the diffusion enhancement of boron changes. Figure 211 is from [Lan97] and shows the secondary ion mass spectrometry (SIMS) profiles of boron spikes after s/ implantation at different dose rates and annealing at 800 C for 3

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45 mi nu tes As the dose rate increases (loop density changes) the amount of interstitial flu x into the r egrown regio n i n creases as we l l. The simulation results of boron profiles, annealed at 800 C for 3 minutes with two different loop densities are shown in Figure 2-12 along with the as grown profile. It Inert Am b ient Annealing at 8 00C 1019 .,,...,....,,....,.....,,....,..... .................................................... .,....,... ..................... ........-t ,, Boron (0.13mA cm-) Boron (0.3mA cm 2 ) )( Boron (As Grown) ,,--._ ":' E u E 1 0 18 0 / '--' f C: { 0 :i ~ I 1-t :/ +-' ! C: / ! 11) i u :J /' C: / 1017 '' 0 , u i: C: i; 0 1-t 0 co 1 016 ..._._..._._ ............................................................................................................................................... ~~~ i;\ ~ "' 0 100 0 2 00 0 30 00 4 00 0 5000 6000 7000 8000 D e p th (A) Figure 2 -1 1 SIMS profiles of D SL after Si+ implantation at different dose rates and annealing at 800 C for 3 minutes. is assumed that E OR point defect p ro file does not change. Since the implantation generate d {311} 's as well as d i s location loops at the EOR region in this experiment { 311} 's were simply modeled by an exponential decay in this simulation Simulations

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46 correctly predict the diffusion enhancement in both below and above the amorphous crystalline interface. The change in the diffusion enhancement rate of the first peak due to dose rate change is not as significant as the experimental data This might be due to the fact that {311} model used is very simple and EOR damage profile is arbitrarily chosen ,-.._ '"';' 8 u 8 0 ...._,, 0 -~ 1--< ..... (!) u 0 u 0 1--< 0 co Inert Ambient Annealing at 800C 1019 ,-,-~~~~~~~~~~,--,-,I 1018 1017 1016 -2 Boron (0.13mA cm ) -2 Boron ( 0 .3mA cm ) Boron (No Loop) )( Boron (As Grown) 0 1000 2000 3000 4000 5000 6000 7000 8000 Depth (A) Figure 2-12. Boron profiles with two different loop density and no loop layer annealed at 800 C for 3 minutes. It is also assumed that there is no interaction between loops and {311} 'sin the model. Figure 2-12 also shows a simulation profile with no loop layer. In this case {311} defects and excess interstitials below amorphous to crystalline interface exist but there are no

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47 loops. The diffusivity enhancement of all boron spikes increases dramatically It is very clear that dislocation loops are efficient sinks for interstitials. 2.4 Summary A single statistical point defect based model for the evolution of dislocation loop s during oxidation and annealing under an inert ambient is developed The model assume s that the radius and the density of dislocation loops follow a log normal distribution. E ach set of data is characterized by its average radius ( RP), its density ( D au ) and total number of interstitials bounded by the dislocation loops ( Nau). The developed model correctl y predicts RP D a u and N a u It also agrees with the depth dependence of the data. Its effects on the dopant diffusion are very clear. So far a model that predicts the evolution of the dislocation loops has been explained. However the nucleation of these loops also has to be modeled and then coupled to the loop evolution model in order to have a single complete dislocation loop model. Such a nucleation model has been developed and will be explained in detail in Chapter 3.

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CHAPTER3 MODELLING THE NUCLEATION AND EVOLUTION OF THREADING DISLOCATION LOOPS As the technology progresses towards the smaller junction depths (i e less than 100 run) for smaller device sizes predictive simulations of dopant diffusion after ion implantation and thermal annealing are essential. This would only be possible if the amplitude the depth the temperature and the time dependencies of the extended defects ( {311} s dislocation loops etc ., ) were known and implemented into the existing software The evolution of these defects in various implant and annealing conditions has been investigated and summarized in Chapter 2 There have been some recent studies on the nucleation growth and dissolution of extended defects [Cla99]. Plekhanov et al. [Ple98] modeled the nucleation and growth of voids and vacancy-type dislocation loops under Si vacancy supersaturation condition during the Si crystal growth. They suggested that similar approaches could be used to model the nucleation of interstitial-type dislocation loops. Lampin et al. [Lam99a] modeled the nucleation and growth of end of range (EOR) dislocation loops. Their model had three distinct stages the nucleation the pure growth and the Ostwald ripening. During the nucleation stage a large part of the interstitials which were located beneath the amorphous to crystalline (ale) interface following an amorphizing implant, is consumed while the others begin to diffuse following their gradients. The nucleation stage is followed by a pure growth stage During this stage, the density of dislocation loops remains unchanged but their size increases with time while the remaining free interstitials concentration decreases. For 48

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49 longer annealing times the Ostwald ripening stage is reached The total number of interstitials bounded by dislocation loops remains constant with time while d e n s i ty o f them decreases. Their model is also used to study anomalous diffusion of boron [Lam99b Lam00]. But they used different set of differential equations at each stage and it is not very clear when to switch from one set of differential equation to another one during the simulation. Their initial concentration of interstitials after the implantation below the ale interface are derived from the Monte Carlo simulations of Hobler et al. [Hob88]. The model also does not take into account interstitial cluster formations and the interaction between the {311} sand dislocation loops. In this chapter a new loop nucleation model will be introduced and the simulation results and experimental data will be compared. The model takes into account the interaction between { 311} 's and dislocation loops. It also uses a set of differential equations to describe the loop behavior through the all stages of nucleation and evolution of the dislocation loops. It is possible to obtain statistical distribution of dislocation from the simulation results, as well. There will be some major differences between the model developed in Chapter 2 and the model developed in this chapter in terms of the loop layer definition In Chapter 2 it is assumed that dislocation loops are confined into a single layer and this single la y er represents all the dislocation loops in the silicon substrate for the simplicity. This assumption showed that the corresponding differential equations correctly model the loop evolution during various annealing conditions. In this chapter loops will be spread o v er the damage region (i.e. Loop layer will be a function of {311} defect concentration ) giving more physical meaning to the simulation results.

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50 3.1 Modeling Dislocation Loop Nucleation As a result of ion implantation large amount of excess interstitials is created around the projected range of the implant or below the ale interface depending on the implant species and implant dose. Upon annealing defects such as {311} s or dislocation UT-MARLOWE Damage Profile Dissolve SMICS SMICS 311 Unfault to Loop and evolve Figure 3-1. Schematic representation of dislocation loop nucleation

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51 loops form where the excess interstitial concentration is high. The developed loop nucleation model assumes that these excess interstitials are the source of the defects. Figure 3-1 schematically explains the loop nucleation model. First, UT-MARLOWE a Monte Carlo simulation program, is used to calculate the damage created in silicon substrate due to ion implantation. The damage profile and the implanted ion distribution are utilized to generate excess interstitial profiles. The excess vacancy profile is also obtained from UT-MARLOWE damage profiles. Second, interstitial and vacancy clusters such as di-interstitials (h) di-vacancies (V 2 ) and sub microscopic interstitial clusters (SMICS) are created upon annealing. Third, {311} defects are nucleated from SMICS [Law00]. During this nucleation, large amount of excess interstitials is consumed. Some of these nucleated become thermally unstable and unfault to dislocation loops and become the source of dislocation loops [Li98]. Then, while the remaining start dissolving, dislocation loops start evolving. In the developed loop nucleation model, unfaulting process is called the nucleation stage of the dislocation loops and the evolution of the loops is called the Ostwald ripening stage. In Chapter 2, Section 2.1, it is shown that total number of interstitials bounded by loops can be expressed as where NZ~: 1 is defined to be nucleation rate of dislocation loops. When a {311} defect unfaults to a dislocation loop, the number of interstitials bounded by that {311} is transferred to the unfaulted loop. This can be shown as N Nall K C rate 311 311 (3.2)

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52 where K 311 is the unfaulting rate of to loops and C 311 is the concentration of interstitials trapped by A similar expression can be derived for the density of dislocation loops. It is previously shown that Dau is given by dDall = NDall 1 2Dall K dt rate (C / C + 10) R 2 R I lb p (3.3) and NDa/1 term is rate (3.4) Nucleation Rate vs time 8 10 7 ,,--.. u 6 10 7 il) Cl) "'; 8 u '--" i Cl 4 10 7 0 z 210 7 0 0 5 10 15 20 Time (minutes) Figure 3-2. Nucleation rate N~~} 1 change with time

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53 Since, only the first term of the Equation (3 .1) is related to the loop nucleation Equation (3 .4) becomes where C nR2n =-31_1 o a D 311 (3.5) (3.6) D 311 is the density of {311} defects. If the Equation (3.6) is substituted in Equation (3.5) Figure 3-3. TEM picture of dislocation loops and threading dislocation loops the nucleation rate of dislocation loops can simply be written as N Da/l K D rate 311 311 (3.7)

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54 In the simulations, K 311 parameter is used as a fitting parameter to calibrate the simulations. Figure 3-2 shows the change in the nucleation rate ( ND 011 ) with time The rat e rate is very high at the short time when the excess interstitial concentration is high and { 311} 's are still nucleating. The nucleation rate diminishes as the time progresses. It is known that the excess interstitial concentration will be high during the nucleation stage due to the damage introduced by ion implantation. Nucleation of loops will be energetically favorable as long as there exists a large super saturation of interstitials. Until interstitial supersaturation is decreased the Ostwald ripening does not occur. At this stage loops are fairly small. Since Equation (3.3) has a -;dependency the RP Ostwald ripening term will be dominant at this stage. In order to suppress the Ostwald ripening term in Equation (3.3) l/(C 1 / C 1 b + 10) term is incorporated into the equation. The term is arbitrarily chosen. C 1 I C 1 b will be much higher than 10 during the nucleation stage and will reach nominal values once the nucleation of {311} sand dislocation loops is complete allowing the Ostwald ripening process to dominate 3 2 Modeling Threading Dislocation Loop Nucleation High energy (i.e. Me V) non-amorphizing implants are commonly used to form retrograde wells for CMOS latch-up immunity improvement and buried layers for bipolar transistor subcollectors [Bou99]. However, heavy lattice damage can be generated near the projected range of the implanted dopant as discussed before. One type of defect associated with the high energy ion implants is the threading dislocation loops (TDLs). The threading dislocation loops are long dislocation dipoles generated in the region of the

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55 ion projected range which grow up to the surface (Che96 Jas99]. Figure 3-3 shows a TEM picture of dislocation loops and TDLs. If the distribution of loops with respect to their radius is known it is possible to obtain TDL information from this distribution. Figure 3-4 shows how to obtain TDL Surface XJ Node 1 R Node 2 R Node 3 R Rc3 Rc>x, TDL Figure 3-4. Schematic representation of TD Ls in a distribution function density from a distribution function. In the process simulators, physical shape of the device is modeled using meshes. Every mesh is composed of nodes that hold the physical data as shown in Figure 3-3 The developed loop nucleation model assumes that loop density and radius follow the log normal distribution function and each node represents a different distribution function. Dislocation loops whose radii are greater than their depth

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56 from the surface are considered as TDLs. In Figure 3-4 Rc 1 Rc 2 and Rc 3 represent the critical radii to be considered as a TDL at each loop depth (i.e. if Re> x loop is a TDL ) The total density of threading dislocation loops can simply be calculated by integrating each distribution function from the critical radius to infinity (shaded areas in Figure 3-3 ) and adding them. The integration is given by DTDL = D a u (l e,f(ln(R J M )) 2 ~s ( 3 8 ) where DTDL is the threading dislocation loop density and Re is the critical radius. The threading dislocation loops are long dipoles and simulations assume all loops are circular. In order to compensate the difference in the simulations Re is taken to be 0 3 x where x is the loop depth from the surface. 3.2.1 Simulation of the Nucleation and Evolution of Threading Dislocation Loops The formation of TD Ls as a function of implant condition is studied in boron implanted silicon by Jasper et al. [Jon00], for various implant doses (lx10 13 to 5xl 0 14 cm2 ). The implant energy is also varied from 180 ke V up to 3 Me V in 500 ke V steps. The major post implant thermal treatments include an oxidation step at 800 C for 20 minutes and an inert ambient annealing at 800 C for 70 minutes. In the simulations 1.5Me V boron implant data was used to calibrate the simulation since the data included more information such as defect density and defect size than the data for other implant energies. In order to simulate loop nucleation, damage profiles are generated for each implant dose using UT-MARLOWE. Figure 3-5 shows the excess interstitial

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57 concentration in the silicon substrate for a 1.5 MeV boron implant at a dose of l x 10 1 4 cm2. The profile represents that all the excess interstitials are generated near the projected 1019 --";' 1018 a u '--,/ u en 10'7 ] -~ .... en I,.., 0 101 6 .... s en en 0 u 1015 >:: 0 <+.. 0 i::::: .9 1014 .... ro I,.., .... i::::: 0 u 1013 i::::: 0 u 1012 2 2.2 2.4 2.6 2 8 3 Depth Figure 3-5. Initial excess interstitial concentration after an implantation of boron with a dose of lxl0 14 cm2 and an energy of 1.5 MeV. range ( =2.3 m). It is composed of the interstitial part of the damage profile obtained from UT-MARLOWE. Excess vacancy profile is also obtained in a similar way. The excess interstitial and vacancy profiles provide the basis for the nucleation of interstitials clusters (h SMICS) and vacancy clusters (V 2), eventually leading to the nucleation of {311} 'sand the dislocation loops. Figure 3-6 shows the simulation results

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58 of the changes in the defect densities with time after a 1.5 Me V boron implantation with a dose of lxl0 14 cm2 First 20 minutes of the simulation is an 800 C oxidation run the remaining 70 minutes is an inert ambient annealing run at the same temperature As seen in the figure density of {311} s D 3 1 i, increases very rapidly at short times then it starts --Nall Dall ------C3 l l 10 15 D311 --r;i s 10 14 u ..._,., en ...... ...... 1013 M en ~ 0.. 10 1 2 0 0 .....:i '0 10" 0 en I=:: (1) 10 10 Q "'0 a I=:: 109 .9 ..... ro .b 10 8 I=:: (1) u ------I=:: 0 u 10 7 0 20 40 60 80 Time (min) Figure 3 6. Changes in defect densities with time after implantation of boron with a dose of lxl0 14 cm2 and an energy of 1.5 MeV. d ecreasing. T o ta l num b er o f interstitials trapped by { 3 11 } 's, C 3 11 follow the s a me trends The nucleation of dislocation lo o ps is slower than the nucleation of { 311 } 's since the

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59 loops nucleate from unfaulted {311} s. Total number of interstitials bounded b y dislocation loops N a u increases very rapidly at short times and continuos to increas e while dissolve This shows that dislocation loops capture some of the interstitials r e leased by { 31 1} s. Once the excess interstitials are consumed by loops and some of these exc e ss interstitials diffuse away from the damage region loops go into Ostwald ripening process No significant change can be seen in N a u for longer annealing times. Ostwald ripening process can be seen in the density of dislocation loops ( D au ) profile as w ell. D au increases very fast at the short times when the nucleation rate is high. When the nucleation rate slows down D a u stay almost constant due to the fact that excess interstitial concentration is still high. Thus dislocation loops follow a pure growth process during this time period. As soon as the excess interstitial concentration drops Ostwald ripening term in Equation (3.3) becomes dominant and D a u starts decreasing Meanwhile N a u stays constant Thus the bigger loops grow at the expense of small ones. Figure 37 shows density of all dislocation loops (D a u) and the threading dislocation loops ( DTDL) as a function of boron implant dose along with the simulation results. As the implant dose increase, Dall and DTDL increase with the increasing dose to a maximum at a dose of lx10 14 cm2 This is often referred to as the critical dose for threading dislocation loops. This rapid increase in dislocation loop growth is due to the increased number of trapped interstitials in the dislocation loops. Increasing the dose of the implant will increase the excess interstitial population in the silicon substrate. Thus this will increase the growth of the loops. At doses beyond lxl0 14 cm2 while D all keeps increasing DTDL decreases rapidly back to close to the minimum detection limit ( 5 x l0 3 cm-2). Same trends can be seen in the simulation results (Figure 3-7 ) including the

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60 dramatic change in the threading dislocation loop density at the critical dose of l x l 0 1 4 cm2 Simulation predicts higher density of dislocation loops at the high implant doses but the results are in good agreement with the experimental results at the other implant dose values. 1 QI I Data-Dall 8 Simulation-Dall 1010 Data-TDL El Simulation-TDL 10 9 --s 10 8 u ..._,, c,i 0.. 0 0 10 7 0 c 10 6 en i::::: 0 0 10 5 10 4 1000 1 1014 2 1014 3 10 14 4 10 14 5 1014 6 10 14 0 -3 Dose (cm ) Figure 37. Density of all dislocation loops and threading dislocation loops vs. boron dose with implant energy of 1.5 MeV. Total number of interstitials bounded by dislocation loops ( Nau) increases with increasing implant dose as shown in the simulation results in Figure 3-8 There is a big

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61 discrepancy between the simulation results and the data. The data is derived from experimental results (loop density average loop radius) using simple relation given in Equation (2 3). 1017 1016 1015 1014 1012 0 D a t a Total # of Int. in Defects 0 Simulation-Nall 1 10 14 2 10 14 3 10 14 4 10 14 5 10 14 6 10 14 -2 Dose (cm ) Figure 3-8. Total number of interstitials bounded by loops for various boron implant dose with implant energy of 1.5 MeV. Since some of defects seen in the TEM pictures (i.e. TDLs) are non-circular using Equation (2.3) generates such discrepancies. Therefore, due to the method of extraction of the data points, it is possible that the data points in Fig 3-8 are more erroneous than the simulation results.

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62 3 3 Summary The loop e v olution model developed in Chapter 2 is expanded to include the nucleation of the dislocation loops. A single set of differential equations is used to characterize the loop behavior through the nucleation and Ostwald ripening stages The model assumes that all the loops come from {311} unfaulting. The excess interstitial and vacancy populations due to ion implantation are obtained from UT-MARLOWE The y are utilized to generate interstitial and vacancy clusters eventually leading to the nucleation of { 311} s and dislocation loops. Since the model keeps track of dislocation loop distribution through the substrate the density of threading dislocation loops is easil y calculated using these profiles Simulation results are verified with the experimental data The work represented so far shows that the model can successfully predict the loop nucleation and evolution. In order to get more physical insight about the nucleation process we should study the nucleation stage through different experiments. In the ne x t chapter these experiments will be explained in detail.

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CHAPTER4 NUCLEATION AND EVOLUTION OF END OF RANGE DISLOCATION LOOPS Ion implantation is the primary source of the introducing impurity atoms into the silicon substrate due to the inherent controllability of the implanted profile. However crystal damage is unavoidable and consequently defects form. Type II defects are some of the more commonly observed defects in high dose implants that are required to form highly activated ultra-shallow junctions. In most cases, depending on the mass of the implanted dopant species implanting at high doses amorphizes the implanted region In some cases, pre-amorphization is needed prior to implantation of light dopants such as boron in order to prevent channeling. In order to repair the crystal damage, post-implant anneals are required. During solid phase epitaxial re-growth of the amorphous layer extended defects form at the amorphous-crystalline interface. They are also known as end-of-range (EOR) defects ranging from small clusters of a few atoms to {311} sand dislocation loops. In Chapter 2, we mainly focused on time evolution of end of range dislocation loops in oxidizing and inert ambients. The discussion on the loop model in Chapter 2 accounts only for the evolution part of the model. The nucleation part of the model was not verified as the experiments described in Chapter 2 were not optimized to study nucleation of dislocation loops. Therefore, the model required the initialization of the density of the distribution of loops and the number of interstitials bounded by loops as input parameters. These initial parameters indirectly depended on the implant dose and energy. Although, a great amount of information resulted from these experimental results the nucleation of dislocation loops should be closely investigated to learn more about the 63

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64 nucleation of Type II defects This effort is also important to improve and calibrate the model. In this chapter due to the aforementioned reasons, the nucleation part of the loop model will be verified through indigenously designed experiments that are specificall y optimized for studying loop nucleation. 4 1 Experimental Details Figure 4-1 shows a schematic representation of the experiment. Single crystal Czochralski silicon wafers ( <100> orientation) were used as the starting material. st ions were implanted at either 80 keV or 40 keV at a dose of2x10 15 cm 2 Under these implant conditions a continuous amorphous layer forms. After the implant the entire wafer was capped with thick SiO 2 before the anneal process to limit any oxidation in the inert ambient. Prior to annealing cross sectional TEM (XTEM) measurements were performed to determine the amorphous/crystalline interface. The wafers were cut into smaller pieces and annealed in a nitrogen ambient at 700 C and 750 C. Annealing times were chosen to be 30 60 90 120 240 minutes for 700 C anneals and 15, 30 60 90 120 minutes for 750 C anneals. The annealing times and temperatures are chosen so that the nucleation and evolution of {311} 'sand dislocation loops will be slow [Sto97]. This allowed us to simultaneously observe the changes in {311} and EOR dislocation densities for longer annealing times at these temperatures. After the anneal, the capped oxide for all the samples were removed by HF dip before mechanical and jet etching. The total loop density, total { 311} density and total number of interstitials bounded by the loops and { 311 } 's were measured from the plan view TEM studies.

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65 2x10 15 cm2 80 keV or 40 keV st Implant ( Amorphizing) EOR Loops at 1600 A or 900 A (Starting Material) Anneal at 700 C (N2 ambient) Anneal at 750 C (N2 ambient) for 30 min 60 min 90min 120 min 240 min PTEM Loop Density, { 311 } Density for 15 min 30 min 60min 90 min 120 min Figure 4-1. Schematic representation of designed experiment 4.2 Experimental Results The XTEM micrographs of 40 keV and 80 keV s/ implants to a dose of2xl0 1 5 cm2 before furnace anneals are shown in Figure 4-2. There is a clear contrast difference

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66 Figure 4-2. Weak beam dark field XTEM images of (a) 40 keV and (b) 80 keV st implanted Si to a dose of2x10 15 cm2 before furnace anneals

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67 between the amorphous and crystalline silicon. The amorphous/crystalline interface i s located around 965 A and 1800 A for 40 ke V and 80 ke V samples respecti ve l y T h e XTEM pictures also shows that a continuous amorphous silicon region extendin g to th e surface. End of range defects form at around the depth of the original amorphous crystalline interface upon subsequent furnace annealing. Figures 4-3-4-4 represent the plan view TEM (PTEM) pictures of the 40 keV samples after furnace anneals at 700 C and 750 C for various annealing times. The g 220 reflection was used to acquire all the PTEMs under the weak beam dark field imagin g conditions. It is observed that when dislocation loops and { 311 } defects are present at the same time it is difficult to distinguish an elongated loop from a {311} defect. In order to obtain an accurate count of defects PTEM pictures were taken with plus ( +) and minus (-) g reflections. If a defect exhibited an outside contrast with +g and inside contrast with -g then it was considered as an extrinsic loop. Those studies showed that all the elongated defects at longer annealing times in all samples were dislocation loops. It is observed from Figures 4-3 and 4-4 that {311} defects nucleate and dissolve very fast at all anneal temperatures and times. The dissolution rate of {311 }defects is slower at 700 C than at 750 C. No {311} defects have been observed after annealing for 120 minutes and 90 minutes at 700 C and 750 respectively It is also observed that dislocation loops nucleate at a slower rate than {311} defects. The density of dislocation loops increases at short times at 700 C. Then it starts decreasing. The density of dislocation loops decreases at a faster rate at 750 C than it does at 700 C. While smaller loops dissolve bigger loops grow (Ostwald ripening). The loops are smaller in size at the lo w annealing temperature The same trends can be observed in the density of {311 } s

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/ ,,. ., / -' .. / , t .. \ ,. ,... 4 y / \ \ "' .~ I!, / / \ \ ., .... ~' .. .# / .. ~. t ,~ :'II" ... \ '-.. .. / \ . r \ toe ., \ .: ,' -,/ 'I> . ,: f.J \ .~/ ~ ... \ ., \ . ,, t "' .. .. ... ' (a) (b) (c) ... ~ .oo 1 ' \ \ ' f) \ I ,, .. \ 1 \ .,. C -~-. (d) (e) Figure 4-3. Weak beam dark field plan view TEM images of 40 keV st implanted Si to a dose of 2 x l0 1 5 cm 2 after an anneal at 700 ~C for (a) 30 min (b) 60 min (c) 90 min (d) 120 min (e) 240 min in N 2 O'\ 00

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~--. .. ( .. -"~. , .,,, .....,_ r .. \ ,t, .. ; '. ,... \ . ~-4' -, -: .. u-1, . t ,.,. I .._....: I -"' I I jl \ ..._,, ' "'-i. ... .. .. 'l ,.~ l i \, ------: I . ,--. .. ' (a) (b) (d) . ; ''\ , '! 1 (e) ', .. () '-.r .... (c) Figure 4-4. Weak beam dark field plan view TEM images of 40 keV Si+ implanted Si to a dose of 2xl0 1 5 cm 2 after an anneal at 750 ~ C for (a) 15 min (b) 30 min (c) 60 min (d) 90 min (e) 120 min in N 2

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" ... f., \ ~,. . .,,,. ... t .. .. . I I .. ., \ A ; t ,.,,,,, ., 0 \ ,_ .. .. ,,.. \ ill .. , ., f .. a .... ...,, f ill: o .. .. (a) (b) (c) r 1 0 0 A 0 .. () ' J ~ .. ) I ,, I I I 'I I . .... i ". I ) I ~ ~,'.f ........ (d) (e) Figure 4-5. Weak beam dark field plan view TEM images of 80 keV st implanted Si to a dose of 2xl0 15 cm2 after an anneal at 700 ~C for (a) 30 min (b) 60 min (c) 90 min (d) 120 min (e) 240 min in N 2 -...J 0

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(a) (b) (c) (d) (e) Figure 4-6. Weak beam dark field plan view TEM images of 80 keV st implanted Si to a dose of 2xl0 1 5 cm 2 after an anneal at 750 ~ C for (a) 15 min (b) 30 min ( c) 60 min (d) 90 min (e) 120 min in N 2

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72 and dislocation loops for the samples implanted with 80 keV st to a dose of 2xl0 15 cm2 in Figures 4-5 and 4-6. Although Figure 4-5 shows the 80 keV sample annealed for 30 minutes at 700 C, the defects as observed in the TEM were too small to count with any reasonable accuracy. Defect counts for each sample will be given in the next section along with simulation results. 4.3 Simulation Results In order to simulate loops nucleation, excess interstitial and vacancy profiles are generated for each implant dose and energy using UT-MARLOWE with kinetic accumulative damage model (KADM). Figure 47 shows the truncated excess interstitial concentration in the silicon substrate for a 80 keV st implant at a dose of 2x10 15 cm2 UT-MARLOWE output files estimate the amorphous depths to be around 1600 A and 950 A for 80 keV and 40 keV implants, respectively. These values correspond very closely with those obtained from XTEM pictures. The excess interstitial concentration is set to the equilibrium interstitial concentration in the amorphous region using a truncation function. The tail of excess interstitial profile seen in Figure 47 has a lot of noise. It is possible to reduce the noise by increasing the number of ions used in UT-MARLOWE simulation. However, increasing the number of ions will dramatically increase the computation time of the UT-MARLOWE simulation. Excess vacancy profiles are obtained in a similar way for all simulations. These excess interstitials and vacancies provide the basis for the nucleation of interstitial and vacancy cluster, eventually leading to the nucleation of { 311} 's and dislocation loops as explained in Chapter 3.

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1022 1018 1017 0 73 1000 2000 3000 4000 5000 6000 7000 8000 Depth (A) Figure 47. Initial truncated excess interstitial concentration after an implantation of st with a dose of2x10 15 cm 2 and energy of 80 keV Figure 4-8 represents the changes in defect densities with time at an anneal temperature of700 C after implantation of st with a dose of2x10 15 cm 2 and energy of 40 ke V. The symbols represent the experimental data and the lines represent the simulation results. As seen from the data, density of {311} 's, D 311 and the number of interstitials bounded by {311} 's, C 311 decrease with increasing anneal time. C 31 1 and D311 show an exponential decay. Meanwhile density of dislocation loops Da11 and the number of interstitials bounded by loops, Na 11 increase with increasing time. There is no

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74 ----:.:.. ... ( ~,~,: - -------C311 C311 Simulation ... Nall Nall Simulation D311 D311 Simulation Dall Dall imulation 0 50 100 150 200 250 Time (min) Figure 4-8. Changes in defect densities with time at 700 C after implantation of st with a dose of 2x10 15 cm 2 and energy of 40 keV. The symbols are experimental results and the lines are simulation results. significant change in the loop density after an initial 60 minutes anneal time while Na11 continues to increase. If the simulation results are considered, it is easy to see that D311 and C3 11 increase very rapidly in short times and then they start decreasing It is also obvious that the nucleation of dislocation loops are slower than the nucleation of {311} 's since the loops nucleate from unfaulted {311} 's. In Figure 4-8, it is possible to observe two of the three distinct stages of loop nucleation and evolution. At short anneal times,

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75 --1015 s u 1014 ..__,, en ... .. _ ...... ...... ... M 1013 Ii o'd en 0. 1012 0 0 .....:i 4-c 0 1011 0 -r~ -.. .... en / !_ i::: il) 10 10 0 ... .__ "'O ---i::: ---ro 10 9 i::: ---0 C311 C311 Simulation ~ I-< 108 .. Nall Nall Simulation ... i::: D311 D31 l Simulation il) u i::: Dall Dall Simulation 0 u 10 7 0 50 100 150 200 250 Time (min) Figure 4-9. Changes in defect densities with time at 700 C after implantation of Si + with a dose of 2xl0 15 cm 2 and energy of 40 keV. The symbols are experimental results and the lines are simulation results. both Na11 and Da11 increases rapidly when the nucleation rate is high. This is usually referred to as the nucleation stage The nucleation stage is followed by the pure growth stage. During this stage Da11 stays almost constant while Na11 keep increasing since exce s s interstitial concentration is still high. In the third stage Ostwald ripening occurs (not v ery clear in Figure 4-8 but can be seen in Figures 4-11-4-13) and the loops go into this sta ge

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76 as soon as the excess interstitial concentration drops. Da11 starts decreasing and N a ll sta y s constant during this stage The bigger loops grow at the expense of smaller ones Simulation results are mostly in good agreement with the experimental data The biggest discrepancy between the data and simulation is seen at the shortest anneal time due to the smaller defect sizes seen in TEM picture (Figure 4-3.a) If the defect sizes are too small it becomes harder to distinguish {311} defects from dislocations and the error increases. Therefore the defects for the shortest anneal time are recounted to obtain the ,..-._ 101 5 <';I E (.) ..._,, 1014 r.n ,..,_, M 1013 ._,_, o'd r.n 0... 101 2 0 0 ..J c..-. 0 1011 >-.. ..... "in C 1010 0 -0 C 109 C 0 ~ I-, 108 ..... C (.) C 0 10 7 u 0 ------------------.-.. : -: .-,:._. .. . . . ;: -----~~~ -=--. ------. ---------50 100 150 200 250 Time (min) C311 Nall e 0311 Dall CJ 11 a=950A -Nall a=950A D311 a = 950 A Dall a=950A CJ 11 a = I 000A Nall a=I000A ------D311 a = l000 A Dall a=l000A Figure 4-10. Changes in defect densities with time at 700 C after implantation of St with a dose of 2xl0 15 cm2 and energy of 40 keV The symbols are experimental results and the lines are simulation results. Amorphous depth is set to 950 A and 1000 A as initial condition for two different simulations.

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77 .. .... ~------.. .. / ~ ~ -+-"O i::: ro 109 i::: 0 -~ 1-, 10 8 +-' i::: V <.) i::: 0 10 7 u "-"'-C31 l C3.1 1 Simulation ... Nall Nal!Slmulation D31 l D311 Simclalion Dall Dall Simulation "'-0 20 40 60 80 100 120 140 Time (min) Figure 4-11. Changes in defect densities with time at 750 C after implantation of s t with a dose of 2xl0 15 cm2 and energy of 40 keV The symbols are experimental results and the lines are simulation results error bars shown in Figure 4-9 The upper bound on the error is obtained by assuming that all defects are either dislocation loops or {311} s. The recount was done aggressivel y to include every small defect. The lower bound on the error bar is obtained by pursuing a non-aggressive approach where only the defects that are clearly {311} s or loops are recounted. The results are shown in Figure 4-9 Error bars show that simulation results lie within range of experimental errors.

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,,--., 1015 N s u ';; 1014 ...... ...... 10 13 od ,;/) g. 1012 0 0 1011 0 ..... ,;/) i:::: 1010 (l) Cl "'O i:::: crj 10 9 C 0 ~ .t:l 10 8 i:::: (l) u i:::: 0 10 7 u 0 78 ---_ --/---. ---C31 l Nall D31 l Dall 50 ------------------C31 l Simulation --Nall Simulation D3 l l Simulation Dall Simulation 100 150 200 Time (min) -----250 Figure 4-12. Changes in defect densities with time at 700 C after implantation of St with a dose of 2xl0 15 cm 2 and energy of 80 keV. The symbols are experimental results and the lines are simulation results Initial conditions used in the simulations also play an important role. Figure 4-10 shows the changes in defect density with time for the case of 700 C, 40 ke V. It also shows two different simulation results with two different initial conditions. The excess interstitial and vacancy profiles are obtained by assuming two different amorphization depths. In the first case, the amorphous depth is set to 950 A and the excess interstitial

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79 and vacancy profiles are truncated using this amorphous depth. Then the simulation i s carried out. In the second case amorphous depth is set to 1000 A and the sam e proc e dur e --10 15 r-;i 8 u ._, 10 14 A en ...... ...... M 10 13 en 0.. 10'2 0 0 .-:l 4-s 10" 0 -~ en s::: 10 10 / -'----(l) Q "'O --........ a 10 9 ..... s::: 0 C311 C3 i !'Simulation -~ 108 A Na l l Nall SimLiJation s::: D311 D311 Simulation ...........__ (l) u s::: all alls ulatio 0 u 10 7 0 20 40 60 80 100 120 140 Time (min) Figure 4-13. Changes in defect densities with time at 750 C after implantation of s t with a dose of 2x10 15 cm2 and energy of 80 keV. The symbols are experimental results and the lines are simulation results. is repeated. As seen in Figure 4-10 the difference between the two simulations could be quite significant. Increasing amorphous depth by 50 A shifts all profiles in negative y directions. This is due to the fact that increasing amorphous depth reduces the number o f excess interstitials available for the nucleation of {311} sand dislocation loops. If Figure

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80 47 is closely examined it can be seen that the slope of the excess interstitial profile is quite steep around the amorphous depth. Even if the amorphous depth is changed by 50 A, the change in the number of excess interstitials will be very significant. Figure 4-11 shows the changes in defect densities with time for the 750 40 ke V sample. Experimental and simulation results have all the characteristics explained above. The nucleation rate of dislocation loops and dissolution rates of {311} sat 750 C are faster than that at 700 C --1015 E (.) ..._, 1014 rJl M 1013 ad rJl 0.. 1012 0 0 ....:l t+--, 1011 0 rJl t:: 1010 Q) Q -0 t:: 10 9 t-::s t:: 0 -~ 108 i... t:: Q) (.) t:: 10 7 0 u ~... i' .A i -->-------, -.,::.. . . . _ ._ ____ I ,,,-. ------------/ ---------. --. --------C311 Nall e D31 l Dall C311 a = 1650 A --NaJla=l650A D3 l l a= 1650 A Dall a=l650 A C3 l l a = 1600 A Nall a = l 600 A D3 11 a = 1600 A Dall a= 1600 A 0 20 40 60 80 100 120 140 Time (min) Figure 4-14. Changes in defect densities with time at 750 C after implantation of st with a dose of 2xl0 15 cm 2 and energy of 40 keV. The symbols are experimental results and the lines are simulation results. Amorphous depth is set to 950 A and 1000 A as initial condition for two different simulations

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81 The changes in defect densities with time at 700 C and 750 C for 80 keV samples are shown in Figures 4-12 and 4-14 respectively. The same trends observed in defect densities in 40 ke V samples are observed for these samples as well. 80 ke V samples generate deeper loop layers than the 40 ke V samples. The surface effects on defects for two cases (700 C and 750 C) would be different. Simulation results are in good agreement with the experimental data in both sample sets. This shows that surface effects are also modeled correctly in the model. The variations in defect densities with time at 750 C for 80ke V samples with two different simulation results are represented in Figure 4-14. The amorphous depths are set to 1600 A and 1650 A to generate excess interstitial and vacancy profiles as two different initial conditions for simulations as explained before. The importance of initial conditions used for the simulations is emphasized in this figure one more time since the shift in the profiles can be significant. 4.4 Summary Since amorphization commonly occurs during ion implantation, EOR defects are hard to avoid upon annealing. Therefore, EOR defects are very common in today s technologies. It is very important to be able to predict their size and density using physical models to design better devices. In this chapter two sets of experiments are designed to investigate the nucleation and evolution of EOR defects. In the first set of experiments, EOR defects are generated around 1600 A and samples are annealed at 700 C and 750 C for various times. Defect densities are obtained from TEM pictures Simulations are carried out using UT-MARLOWE damage profiles. It is seen that experiments and simulations are in good agreement. Performing the experiment at two

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82 different temperatures helped to calibrate the model and determine the temperature dependence of the fitting parameters used in the model. In the second set of experiments EOR defects are generated at around 900 A. Samples are annealed analyzed and simulations are carried in the same way as for the first set of experiments Simulations showed the same trends seen in experimental data. Having loops at two different depths helped us to investigate surface effects on the nucleation of dislocation loops The importance of the initial conditions on the simulations is also emphasized. So far we have investigated only defects formed by st into silicon implantation. It is important to know how well the model works with other implant species. In the ne x t chapter we will carry out some simulations with different implant species and compare the results with the published data.

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CHAPTERS VERJFICATION OF THE LOOP MODEL USING DIFFERENT IMPLANT SPECIE So far, our studies have mainly focused on the formation and evolution of end of range (EOR) defects in Si+ implanted wafers. The developed loop model is validated for various experiments by changing the implant dose, energy and the annealing temperature. It was shown [Jon88] that implant species play an important role on the defect formation and defect evolution. Light ions, such as boron, cannot produce enough damage to cause amorphization. They usually form {311} 'sand dislocation loops around the projected range after annealing which are classified as type I defects (Section 1.1.2). Meanwhile arsenic and germanium are heavy ions and they can produce amorphous layers if the implant dose exceeds the critical dose. EOR defects are the product of these heavy ions. Since most of the defects are extrinsic in nature, the amount of the excess interstitials generated by the implant species will affect the defect densities. In contrast to silicon self implants, some of these implant species may interact with the excess interstitials and vacancies generated during the implantation process. They may pair with interstitials and vacancies and diffuse away from the damaged region. Doing so, they reduce the super saturation of excess interstitials and vacancies in the damaged region. Thus, they indirectly affect the defect densities. In this chapter, the developed loop model will be tested using Liu s boron [Liu96], Gutierrez's germanium [Gut0l], and Brindos' arsenic [Bri00] implant studies The limits of the model, where it fails or does a good job in predicting the experimental results, will be discussed. 83

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84 5 .1 Defects in Boron Implanted Silicon Liu [Liu96] systematically studied the defect formation threshold in the low energy implant regime in order to understand how the sub-amorphization defects influence dopant diffusion. Liu implanted n-type wafers with boron ions at energies of 5 ke V 10 keV, 20 keV, 30 keV and 40 keV at doses of 5x10 13 cm-2, lxl0 14 cm2 2x10 14 cm-2, 5x10 14 cm2 and lxl0 15 cm2 Liu performed furnace anneals at 750 C for 5 minutes in a nitrogen ambient to study the formation threshold of {311} defects. She also performed furnace anneals at 900C for 15 minutes to study sub-amorphization dislocation loops. PTEM analyzes were performed to determine defect densities. Liu chose a defect density of 1.2x10 7 cm2 to distinguish between samples with and without extended defects. Table 5-1 lists the formation threshold for both {311} defects and dislocation loops for the whole implant matrix after anneals at 750 C for 5 minutes and at 900C for 15 minutes. Liu observed that there were no {311} defects in the 5 keV samples at a dose of lx10 14 cm2 When the dose was doubled to 2x10 14 cm2 there were still no {311} defects in the 5 ke V sample, but more defects were present in the other two implants. Increasing the dose further to 5xl 0 14 cm2 resulted in {311} defects and sub-threshold dislocation loops. The results showed that the critical dose for forming {311} defects decreased with increasing implant energy. The defect density also increased with increasing energy. It was concluded that the interstitial supersaturation necessary to nucleate { 311} defects was far less than that for dislocation loops, as well. In addition, the threshold dose for {311} defects in a 20 keV boron implant was found to be around 2xl0 14 cm2 which was much greater than the threshold dose of 7x10 12 cm2 for a 40 keV silicon implant at

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Table 5-1. Types of extended defects formed in B + implanted silicon 5 keV 10 keV 20 keV 30keV 40keV 5x10 13 cm2 None None None None None lxl0 14 cm2 None None {311}'s {3ll}'s {3ll}'s 2xl0 14 cm2 None {311}'s {311}'s {311}'s& {311}'s& Loops Loops 5x10 14 cm2 {311}'s& {3ll}'s& {311}'s& {31l} s& {311}'s& Loops Loops Loops Loops Loops l x l0 1 5 cm2 {3 11}'s& {311}'s& {31l}'s& {311} s& {3 11 }'s& Loops Loops Loops Loops Loops

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86 comparable depth. This was presumably due to the formation of immobile boron interstitial clusters and mobile boron interstitial pairs that reduced the concentration of free interstitials available to form { 311 } defects Liu observed that 40 keV samples produced dislocation loops at a dose of2x10 14 cm2 20 ke V and 5 ke V implants did not show loops until the dose was increased to 5x10 14 cm2 Results showed that the critical dose for type I loop formation ;ppeared to decrease with increasing implant energy. 5.1.1 Simulation Results Formation of defects in boron implanted silicon is simulated in FLOOPS. Excess interstitial and vacancy profiles are generated for each implant dose and energy using UT-Marlowe with kinetic accumulative damage model. Since boron has a low mass and the damaged surface layer does not amorphize, excess interstitial and vacancy profiles are not truncated as was done in Chapter 4 for amorphizing implants. While implant damage is present, diffusion of boron is not trivial. It is shown that implanted boron ions can form clusters in which boron atoms are bound to silicon interstitials into thermally stable and immobile complexes Lilak [LilO 1]. They also pair with silicon interstitials and diffuse away. Consumption of excess interstitials by immobile clusters and mobile pairs reduces the concentration of free interstitials available to form { 311} defects and dislocation loops. Lilak develop a continuum model that is capable of predicting several transient phenomena in boron-implanted silicon. Lilak's model is based upon the theoretical calculations performed at Lawrence Livermore National Laboratories and has been found

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Table 5-2. Simulation results for the types of extended defects formed in B + implanted silicon after an anneal at 75OC for 5 mm No{3ll}'s ., {311}'s Mismatch 5x1O 13 cm2 lxlOI 4 cm2 2x10I 4 cm2 5x1O 14 cm2 5 keV D311=2.4xlO 10 A. L. = 338 A D3 I I =4 .1X10 I 0 A. L. = 383 A 10 keV D3ll=l.2xl 0 10 A. L. = 330 A DJI 1=4.3xl 0 10 A. L. =462A DJI I=7.8xl 0 10 A. L. = 520 A 20 keV D3II=9.5x10 9 A. L. = 387 A D3I I=2.8xl 0 10 A. L. = 485 A D3II=7.7x10Io A. L. = 581 A D3 I I= 1. 9x 1 0 I I A. L. = 672 A 30 keV D3I I=l .4xl 0 10 A. L. = 467 A D3II=3.7x10Io A. L. = 544 A DJI I=lxl oI I A. L. = 624 A O il DJI1=2.lxl A. L. = 690 A 4OkeV D3II=l. 7xl 0 10 A. L. = 510 A D311 =4 .1X10 9 A. L. = 575 A D3I1=l. l xlOI I A. L. = 641 A D31I=2.3xlO 11 A. L. = 707 A 00 --..J

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Table 5-3 Simulation results for the types of extended defects formed in B+ implanted silicon after an anneal at 900oC for 15 mm No Loop _) Loop 5 keV 10 keV 20keV 30keV 40keV 5x10 13 cm 2 Da11 = 0 Dau= 2xl0 6 Dan= 7x10 6 Dau= 2.9xl 0 7 Da11 = 5.lxl0 7 lx10 14 cm 2 Da11 =4xl0 6 Dau =2.2xl 0 7 Da11 = 9.7xl0 7 Dau= l 7x10 8 Da11 = 2.6xl0 8 2x10 14 cm 2 Dall= 6.2xl0 7 Da11 = 2.4x10 8 Dall= 5.9xl0 8 Da11 = lx10 9 Dau= l. lxl0 9 5x10 14 cm 2 Dau= 1.4 xl0 9 Dall= 2.5x10 9 Dau= 3.9x10 9 Dall= 4.8x10 9 Dau= 5.4x10 9 lx10 15 cm 2 Dau= 5.4x10 9 Dau =7x10 9 Dau =lxl0 10 Dall =1.2x10 10 Dau =1.4x10' 0 00 00

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89 to be fairly consistent with the experimental work obtained as part of this work and also results of previous researchers. In order to study defect formation in boron implanted silicon, Lilak's model is coupled with the developed loop model. As an initial condition all of the implanted boron is assumed to be in the substitutional position. Simulations are carried out for each implant condition at 750 C for 5 minutes and at 900C for 15 minutes. Table 5-2 and 5.3 summarize the simulation results. Table 5-2 shows the average {311} defect length and density for each implant condition. Table 5-3 represents the density of loops whose radii are greater than 100 A. In order to determine whether the simulation results predict enough { 311 } defects, the average {311} length is studied for each implant condition. If the average length of { 311 } 's is greater than 3 3 0 A, then it is assumed that { 3 11 } defects exist. Although the chosen average length is large, it is within the error limits of Liu's TEM pictures where the scale is set to 2000 A and visible defects are around 300 A. A similar approach is followed to determine whether loops exist for an implant condition or not. First, the density of loops whose radii greater than 100 A is calculated from the distribution functions. The minimum radius value is chosen from TEM pictures as well. Then, in order to determine if loops are present, a defect density of lx10 9 cm2 is chosen If the density of dislocation loops is greater than lxl0 9 cm2 it is assumed that the loops exist. The chosen defect density is much greater than the defect density selected by Liu but visible defect densities reported are usually above lx10 9 cm2 It should also be considered that the developed loop model and Lilak's boron clustering model used in the simulations are individually calibrated. Even though, calibration will play an important

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90 role in the outcome of the simulations, the results will be a qualitative representation of experimental results regardless of the calibration. Table 5-2 shows that the simulation results for {311} formation are in good agreement with Liu's observations in almost all cases The discrepancy exist between the data and simulation results for 5xl0 14 cm-2, 30keV and 40keV implant conditions. Table 5-3 represents the simulation results for dislocation loop formation after an anneal of 900C for 15 minutes It is clearly seen that simulation and experimental results are in good agreement. Simulation results also agree with the experiments in that the critical dose for forming {311} defects decreases with increasing implant energy. They also follow the observation that the interstitial supersaturation required to nucleate {311} defects is far less than that for dislocation loops and loops are more likely to nucleate with increasing implant energy 5.2 Defects in Germanium Implanted Silicon The effects of Ge+ implant energy and dose on the evolution of defects created via the annealing of the implant damage were studied by Gutierrez [GutOl] Gutierrez's experiments can be summarized as follows: PTEM analysis was performed on 10 and 30 keV lxl0 15 cm2 Ge+ implanted samples and 5 keV, 5x10 14 cm2 and 3xl0 15 cm2 Ge+ implanted samples. For the short annealing times ( < 120 sec), a Rapid Thermal Anneal (RTA) was employed. A conventional furnace was used for longer annealing times. Annealing times were varied from 10 seconds to 360 minutes and all anneals were carried

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91 T ota l # o f Int. Total # of Int. Simulation ... D311 D3 l 1 Simulation 1015 Dall Dall Simulation --';1 1014 8 ----. ----. ... u '--" ---0 ..... 101 3 Cl) s:: Cl) 0 ..... 1012 u Cl) 0 ""O 1011 s:: ro Cl) ] 1010 ..... ..... ..... Cl) 1-, Cl) 10 9 ..... s:: ........ ""O Cl) 0.. 10 8 1-, E-< 107 100 1000 105 Time (seconds) Figure 5-1. Experimental and simulation results for the defect evolution for a 30 keV lxl0 15 cm 2 Ge+ implant on silicon, annealed at 750 C. out in a nitrogen ambient at 750 C. Some of the 30 keV samples were also annealed at 825C. In order to carry out the simulations, damage profiles are obtained for each implant condition using UT-Marlowe and truncated to the amorphous/crystalline interface. Implanted Ge atoms are assumed to be in the substitutional position as an initial condition. It is also assumed that there was no interaction between Ge and Si atoms. Simulations are performed at 750 C and 825 C for 360 minutes.

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9 2 T o ta l # o f In t. Total# of Int. Simulation .. D 3 1 l D3 ll Simul a tion 101 4 Dall Dall Simulation ,,-..._ "'Ill 8 101 3 .... __ u '--" 0 ri) 101 2 11) Q ..... u 1011 11) Q "O ro 101 0 r/l :..... ..... r/l 1-o 10 9 11) ..... "O 11) 108 0.. 1-o t'""" 10 7 100 1000 10 4 10 5 Time ( seconds ) Figure 52. E x perimental and simulation results for the defect evolution for a 30 k e V l x l0 15 cm2 Ge+ implant on silicon annealed at 8 2 5 C Figure 5-1 shows both the e x perimental and simulation results for the defect e v olution for 30 keV lxl0 15 cm 2 Ge + implanted samples Gutierrez observed that both { 311 } defects and dislocation loops were present for this case. It is clear from the figure that {311 } defects rapidly dissolve with increasing time whereas the loop population stabilizes and becomes the dominant defect type Although simulation results predict the total number of interstitials trapped in defects and density of loops pretty well for short annealing times there is some discrepancy between the data and the simulation results at

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93 longer annealing times. Simulation results do not predict loop dissolution at 750 C for any time duration. There is a good correlation between the loop density data and simulation results at longer annealing times. The difference seen between them in s h o rt annealing times could be attributed to counting errors since it is very difficult to di s cern between defects on short anneals. A qualitative fit is the most could be hoped for. The fit to { 311 } density is also off. Figure 5-2 represents the experimental and simulation results for defect e v olution at 825 C from 30 keV lxl0 15 cm2 Ge + implanted silicon. Simulation results predict the dislocation loop density and the number of interstitials trapped in defects within error margins of data. Simulation predicts faster {311} dissolution than that of experimental results. Gutierrez s work did not agree well with simulation results for low energy implants. Gutierrez s experiments showed that only dislocation loop defects formed for 10 keV lxl0 15 cm2 Ge + implanted silicon wafers It was also observed that these dislocation loops undergo a coarsening/ripening process with time resulting in an decreased defect density and an increased defect size as shown in Figure 5-3. Gutierrez concluded that interstitial evolution followed an alternate path from low energy germanium implants in which {311} defect formation from initial clusters did not take place but only stable dislocation loops were formed. Unfortunately the developed model assumes that all dislocation loops come from {311} unfaulting. Dislocation loop nucleation follows the {311} nucleation process. Thus {311} sand dislocation loops were present in all simulations for low energy germanium implants Figure 5-3 s ho ws th e

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94 --101 4 r;i ,--.-~ Total # of Int. a u :----tl '-_,/ ...... r ------:":-.,. 0 10 13 . :-.. -en N .---, all \. C Q 101 2 3 11 +-' u : Total# of Defects Q 1011 ... ~ :' ... \ '"O II; ... ... c,::S IZl ... ] 10 10 .,.-: ~ .. -~ .. -~ -+;::: _,,,,,,' +-' \ IZl I-, / D al l 10 9 D +-' 31! / 1:'"O 1 0.. 10 8 w I-, E-< 10 7 : 1 ; 10 100 1000 10 4 10 5 Time ( seconds ) Figure 5-3. E x perimental and simulation results for the defect e v olution for a 10 keV lxl 0 1 5 cm 2 Ge+ implant on silicon annealed at 750 C simulation results for the total number of defects and total number of interstitials trapped in defects along w ith Nau Dau ,. C 3 11 and D 3 11 Simulation results are in good agreement with the experimental results It should be noted that defects at short annealing times are mostl y { 311 } sand at long annealing times are dislocation loops. This suggests that defects observed by Gutierrez might not be all dislocation loops Although there is a good correlation between the data and simulation results at longer annealing times the discrepancy at shorter annealing times is apparent. Simulation

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101 4 101 3 --r;i s u .,_, (/) 101 2 ] .;,:::: (/) 1-, Q) i::::: 1011 "'O Q) 0.. 1-, 1010 95 ~ -,, / ""' ""' Total # of 111.t. Total# oflnt.\imulation Nall Simulation ""' C311 Simulation 500 1000 1500 2000 2500 3000 3500 4000 Time (seconds) Figure 5-4. Experimental and simulation results for the defect evolution for a 5 keV 5x10 14 cm2 Ge+ implant on silicon annealed at 750 C. results show much slower nucleation rate for defects due to the slower temperatur e ramp up rate. Even though Gutierrez used RT A for short annealing times a slower t e mp era tur e ramp-up rate was used in the simulations since the model was calibrated with furnac e annealed-data sets where the temperature ramp-up rates were much slower than R T A rates. Thus simulations predict a slower nucleation of defects at v e ry short anneal ing times.

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1010 10 9 0 96 "" --~---=-:::--.:_-:7:-:-~~~~--= =-----=! Total # of Int --,. rotal # of Int ~ Si1nt1l,1tio11 Nall Simu l ation C311 Simulation 500 1000 1500 2000 2500 3000 3500 4000 Time (seconds) Figure 5-5. Experimental and simulation results for defect evolution from 5 keV 3xl0 15 cm 2 Ge+ implant on silicon annealed at 750 C. Defect evolution with time at 750 c for 5 keV Ge+ implants is shown in Figures 5-4 and 5-5 for doses 5xl0 14 cm 2 and 3x10 15 cm 2 respectively. Gutierrez observed from PTEM micrograph images that only dislocation loops were present for both implant conditions They were small in size and completely dissolved within a narrow time window indicating their instability. Simulation results for both implant conditions predicted the formation of {311} defects as was explained before. Total number of interstitials obtained from simulation results along with the interstitials trapped in

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97 {311} 's (C311) and loops (Nau) is shown in Figures 5-4 and 5-5. The simulation results contradicts with the experimental results, especially at the long anneal times The model does not predict any loop dissolution and fails for both implant conditions. 5.3 Defects in Arsenic Implanted Silicon Brindos [Bri0 1] investigated enhanced diffusion of high concentration low energy arsenic implants (3 keV at doses of 5xl 0 14 cm2 lxl 0 15 cm2 and 5xl 0 15 cm 2 ) when annealed at 800 C for 1 hour. Brindos observed that EOR defects did not form for these implant conditions. Also in previous experiments by Jones et al. [Jon98] it was suggested that interstitials present at EOR were responsible for a lack of extended defects. To test this theory, Brindos's As-I (Arsenic Interstitial) pair formation model was combined with the developed loop model and applied to low energy, high dose simulations. Equation (5.1) represents Brindos' As-I interaction model as a basic pair reaction where As is an arsenic atom and Si(!) is a silicon interstitial atom. As + Si c /) <=> As/ (5.1) Arsenic implants were simulated using UT-Marlowe to obtain damage profiles for 3 keV implants at doses of 5x10 14 cm2 lxl0 15 cm2 and 5x10 15 cm2 Since the implants were amorphizing implants, the initial damage profiles were truricated to the amorphous depth. Diffusion of As-I is set to the values obtained by Brindos. Figure 5-6 shows the defect density change with time at 800 C for three implant conditions. It is seen that {311} defects nucleate very fast at the short annealing times and their density drops below TEM detection limit of 1.0x10 7 cm2 very quickly. There is no loop nucleation at

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10 8 10 7 1 98 D (5xl0 15 cm2 simulation) / I 1/ I I ii !' D (lx10 15 cm2 simulation) 311 D (5xl0 15 cm2 simulation) j D (lxl0 15 cm2 simulation ---..._ all/ .... --...... -----......... ---..... .... "10 Time (Minutes) Figure 5-6 Simulation results for the defect evolution for 3 keV, 5xl0 14 cm2 lxl 0 15 cm2 and 5x10 15 cm2 As implants on silicon annealed at 800 C for 60 minutes. all for the lowest dose which does not appear in the figure. For higher doses, the density of loops also falls below the TEM detection limit at the end of the annealing cycle. The results are in direct correlation with the Brindos' experimental results.

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99 5.4 Summary The developed loop nucleation and evolution model is used to predict the defect behavior in boron, germanium and arsenic implanted silicon. Overall results showed that the model agrees with experimental results in most cases. Liu's observation of decrease in the critical dose for forming {311} defects with increasing implant energy is verified with simulation results. It was also shown that loops were more likely to nucleate with increasing implant energy. Simulation results followed Liu's observations for almost all implant conditions for {311} formation. They were in excellent agreement with loop formation data. The model worked very well for the high energy Ge+ implants done by Gutierrez but failed to predict the defect dissolution for low energy implants. It also predicted { 311} defect formation for low energy implants whereas experiments showed no formation of { 311 } defects. The model was in agreement with Brindos' observation that no defects formed in low energy, high dose arsenic implanted samples, upon annealing at 800C for an hour. The model showed that { 311 } defects and dislocation loops nucleate in short annealing times and their density drops below the TEM detection limit at the end of the annealing cycle. The limits or the 'boundaries' of the model are pointed out in this chapter using various implant species and implant conditions. In the next chapter, the effects of the mechanical stress that surface during fabrication process on dislocation loops will be studied.

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CHAPTER6 PROCESS INDUCED STRESS EFFECTS ON DISLOCATION LOOPS Increased packing density and reduced device dimensions are two major trends seen in device scaling of each succeeding generation of integrated circuits Unfortunately the two trends lead to processes in which stress levels increase. Higher packing densities are achieved by developing smaller devices and by packing them closer together. However devices must be electrically isolated from each other by isolation regions Shallow Trench Isolation (STI) is a predominant isolation technology seen in today s integrated circuits. The general STI process flow includes a nitride patterned reactive ion etch sacrificial sidewall oxidation oxide deposition and finally a chemical mechanical polish All of the above processes induce stress in the silicon substrate as explained in Chapter 1 Section 1.3 .1. Stress can have dramatic effects on the nucleation of dislocation loops when combined with the ion implantation process [Fah92]. One of the goals of this research is to investigate the process induced stress effects on the nucleation of EOR dislocation loops. Chaudhry [Cha96] investigated stress in the silicon substrate as a function of nitride film thickness and stripe width. He found that the stress levels in the substrate are a strong function of nitride film thickness and stripe width. He also investigated tensile and compressive stress effects on the evolution of dislocation loops. His experimental results showed that under compressive stress dislocation loops dissolve faster and dislocation loop density and average loop radius are smaller than the ones under tensile stress. 100

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101 In this chapter first the design and results of an experiment will be di s cu sse d t o investigate loop nucleation and evolution under tensile stress regions. The de ve loped l oo p model will be modified to take into account stress in the silicon substrate and experimental results will be compared with the simulation results. Later Chaudhry s [Cha96] experimental results will be simulated with the modified loop model. The result s will be discussed and discrepancies between the experimental and simulation results will be pointed out. Figure 6-1. SEM image of Intel wafer with various patterns. Some structures are as small as 0.5 m.

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102 6.1 Dislocation Loop Nucleation and Evolution under Tensile Stress 6.1.1 Experimental Details In order to investigate stress effects on dislocation loops patterned wafers from Intel were used for this study. The wafers had the following process steps. First a 100 A pad oxide was thermally grown. Then a 1500 A thick nitride layer was deposited on the surface These processes were followed by photolithography and etching processes. Later st ions were implanted at 40 keV and a dose of lxl0 15 cm2 forming a continuos amorphous layer. Since the patterned wafers had various structures Figure 6-1 scanning electron microscopy (SEM) was used to find repeating patterned nitride stripes with varying Figure 6-2. SEM image of three bars on the wafers. Each bar consists of repeating nitride patterns. Nitride stripes run from top to bottom of the page.

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103 nitride widths. Although there were a lot of repeating patterns on the wafers the size of most of these patterns were not large enough to make plan view transmission electron microscopy (PTEM) samples to investigate the defect densities and sizes. Figure 6-2 shows one of the structures used in the experiment. In the figure there are three large bars consisting of repeating nitride stripes. The nitride stripes run from the top to the bottom of the page. A close up image of one of these bars is shown in Figure 6-3 The nitride width was measured to be 10.0 m and the spacing in between them was measured to be 3 .5 m. The St implants mentioned earlier goes into the area in between the nitride stripes. Figure 6-4 shows the PTEM image of the same structure. Nitride stripe Figure 6-3. Magnified SEM image of three bar structure shown in Figure 6-2. Nitride bars are 10 m wide and the spacing between them is 3. 5 m.

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104 Figure 6-4. PTEM image of three bar structure shown in Figure 6-2. Nitride bars are I 0 m wide and the spacing between them is 3. 5 m. Figure 6-5. SEM image of the other structure used in the experiment. Nitride stripes run from left to the right of the page.

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105 Figure 6-6. Magnified SEM image of structure shown in Figure 6-4. Nitride stripes run from left to the right of the page. Figure 67. PTEM image of structure shown in Figure 6-4. The spacing between nitride bars is 3.5 m.

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106 stripe widths and areas in between them are also confirmed with this image. The second structure used in the experiment is shown in Figure 6-5. The single bar shown in the middle of Figure 6-5 consists of repeating nitride stripes. The nitride stripes run from the left to the right of the page. A more detailed image of the single bar is shown in Figure 6-6. It was determined from SEM images that nitride stripes are 150 m wide and the spacing in between them was 3.5m. These dimensions can also be seen in the PTEM image Figure 67. After determining the patterned structures on the wafer using SEM the samples were subsequently annealed in nitrogen ambient at 700C and 750C. The annealing times were chosen to be 60 minutes, 120 minutes and 180 minutes at 700C and 30 minutes 60 minutes and 120 minutes at 750C. Total loop density total {311} density and total number of interstitials bounded by the loops and { 311 } s were measured from the TEM images. Cross sectional TEM (XTEM) images were also taken to determine the amorphous depth. Figures 6-8 and 6-9 show cross sections of the un-annealed samples Figure 6-8. XTEM image of one of the un-annealed samples. The amorphous depth is clearly visible and found to be 900A

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107 Figure 6-9. XTEM image of one of the un-annealed samples. The amorphous region and nitride pattern are visible. The amorphous depth and nitride thickness were found to be 900 A and 1500 A respectively. of the structure shown in Figure 6-3. The amorphous to crystalline interface in both figures is visible. The amorphous depth and nitride thickness were found to be 900 A and 1600 A respectively. The lateral damage around the nitride stripe edge is clearly visible in Figure 6-9. The damaged region does not extend under the nitride stripe. Figure 6-10 presents the defect formation around the nitride stripe edges and amorphous to crystalline interface after annealing at 750C for 120 minutes. The XTEM image clearly shows that defects were present inside the trench structure where the implant damage existed. On the other hand, there were no visible defects under the nitride stripes since the implant damage did not extend into this region. It is also notable that defects curved towards the surface at the nitride edges. This is due to the implant damage shown in Figure 6-9. A magnified image of the structure shown in Figure 6-10 is given in Figure 6-11.

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108 Figure 6-10. XTEM image of the annealed sample showing the damage in the trench area. Defects curve towards the surface around the nitride edges. Figure 6-11. Magnified XTEM image of the structure shown in Figure 6-10. The defects in the trench area are visible. 6.1.2 Stress-Assisted Loop Nucleation and Evolution Model Chaudhry [ Cha96] showed that the dislocation loops were sparser and smaller in regions of compression when compared to the adjacent tensile regions. In order to include stress effects on the nucleation of dislocation loops, the loop nucleation and evolution model developed in Chapter 3 was modified as follows dNa/1 -P!1v; P/1 oof C C )+ (R)dR -= K3Jlc311 exp(---)+exp(--)K/L ( / lb JD dt kT kT o+ loop boundary (6.1)

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109 where Vi and V 2 are defined to be activation v olumes. P is the spatiall y d e p e nd e nt magnitude of the pressure field and given by (a xx +a yy ) P=---2 ( 6 .2) where CJ xx and CJ .vy are normal components of stress Since K V L is set to zero v acanc y terms in Equation (6.1) are not shown. Equation (6 1) represents the change in th e number of interstitials bound by dislocation loops with time when stress is present in the substrate. Since stress effects are not incorporated into the { 311} nucleation model two different activation volumes were used in the equations to account for these effects. The density of dislocation loops equation Equation (3.3) was also modified in a similar manner dDall K D (-P~Vi) 1 2D a ll K dt311 311 exp kT (C IC + 10) R2 R ( 6.3 ) I lb p It should be noted that the unfaulting terms in Equations (6 1) and (6.3) have the same activation volume since they correspond to the same unfaulting {311} defect. In the presence of a pressure field the density and size of dislocation loops will change. To illustrate this point, assume that the pressure in a given region is compressive. The nucleation terms in Equations (6.1) and (6.3) will decrease At the same time the second term in Equation (6.1) will increase and therefore increase the dissolution rate of dislocation loops. Thus the rate of growth of dislocation loops will be reduced in the presence of compressive stress. If the pressure is tensile in a given region the reverse effects will be observed. The nucleation rate of dislocation loops will increase and the dissolution rate of dislocation loops will decrease. Hence the average rate of growth of

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110 dislocation loops in a tensile region will increase This agrees qualitatively with the experimental results of Chaudhry [Cha96]. In the next section first the results of the experiment described in previous sub section along with the simulation results will be presented. Then simulation results will be compared with Chaudhry s experimental results. 6.1.3 Experimental and Simulation Results As explained in the previous section the samples with 1 0m and l 50m nitride stripes were annealed in nitrogen ambient at 700C and 750C for various times. Figures 6-12 and 6-13 represent the plan view TEM (PTEM) images of the 40 ke V samples after furnace anneals at 700 C and 750 C for various annealing times. It was observed from the PTEM images that { 311} defects nucleated and dissolved very fast at all the anneal temperatures and times. Although they are more stable at 700 C than at 750 they dissolved with increasing annealing times. Dislocation loops are much more stable than { 311} defects. It was observed that dislocation loops nucleate at a slower rate than { 311} defects. Although the density of dislocation loops decreases at longer annealing times the number of interstitials trapped by dislocation loops does not change with time at these annealing temperatures. While smaller loops dissolve bigger loops grow (Ostwald ripening) These trends are similar to the trends explained in Chapter 4. Density of dislocation loops { 311} 's and the number of interstitials bound by these defects were measured from the PTEM images shown in Figure 6-12 and 6-13. The results along with the simulation results are given in Figures 6-14 and 6-15.

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' 11/1 ... -... ....... .... 100A .. .. ,,. ' ... I t ~ .... I ' .; .. :, f .. .. ,. I .. ,., ' ' ,,,. ._ / \ . I ~ ti, .,, ..... ,f ' ... .. .. .... l 50m stripes (a) (b) (c) IO m stripes (d) (e) (f) Figure 6-12. Weak beam dark field plan view TEM images of 40 keV Si + implanted Si to a dose of 1 xl0 1 5 cm 2 after an anneal at 700 ~ C for (a) 60 min (b) 120 min (c) 180 min (d) 60 min (e) 120 min (f) 180 min in N 2 ...... ...... ......

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w o ~ A \ ; / ....... \ \ . ,, r t ,.,.... 150m stripes (a) K "' ,,. .... -~ 41 .. 'f 1 \ ~ \, ,, t) D "! ' ~' ;1 1 0m stripes (d) , f \ \ \ ' \ (b) ) ,.,, ./ (e) ,,. .. ... ...... , .. ..,. ,,, ... ., ~ /I' ) t (c) .-A' _, //lfl!'I" .,,...... -111' ,. .. I (f) Figure 6-13. Weak beam dark field plan view TEM images of 40 keV st implanted Si to a dose of lxl0 15 cm 2 after an anneal at 750 ~C for (a) 30 min (b) 60 min (c) 120 min (d) 30 min (e ) 60 min (f) 120 min in N 2 ...... ...... N

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.... t::::: 0 -~ i= (l) u t::::: 0 u C311-l 50m stripe D311-l 50m stripe Nall-15 0m stri pe DallI 50um ')tripe 10 1 5 0 LJ 'v 113 311-l0m tripe D311-I0m trip all-1 0m s tripe Dall-I 0m stripe 1014 10'3 !_ ... -.-----e -. t __ 10" 10'0 0 / 50 100 Time (min) 150 a ll ----D311 311 -Dall 200 Figure 6-14. Changes in defect densities with time at 700 C after implantation of s t with a dose of lx10 15 cm2 and energy of 40 keV. The symbols are experimental results and the lines are simulation results. Figure 6-14 represents the change in defect density and trapped interstitials by these defects with time at 700C. The simulations were carried out in the same way as explained in Chapter 4, Section 4.3. The amorphous depth used in the simulations was 850A which was very close to the 900A measured from the XTEMs Symbols in Figure 6-14 represent the experimental results. It is clear that the experimental data for 10 m

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114 and 150 m nitride stripes lies within the experimental error range. Therefore the results are not clear enough to quantify the stress effects on dislocation loops. Simulation results also showed less than a one percent change in defect densities for samples with 10 m and 150 m nitride stripes. Thus only one of the simulation results is shown in Figure 614. Although simulation results were in agreement with defect densities there was some discrepancy between the trapped interstitial data and simulation results. These C311-150m stripe 0 C31 l-1 0m stripe Nall .. D311-150m stripe 6 DJ 11-1 0~Lm stripe D3 l 1 Nall -l 50 m st r ipe Nall-1 0m strip e C 311 ,, Dalll 50~tm sa-ipe V Dall-I 0m stripe Dall "';l 1015 a u _en 1014 0 ...... ---...... : : ~~ ~ M 10 13 1 / ---""O i:::: --.. Cl:! --.. V'l ---0.. 101 2 0 ---0 ....:i --.. 0 1011 0 --.. V) 'V i:::: Cl) 1010 Q ""O 10 9 i:::: 9 ..... Cl:! '""' 10 8 ..... i:::: Cl) u i:::: 0 10 7 u 0 20 40 60 80 100 120 140 Time (min) Figure 6-15. Changes in defect densities with time at 750 C after implantation of st with a dose of lxl0 15 cm 2 and energy of 40 keV. The symbols are experimental results and the lines are simulation results.

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115 could be attributed to the initial conditions chosen for the simulation or counting error s a s explained in Chapter 4. Change in defect densities and trapped interstitials with time at 750 C are given in Figure 6-15. The symbols are experimental data and lines are simulation results. The same trends seen in Figure 6-14 can be seen here as well. Since experimental results for samples with 10 m and 150 m nitride stripes. were within the experimental error range it would be difficult to quantify the stress effects on dislocation loops. Simulation results 1 1 0 I O .----,----.-----,.----.---.-------.---....--....--..-.......... ----.-----,.----.---.------, --150m stripe l0m stripe 0 -2 10 9 0 0.2 0.4 0.6 0.8 1 Depth (m) Figure 6-16. Variation of the hydrostatic pressure in the silicon substrate for samples with 10 m and 150 m nitride stripes.

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116 did not show more than a one percent change in dislocation loop and {311} defect densities. Therefore only one simulation result is given in Figure 6-15. The lack of stress effects on dislocation loops observed in the experiments could be explained by Figure 6-16. Figure 6-16 shows the stress/pressure levels in the bulk for samples with 10 m and 150 m nitride stripes in the presence of dislocation loops. The stress/pressure levels were very close to each other. Thus, density of defects would be almost identical as well. Indeed this was the case observed from the experimental results. 6.2 Effects of Patterned Nitride Stripes on Dislocation Loops 6.2.1 Experimental Details Effects of patterned nitride stripes on the evolution of dislocation loops in silicon were investigated by Chaudhry [Cha96]. His experimental procedure can be summarized as follows: First, a 300 A thick oxide was grown. This process step was followed by a high dose (2xl0 15 cm2 ) amorphizing implant at an energy of 100 keV. The oxide was patterned and etched to form stripes ranging in width from 1 to 1000 m. A low pressure chemical vapor deposition (LPCVD) silicon nitride was deposited on the wafer to generate the stress in the substrate. The samples were then annealed in nitrogen ambient at 900C. TEM analysis of these defects was carried out to determine the defect densities. The details of the experiment can be found in [Cha96]. Figure 6-17 shows the structure used to study the effects of nitride stripes on the evolution of dislocation loops. When the nitride stripe was directly on top of the silicon, they exerted compressive stress on the substrate. When a thick oxide buffer was placed in between the oxide and silicon, the stress in the substrate becomes tensile. The regions, which were in tension or compression, are shown in Figure 6-17

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117 Oxide Nitride (Tensile) ... ............. .. ....... . .. ....... .. . . . . ... . . . . .. . . . . . . . .. . . . . . . . . . . . { \ \ \l! l l l({\ \) l/\!)l l / l \!l(/\ : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :;\ l 1 ~l l ~ l i l ~ l l~III~ 1 ~ 1 1~1 l~I ~i l ~ I I I : 0 ::::: 0 ; ;:; 0 : : : 0 :::: : : : Tension ... .. ... ....... .. .... .. .. . . . . .. . . . . .... . . . . . .... ... Compression 111111111 1 111 1 11:1111111111111111111111111 1 1111111111 1 11 : :: : : : :~~~'.'.'.'.n: Bu;k: : .... ..... ... ... . . ....... ... ~....,_ __ 1 _ 1o o o __ m __ ~-... ~.,_ __ 1 _ 1o o o_ m __ _.._ Figure 6-17. Structure used to study the effects of nitride stripes on the evolution of dislocation loops in silicon 6.2 2 Experimental and Simulation Results For ease in simulation the oxide buffer and nitride stripe on top of the o x ide buffer shown in Figure 6-17 were removed. This structure approximated the real structure in the experiment. A 2D structure was used to calculate the stress in the tensile and compressive regions. The pressure in the substrate was calculated by using Equation (6.2). In order to simulate loop nucleation under tensile and compressive stress first excess interstitial and vacancy profiles were generated for the implant conditions used in the experiment using UT-MARLOWE. The excess interstitial and vacancy profiles w ere truncated at the amorphous depth as explained in Chapter 4. The amorphous depth w a s

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118 found to be 1500 A from UT-MARLOWE simulations which was consistent with the experimentally observed amorphous depth of 1500 A An intrinsic stress of 4.0x 10 10 dynes cm2 was initialized in the nitride. The stress due to dislocation loops is also included in the model. Figure 6-18 shows the variation in the pressure/stress as a function of depth The dislocation loops can significantly alter 21010 ---0--Tensile 1.5 10 1 0 0 Compressive ...--.. 1 1010 N s u en Q) c:: 5 10 9 >-. "'O '--" Q) en en Q) 0 $.., 0... 5 10 9 -1 1 0 IO '---L--...l-----'-----'----'----'------'-----'----'---__.___,_ __,_ __,_~ ~ ~~ ~~ 0 0.2 0.4 0.6 0.8 1 Depth (m) Figure 6.18. Variation of the hydrostatic pressure in the silicon substrate in compressive and tensile regions under the patterned nitrides. Dislocation loops are formed around the ale interface

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119 60 50 8 Simulation Experimental 40 ,._ 30 ..._.., 11) ;> "' :a 20 10 0 -10 1 10 100 1000 Stripe Width (m) Figure 6-19. Experimental [Cha96] and simulated values of the net change in the average radius of the dislocation loops from the tensile to compressive regions as a function of nitride stripe width. the hydrostatic pressure. Since the total pressure in the silicon substrate is an algebraic superposition of the pressure from the nitride stripes and dislocation loops the tensile pressure in the substrate may become compressive pressure around the regions close to the center of the loop layer. Simulations were performed to investigate the stripe width dependence of the data given in [Cha96]. The data showed that Ma ve changed as a function of nitride stripe

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120 width and decreased with increasing stripe width of the patterned nitride film. M ave is gi v en by ( 6.4 ) where c represents the average radius in tensile or compressive stress regions Figure 6-19 shows the experimental and simulation results for the change in M ave with 60 50 40 ,.-.._ 30 '-" 0 <] 20 10 0 -10 1 Experimental 0 Simulation 10 100 Stripe Width (m) 1000 Figure 6-20. Experimental [Cha96] and simulation results of the net change in the total density of dislocation loops from the tensile to the compressive regions as a function of nitride stripe width.

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121 increasing nitride stripe width. As the nitride stripe width was decreased the s tr ess l eve l s in the bulk increased as did fl.R ave Simulation results predicted the e x perimental r es ult s qualitatively. It should be noted that the average radius of the loops was smaller than 100 A for this experiment. A few angstrom change in the average loop radius accordin g to Equation (6.4) may result in a much higher or lower fl.R ave value. If a standard 20 % error is assumed for measured quantities the total error from Equation (6.4) for fl.R ave w ould have been as high as 50%. Therefore, it could be concluded that the simulation results captured the behavior of fl.Ra ve seen in the experimental results. Figure 6-20 represents the experimental and simulated values of the net chan ge in the total density of dislocation loops from the tensile to compressive regions as a function of nitride stripe width. Wall value was calculated in a similar way to the fl.R ave value The experimental results showed that Wall was relatively a weak function of the nitride stripe width. The model predicted a weak dependence as well. Although there were discrepancies between the modeling data and experimental results for wider nitride stripes, these could be attributed to the fact that it was not possible to count the loops in a region exactly in the middle of the stripes [Cha96]. The net change in the number of interstitials trapped by dislocation loops from the tensile to the compressive regions was a strong function of nitride stripe width as shown in Figure 6-21. The loops in compressive stress region lost more interstitials to the bulk than the ones in tensile stress region. This was reflected in the experimental section ~all decreased with shrinking stripe width. The simulations (Figure 6-21) predicted this trend correctly but there was a large discrepancy for 20 m stripe width.

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120 100 80 ---.__, 60 z
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123 quantitative TEM images and simulations were carried out. The experimental results showed no significant change in defect densities due to stress from the 1 Om and l SOm nitride stripes. Simulations confirmed the experimental results. The lack of stress effects on dislocation loops was attributed to the insignificant stress differences between the samples studied. Chaudhry's [Cha96] experimental results were used to calibrate the model. Simulation results showed the same trends observed in his experiments. It is seen that Mave and f1M all were strong function of nitride stripes and Wall was a weak function of nitride stripes.

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CHAPTER 7 SUMMARY AND FUTURE WORK 7.1 Summary Due to its reproducibility accurate dose control and the ability to tailor dopant profiles ion implantation is the most widely used technique to introduce dopant atoms into the crystalline substrate. However, damage to the silicon substrate is unavoidable with ion implantation and annealing is required to repair the damage Upon annealing several types of extended defects ( {311} s dislocation loops etc.) may form along with point defects. Jones et al. [Jon88] categorized these defects into Types I II III IV and V These defects may directly or indirectly influence the dopant diffusion in the substrate They may also eventually lead to degradation of device performance or even to the device failure Therefore predictive simulations of dopant diffusion after ion implantation and thermal annealing are essential. This is only possible if the amplitude the depth the temperature and the time dependencies of the extended defects are known and implemented into the existing software. In this thesis the nucleation and evolution of extended defects for different dopant species and various implant and annealing conditions have been explored. Also the process induced stress effects on extended defects has been investigated A statistical point defect based model for the nucleation and evolution of dislocation loops in silicon was developed. The model encapsulated the process induced stress effects on dislocation loops as well. The predictive capability of the model was verified with experimental data. 124

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125 The model was implemented using ALA GA TOR script language in the proce ss simulator FLOOPS In Chapter 1 a general summary of the existing literature on the subject was introduced. Advantages and disadvantages of ion implantation were presented A brie f description of point defects and extended defects ( {311} s dislocation loops ) w er e g i ve n Interaction of {311} defects and dislocation loops were emphasized. The effects of dislocation loops on device characteristics were discussed. Since stress from dislocation loops and other process steps played an important role in defect nucleation and evolution fundamentals of stress/strain were also presented in this chapter. Three different sources of stress; film stress, oxidation/isolation induced stress and dopant induced stress were summarized. First a single statistical point defect based model for the evolution of dislocation loops during oxidation and annealing under an inert ambient was developed in Chapter 2. It was assumed that loops followed a log normal distribution. The distribution was characterized by average loop radius total loop density and total number of interstitials trapped by dislocation loops. For the ease of simulations the stress from dislocation loops was calculated using dopant induced stress-calculation techniques. Since the trapped interstitials by dislocation loops would vary the lattice constant at the loop la y er this approximation was found to work quite well. The model was verified with the experimental results obtained from the literature. The model showed that dislocation loops grew by capturing interstitials injected during oxidation as observed by Meng, et al. [Men93]. The model also captured the experimental observation that while the loop density decreased with annealing time the

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126 average loop radius increased. The model was tested to predict dislocation loop evolution during inert annealing [Liu95] as well. It was observed that dislocation loops coarsened more at the temperatures in the 800C-900C range than at low temperatures ( ~ 700 c ) range Also dislocation loops were in the dissolution regime at high temperatures ( ~ 1000C). Furthermore The effects of surface proximity on the dislocation loops were simulated and the results were compared to the experimental data [Ram99]. As the dislocation loop layer was placed closer to the surface the loss of interstitials from dislocation loops increased. The effects of dislocation loops on boron diffusion were also qualitatively explained. It was shown that the dislocation loops acted as efficient sinks for interstitials. It was also shown that boron diffusion was retarded in the amorphous region compared to boron diffusion beyond the amorphous/crystalline interface Second the dislocation loop evolution model was expanded to account for the nucleation of dislocation loops in Chapter 3. A single set of differential equations was used to characterize the loop behavior through the nucleation, pure growth and Ostwald ripening stages. During the nucleation stage the density of dislocation loops and number of interstitials trapped by dislocation loops increased. Note most of the excess interstitials were consumed at this stage. The nucleation stage was followed by the pure growth stage. During the pure growth stage density of the dislocation loops did not change. However interstitials trapped by the dislocation loops continued to increase. When the number of interstitials trapped by the dislocation loops stopped increasing and the density of dislocation loops started decreasing, then the Ostwald ripening stage was reached

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127 The loop nucleation and evolution model assumed that all the loops came from {311} unfaulting. The excess interstitial and vacancy profiles due to ion implantation were obtained from UT-MARLOWE. The profiles were used for the nucleation of interstitial and vacancy clusters which eventually lead to the nucleation of {311 } sand dislocation loops. Since the model included the distribution of dislocation loops in the substrate, the density of threading dislocation loops were easily obtained from simulation results by comparing average loop radius to loop depth. Third, the loop nucleation and evolution model was verified with experimental results in Chapter 4. Two sets of experiments were designed to investigate temperature and energy dependence of the model. In the frrst set of experiments, the loop depth was set to 1800 A. In the second set, the loop depth was set to 965 A. To investigate the nucleation of dislocation loops, samples from each experimental set annealed at 700 C and 750 C. The nucleation rate at these temperatures was known to be slower. Simulation results were in good agreement with the experimental results. The nucleation pure growth, and Ostwald ripening stages of the dislocation loops were correctly simulated. Since loops came from { 311 } 's unfaulting, the nucleation of the dislocation loops was slower than the nucleation of {311} 's. This was also observed in the experimental results. Varying the annealing temperature helped to calibrate the model and determine the temperature dependence of the fitting parameters used in the model. Accuracy of the model was also tested by varying the implant energy. Also it was observed that the initial conditions used in the simulations played a big role for predicting defect densities.

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128 Fourth the validity of the loop nucleation and evolution model was tested using different implant species such as boron germanium and arsenic in Chapter 5. Some of this implant species could interact ( i.e. clustering pairing) with excess interstitials and vacancies. This would influence the supersaturation of these point defects around the loop layer. Thus defect densities should be different for different implant species. In order to verify this Liu s boron [Liu96] Gutierrez s germanium [GutOl] and Brindos arsenic [Bri0 1] implant studies were simulated Simulation results followed Liu's observation that a decrease in the critical dose for forming {311} defects occurs with increasing implant energy. It was also obser v ed that loops were more likely to nucleate with increasing implant energy. Although the model correctly predicted defect formation for the high energy Ge + implants [GutOl] it failed to predict the defect dissolution for the low energy implants. The simulations also predicted {311} defect formation for low energy implants. However the experiments showed no formation of {311} defects. On the other hand results were in excellent agreement with Brindos observation that no defects formed in low energy high dose arsenic implanted samples after one hour 800C anneals The results demonstrated that {311} defects and dislocation loops nucleated in short annealing times and their density droped below the TEM detection limit at the end of the annealing cycle. Finally the effects of the mechanical stress that surface during the fabrication process on dislocation loops were studied in Chapter 6. An experimental procedure was carried out to investigate the effects of patterned nitride stripes on the dislocation loop nucleation and evolution. Patterned wafers were provided by Intel. The loop nucleation and evolution model was extended to accommodate the process induced stress effects.

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129 Although two different nitride stripe widths were used to v ary the stre ss le ve l s in t h e bulk experimental results did not show a significant change in loop den s iti es. It was determined from simulation results that stress levels from two different nitrid e s tr i p es were almost identical. Therefore results were not conclusive enough to quanti fy stress effects on dislocation loops. On the other hand Chaudhry s experimental data w a s u se d to calibrate the modified model. The data showed that dislocation loops were small e r and sparser in regions of compression when compared to their distribution characteristic s in regions of tension. Simulation results were in agreement with the experimental results in most cases. It was observed that average radius and number of interstitials trapped b y dislocation loops were a strong function of nitride stripe width. Meanwhile the density of dislocation loops was a weak function of nitride stripe width 7.2 Future Work Although this research provided insight into the nucleation and evolution of dislocation loops and some process induced mechanic stress effects on dislocation loops many more topics are awaiting exploration The followings are suggestions for future work relevant to this thesis: It was noted many times that the initials conditions used in the simulations played an important role. Excess interstitials and vacancies profiles (point defects) were obtained from ion implantation simulator UTMARLOWE. Therefore the accurac y o f the predictive loop nucleation and evolution model depended on the accuracy of UTMARLOWE. It would be very interesting to look into different ion implantation software (i.e TRIM IMSIL etc.) to utilize their excess interstitials and vacancies profiles and compare simulation results. Of course, direct measurements of excess

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130 interstitial and vacancy profiles would be more beneficial to the whole process simulation society. It would also be very interesting to look at the defect evolution in 2D Currently publicly available ion implantation software does not provide an accurate picture of point defect distribution in 2D structures. The software usually uses simpler algorithms to calculate point defect distribution to avoid enormous computation time in 2D. However software such as TOMCAT with more advanced algorithms to calculate point defect distribution are becoming available It would be possible to obtain more accurate 2D point defect profiles and use them in loop nucleation models. In Chapter 2 a qualitative picture for the influence of dislocation loops on boron diffusion in amorphous and crystalline regions was given. The loop nucleation model was also integrated with the nitrogen diffusion model by Adam et al. [ Ada0 1] to successfully model nitrogen diffusion behavior under amorphizing conditions Similar experiments for different implant and annealing conditions can be repeated to obtain more quantitative data Since the defect nucleation and dopant diffusion models are individually calibrated the models may need to be re-calibrated. Although the developed loop model assumes that dislocation loops are immobile modeling dislocation loop glide and migration in high stress areas (i.e comers of shallow trench isolations) would be beneficial to device engineers. The focus of this thesis was on ion implantation induced dislocation loop nucleation and evolution. The formation misfit dislocation loops in the strained materials, such as SiGe or Si/SiGe heterojuction bipolar transistors needs to be explored

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131 More work is needed to quantify stress effects on dislocation loops Designing an experiment to investigate stress effects on dislocation loops proved to be challenging due to process issues. Although using a series of nitride stripes to introduce stress into substrate is very useful because compressive and tensile stress can be produced simultaneously, controlling stress levels in the substrate and avoiding loop nucleation during film deposition can be difficult. These issues can be avoided if equipment could be designed to bow the implanted wafers to generate desired tensile or compressive stress levels in the bulk and hold the wafers in this position during the annealing. Stress in the substrate would effect the nucleation of {311} 'sand interstitial and vacancy clusters as well. These effects were simply incorporated into the loop model. It would be beneficial to investigate stress effects on {311} 's separately and simplify the loop nucleation model. It would always be interesting if loop nucleation simulation results could be incorporated into a device simulator and compared with the actual device measurements.

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APPENDIX EXTRACTED PARAMETERS This appendix describes the parameters used in Chapters 4 5 and 6 Il a = 1.5x 10 15 cm2 =7 55x10 11 dynes/cm 2 b=3 84x108 cm; Magnitude of Burgers vector Q=2x 1023 ; Atomic volume of Silicon v=0.27 ; Poisson s rate K vL =0 ; Vacancy capture rate KrL = KxRpx4n:xDox2xa x Da11 ; Interstitial capture rate K=4.97x10 14 e < 2 37 lkT ) cm 2 D 0 =0.138x e ( -1.3?/kT ) cm 2 /sec. a=2.7x108 cm. KRp=2.99x 107 e < -L 9 3 lk T ) cm 2 /sec ; Ostwald term K311=360 59 e < -1. 2 /kT ) /sec; Unfaulting rate ~V 1 =0.0634x1024 cm3 ; Interstitial expansion volume ~Vv=4.77x1024 cm3 ; Vacancy expansion volume ~V 1 =3.17x1024 cm3 ; Activation volume for nucleation term ~V 2 =78 5.05x1024 cm3 ; Activation volume for interstitial capture term The loop model in "tel" script language is given below. proc logN { A vrRad } { return "exp(-0.5*((log($AvrRad)-Mean )"' 2) / (ssqr))" } proc LoopEng { pdbMat Sol AvgRad sign} { 132

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} 133 set mu [pdbGetDouble $pdbMat $Sol mu] ;# shear modulus dyne / cm 2 set b [pdbGetDouble $pdbMat $Sol b] ;# mag. of Burgers vec cm set ohm [pdbGetDouble $pdbMat $Sol ohm] ; #atomic volume of Si 2 0e-2 3 set kerg [pdbGetDouble $pdbMat $Sol kerg] ;# erg/K set nu [pdbGetDouble $pdbMat $Sol nu] ;#Poisson's ratio set er 1.0 ; #0 0 < er < 1 0 set pi 3.141592 set TempK { ([simGetDouble Diffuse temp] + 273 0)} set pre 11 ([expr -1.0 *$mu* $b *$ohm / (4*$pi*(l.0-$nu)*$kerg)]) 11 set coef 11 [ expr 8 / $b] 11 set loopengeqn 11 exp(($sign*$pre / $A vgRad) / $TempK log($coef*$A vgRad )) 11 return $loopengeqn proc IntNumlntegral { pdbMat Sol sgn} { set sgn [expr -1.0*$sgn] } set R 11 (2.0*([pdbGetString $pdbMat $Sol CpEqnRp ]+ l 0e-8)) 11 ;#upper limit of integral set x II l.0e-8 11 ;# lower limit of integral set spacing [pdbGetDouble $pdbMat $Sol NumericallntegralSpacing] set al 11 ([expr l.0 / $spacing]*($R-$x)) 11 set a2 [logN $x] set a3 [LoopEng $pdbMat $Sol $x $sgn] set eqnl 11 ($a2*$a3) / ($x) 11 set sumeqn 11 0 0 11 set i I ; #i=l..$spacing-l set uplmt [ expr int([ expr $spacing -1])] ; while { $i < = $uplmt } { } set step 11 ($x+$i*$al) 11 set a4 [logN $step] set a5 [LoopEng $pdbMat $Sol $step $sgn] term name= Intsum${i} add eqn = 11 ($a4*$a5) / $step 11 set sumeqn 11 $sumeqn+ Intsum$i 11 incr i set a6 [logN $R] set a7 [LoopEng $pdbMat $Sol $R $sgn] set eqn2 11 ($a6*$a7) / ($R) 11 set integraleqn 11 (0 5*$al *($eqnl +2.0*($sumeqn)+$eqn2)) 11 return $integraleqn proc VacNumlntegral { pdbMat Sol sgn} { set sgn [expr -l.0*$sgn] set R 11 (2.0*([pdbGetString $pdbMat $Sol CpEqnRp]+ l .0e-8))" ;# upper limit of integral set x "l.0e-8" ; #lower limit of integral set spacing [pdbGetDouble $pdbMat $Sol NumericallntegralSpacing] set al 11 ([expr l .0 / $spacing]*($R-$x)) 11 set a2 [logN $x] set a3 [LoopEng $pdbMat $Sol $x $sgn] set eqn l 11 ($a2*$a3) / ($x)" set sumeqn 11 0.0 11 set i 1 ; #i= 1..$spacing-l set uplmt [ expr int([ expr $spacing -1])] ; while { $i <= $uplmt } { set step 11 ($x+$i*$al) 11 set a4 [logN $step] set a5 [LoopEng $pdbMat $Sol $step $sgn] term name= Vacsum${i} add eqn = "($a4*$a5) / $step 11

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} } set sumeqn "$sumeqn + Vacsum$i" mer 1 set a6 [logN $R] set a7 [LoopEng $pdbMat $Sol $R $sgn] set eqn2 "($a6*$a7) / ($R)" 134 set integraleqn "(0 5*$al *($eqn 1 +2 0*($sumeqn)+$eqn2))" return $integraleqn proc SoRBulk {Mat Sol } { set pdbMat [pdbName $Mat] set KsO 0 33 set Ksl 5e4 pdbSetString $pdbMat $Sol Equation "$Sol-($Ks0+$Ksl *Rp)" proc LoopBulkNall { Mat Sol} { set pdbMat [pdbNarne $Mat] set eqnNall "ddt($Sol)" set CpEqRp [pdbGetString $pdbMat $Sol CpEqnRp] set detlist [pdbGetString $pdbMat $Sol DefectsGrow] foreach def $
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135 if { [pdbGetBoolean $pdbMat $Sol NoNucleation] } { set Ktemp 0 0 ; #this will eliminate 311 unfaulting terms in Nall & Dall # {311} unfaulting term term name = Prseff add eqn = {e x p ( -1.0 *( l.O HPressure 3. 17e24) / (( [ si mGetD o ubl e D iffuse temp] + 273 0 ) l.38062e-16 )) } set K3 l 1 [pdbDelayDouble $pdbMat $Sol K311] set C311 [pdbGetString $pdbMat $Sol 311] term add name = LpNall311 eqn = "(Prseff*$Ktemp*$K311 $C3 l l)" #add the term to C3 l 1 eqn set equ [pdbGetString $pdbMat $C3 l l Equation] pdbSetString $pdbMat $C3 l 1 Equation "$equ + LpNall3 l 1" # Now Nall Equation set eqnN all "$eqnN all (Loop$ {def}) LpN all3 l 1" set deflist [pdbGetString $pdbMat $Sol DefectsShrink] foreach def $
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set K31 l [pdbDelayDouble $pdbMat $Nall K31 l] set D311 [pdbGetString $pdbMat $Sol 311] 136 term add name= LpDall3 l l eqn = "(Prseff"$Ktemp*$K3 l l *$D311 )" #add the term to D311 eqn set equ [pdbGetString $pdbMat $D311 Equation] pdbSetString $pdbMat $D311 Equation "$equ + LpDall3 l l" #set up Dall equation pdbSetString $pdbMat $Sol Equation "ddt($Sol)+ 1.0/(10.0+Int/Cib)*$KRp*$Sol*(2.0/($CpEqnRp)"2)LpDall31 l"

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LIST OF REFERENCES [Ada0l] L. S. Adam M. E Law, S. Hegde 0. Dokumaci Comprehensive model for nitrogen diffusion in silicon ," IEDM 2001 [Ben97] J. L. Benton S. Libertino, P. Kringhoj D. J. Eaglesham and J.M Poate S. Coffa Evolution from point to extended defects in ion implanted silicon ," Journal of Applied Physics Vol. 82 No 1 pp. 120-125 1997 [Bon98] C Bonafos D Mathiot, and A. Claverie Ostwald ripening of end-of-range defects in silicon ," Journal of Applied Physics Vol. 83 No 6 pp. 3008-3017 1998. [Bor92] L. Borucki Modeling the Growth and Annealing of Dislocation Loops I EEE NUPAD IV pp. 27-32 1992 references therein. [Bou99] K .K. Bourdelle D. J. Eaglesham D. C. Jacobson and J.M. Poate The effect of as-implanted damage on the microstructure of threading dislocations in MeV implanted silicon Journal of Applied Physics Vol. 86 No 3 pp 12211225, 1999 references therein. [Bri0 1] R. E. Brindos "Determination and modeling of the interaction between arsenic and silicon interstitials in silicon ," Ph.D. Dissertation University of Florida Gainesville Florida 2001. [Bul78] C. Bull P. Ashburn G. R. Booker and K. H. Nicholas Effetcs of Dislocations in Silicon Transistors with Implanted Emitters ," Solid State Electron Vol. 22, No 1, pp. 95-104 1979 [Cea96] S. Cea Multidimensional Viscoelastic Modelling of Silicon Oxidation and Titanium Silicidation ," Ph.D. Dissertation University of Florida Gaines v ille Florida 1996 [Cha95] S. Chaudhry, J. Liu, K. S. Jones and M Law Evolution of Dislocation Loop s in Silicon in an Inert Ambient II ," Solid-State Electronics Vol. 38 No 7 pp. 13 13-13 19, 199 5 [Cha96] S. Chaudary "Analysis and modeling of stress related effects in scaled s ilicon technology ," Ph.D. Dissertation University of Florida Gaines v ille F lorida 1996. 137

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139 [Fah89] P. M. Fahey P. B. Griffin and J. D. Plummer Point defect and dopant diffusion in silicon Reviews of Modem Physics Vol. 61 No 2 April 1989 [Fah92] P. M. Fahey S. R. Mader S. R. Stiffler, R. L. Mohler J. D. Mis J. A. Slinkman, "Stress-induced dislocations in silicon integrated circuits IBM Journal of Research and Development, Vol. 36 No 2 March 1992 [Fin79] M. Finetti, R. Galloni, and M. Mazzone, "Influence of impurities and crystalline defects on electron mobility in heavily doped silicon Journal of Applied Physics Vol. 50, No 3, 1979. [Gav76] S. D. Gavazza, D. M. Barnett, "The self force on a planar dislocation loop in an anisotropic linear-elastic medium," Journal of Mech. Phys. Solids Vol. 24 pp. 171-185 1976. [Gha94] S. K. Ghandhi, VLSI Fabrication Principles Silicon and Galium Arsenide Second Edition. Wiley Inter Science 1994. [Gil99] L. F. Giles, M. Omri, B. de Mauduit, A. Claverie, D. Skarlatos, D. Tsoukalas and A. Nejim, "Coarsening of End-of-Range defects in ion-implanted silicon annealed in neutral and oxidizing ambients," Nuclear Inst. and Meth. in Physics Research B, Vol. 148, pp. 273-278, 1999. [GutOl] A. F. Gutierrez, "Defect Evolution from low energy germanium implants in silicon," Masters thesis, University of Florida, Gainesville, Florida 2001 [Hob88] G. Hobler, S. Selberherr, "Two Dimensional Modeling oflon Implantation Induced Point Defects," IEEE Transactions on Computer Aided Design Vol. 7 No 2, pp. 174-180, 1988. [Hu78] S. M. Hu, R. 0. Schwenkar, "Effects of ion implantation on substrate hardening and film stress reduction and their effect on the yield of bipolar transistors" Journal of Applied Physics, Vol. 49 No 6 pp. 3259-3265, 1978 [Hu90] S. M. Hu, "Stress from isolation trenches in silicon substrate," Journal of Applied Physics, Vol. 67, No 2, pp. 1092-1101 1990 references therein. [Hu91] S. M. Hu, "Stress related problems in silicon technology Journal of Applied Physics, Vol. 70, No 6, pp. R53-r80, 1991 [Hua93] R. Y. S. Huang, and R. W. Dutton, "Experimental investigation and modeling of the role of extended defects during thermal oxidation Journal of Applied Physics, Vol. 74, No 9, 1993.

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140 [Iso85] S Isomae "Stress in silicon at Si3N4/SiO2 film edges and viscoelastic behavior of SiO2 films Journal of Applied Physics Vol. 57, No 2 pp 216223 1985. [Jas99] C. Jasper A. Hoover K S Jones "The effect of implantation energy and dose on extended defect formation for Me V phosphorus implanted silicon Applied Physics Letters Vol. 75 No 17 pp. 1-3 1999. [Jon00] K. S. Jones "Effect of annealing time and temperature on the formation of threading and projected range dislocations in 1 MeV boron implanted Si Applied Physics Letters Vol. 78 No 12 pp. 1664-1666 2001. [Jon88] K S. Jones S Prussin and E. R. Weber "A Systematic Analysis of Defects in Ion-Implanted Silicon Applied Physics Vol. A 45 pp. 1-34 1988 [Jon95] K S Jones J. Liu L. Zhang V Krishnamoorthy and R. T. DeHeff "Studies of the interactions between (311) defects and type I and II dislocation loops in Si+ implanted silicon Nuclear Instruments and Methods in Physics Research B Vol. 106 pp 227-232 1995 [Jon98] K. S. Jones D Downey H Miller J Chow J. Chen M Puga-Lambers K Moller M. Wright E. Heitman J. Glassberg M E. Law L. Robertson and R. Brindos Proceedings of the International Conference on Ion Implantation Technology Vol. 2 p. 841 1998 [Kan96] S.-M Kang and Y. Leblebici in CMOS Digital Integrated Circuits Analysis and Design ; The McGraw-Hill Companies, Inc. p. 79 1996. [Lam00] E. Lampin V. Senez A. Claverei "Modelisation of extended defects to simulate the transient enhanced diffusion of boron Materials Science and Engineering Vol. B71 pp 155-159 2000. [Lam99a] E. Lampin V. Senez "Modeling of the kinetics of dislocation loops Nuclear Inst. and Meth. in Physics Research B Vol. 147 pp. 13-17, 1999 [Lam99b] E. Lampin V. Senez A. Claverie "Modeling of the transient enhanced diffusion of boron implanted into preamorphized silicon Journal of Applied Physics Vol. 85 No 12 pp 8137-8144 1999 [Lan97] L. S. Robertson A. Lilak M. E. Law, K. S. Jones P. S Kringhoj L. M. Rubin J. Jackson D. S. Simons, and P. Chi, "The effect of dose rate on interstitial release from the end-of-range implant damage region in silicon Applied Physics Letters Vol. 71 No 21 1997. [Law00] M. E Law and K S. Jones "A new model for {311} defects based on in-situ measurements IEDM 2000 pp. 511-514 2000.

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141 [Law98] M. E. Law, S. M. Cea, "Continuum based modeling of silicon integrated circuit processing: An object oriented approach," Computational Materials Science Vol. 12, pp. 289-308, 1998 [Li98] J. Li, and K. S. Jones, "{311} defects in silicon: The source of the dislocation loops," Applied Physics Letters, Vol. 73, No 25, pp. 3748-3750 1998. [Lia0l] A. D. Lilak, "Analysis and modeling of transient phenomena in boron doped silicon," Ph.D. Dissertation, University of Florida, Gainesville Florida 2001. [Liu95] J. Liu, M. E. Law, and K. S. Jones, "Evolution of dislocation loops in silicon in an inert ambient-I," Solid-State Electronics, Vol. 38, No 7, pp. 1305-1312 1995 [Liu96] J. Liu, "Defect and diffusion study in boron implanted silicon," Ph.D. Dissertation, University of Florida, Gainesville, Florida, 1996 [Mau94] B. de Mauduit, L. Laanab, C. Bergaud, M. M. Faye, A. Martinez and A Claverie, "Identification of EOR defects due to the regrowth of amorphous layers created by ion bombardment," Nuclear Inst. and Methods in Physics research B, Vol. 84, pp. 190-194, 1994. [Men93] H. L. Meng, S Prussin, M. E. Law, and K. S. Jones, "A study of point defect detectors created by Si and Ge implantation," Journal of Applied Physics Vol. 73, No 2, pp. 955-960, 1993. [Miy97] M. Miyake, M. Takahashi, "Defects Induced by Deep Preamorphization and Their Effects on Metal oxide semiconductor Device Characteristics Journal of Electrochemical Soc. Vol. 144, No 3, 1997. [Pan96] G. Z. Pan, K. N. Tu, S. Prussin, "Size distribution of end-of-range dislocation loops in silicon-implanted silicon," Applied Physics Letters, Vol. 68, No 12 pp. 1654-16561996 [Pan97a] G. Z. Pan, and K. N. Tu, "Transmission electron microscopy on { 113} rodlike defects and { 111} dislocation loops in silicon-implanted silicon Journal of Applied Physics, Vol. 82, No 2, pp. 601-608, 1997. [Pan97b] G. Z. Pan, K. N. Tu, and S. Prussin, "Microstructural evolution of {113} rodlike defects and { 111} dislocation loops in silicon-implanted silicon" Applied Physics Letters, Vol. 71, No 5, 1997. [Par93] Hemyong Park, "Point-Defect-Based two dimensional modeling of dislocation loops and stress effects on dopant diffusion," Ph.D. Dissertation University of Florida, 1993, and references therein.

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143 Journal of Electrochemical Society Solid State cience and T chnolo gy Vol. 128 pp.644-648 1981 [Tau99] Yuan Taur "Th incredible shrinking transistor I E pectrum pp 25 29 July 1999. [Tho98] S. Thompson P. Packan and M. Bohr "MOS caling: Transi tor Chall n g for the 21 s t Century Intel Technology Journal, Q398 1 1998. [Tso00] D Tsoukalas D. Skarlatos J. Stoemenos "Investigation of the interaction between silicon interstitials and dislocation loops using the wafer bondin g technique Journal of Applied Physics Vol. 87 No 12 pp. 8380-8384 2 000. (Wol86] S Wolf R N Tauber "Silicon processing for the VL I era Volume 1 Process Technology Lattice Press 1986 [Y ar97] M.I. Current in Materials and Process Characterization of Ion Implantation ; M.I. Current and C.B. Yarling eds ., Ion Beam Press p. 3 1997.

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BIOGRAPHICAL SKETCH Ibrahim Avci was born in Izmir, Turkey, on December 24, 1969. He earned his Bachelor of Science degree in electrical engineering in May 1992. In fall 1994 he began his graduate studies at Rensselaer Polytechnic Institute. He received his Master of Science degree in December 1996. From then until August 2002, he pursued a Ph.D. at the University of Florida His doctorate research focused on modeling and characterization of dislocation loop nucleation and evolution. 144

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I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequat e, in scope and quali ty, as a thesis for the degree of Doctor of Philosophy. Mark E. Law Chairman Professor of Electrical and Computer Engineering I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate in scope and quality as a thesis for the degree of Doctor of Philosophy. Z-> Kevin S Jones / Professor of ~erials Science and Engineering I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate in scope and quality as a thesis for the degree of Doctor of Philosophy ~~ Gijs Bosman Professor of Electrical and Computer Engineering I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate in scope and quality as a thesis for the degree of Doctor of Philosophy. Associate Professor of Electrical and Computer Engineering

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I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality as a thesis for the degree of Doctor of Philosop y z 1 ~ _1 ~1Timothy i,-efa~ Associate Professor of Computer and Information Science and Engineering This dissertation was submitted to the Graduate Faculty of the College of Engineering and to the Graduate School and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy. August 2002 t.---------Pramod P. Khargonekar Dean College of Engineering Winfred M. Phillips Dean Graduate School

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