Loop nucleation and stress effects in ion-implanted silicon

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Loop nucleation and stress effects in ion-implanted silicon
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Ion implantation   ( lcsh )
Semiconductors -- Defects   ( lcsh )
Semiconductor doping   ( lcsh )
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Thesis (Ph.D.)--University of Florida, 2002.
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Includes bibliographical references (leaves 137-143).
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by Ibrahim Avci.
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Vita.

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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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